Investimentos na Infância Impacto no Ensino Superior e Conclusão de Curso - Evidências Experimentais

Experimental Evidence on the Effect of Childhood Investments on Postsecondary Attainment and Degree Completion Susan Dynarski Joshua Hyman Diane Whitmore Schanzenbach Abstract This paper examines the effect of early childhood investments on college enrollment and degree completion We used the random assignment in Project STAR the Tennessee StudentTeacher Achievement Ratio experiment to estimate the effect of smaller classes in primary school on college entry college choice and degree completion We improve on existing work in this area with unusually detailed data on college enrollment spells and the previously unexplored outcome of college degree completion We found that assignment to a small class increases students probability of attending college by 27 percentage points with effects more than twice as large among black students Among students enrolled in the poorest third of schools the effect is 73 percentage points Smaller classes increased the likelihood of earning a college degree by 16 per centage points and shifted students toward highearning fields such as STEM science technology engineering and mathematics business and economics We found that testscore effects at the time of the experiment were an excellent predictor of longterm improvements in postsecondary outcomes C 2013 by the Association for Public Policy Analysis and Management INTRODUCTION Education is intended to pay off over a lifetime Economists conceive of education as a form of human capital requiring costly investments in the present but promising a stream of returns in the future Looking backward at a number of education inter ventions eg Head Start compulsory schooling researchers have identified causal links between these policies and longterm outcomes such as adult educational at tainment employment earnings health and civic engagement Angrist Krueger 1991 Dee 2004 Deming 2009 LlerasMuney 2005 Ludwig Miller 2007 But decisionmakers who attempt to gauge the effectiveness of current education inputs policies and practices in the present cannot wait decades for these longterm effects to emerge They therefore rely upon shortterm outcomesprimarily standardized test scoresas their yardstick of success A critical question is the extent to which shortterm improvements in test scores translate into longterm improvements in wellbeing Puzzling results from several evaluations make this a salient question Three smallscale intensive preschool experiments produced large effects on contemporaneous test scores that quickly faded Anderson 2008 Schweinhart et al 2005 Quasiexperimental evaluations Journal of Policy Analysis and Management Vol 32 No 4 692717 2013 C 2013 by the Association for Public Policy Analysis and Management Published by Wiley Periodicals Inc View this article online at wileyonlinelibrarycomjournalpam DOI101002pam21715 Effect of Childhood Investments on Postsecondary Attainment 693 of Head Start a preschool program for children from lowincome families revealed a similar pattern with testscore effects gone by middle school In each of these studies treatment effects had reemerged in adulthood as increased educational attainment enhanced labor market attachment and reduced crime Deming 2009 Garces Thomas Currie 2002 Ludwig Miller 2007 Further several recent papers have shown large impacts of charter schools on test scores of disadvantaged children Abdulkadiroglu et al 2011 Angrist et al 2012 Dobbie Fryer 2011 A critical question is whether these effects on test scores will persist in the form of longterm enhancements to human capital and wellbeing We examined the effect of smaller classes on educational attainment in adulthood including college attendance degree completion and field of study We exploited random variation in class size in the early grades of elementary school created by the Tennessee StudentTeacher Achievement Ratio experiment Project STAR Participants in Project STAR are now in their 30s an age at which it is plausible to measure completed education Our postsecondary outcome data was obtained from the National Student Clearinghouse NSC a national database that covers approximately 90 percent of students enrolled in colleges in the United States We found that being assigned to a small class increased the rate of postsecondary attendance by 27 percentage points The effects were considerably higher among populations with traditionally low rates of postsecondary attainment For black students and students eligible for a subsidized free or reduced price lunch the effects are 58 and 44 percentage points respectively At elementary schools with the greatest concentration of poverty measured using the fraction of students receiving a subsidized lunch smaller classes increased the rate of postsecondary attendance by 73 percentage points We further found that being assigned to a small class increased the probability of students earning a college degree by 16 percentage points Smaller classes shifted students toward earning degrees in highearning fields such as science technology engineering and mathematics STEM business and economics Our results shed light on the relationship between the short and longterm effects of educational interventions The shortterm effect of small classes on test scores it turns out is an excellent predictor of the longterm effect on adult outcomes We show this by adding K3 test scores to our identifying equation the coefficient on the class size dummy drops to zero The coefficient on the interaction of class size and test scores is also zero indicating that the scores of children in small classes are no less or more predictive of adult educational attainment than those of children in the regular classes Our analysis identifies the effect of manipulating a single policyrelevant edu cational input on adult educational attainment By contrast the earlychildhood interventions for which researchers have identified lifetime effects eg Head Start Abecedarian are multipronged including home visits parental coaching and vac cinations in addition to time in a preschool classroom We cannot distinguish which dimensions of these treatments generate shortterm effects on test scores and whether they differ from the dimensions that generate longterm effects on adult wellbeing The effective dimensions of the treatment are also ambiguous in the recent literature on classroom and teacher effects For example Chetty et al 2011 showed very large effects of kindergarten classroom assignment on adult wellbeing In those estimates the variation in classroom quality that produced sig nificant variation in adult outcomes excluded class size but included anything else that varied at the classroom level including teacher quality and peer quality both of which are extremely difficult to manipulate with policy By contrast the effects we measured for this paper both shortterm and longterm can be attributed to a welldefined and replicable intervention reduced class size Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 694 Effect of Childhood Investments on Postsecondary Attainment PROJECT STAR Project STAR the Tennessee StudentTeacher Achievement Ratio experiment ran domly assigned class sizes to children in kindergarten through third grade The experiment was initiated in the 1985 to 1986 school year when participants were in kindergarten A total of 79 schools in 42 school districts participated with oversam pling of urban schools An eventual 11571 students were involved in the experiment The sample was 60 percent white and 40 percent African American About 60 per cent of the students were eligible for subsidized lunch during the experiment The experiment is described in greater detail elsewhere Achilles 1999 Finn Achilles 1990 Folger Breda 1989 Krueger 1999 Word et al 1990 Students in Project STAR were assigned to either a small class target size 13 to 17 students or a regular class 22 to 25 students1 Students who entered a participating school after kindergarten were randomly assigned during those entry waves to a small or regular class Teachers were also randomly assigned to small or regular classes All randomization occurred within schools The documentation of initial random assignment in Project STAR is incomplete Krueger 1999 Krueger 1999 examined records from 18 STAR schools for which assignment records were available He found that as of entry into Project STAR 997 percent of students were enrolled in the experimental arm to which they were initially assigned Kruegers approach and that of the subsequent literature was to assume that the class type in which a student was first enrolled was the class type to which the student was assigned We followed that convention in our analysis Numerous papers have tested and generally validated the randomization in Project STAR Krueger 1999 There are no baseline outcome data eg a pretest available for the Project STAR participants On the handful of covariates available in the Project STAR data subsidized lunch eligibility race sex the arms of the ex periment appear balanced at baseline see Table 1 for a replication of these results Recent work by Chetty et al 2011 has shown that the STAR entry waves were balanced at baseline on a detailed set of characteristics eg family income home ownership obtained from the income tax returns of Project STAR participants parents PREVIOUS RESEARCH ON THE LONGTERM EFFECTS OF SMALL CLASSES A substantial body of research has examined the effect of Project STAR on short and mediumrun outcomes We do not comprehensively discuss this literature but instead summarize the pattern of findings which show that students assigned to a small class experience contemporaneous testscore gains of about one fifth of a standard deviation These testscore results diminished after the experiment ended in third grade2 There is evidence of lasting effects on other dimensions Krueger and Whitmore 2001 showed that students assigned to small classes were more likely to take the ACT and SAT required for admission to most fouryear colleges Schanzen bach 2006 reported that smaller classes reduced the rate of teen pregnancy among 1 A third arm of the experiment assigned a fulltime teachers aide to regular classes Previous research has shown no difference in outcomes between the regularsized classes with and without an aide We followed the previous literature and pooled students from both types of regular classes into a single control group The results were substantively unchanged if we included an indicator variable for the presence of a fulltime teachers aide 2 Cascio and Staiger 2012 showed that fadeout of testscore effects is at least in some settings a statistical artifact of methods used by analysts to normalize scores within and across grades However they specifically note that the sharp drop in estimated effects that occurred after the end of Project STAR cannot be explained in this way Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 695 Table 1 Means of demographics and outcome variables by class size Regular class Small class Regression adjusted difference 1 2 3 Demographics White 0620 0660 0003 0005 Female 0471 0473 0000 0011 Subsidized lunch 0557 0521 0015 0011 College attendance Ever attend 0385 0420 0027 0011 Ever attend fulltime 0278 0300 0013 0011 Enrolled on time 0274 0308 0024 0011 Number of semesters Attempted 307 339 0219 0133 Attempted conditional on attending 798 808 0132 0209 Degree receipt Any degree 0151 0174 0016 0009 Associates 0027 0034 0007 0004 Bachelors or higher 0124 0141 0009 0008 Degree type STEM business or economics field 0044 0060 0013 0006 All other fields 0085 0094 0003 0006 First attended Two years 0215 0245 0025 0009 Public four years 0127 0132 0005 0007 Private four years 0042 0043 0003 0004 Number of schools 79 Number of students 8316 2953 Notes Column 3 controls for schoolbywave fixed effects and demographics Standard errors in paren theses are clustered by school female participants by about a third In addition Fredriksson Ockert and Ooster beek 2013 found positive longterm effects of reduced class size in grades 4 through 6 in Sweden on educational attainment and wages The paper most closely related to our own examined the impact of Project STAR on adult outcomes using the income tax records of Project STAR participants and their parents Chetty et al 2011 That paper emphasized the differential long term impacts of being randomly assigned to classrooms of different quality levels stemming from higher quality teachers or classmates after accounting for class size Chetty et al 2011 documented the sizable longterm payoff to having a highquality classroom though they recognized that this cannot be directly manipulated by public policy By contrast we focus on the longterm impacts of randomly assigned class size which is an easily measured input that can be manipulated by policy EMPIRICAL STRATEGY The experimental nature of Project STAR motivated the use of a straightforward empirical specification We compared outcomes of students randomly assigned to small and regular classes by estimating the following equation using ordinary least Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 696 Effect of Childhood Investments on Postsecondary Attainment squares yisg β0 β1SMALLis β2 Xis βsg εisg 1 where yisg represents a postsecondary schooling outcome of student i who entered Project STAR in school s and in grade g X is a vector of covariates including race sex and subsidized lunch status an indicator for whether the student ever received free or reducedprice lunch during the experiment included to increase precision βsg is a set of schoolbyentrygrade fixed effects We included these because stu dents who entered STAR schools after kindergarten were randomly assigned at that time to small or regular classes The variable of interest is SMALLis an indicator set to 1 if student i was assigned to a small class upon entering the experiment The omitted group to which small classes are compared is regular classes with or with out a teachers aide We clustered standard errors by school the most conservative approach Standard errors were about 10 percent smaller if we clustered at the level of schoolbywave DATA We used the original data from Project STAR which includes information on the type of class in which a student was enrolled basic demographics race sex subsi dized lunch status school identifiers and standardized test scores These data also include the name and date of birth of the student which we used to match to data on postsecondary attainment and completion Data on postsecondary outcomes for the STAR participants come from the NSC The NSC is a nonprofit organization that was founded to assist student loan com panies in validating students college enrollment Borrowers can defer payments on most student loans while in college which makes lenders quite interested in tracking enrollment Colleges submit enrollment data to the NSC several times each academic year reporting whether a student is enrolled at what school and at what intensity eg parttime or fulltime The NSC also records degree completion and the field in which the degree is earned States and school districts use NSC data to track the educational attainment of their high school graduates Roderick Nagaoka Allensworth 2006 Recent academic papers making use of NSC data include Dem ing et al 2011 and Bettinger et al 2012 With the permission of the Project STAR researchers and the state of Tennessee we submitted the sample of Project STAR participants to the NSC in 2006 and again in 2010 The STAR sample was scheduled to graduate high school in 1998 We therefore captured college enrollment and degree completion for 12 years after ontime high school graduation to when the STAR participants were about 30 years old The NSC matches individuals to its data using name and date of birth3 If birth date is missing the NSC attempts to match on name alone Some participants in the STAR sample are missing identifying information used for the NSC match 12 percent have incomplete name or birth date In our data a student who attended college but failed to produce a match in the NSC database is indistinguishable from a student who did not attend college If the absence of these identifiers is correlated with the treatment then our estimates may be biased To determine whether identifiers were missing at a differential rate across treatment groups 3 In 2006 the NSC used social security number as well as name and date of birth in its matches As of 2010 NSC had ceased to use social security numbers for its matches Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 697 we estimated equation 1 replacing yisg with an indicator variable equaling 1 if a student had a missing name or date of birth We found a precisely estimated zero for β1 0008 SE 0008 indicating that the probability of missing identifying information is uncorrelated with initial assignment In the concluding section of this paper we present the results of a second test exploring the possible bias in our main result associated with missing identifiers Not all schools participate in NSC the organization estimates they currently capture about 93 percent of undergraduate enrollment nationwide During the late 1990s when the STAR participants would have been graduating from high school the NSC included colleges enrolling about 80 percent of undergraduates in Tennessee Dynarski Hemelt Hyman 20124 Since we miss about 20 percent of undergraduate enrollment using the NSC data we expect that we will underestimate the college attendance rate of the STAR sample by about a fifth The NSC data indi cate that 394 percent of the STAR sample had attended college by age 30 Among those born in Tennessee in the same years as the STAR sample the attendance rate is 528 percent in the 2005 American Community Survey ACS Ruggles et al 20105 Our NSC estimate of college attendance is therefore as expected about four fifths of the magnitude of the ACS estimate In the NSC data we found that 151 percent of the STAR sample had earned a college degree This is substantially lower than the corresponding rate we calculated from the 2005 ACS 293 percent Not all of the colleges that report enrollment to the NSC report degree receipt and this explains at least part of the discrepancy6 The exclusion of some colleges from the NSC will induce measurement error in the dependent variable If this error is not correlated with treatment ie classical measurement error then the true effect of class size on college enrollment will be larger than our observed effect by the proportion of enrollment that is missed approximately 20 percent7 This is because the true treatment effect is the sum of the observed treatment effect and the treatment effect of the unobserved college attenders Bound Brown Mathiowetz 2001 However if the measurement error in college attendance is correlated with assignment to treatment then our effect could be either downward or upward biased This would be the case for example if colleges attended by marginal students are disproportionately undercounted by the NSC To determine whether the NSC systematically misses certain types of schools we compared the schools that participate in NSC with those in IPEDS Along all measures we examined ie sector racial composition selectivity the NSC colleges were similar to the universe of IPEDS colleges with a single exception the NSC tends to exclude forprofit institutions8 These are primarily trade schools such 4 Dynarski Hemelt and Hyman 2012 calculate this rate by dividing undergraduate enrollment at Tennessee colleges included in NSC as of 1998 by enrollment at all Tennessee colleges in 1998 The list of colleges participating in the NSC and the year that they joined is accessible on the NSC Web site Enrollment data are from the Integrated Postsecondary Education Data System IPEDS a federally generated database that lists every college university and technical or vocational school that participates in the federal financial aid programs about 6700 institutions nationwide National Center for Education Statistics 2010 5 We reweighted the Tennessee born in the ACS data to match the racial composition of the STAR sample which was disproportionately black 6 Using IPEDS we calculate that 70 percent of undergraduate degrees are conferred by institutions that according to the NSC Web site report degrees to the NSC Dynarski Hemelt and Hyman 2012 also find lower degree coverage in the NSC relative to enrollment coverage 7 This is true in terms of percentage points The percent increase in college attendance would remain unchanged 8 The conclusion was the same when we weighted coverage by the number of degrees conferred rather than by undergraduate enrollment Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 698 Effect of Childhood Investments on Postsecondary Attainment as automotive technology business nursing culinary arts and beauty schools If small classes tend to induce those students who would not otherwise attend college into such schools we will underestimate the effect of small classes on college attendance If on the other hand small classes induce students out of such schools into colleges that we tend to observe such as community colleges then our estimates will be upward biased In the concluding section of our paper we conduct a back oftheenvelope exercise to bind the possible upward bias that could be due to this phenomenon RESULTS In this section we examine the effect of assignment to a small class on a set of post secondary outcomes college entry timing of college entry college choice degree receipt and field of degree College Entry In Table 2 we estimate the effect of assignment to a small class on the probability of college entry by age 30 The effect is close to 3 percentage points column 1 28 percentage points which is an impact of approximately 7 percent relative to the control mean of 385 percent control means are italicized in the tables This estimate is statistically significant with a standard error of about 1 percentage point Including covariates did not alter the estimate as is expected with random assignment For the balance of the paper we report results that include covariates since they are slightly more precise Splitting the sample by race revealed that the effects were concentrated among blacks 58 points relative to a mean of 308 percent and those eligible for subsidized lunch 44 points relative to a mean of 272 percent The effects were twice as large for boys 32 points relative to a mean of 324 percent than for girls 16 points relative to a mean of 455 percent Breaking down the effects even more finely showed that the effects were largest for black females 72 points standard error of 35 with no effect on white females 13 points standard error of 23 The effects for black and white males were indistinguishable 31 and 44 points respectively standard error of 18 and 24 points One caveat to consider when examining results by race and sex is that the prob ability of enrolling in a college not in the NSC could be correlated with race or sex which could cause bias in the estimates Dynarski Hemelt and Hyman 2012 showed that NSC coverage is similar by sex but is lower for black students than white students To examine this issue for a population similar to the STAR sample we examined the share of firsttime college students in Tennessee in 1998 in IPEDS by race and sex attending any type of college and attending forprofit institutions which tend not to appear in the NSC We found that black and female students tended to enroll in higher proportions in forprofit colleges This suggests that part of the large treatment effect for black females could be due to these students being induced from nonNSC colleges to those that participate in NSC Our results by student demographics indicate that there is substantial hetero geneity by race and income in the effect of class size However policy decisions regarding staffing levels and class size tend to be set at the school level rather than the student level Schoollevel characteristics rather than studentlevel char acteristics may therefore be the more policyrelevant dimension along which to measure heterogeneity in effects In order to capture this policyrelevant variation in effects we divided the STAR schools into three groups those with low medium and high levels of poverty which we proxied with the share of children eligible for a Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 699 Table 2 The effect of class size on college attendancelinear probability models Tercile of poverty share Total White Black No subsidized lunch Subsidized lunch High Middle Low Middle and low P value high versus middle low Dependent variable 1 2 3 4 5 6 7 8 9 10 11 College attendance Ever attend 0028 0027 0011 0058 0010 0044 0073 0010 0022 0006 0008 0012 0011 0013 0022 0017 0015 0021 0017 0018 0012 0385 0432 0308 0563 0272 0262 0417 0476 0446 Ever attend fulltime 0014 0013 0000 0037 0000 0025 0048 0012 0008 0003 0048 0011 0011 0013 0021 0016 0014 0022 0015 0018 0012 0278 0317 0212 0440 0175 0173 0297 0363 0330 Enrolled on time 0025 0024 0018 0036 0025 0024 0047 0007 0023 0015 0228 0012 0011 0013 0021 0017 0014 0023 0017 0018 0013 0274 0321 0197 0449 0163 0163 0296 0363 0329 Demographics No Yes Yes Yes Yes Yes Yes Yes Yes Yes Number of schools 79 79 79 24 29 26 55 Number of students 11269 11269 7160 4109 4454 6815 3681 3784 3804 7588 Notes All regressions control for schoolbyentrywave fixed effects Demographics include race sex and subsidized lunch status Standard errors in parentheses are clustered by school Control means are in italics below standard errors Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 700 Effect of Childhood Investments on Postsecondary Attainment subsidized lunch We sorted students by this share and constructed the groups such that the number of students in each group was nearly identical see Appendix Table A19 Note that the STAR sample was disproportionately lowincome and urban so even the schools with the lowest levels of poverty were relatively disad vantaged When we estimated equation 1 separately for these three groups of schools we found that the treatment effect was concentrated in the poorest schools At schools with low to medium concentrations of poverty the estimated effect of class size on postsecondary attainment was indistinguishable from zero Table 2 columns 7 and 8 But the estimated effect was 73 percentage points in the poorest schools This is a 28 percent increase relative to the control mean in these schools A test of the equality of the coefficients for the poorest schools versus the combined bottom two terciles is strongly rejected P value of 0008 column 11 Inequality in postsecondary education has increased in recent decades with the gap in attendance between those born into lower income and higher income families expanding Bailey Dynarski 2011 Belley Lochner 2007 The pattern of effects described above will tend to decrease gaps in postsecondary attainment Figure 1 shows this graphically The top of Figure 1 depicts the gap in college attendance between blacks and whites in regular classes left and in small classes right The blackwhite gap is about half as large in small classes 77 percentage points as it is in regular classes 124 percentage points The drastic reduction in the race gap in college attendance is driven by females for whom the race gap virtually disappears in small classes results not shown In the control group students who were eligible for subsidized lunch were 291 percentage points less likely to attend college than were their higher income classmates The gap was slightly smaller in the treatment group 257 percentage points Finally we compared the effect of small classes on the gap in postsec ondary outcomes between schools with high and moderate levels of poverty Among students in regularsized classes the gap in postsecondary attendance was 181 per centage points Among students in small classes the gap was nearly halved to 98 percentage points Class size could plausibly affect the intensity with which a student enrolls in col lege in addition to the decision to enroll at all The overall impact on the intensity of enrollment is theoretically ambiguous students induced into college by smaller classes may be more likely to enroll parttime than other students while treatment could induce those who would have otherwise enrolled parttime to instead enroll fulltime In the control group about threequarters of college entrants ever attend college fulltime while a quarter never do Table 2 second row When we reesti mated equation 1 with these two variables as dependent variables we found that the effect on entry was evenly divided between parttime and fulltime enrollment While the standard errors preclude any firm conclusions these results suggest that the marginal college student is more likely than the inframarginal student to attend college exclusively on a parttime basis Timing of College Attendance Class size could plausibly affect the timing of postsecondary attendance The net effect is theoretically ambiguous Smaller classes may lead students who would otherwise have attended college to advance through high school more rapidly enter 9 All appendices are available at the end of this article as it appears in JPAM online Go to the publishers Web site and use the search engine to locate the article at httpwww3intersciencewileycomcgibin jhome34787 Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 701 Notes Subparts a c and e plot the fraction ever attended college by year for STAR students assigned to regular size classes and b d and f for STAR students assigned to small classes Subparts a and b compare college attendance by race c and d by subsidized lunch status and e and f by school poverty share Figure 1 The Effect of Class Size on Racial and Income Gaps in Postsecondary Attainment college sooner after graduation and move through college more quickly On the other hand students induced into college by smaller classes may enter and move through college at a slower pace than their inframarginal peers We first estimated the effect of class size upon ontime enrollment which we defined as entering college by fall of 1999 or about 18 months after the Project STAR cohort was scheduled to have graduated high school This variable captures the pace at which students completed high school how quickly they entered college Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 702 Effect of Childhood Investments on Postsecondary Attainment and whether they attended college at all By this measure 274 percent of the control group had enrolled on time or about threequarters of the 385 percent who ever attended college Table 2 Assignment to a small class increased the likelihood of students entering college on time by 24 percentage points Among those students enrolled in the poorest third of schools the effect was 47 points a 29 percent increase relative to this groups control mean of 16 percent These results suggest that students in smaller classes are no less likely to start college on time than control students 72 percent of the treatmentgroup students who attended college did so on time while among the control group the share of attendance that was on time was 71 percent We next looked at the yearbyyear evolution of the effect of class size on post secondary attainment For each year we plotted the share of students who had ever attended college separately for the treatment and control group Figure 2 top panel We also plotted the treatmentcontrol difference along with its 95 percent confidence interval Figure 2 bottom panel The fraction of the sample that had ever attended college rose from under 5 percent in 1997 to over 20 percent in 1998 when students were 18 The rate rose slowly through age 30 when the share of the sample with any college experience reached nearly 40 percent The difference between the two groups reached about 3 percentage points by age 19 and remained at that level through age 3010 When we examine the shares of students currently enrolled in college Figure 3 we see that the treatment group was more likely to be enrolled in college at every point in time peaking at around 25 percent in 1999 Plausibly smaller classes could have sped up college enrollment and completion and the control group could eventually have caught up with the treatment group in its rate of college attendance This is not what we see however The effect was always positive and was largest right after high school when the participants were 18 to 19 years old11 College Choice By boosting academic preparation smaller classes in primary school may induce students to alter their college choices For example those who would have oth erwise attended a twoyear community college may instead choose to attend a fouryear institution Bowen Chingos and McPherson 2009 have suggested that attending higher quality colleges which provide more inputs including better peers is a mechanism through which students can increase their rate of degree completion In Table 3 we examine the effect of class size on college choice Across the entire sample we found little evidence that exposure to smaller classes shifts stu dents toward higher quality schools The treatment effect is concentrated on at tendance at twoyear institutions While 22 percent of the control group started college at a twoyear school the rate is 25 percentage points higher in the treatment group with a standard error of 09 percentage points The effect is 10 To obtain the figures we replaced the smallclass indicator variable in our identifying equation with a full set of its interactions with year fixed effects The coefficients on these interactions and their confidence intervals are plotted in the bottom panel In the top panel we added these interactions to the yearspecific control means 11 This pattern of findings sheds light on the difference between our findings and those of Chetty et al 2011 We can reconcile our findings with Chetty et al 2011 if we censor the NSC data so that they ex clude the same enrollment spells that are unobserved in their data see Appendix Table A2 All appendices are available at the end of this article as it appears in JPAM online Go to the publishers Web site and use the search engine to locate the article at httpwww3intersciencewileycomcgibinjhome34787 Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 703 Notes Subpart a plots the mean fraction ever attended college by year for students assigned to small versus regular size classes It controls for both schoolbywave fixed effects and demographics including race sex and subsidized lunch status Subpart b plots the difference and its 95 percent confidence interval by year Standard errors are clustered by school Figure 2 College Attendance over Time by Class Size 63 percentage points among students in the poorest third of schools We found positive but imprecise effects on the probability of students ever attending a fouryear college attending college outside Tennessee or attending a selective college12 12 We measured selectivity using Barrons quality categories Barrons Educational Series 2004 Thank you to Michael Bastedo and Ozan Jaquette for use of the Barrons data Using an index that includes multiple proxies for college quality such as acceptance rate tuition and the average ACTSAT score of entering students provides similar results Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 704 Effect of Childhood Investments on Postsecondary Attainment Notes Figures plot the fraction currently attending college by year for STAR students assigned to small versus regular size classes All figures control for both schoolbywave fixed effects and demographics including race sex and subsidized lunch status Figure 3 Fraction Currently Enrolled in College over Time by Class Size and Enrollment Status Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 705 Table 3 The effect of class size on college choicelinear probability models Tercile of poverty share Total High Middle and low P value high versus middlelow Dependent variable 1 2 3 4 College attendance 0027 0073 0006 0008 0011 0021 0012 0385 0262 0446 First attended Two years 0025 0063 0007 0009 0009 0019 0010 0215 0162 0242 Public four years 0005 0009 0003 0690 0007 0011 0010 0127 0070 0156 Private four years 0003 0001 0004 0491 0004 0004 0005 0042 0030 0049 Ever attended Out of state 0013 0029 0006 0197 0009 0013 0012 0138 0100 0157 Selective 0009 0007 0011 0839 0009 0016 0011 0184 0090 0231 Number of schools 79 24 55 Number of students 11269 3681 7588 Notes All regressions control for schoolbyentrywave fixed effects and demographics including race sex and subsidized lunch status Standard errors in parentheses are clustered by school Control means are in italics below standard errors Persistence and Degree Completion While college entry has been on the rise in recent decades the share of college entrants completing a degree is flat or declining Bound Lovenheim Turner 2010 About half of college entrants never earn a degree A key concern is that marginal students attending college may drop out quickly in which case the atten dance effects discussed above would overestimate the effect of class size on social welfare We explored this issue by examining the effect of small classes on the number of semesters that students attended college as well as on the probability that they completed a college degree Overall the number of semesters attempted including zeros was quite low the control group attempted an average of three semesters by age 30 Among those in the control group with any college experience the average number of semesters attempted was eight The treatment group spent 022 more semesters in college than did the control group Figure 4 top Table 4 The effects were somewhat larger among students in the poorest schools coefficient of 032 though the effect is imprecisely estimated and the difference across terciles is less stark than with the college entry effects The size of these effects is comparable to treatment effects found in the Opening Doors demonstration which gave shortterm rewards to community college students for achieving certain enrollment and grade thresholds Barrow et al 2009 Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 706 Effect of Childhood Investments on Postsecondary Attainment Notes Subpart a plots the mean cumulative number of semesters attended by year for STAR students assigned to small versus regular size classes Subpart b plots the mean fraction ever receiving any post secondary degree associates or higher Subpart c plots the mean fraction receiving any postsecondary degree in the current year All figures control for both schoolbywave fixed effects and demographics including race sex and subsidized lunch status Figure 4 Postsecondary Persistence and Degree Receipt over Time by Class Size Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 707 Table 4 The effect of class size on persistence and degree receiptlinear probability models Tercile of poverty share Total High Middle and low P value high versus middlelow Dependent variable 1 2 3 4 Number of semesters attempted 022 032 019 0651 013 026 015 307 191 365 Receive any degree 0016 0011 0019 0624 0009 0012 0012 0151 0071 0191 Highest degree Associates 0007 0007 0007 0918 0004 0006 0006 0027 0013 0034 Bachelors or higher 0009 0003 0012 0532 0008 0011 0010 0124 0058 0157 Degree type STEM field 0005 0000 0008 0194 0003 0004 0004 0019 0008 0024 Business or economics field 0007 0001 0011 0189 0005 0004 0006 0026 0012 0033 All other fields 0003 0013 0000 0279 0006 0008 0008 0085 0039 0108 STEM business or economics 0013 0001 0019 0092 field economics field 0006 0006 0008 0044 0020 0057 Number of schools 79 24 55 Number of students 11269 3681 7588 Notes All regressions control for schoolbyentrywave fixed effects and demographics including race sex and subsidized lunch status Standard errors in parentheses are clustered by school Control means are in italics below standard errors Assignment to a small class increases the likelihood of students completing a col lege degree by 16 percentage points Table 4 the result is statistically significant at the 10 percent level When we examined effects separately by highest degree earned we found that the 16 percentage point effect was driven evenly by increases in two year associates and fouryear bachelors degree receipts 07 and 09 percentage points respectively When we turned to the timing of degree completion we saw that there is a positive treatment effect at every age The difference was largest be tween ages 22 and 23 Figure 4 panel C Students assigned to small classes during childhood continued to outpace their peers in their rate of degree completion well into their late 20s This may explain why Chetty et al 2011 did not find an effect of small classes on earnings which they observed at age 27 Members of the treatment group were still attending and completing college at this age and so had likely not yet spent enough time in the labor market for their increased education to offset experience forgone while in college Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 708 Effect of Childhood Investments on Postsecondary Attainment Field of Degree The earnings of college graduates vary considerably by field In particular students who study STEM fields as well as business and economics enjoy higher returns than other college graduates Arcidiacono 2004 Hamermesh Donald 2008 In this section we examine whether class size affects the field in which a student completes a degree13 We divided degrees into three categories a STEM fields b business and eco nomics concentrations and c all others14 Students can earn more than one degree eg an AA and a BA we coded them as having a STEM degree if any degree fell in this category and as having a business or economics degree if any degree fell in this category and they had not earned a STEM degree In practice very few students earn both a STEM and a business or economics degree Assignment to a small class shifted the composition of degrees toward STEM business and economics While 19 26 percent of the control group earned a degree in a STEM business or economics field the rate was 24 33 percent in the treatment group Table 4 However these estimates are imprecisely estimated In order to increase precision and to group fields by whether or not they are high paying we combined the STEM business and economics fields into one category Assignment to a small class increased degree receipt in these highpaying fields by 13 percentage points This difference is statistically significant at the 5 percent level with a standard error of 06 percentage points There was no difference in the rate at which students received degrees in other fields These results are consistent with two scenarios a those students induced into completing a degree tend to concentrate in STEM business or economics or b inframarginal degree completers are shifted toward STEM business or economics While we cannot conclusively identify those who are and are not on the margin of completing a degree our analysis by schoollevel poverty tercile Table 4 columns 2 and 3 suggests that the second scenario is at work The effect of small classes on graduating in a STEM business or economics degree was 19 percentage points standard error of 08 points among the lesspoor schools where students were more likely to be inframarginal degree completers The effect was zero among the poorest third of schools where students were more likely to be induced into com pleting a degree These effects are statistically different from one another at the 10 percent level Testing for Sources of Heterogeneity in Effects One interpretation of these results is that the groups with the lowest control means are most sensitive to class size An alternative interpretation however is that the groups that display the largest response are actually exposed to a more intense dosage of the treatment All of our estimates so far have been of the effect of the intenttotreat ITT which is attenuated toward zero when there is crossover and noncompliance The groups that show the largest ITT effects may have received larger dosages of the treatment in the form of particularly small classes or more 13 Field of study was available only for students who completed a degree we were therefore unable to examine the field of study for noncompleters 14 We followed a degreecoding scheme defined by the National Science Foundation National Science Foundation 2011 We applied this scheme to two text fields included in the NSC degree title eg associate of science or bachelor of science and college major eg biology A small number of students who received a degree are missing both degree title and college major and were excluded from this analysis Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 709 years spent in a small class Krueger and Whitmore 2002 showed that disad vantaged students in the treatment group were not systematically assigned to the smallest of the small classes Here we examine whether they were exposed to more years in a small class We generated subgroup estimates of the effect of assignment to a small class on years spent in a small class To do so we instrumented for years actually spent in a small class with years potentially spent in a small class Potential years in a small class is the product of assignment to a small class and the number of years the student could have been enrolled in a small class based on year of entry into Project STAR For example a student who entered Project STAR in kindergarten could have spent as many as four years in a small class while a child who entered in third grade could have spent only one15 We estimated the following equations YEARSis δ0 δ1Zis δsg ψisg 2 COLLisg α0 α1YEARSis αsg εisg 3 where COLLisg is an indicator variable for whether student i who entered Project STAR in school s and in grade g ever enrolls in college YEARS is the number of years the student spends in a small class Z is the potential number of years a student could attend a small class multiplied by an indicator for whether the student was assigned to a small class Schoolbyentrygrade fixed effects are included in each equation We estimated these equations separately by subgroup Table 5 reports the estimates of the firststage equation the reducedform ITT model and the twostage leastsquares model 2SLS The firststage results in col umn 1 measure compliance reporting the number of years actually spent in a small class for each year assigned to a small class Overall for each year of potential smallclass attendance students on average attend 064 years in a small class The compliance rate is consistently smaller for the groups for whom we have estimated the largest effects of ITT This is likely driven by higher mobility among black and poor students The 2SLS estimates column 3 indicate that each year spent in a small class increases college attendance rates by 1 percentage point for the entire sample but by 28 points for students attending the poorest schools 24 points for black students and 16 points for poor students These results indicate that students who are black poor or attend highpoverty schools benefit more from a year spent in a small class than do their peers Do ShortTerm Effects Predict LongTerm Effects We have shown that random assignment to small classes increases college entry and degree completion and shifts students toward highpaying fields Could these effects have been predicted by the shortterm effects of Project STAR on test scores That is are the effects measured at the time of the experiment predictive of the programs longterm effects A backoftheenvelope prediction would combine the experiments effect on scores with information from some other data source on the relationship between scores and postsecondary attainment We now make such an informed guess about 15 Abdulkadiroglu et al 2011 and Hoxby and Murarka 2009 used a similar approach when they instrumented for years spent in a charter school with potential years spent in a charter school where potential years was a function of winning a charter lottery and the grade of application Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 710 Effect of Childhood Investments on Postsecondary Attainment Table 5 Examining whether heterogeneity is in treatment effects or dosage First stage Reduced form Twostage leastsquares Control mean 1 2 3 4 Everyone 0643 0006 0009 0385 N 11269 0016 0003 0005 Highpoverty share 0602 0017 0028 0262 n 3681 0025 0006 0010 Middlelowpoverty share 0662 0001 0002 0446 n 7588 0019 0004 0005 Black 0589 0014 0024 0308 n 4109 0019 0006 0010 White 0669 0003 0004 0432 n 7160 0019 0004 0006 Subsidized lunch 0628 0010 0016 0272 n 6815 0015 0004 0007 Nonsubsidized lunch 0665 0002 0003 0563 n 4454 0024 0005 0008 Notes All regressions control for schoolbyentrywave fixed effects and demographics including race sex and subsidized lunch status Standard errors in parentheses are clustered by school the longterm effects of Project STAR then compare our guess with the papers findings The guess requires information about the relationship between standardized scores in childhood and adult educational attainment ideally for a cohort born around the same time as the Project STAR participants The NLSY79 MotherChild Supplement contains longitudinal data on the children of the women of the National Longitudinal Survey of Youth Bureau of Labor Statistics 2012 These children were born at roughly the same time as the Project STAR cohort The children of the NLSY CNLSY were tested every other year including between the ages of 6 and 9 the ages of the Project STAR participants while the experiment was under way Postsecondary attainment is also recorded in CNLSY In the CNLSY a 1 standard deviation increase in childhood test scores is associ ated with a 16 percentage point increase in the probability of attending college16 Assignment to a small class in Project STAR increases the average of K3 scores by 017 standard deviations Under the assumption that the relationship between scores and attainment is the same for the Project STAR and NLSY79 children a reasonable prediction of the effect of Project STAR on the probability of college attendance is 272 percentage points 017 16 This backoftheenvelope cal culation is nearly identical to the 27 point estimate we obtained in our regression analysis indicating that the contemporaneous effect of Project STAR on scores is an excellent predictor of its effect on adult educational attainment Another way to approach this question is to examine whether the estimated effect of small classes on postsecondary attainment disappears when we control for K 3 test scores This is an informal test of whether class size affects postsecondary attainment through any channel other than test scores This sort of informal test is 16 We regressed an indicator for college attendance against the average scores in multiple standardized tests administered when the participants were between ages 6 and 9 Scores were normalized within age to mean 0 and standard deviation 1 We measured college attendance by 2006 when the children were 25 to 29 years old Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 711 Table 6 Examining whether shortterm gains predict longterm gainslinear probability models College enrollment Degree receipt 1 2 3 4 Mean grades K3 test scores Small class 0027 0002 0016 0001 0011 0009 0009 0009 Test score 0169 0096 0006 0007 Small class test score 0008 0000 0010 0008 Mean grades 6 to 8 test scores Small class 0027 0020 0016 0010 0011 0010 0009 0008 Test score 0230 0141 0005 0006 Small class test score 0014 0009 0008 0008 Control mean 0385 0385 0151 0151 Number of students 11269 11269 11269 11269 Notes All regressions control for schoolbyentrywave fixed effects and demographics including race sex and subsidized lunch status Missing testscore indicators included for students with no test scores in grade range Standard errors in parentheses are clustered by school often used when checking whether an instrument eg assigned class size affects the outcome of interest eg postsecondary attainment through any channel other than the endogenous regressor eg test scores We first reestimated equation 1 and report the main result in column 1 of Table 6 We then added to this regression a students test scores and the interaction of the test scores and assignment to a small class The interaction allowed the relationship between test scores and postsecondary attainment to differ between small and regular classes Collisg β0 β1SMALLis β2TESTis β3SMALLis TESTis β4Xis βsg εisg 4 Here Collisg is a dummy that equals 1 if student i who entered Project STAR in school s and grade g ever attended college TESTis is the average of student is non missing kindergarten through thirdgrade math and reading test scores normalized to mean 0 and standard deviation of 1 Results are presented in Table 6 column 2 First looking to the coefficient on test scores in Project STAR a 1 standard devia tion increase in K3 scores is associated with a 17 percentage point increase in the probability of attending college17 This is very similar to the relationship estimated among the children of the NLSY The estimated coefficient on the interaction term between smallclass assignment and average test score is zero indicating that scores have no differential predictive power for postsecondary attendance across students in small and regular classes Similarly the estimated coefficient on the smallclass indicator variable is also zero suggesting that there is no additional boost to the likelihood a student attends postsecondary school from smallclass assignment after 17 The results were unchanged when we excluded the schoolbywave fixed effects and demographics Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 712 Effect of Childhood Investments on Postsecondary Attainment accounting for contemporaneous test scores which are boosted by smaller classes The pattern was similar when we replaced college attendance with degree receipt columns 3 and 4 These findings indicate that shortterm gains in cognitive test scores are indeed predictive of longterm benefits In contrast we found that scores from tests administered after students left Project STAR were not nearly so predictive of the experiments longterm effect We esti mated the equation just described replacing contemporaneous scores with those obtained from tests administered in grades 6 through 8 three to five years after the experiment had ended Even after controlling for test scores smallclass assignment raised the likelihood of attending college by a statistically significant 2 percentage points Further the negative coefficient on the interaction term indicates that these subsequent test scores have less predictive power in small than in regular classes We conclude that scores recorded several years after the experiment do a significantly poorer job than contemporaneous scores in predicting the effect of the experiment on adult outcomes One caveat to this analysis is that there could be omitted vari ables that are correlated with assignment to a small class with test scores and with college attendance If this is the case then it might not be the contemporaneous test scores that are mediating the effect of smallclass assignment but rather the omitted variables CONCLUSION We estimated the effect of class size in early elementary school on postsecondary attainment Assignment to a small class increases students probability of attending college by 27 percentage points Enrollment effects are largest among black stu dents students from lowincome families and students from highpoverty schools which indicates that classsize reductions during early childhood can help to close income and racial gaps in postsecondary attainment Assignment to a small class also increases students probability of completing a degree by 16 percentage points with the effects concentrated in highearning fields such as STEM business and economics As a final check on the sensitivity of our main result to possible sources of bias we conducted two exercises First we examined the extent to which missing name and date of birth of students could influence the results given that the NSC uses these identifiers to match students to college enrollment data We assigned all students with a missing name or date of birth first as having enrolled in college and then as having not enrolled in college regardless of their observed enrollment status After each of these imputations we reestimated equation 1 Imputing students with missing identifiers as enrolled not enrolled yielded a point estimate of 0017 0025 and standard error of 0009 0011 These coefficients are somewhat attenuated relative to our main result of 0027 SE 0011 However this check showed that even if we imputed the most extreme cases of possible bias due to missing identifiers our result remains positive statistically significant and similar in magnitude to our main result Our final check was a backoftheenvelope exercise to bound the possible upward bias that could be due to smallclass assignment inducing students out of colleges not participating in the NSC eg forprofit colleges and into colleges that do participate eg community colleges Using the NSC participant list and IPEDS enrollment data we calculated that 87 percent of firsttime enrollment in Tennessee during 1998 is in forprofit colleges If small classes induced all of these students out of forprofit institutions and into colleges that we observed in the NSC an extreme assumption then our estimated effect on college enrollment would be Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 713 biased upward by 37 percentage points18 This upper bound on the upward bias is larger than our observed treatment effect However a somewhat more realistic estimate based on past studies of Project STAR would be to assume that treatment induces 10 percent of students out of forprofit institutions and into colleges that we observe via NSC Krueger Whitmore 2001 This would cause our estimates to be biased upward by 04 percentage points This excludes any possible attenuation bias due to classical measurement error in the unobserved nonprofit college attendance and any possible downward bias due to small classes inducing noncollege attenders into forprofit institutions This is thus a source of potential upward bias that under a somewhat plausible worstcase scenario would explain only a small fraction of our treatment effect Is the nearly 3 percentage point increase due to reduced class size that we es timate a large effect To put this effect in context we compared the estimate to those of other interventions that boost postsecondary attainment We focused on the results of randomized trials when possible turning to plausibly identified quasi experiments where no controlled experiment has been conducted Deming and Dy narski 2010 have provided a review of this literature from which much of this information was drawn We focused on evaluations of discrete replicable interven tions We deliberately ignored several excellent papers that demonstrate that schools or teachers matter for postsecondary attainment since they do not identify the effect of a manipulable parameter of the education production function eg Chetty et al 2011 Deming et al 2011 Two small experiments tested the effect of intensive preschool on longterm out comes Abecedarian produced a 22 percentage point increase in the share of children who eventually attended college The Perry Preschool Program had no statistically significant effect on postsecondary outcomes Anderson 2008 The participants in these experiments were almost exclusively poor and black Head Start a less intensive preschool program increased college attendance by 6 percentage points Deming 2009 with larger effects for blacks and females 14 and 9 percentage points respectively Upward Bound provided atrisk high school students with in creased instruction tutoring and counseling The program had no detectable effect on the full sample of treated students but it did increase college attendance among students with low educational aspirations by 6 percentage points Seftor Mamun Schirm 2009 There are no experimental estimates of the effect of financial aid on college en try However there are several wellidentified quasiexperimental studies showing that student aid can boost postsecondary enrollment by several percentage points depending on how much aid is provided Deming Dynarski 2010 Another way of increasing college enrollment is by assisting students with the administrative requirements of enrolling in college Bettinger et al 2012 randomly assigned fam ilies to a lowcost treatment that consisted of helping them to complete the FAFSA Free Application for Federal Student Aid the lengthy and complicated form re quired to obtain financial aid for college Their intervention increased enrollment by 8 percentage points The costs of the above interventions varied dramatically We created an index of costeffectiveness for increasing college enrollment by dividing each programs 18 In other words if we assume that none of the treatment group attends forprofit colleges but 87 per cent of the control group does the implied total college enrollment rate among the control group would be 0422 This rate is 37 percentage points higher than the observed college attendance rate excluding forprofit colleges among the control group which is 0385 Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 714 Effect of Childhood Investments on Postsecondary Attainment costs by the proportion of treated students it induced into college19 Head Start costs 8000 per child Given the 6 percentage point effect noted above the amount spent by Head Start to induce a single child into college is therefore 133333 8000006 For Abecedarian the figure is 410000 90000022 The cost of reduced class size is 12000 per student larger than that of Head Start but considerably smaller than that of Abecedarian The amount spent in Project STAR to induce a single child into college is 400000 12000003 If the program could be focused on students in the poorest third of schools the subpopulation that most closely matches that of the preschool interventions then the cost would drop to 171000 per student induced into college Upward Bound costs 5620 per student If the program could be targeted to stu dents with low educational aspirations the implied cost of inducing a single student into college would be 93667 5620006 Dynarski 2003 examined the effect of the elimination of the Social Security Student Benefit Program which paid college scholarships to the dependents of deceased disabled and retired Social Security beneficiaries Eligible students were disproportionately black and lowincome The estimates from that paper indicate that about twothirds of the treated students who attended college were inframarginal while the other third was induced into college by the 7000 scholarship These estimates imply that three students are paid a scholarship in order to induce one into college The cost per student induced into college is therefore 21000 Finally the cost per treated subject in the FAFSA experiment Bettinger et al 2012 was 88 for an implied cost per student induced into college of 1100 88008 A fair conclusion from this analysis is that the effects we find in this paper of class size on college enrollment alone are not particularly large given the costs of the program If focused on students in the poorest third of schools then the cost effectiveness of classsize reduction is within the range of other interventions There is no systematic evidence that early interventions pay off more than later ones when the outcome is limited to increased college attendance In addition to estimating the effects of reduced class size during childhood on ed ucational attainment the results in our paper shed light on the relationship between the short and longterm effects of an educational intervention We found that the shortterm effect of smallclass assignment on test scores was an excellent predictor of its effect on adult educational attainment In fact under the assumption that there are no omitted variables correlated with smallclass assignment test scores and college enrollment the effect of small classes on college attendance is com pletely explained by their positive effect on contemporaneous test scores Further the relationship between scores and postsecondary attainment is the same in small and regular classes that is the scores of children in the small classes are no less or more predictive of adult educational attainment than those of children in the regular classes This is an important and policyrelevant finding given the necessity to evaluate educational interventions based on contemporaneous outcomes A further contribution of this paper is to identify the effect of manipulating a single educational input on adult educational attainment The earlychildhood in terventions for which researchers have identified lifetime effects eg Head Start Abecedarian are intensive and multipronged including home visits parental coach ing and vaccinations We cannot distinguish which dimensions of these treat ments generate shortterm effects on test scores and whether they differ from the 19 All costs in this section are in 2007 dollars and come from Deming and Dynarski 2010 unless otherwise indicated The costs for the early childhood programs and Project STAR have been discounted back to age 0 using a 3 percent discount rate Costs of the high school and college interventions have not been discounted Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment 715 dimensions that generate longterm effects on adult wellbeing By contrast the ef fects we measure in this paper both shortterm and longterm can be attributed to a welldefined and replicable intervention reduced class size SUSAN DYNARSKI is Professor of Public Policy Education and Economics in the Gerald R Ford School of Public Policy School of Education and Department of Economics University of Michigan Weill Hall 735 South State Street No 5212 Ann Arbor MI 481093091 and Research Associate at the National Bureau of Economic Research 1050 Massachusetts Avenue Cambridge MA 02138 JOSHUA HYMAN is a Doctoral Candidate in the Department of Economics and Gerald R Ford School of Public Policy University of Michigan Weill Hall 735 South State Street No 5212 Ann Arbor MI 481093091 DIANE WHITMORE SCHANZENBACH is Associate Professor in the School of Ed ucation and Social Policy Northwestern University Annenberg Hall No 205 2120 Campus Drive Evanston IL 60208 and Research Associate at the National Bureau of Economic Research 1050 Massachusetts Avenue Cambridge MA 02138 ACKNOWLEDGMENTS We thank Jayne ZahariasBoyd of HEROS and the Tennessee Department of Education for allowing the match between the Project STAR and National Student Clearinghouse data The Education Research Section at Princeton University generously covered the cost of this match Monica Bhatt David Deming and Nathaniel Schwartz provided excellent research assistance We benefited from discussions at Cornell the Federal Reserve Bank of Atlanta the Swedish Institute for Labour Market Evaluation University of California at Davis Univer sity of Michigan Vanderbilt Yale and the 2012 Rome conference on Improving Education Accountability and Evaluation REFERENCES Abdulkadiroglu A Angrist J D Dynarski S M Kane T J Pathak P A 2011 Ac countability and flexibility in public schools Evidence from Bostons charters and pilots Quarterly Journal of Economics 126 699748 Achilles C M 1999 Lets put kids first finally Getting class size right Thousand Oaks CA Corwin Press Anderson M L 2008 Multiple inference and gender differences in the effects of early inter vention A reevaluation of the Abecedarian Perry Preschool and Early Training Projects Journal of the American Statistical Association 103 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StudentTeacher Achievement Ratio STAR Project Technical Report 19851990 Nashville TN Tennessee State Department of Education Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management Effect of Childhood Investments on Postsecondary Attainment APPENDIX Table A1 Student demographics by school poverty share High poverty Middle poverty Low poverty Middlelow poverty 1 2 3 4 Share white 0253 0746 0881 0814 Share female 0471 0475 0469 0472 Share eligible for subsidized lunch 0855 0504 0292 0398 Number of schools 24 29 26 55 Number of students 3681 3784 3804 7588 Note School poverty share is measured as the fraction of the school that is eligible for a subsidized lunch Table A2 The effect of classsize censoring to match IRS data spanlinear probability models Baseline all years of enrollment Exclude pre1999 enrollment Exclude post2007 enrollment Include 1999 to 2007 enrollment only Dependent variable 1 2 3 4 Ever attend 0027 0018 0023 0015 0011 0011 0011 0011 0385 0369 0372 0357 Number of students 11269 11269 11269 11269 Notes All regressions control for schoolbyentrywave fixed effects and demographics including race sex and subsidized lunch status Standard errors in parentheses are clustered by school Control means are in italics below standard errors Journal of Policy Analysis and Management DOI 101002pam Published on behalf of the Association for Public Policy Analysis and Management 1 Microeconomia IV Aleatorização LATE 1 2 2 Como determinar se há efeito causal de um programatratamento em alguma variável de interesse Avaliação de programas de treinamento para funcionários Impacto da Lei do Simples sobre o grau de formalização das empresas Efeito do aumento da licença maternidade sobre o salário e emprego da mulher Efeito da crise cambial de 2002 sobre os investimentos das empresas brasileiras Introdução 3 3 Exemplo Programa de treinamento de trabalhadores implementado nos Estados Unidos na década de 70 conhecido como National Supported Work NSW Lalonde 1986 Dehejia e Wahba 19992002 Comparamse trabalhadores que se submeteram ao programa grupo tratamento e trabalhadores que não foram submetidos grupo controle Pergunta Em geral podese dizer que a diferença média de rendimentos entre os grupos é devida de forma inequívoca ao efeito do programa de treinamento tratamento Introdução 4 4 Quais são as condições em que se pode determinar se há efeito causal Como foi feito o desenho do tratamento Grupos escolhidos de forma aleatória Grupos escolhidos com base em características observáveis Grupos autoselecionados Hipóteses sobre autoseleção Feita com base em variáveis observáveis ao pesquisador Feita com base em variáveis não observáveis ao pesquisador Sugestão de leitura inicial RAVALLION Martin The mystery of the vanishing benefits An introduction to impact evaluation The World Bank Economic Review v 15 n 1 p 115140 2001 Algumas perguntas importantes 5 5 No texto de Ravallion 2001 Ms Speedy Analyst técnica do Ministério da Fazenda de um país em desenvolvimento é incumbida de fazer a análise do impacto de um programa igual ao BolsaFamília Primeira pergunta que ela se faz é Qual o objetivo do programa Reduzir pobreza no curto transferência de renda e no longo escolaridade prazos Segunda pergunta O programa parece não ter nenhum efeito sobre escolaridade ou matrícula Por quê Ravallion 2001 6 6 A resposta à segunda pergunta tem sua origem no desenho da avaliação Método experimental aleatorizaçãosorteio Obtém um grupo controle que é o contrafactual perfeito dos tratados pois a forma de seleção garante estatisticamente grupos semelhantes em variáveis que se observa e que não se observa Método não experimental regressão linear múltipla Quando não se realizou o sorteio dos tratados o grupo controle não é estatisticamente semelhante ao tratado Para corrigir as implicações das diferenças do indicador de impacto antes do projeto entre os grupos estimase o impacto controlando pelas variáveis que se observa Note esse método controlacorrige o impacto ao considerar variáveis que se observa mas ainda resta os problemas causados por variáveis não observadas Ravallion 2001 7 7 Método de Aleatorização Considerado o padrãoouro o primeiro método baseiase na aleatorização de indivíduos para passar ou não pelo tratamento Esse procedimento de aleatorização gera dois grupos experimentais o de tratamento e o de controle O fato da participação ou não no tratamento ser definida pelo procedimento de aleatorização sorteio garante que os grupos de tratamento e controle sejam parecidos tanto nas características observáveis quanto nas não observáveis 8 8 Dessa forma por construção o método permite criar uma situação na qual não há correlação entre ser ou não tratado e os atributos das unidades amostrais Portanto o viés de seleção fica contornado permitindo que a comparação entre os grupos identifique o efeito causal da intervenção Não se espera encontrar diferenças significativas em características prétratamento entre os grupos de tratamento e de controle Método de Aleatorização 9 9 Assim testes de comparação de médias e variâncias nas variáveis de controle observadas antes do tratamento fornecem uma boa medida da qualidade da aleatorização A avaliação aleatorizada é utilizada em diversas áreas como por exemplo na medicina sendo considerado o procedimento referência para se estabelecer causalidade e medir impacto de vários tipos de tratamentos Método de Aleatorização 10 10 Em Ravallion 2001 Ms Analyst descobre rapidamente que comparar médias entre tratados e não tratados só tem interpretação causal se o programa tivesse sido alocado de maneira aleatória Por quê Seja 𝑌 a variável de remuneração e 𝑇 uma dummy que indica se o trabalhador participou do programa de treinamento Comparação entre médias de tratados e nãotratados pode ser escrita como 𝑨𝑻𝑬 𝑬 𝒀𝟏 𝑬 𝒀𝟎 Ravallion 2001 11 11 Aleatorização Pergunta esse é o efeito causal do programa de treinamento sobre a remuneração do trabalhador Para responder precisamos pensar qual teria sido a remuneração dos trabalhadores atendidos pelo programa se eles não estivessem no programa CONTRAFACTUAL Defina 𝑌1 como a remuneração do trabalhador caso ele tivesse participado do programa de treinamento Defina 𝑌0 como a remuneração do trabalhador caso ele não tivesse participado do programa de treinamento Observamos a remuneração 𝑌 𝑌1 𝑇 𝑌0 1 𝑇 Isto é observamos Y1𝑇 1 e Y0𝑇 0 12 12 Mas nunca observamos Y1𝑇 0 ou Y0𝑇 1 Esse problema é conhecido como problema fundamental da inferência causal Holland 1986 Suponha que queremos olhar para o seguinte parâmetro 𝐴𝑇𝑇 𝐸 𝑌1𝑇 1 𝐸 𝑌0𝑇 1 ou seja o ganho de remuneração associado ao programa para a subpopulação de interesse a que é atendida pelo programa Podemos usar a diferença de médias entre tratados e controles para estimar o ATT Aleatorização 13 13 O viés aparece se o comportamento do grupo de controle não for um bom espelho para o que aconteceria com o tratado caso ele não fosse tratado B viés de seleção Os trabalhadores que não receberam o programa de treinamento podem ter um comportamento muito diferente de trabalhadores que receberam o programa teriam tido caso não o tivessem recebido Aleatorização Podemos usar a diferença de médias entre tratados e controles para estimar o ATT 𝐸 𝑌 𝑇 1 𝐸 𝑌 𝑇 0 𝐸 𝑌1 𝑇 1 𝐸 𝑌0 𝑇 0 𝐸 𝑌1 𝑇 1 𝐸 𝑌0 𝑇 1 𝐸 𝑌0 𝑇 1 𝐸 𝑌0 𝑇 0 ATT B 14 14 Qual a diferença entre estimar o ATE e o ATT A diferença entre ATE e ATT é S também chamado de ganho de sorting 𝑺 𝑨𝑻𝑬 𝑨𝑻𝑻 𝐸 𝑌 𝑇 1 𝐸 𝑌 𝑇 0 𝐸 𝑌1𝑇 1 𝐸 𝑌0𝑇 1 𝐸 𝑌1 𝑌0 𝐸 𝑌1 𝑌0𝑇 1 Esse viés surge devido a uma seleção do grupo de tratado Exemplo Suponha que trabalhadores que receberam o programa de treinamento sejam os que estavam desempregados há mais de 12 meses Esse grupo é bem diferente da população total de trabalhadores Aleatorização 15 15 O que acontece em um experimento aleatório Experimento T é independente de Y1 e Y0 sorteio Recebimento do tratamento T1 se a unidade é tratada é independente dos resultados potenciais Y1 Y0 𝐸 𝑌1𝑇 1 𝐸 𝑌1𝑇 0 𝐸 𝑌1 𝐸 𝑌0𝑇 0 𝐸 𝑌0𝑇 1 𝐸 𝑌0 Neste caso B0 viés de seleção e S0 ganho de sorting ATEATT Aleatorização 16 16 Podemos usar a comparação de médias para estimar o efeito médio do tratamento Essa diferença de médias pode ser obtida por uma regressão linear de Y em T incluindo o intercepto Como verificar a qualidade da aleatorização Vamos discutir o famoso exemplo de early childhood da Colômbia Aleatorização 17 17 Exemplo Intervenção na Colômbia Experimento aleatório de um programa integrado para early childhood Voltado para crianças entre 12 e 24 meses Intervenção Estímulos psicossociais e nutrição suplementar para as crianças de famílias vulneráveis que eram beneficiárias de um programa de transferência condicional de renda Familias em Acción Estímulos psicossociais visitas domiciliares semanais que desenvolviam atividades com as crianças juntamente com seus pais de acordo com um currículo específico Nutrição zinco e ferro Familias em Acción as famílias recebem uma transferência complementar de renda se as crianças abaixo de 6 anos tem checkups de saúde regulares e as crianças acima de 5 anos vão para a escola Aleatorização 18 18 Exemplo Intervenção na Colômbia Selecionaram 3 regiões próximas de Bogotá Em cada uma das regiões foram selecionados 32 municípios Aleatorização feita dentro de cada região Cada 8 clusters de cada região foram alocados de forma aleatória a um dos braços do tratamento Antes de fazer a análise precisamos mostrar o teste de balanceamento entre tratados e controles Aleatorização 19 19 ATTANASIO Orazio P et al Using the infrastructure of a conditional cash transfer program to deliver a scalable integrated early child development program in Colombia cluster randomized controlled trial BMJ v 349 2014 Aleatorização Exemplo Intervenção na Colômbia 20 20 Aleatorização Exemplo Intervenção na Colômbia Teste de Balanceamento 21 21 Resultados Aleatorização Exemplo Intervenção na Colômbia 22 22 I Algumas unidades que foram alocadas para o grupo de tratamento decidem que não querem receber o tratamento Onesided Compliance II Algumas unidades que foram alocadas para o grupo de controle acabam sofrendo algum efeito da intervenção contaminação O que podemos fazer nesses casos Quando a aleatorização falha 23 23 Exemplo Experimento em 1960 para detectar se o exame de mamografia é eficaz em detectar o câncer de mama em estágio inicial 6200 mulheres com idade entre 40 e 64 anos foram alocadas de forma aleatória no grupo de tratamento e controle Grupo de controle foram convidadas a fazer o checkup regular Grupo de tratamento foram convidadas para 4 visitas anuais para o exame de mamografia e fizeram o checkup regular Quando a aleatorização falha 24 24 Como estimamos o efeito médio do tratamento nesse caso Existe algum outro efeito que conseguimos estimar Quando a aleatorização falha 011 015 25 25 Usamos variáveis instrumentais VI quando temos seleção baseada em nãoobserváveis Exemplo 1 Guerra do Vietnam Angrist Como ir à guerra afeta renda e saúde Y após a guerra Ir a guerra T é claramente endógeno Angrist propôs usar o sorteio dos dias de nascimento como instrumento Z Exemplo 2 Trimestre de nascimento Angrist e Krueger 1991 Como a educação T afeta renda Y Educação é endógena Angrist e Krueger propõem usar o trimestre de nascimento como instrumento para educação sob argumento de que dada a regra de entrada na escola por trimestre de nascimento a escolaridade final poderia ser afetada LATE 26 26 Precisamos de uma variável exógena Z que afeta a decisão de participação e que não está correlacionada com nenhum fator não observável relacionado ao resultado potencial No caso clássico de variável instrumental com efeitos homogêneos do tratamento estamos pensando no seguinte sistema de equações 𝑌𝑖 𝛼 𝛽𝑇𝑖 𝜀𝑖 𝑇𝑖 ቊ1 se 𝛾 𝛿𝑍𝑖 𝜗𝑖 0 0 cc no qual 𝑇𝑖 é igual a 1 se o indivíduo recebeu tratamento e 0 se o indivíduo é não tratado Além disso 𝐶𝑜𝑣 𝑍𝑖 𝜀𝑖 0 e 𝐶𝑜𝑣 𝜗𝑖 𝜀𝑖 0 Seleção em nãoobserváveis VI 27 27 Nesse sistema os fatores nãoobserváveis que afetam a decisão de participar do programa estão correlacionados com os fatores não observáveis que afetam o resultado de interesse Precisamos de um instrumento Z que permita captar uma variação exógena na decisão de participar do programa e que ao mesmo tempo não está relacionado de forma direta com o resultado potencial Esse modelo pode ser estimado por mínimos quadrados em dois estágios Nesse caso em um primeiro estágio estimamos um modelo de probabilidade linear que relaciona T com Z e obtemos o valor predito 𝑇𝑖 𝛾 መ𝛿𝑍𝑖 Esse valor predito representa uma variação exógena na decisão de participar ou não do programa que não está relacionada a nenhum outro fator que possa influenciar o resultado de interesse Seleção em nãoobserváveis VI 28 28 Em um segundo estágio estimamos uma regressão linear que relaciona o resultado de interesse Y com este valor predito 𝑌𝑖 𝛼 መ𝛽 𝑇𝑖 No sistema de equação acima a variável Z não afeta diretamente Y Ela só afeta o resultado de interesse pela sua relação com a participação ou não no tratamento Além disso assumimos que o efeito de tratamento é homogêneo isto é 𝛽 𝛽𝑖 para todo indivíduo i No caso de tratamento homogêneo o resultado do indivíduo depende apenas da sua participação ou não no programa e não está relacionado a como a participação no programa é afetada pelo instrumento Z O ATE efeito médio do tratamento é igual ao ATT efeito médio do tratamento sobre os tratados 𝑨𝑻𝑻 𝑨𝑻𝑬 𝜷 Seleção em nãoobserváveis VI 29 29 Se os indivíduos souberem que os ganhos de participação podem diferir para certos grupos eles irão levar em consideração essa informação na hora de decidir se participam ou não do programa Nesse caso tanto seus ganhos individuais 𝛽𝑖 como Z irão afetar a decisão de o individuo i participar e variações em Z irão afetar a decisão de participar de forma diferente para cada indivíduo dependendo do seu ganho com o tratamento 𝛽𝑖 Nesse caso a hipótese de homogeneidade do tratamento é violada e o estimador de variável instrumental não identifica o ATE ou o ATT Seleção em nãoobserváveis VI 30 30 Imbens e Angrist 1994 mostraram que quando os efeitos do tratamento são heterogêneos o arcabouço de variável instrumental permite identificar um efeito médio de tratamento local LATE isto é um efeito médio do tratamento para uma subpopulação específica Nesse caso 𝛽 será o efeito médio do tratamento para aqueles indivíduos cuja variação em Z provoca uma variação no status de participação sem afetar os resultados potenciais Para estes indivíduos a diferença na média dos resultados potenciais do grupo de tratados e do grupo de não tratados ocasionada por uma variação em Z se dá exclusivamente pelo efeito de Z na taxa de participação do programa Seleção em nãoobserváveis VI 31 31 Exemplo Guerra do Vietnã Angrist Os homens foram selecionados para guerra através de uma loteria Para cada homem era alocado um número de forma aleatória Se esse número fosse baixo o homem deveria se alistar para a guerra Z variável binária que indica o resultado da loteria Z1 se o número é baixo e 0 caso contrário Quem são os homens que tiveram o seu comportamento afetado pela loteria A variação exógena em Z vai permitir estimar o efeito da guerra na renda futura Seleção em nãoobserváveis VI 32 32 De volta ao Exemplo da mamografia As mulheres que aceitaram os convites são geralmente mais bem instruídas preocupam se mais em realizar os seus exames periódicos para detecção de doenças e tem hábitos mais saudáveis tendo na média saúde melhor que as mulheres que rejeitaram o convite Logo para encontrar o efeito médio do tratamento sobre a probabilidade de detectar câncer de mama não podemos comparar a proporção de mulheres que fizeram o exame e foram diagnosticadas com câncer de mama com a proporção de mulheres que não fizeram o exame e receberam o diagnostico da doença pois nesse caso estaríamos misturando o efeito do programa com o efeito de vida mais saudável Nesse caso estamos no arcabouço em que o instrumento vem de um experimento real e foi alocado de forma aleatória entre as mulheres O instrumento seria uma variável binária que assume valor igual a 1 se a mulher tivesse sido convidada a fazer o exame e 0 caso contrário Nesse caso LATE é o efeito médio sobre as mulheres que mudaram o seu comportamento devido ao convite feito via carta O efeito médio para as mulheres compliers LATE e Experimento Aleatório 33 33 I Peixoto B Pinto C C D X Lima L Foguel M N Barros R D Menezes Filho N 2017 Avaliação econômica de projetos sociais 3a edição Capítulos 2 3 e 6 Fundação Itaú Social II Gertler P Martínez S Premand P Rawlings L and Vermeersch C Avaliação de impacto na prática 2a edição Capítulos 3 4 e 5 World Bank Publications 2016 Referências didáticas Insper 20092022 1 Com base nas referências do Bloco de Economia da Educação A 15 ponto Em linha com o modelo de formação de habilidades de Cunha Heckman visto em aula a teoria de Attanasio 2015 propõe um modelo de produção de capital humano com foco especialmente na acumulação de capital humano nos primeiros anos de vida Estruture formalmente com equações e suas palavras o modelo microeconômico de Attanasio 2015 deixando claro quais as premissas o problema de maximização dos pais e qual o principal resultado teórico do modelo Finalize sua exposição elencando a hipótese econômica do artigo Dica Em sua resolução sugerimos que tenha em mente qual a pergunta de investigação deste artigo Não é necessário trazer o desenvolvimento integral do modelo A ideia aqui também não é fazer um resumo do modelo e sim estruturálo para ter um início meio e fim O desfecho será a hipótese econômica B 10 ponto Explique com as suas palavras qual a estratégia de identificação empregada na análise empírica do artigo de Afridi 2010 Explique também o racional que baseou a exposição dos resultados nas Tabelas 2 a 9 Em seguida interprete ao menos 1 coeficiente estimado aquele que seu Grupo julgar mais importante para a análise de cada Tabela Finalize identificando qual é a principal Tabela e o principal resultado deste artigo Justifique C 05 ponto Explique por que o Experimento investigado por Dynarski et al 2013 de alocação dos alunos em turmas de diferentes tamanhos é considerado um marco importante na identificação do efeito causal do tamanho da turma no desempenho educacional dos alunos Explique quais seriam as limitações se ao invés de realizar um experimento aleatório fossem coletados dados observacionais como do Censo Escolar que possui características dos estudantes e escolas e da Prova Brasil que contém as notas dos estudantes para identificar o efeito do tamanho da turma nas notas dos estudantes wwwinsperedubr 1 Primeiros passos em Economia da Educação Microeconomia IV wwwinsperedubr 2 Dois temas que abordaremos nesta aula 1 Early childhood education and early interventions Qual importância de programas de educação infantil na formação de habilidades O modelo de Cunha Heckman 2 O dilema do tamanho da turma Qual o tamanho ótimo da turma sob a perspectiva da escola O tamanho da turma influencia no aprendizado dos alunos O modelo de Edward Lazear wwwinsperedubr 3 Early childhood education early interventions Tópico 1 Economia da Educação wwwinsperedubr 4 4 Fonte UNESCO wwwinsperedubr 5 Early childhood intervention Quais são os objetivos Termo usado para descrever as políticas públicas serviços e apoios que estão disponíveis para mães bebês e crianças pequenas e suas famílias Entre seus objetivos podese destacar em especial que uma Early childhood intervention seja importante no desenvolvimento de habilidades das crianças em três áreas i habilidades cognitivas ii prontidão para a escola e iii desenvolvimento socioemocional wwwinsperedubr 6 Early childhood intervention Por que Economistas se interessam Por que o setor público costuma agir wwwinsperedubr 7 Early childhood intervention Por que Economistas se interessam Por que o setor público costuma agir Um argumento para a ação do governo é pensando na Equidade Os indivíduos que começam com dotações muito desiguais tem chances altas de continuar com alocações muito desiguais ao longo da vida Um governo que se preocupa com a equidade pode compensar as diferenças nos resultados finais eou tentar igualar as dotações iniciais Em geral equalizar as dotações iniciais por meio de programas de intervenção na primeira infância costuma ser uma abordagem melhor para o problema de alocações desiguais Por quê Outra justificativa para a ação do governo na infância é a presença de falhas de mercado wwwinsperedubr 8 Existe uma idade ótima para a intervenção Os primeiros anos de vida são fundamentais para o desenvolvimento da saúde mental e habilidades socioemocionais Em particular os primeiros 3 anos são um período crítico para o desenvolvimento do cérebro sendo ideais para uma Early intervention A curva de Heckman feito na lousa wwwinsperedubr 9 Exemplo Early Childhood Intervention na Colômbia Attanasio et al 2014 2017 e 2021 Experimento aleatório de um programa integrado para early childhood Voltado para crianças entre 12 e 24 meses Intervenção Estímulos psicossociais e nutrição suplementar para as crianças de famílias vulneráveis que eram beneficiárias de um programa de transferência condicional de renda Familias em Acción Estímulos psicossociais visitas domiciliares semanais que desenvolviam atividades com as crianças juntamente com seus pais de acordo com um currículo específico Nutrição zinco e ferro Familias em Acción as famílias recebem uma transferência complementar de renda se as crianças abaixo de 6 anos tem checkups de saúde regulares e as crianças acima de 5 anos vão para a escola Impacto a Childrens cognitive skills baseline b Childrens socioemotional skills baseline c Childrens cognitive skills followup d Childrens socioemotional skills followup Treated Control pvalue diff 1 Treated Control pvalue diff 0603 Treated Control pvalue diff 001 Treated Control pvalue diff 0061 wwwinsperedubr Insper wwwinsperedubr 11 Mecanismo Attanasio O Cattan S Fitzsimons E Meghir C RubioCodina M 2020 Estimating the production function for human capital results from a randomized controlled trial in Colombia American Economic Review 1101 4885 wwwinsperedubr 12 Modelo Econômico do Crime de Becker Teoria Micro em Economia da Educação Modelo 1 O modelo de Formação das habilidades de Cunha Heckman wwwinsperedubr 13 Um Modelo de Formação das habilidades ao longo da vida O modelo de Cunha Heckman wwwinsperedubr 14 Um Modelo de Formação das habilidades ao longo da vida O modelo de Cunha Heckman O mecanismo central deste modelo é a tecnologia de formação de habilidades wwwinsperedubr 15 Um Modelo de Formação das habilidades ao longo da vida Pilares do modelo de Cunha Heckman 1 As habilidades são múltiplas Os indivíduos possuem muitas habilidades relevantes ao longo vida e estas vão muito além das habilidades cognitivas medidas por testes de QI wwwinsperedubr 16 Um Modelo de Formação das habilidades ao longo da vida Pilares do modelo de Cunha Heckman 2 As habilidades são autoprodutivas e se complementam As habilidades não são apenas autoprodutivas mas também promovem a produção de outras habilidades wwwinsperedubr 17 Um Modelo de Formação das habilidades ao longo da vida Pilares do modelo de Cunha Heckman 3 As habilidades complementam o investimento Ao promover habilidades na primeira infância facilitase o acúmulo de habilidades mais tarde na vida wwwinsperedubr 18 Um possível desfecho deste modelo teórico é Hipótese econômica Fundamentado pelo modelo de Cunha Heckman um aumento dos investimentos nas primeiras fases da vida se acumulam e tem influência direta na formação de habilidades ao longo da vida wwwinsperedubr 19 O tamanho da turma influencia no aprendizado dos alunos Tópico 2 Economia da Educação wwwinsperedubr 20 Tamanho da classe e Desempenho da Turma Perguntas Qual o tamanho ótimo da turma sob a perspectiva da escola Classes menores melhoram o aprendizado dos alunos wwwinsperedubr 21 Tamanho da classe e Desempenho da Turma Pergunta Qual o tamanho ótimo da turma sob a perspectiva da escola Classes menores melhoram o aprendizado dos alunos O Experimento Projeto STAR StudentTeacher Achievement Ratio As crianças são aleatoriamente designadas a três tipos de turmas i pequenas classes com 1317 estudantes ii classes regulares com 2225 estudantes e iii classes regulares com um assistente para ajudar o professor Objetivo Determinar o efeito do tamanho da turma no aprendizado dos alunos medido por testes padronizados wwwinsperedubr 22 Modelo Econômico do Crime de Becker Teoria Micro em Economia da Educação Modelo 2 O modelo de Tamanho de Turmas de Edward Lazear wwwinsperedubr 23 O dilema do tamanho das turmas O modelo de Edward Lazear Embora exista uma vasta literatura empírica sobre educação e seus determinantes existe uma literatura teórica relativamente pequena que trata sobre o dilema do tamanho da classe A estrutura básica desse modelo começa com a ideia de que a educação em um ambiente de sala de aula é um bem público Como acontece com a maioria dos bens públicos o aprendizado em sala de aula tem efeitos de congestionamento externalidades negativas que ocorrem por exemplo quando um aluno impede o aprendizado dos outros colegas wwwinsperedubr 24 O dilema do tamanho das turmas O modelo de Edward Lazear Bad apple principle Se uma criança está se comportando mal toda a classe sofre Seja 𝑝 a probabilidade de que um aluno não esteja impedindo o seu próprio aprendizado ou o de outro aluno em qualquer momento Então a probabilidade de que todos os alunos em uma classe de tamanho 𝑛 estejam se comportando é 𝑝𝑛 de forma que a disrupção ocorre em 1 𝑝𝑛 do tempo wwwinsperedubr 25 O dilema do tamanho das turmas O modelo de Edward Lazear Podese pensar em 𝑝 como a proporção de tempo em que um determinado aluno não interrompe o processo de aprendizado em sala de aula Assim a suposição feita é que a disrupção de uma criança prejudica a capacidade de aprendizado de todos os alunos incluindo ela mesma de aprender naquele momento wwwinsperedubr 26 O dilema do tamanho das turmas O modelo de Edward Lazear Exemplo feito na lousa wwwinsperedubr 27 O dilema do tamanho das turmas O modelo de Edward Lazear Para entender as ações das instituições precisamos formular o problema de otimização das escolas Vamos começar perguntando quanto um aluno pagaria para estar em uma classe de tamanho 𝑛 Suponha que o valor de uma unidade de aprendizagem seja dado por 𝑉 determinado pelo valor de mercado do capital humano e a probabilidade de que um aluno esteja focado na aprendizagem naquele instante Para determinar o tamanho ótimo da turma considere uma escola de 𝑍 alunos com 𝑚 professores e 𝑚 turmas Suponha que o custo de um professor e o valor do aluguel do capital associado para a sala de aula sejam denotados por 𝑊 Então uma escola particular que deseja maximizar os lucros pode vender a experiência na escola por 𝑍𝑉𝑝𝑛 a um custo total de 𝑊𝑚 wwwinsperedubr 28 O dilema do tamanho das turmas O modelo de Edward Lazear A maximização de lucro da escola significaria escolher 𝑚 de modo a maximizar 𝐿𝑢𝑐𝑟𝑜 𝑍𝑉𝑝𝑛 𝑊𝑚 Equação 1 Ou equivalentemente 𝐿𝑢𝑐𝑟𝑜 𝑝𝑜𝑟 𝑒𝑠𝑡𝑢𝑑𝑎𝑛𝑡𝑒 𝑉𝑝𝑛 𝑊 𝑛 Equação 1a Pois cada classe tem 𝑛 𝑍𝑚 estudantes wwwinsperedubr 29 O dilema do tamanho das turmas O modelo de Edward Lazear A maximização de lucro da escola significaria escolher 𝑚 de modo a maximizar 𝐿𝑢𝑐𝑟𝑜 𝑍𝑉𝑝𝑛 𝑊𝑚 Equação 1 Ou equivalentemente 𝐿𝑢𝑐𝑟𝑜 𝑝𝑜𝑟 𝑒𝑠𝑡𝑢𝑑𝑎𝑛𝑡𝑒 𝑉𝑝𝑛 𝑊 𝑛 Equação 1a Pois cada classe tem 𝑛 𝑍𝑚 estudantes CPO da Equação 1 é 𝑚 𝑉 𝑍2 𝑚2 𝑝 Τ 𝑍 𝑚ln 𝑝 𝑊 0 Equação 2 Ou usando a Equação 1a 𝑛 𝑉 𝑝𝑛 ln 𝑝 𝑊 𝑛2 0 Equação 2a wwwinsperedubr 30 O dilema do tamanho das turmas O modelo de Edward Lazear Proposição O tamanho ideal da classe 𝑛 aumenta conforme aumenta o salário do professor 𝑊 cai conforme aumenta o valor de uma unidade de aprendizagem 𝑉 e mais importante aumenta quanto maior for probabilidade de os alunos se comportarem bem 𝑝 Neste modelo é uma estratégia ótima reduzir o tamanho da classe quando os alunos se comportam menos Obs A título de curiosidade a demonstração completa desta proposição encontrase no Apêndice do artigo e usa o Teorema da Função Implícita na CPO o que resulta em 𝑚 𝑊 0 𝑚 𝑝 0 𝑚 𝑉 0 𝑚 𝑍 0 Como 𝑚 𝑍𝑛 𝑛 𝑊 0 𝑛 𝑍 0 𝑛 𝑉 0 𝑛 𝑝 0 wwwinsperedubr 31 O dilema do tamanho das turmas O modelo de Edward Lazear Da Equação 2 𝑉 𝑍2 𝑚2 𝑝 Τ 𝑍 𝑚 ln 𝑝 𝑊 𝐺 Aplicando o Teorema da Função Implícita em 𝐺 𝒎 𝒑 𝑮𝒑 𝑮𝒎 Temos 𝐺𝑚 2𝐿𝑢𝑐𝑟𝑜 𝑚2 𝑉𝑍2𝑝 Τ 𝑍 𝑚 ln 𝑝 2𝑚𝑍 ln p 𝑚4 0 para ter uma solução interior 𝐺𝑝 𝑉 𝑍2 𝑚2 𝑍 𝑚 𝑝 Τ 𝑍 𝑚 1 ln 𝑝 𝑉 𝑍2 𝑚2 𝑝 Τ 𝑍 𝑚 1 𝑝 Logo 𝑚 𝑝 0 Como 𝑚 𝑍 𝑛 temos que 𝑛 𝑝 0 wwwinsperedubr 32 O dilema do tamanho das turmas O modelo de Edward Lazear À medida que 𝑝 diminui 𝑛 diminui até 𝑝 atingir 𝑝 ponto em que não valeria a pena fornecer qualquer educação Neste modelo crianças com 𝑝 suficientemente baixo não seriam alocadas em uma escola particular assumindo que esta deve gerar lucros não negativos Isso vem da Equação 1 uma vez que para 𝑝 0 os lucros são negativos para qualquer valor positivo de 𝑚 No setor público tanto as escolas quanto os alunos podem ser forçados a tentar fornecer educação mesmo para alunos com 𝑝 muito baixo feito na lousa wwwinsperedubr 33 Um possível desfecho deste modelo teórico é Hipótese econômica Fundamentado pelo modelo de Lazear da perspectiva da escola temos que o tamanho ótimo da classe aumenta conforme aumenta a probabilidade de comportamento dos alunos wwwinsperedubr 34 O dilema do tamanho das turmas O modelo de Edward Lazear Um refinamento do modelo considerar que p é endógeno A escolha do nível de disciplina pode ser modelada e 𝑝 a probabilidade de se comportar ser endógena Seja 𝑝 𝑝𝑑 onde 𝑑 é a disciplina Neste refinamento do modelo o nível de disciplina é uma forma de produzir um 𝑝 mais alto na sala de aula A disciplina rígida seria um substituto a ter turmas pequenas dada a tecnologia de produção postulada neste modelo O autor demonstra que a fim de aumentar o tamanho da classe por um fator de 𝑘 é necessário melhorar a disciplina da turma de modo que 𝑝 suba para 𝑝1𝑘 ceteris paribus wwwinsperedubr 35 Pergunta Como mensurar o 𝑝 O modelo de Edward Lazear A fração do tempo em que um aluno não é um iniciador de disrupção denotada por 𝑝 não é uma mera abstração mas sim uma variável que pode ser observada Operacionalmente pode ser mais fácil observar 𝑝𝑛 do que 𝑝 Por quê Exemplo A pesquisa Longitudinal Study of American Youth fornece informações sobre o tempo gasto com aprendizagem e o tempo gasto cobrando disciplina com informações relatadas pelos professores Também é interessante comparar as características dos alunos com 𝑝 Por exemplo como 𝑝 varia com a idade e background familiar Compreender as variações em 𝑝 pode fornecer insights em políticas públicas de educação wwwinsperedubr 36 Referências didáticas Currie J 2001 Early childhood education programs Journal of Economic perspectives 152 213238 Elango S García J L Heckman J J Hojman A 2016 4 Early Childhood Education pp 235298 University of Chicago Press Lazear E P 2001 Educational production The Quarterly Journal of Economics 1163 777803 Mueller S 2013 Teacher experience and the class size effectExperimental evidence Journal of Public Economics 98 4452 THE DETERMINANTS OF HUMAN CAPITAL FORMATION DURING THE EARLY YEARS OF LIFE THEORY MEASUREMENT AND POLICIES Orazio P Attanasio University College London and Institute for Fiscal Studies Abstract In this paper I discuss a research agenda on the study of human capital accumulation in the early years with a particular focus on developing countries I discuss several methodological issues from the use of structural models to the importance of measurement and the development of new measurement tools I present a conceptual framework that can be used to frame the study of human capital accumulation and view the current challenges and gaps in knowledge within such an organizing structure I provide an example of the use of such a framework to interpret the evidence on the impacts of an early years intervention based on randomized controlled trial JEL O15 1 Introduction In recent years a considerable amount of attention has been devoted to human capital accumulation Scholars have looked at the role of human capital in the process of economic development and stressed the fact that many developing economies that have experienced fast increases in growth have also experienced considerable increases in human capital Macroeconomists and development economists have been interested in The editor in charge of this paper was Dirk Krueger Acknowledgments This paper was presented as the Presidential Address at the Meetings of the European Economic Association in Toulouse August 2014 It draws on my research with a number of coauthors and collaborators Caridad Araujo Sarah Cattan Flavio Cunha Emla Fitzimons Camila Fernandez Sally GranthamMcGregor Jena Hamadami Pamela Jervis Costas Meghir Emily Nix Marta RubioCodina and Marcos VeraHernandez I would like to thank all of them without implying them on the opinions expressed here I have also learned much from conversations with many people In particular I would like to mention Jere Behrman Raquel Bernal Pedro Carneiro Gabriella Conti Anne Fernald Lia Fernald Jim Heckman Norbert Schady Finally special thanks go to Sarah Cattan Gabriella Conti Flavio Cunha Maria Cristina DeNardi Emla Fitzsimons Marta RubioCodina and Norbert Schady for reading the first draft of this paper and giving me very valuable suggestions and feedback The paper has also benefitted from feedback from the Editor and two anonymous referees My research is partially financed by ESRC professorial fellowship ESK0107001 on the accumulation of human capital in developing countries Attanasio is a Research Associate at NBER and a Research Fellow at CEPR and BREAD Email oattanasiouclacuk This is an open access article under the terms of the Creative Commons Attribution License which permits use distribution and reproduction in any medium provided the original work is properly cited Journal of the European Economic Association December 2015 136949997 DOI 101111jeea12159 2015 The Authors Journal of the European Economic Association published by John Wiley Sons Ltd on behalf of European Economic Association 950 Journal of the European Economic Association the relationship between human capital and GDP growth and have proposed models with human capital externalities1 The process of growth and development at the same time if associated with the adoption of skillintensive technologies will induce an increase in the returns to skills and therefore a change in the incentives to accumulate skills2 Moreover human capital is seen as relevant for distributional issues cross sectional inequalities in a variety of dimensions including cognition health socio emotional skills among individuals in many societies seem to emerge very early in life and seem to be strongly linked to inequality of human capital This is particularly true of certain societies such as Latin America as discussed for example in Lopez and Perry 20083 One could therefore argue that understanding the process of formation of human capital over the life cycle and in particular how specific skills that are remunerated by the market develop is key for the design of policies that want to reduce inequality in the long run It is becoming increasingly clear that human capital is a complex object with many different dimensions Labor markets in different economies reward different skills in different ways or in other words different skills play different roles in the productive process and as a consequence have different market prices In agricultural economies physical strength might be important Cognitive skills can be more important in industrial and postindustrial economies Also socioemotional skills such as determination drive motivation sociability locus of control and so on are receiving considerable attention Changes in technology imply changes in the returns to different dimensions of human capital and changes in the incentives to accumulate certain skills as in the comparative advantage models used by Pitt et al 2012 and Rosenzweig and Zhang 2013 Therefore to assess the economic consequences that different levels of human capital might have on an individual it is necessary to understand its various components Of course different skills cognition but also selfcontrol commitment drive also have important implications for noneconomic outcomes such as physical and mental health that are important for individual wellbeing The multidimensionality of human capital is also important to understand the process of its formation which is a very complex one A large and growing body of evidence points to the fact that different dimensions health cognition socio emotional development interact with each other to enhance or hinder the productivity of different inputs that affect the accumulation of human capital The presence of these interactions which start very early probably even before birth together with the fact that past levels of human capital are relevant for its growth in later periods makes 1 See for instance Lucas 1988 Romer 1990 Hanushek and Kimko 2000 Hanushek and Woessmann 2008 2 These processes have wideranging implications for the overall return to skills for the accumulation of human capital and for the evolution of gender differences if men and women have different comparative advantages in brawn versus skill as discussed in Pitt et al 2012 and Rosenzweig and Zhang 2013 who propose versions of the Roy model where individuals select into different occupations depending on their comparative advantage 3 Recently some authors have argued that increases in wealth inequality during the last few decades are selfreenforcing in developed countries see in particular Piketty 2014 Attanasio The Determinants of Human Capital Formation 951 the entire process dynamic Processes of this type imply the presence of important complementarities over time and across different inputs that in turn imply the presence of salient periods and windows of opportunities Yet the details of these processes are far from being well understood Interestingly a similar message can be found in Hackman et al 2010 which reviews recent contributions in neuroscience that have tried to understand the association between socioeconomic status and brain development The emphasis there as here is in the identification of the mechanisms through which socioeconomic factors can have an impact on human development On the one hand there are the biological pathways which are particularly important in the early years These may include for instance the effect of nutrition or exposure to toxins on brain development in utero or in the first few years or even the effect that specific parental practices and traits attachment stimulation and so on might have on development On the other hand there are the mechanisms that might give rise to specific forms of investment on the part of parents that eventually generate extremely unequal outcomes The scope for interactions and synergies among different disciplines including medicine neuroscience psychology psychiatry epidemiology genetics and economics is obvious The early years seem to be extremely important in the whole process both because events during those years seem to have very longrun consequences and because very young children seem to be very malleable or conversely particularly vulnerable to negative environmental factors and different types of shocks These considerations make the early years particularly salient for policy interventions Not only might early years interventions be more effective in closing developmental gaps but they could also make subsequent policies aimed at say schoolaged children more effective Heckman and his collaborators have been particularly vocal in stressing the importance of the early years The fact that early years are important does not mean however that everything is determined by say age 3 or by some other specific date Indeed much recent research shows that there exist other important windows of opportunities such as for instance adolescence see for instance Blakemore and Mills 2014 The early years however can be particularly important not only because of the development that is achieved in those years but because that same development might facilitate and enhance subsequent growth and the productivity of subsequent investments An interesting research question is whether different ages should be targeted by different interventions and whether specific traits and domain develop more rapidly during certain phases of the childs life cycle The importance of the early years and their salience for policy is particularly relevant in developing countries The Lancet series in 2007 and 2011 see McGregor et al 2007 Walker et al 2011 Engle et al 2011 have claimed that there are 200 million children at risk of not developing their full potential and most of these children are in developing countries These children are particularly vulnerable because of the high incidence and burden of infectious diseases undernutrition in the perinatal period and early childhood micronutrient deficiency lack of clean water and limited hygiene as well as many psychosocial factors such as violence lack of stimulation maternal 952 Journal of the European Economic Association depression and poor parenting practices The damage inflicted on these children is likely to be permanent and delays accumulated in the early years will be difficult if not impossible to fill There is overwhelming evidence that socioeconomic disparities are associated with developmental delays and that these delays emerge very early on and grow dramatically during the first few years of life For instance RubioCodina et al 2014 show that in Bogota Colombia significant differences in cognitive and language development among children of different socioeconomic backgrounds emerge at around 12 months and grow considerably over time Paxson and Schady 2007 show that in Ecuador the difference in vocabulary at age 6 between children in the fourth decile and children in the first poorest decile of the wealth distribution is equivalent to three standard deviations of a zscore This is equivalent to a delay of 25 years in language development These children who will start attending schools designed for sixyear olds will not be able to benefit from that experience and will accumulate further delays Fernald et al 2012 report similar evidence from India Indonesia Peru and Senegal While these analyses are based on crosssectional data a few studies have used longitudinal data from developing countries Hamadani et al 2014 using a longitudinal data set from Bangladesh show that significant cognitive delays between children of different socioeconomic backgrounds emerge as early as seven months after birth and increase as the children age By the time they are 64 months the difference in cognitive development between the poorest and less poor children is as large as 12 standard deviations of a zscore This is a remarkable difference as all the households in the study are living in small rural villages and are quite poor Schady et al 2015 report evidence based on longitudinal studies from several other developing countries The salience of the early years for policy is also confirmed by the growing evidence that welldesigned and welltargeted interventions can achieve spectacular results A number of longterm longitudinal studies that have followed children who received intense and highquality interventions in the 1960s 1970s and 1980s are now available and in some cases show strong effects on a variety of adult outcomes Some of the best known programs which I discuss in some detail in Section 3 are the High Scope Perry Preschool Project the Abecedarian and in a developing country context the INCAP nutrition intervention in Guatemala and the home visits and stimulation intervention in Jamaica Of course given that some of these interventions are intensive and costly they should be justified by a costbenefit analysis However when despite its intrinsic difficulties partly related to the longterm nature of the benefits this analysis has been performed the implied internal rates of returns seem extremely high An example of such an exercise for the Perry Preschool Project is contained in Schweinhart et al 2005 Many recent discussions have stressed that the rate of returns on early years is very high and presumably higher than a number of alternative investments Heckman et al 2009 and Heckman 2012 for instance put the return to the High School Perry Preschool Project at between 6 and 10 The existence of such a differential is an Attanasio The Determinants of Human Capital Formation 953 indication of important frictions that prevent investment in human capital in the early years The type of frictions that generate such inefficiencies can be many ranging from basic credit constraints and imperfections in credit and insurance markets to information problems and myopic behavior to the lack of altruism Imperfections to credit markets can in turn be generated by many factors linked to asymmetric information and difficulties in enforcing contracts on investment whose return is uncertain and is received many years after the initial investment The fact that returns on human capital are enjoyed by individuals who are different from those who make the investment children and parents might also be a problem Poor parents might also lack the information and sophistication to assess the size of the returns to education Or given the stress to which they are subject they might like the ability of formulating and executing longterm plans that include constant investment of time stimulation and resources for their children In addition to these efficiency arguments that can justify policy interventions in human capital an important justification for interventions targeted to early years is a redistributive one given the size of the returns of these interventions and their very dynamic nature they might be extremely effective in reducing inequalities and in fostering equality of opportunities The fact that early years interventions can be effective and the fact that large gaps in development which are later associated with large differences in earnings health and other welfare indicators emerge very early make these interventions potentially very important These are policies that have the potential of greatly increasing the efficiency of an economy whilst at the same time reducing the level of inequality and disparities both in economic and other domains However not all policies are effective and the design of policies that are effective at scale given the available resources including human resources is particularly difficult Having established that interventions to foster the accumulation of human capital in the early years is desirable the biggest challenge is to develop policies that are scalable in a variety of different contexts and can be implemented with the resources available A welldesigned and effective policy needs a good understanding of the mechanisms that drive its impacts This challenge is what motivates the research agenda that I describe in this paper An understanding of these mechanisms requires a unifying model that frames the main issues I start my discussion in what follows with the elements of such a framework in Section 2 where I sketch the main components of the framework without specifying its details The main research questions this framework can address are the following 1 How does human capital develop in the early years What are the roles of different types of investment at different points in time What are the relevant dimensions of human capital and how do they interact in the process of their development among themselves and with different inputs How large are dynamic complementarities and are there windows of opportunities in different dimensions 954 Journal of the European Economic Association 2 How do parent behave What are the constraints financial informational attitudinal they face in choosing investment in human capital How do parents react to interventions 3 Are policy interventions desirable and what does it take to design an effective policy that can be developed at scale What aspects of human capital should policies target and when As I discuss in Section 3 much has been learned but much is still unknown The framework I present in Section 2 helps in organizing what we know and what we need to learn In Section 4 I present a specific example of the conceptual framework and I exemplify the use of such a framework by discussing a specific intervention and apply the theoretical framework to the analysis of its impacts I borrow from two recent papers that have performed this analysis In Section 5 I discuss the role that parental beliefs can play in child development After that I discuss two methodological issues the controversy about the use of a structural model versus an atheoretical analysis of policy interventions and the importance of measurement for the entire research agenda Section 7 concludes with some reflections on future challenges 2 A Theoretical Framework One first step towards the understanding of the mechanisms behind human capital formation is the construction of a coherent theoretical framework In this section I sketch one such a framework and discuss its features In Section 4 I will then use a particular specification of the framework I present here without details to illustrate a possible use and interpret the evaluation of a specific intervention The main components of the conceptual framework I consider are the process of human capital formation and the decision process that determines investment decisions The latter in turn depends on household preferences information and resources 21 The Production Function of Human Capital The work on the production function for human capital has a long tradition in economics going back to the seminal work of Gary Becker see Becker 1964 Becker and Tomes 1994 More recently Heckman and his collaborators have greatly advanced the study of human capital formation and proposed a very useful framework see for instance Cunha et al 2006 Cunha and Heckman 2008 Heckman 2007 We consider human capital as a multidimensional object that starts evolving very early in life possibly before birth I will be calling these different dimensions factors One factor could be cognition another factor could be health and nutritional status yet another factor could be socioemotional skills I will not specify how many factors are relevant and whether a given factor could or should be decomposed into several factors The different human capital factors change over time according to a process that depends on past levels of the factors and on several environmental variables some Attanasio The Determinants of Human Capital Formation 955 of which are fixed such as parental background and others that are changing over time Among the latter set of variables one could distinguish between variables that are chosen by parents or other individuals andor institutions and others that can be safely considered as exogenous variables The main difference between the two sets of environmental factors is that the former which I will call investments are chosen by agents who might be reacting to the evolution of the various factors while the latter can be safely considered as having an evolution that is independent of what happens to the various dimensions of human capital I will call the process of formation of human capital its production function Environmental factors and shocks inputs of various nature and the existing level of human capital in its various dimensions enter the production function in complex and nonlinear ways Some arguments of the production function could be complements while other might be substitutes The presence of lagged values of the factors in the production function makes the process dynamic and in the presence of complementarities among different arguments can create windows of opportunities that make investment in certain periods particularly salient and important for future developments A flexible specification of the production function when bringing this framework to data is therefore essential in order not to preclude the identification of interactions and complementarities From the point of view of researchers some factors are observable while others are not The same applies to the environmental factors and investments that enter the production function The omission of relevant inputs can imply the introduction of important biases in the estimation of the production function I will discuss briefly these issues in what follows they are an important area of research Investments are chosen by parents making them endogenous variables in the production function The endogeneity of investment clearly poses a problem for the empirical identification of the parameters of the production function If parents react to specific shocks to the childs development that might be unobservable to the researcher the productivity of investment will be underestimated if parents compensate these shocks while it will be overestimated if they tend to reinforce them It is therefore important to model parental behavior and determine whether enough data are available to identify the parameters that inform it as well as the parameters of the production function 22 Preferences In the model I am proposing parents are assumed to maximize an objective function which depends on their current consumption and on their childrens developmental status Higher development implies higher welfare as smarter healthier children are more likely to command higher resources as adults The dependence of the objective function on child development can be driven by altruism towards the children or by the fact that children can provide support during old age The fact that parents maximize some sort of objective function does not necessarily mean as I discuss in what follows that they make optimal choices 956 Journal of the European Economic Association One first issue that needs to be addressed is whether the number of children is taken as given or whether fertility choices are also modeled Of course the choice between these two modeling alternatives depends on the nature of the problem that one is interested in analyzing However if it is assumed that the number of siblings is a variable that enters the production function of the human capital of a given child it might be necessary to take a stance on this issue There is an extensive literature on the quantityquality of tradeoffs in the determination of fertility choices in developing countries that is relevant in this context see for instance Becker and Lewis 1973 Willis 1973 Becker 1991 In the presence of more than one child another important issue is the specification of parental preferences across different children One view could be that parents maximize the total resources their children can command and therefore might want to focus investment on the smarter children if given the nature of the production function these are the children for whom such an investment would be most productive A possible justification of such an assumption is that parents could enforce transfers among siblings to compensate the children who receive the lowest investment If such transfers are unenforceable or perceived as such by parents then it is possible that they would try to compensate initial differences among siblings and possibly focus their investment on the weakest children This would be the case if they have a taste for equality among their offspring Often in models of parental behavior households are considered as a unitary decision unit In reality households often include more than one adult and these adults might not share the same objectives and tastes How decisions are made within the households will then be determined by implicit or explicit bargaining processes between fathers and mothers or possibly other adults present such as grandparents 23 Resources Information and Beliefs An obvious constraint parents face is that of resources The resources parents can access depend on their human capital the wage they can command on the labor market and their nonlabor income The evolution of these variables can depend on a variety of factors including changes in economywide prices and wages and idiosyncratic shocks to productivity In the presence of uncertainty parental investment strategies will depend on the ability they have to absorb shocks which in turn depends on the availability of different smoothing mechanisms ranging from individual savings to formal and informal insurance contracts to credit to changes in labor supply of various family members An important resource that could constitute an important constraint on parental behavior and that is often ignored in the literature is information Parents make decisions taking as given the production function of human capital They invest time and material resources in their children as they will expect these investments to have a return in terms of human capital development How much they will invest will depend in addition to their tastes and their material resources on their perception of the production function and in particular their beliefs about the productivity of the Attanasio The Determinants of Human Capital Formation 957 various inputs Assuming that parents maximize a certain objective function taking as given resources and the production function does not necessarily mean that parents behave optimally It is possible that they misestimate the returns to certain types of investment Information can indeed be an important constraint and a scarce resource I discuss these issues in Section 64 This theoretical framework needs to be fleshed out with specific details The analysis of different problems requires the specification of different details of the model In Section 5 I use a similar model with some stark simplification and remorseless omissions to analyze and interpret the results of a randomized controlled trial RCT run to evaluate a policy This general structure is also useful to organize the various components of a research agenda and to take stock of what we know and what we do not and the need to learn for a better understanding of the process of human capital formation and for the design of policies to foster it 3 Knowns Much has been learned on the importance of the early years and on some of the mechanisms that make these years so salient for human development and for adult outcomes The evidence that early years events have longrun consequences is extremely strong Almond and Currie 2011a present a comprehensive survey of much of the available evidence showing that early events starting at conception and in the womb followed by the first few years have longlasting impacts on a wide variety of adult outcomes from schooling to earnings to health and others Researchers have used a variety of ingenious techniques to control for confounding factors to isolate the causal impacts of early shocks Currie and Hyson 1999 for instance used the British National Child Development Survey to study the impact of low birth weight on education and employment Twin studies have been used extensively to control for genetic factors and more generally initial conditions that might be correlated with the prevalence of certain shocks Behrman and Rosenzweig 2004a for instance used twins to estimate the return to birth weight Analogously many studies have used a variety of natural experiments such as epidemics and other methods to isolate the causal impact of early life shocks on subsequent outcomes Almond 2006 for instance documents the impacts of the in utero exposure to the 1918 influenza pandemic in the United States He finds that individuals exposed to the pandemic in utero experienced reduced educational attainment increased rates of physical disability lower income lower socioeconomic status and higher transfer payments Almond 2006 p 672 There is a huge literature that associates child development with socioeconomic factors Duncan et al 1994 for instance stresses the effect that poverty as well as the 4 An interesting angle to this issue has recently been stressed by Mullainathan and Shafir 2013 who argue that poor individuals who live with very scarce resources are constrained in terms of their ability to make forwardlooking and optimal choices 958 Journal of the European Economic Association duration and timing of exposure to poverty can have on childrens development More recently Hackman et al 2010 reviewed the approaches taken in neurosciences in this context and stressed the need to understand the causal links and the identification of the processes that lead to the observed associations The analysis of specific mediating factors such as parenting practices can be particularly informative Hackman et al argue that useful evidence on these pathways can come from animal studies that can shed light on the biological channels that can be affected by specific practices The voluminous literature on human capital development indicates that the early years are important Nutrition seems to be particularly relevant especially in the very first phases of human development before and immediately after birth Indeed a large fraction of the 200 million children at risk of not developing their full potential identified in McGregor et al 2007 are affected by malnutrition Current estimates identify around 170 million children under five to be stunted mostly in developing countries and particularly in South Asia and SubSaharan Africa see de Onis et al 2012 The nutritional status of pregnant mothers affects in crucial ways the development of the foetus birth weight and subsequent development In epidemiology Barkers foetal hypothesis according to which events that affect foetal development during pregnancy and in particular nutrition trigger a number of biological effects that have longrun health consequences and may determine chronic conditions such as high blood pressure and diabetes has received much attention see Barker 1995 Economists have more recently paid attention to this hypothesis and have unearthed a substantial amount of evidence on longrun effects of foetal growth on a variety of variables including test scores earnings and educational attainment see Almond and Currie 2011b An impressive study that studied individuals born around the Dutch famine caused by the Nazi embargo in 19441945 see Heijmans et al 2008 identified epigenetic modifications and in particular in the expression of the insulinlike growth factor 2 IGF2 gene5 The Dutch famine study identified such effects by comparing the genetic material of subjects exposed to the famine while in womb to their siblings born after the famine After birth nutrition in the very early years seems to be important Some studies6 have found association between breastfeeding early height per age and other indicators of nutritional status in the early years and subsequent outcomes both in cognitive development and health Although it is difficult to establish the causal link between breastfeeding and subsequent development a number of papers have now presented some strong evidence suggesting that breastfeeding causes a number of positive 5 This gene is a key factor in human growth and development and is maternally imprinted Heijmans et al 2008 p 17046 Imprinted genes are important since their expression in the present generation depends on the parental environment in which they resided in the previous generation Jirtle and Skinner 2007 6 See for instance the studies cited in the 2011 Lancet series on Child Development Walker et al 2011 and Engle et al 2011 Attanasio The Determinants of Human Capital Formation 959 outcomes Kramer et al 2001 present evidence from an experiment that evaluated the impact of an intervention aimed at promoting breastfeeding in Belarus while Fitzsimons and VeraHernandez 2013 present evidence from the UK Millennium Cohort Study exploiting the different availability of breastfeeding coaching during the weekend to identify the effect of breastfeeding on later outcomes Both papers show strong impacts of breastfeeding in the case of the Belarus evidence breastfeeding reduced infections and other health conditions while in the case of the UK the children of mothers with low educations born at the weekend were less likely to be breastfed and crucially showed lower indices of child development at ages 3 5 and 7 In addition to breastfeeding nutrition seems to be particularly relevant for child health status and more generally for child development Many papers have shown that stunting in the early years can lead to longterm adverse consequences In what follows I discuss the evidence from the influential INCAP intervention in Nicaragua where children in that study were followed over a period of 40 years The INCAP study was one of a number of cohort studies in five countries Brazil Guatemala India the Philippines and South Africa that followed children over a period of time and related both maternal and child nutrition to longterm outcomes These influential studies reviewed in Victora et al 2008 found strong associations between the nutrition status of mothers and children and a variety of outcomes such as height schooling income or assets offspring birthweight bodymass index glucose concentrations and blood pressure7 Similar associations are also found in a data set from Bangladesh analyzed in Hamadani et al 2014 which I have already cited This study however while controlling for nutrition and physical growth factors in the first months of life focuses on the home environment and stimulation In particular the study finds a strong association between indicators of home environment as measured at 18 and 60 months and cognitive development at 60 months among poor Bangladeshi children As already mentioned socioeconomic variables are strongly associated with cognitive development in that sample Similar associations are documented in Paxson and Schady 2007 and RubioCodina et al 2014 with data from Ecuador and Colombia and by Fernald et al 2012 and Schady et al 2015 with data from several other developing countries However in the Bangladesh study after controlling for the quality of the home environment the association is much less strong Similar results are found in the mediation analysis conducted in RubioCodina et al 2015 This evidence stresses the importance of the home environment and stimulation these factors seem to be particularly important to explain a large fraction of the variability in children cognitive development and presumably adult outcomes Along the same lines Schady 2011 shows that in a longitudinal study of relatively poor children in Ecuador the unimodal distribution of PPVT Peabody 7 See Adair et al 2009 Martorell et al 2010 Stein et al 2010 Fall et al 2011 Kuzawa et al 2012 and Lundeen et al 2014 960 Journal of the European Economic Association Picture Vocabulary Test scores at age 3 becomes a bimodal distribution by age 5 and that the two modes of the distribution correspond very closely to children of mothers with high and low TVIP Test de Vocabulario en Imagenes Peabody scores respectively This evidence illustrates powerfully the importance that maternal and more generally parental inputs have in the development of childrens language and cognitive skills The other fact that seems apparent from the literature is that human capital cannot be considered a monolithic and unidimensional object Rather it is a complex construct that is made of many different components This multidimensionality is important and relevant in two different ways On the one hand from an economic point of view it is clear that different skills command different prices in the labor market reflecting probably the different roles they play in the production process On the other hand cognitive skills are certainly important but other skills which have been called socio emotional or soft skills also play a very important role Socioemotional skills which include the ability to interact with others but also to delay gratification to focus and pay attention and to be organized are important for several reasons First they might have a direct value in the production process and therefore might be remunerated in the labor market Second and more subtly they might facilitate the accumulation of cognitive and other aspects of human capital8 Third there is some evidence that these skills are malleable over longer time periods while there is evidence that cognitive skills might become difficult to affect after the first few years As such these skills might be particularly salient for policy The fact that certain skills developed in the early years might affect the ability to accumulate other dimensions of human capital later is a reflection of the fact that the different domains of human capital follow over the life cycle of children who enter young adulthood and adulthood intertwined paths that interact continuously among them and with other inputs in the process of human development This process is characterized by what the literature defines as dynamic complementarities see for example Cunha et al 2006 2010 Certain skills such as socioemotional skills see for instance Duckworth and Seligman 2005 accumulated in the first five years of life seem to be key to the ability to the accumulation of cognitive skills in subsequent periods The presence of these interactions and dynamic complementarities might give rise to key periods and windows of opportunities that could be particularly salient from the point of view of policy design 4 Unknowns The picture that is emerging from this voluminous and growing literature that spans different fields is therefore one that is starting to make clear several important features of 8 For instance individuals who can delay gratification might be more likely to lead healthier life styles and therefore be healthier Attanasio The Determinants of Human Capital Formation 961 the process of human development and of the gaps that are accumulated by vulnerable children The Lancet 2011 review for instance states Three translational processes influence how risk factors and stress affect brain and behavioral development the extent and nature of deficits depend on timing cooccurring and cumulative influences and differential reactivity Walker et al 2011 p 1326 41 The Mysteries of Human Development Yet many important details are still unknown or extremely vague These range from the biological mechanisms that affect the process of human development from conception and during the first years of life to the factors that influence parental decisions and parental practices For example the evidence on the impact that micronutrient deficiency during the first years of life may have on child development is still very patchy as is apparent from the discussion in the recent Lancet series Despite the fact that many children in developing countries present important deficiencies in many micronutrients the authors of the series Walker et al 2011 p 1328 conclude that there are insufficient data to establish whether supplementation with multiple micronutrients is more effective than iron alone in improving development Analogously when discussing infectious diseases the survey states that evidence is insufficient to establish if early parasitic infections affect child development Walker et al 2011 p 1329 In a similar vein although the emergence of evidence of epigenetic effects in animal studies is fascinating whether this evidence is of conceptual and practical relevance for the development of human capital is still a contentious issue Analogously whether specific genetic configurations mediate the impact of environmental factors is also not completely established despite some studies pointing to these effects9 Several recent studies have stressed the importance of complementarities among different inputs which is echoed in the importance of cooccurring and cumulative influences mentioned in the previous quote from the Lancet review The work of Heckman and several coauthors has been particularly forceful in this respect see for instance Cunha et al 2010 At the same time the size of these complementarities and the nature of the dynamic relationship between different inputs are still not fully understood A number of studies now reject the linearity of the production function10 However we still do not know the details of how the production function of human capital evolves in the early years and how the foundations for further learning are posed 9 On epigenetics effects see for instance Meaney 2010 and Murgatroyd and Spengler 2011 while on the mediation role that certain genetic configurations may have see among others Pluess et al 2013 and Caspi et al 2010 10 See Cunha et al 2006 2010 Heckman et al 2013 Cunha and Heckman 2008 and Attanasio et al 2015a 962 Journal of the European Economic Association 42 Parental Behavior In addition to the characterization of the production function for human capital the other aspect that is key for the design of policies targeted at reducing developmental gaps of vulnerable children both in developed and developing countries is the characterization of parental investment and practices What determines parental choices What are the constraints that parents face How do parents react to a specific policy These are all questions that are key to the successful design of early years interventions Yet much still needs to be learned Parental decisions are complex and several factors such as available resources mother labor supply possibilities and beliefs about optimal parental practices interact to determine them Parents will invest in children by dedicating time to them and buying toys and books depending on the costs of these investments how effective they think these activities are and on the amount of resources they have They will also consider the tradeoffs between spending time with children work and leisure Moreover it is likely that parents choices react to the evolution of the childs development to possible shocks that might affect children and to their understanding of how their investments can remediate in the case of a negative shocks them Finally parents often have to make decisions to allocate scarce resources among several children who differ in their age gender perceived ability and so on In his seminal contribution Griliches 1979 conjectured that parents might tend to alleviate preexisting differences in abilities Despite the importance of these issues not many studies have looked at them see for instance Behrman et al 1982 1994a Becker and Tomes 1976 There are several papers that consider gender biases in investment which is an important special case of withinhousehold allocation of resources11 Rosenzweig and Wolpin 1988 find some evidence in favor of Griliches conjecture while Rosenzweig and Zhang 2009 find that parents in China exhibit higher education expenditure on children with higher birth weight therefore exhibiting reinforcing behavior Behrman 1988 finds that parents in South India exhibit some degree of inequality aversion although they seem to favor boys In a very recent paper Yi et al 2015 consider different dimensions of human capital and find that in response to early health shocks affecting a sample of twins parents in China might be pursuing a compensating strategy in terms of health investment and a reinforcing strategy in terms of educational investment A recent survey Almond and Mazumder 2013 discusses some of these issues and in particular whether parents reinforce or compensate the effect of shocks to the accumulation of human capital or initial conditions Concluding they state Almond and Mazumder 2013 p 318 we expect this area to be a focus of continued research attention because the nature of the behavioral response and its importance to longterm effects are still being debated There is a vibrant literature on models of intrahousehold allocations that I cannot summarize here It is clear however that in the presence of two decision makers who 11 See for instance Hazarika 2000 Behrman and Deolalikar 1990 and more recently Jayachandra and Pandi 2015 Attanasio The Determinants of Human Capital Formation 963 differ in their tastes it is likely that as a result of changes in their relative bargaining power allocations could change Thomas 1990 was one of the first papers to recognize that male and female labor incomes have a different impact on childrens development Economists have looked at many different models of intrahousehold allocations that differ from those that would prevail under a unitary framework One of the most successful approaches has been that of the socalled collective model proposed by Chiappori 1988 1992 The collective model is attractive because it is agnostic about the specific bargaining process couples engage in and it only assumes that the resulting allocation of resources is efficient In this context an important observation about the resources allocated to children is made by Blundell et al 2005 who note that in the collective model a shift in relative bargaining power in favor of one of the two partners results in an increase in the resources allocated to children only if the marginal propensity to consume on childrens goods for that person is higher than that of their partner That is it is not the absolute taste for children that determines the effect of a shift in the resources that go to children but the relative marginal propensity to consume This result has implications for the effect of programs that target specific subsidies to women such as most recently Conditional Cash Transfers Related to the issue of intrahousehold allocation of resources is the more general issue of the role played by the family and the family environment over and above the resources that different family structures can provide child care givers In many different contexts vulnerable children often grow within single adult households Our understanding of the implications that these different family environments have for child development is still very limited 43 Interventions and Policies In the Introduction I mentioned a few interventions both in developed and developing countries that have been shown with the help of randomized controlled trials and longitudinal data to have had large and sustained impacts that have been visible over long periods of time One of the best known cases is that of the HighScope Perry Preschool Project PPP developed in Ypsilanti Michigan in the mid1960s 123 disadvantaged and highrisk children living near the Perry elementary school in that town were recruited into a study when aged between 3 and 4 Of these 58 randomly chosen were assigned to a highquality preschool program The study followed them into adulthood The pattern of results that emerged from that study which have been analyzed in a number of papers12 is particularly interesting for a variety of reasons Although the intervention initially boosted cognition as measured by the StanfordBinet IQ test this effect faded a few years later By age 8 treated boys were indistinguishable in terms of IQ from their control counterparts For girls the effect of the program on IQ was reduced by remaining statistically different from zero However as noted by Heckman et al 2013 the programs effects on other 12 See Heckman et al 2010 2013 and the citations therein 964 Journal of the European Economic Association personality and social skills such as those measured by externalizing behavior remained statistically significant More importantly the program seemed to affect academic achievement and in the long run a variety of economic outcomes and criminal behavior One possible interpretation of these results therefore is that even when interventions especially those delivered after age 313 have a limited impact on IQ they might affect the longrun welfare of child and adult outcomes through other channels for instance through the impact on socioemotional skills Another wellknown study is that of the Abecedarian ABC project that was developed in the mid1970s in North Carolina In that study 111 disadvantaged children were randomly assigned between a treatment 57 and control 54 group The program consisted of two stages one designed for children aged between 0 and 5 and one for children aged between 6 and 8 The first stage was very intense including playbased adultchild activities to support childrens language motor cognitive development and socioemotional competence including task orientation for up to nine hours each day for 50 weeksyear see Ramey et al 1976 Sparling and Lewis 1979 The two stages of the intervention were evaluated with a double randomization design and the first stage has been shown to have a variety of longrun impacts14 Most recently Campbell et al 2014 show that ABC had an impact on a variety of health outcomes including the prevalence of obesity and blood pressure when the subjects were in their mid30s In addition to PPP and the ABC project many other interventions have been studied in the United States and other developed countries15 Some successful interventions however have also been implemented in developing countries A first program that is worth mentioning is the INCAP study in Guatemala a nutrition intervention that was evaluated through a randomized controlled trial and whose subjects were followed for over 40 years Remarkably even the offspring of the original subjects were observed The intervention consisted in providing from 1969 to 1977 a nutritional supplement rich in calories in the treatment villages The children in the control villages were instead provided with a similar beverage which however lacked the additional calories From 1971 both treatment and control beverages were fortified with micronutrients As the study went on for several years children in both treatment and control villages entered the study at different ages some from birth some when they were already a few years old This intervention found impressive longrun impacts Interestingly the gains in various dimensions including adult wages were significant only for those children that were exposed sufficiently early to the intervention see for instance Hoddinott et al 2008 Maluccio et al 2009 Even more impressively Behrman et al 2009 find that the program had intergenerational impacts regardless 13 Interestingly the previously mentioned nutrition intervention in Guatemala had significant longrun impacts on wages when delivered before the age of 3 14 See for instance Campbell et al 2002 2012 Most of the effects have been documented for the first stage The second stage did not seem to have detectable effects 15 Such as for instance the Nurse Family Partnership in the United States which has been evaluated in a number of randomized controlled trials see for instance Olds 2006 Olds et al 2007 2010a b Eckenrode et al 2010 Kitzman et al 2010 OwenJones et al 2013 A similar program the Family Nurse Partnership is being evaluated in the United Kingdom see OwenJones et al 2013 Attanasio The Determinants of Human Capital Formation 965 of the timing of exposure the children of the treated girls but not boys seemed to be growing faster One of the most cited studies and one that obtained the most spectacular results is the wellknown Jamaica study GranthamMcGregor et al 1991 Walker et al 2005 2006 which included both a nutrition component caloric supplementation and a psychosocial stimulation component In that study 129 stunted children in Kingston Jamaica were randomly assigned to four groups In addition to a control group there was a psychosocial stimulation treatment a nutrition treatment and a combination of the two The intervention targeted children aged between 9 and 24 months at baseline and lasted for two years The results were remarkable At the end of the intervention both treatments nutrition and stimulation seemed to have an impact on cognitive development and the effect seemed to be cumulative to the point that the development of children receiving both of them was not very different from that of nonstunted children from the same neighborhoods observed over the same period After the end of the intervention the children were observed at ages 78 1112 and 1718 Although the effect of the nutrition intervention faded completely that of the stimulation one was significantly different from zero at all observation points and by sizable amounts A more recent followup Gertler et al 2014 at age 22 observed significant effects on earnings which were increased by 25 enough for the treated to catch up with the earnings of a nonstunted comparison group The few examples I have cited demonstrate that welldesigned and welltargeted interventions can yield spectacular results This is particularly true for early years interventions Notice for instance that while in the case of the PPP the initial impact on the IQ of the treated children fades away a few years after the end of the intervention although gains in other dimensions in particular socioemotional skills remain significant in the case of the Jamaica intervention the IQ impacts remain significant many years after the end of exposure and into adulthood Such a difference might be explained by the fact that the Jamaica study was targeted at children much younger than those targeted by the PPP In the case of the ABC project the IQ impacts also lasted longer The fact that the ABC like the Jamaica intervention also started earlier than PPP is intriguing However one should also consider the fact that the ABC was probably more intensive than both PPP and the Jamaica intervention Not all interventions however are successful and even successful interventions might have systematically heterogeneous effects so that some interventions might be more appropriate for certain children while different types of interventions might be more effective for different children While we are starting to have an idea on which are the elements that generate success many unknowns still loom large Open questions include the following What is the optimal timing of different interventions What is the optimal duration and intensity of different interventions What is the best mode of delivery home visits centerbased care and so on What are the key elements in terms of quality that determine success What dimensions of human capital are better affected by specific interventions at different ages Should interventions focus on specific dimensions and domains of child development What is the most appropriate 966 Journal of the European Economic Association curriculum How important is it that effective interventions in early years are followed by access to highquality preschools and education These unanswered questions resonate even in my brief summary of the impacts of wellknown interventions such as the PPP the ABC project and the Jamaica intervention PPP which started by and large past age 3 seems to have affected socio emotional and soft skills in the long run which in turn seem to have had an impact on other outcomes ranging from health to economic variables ABC and in particular the Jamaica intervention instead seem to have affected cognition and intelligence in a sustainable fashion Are these differences due to the timing or the content of the intervention Should the content of intensive interventions be targeted to specific domains To what extent do the gains in specific domains such as socioemotional skills allow children to exploit better education opportunities There is still not enough evidence about these issues Also these questions to a large extent overlap with the main research questions that I have already discussed How do interventions get their impacts What is the nature of the production function of human capital What do parents do and how do they react to interventions Do interventions crowd parental investment in or out Above all policy makers struggle to build costeffective and affordable interventions that can be expanded and sustained at scale Cost is only one aspect of scalability The availability of appropriate infrastructure the human resources in the territory monitoring and supervision schemes that guarantee fidelity and effectiveness of interventions are big issues especially in developing countries A proper understanding of the mechanisms behind human development in the early years both in terms of the features of the production function for human capital and of the determinants of investment in human capital is key to the scalability of policies In addition to design policies that are effective and that can be deployed on a large scale it is also key to understand individual behavior and how it reacts to specific interventions 5 A Theoretical Framework and its Use In this section I will present a specific example of the theoretical framework I sketched in Section 2 and then use it to interpret the impacts of an intervention evaluated with a randomized control trial In the process I will draw on Attanasio et al 2014a 2015a 51 The Model In what follows I will borrow from the model used by Attanasio et al 2015a who extend the approach proposed by Cunha et al 2010 I will use some of the empirical results in this former paper in my discussion in Section 52 I will assume that parents in household i choose investment to maximize utility that depends on their childrens human capital and consumption Their choices are made considering a budget constraint and a production function for human capital At this point I assume that parents have information about the production function of human capital that corresponds to the actual production function In Section 6 I will explore models in which parents have a distorted view of the production function of human capital Given what I want to stress and the context to which I will apply this model I use a static framework If the focus had been on liquidity constraints and on crucial windows in the process of development it would have been better to formulate the problem as a dynamic one where parents enjoy utility at different points in time and possibly enjoy the returns to human capital investments only much after the investment on human capital was made To formalize let Hit be the human capital of a child of age t being raised in household i Hit is a multidimensional vector reflecting the different components of human capital such as cognition and socioemotional skills and health The production function of human capital is assumed to depend on the initial level of human capital Hit on background variables Zit either fixed or time varying including mother m father f and other r on investments in human capital Xit including materials M and time T and on a vector of random shocks eitH The shocks eitH can also be interpreted as reflecting inputs in the production function that are not directly observed or considered by the researcher16 The production function is given by Hit1 gt Hit Xit Zit eitH 1 The variables Hit Zit Xit and eitH are multidimensional Hit θitC θitS θitH Zit θitM θitF θitR Xit θitM θitT where I have assumed that in this particular case human capital has three dimensions cognitive skills c socioemotional skills s and health h Most empirical applications I am aware of partly for data reasons consider only two dimensions For instance Cunha et al 2010 and Attanasio et al 2015a model cognitive and socioemotional skills while Attanasio et al 2014b model cognitive skills and health Analogously the number of investment factors and the number of parental background factors are somewhat arbitrary Given the available data and the specific context under study preliminary factor analysis can be helpful in making the adequate modeling choices 16 If this interpretation of eit is adopted I will be assuming that these inputs are not chosen by the parents in the problem I consider in what follows Parents are assumed to maximize max CitXit U Cit Hit1 2 subj to Cit Pxt Xit Yit 3 and Hit1 gt Hit Xit Zit eit where Cit is consumption and Pxt is the vector of prices of investments Xit The production function gt in equation 1 is assumed to be time varying so that its parameters or even its shape can be different at different points in time Notice also that in this simple model there is no saving and only one child Additional complications and meaningful dynamics could be added to this framework but do not add much to the main message I want to stress For the time being I assume that parents know the production function in equation 1 and take it as a technology constraint to their maximization problem I will discuss how to relax this assumption in Section 6 Under this assumption the problem in equation 2 can be solved to derive investment and consumption functions for the parents Their choices will depend on their tastes on the parameters of the production function on prices Pxt and on the available resources Yit The investment functions can be written as Xit ft Hit Pit Zit eix Yit π 4 where π is a vector of parameters that includes those that characterize the utility function and those that characterize the production function as perceived by the parents The presence of Pit and Yit in the investment function but not in the production function plays an important role in the identification of the latter as I discuss in what follows This model while a special case of the framework described in Section 2 is very tightly parameterized and makes some very strong assumptions It does not consider fertility choices or the quantityquality tradeoff in any way it is silent about intergenerationally transmitted endowments which have been shown to be important to explain certain correlations17 there is limited scope for heterogeneity of parameters and preferences Most importantly this structure assumes that all relevant inputs and factors are included and incorporated into the model and that those excluded are completely captured by the term eitH which is assumed to be uncorrelated with other factors If all the variables in equations 1 and 2 with the exception of the shocks eitH and eix were observable it would be possible to bring this model to the data in a relatively straightforward fashion by specifying functional forms for the utility function and the production function In that case the main problem in estimating the production 17 On the relationship between maternal and child schooling for instance see Ashenfelter and Krueger 1994 Behrman et al 1994b Behrman and Rosenzweig 2002 2004b Rosenzweig and Zhang 2013 and Amin et al 2014 function that determines human capital at age t 1 would be the fact that one of the inputs namely the investment depends on the shock eitH Parents might be reacting to shocks that affect child development in a compensatory or reinforcing way depending on their preferences their resources the nature of the shock and their beliefs on the technology To obtain consistent estimates of the parameters of the production function one would need to take this endogeneity issue into account An attractive approach to this problem is to use an instrumental variable or a control function strategy In either case identification stems from the availability of variables that affect investment choices and do not enter the production function directly Prices Pxt are particularly attractive in this respect as it is plausible to assume that households take them as given Taking the model as written above one could also use total resources as a source of identification In this case however more caution is needed especially if resources include earnings which are obviously related to labor supply choices that in turn can indirectly affect the production function through the time inputs An obvious generalization here would be to include explicitly labor supply choices into the model and to consider alternative uses of parental time Following this route then one could think of using wages or labor market conditions as the source of identification Another important caveat to the use of prices as a source of identification for the role of investment in the production function of human capital is the availability of enough variation Data from a single time period and a single location might not provide enough variability However in some situations one can use geographic variation in prices The other major issue to tackle in bringing the model in equations 1 and 2 to the data is the fact that most of its variables are not directly observable Instead what researchers usually have is a collection of imprecise measures of the factors that constitute human capital and of the factors that enter its production function In this respect the approach proposed by Cunha et al 2010 is particularly useful18 They explicitly consider a measurement system that relates the factors of interest in the model to the available measures In particular they consider the following system mktkj αtjk θtj εtkj j c s h m f r M T k 1 2 5 Here mktkj is measurement k corresponding to factor j αtjk are the loading factors that relate factor j at age t to measure k at age t and εtkj are measurement errors that make the observable variables mktkj noisy signals of the factors The way that equation 5 is written implies that each measurement k is affected only by a single factor This assumption can be somewhat relaxed but some exclusion restrictions ie some factors excluded from certain measurements are necessary to achieve identification I will discuss some of these issues in the application of this model in Section 52 The approach proposed by Cunha et al 2010 is particularly useful because it considers simultaneously the theoretical framework with its conceptual issues 18 See Wolfe and Behrman 1984 for an earlier similar approach 970 Journal of the European Economic Association including the nature of the production function the interaction between different inputs the endogeneity of investment and the measurement system with its own set of issues It also provides good discipline in the use of multiple measures and a good way to summarize the available information within a theoretical coherent fashion Notice that an important step a researcher implementing this approach has to take is to map measures into factors Cunha et al 2010 use an old theorem by Kotlarski 1967 to establish the nonparametric identification of the joint distribution of the factors and of measurement error In particular what is required for the identification of these joint distributions from the empirical distributions of measurement is at least two measurements for each factor and three for at least one It is also necessary that the measurement error is independent across measures for at least two measures The intuition of this result is quite clear to identify the distribution of the factors it is necessary to average out measurement error Although the identification is nonparametric in practice researchers often specify a flexible functional form for the joint distributions of the factors and proceed to the estimation accordingly Once the joint distribution is identified the estimation of structural relations such as the production function and the investment function discussed previously is relatively straightforward One possible approach for instance developed in Attanasio et al 2014b and used in Attanasio et al 2015a is to take draws from the joint distribution estimated into a first step and use these simulated data to estimate the structural relation of interest by standard techniques such as nonlinear least squares or nonlinear instrumental variables Notice that such relations represent a restriction among the conditional means of several of the factors As such they have implications for the joint distribution of the factors one estimates in the first step of the procedure Normality for instance will imply a linear or possibly loglinear relationship between the means of the various factors As such it would be inconsistent with a nonlinear production function that implies the presence of complementarities between the various inputs Suppose for instance that one wants to allow the production function in equation 1 to be a CES function in which initial conditions background variables and investments interact with a certain finite elasticity of substitution to generate human capital at age t C 1 Then the joint distribution of age t C 1 human capital and the age t human capital and investment factors is necessarily nonGaussian It is therefore important if one does not want to preempt answering questions about the nature of the production function to work with a flexible specification of the joint distribution of the factors These issues are discussed at length in Attanasio et al 2014b The issue of endogeneity of investment can also be dealt easily within this approach The instruments considered in the model previously outlined such as prices Px t and resources Y i t can be added to the measurement system in equation 5 as additional factors possibly observed without error and their joint distribution can be estimated In a second step then data for the instruments can be drawn from the joint distribution along with data for the factors and one can apply a nonlinear instrumental variable or a control function approach Attanasio et al 2014b 2015a use the latter Attanasio The Determinants of Human Capital Formation 971 52 Using the Model Having set up a framework for the analysis of the accumulation of human capital I will now show how it can be profitably used in the context of the evaluation of an intervention aimed at fostering the development of young disadvantaged children I will start with the description of the intervention and its impacts before moving on to the use of the evaluation data to estimate the production function within the framework laid out in Section 5 521 An Intervention and its Impacts As I mentioned in the Introduction one of the most successful interventions targeted at vulnerable young children in the early years in developing countries was the Jamaica study I referred to Although the impact of that intervention was impressive and well documented it also left some open questions First the mechanisms through which the intervention operated are not completely obvious The comparison of IQ scores between treatment and control children is silent about what generated the impressive impacts that were measured Second it is not clear whether such an intervention can be scaled up to a large scale which would imply the use of local resources and possibly a loss in fidelity to the original curriculum In 2009 in collaboration with Sally GranthamMcGregor and other researchers from UCL and IFS as well as from Colombia we set up a large randomized controlled trial in Colombia to answer these two questions Some of the impacts of this intervention which I discuss in what follows are reported in Attanasio et al 2014a The Intervention The first step of the project was the adaptation of the Jamaica curriculum to the Colombian context This involved not only the translation of the curriculum but also its cultural adaptation The Jamaica curriculum is delivered through weekly home visits roughly one hour long during which a trained visitor engages in a series of structured activities with the target child and their mother or main care giver The activities are designed to be appropriate for the developmental status of the child They become progressively more complex as the child develops The activities put much emphasis on language through language games and a continuous encouragement of the mother to engage the child with language in everyday activities and cognitive development through stimulation games including puzzles and other toys books and so on The visits are well structured in that each visit is described in one page of the curriculum which specifies what activities are to be performed and the rough order in which they should be performed The activities are explained in the curriculum in fairly simple and direct language so as to be accessible to visitors who are not necessarily well educated The intervention also provides the visitors with some materials including conversation scenes books and toys and includes teaching mothers how to build a number of toys from recycled materials such as plastic bottles wooden blocks etc One important innovation relative to the Jamaica study was the use of the infrastructure of an existing welfare program to deliver the intervention In Colombia as in many other Latin American countries there is a large Conditional Cash Transfer 972 Journal of the European Economic Association Program called Familias en Accion FeA which is targeted to the poorest 20 of the population Within this program households receive cash if they comply with certain conditions which include sending children to school and in the case of young children taking them to growth and development checkups in the local health centers The program also has an important social component in that beneficiary mothers meet periodically to discuss a variety of issues in what are called Encuentros de Cuidado Roughly every 50 or 60 beneficiaries of FeA elect a representative called Madre Lıder ML who is in charge of organizing the Encuentros de Cuidado and of the relationship between the beneficiaries and the program officials Effectively the ML constitutes the first port of call for any beneficiary that might have a problem with the program The ML are not paid by the program and perform their activities on a voluntary basis Such a charge however is seen as a prestigious position that confers a status to the ML in the neighborhood The MLs although beneficiaries of FeA themselves are typically more educated more entrepreneurial and as their title would imply show more leadership qualities than a typical beneficiary We therefore had the idea of using them to deliver the intervention In particular with the help of the program in the towns where the study was conducted we contacted some MLs trained them and hired them for the duration of the intervention The use of local women identified through an existing welfare program is key for the scalability of the intervention that is being investigated First obviously there is the issue of cost Local women are likely to be cheaper to hire than social workers Second we identify women who are likely to be effective in delivering the intervention through the network of a preexisting welfare program that is very widespread Such an intervention therefore could be replicated throughout Colombia as the program is present in every municipality of the country Finally and more subtly an intervention that aims at changing parental practices and behavior might be more effective if its key messages are delivered and channeled through women in the community The MLs might be more attuned with closer to and more trusted by the mothers whose behavior the intervention tries to change than external social workers Of course this approach is not without problems The MLs are typically much less educated than social workers and therefore the quality of the intervention could be considerably diluted The MLs commitment to the intervention might also not be complete These issues imply that mentoring monitoring and supervising might be key to the success of such an intervention The necessity of mentors supervisors and monitors increases the cost of the intervention Moreover the intervention itself has to be designed so that it can be delivered by visitors with relatively low level of education and literacy The Evaluation To evaluate the impact of the intervention we designed a cluster randomized controlled trial and 96 small towns with populations of between 5000 and 50000 inhabitants were randomly allocated among four groups i a control group ii a stimulation only group iii a nutrition intervention group and iv a nutrition and stimulation intervention group The nutrition intervention consisted of Attanasio The Determinants of Human Capital Formation 973 the provision of micronutrients containing iron folic acid zinc and Vitamins A and C In each town three MLs were recruited and children aged between 12 and 24 months of beneficiaries represented by those MLs were included in the study19 Among the families represented by each ML we randomly selected five children in the right age range so that we ended up with a sample of about 1440 children at baseline The towns we chose were located in the central part of Colombia covering eight different states Given our resources we could not cover the entire country and at the same time we wanted to have some level of homogeneity across towns to improve the efficiency of our estimates However the area studied is relatively large roughly three times the size of England The logistical problems we faced would not be different from those that would be faced by a scaledup version of the program We recruited six professionals who acted as trainers supervisors and mentors of the MLs Each supervisor was assigned 8 of the 48 towns in which stimulation was part of the intervention These were women with a university degree from medium level universities or a background in child development Even in this phase we paid attention to the scalability of the intervention it should be possible to identify professionals at this level throughout the country Our supervisors having been themselves trained for six weeks in Bogota trained the MLs in each town for two weeks after which the intervention started An additional week of training was provided a month later After training the supervisors became monitors and mentors of the MLs They circuited across the towns each supervisor visiting each of the towns assigned to her roughly every six weeks During their stay in a town they would check on the MLs activities accompany them to some home visits and give them advice Moreover they were in constant contact with the MLs through mobile phones and text messages Before the intervention started a baseline survey gathered a considerable amount of information on child development as well as comprehensive information on the families where they lived The survey included several tests on childrens cognitive socioemotional and physical development including the Bayley scales of Infant and Toddler Development third edition BayleyIII the MacArthur Bates Communicative Development Inventories I II and III Spanishlanguage short forms and the Infant Characteristics Questionnaire ICQ which measures child temperament and others We also measured mothers and childrens height weight and haemoglobin levels to assess anaemia The socioeconomic survey in addition to a wide variety of household level variables contained detailed information on the home environment including several components of the HOME index The intervention ran for 18 months At the end of that period we collected a follow up survey within which children were assessed again in several dimensions We also collected information on mothers home visitors and more generally the household 19 If in a treatment town a ML did not want to participate into the study we replaced her with another local woman indicated by her possibly another ML but maintained the original children in the study TABLE 1 Impacts of the stimulation and nutrition interventions standardized treatment effects Stimulation MNP Stimulation MNP Bayley III cognition 0239 0029 0227 0057 0058 0058 Bayley III receptive language 0197 0021 0164 0063 0064 0063 Bayley III expressive language 0025 0056 0077 0064 0065 0065 Bayley III fine motor 0089 0076 0096 0055 0055 0055 Bayley III gross motor 0019 0015 0096 0066 0067 0066 MacArthurBateswords 0108 0079 0191 0066 0067 0066 MacArthurBatesphrases 0022 0037 0053 0065 0065 0065 Batesunstoppable 0069 0029 0052 0077 0077 0077 Batesdifficult 0147 0007 0088 0073 0074 0074 Notes Cluster robust standard errors in parentheses All effects are standardized using the estimated standard deviation of the control group All estimates control for sex age secondorder polynomial tester effect region effect baseline level of all test outcomes Treatment effects estimated on a homogeneous sample of 1260 children 318 controls 318 stimulation only 308 MNP only 316 stimulation MNP Significant at 10 significant at 5 significant at 1 using a onesided hypothesis test for Bayley and MacArthurBates the onetailed alternative hypothesis b 0 for Bates it was b 0 Attrition between the baseline and followup was not large as we managed to recontact 1229 of the original children Moreover attrition was not different between the control group and the various treatment arms Impacts The fact that we allocated the 96 towns in our sample randomly to the various types of intervention stimulation micronutrient supplementation and the combination of the two and the control group allowed us to evaluate the impact of the various interventions in a straightforward fashion comparing the mean outcomes of the various groups The presence of a baseline survey allowed us to check the balance among the various samples and also to improve the efficiency of the estimates Although the number of clusters in the intervention is not huge 24 per arm conditional on baseline observables the intracluster correlation for most outcomes was remarkably low at around 004 making this experiment one of the largest in this area With the observed intracluster correlation the 1267 children are equivalent to a sample of about 880 or 220 per arm20 The main impacts of the intervention are reported in Attanasio et al 2014a In Table 1 I reproduce some of the results reported in that paper and describe the 20 The PPP study included 123 children the Abecedarian 111 and the Jamaica study 129 Attanasio The Determinants of Human Capital Formation 975 impact of that evaluation21 The stimulation intervention with or without nutrition increased cognitive development as measured by the cognitive scale of the Bayley III by 024 of a standard deviation of the internally standardized zscore22 The intervention also had an impact of 020 on receptive language as measured by the corresponding scale of the BayleyIII Finally we also notice some modest impacts on fine motor skills which are often considered as a cognitive skill in children of that age The main points that should be taken from the table is that the stimulation intervention had a significant impact on cognitive development and on receptive language The impacts on expressive language are smaller and not statistically significant from zero There are also some impacts on temperament which might be an indicator of socioemotional skills as measured by the ICQs There is no significant impact of the nutrition intervention either on its own or in combination with the stimulation intervention Remarkably the nutrition intervention did not have an impact on physical growth and nutritional status as discussed in Andrew et al 2014 One issue is whether the impact found on cognitive development is significant not only from a statistical but also from a substantive and economic point of view To interpret the size of the impact in Figure 1 I report the standardized cognitive scale of the Bayley Scale of Infant Development BSID in Bogota plotted against age The two dotted lines refer to the cognitive development of children living in households in the bottom and top quartiles of the wealth distribution in Bogota The gap between these two groups is equivalent to about 08 of a standard deviation The thin red line refers to the control group in the RCT These children are similar to the bottom quartile of the Bogota sample The thick blue line is the cognitive development of the children in the treatment group of the intervention As can be seen the intervention fills about a third of the gap in cognition between the bottom and top quartiles in Bogota If this impact is sustained over time it is not negligible and its economic benefits in the long run could be substantial Having said that it is difficult given the available evidence to convert a gain in cognition or some other developmental outcome for a Colombian child into a longrun gain in say earnings or academic achievement These anchoring issues are discussed in Cunha et al 2010 As a first indication of the mechanism that might have given rise to the impacts we observe in Table 1 in Table 2 we report the impacts that the intervention had on various parental investments see Attanasio et al 2013 What is evident from this table is that the stimulation intervention incremented considerably parental investment as 21 The results are very slightly different from those in Attanasio et al 2014a because of small differences in the specification of the regression model 22 The standardization was performed considering the raw scores for the control group We first estimated the mean of the zscore as a flexible function of age and gender We then estimated a similar function for the standard deviation and obtained the zscore for each of the subscales considered by subtracting from the individual raw score the conditional mean and dividing the result by the estimated standard deviation We report all the impacts in terms of standard deviation of the these zscores FIGURE 1 Impact on cognitive development relative to Bogotá sample TABLE 2 Standardized effects on play investments Stimulation MNP Stimulation MNP Number unique play materials 0277 0029 0297 0071 0071 0071 Number unique play activities 0264 0059 0428 0072 0072 0072 Proportion with 4 bought toys 0146 0144 0071 0070 0071 0070 Proportion with homemade toys 0074 0096 0203 0080 0080 0080 Notes Cluster robust standard errors in parentheses All effects are standardized using the estimated standard deviation of the control group All estimates control for sex age secondorder polynomial tester effect region effect baseline level of all test outcomes Treatment effects estimated on a homogeneous sample of 1260 children 318 controls 318 stimulation only 308 MNP only 316 stimulation MNP Number of unique play materials refers to the last seven days Number of unique play activities refers to the last three days Significant at 5 significant at 1 using a onesided hypothesis test for all outcomes the onetailed alternative hypothesis was b 0 measured by several indicators in the data As I will discuss in what follows for some reason parents were convinced to invest more in time and commodities in their young children This evidence constitutes a first hint of the way the impact of the stimulation intervention might have worked 522 Estimating the Model and Interpreting the Impacts The next step in the study of the intervention that I have been describing is the estimation of the model discussed in Section 5 Here I will draw on Attanasio et al 2015a where my coauthors and I specify two production functions one for cognitive development and one for socioemotional skills and two investment functions We let the child outcomes we consider depend on initial conditions parental investments parental background variables and shocks The specification we use is that of a CES production function θit1j Aji γ1κj yitjκθ cρjit γ2κj θitsρj γ3κj θitmcρj γ4κj θitmsρj γ5κj θit1Mρj γ6κj θit1Tρj1ρj eitηj j c s κ d n Here θitj represents factor j j c s at age t for child i θit1T and θit1M are investments in time and materials respectively and θitmc and θitms are maternal cognitive and socioemotional skills Although such a specification might be considered restrictive it allows for complementarities between the various inputs and nests as special cases several interesting cases such as that of separability which would occur for ρj 1 or that of CobbDouglas ρj 0 We also tried other cases such as a nested CES which include equation 6 as a special case and could not reject the restrictions that would yield it In equation 6 the term Aj represents total factor productivity while the random variable ηitj represents random shocks that affect the development of skill j at age t The subscript κ in equation 6 allows the coefficients of the production function to be a function of the treatment d treatment n notreatment Finally we consider two investment factors θM and θT the former representing commodities and the latter representing time investment Both factors are allowed in principle to affect both cognitive and socioemotional skills For the two investment factors we take a linear approximation of equation 4 θit1s ψsκ Wt νt1s s M T κ d n 7 where the vector Wt includes all the determinants of investment in equation 4 Notice that we let the parameters of the investment functions ψsκ depend on the treatment status of the children to reflect the possibility that the intervention changes the way parents approach the investment problem as I discuss in what follows As we allow the intervention which is assigned randomly to influence investment one could argue that the assignment could be a good instrument for taking into account the endogeneity of parental investment in the production function However this strategy is precluded if we consider the possibility that the intervention may also affect the production function directly That is despite being randomly allocated the treatment is not a valid instrument as it can enter the production function directly 978 Journal of the European Economic Association Within this framework we can see that the intervention can affect child development in three different ways First it can change the parameters of the production function increasing either the productivity of specific inputs or total factor productivity Second it can change parental investment for some reason inducing parents to invest more in their children Table 2 presents some evidence of this second mechanism Finally it is possible that the intervention improves mothers skills By estimating the parameters of equation 6 and the distribution of factors we can test these hypotheses explicitly In order to estimate the parameters of equation 6 we follow a twostep procedure which is discussed extensively in Attanasio et al 2014b In particular we first estimate the joint distribution of the factors and measurement errors We augment the measurement system in equation 5 to consider also the distribution of the instruments we use which we estimate jointly with the distribution of factors and measurement errors Although these distribution are nonparametrically identified we make some flexible parametric assumption to obtain them more precisely In particular we assume that the factors are jointly distributed as a mixture of two lognormal distributions while the measurement errors are assumed to be jointly lognormal We perform maximum likelihood estimation implementing an EM algorithm Having estimated distributions for the factors including the instruments we draw from it to create a data set and estimate both the investment function and the production function This is performed by implementing a control function approach and nonlinear GLS on the simulated data To compute standard errors and confidence intervals we bootstrap the whole procedure taking into account the clustered nature of the data ie allowing for correlation within each municipality in the sample From this procedure the importance of using a flexible functional form assumption for the joint distribution of the factors is clear The production function in equation 6 imposes some restrictions on the conditional means of the various factors at age t and t C 1 In particular it implies certain nonlinear relations between the mean of the factors at t C 1 and those at t The nonlinear structure in equation 6 would be inconsistent with say joint normality of the factors distribution I will not report the tables of estimates of the investment functions and the production functions in Attanasio et al 2015a However the main findings in that paper can be summarized as follows 1 The production function seems to be well approximated by a CobbDouglas production function The elasticity of substitution between the various inputs considered is not statistically different from 1 Additive separability instead is strongly rejected This is true both for the production function of cognitive skills and that for socioemotional skills 2 Initial conditions matter Initial cognition is a very important determinant of cognition in the second period and initial socioemotional development is important for subsequent socioemotional development Crosseffects are also somewhat important initial cognition at ages 1224 months is important for socioemotional development at ages 3042 months Initial socioemotional Attanasio The Determinants of Human Capital Formation 979 development however does not seem to affect subsequent cognition These last two results contrast with what Cunha et al 2010 find on a US sample at much older ages In particular they find that early socioemotional development seems to be important for subsequent cognition It should be stressed that there is not much evidence on this issue for the age group considered here 3 Parental investments also matter Investment in materials seems to matter for cognitive development while investment in time matters for socioemotional development This evidence is also consistent with the mediation analysis in RubioCodina et al 2015 on data from Bogota where it is found that play materials seem to be more relevant for cognition and fine motor skills while time investments relate more to language and socioemotional development 4 Parental background has mainly an effect through parental investment Once we control for investment choices maternal skills are not very important Once again this evidence is consistent with the results on the data from Bogota in RubioCodina et al 2015 5 Allowing for endogenous investment is important The coefficients on investment are estimated to be considerably lower when the production function is estimated by nonlinear least squares ignoring the endogeneity of investment This finding is important not only for the identification of the marginal product of investment in the production function of human capital but also because the direction of the bias is indicative of the nature of parental investment A downward bias in the estimates of the coefficients when endogenous parental reactions are ignored probably indicates that parents tend to compensate rather than accentuate shocks23 6 The intervention shifts significantly the distribution of the two investment factors considered Parental investment in time and material is considerably higher in treatment villages than in control ones This is consistent with the simple mean comparisons reported in Table 2 7 The parameters of the production function do not seem to be affected by the intervention This is also true for the total factor productivity This finding and the one about investment is important for interpreting the way in which the intervention obtained the effects reported in Table 1 Rather than making parents or other factors more productive the intervention increased parental investment in child development The value of this exercise should be apparent from the list of main findings First the estimation of the production function of human capital allows the characterization of the process through which young children develop and the role played by different factors This is a first step towards filling some of the gaps in our knowledge of such 23 On this point see the discussion in Almond and Mazumder 2013 OLS would yield biased estimates if there is an omitted initial condition that is negatively correlated with the investment or in the presence of measurement error in investment The factor structure takes the latter into consideration 980 Journal of the European Economic Association a process The fact that the nature of dynamic complementarities between different dimensions of human capital is different from what was found for instance by Cunha et al 2010 at different ages is an indication of the fact that the process of human capital formation is quite complex and we are still far from a full understanding of its features24 Such an understanding is key for the design of policy The nature and size of dynamic complementarities for instance are key to identify crucial periods and windows of opportunities to target interventions Moreover if certain dimensions at a certain age turn out to be particularly important one might want to use interventions that target that specific dimension Second the previously outlined findings give a good idea of the way in which the intervention we have described worked It seems that for some reason the home visits induced parents to invest more both in terms of money and time in their children The next logical step in this research agenda is to understand why parents were not investing enough before the intervention 6 Beliefs A number of interventions seem to have an impact without providing targeted individuals any resources besides information Information can have an impact on actual outcomes either because it makes the targeted individuals more productive in getting the outcomes of interest or because it changes their investment strategies The intervention in Colombia I have discussed in Section 521 according to the results in Attanasio et al 2015a did not make parents more effective or change the production function Instead it increased parental investment Fitzsimons et al 2014 discuss an information intervention in Malawi that increased child nutritional status by increasing childrens protein consumption which was in turn financed by an increase in male labor supply The questions these results and others in similar areas pose are therefore the following Why was this not happening before the intervention Why did parents not invest before the intervention in Colombia Why were parents not working harder to feed their offspring with more proteins before the intervention in Malawi Several possibilities exist It is possible that these interventions change parental tastes so as to make them more altruistic towards their children or changing the valuation they give to children outcomes Or in the case of the Colombian stimulation program it is possible that the intervention changed the psychic cost of interacting with the children An alternative possible answer is that they were not aware of the productivity of their investments Their choices as in the model sketched previously depended on their perception of the production function If they held a distorted view of the production function and in particular underestimated the marginal productivity of 24 Of course there may be many other reasons in addition to age behind the difference in results between Cunha et al 2010 and Attanasio et al 2015a such as the different contexts of a developing and developed country Attanasio The Determinants of Human Capital Formation 981 parental investment an intervention that would change that view and move them towards the correct one would increase investment and improve outcomes The fact that disadvantaged children are exposed to much less stimulating environments is increasingly documented25 The view that the parents of disadvantaged children seem to underestimate the productivity of investment is consistent with some of the hypotheses discussed by Lareau 2003 who argues that middleclass families in their parental investment strategies use what she defines concerted cultivation while working class and poor families use parental strategies that rely on natural growth Unlike their betteroff counterparts many poor parents do not think children need special inputs and develop naturally unless they are affected by severe shocks An interesting research agenda therefore is to try to estimate parental beliefs on the nature of the production function of human capital There are several possible approaches to the identification of parental perceptions of the production function One possibility would be the direct elicitation of such beliefs This is a good example of the design of innovative measurement tools that I discuss in Section 72 Cunha et al 2013 implement such an approach in an innovative study that looks at the beliefs of pregnant disadvantaged mothers in a hospital in Philadelphia In Attanasio Cunha and Jervis 2015b we have started the analysis of subjective beliefs elicited in the second followup of the children in the Colombian experiment already discussed Preliminary results indicate that subjective beliefs seem consistent with the idea that parents see investment as productive and necessary especially for children with some problems and delay This is also consistent with the compensatory nature of parental investment identified in Attanasio et al 2015a Obviously the elicitation of parental beliefs on the production function is not easy This is a very promising research agenda but much work is needed on validating different measures and on establishing what is the best way to structure the questions An alternative approach to the direct elicitation of beliefs is to try to infer them from investment choices As I mentioned in Section 5 the parameters of the investment function 4 depend on individual preferences and on individual perception of the production function To be able to disentangle them we need to impose some structure on the problem and some variation in the data that allow us to identify taste parameters independently from the parameters of the production functions as perceived by the parents In Attanasio and Cattan 2015 we use the idea that an intervention by providing information but no resources to parents might be changing individual perceptions of the production function If such an intervention is randomly allocated to different groups of individuals as is the case for instance in the case of the Colombian intervention already mentioned one can assume that treated parents have acquired knowledge of the actual production function and one can use data on child development and parental investment from this group to identify the taste and technology parameters 25 Hart and Risley 1995 for instance report In professional families children heard an average of 2153 words per hour while children in working class families heard an average of 1251 words per hour and children in welfarerecipient families heard an average of 616 words per hour 982 Journal of the European Economic Association in equations 1 and 4 Having obtained taste parameters one can then use investment choices of the control parents to identify the parameters of the production function as perceived by these parents and therefore assess the extent to which their beliefs are distorted 7 Research Tools In this section I discuss two methodological issues that are relevant not only for what I have discussed so far but also at a much more general level First I will briefly go over the debate between the proponents of structural models versus those who prefer simpler approaches that make little or no use of economic and behavioral models in analyzing data and in particular in evaluating the impacts of social policies I will then move on to discuss the opportunities afforded by new measurement tools and how they should be constructed 71 Structural Models and Randomized Controlled Trials When looking at data and at what can be learned from correlations economists are trained to look at behavioral responses that might prevent the inference of a causal relationship among certain variables Over the last few decades this set of issues has been taken extremely seriously by most applied researchers in economics These are of course identification issues which can be addressed either by the availability of exogenous variation such as that induced by a controlled experiment or by the imposition of some restrictions that might be derived from economic theory or other knowledge and that can achieve point or set identification A part of the profession has taken the view that restrictions derived from theoretical models are essentially arbitrary and that reliable causal evidence can only come from the comparison of means of different samples exogenously exposed to different treatments Another part of the profession instead does not mind imposing restrictions justified by economic theory and possibly functional form assumptions to achieve identification The approach taken by the first group is often identified misleadingly26 in my opinion as the reduced form approach as opposed to the structural approach The fact that the profession thinks very carefully about the source of variation in the data that are used to identify certain parameters of interest is an extremely positive development which distinguishes economists from other social sciences 26 Misleadingly because a reduced form is derived from a structural model so that implicitly the economic model should be on the background of any reduced form exercise Analogously researchers using instrumental variables implicitly assume that the endogenous variable being instrumented is generated by a model that contains the instrument which in addition has to be excluded from the main relation of interest Attanasio The Determinants of Human Capital Formation 983 However to reduce the empirical analysis to simple comparison of means of different groups in a randomized control trial is in my opinion very limitative and narrow Experiments can be very useful because they introduce variation which is if the experiment is constructed carefully by construction exogenous This variation can then be used to estimate behavioral models that are richer and use weaker assumptions than models estimated without the luxury of the experimental variation Inference from such models is crucial for the design and evaluation of public policies without a model it is impossible to extrapolate the results of an experiment to a different context or to estimate the impacts of a slightly different policy in the same context More importantly without a model of behavior it is not possible to understand the mechanisms behind the impacts that one observes in an experiment I should also add that the exercise of thinking through the lens of a model of individual behavior or even better a model that incorporates general equilibrium effects that take into account the aggregate consequences of a large intervention is where the comparative advantage of economists lies in this context Randomized controlled trials have been around in many sciences for a long time and have also been used in social sciences for a long time Moreover there is no reason why economists should be running randomized trials in education nutrition child development or disease control Many researchers in these disciplines have a much deeper understanding of the specifics of the interventions and of the problems that they try to address What economists can offer however are models of individual behavior that generate the responses that one observes in the data including in some situations general equilibrium effects specific ways to model the selection and endogeneity issues that affect the working of most interventions in fundamental ways These models can then be used to extrapolate the results of a specific evaluation to wider contexts The work on the ECD intervention I have discussed in Section 52 should give an example of the approach I have in mind In that context the estimation of the production function for human capital helps to understand how the intervention had its impact As discussed in Attanasio et al 2015a while the experiment can be used to measure the impact of the intervention further structure is necessary to estimate the production function and in particular the role that parental investment plays in explaining child development In that context we used variation in prices and family resources rather than the experiment to instrument investment This approach allowed us to consider the possibility that the intervention affected directly the production function Other examples are available in the literature For instance in the context of the conditional cash transfer program PROGRESA in Mexico whose impacts have been estimated using a cluster randomized controlled trial Todd and Wolpin 2006 and Attanasio et al 2012 used the evaluation data to estimate a structural model of enrolment decisions in school which they use amongst other things to infer the impact of versions of the program with a different grant structure In the context of India Duflo et al 2012 used the data from a randomized controlled trial of an intervention aimed at reducing absenteeism of school teachers by providing a system of incentives to estimate a structural model of labor supply in which effort depends on the nonlinear structure implied by the program These exercises make a 984 Journal of the European Economic Association profitable use of the experimental variation to understand the mechanisms behind the impacts These instances indicate that RCT and structural models are not substitutes but complements RCTs allow economists social scientists and policy makers to estimate the impact of interventions in a rigorous and at the same time simple way If these experiments are complemented with rich enough data they can then allow researchers to estimate richer behavioral models that can be used to extrapolate the results of the experiment to different contexts or to slightly different interventions These models can also be used to interpret the intervention impacts and to understand the mechanisms that generate them This understanding is useful both to perform welfare analysis and to design better interventions Finally the results of the experiment can and should be used to validate and test different models Data should talk to theory and improve it What is central to this discussion is the availability of rich data that gather information not only on the outcomes of interest but on many environmental variables These data are necessary to estimate the structural models that can interpret the impacts 72 Measurement Many strong assumptions which are sometimes made to achieve identification of structural models are necessary because of the lack of information on certain variables that while crucial to individual choices are typically not observed in standard socioeconomic surveys A good example is that of subjective expectations about future and uncertain variables In many dynamic models where uncertainty is relevant individual agents base their choices on their subjective probability distributions about future events Expected values of investment returns as well as risk perceptions are bound to be relevant for individual investment decisions In the absence of direct information on individual perceptions researchers typically use strong assumptions such as rational expectations to model these choices empirically Even if one is willing to accept rational expectations and consider actual realizations as measurement errorridden signals of expectations further and stronger assumptions are needed if one wants to use subjective perceptions of risk such as variances or standard deviations Analogous considerations apply to a variety of other situations such as individual beliefs on the nature of the returns to certain investments In the case of the Colombian intervention we have already discussed parental investment depends clearly on parents perception of the production function The standard practice when modeling investment choices is to assume that parents know the form and the parameters of the production function Yet as I discuss in what follows in many situations this is clearly not the case One attractive possibility which has received considerable attention in recent years is that of the direct elicitation of subjective perceptions be it of subjective probability distributions or of the return to investments This approach has a long history Tom Juster and his colleagues in Michigan played a big role in developing alternative and Attanasio The Determinants of Human Capital Formation 985 innovative measurement tools Juster 1966b cited by Manski 2004 was probably one of the first researchers to try to collect subjective expectations data in a survey The measurement of subjective expectations is one example but others exist Juster 1966a for instance studied liquidity constraints in consumption choices by eliciting consumer elasticities in the demand for auto loans to interest rates and maturity The study cleverly allocated different hypothetical scenarios to randomly chosen groups of consumers This type of approach however where survey respondents are asked hypothetical questions has faced much resistance for a long time in the economic profession Economists have refrained from using information elicited through hypothetical questions that do not relate to actual choices individuals make Economic surveys typically focus on revealed preferences and give no space to subjective answers or as Manski 2004 puts it economists believe what people do not what they say The history of this aversion of economists to data not based on choices is briefly discussed by Manski 2004 who in the context of subjective expectations strongly advocates the elicitation of subjective probability distributions In recent years many studies have shown that this is possible even in the context of developing countries27 An increasing number of researchers and economists are now systematically going beyond measures based exclusively on choices and revealed preferences In my opinion this is a very desirable development which goes hand in hand with the development of a variety of measurement tools that are increasingly used in household surveys These new methods include the elicitation of subjective probability distributions on a variety of outcomes the elicitation of preferences such as risk attitudes patience present bias and so on the elicitation of beliefs on the return to different types of investments such as school enrolment the use of experimental games to measure trust social capital and so on To be sure the measurement of individual attitudes beliefs expectations tastes and so on is not easy Measurement tools can be extremely fragile and subject to a number of issues such as framing anchoring recall biases as well as many other biases Economists have much to learn from cognitive psychologists survey designers and researchers in other disciplines who have developed many measurement tools that can be adapted and used in economic surveys Careful piloting and validation of new instruments is necessary I believe that much can be learned and obtained from clever survey designs and new measurement tools The economic profession has a strong tradition in developing new successful methods for the measurement of important variables that had been proven difficult to obtain A good example is the progress made in the measurement of household financial wealth A few decades ago it seemed impossible to obtain reliable measures of household financial wealth The development of new survey methodologies such as that of the unfolding brackets pioneered in the Panel Study of Income Dynamics have changed that perception considerably These methodologies have now become standard and are used in many surveys around the 27 See for instance the recent survey by Delavande 2014 986 Journal of the European Economic Association world One would hope that similar successes can be obtained in developing new measurement tools in a variety of different contexts Recent developments in computer power and technology afford a large number of new possibilities in a variety of dimensions One first and important development is the increasingly common use of administrative data sources sometimes linked across different data bases and sometimes linked with surveys Obviously the use of these data poses a large number of delicate problems concerning privacy and confidentiality However their availability constitutes a remarkable opportunity for the progress of social sciences Another important development is the use of new technologies to collect accurate data New data sources collected with new technologies range from scanner data on consumer purchases which provide extremely fine details on household consumption behavior to the use of detailed weather data in the study of environmental issues or agriculture to the integration of new and sophisticated biomarkers including genetic information in an increasing number of surveyssuch the Health and Retirement Study HRS the English Longitudinal Survey of Aging ELSA and the Survey of Health Ageing and Retirement in Europe SHAREto the use of video technology to obtain information on teacher quality eg the Classroom Assessment Scoring System CLASS 721 Measuring Child Development In the field of early childhood development these issues are particularly salient Measuring the development physical cognitive and socioemotional of young children is not easy especially below the age of 36 months The best available measures for those age ranges such as the Bayleys scales of Infant and Toddler Development third edition BayleyIII can be very costly and potentially impossible to use in many countries In addition to the monetary and time cost28 the BayleyIII has to be administered by a qualified psychologist especially trained in the administration of this test Moreover the test has to be administered in standardized settings so it cannot be done in the childs home To all this one has to add the necessity to administer the test in the childs language and therefore the necessity to adapt the existing version of the BSID to such a language and cultural context A number of shorter and much cheaper tests do exist and are routinely used These include the Ages and Stages Questionnaire the Denver Developmental Screening Test the MacArthurBates Communicative Inventories the Battelle Developmental Inventory the World Health Organization Motor Milestones and many others Many of these tests are based on maternal report and can be administered by a reasonably skilled interviewer rather than a specialized psychologist The issue of course is whether they measure accurately the domains of child development captured by the various scales of the BayleyIII In a recent study Araujo et al 2014 relate the results of the five tests listed above to five subscales of the BayleyIII where the former were 28 BayleyIII tests on young children can easily take 15 hours or more to administer The cost ranges depending on the context where they are implemented but it is above US120 per child in most countries Attanasio The Determinants of Human Capital Formation 987 administered by a survey interviewer and the latter by a trained psychologist The results are disheartening the correlations between the short tests and the BayleyIII are extremely low especially at young ages and for children of mothers with low levels of education In some cases the correlations are not even significantly different from zero this is the case for many components of the ASQ tests and the cognition and language scales of the BSID for children younger than 18 months The ASQ performs badly for cognition even for older children In general tests that attempt to measure expressive language perform better perhaps not surprisingly For instance the MacArthurBates has a correlation with the expressive language scale of the Bayley III of around 065 for children between 19 and 30 months In general all tests perform better at least in terms of correlation with the BayleyIII for older children Measuring the development of young children in different domains accurately is important both to evaluate the effectiveness of different interventions and to better understand the process of child development As I mentioned previously the nature and size of dynamic complementarities between different dimensions of human capital are crucial for policy design it is necessary to identify the key periods in child development and the role played by specific skills in each period in fostering further development in subsequent stages Without accurate measures this is not possible Analogous considerations are also relevant for measuring inputs in the process of human capital accumulation Children are exposed to a variety of environmental stimuli that are likely to play important roles in their development Modeling and understanding the process of child development and human capital growth in the early years requires good measures of inputs including parental investments in time and commodities school or child care inputs nutrition and so on Measuring the quantity and quality of the inputs in the process of human capital formation is as hard as measuring children outcomes Given these issues it is clear that new measures possibly exploiting new technologies might offer important insights A number of new measures are being developed and studied Just to mention a few Neil Marlow and colleagues have developed a new test PARCAR still based on maternal report which seems to perform better than the ASQ in measuring the development of premature children29 Anne Fernald and her collaborators at Stanford have developed a test LookWhile Listening LWL that uses eye tracking and measure the speed of reaction of children to certain stimuli They have shown how such a measure changes with age and how it relates to socioeconomic status see Fernald et al 2008 2013 Another interesting instrument to measure the quality of the home environment is the LENA software which is used to decode daylong recordings to assess the quality of the language environment children are exposed to30 LENA has recently been used together with LWL to analyze pathways of language development in young children by Weisleder and Fernald 2013 29 See Johnson et al 2004ab and Martin et al 2012 30 See Ford et al 2009 LENA also offers a measure of language development The software produces a scale that depends on the number and complexity of child vocalization 988 Journal of the European Economic Association These developments are potentially very important The development of measures that can be implemented at an affordable cost within largescale surveys is extremely important for the reasons I have discussed Much more work is necessary however on many of these measures to gain a better understanding of what they are actually measuring We need to understand which domains of child development they are relevant for what is their concurrent validity and what is their predictive power of subsequent outcomes This is also true for recently developed measures of brain activity In an interesting recent paper LloydFox et al 2014 for instance show that nearinfrared spectroscopy can be implemented at reasonable costs in very remote locations in Africa It is not completely clear however what aspect of child development the resulting brain imaging measures Many of the studies and data sets that I have mentioned so far were developed around the evaluations of interventions that were implemented on a relatively small scale As a consequence many of these surveys were not representative at any large scale It should be clear however that large representative surveys are extremely important and that the development of accurate and affordable measurement tools gives the possibility of making them much richer Over the last few decades we have seen the development of several such surveys both in developed and in developing countries Databases such as the Cohort Studies in the UK the Young Lives initiative and more recently the Encuesta de Primera Infancia in Chile constitute an important tool for research At the same time many established large multipurpose surveys such as the PSID in the United States or ELCA in Colombia have been including modules with rich measures of child development These are very positive developments 722 Measurement and Theory New measurement tools when properly validated can obviously be very valuable for a variety of purposes As already hinted the development of such tools could yield some easily achieved targets The constriction of new measurement tools however is far from trivial and as I mentioned previously poses a number of challenges Moreover there are some important principles that should drive the construction of new tools Which tools are needed should be driven by theory and by the knowledge accumulated from previous empirical studies In the case of human capital the theory of child development should define what domains are relevant and should be subject to measurement More generally in different contexts the relevant theory should inform the construction of new measurements This has been the case in the past For instance the development of the system of National Accounts was to a large extent induced by the macroeconomic theories that had been developed in previous years and by the necessity to bring those models to data As it becomes more common for researchers in economics to be involved in data collection and to have the possibility of influencing the measurements deployed in field surveys it is also important that the needs of proper econometric approaches inform data collection For instance in the case of the factor models I discussed in Section 522 identification requires at least two measurements for each factor and that the errors associated with each measurement be uncorrelated Data collection could be Attanasio The Determinants of Human Capital Formation 989 organized so that such assumptions are likely to be satisfied in the data In the case of the Colombia study I discussed some measures of child development such as the BayleyIII were collected by a psychologist working with the child while others such as the MacArthurBates inventories were collected by an interviewer working with the mother The assumption that the measurement errors on these different measures collected on different days by different individuals and based on child observation or maternal report are independent is probably not very farfetched The other consideration to be made is that the perfect measurement probably does not exist Measurement error is always going to be present to an extent Moreover while certainly related to concepts of interest often available measurements do not coincide with the theoretical concepts that researchers are interested in In this sense the factor model in Cunha et al 2010 is particularly attractive because it makes explicit the presence of measurement error and keeps the theoretical structure and available measures on parallel levels related by the measurement system The context of child development and human capital is not the only one in which this is relevant Models of risk sharing and consumption smoothing typically studied in the literature can be interpreted as factor models where the theoretical framework poses some restrictions on the empirical measures From a practical point of view the consideration made by Browning and Crossley 2009 that often it might be worthwhile to invest resources in the collection of two or more imperfect measures rather than pursuing the unachievable task of constructing a perfect measure is certainly relevant see also Schennach 2004 8 Conclusions A Research Agenda in Child Development In this paper I have discussed a large research agenda that has grown around the recent renewed interest in the accumulation of human capital during the early years It has become increasingly clear that the early years are extremely important and that what happens to individuals early on has longlasting consequences Vulnerable children living in adverse conditions accumulate lags that might be difficult to remediate later in life This mounting body of evidence indicates that the early years might be particularly salient for policy interventions as strongly argued by Heckman 2008 Much work is still needed however In Section 4 I have suggested already what I think are the main challenges for current research on early child development and the accumulation of human capital It might be however useful to summarize them here Again the theoretical framework whose component I sketched in Section 2 is useful to organize this discussion The two big components of such a research agenda are in my opinion the characterization of the production function of human capital and the characterization of parental behavior Our understanding of the production function of human capital in the early years is still very incomplete Human capital is now understood as a multidimensional object where different domains ranging from physical growth to cognition and language to socioemotional skills develop in a intertwined fashion over time The nature of 990 Journal of the European Economic Association these dynamic interactions is still not completely understood We need to quantify the complementarities between different components of human capital and the various inputs that enter the production function and crucially how these complementarities change over the life course as children develop Parental investment and the inputs from child care or schools have different dimensions and these different dimensions can affect different components of human capital differently The pathways through which these investments manifest into developmental outcomes need to be fully characterized This evidence is key for the design of effective policies as they are key for the identification of windows of opportunities and for the identification of specific domains that should be targeted in specific periods by specific forms of investment From a methodological point of view a systematic use of flexible latent factor models can be useful An explicit treatment of measurement error and the recognition that complete measurement of all relevant factors and inputs can be extremely difficult if not impossible is important An analysis of the biases that can be introduced by ignoring certain domains of human capital or certain types of investment would be very useful Many of the available studies make some very strong assumptions on the dynamics of human capital For instance all the studies I am aware of assume a Markov structure so that the current level of development is a sufficient statistics for the effect of past levels of human capital in the production function It would be important in particular for the identification of key stages to check whether such an assumption is a realistic one or whether it is violated in practice Or for tractability it is often assumed that the relevant periods in the development of human capital coincide with those for which developmental outcomes are available Data sets containing good quality data for a long period and with a sufficiently high frequency could be used to investigate how robust inferences are when some of these assumptions are violated Furthermore additional theoretical and empirical research is needed to establish what types of biases are introduced in the study of the production function from the omission of important factors that might be unobserved in many data sets Parental investment which is crucial in shaping child development depends on parents objectives on their resources and on their beliefs about the nature of the production function Yet we have only a partial understanding of each of these components Much work is needed in studying parental tastes and objectives especially when considering the allocation of resources among several siblings of different gender and possibly ability Also as already discussed gender issues can also be relevant as mothers and fathers might differ in their preferences and in their attitudes towards children We also have a limited understanding of and information about parental investment Parents can do many different activities to foster their childrens development which range from spending time with them on different activities to buying toys and books to contracting services such as private lessons etc Different inputs might be targeted at different domains of human capital Better information on these items is needed to model parental behavior empirically Finally parental choices will crucially depend on parental beliefs about the production function A better understanding of these issues is in my opinion key in characterization of parental investments in children Attanasio The Determinants of Human Capital Formation 991 A number of interventions both in developed and developing countries have proven to be effective in achieving sustainable impacts that in some cases have had large longrun effects on adult outcomes However the mechanisms through which these interventions work are not fully understood Moreover the biggest challenge probably lies in designing affordable interventions that are effective at scale In order to tackle these outstanding 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