This paper estimates models of the evolution of cognitive and noncognitive skills and explores the role of family environments in shaping these skills at different stages of the life cycle of the child. Central to this analysis is identification of the technology of skill formation. We estimate a dynamic factor model to solve the problem of endogeneity of inputs and multiplicity of inputs relative to instruments. We identify the scale of the factors by estimating their effects on adult outcomes. In this fashion we avoid reliance on test scores and changes in test scores that have no natural metric. Parental investments are generally more effective in raising noncognitive skills. Noncognitive skills promote the formation of cognitive skills but, in most specifications of our model, cognitive skills do not promote the formation of noncognitive skills. Parental inputs have different effects at different stages of the child’s life cycle with cognitive skills affected more at early ages and noncognitive skills affected more at later ages.

This paper formulates and estimates multistage production functions for children’s cognitive and noncognitive skills. Skills are determined by parental environments and investments at different stages of childhood. We estimate the elasticity of substitution between investments in one period and stocks of skills in that period to assess the benefits of early investment in children compared to later remediation. We establish nonparametric identification of a general class of production technologies based on nonlinear factor models with endogenous inputs. A by-product of our approach is a framework for evaluating childhood and schooling interventions that does not rely on arbitrarily scaled test scores as outputs and recognizes the differential effects of the same bundle of skills in different tasks. Using the estimated technology, we determine optimal targeting of interventions to children with different parental and personal birth endowments. Substitutability decreases in later stages of the life cycle in the production of cognitive skills. It increases slightly in later stages of the life cycle in the production of noncognitive skills. This finding has important implications for the design of policies that target the disadvantaged. For some configurations of disadvantage and for some

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An electronic version of the paper may be downloaded • from the SSRN website: www.SSRN.com • from the RePEc website: www.RePEc.org • from the CESifo website: Twww.CESifo-group.org/wp T

This paper studies the determinants of children’s scores on tests of cognitive achievement in math and reading. Using rich longitudinal data on test scores, home environments, and schools, we implement alternative specifications for the cognitive achievement production function that allow achievement to depend on the entire history of lagged home and school inputs as well as on parents ’ ability and unobserved endowments. The empirical results show that both contemporaneous and lagged inputs matter in the production of current achievement and the importance of allowing for unobserved endowment effects. We use cross-validation methods to select among competing specifications and find support for a variant of a value-added model of the production function augmented to include information on lagged inputs. Using this specification, we study the sources of test score gaps between black, white and Hispanic children. The estimated model captures key patterns in the data, such as the widening of minority-white test score gaps with age and differences in the gap pattern between Hispanics and blacks. We find that differences in mother’s ability (as measured by AFQT) accounts for about half of the test score gap. However, home inputs also account for a significant proportion. Equalizing home inputs at the average levels of

University, Rand, and UC Davis. We also gratefully acknowledge the research support of SSHRC

at DIW Berlin This series presents research findings based either directly on data from the German Socio-Economic Panel Study (SOEP) or using SOEP data as part of an internationally comparable data set (e.g. CNEF, ECHP, LIS, LWS, CHER/PACO). SOEP is a truly multidisciplinary household panel study covering a wide range of social and behavioral sciences: economics, sociology, psychology, survey methodology, econometrics and applied statistics, educational science, political science, public health, behavioral genetics, demography, geography, and sport science. The decision to publish a submission in SOEPpapers is made by a board of editors chosen by the DIW Berlin to represent the wide range of disciplines covered by SOEP. There is no external referee process and papers are either accepted or rejected without revision. Papers appear in this series as works in progress and may also appear elsewhere. They often represent preliminary studies and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be requested from the author directly.

Are teachers ’ impacts on students ’ test scores (“value-added”) a good measure of their quality? One reason this question has sparked debate is disagreement about whether value-added (VA) measures provide un-biased estimates of teachers ’ causal impacts on student achievement. We test for bias in VA using previously unobserved parent characteris-tics and a quasi-experimental design based on changes in teaching staff. Using school district and tax records for more than one million children, we find that VA models which control for a student’s prior test scores ex-hibit little bias in forecasting teachers ’ impacts on student achievement. How can we measure and improve the quality of teaching in primary schools? One prominent but controversial method is to evaluate teachers based on their impacts on students ’ test scores, commonly termed the “value-added ” (VA) approach.1 School districts from Washington D.C. to Los Angeles have begun to calculate VA measures and use them to evaluate teachers. Advocates argue that selecting teachers on the basis of their VA can generate substantial gains in achievement (e.g., Gordon, Kane, and Staiger

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