On the Production of Cognitive Achievement and Gaps in Test Scores
| Date | 01 April 2016 |
| DOI | http://doi.org/10.1111/obes.12104 |
| Published date | 01 April 2016 |
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©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 78, 2 (2016) 0305–9049
doi: 10.1111/obes.12104
On the Production of Cognitive Achievement and
Gaps in Test Scores*
Michael Creel† and Montserrat Farell†
†Department of Economics and Economic History, Edifici B, Universitat Aut`onoma de
Barcelona, 08193, Bellaterra (Barcelona), Spain (e-mail: michael.creel@uab.cat,
montse.farell@uab.cat).
Abstract
Accumulation of cognitive achievement is investigated using an indirect production func-
tion, a dynamic econometric model and a rich data set. Gaps between scores of black
and white children remain constant, narrow, or disappear entirely as children grow older,
depending upon the measure and the family structure. Income elasticities are higher for
children of black families, and there are differences in elasticities with respect to parents’
educational levels. The effects of fathers’ and mothers’ educational levels differ. Between
children of two-parent families and mother-only families, there is a gap that is at least as
important as the racial gap.
I. Introduction
Much has been written on children’s cognitive achievement, its evolution over time, and
its determinants.1This is hardly surprising, given the magnitude of society’s investment
in education, and the fundamental role of learning in the future course of a child’s life.
Both individually and collectively, few issues are equally important in terms of long-term
welfare. Some recent contributions that reference and summarize previous findings are
Carneiro, Heckman and Masterov (2005), Fryer and Levitt (2004), and Todd and Wolpin
(2007). These papers find evidence that gaps widen as children grow older. Fryer and
Levitt find that controlling for covariates substantially explains gaps in scores for children
entering kindergarten, but that they subsequently increase with age. Todd and Wolpin note
that gaps in raw scores, without controlling for different levels of covariates, increase with
age. They find that the magnitude of the gaps decreases when covariates are equalized, but
they do not look at how covariate-adjusted gaps evolve as children grow older.
Using a new data set and a flexible, dynamic econometric model, weexamine two mea-
sures of cognitive achievement,the letter-word (LW)and applied problems (AP) tests from
JEL Classification numbers: D13; I20; J15; J24
*Wethank Francesc Obiols, David P´erez-Castrillo,Ferran Sancho and anonymous reviewersfor helpful comments
and suggestions.
1Haveman and Wolfe (1995) offer a general survey of the literature.
Achievement and gaps 229
the Woodcock–Johnson Revised Tests of Achievement (Woodcock and Johnson, 1989).
Wefind that gaps in covariate-controlled LW andAP test scores do not widen with age. For
stable two-parent families, gaps either narrow substantially (the LW score) or remain more
or less constant (the AP score) over the ages 6–17. For mother-only families, the result
is even stronger, with gaps in both scores narrowing and finally disappearing as children
enter their teenage years. We calculate the elasticities of LW and AP scores with respect to
conditioning variables, including parental education and family income, and look at how
these elasticities evolve over the course of childhood. The scores of black children respond
more strongly to changes in family income and mother’s education than do the scores of
white children. We also find that there is a gap in test scores between children of stable
two-parent families and children of mother-only families.This gap is especially important
for white children, and in general, the instability gap is at least as important as is the racial
gap. This adds evidence to previousresults that parental absences have a detrimental effect
on child’s academic performance (Lyle, 2006).
We begin by re-examining the theoretical underpinnings of the econometric approach
to data on cognitive achievement, from the perspective of the production function litera-
ture (Ben-Porath, 1967; Leibowitz, 1974; Todd and Wolpin, 2003). This helps us to more
carefully select which variables to include in the econometric model, and makes it clear
that endogeneity of at least some variables is likely to be of concern. We also take into
serious consideration the issue of the functional form of the cognitive achievementproduc-
tion function, in contrast to much of the literature which assumes a simple linear form. A
simple linear model is strongly rejected by statistical tests, and a more richlyparameterized
model is needed to explain the data. The richness of the econometric model allows us to
uncover dynamics in the evolution of test scores and elasticities that may be hidden by
more restrictive econometric models that impose stronger forms of parameter constancy
across groups.
Much of the literature on the evolution of cognitive achievement in economics has
made use of the National Longitudinal Survey of Youth (NLSY) and the associated Chil-
dren of the NLSY (CNLSY) data (Bureau of Labor Statistics, 2001). Korenman, Miller
and Sjaastad (1995), Neal and Johnson (1996), Blau (1999), Hansen, Heckman and Mullen
(2004), Todd and Wolpin (2007) and Carneiro et al. (2005) are examples of papers that
rely at least in part on this data. Other data sets have also been used, to a lesser extent. For
example, Fryer and Levitt (2004) use the Early Childhood Longitudinal Survey (ECLS;
National Center of Educational Statistics, 2002). Our results are based upon the Child
Development Supplement (CDS) to the Panel Study of Income Dynamics (PSID) data
(Mainieri, 2006). This data set is based upon two waves of survey data, so that cur-
rent and historical information is available for each child. Among other benefits, this
allows for conditioning on previous measures of achievement. To our knowledge, this
is the first paper that uses this data to estimate an educational achievement production
function.
The next section considers the educational production function and the econometric
issues faced when attempting to estimate it. Section III discusses the data. Section IV
presents the econometric model in detail and gives results related to the choice of the final
specification and the estimation method. Section V presents the principal findings, and
section VI gives conclusions and discusses directions for future work.
©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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