Testing the Technology of Human Capital Production: A General‐to‐Restricted Framework
| Author | Sam Jones |
| Date | 01 December 2021 |
| Published date | 01 December 2021 |
| DOI | http://doi.org/10.1111/obes.12374 |
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©2020 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 82, 6 (2020) 0305–9049
doi: 10.1111/obes.12374
Testing the Technology of Human Capital Production:
A General-to-Restricted Framework
Sam Jones†
†UNU-WIDER, Maputo, Mozambique
(e-mail: jones@wider.unu.edu)
Abstract
Studies of childhood developmenthave suggested human capital is accumulated in complex
and nonlinear ways. Nonetheless, empirical analyses of this process often impose a linear
functional form. This paper investigates which technology assumptions matter in quan-
titative models of human capital production. I propose a general-to-restricted procedure
to test the production technology, placing constraints on a modified McCarthy function,
from which transcendental, constant elasticity of substitution, log-linear and linear models
are obtained as special cases. Applying the procedure to data on child height from the
Young Lives surveys, as wellas cognitive skills, I find that the technology of human capital
production is neither log-linear nor linear-in-parameters; rather, past and present inputs
act as complements. I recommend that maintained hypotheses underlying functional form
choices should be tested on a routine basis.
I. Introduction
Implicitly or explicitly, the notion of a production function sits at the heart of quantita-
tive analyses of how human capital is produced, providing a framework for investigating
systematic relationships between inputs (e.g. parental background) and outputs (e.g. cog-
nitive skills). In empirical applications, estimates of such production functions invariably
invoke substantive economic assumptions regarding the nature of the available technol-
ogy of production, from which expected behavioural responses and policy insights follow
(Pritchett, 2004; Jones, 2005). For instance, if there are diminishing marginal returns to
school inputs then it may not be efficient to address learning deficits simply by increasing
the amount of schooling. Similarly, important complementarities between inputs, such as
between schooling and nutrition, may well require policy-makers to attend to inputs that
are most scarce, even though doing so may be more costly.
Although production functions play a central role in quantitative analyses of human
capital accumulation, there remains little consensus regarding which technology assump-
tions matter. Static linear technologies continue to be used extensively, particularly to
quantify educational production functions in both developed and developing countries
JEL Classification numbers: I0, J13, J24.
1430 Bulletin
(e.g. Glewwe, Jacoby and King, 2001; Glick and Sahn, 2006; Hanushek and Woessmann,
2011; Aturupane, Glewwe and Wisniewski, 2013; Rolleston, 2014). Similarly, dynamic
linear functional forms underpin a vast number of quantitative analyses of (other) human
capital outcomes, including height (Mani, 2012; Rieger and Wagner, 2015), non-cognitive
skills (Helmers and Patnam, 2011) and health (Outes and Porter, 2013; S´anchez, 2017).
Departures from a linear model are less common; but various scholars highlight statis-
tically important interaction effects across inputs in the production of education (e.g.
Becker, 1983; Behrman et al., 1997; Figlio, 1999; Baker, 2001; Levaˇci´c and Vignoles,
2002), as well as diminishing marginal returns (e.g. Harris, 2007; Ag¨uero and Beleche,
2013).
The importance of attending to nonlinearities in human capital accumulation is un-
derlined by studies of early childhood development that show early-life experiences cast
a long shadow on later life outcomes (e.g. Cunha and Heckman, 2007; Heckman, 2007;
Case and Paxson, 2009; Bleakley, 2010; Venkataramani, 2012). Even so, a limitation of
existing literature is that functional forms, be they linear or nonlinear, are often imposed
rather than explicitly tested. To address this gap, I propose a practical framework to test
the technology of human capital production. Based on a modified McCarthy function, I
show how parameter restrictions on this quite general technology yield a range of con-
ventional forms including both the transcendental and constant elasticity of substitution
functions, as well as simple Cobb–Douglas or linear models. Formally, testing down from
general to more restricted functional forms allows me to determine which technology
assumptions are (more) supported by the data. As such, this procedure incorporates ex-
plicit tests for non-constant returns to scale, substitution elasticities and parameter (log-)
linearity.
To demonstrate this general-to-restricted procedure in practice, I apply it to theYoung
Lives data from Ethiopia, India and Vietnam, focussing on child height as a general proxy
for accumulated human capital. Later, I extend the analysis to learning outcomes, using
tests of literacy and numeracy from the Uwezo surveys from East Africa. In both appli-
cations the results consistently point to fundamental nonlinearities in human capital pro-
duction – that is, both linear and simple log-linear (e.g. Cobb–Douglas) functional forms
are consistently rejected. The findings are supported by estimates from an unrestricted
translog specification, motivated as an approximation to a point in variable space (not the
true functional form), which has the advantage of a more straightforward econometric
implementation.
Before proceeding, I do not dispute that linear functional forms have a valuable role to
play in empirical work.To make conditional predictions or estimate the (short-run) impact
of policy interventions, linear estimators from the program evaluation literature are gener-
ally adequate. Nonetheless, as in previous studies, the validity of linear models becomes
suspect where the aim is to identify structural (technology) parameters or to compare es-
timates across very different contexts (White, 1980; Leamer, 2010). The contribution of
this paper is to propose a simple procedure to discriminate between alternative functional
forms and, through the empirical application, it highlights the likely inadmissibility of
linear production technologies in a range of contexts. In doing so, the study adds support
to existing studies that note the value of nonlinear functional form(s) and shows the same
insights apply quite broadly, including to research on educational development.
©2020 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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