MISMATCH IN HUMAN CAPITAL ACCUMULATION

• Author: Huacong Liu,Russell Cooper
• DOI: http://doi.org/10.1111/iere.12386
• Published date: 01 August 2019
• Date: 01 August 2019

INTERNATIONAL ECONOMIC REVIEW

Vol. 60, No. 3, August 2019 DOI: 10.1111/iere.12386

MISMATCH IN HUMAN CAPITAL ACCUMULATION∗

BYRUSSELL COOPER AND HUACONG LIU1

Pennsylvania State University, U.S.A., European University Institute, Italy,and NBER;

University of Hamburg, Germany

This article studies the allocation of heterogeneous agents to levels of educational attainment. The goal is

to understand the magnitudes and sources of mismatch in this assignment, both in theory and in the data. The

article presents evidence of substantial mismatch between ability and educational attainment across 21 OECD

countries, with a main focus on Germany, Italy, Japan, and the United States. Model parameters are estimated

using a simulated method of moments approach. The main empirical finding is that measured mismatch arises

largely from noise in test scores and does not reflect borrowing constraints. Taste shocks play a minor role in

explaining mismatch.

1. INTRODUCTION

As noted by the OECD,

Skill mismatch is one of the main challenges faced by economies. Empirical evidence shows that, in far

too many cases, workers are not well-matched with their current jobs.2

Efficiency requires the matching of high-ability people to appropriate education and eventu-

ally to productive jobs. Inefficiencies can arise along a couple of dimensions. First, the sorting

of individuals to education opportunities may be distorted. Second, frictions in labor markets

may prevent the matching of individuals, distinguished by ability and education, with appropri-

ate jobs.

This article studies the first part of the matching process: the allocation of heterogeneous

agents to levels of educational attainment. To the extent high-ability individuals have low

educational attainment and thus low-skill jobs, these forms of mismatch are related.3As we shall

see in some detail, observed educational outcomes are often at odds with the stark predictions

of assortative matching: that is, mismatch occurs when high-ability agents are not always the

most educated and some low-ability agents have high educational attainment. Our primary goal

is to understand the magnitudes, sources, and consequences of this mismatch, both in theory

and in the data.

∗Manuscript received April 2016; revised November 2018.

1Comments and suggestions from Jonathan Eaton, Martin Hackmann, Eric Hanushek, Marc Henry, Kala Krishna,

Immo Schott, Jon Willis, and Guozhong Zhu as well as seminar participants at the Federal Reserve Bank of Kansas City,

The University of Montreal, the Pennsylvania State University, the University of Alberta, and the “Occupational Skills

and the Labor Market” conference sponsored by the ZEW in Mannheim Germany are greatly appreciated. Referees

and the editor, Hanming Fang, provided guidance and suggestions that significantly improved this article. Please address

correspondence to: Russell Cooper, Department of Economics, European University Institute, Villa La Fonte, Via delle

Fontanelle, I-50014 San Domenico di Fiesole (FI), Italy. Phone: +39 3271388903. E-mail: russellcoop@gmail.com.

2This was part of a hot issues discussion by the OECD in March 2016. Source: http://skills.oecd.org/

hotissues/skillsmismatch.html. The importance of skills imbalances remains in the policy focus of the OECD. The

OECD Skills for Jobs Database provides timely information for European countries about skill shortages and surpluses.

See more interactive SKILLS FOR JOBS WEB TOOL at http://www.oecd.org/employment/skills-for-jobs-dataviz.htm

3An example is the famous taxi driver in Singapore with a Ph.D.: https://en.wikipedia.org/wiki/Cai_Mingjie. Is

he undermatched in his job or overmatched in education? Subsection 8.3 returns to this theme and discusses the

contribution of education mismatch to apparent job mismatch.

1291

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(2019) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1292 COOPER AND LIU

The article presents and analyzes cross-country OECD data. The measure of educational

attainment is dichotomous: (i) below college and (ii) college and above. Programme for the

International Assessment of Adult Competencies (PIAAC) scores, an OECD-coordinated

assessment of adult skills, are used in our analysis as noisy measures of ability for each individual

by country.4The use of these data is key to facilitating a cross-country comparison of the

relationship between ability and educational attainment.5

The empirical analysis starts with an assessment of the relationship between PIAAC scores

and educational attainment across countries. Not surprisingly, the distributions of these scores

conditional on educational attainment overlap: There are individuals with a low level of educa-

tion (no college) but a higher PIAAC score than those with high education (college). This is a

simple, but informative, indicator of undermatch.

Our formal analysis of mismatch estimates the probability an individual obtains higher ed-

ucation given an observed PIAAC score.6Using these estimates, “undermatching” occurs if

the predicted probability of a college education is relatively high but the agent does not have a

college degree. In a similar manner, “overmatching” occurs for individuals with a college degree

but a relatively low predicted probability of attending college. These estimates are obtained

using country-specific regressions. In the United States, for example, the undermatch rate is

5.5%, whereas it rises to nearly 15% in Italy. In Japan, the overmatch rate is almost 11%.

These numbers motivate our analysis. What are the sources of this measured mismatch? Does

it signal inefficiency in the allocation of individuals to education outcomes?

The theoretical framework focuses on the assignment of individuals to education levels. It

allows individuals to differ in a number of dimensions: (i) ability, (ii) tastes, and (iii) wealth. If the

only source of heterogeneity is ability, then the optimal allocation will assign higher ability agents

to higher levels of education. There is no mismatch. Once differences in tastes are present, the

optimal allocation assigns educational attainment based on both ability and tastes so that some

high-ability agents will attain relatively low levels of education. The methodology described

above would indicate mismatch, though the allocation may still be efficient. Differences in wealth

are relevant to the assignment process in a decentralized setting with borrowing restrictions. In

this case, relatively high-ability agents may choose a low level of education simply because of

a binding borrowing constraint. So both variations in tastes and binding borrowing constraints

can induce mismatch. Importantly, the borrowing constraint produces undermatch but, given

the cost of education, no overmatch.

In the model, there is another source of mismatch associated with ability being measured

instead of observed. Individuals make education decisions based upon their true ability. Test

scores, such as the PIAAC assessment, are imperfect indicators of ability. Hence, some agents

may appear to be high ability based upon test outcomes though they choose low educational

attainment based upon their true, relatively low ability. This form of mismatch reflects noise

in the measure of ability. As we shall see, this is an important source of measured mismatch in

the data.

The analysis uses this theoretical framework to identify the sources of measured under- and

overmatching. To do so, the country-specific parameters of the individual choice problems

are estimated using a simulated method of moments approach.7The degrees of over- and

undermatching, the mean education rate, the coefficients from the logistic regression used to

4See http://www.oecd.org/site/piaac/ for a complete description of this “survey of adult skills.” The use of this test in

our analysis as a proxy for ability is explained in detail below.

5Hanushek et al. (2015) use the PIAAC score as a measure of cognitive skills in Mincer wage regressions. It is clear

from that analysis that the PIAAC score is highly correlated with labor market outcomes; it is not simply noise. The

PIAAC score is statistically significant in predicting wages even when schooling is included. We use these results as

moments in our estimation. Section 5 of Hanushek et al. (2015) discusses causal interpretations, particularly reverse

causality whereby individuals with particular high skilled jobs, say obtained as the outcome of a training program,

consequently score higher on the PIAAC test.

6This follows Dillon and Smith (2017b), Smith et al. (2013), and others.

7The parameters estimated include the borrowing constraint of the household, the distributions of ability, taste

shocks, and noise in the test score as well as the returns to education.

MISMATCH IN HUMAN CAPITAL ACCUMULATION 1293

predict education outcomes, and coefficients relating wages to PIAAC scores are computed

for each of the countries.8These moments are used as a basis for the estimation of model

parameters. The estimation allows us to determine the source of mismatch across countries.

This article is clearly related to extensive studies of the effects of borrowing constraints and

educational attainment. The empirical results are mainly based on U.S. data. Using National

Longitudinal Study of Youth 1979 (NLSY79) data, Keane and Wolpin (2001), Cameron and

Heckman (2001), Carneiro and Heckman (2002), and Cameron and Taber (2004) show that,

although cost is a significant barrier to college attendance and completion, and family income

plays little role in college attendance after controlling for individual ability. Johnson (2013)

takes a more direct approach and estimates a dynamic model of education, borrowing, and

work decisions of high school graduates using the NLSY97 data. His findings indicate that

borrowing constraints have a small impact on college attainment. In examining the trends of the

effect of credit constraints on educational attainment, Belley and Lochner (2007) and Lochner

and Monge-Naranjo (2011) find that, conditional on ability and family background, parental

income matters much more for educational attainment for the NLSY97 cohort compared to the

NLSY79 cohort.

Our analysis adds to this literature in three important ways. First, we study a cross section

of countries instead of using U.S. data alone.9For European countries, there are very few

empirical studies analyzing how borrowing constraints affect educational attainment, and none

of them relates to mismatch, perhaps reflecting the relatively low cost of higher education.

Second, there is potentially larger variation in tastes, capital market structures, and educational

outcomes across these countries compared to within a single country. Third, we evaluate the

role of borrowing constraints in a structural model, focusing on the effects of these market

imperfections on mismatch.

There are four main findings in this study. First, there is evidence of substantial mismatch in

our sample, including both overmatching and undermatching.

Second, by country, mismatch reflects noise in the test scores and is not due to imperfect

capital markets or to variations in tastes for education across agents. The estimation of the

model finds no support for the presence of binding borrowing constraints.10 Further, taste

shocks contribute essentially nothing to the fit of the model. Instead, noise in the test score is

enough to generate the observed mismatch in a manner that is consistent with the estimated

dependence of the education decision and compensation on the test score. Matching these latter

moments in the estimation critically disciplines the explanatory power of noise in the test score.

From this overidentification, matching these moments from noise in the test score is nontrivial.

Third, mismatch is not a signal of inefficiency. Our simple model, relying solely on a noisy test

score, does a remarkable job of capturing cross-country variations in education rates, mismatch,

and wage premia. It does so by estimating differences in the distribution of ability, the noise

in test scores, and the return to higher education across countries. None of these sources of

variation signal an inefficiency in the allocation of individuals to educational attainment.

Stated differently, as a direct response to the above OECD quote, the mismatch in educational

attainment itself is not a direct source of inefficiency. A model of individuals, making education

choices based on their ability without borrowing constraints and minimal influence of tastes, is

perfectly consistent with data on educational outcomes, including college rates and measured

8Some of these moments are taken from Hanushek et al. (2015).

9An alternative would be to look at evidence of mismatch over time. Hoxby (2009) provides an analysis of the

changing selectively of colleges within the United States. From that analysis, sorting by test scores appears to have

changed over time, with more elite institutions evidently becoming more selective. Dillon and Smith (2017a) compare

mismatch calculated from the NLSY79 sample with that from the NLSY97 sample and find evidence of a “modest

decline” between the two samples.

10 It is interesting to contrast this with the findings of Keane and Wolpin (2001), who also study the interaction of

borrowing constraints and taste shocks. They state: “Although, as noted, borrowing constraints are estimated to be

severe, in neither of these experiments does relaxing the borrowing constraint have a significant effect on completed

schooling” (p. 1053). We do not even find that borrowing constraints bind.