CHAPTER 13 Education production functions Eric A. Hanushek Hoover Institution, Stanford University, CESifo, IZA and NBER, Stanford, CA, United States Glossary The attention to education production func- tions is driven largely by recognition that indi- Educational production function A function that relates various inputs to education including those of families, vidual skills have significant payoffs in the peers, and schools to the maximum level of student labor market and elsewhere. Thus, a natural achievement that can be obtained question is how skills can be developed and Fixed effects A form of statistical analysis that removes the enhanced, leading to the analysis of how schools average effects of a factor (such as individual schools) and other educational inputs enter into skill from the analysis; in the case of teachers, the fixed effect in models of achievement growth is often interpreted as a development. measure of teacher quality This discussion focuses largely on evidence Value-added In the context of education production func- from the US where there is a lengthy history of tions, the value-added of an input would be the separate analysis of education production functions. The contribution of learning after allowing for other inputs focus of this work has changed over time, mov- and the base level of knowledge of the students ing from standard inputs and resources to the effectiveness of teachers. This analysis has been Overview aided by the development of much more exten- sive data bases on school performance that Much of the analysis in the economics of edu- come from school accountability systems. There cation flows from a simple model of production. has also been wider analysis of educational pro- The common inputs are things like school re- duction from other countries (Woessmann, sources, teacher quality, and family attributes; 2016). and the outcome is some measure of student achievementdfrequently but not always student test scores. Knowledge of the production func- Measuring skills and human capital tion for schools can be used to assess policy alter- natives and to judge the effectiveness and Education production functions have their efficiency of public provided services. This area roots in the more general analysis of human cap- of research is, however, distinguished from ital, but the two different streams of analysis many because the results of analyses enter quite have largely diverged in the past. Most human directly into the policy process. capital analysis has strong and direct linkages The Economics of Education, Second Edition https://doi.org/10.1016/B978-0-12-815391-8.00013-6 161 Copyright © 2020 Elsevier Ltd. All rights reserved. 162 13. Education production functions to labor market outcomes and the determination happens in schoolsdthus, it does not provide a of earnings. Education production functions, complete or accurate picture of outcomes. It as- while ostensibly closely related, have focused sumes a year of schooling produces the same more on the underlying determination of skills amount of student achievement, or skills, over and human capital. Until recently, the two time and in every country. Importantly, it also different foci have led to quite different perspec- assumes that schooling is the only input into skill tives on both the measurement of human capital development, ignoring the extensive contrary and implicitly the fundamental modeling of eco- evidence discussed below. Finally, this measure nomic outcomes. of school outcomes ignores the extensive policy Historically, human capital has been consid- debates about ways to improve school quality. ered from the labor market perspective of the in- A common extension in the investigation of dividual. In its simplest form, individuals make individual human capital and labor market out- investments that develop their skills, and this comes is the addition of cognitive skills as stock of skills is optimized for the labor market. gauged by standardized test scores to the empir- In this analysis, the most frequently employed ical models. Such skill measures have found measure of individual skills, or human capital, their way into the literature slowly, because has been school attainment, or simply years of they have just been available for a limited num- schooling completed. ber of surveys that include both achievement There are several justifications for relying on and labor market outcomes. Moreover, in these years of schooling to measure individual skills. analyses the common interpretation of these First, a prime motivation for the schools is the measures is that they represent individual “abil- acquisition of knowledge and skills, and this jus- ity” and thus can be added to a standard Mincer tifies the heavy governmental investment in earnings function to correct for any school selec- schools of nations around the world. Second, in tion bias arising from people with higher ability the early development of human capital theory, continuing longer in school. Such investigations Mincer (1970, 1974) developed a simple but of the impact of cognitive achievement include, elegant investment model for individuals that for example, Lazear (2003); Mulligan (1999); emphasized time spent in school. This theoretical and Murnane, Willett, Duhaldeborde, & Tyler development translated into one of the most suc- (2000)). In these, however, the general interpreta- cessful empirical modelsdthe “Mincer earnings tion is still that school attainment is the measure function”dthat relates individual earnings to of human capital. school attainment and to labor market experi- A complementary line of research has consid- ence. The value of school attainment as a rough ered aggregate human capital and how it affects measure of individual skill has subsequently national productivity and growth. The surge in been verified by a wide variety of studies of la- empirical analyses of growth differences across bor market outcomes (Card, 2001). Third, reli- countries begun in the early 1990s invariably ance on years of school as the human capital included measures of school attainment to reflect measure is expedient. School attainment is very the skills of the population (see Barro, 1991; commonly measured in censuses and surveys, Romer, 1990). In a subsequent comparison of allowing, for example, estimation of Mincer alternative drivers of growth rate differences, earnings functions in 139 countries (see the re- Sala-i-Martin, Doppelhofer, and Miller (2004) view in Psacharopoulos & Patrinos, 2018). found primary school enrollment to be among However, the difficulty with this common the strongest explanatory factors. Nonetheless, measure of outcomes is that it simply counts the estimated impacts of human capital and the time spent in schools without judging what other inputs appeared very unstable, casting III. Production, costs and financing Basic production function estimates 163 doubt on the line of empirical growth analyses readily interpreted in a human capital frame- (Levine & Renelt, 1992). work. Similarly, looking at long run growth in The parallel line of research into education termsofcognitiveskillshelpsresolvemanyof production functions has concentrated on under- the difficulties with empirical growth models standing the determinants of human capital. Test built on school attainment (Hanushek & Woess- scores, or measures of cognitive skills more mann, 2008). Hanushek and Kimko (2000) generally, have been interpreted as proxies for demonstrate that quality differences measured skills that are valued in the labor market and by achievement have a dramatic impact on pro- elsewhere and, as such, more immediate mea- ductivity and national growth rates. This is rein- sures of human capital differences. As described forced and extended in Hanushek and below, the overall focus of this work has then Woessmann (2012, 2015), who show that been understanding how schools and other fac- three-quarters of the variation in country tors determine the skills of individuals. growth rates can be explained by a simple But, this latter focus also leads to a very growth model that focuses on cognitive skills. different interpretation of the prior labor market Theycalltheaggregatetestscoresforcountries studies focused on school attainment. Moreover, “knowledge capital” to distinguish it from the reconsideration of the interpretation of school attainment measures that are frequently measured cognitive skills in the prior human referred to as being synonymous with human capital/labor market analyses helps to clarify capital. the problems with these prior analyses and to These recent analyses of labor market rela- point toward an alternative empirical approach. tionships with standardized achievement test Specifically, these achievement measures have scores complete the linkage between human cap- been interpreted as proxies for skills that are ital analysis from the individual labor market valued in the labor market, albeit the ability perspective and education production functions designation implies that these are fixed skills. that seek to explain differences in test scores. An alternative interpretation is that the tested This linkage provides the rationale for interpret- skills represent an explicit measure of human ing the results of education production estimates capital. If so, whether skills were determined as indicating the longer run economic effects of by schools or by other inputs would in general schools and other inputs. not affect their use and interpretation in under- standing