Chapter 7 EARNINGS FUNCTIONS, RATES OF RETURN AND TREATMENT EFFECTS: THE MINCER EQUATION AND BEYOND1 JAMES J. HECKMAN Department of Economics, University of Chicago, 1126 East 59th Street, Chicago, IL 60637, USA e-mail: [email protected] LANCE J. LOCHNER Department of Economics, University of Western Ontario, 1151 Richmond Street N, London, ON, N6A 5C2, Canada e-mail: [email protected] PETRA E. TODD Department of Economics, University of Pennsylvania, 20 McNeil, 3718 Locust Walk, Philadelphia, PA 19104, USA e-mail: [email protected] Contents Abstract 310 Keywords 310 1. Introduction 311 2. The theoretical foundations of Mincer’s earnings regression 315 2.1. The compensating differences model 315 2.2. The accounting-identity model 316 Implications for log earnings–age and log earnings–experience profiles and for the inter- personal distribution of life-cycle earnings 318 1 Heckman is Henry Schultz Distinguished Service Professor of Economics at the University of Chicago and Distinguished Professor of Science and Society, University College Dublin. Lochner is Associate Professor of Economics at the University of Western Ontario. Todd is Professor of Economics at the University of Pennsylvania. The first part of this chapter was prepared in June 1998. It previously circulated under the title “Fifty Years of Mincer Earnings Regressions”. Heckman’s research was supported by NIH R01-HD043411, NSF 97-09-873, NSF SES-0099195 and NSF SES-0241858. We thank Christian Belzil, George Borjas, Pedro Carneiro, Flavio Cunha, Jim Davies, Reuben Gronau, Eric Hanushek, Lawrence Katz, John Knowles, Mario Macis, Derek Neal, Aderonke Osikominu, Dan Schmierer, Jora Stixrud, Ben Williams, Kenneth Wolpin, and participants at the 2001 AEA Annual Meeting, the Labor Studies Group at the 2001 NBER Summer Institute, and participants at Stanford University and Yale University seminars for helpful comments. Our great regret is that Sherwin Rosen, our departed friend and colleague, who thought long and hard about the issues discussed in this chapter could not give us the benefit of his wisdom. Handbook of the Economics of Education, Volume 1 Edited by Eric A. Hanushek and Finis Welch © 2006 Elsevier B.V. All rights reserved DOI: 10.1016/S1574-0692(06)01007-5 308 J.J. Heckman et al. 3. Empirical evidence on the Mincer model 320 4. Estimating internal rates of return 327 4.1. How alternative specifications of the Mincer equation and accounting for taxes and tuition affect estimates of the internal rate of return (IRR) 330 4.2. Accounting for uncertainty in a static version of the model 338 5. The internal rate of return and the sequential resolution of uncertainty 342 6. How do cross-sectional IRR estimates compare with cohort-based estimates? 358 7. Accounting for the endogeneity of schooling 364 7.1. Estimating the mean growth rate of earnings when ri is observed 367 7.2. Estimating the mean growth rate when ri is not observed 369 7.3. Adding selection bias 369 7.4. Summary 370 8. Accounting systematically for heterogeneity in returns to schooling: What does IV estimate? 370 8.1. The generalized Roy model of schooling 374 8.2. Defining treatment effects in the generalized Roy model and relating them to true rates of return 381 8.3. Understanding why IV estimates exceed OLS estimates of the schooling coefficient 386 8.4. Estimating the MTE 390 8.5. Evidence from the instrumental variables literature 392 8.6. The validity of the conventional instruments 403 8.7. Summary of the modern literature on instrumental variables 406 9. Estimating distributions of returns to schooling 407 Example 1. Access to a single test score 413 Example 2. Two (or more) periods of panel data on earnings 415 10. Ex ante and ex post returns: Distinguishing heterogeneity from uncertainty 417 10.1. A generalized Roy model 418 10.2. Identifying information sets in the Card model 420 10.3. Identifying information sets 422 10.4. An approach based on factor structures 424 10.5. More general preferences and market settings 428 10.6. Evidence on uncertainty and heterogeneity of returns 429 10.6.1. Identifying joint distributions of counterfactuals and the role of costs and ability as determinants of schooling 430 10.6.2. Ex ante and ex post returns: Heterogeneity versus uncertainty 437 10.6.3. Ex ante versus ex post 438 10.7. Extensions and alternative specifications 441 10.8. Models with sequential updating of information 441 11. Summary and conclusions 442 Appendix A: Derivation of the overtaking age 446 Appendix B: Data description 448 Census data 448 Current Population Survey (CPS) data 449 Ch. 7: Earnings Functions, Rates of Return and Treatment Effects 309 Tuition time series 449 Tax rate time series 449 Appendix C: Local linear regression 450 Tests of parallelism 451 References 451 310 J.J. Heckman et al. Abstract Numerous studies regress log earnings on schooling and report estimated coefficients as “Mincer rates of return”. A more recent literature uses instrumental variables. This chapter considers the economic interpretation of these analyses and how the availabil- ity of repeated cross section and panel data improves the ability of analysts to estimate the rate of return. We consider under what conditions the Mincer model estimates an ex post rate of return. We test and reject the model on six cross sections of U.S. Cen- sus data. We present a general nonparametric approach for estimating marginal internal rates of return that takes into account tuition, income taxes and forms of uncertainty. We also contrast estimates based on a single cross-section of data, using the synthetic cohort approach, with estimates based on repeated cross-sections following actual co- horts. Cohort-based models fitted on repeated cross section data provide more reliable estimates of ex post returns. Accounting for uncertainty affects estimates of rates of return. Accounting for se- quential revelation of information calls into question the validity of the internal rate of return as a tool for policy analysis. An alternative approach to computing economic rates of return that accounts for sequential revelation of information is proposed and the evidence is summarized. We distinguish ex ante from ex post returns. New panel data methods for estimating the uncertainty and psychic costs facing agents are reviewed. We report recent evidence that demonstrates that there are large psychic costs of schooling. This helps to explain why persons do not attend school even though the financial re- wards for doing so are high. We present methods for computing distributions of returns ex ante and ex post. We review the literature on instrumental variable estimation. The link of the estimates to the economics is not strong. The traditional instruments are weak, and this literature has not produced decisive empirical estimates. We exposit new methods that interpret the economic content of different instruments within a unified framework. Keywords rate of return to schooling, internal rate of return, uncertainty, psychic costs, panel data, distribution JEL classification:C31 Ch. 7: Earnings Functions, Rates of Return and Treatment Effects 311 1. Introduction Earnings functions are the most widely used empirical equations in labor economics and the economics of education. Almost daily, new estimates of “rates of return” to school- ing are reported, based on numerous instrumental variable and ordinary least squares estimates. For many reasons, few of these estimates are true rates of return. The internal rate of return to schooling was introduced as a central concept of human capital theory by Becker (1964). It is widely sought after and rarely obtained. Under certain conditions which we discuss in this chapter, high internal rates of return to ed- ucation relative to those of other investment alternatives signal the relative profitability of investment in education. Given the centrality of this parameter to economic policy making and the recent interest in wage inequality and the structure of wages, there have been surprisingly few estimates of the internal rate of return to education reported in the literature and surprisingly few justifications of the numbers that are reported as rates of return. The reported rates of return largely focus on the college–high school wage differential and ignore the full ingredients required to obtain a rate of return. The re- cent instrumental variable literature estimates various treatment effects which are only loosely related to rates of return. In common usage, the coefficient on schooling in a regression of log earnings on years of schooling is often called a rate of return. In fact, it is a price of schooling from a hedonic market wage equation. It is a growth rate of market earnings with years of schooling and not an internal rate of return measure, except under stringent conditions which we specify, test and reject in this chapter. The justification for interpreting the coefficient on schooling as a rate of return derives from a model by Becker and Chiswick (1966). It was popularized and estimated by Mincer (1974) and is now called the Mincer model.1 This model is widely used as a vehicle for estimating “returns” to schooling quality,2 for measuring the impact of work experience on male–female wage gaps,3 and as a basis for economic studies of returns to education in developing countries.4 It has been estimated using data from a variety of countries and time periods. Recent studies in growth economics use the Mincer model to analyze the relationship between growth and average schooling levels across countries.5 Using the same type of data and the same empirical conventions employed by Mincer and many other scholars, we test the assumptions that justify interpreting the coefficient on years of schooling as a rate of return. We exposit the Mincer model, showing con- ditions under which the coefficient in a pricing equation (the “Mincer” coefficient) is 1 See, e.g., Psacharopoulos (1981), Psacharopoulos and Patrinos (2004) and Willis (1986) for extensive surveys of Mincer returns.