Bayesian inference in a correlated random coefficients model: Modeling causal effect heterogeneity with an application to heterogeneous returns to schooling

We consider the problem of causal effect heterogeneity from a Bayesian point of view. This is accomplished by introducing a three-equation system, similar in spirit to the work of Heckman and Vytlacil (1998), describing the joint determination of a scalar outcome, an endogenous “treatment” variable, and an individual-specific causal return to that treatment. We describe a Bayesian posterior simulator for fitting this model which recovers far more than the average causal effect in the population, the object which has been the focus of most previous work. Parameter identification and generalized methods for flexibly modeling the outcome and return heterogeneity distributions are also discussed.Combining data sets from High School and Beyond (HSB) and the 1980 Census, we illustrate our methods in practice and investigate heterogeneity in returns to education. Our analysis decomposes the impact of key HSB covariates on log wages into three parts: a “direct” effect and two separate indirect effects through educational attainment and returns to education. Our results strongly suggest that the quantity of schooling attained is determined, at least in part, by the individual’s own return to education. Specifically, a one percentage point increase in the return to schooling parameter is associated with the receipt of (approximately) 0.14 more years of schooling. Furthermore, when we control for variation in returns to education across individuals, we find no difference in predicted schooling levels for men and women. However, women are predicted to attain approximately 1/4 of a year more schooling than men on average as a result of higher rates of return to investments in education.     

Reanalyzing Zero Returns to Education in Germany

Pischke and von Wachter (Review of Economics and Statistics 2008; 90 (3): 592–598) find zero earnings returns to compulsory schooling in the basic school track in Germany. We reanalyze their study using a different dataset. In an extension, we use additional instruments which allow estimation of heterogeneous effects for different groups of compliers. We can confirm the previous result and also find zero returns for other compliers in higher track schools. Moreover, we do not find a causal effect of schooling on cognitive skills. This is in line with a potential reason Pischke & von Wachter (2008) give for their result, namely that basic skills are learned earlier in Germany and additional years of schooling are no longer effective. Copyright © 2015 John Wiley & Sons, Ltd.     

Doubly Robust Estimation of Causal Effects with Multivalued Treatments: An Application to the Returns to Schooling

This paper provides doubly robust estimators for treatment effect parameters which are defined in a multivalued treatment effect framework. We apply this method to the unique dataset of the 1970 British Cohort Study (BCS70) to estimate returns to various levels of schooling. The analysis is carried out for female and male samples separately to capture possible gender differences. Average returns are estimated for the entire population, as well as conditional on having a specific educational achievement. For males, relative to no qualification, we find an average return to O‐levels of 6.3%, to A‐levels of 7.9% and to higher education of 25.4%. The estimated average returns to O‐level and A‐level relative to no qualification are insignificant for females, whereas the return to higher education is 19.9%.Copyright © 2014 John Wiley & Sons, Ltd.     

After, before and during: returns to education in Hungary (1986–1998)

How valuable are the skills acquired under socialism in a market economy? This paper throws light on this question using unique data covering the years before and during transition (1986–1998) for about 3 million Hungarian wage earners. We find that returns to a year of schooling increased by 75% from 6.4% in 1986 to 11.2% in 1998. We also find that the private sector rewards formal education more than the public and, in terms of gender, although in 1986 women had greater returns to schooling than men, by 1998 this difference had been eliminated.     

Estimates of the return to schooling and ability: evidence from sibling data

We use sibling data on wages, schooling, and aptitude test scores from the 1979 National Longitudinal Survey of Youth (NLSY79) to obtain OLS, family fixed effects, and fixed effects instrumental variable estimates of the return to schooling for a large sample of non-twin siblings. Following recent studies that use identical twin samples, we use sibling-reported schooling as an instrument for self-reported schooling. Controlling for aptitude test scores has a substantial impact on estimated returns to schooling even within families, and there is a large return to test scores that is comparable in size within and between families. We also find that the return to schooling is higher for older brothers than for younger brothers and for women than men. Finally, because the NLSY79 contains multiple sibling reports of education for the same individual, we are able to test and reject the overidentifying restrictions for the validity of sibling-reported schooling as an instrumental variable.     

The effects of families and ability on men's education and earnings in Britain

The paper estimates the returns to education for a cohort of men born in Britain in March 1958 who have been followed since birth until the age of 33. The data used has a wealth of information on family background including parental education, social class and interest shown in the child's education as well as measures of ability. These variables are typically missing in studies looking at the returns to schooling. In the paper, we find that the average return to an additional year of full-time education for the UK men is somewhere around 5 1/2% to 6% even after correcting for the effects of measurement error. The paper also presents evidence that the returns to an additional year of schooling in the UK are heterogeneous. In particular, the paper finds some evidence that men with lower tastes for education, have significantly higher marginal returns to education. The results of the paper suggest that recent IV estimates of the returns to schooling in the UK, which exceed typical OLS estimates, may overestimate the average marginal return for the population of men as a whole.     

THE COLLAPSE OF PRIMARY SCHOOLING RETURNS IN SOUTH AFRICA 1960–90

By 1975, the effect of a year's primary schooling upon the wages of Africans in South Africa had fallen to about 2.5 percent — one of the lowest primary schooling returns in the world. Secondary schooling returns were high throughout the period 1960–90. The collapse of primary schooling returns was due to declining school quality, an increase in the supply of primary school graduates, an increase in mining wages in the mid-seventies, and wage regulation by the Industrial Councils and Wage Boards. The low level of the return, compared with the returns to other races in South Africa, is due to the low quality of African primary schools. Implications for education spending patterns and wage regulation are pointed out.     

Multidimensional skills and the returns to schooling: Evidence from an interactive fixed-effects approach and a linked survey-administrative data set

This paper presents new evidence on returns to schooling based on an interactive fixed-effects framework that allows for multiple unobserved skills with potentially time-varying prices as well as individual-level heterogeneity in returns. This constitutes a substantive generalization of most existing approaches. Our empirical analysis employs a unique linked survey-administrative panel data set on education and earnings. We find average marginal returns to schooling of about 2.8–4.4% relative to least squares/instrumental variable estimates between 7.7% and 12.7%. Omitted ability accounts for a larger fraction of the aggregate least squares bias compared to heterogeneity. We also find considerable heterogeneity in individual returns.     

EDUCATION AND ENTREPRENEURSHIP SELECTION AND PERFORMANCE: A REVIEW OF THE EMPIRICAL LITERATURE

Abstract This paper provides a review of empirical studies into the impact of formal schooling on entrepreneurship selection and performance in industrial countries. We describe the main effects found in the literature, we explain the variance in results across almost a hundred studies, and we put the empirical results in the context of related economic theory and the much further developed literature in labor economics (studying the rate of return to education among wage employees). Five main conclusions result from this meta‐analysis. First, the impact of education on selection into entrepreneurship is insignificant. Second, the effect of education on performance is positive and significant. Third, the return to a marginal year of schooling is 6.1% for an entrepreneur. Fourth, the effect of education on earnings is smaller for entrepreneurs than for employees in Europe, but larger in the USA. Fifth, the returns to schooling in entrepreneurship are higher in the USA than in Europe, higher for females than for males, and lower for non‐whites or immigrants. In conclusion, we offer a number of suggestions to move the research frontier in this area of inquiry. The entrepreneurship literature on education can benefit from the technical sophistication used to estimate the returns to schooling for employees.     

The external returns to education: UK evidence using repeated cross-sections

Augmenting a Mincerian earnings function with industry level data we estimate the external return to schooling for a repeated cross-section of individuals in the UK over the period 1994–2004. For men age 30–49 we find that a one year increase in the industry average level of schooling is associated with an increase in individual wages of 2.6 to 3.9%, around 2 to 3 fifths of the private return to schooling. We illustrate the sensitivity of external return estimates to industry ICT use and union density, and individuals' own level of schooling.     

Were there no returns to education in the USSR? Estimates from Soviet-period household data

The relation between wages and schooling in the USSR is studied, by estimating log–linear wage-equations for a sample of a Russian city in 1989. Estimates, made separately for men and women, show that there were rewards to education, contrary to claims by many Soviet and Western scholars. The low wages of some professionals, relative to skilled workers, were partly caused by gender differentials, partly by excess demand for manual labour. In addition, private costs of schooling were low and there were important non-monetary incentives connected with higher education.     

Average and Marginal Returns to Upper Secondary Schooling in Indonesia

This paper estimates average and marginal returns to schooling in Indonesia using a semiparametric selection model. Identification of the model is given by geographic variation in access to upper secondary schools. We find that the return to upper secondary schooling varies widely across individuals: it can be as high as 50% per year of schooling for those very likely to enroll in upper secondary schooling, or as low as ?10% for those very unlikely to do so. Average returns for the student at the margin are substantial, but they are also well below those for the average student attending upper secondary schooling. Copyright © 2016 John Wiley & Sons, Ltd.     

How Does Education Affect the Earnings Distribution in Urban China?*

It is widely believed that investing in education could be an effective strategy to promote higher standards of living and equity. We empirically assess this claim by estimating returns to education across the whole earnings distribution in urban China and find supporting evidence. In particular, we find that returns to education are more pronounced for individuals in the lower tail of the distribution than for those in the upper tail and that returns to education are uniformly larger for women than men. We also find that returns to education increased over time across the whole earnings distribution.     

The Returns to Education: Microeconomics

In this paper we focus on education as a private decision to invest in "human capital" and the estimation of the rate of return to that private investment. While the literature is replete with studies that estimate the rate of return using regression methods where the estimated return is obtained as the coefficient on a years of education variable in a log wage equation that contains controls for work experience and other individual characteristics, the issue is surrounded with difficulties. We outline the theoretical arguments underpinning the empirical developments and show that the evidence on private returns to the individual is compelling. Despite some of these issues surrounding the estimation of the return to schooling, our evidence, based on estimates from a variety of datasets and specifications, is that there is an unambiguously positive effect on the earnings of an individual from participation in education. Moreover, the size of the effect seems large relative to the returns on other investments.     

Estimating the returns to education for Australian youth via rank-order instrumental variables

This paper employs the rank-order instrumental variable (IV) procedure of Vella and Verbeek [Vella, F., Verbeek, M., 1997. Using rank order as an instrumental variable: an application to the return to schooling, CES Discussion Paper 97.10, K.U. Leuven.] to estimate the returns to education for Australian youth. The attraction of this approach is that it can account for the endogeneity of schooling in the wage equation via the use of instrumental variables without the use of exclusion restrictions. We find, after accounting for the endogeneity of schooling, that an additional year of schooling is associated with an increase in wages of approximately 8%. Furthermore, we find that the rank-order IV approach is able to identify the presence of endogeneity in this particular empirical example. However, despite this, the adjusted estimate of how schooling affects wage is close to the ordinary least squares (OLS) estimate.     

Gender and competition

In almost all European Union countries, the gender wage gap is increasing across the wage distribution. In this 2008 presidential lecture I briefly survey some recent studies aiming to explain why apparently identical women and men receive such different returns and focus especially on those incorporating psychological factors as an explanation of the gender gap. Research areas with high potential returns to further analysis are identified. Several examples from my own recent experimental work with Patrick Nolen are also presented. These try to distinguish between the role of nature and nurture in affecting behavioural differences between men and women that might lead to gender wage gaps.     

Training subsidies and the wage returns to continuing vocational training: Evidence from Italian regions

We use the regional and time variation of training grants in Italy to identify the causal effect of (formal continuing vocational) training on earnings. We estimate log-linear earnings regressions with constant marginal returns to training and find that one additional week of training increases monthly net earnings by 1.36%, substantially less than the 3% or more often found in the literature. Estimated returns vary significantly by firm size, and range from 0.40% in firms with more than 100 employees to 2.51% in smaller firms, the bulk of the Italian private sector. A simple back of the envelope comparison of the marginal costs and benefits of training policy suggests that the latter are higher than the former.     

Returns to Schooling and Bayesian Model Averaging: A Union of Two Literatures

Abstract.  In this paper, we review and unite the literatures on returns to schooling and Bayesian model averaging. We observe that most studies seeking to estimate the returns to education have done so using particular (and often different across researchers) model specifications. Given this, we review Bayesian methods which formally account for uncertainty in the specification of the model itself, and apply these techniques to estimate the economic return to a college education. The approach described in this paper enables us to determine those model specifications which are most favored by the given data, and also enables us to use the predictions obtained from all of the competing regression models to estimate the returns to schooling. The reported precision of such estimates also account for the uncertainty inherent in the model specification. Using U.S. data from the National Longitudinal Survey of Youth (NLSY), we also revisit several 'stylized facts' in the returns to education literature and examine if they continue to hold after formally accounting for model uncertainty.     

Investment and concern for relative position

Economists typically analyze individuals' market behavior in isolation from their nonmarket decisions. While this research strategy has generally been successful, it can lead to systematic errors when agents' nonmarket behavior affects their market choices. In this paper we analyze how individuals' investment behavior changes as a result of nonmarket behavior. Specifically, we analyze a model in which individuals must decide how to allocate their initial endowment between two random investments, where the returns are perfectly correlated across individuals for the first investment but independent across individuals for the second. We consider an environment in which men and women match, with wealthier individuals more successful in matching. We show how individuals' concern about relative wealth can affect their investment decisions, and we provide conditions under which individuals bias their investments either toward or away from the investment with correlated returns. A modification of the model is used to explain why agents' investments might exhibit a home country bias.     

New Men and New Women? A Comparison of Paid Work Propensities from a Panel Data Perspective

British Household Panel Survey data for waves 1–5 (1991–5) is used to compare paid work participation rates of men and women. Year-on-year persistence in paid work propensities is high, but greater for men than women. Non-work persistence is higher for women. Using panel data probit regression models, we also investigate why men's and women's participation rates differ, comparing the roles of differences in observable characteristics and differences in rates of return to these characteristics, while also controlling for unobserved heterogeneity. Most of the difference in participation rates is accounted for by the differences in returns associated with the presence of children, especially young ones.