Compensation for earnings risk under worker heterogeneity.

• Author: Berkhout, Peter

1. Introduction

   In the standard Mincer earnings equation, the rate of return to education is estimated as the regression coefficient of log earnings on years of schooling. Under strict conditions, it is the compensation for postponing earnings by going to school. The basic model underlying the equation assumes a world without risk: Future earnings for any length of schooling are known for sure at the time the schooling entry decision has to be made. Yet, the prevalence of risk surrounding the choice of education and occupation barely needs elaboration. An individual considering an education does not anticipate some level of post-school earnings but an entire distribution of earnings. And generally, the individual will not know for sure where in that distribution she will end up. She cannot fully anticipate her abilities to benefit from the education, she does not know her future proficiency in the occupations that follow after school, and she cannot predict with perfection the future market value of the skills learned in school--uncertainties abound. The uncertainties will not be identical for every potential education, and hence, they will affect the individuals' choices. And with individuals generally shying away from risk, a properly functioning labor market will generate compensation for such risk. Much recent research seeks to refine or even question the standard Mincer model by focusing on endogeneity biases and on the theoretical basis of the simple model itself (heterogeneity and self-selection). Here, we tackle the issue of compensation for risk; we will do so in a conventional setting.

   The first article to test the hypothesis of compensation for unpredictable earnings variation with individual data is Feinberg (1981), with positive results on data for the United States. (1) In a series of recent articles, compensation for earnings risk has also been established for several other countries: the Netherlands, Denmark, Portugal, Germany, Spain, and China (2) (for a survey of results, see Hartog [2007]). Expected earnings are indeed higher for occupations and educations with higher earnings variance. Most interestingly, they are lower for occupations and education types that are more skewed. The relevance of skew was first established by King (1974) and later reiterated by McGoldrick (1995). Intuitively, positive skew points to the favorable odds of ending up with a very high income rather than with a very low income, something people appreciate and are willing to pay for. Appreciation for skew (or skew affection) can also be shown to be required for absolute risk aversion declining in wealth (or income), a condition one can hardly dispute. Skew affection has been confirmed empirically in betting behavior and lottery participation (see Hartog and Vijverberg [2007] for references).

   In most studies, compensation for risk aversion and skew affection has been established at the level of occupations, sometimes in combination with a few education types. Risk and skew are measured as variance and third moment of residuals from a Mincer earnings equation, after grouping residuals by occupation. However, observation of occupational attachment may severely be affected by risk, as workers may move out after receiving bad earnings draws. Such selective mobility is not possible at the level of education, as individuals cannot undo their accomplished education. In this article, we will use observations grouped by 66 to 100 types of education for the Netherlands. (3)

   Using residuals of a contemporaneous Mincer equation has been criticized as confounding unobserved heterogeneity and risk. Jacobs, Hartog, and Vijverberg (2009) shows that if individuals have superior information on their ability, and therefore also better information on their risk, this may indeed bias the estimated coefficient of risk compensation, but the direction of the bias cannot be predicted. The risk compensation coefficient is essentially estimated as the ratio of the wage gap between a risky and a riskless education and the variance of earnings in the risky education. Both terms are biased upward: The wage gap contains the reward for the superior ability that allows absorption of some risk, and the observed variance contains the effects of ability heterogeneity. Hence, the direction of the bias in the ratio cannot be predicted. Therefore, one cannot play down the results obtained thus far as obvious overestimates of the risk compensation coefficient. Not only the magnitude but also the direction of the bias should be established by further empirical investigation.

   Actually, it is not at all obvious that we should be concerned about this kind of unobserved heterogeneity. A market will establish compensation for risk based on what students perceive this risk to be. We are not dealing with true risk but with the risk that must be compensated. This leads to the question of what factors student perceptions are based on. Direct evidence on students' expectations on the financial benefits of education indicates that they seem mostly anchored on perceptions of earnings for graduates already in the labor force, without adjustment for the individual's specific characteristics. This implies that we would be justified in using the residual variance from market wages as our measure of risk, without correction for selectivity (Wolter 2000; Nicholson and Souleles 2001; Brunello, Lucifora, and Winter-Ebmer 2004; Webbink and Hartog 2004; Schweri, Hartog, and Wolter 2007). To some extent this is also an empirical question: We can try to discover what happens if we add person-specific information on ability. In this article, we will use examination grades from secondary school as an indicator of ability and test whether it has an impact on estimated risk compensation. Of course, the results will not settle the big question on the disputed need for selectivity correction, but big questions can be addressed by many small pieces of evidence. We will condition individuals' perceptions of risk (and skew) associated with tertiary education on their school grades in secondary education. We partition the sample of students in quartiles and calculate risk and skew as the residual variance (and skew) for the school grade quartile to which they belong. (4)

   McGoldrick (1995) focuses on differences in risk compensation between men and women. She finds that American women, in 1980, get a higher premium for risk and a lower penalty for skew. This is an interesting result, as women are commonly found to be more risk averse than men. We will analyse differences between men and women but also between natives and immigrants and between the private and the public sector. We will do this in a context of potentially heterogeneous risk attitudes.

   The Mincer earnings function, with log wages linear in schooling years and quadratic in potential experience, is a standard specification in empirical work. As noted above, research in the last decade has emphasized the endogeneity of schooling, heterogeneity, and self-selection (see Card 1999; Polachek 2007). The models that have been developed and estimated have painted a richer picture of the returns to education than the ordinary least squares (OLS) Mincer equation suggests. Still, in this article we will start out from the basic homogenous model underlying the Mincer equation. This is simply a matter of research strategy, as we consider the canonical earnings equation a natural starting point for our empirical work.

   The contributions of this article are the following. First, we improve on earlier work for the Netherlands and the United States by using observations by education rather than by occupation, thus eliminating the problem of selective mobility once individuals are in the labor market. Our regressions solidly replicate the standard results. Second, we will show that the basic results survive if we control for ability as evidenced by school grades. And finally, we will analyze differences between different groups of individuals and determine whether they match with anticipations: men and women, natives and immigrants, public and private sector, vocational and academic training. Here we find mixed results, and perhaps the main conclusion is that more complicated modeling is needed. We will briefly outline the underlying model in section 2, introduce the data in section 3, present the basic results in section 4, and then compare results for subgroups in section 5. Section 6 concludes the discussion.

2. The Risk Augmented Mincer Equation

   Hartog and Vijverberg (2007) formally derive the Risk Augmented Mincer equation; this article just presents the main argument. Assume individuals face two alternatives: They can go straight to work and earn an annual nonstochastic income [Y.sub.0] for the rest of their working life (5) or go to school for s years and after school earn income [Y.sub.s] for the rest of their working life; [Y.sub.s] is stochastic with realization of [Y.sub.s] revealed right after completing schooling. We assume individuals have an uninhibited choice between alternatives, just as in the seminal Mincer framework. In equilibrium, lifetime utility should be equal. Hence, we require

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

   Working life has length T, schooling takes s years, [delta] is the discount rate, [Y.sub.0] is riskless no-schooling earnings, [Y.sub.s] is earnings after s years of schooling with expected value [[mu].sub.2]. In line with Mincer's logarithmic earnings function, we specify a multiplicative stochastic component [epsilon]. We seek to determine the compensation for s years of schooling and a risky outcome as opposed to starting work right away at a certain wage.

   We write the stochastic post-school earnings option as markups (6) on the safe no-schooling alternative, [[PI].sub.s] for risk [M.sub.s] for postponing earnings:

   [Y.sub.s] = [[mu].sub.s] [e.sup.[epsilon]] = [(1 -...