Compensating Wage Differentials for
*Schooling Risk in Denmark
National University of Ireland, Maynooth
SCHOLAR, University of Amsterdam
，Helena Skyt Nielsen
University of Aarhus
Abstract: In this paper we test for risk compensation in wages using Danish panel data. With the conviction that the type of education is as important as the education length, we use a very detailed description of the type of education reached by the Danish population to calculate different measures of risk. Our long panel data set also allows us to decompose shocks in earnings in a permanent and a transitory component. We test the role of the risks associated to both components in wage compensation. We also experiment with new measures of risk based on intertemporal fluctuations on transitory shocks in earnings. Thus, we get closer to risk measures catching the intrinsic long-run feature of schooling-risks and the required compensation. In concordance to what theory predicts, we find that the labor market compensates for such foreseeable risks. Hence, we state a return-risk trade-off for the human capital investments in Denmark.
Keywords: Risk-premium, skewness affection, Schooling risk, earnings shocks. JEL classification: D8, J3
Preliminary version, please do not quote.
This version: 23/9/2003
* We appreciate financial support from the Danish Research Agency. This paper has been written while Luis Diaz-Serrano visited the Aarhus School of Business. ? Department of Economics, National University of Ireland Maynooth, Co. Kildare, Ireland. E-mail: Luis.Diaz@may.ie. ： Department of Economics. Universiteit van Amsterdam. Roetersstraat, 11. 1018WB Amsterdam. (The Netherlands). E-mail: J.Hartog@uva.nl; Hartog is a Fellow of Tinbergen Institute, IZA and CESifo ， Department of Economics, University of Aarhus, Ndr. Ringgade 1, DK-8000 Aarhus C (Denmark). E-mail: firstname.lastname@example.org
1. Introduction and motivation
After many decades of empirical research, there is no doubt that education is, on average, a profitable investment. A general agreement exists that besides being profitable, education is also a risky investment. At least two possible sources of risk can be found. First, a priori individuals may not be able to evaluate if their abilities will suffice to successfully complete the chosen level of education. And second, even if the educational process is completed successfully, they do not know where in the earnings distribution they will end up. In this paper we study the effect that this second source of risk (earnings uncertainty) exerts on wages. To the extent that the individual cannot ensure his/her returns to schooling and the variance of earnings is not constant across education, the risk premium in wages becomes as important as the average returns. While the latter has been widely studied, the risk premium has received little attention. Even though risk has been accounted for in several theoretical models, it has rarely been tested in an empirical context. Theory suggests that if risks are foreseeable they should be compensated for. The small empirical evidence on this subject
1confirms this theory. Moreover, Hartog and Vijverberg (2002) claim that individuals
display preference for a skewed earnings distribution, since they appreciate the low probabilities to obtain substantial incomes. Thus, in addition to testing the existence of risk compensation in wages, we also try to find evidence for what they call skewness “affection”.
Previous works dealing with risk compensation in wages have estimated risk as the variance in earnings by occupation cells. Skewness is measured in a similar way. In an attempt to assess risk compensation in wages more accurately, Hartog and Vijverberg (2002) used occupation-education level cells. In this paper we are able to measure the risk and skewness of the earnings associated with the type of education only. We use a variable containing a detailed description on the highest educational level reached by Danes. We consider that a risk measure based only on education cells is closer to the true risk associated with the schooling investment. When the investment decision is made, individuals do not know their future occupation only their education. With observations by schooling type, there is no problem of selective mobility that beset observations by occupation as used by Hartog and Vijverberg (2002) to generate sufficient observations on risk. Thus, our data base
1 King (1974), Feinberg (1981), McGoldrick (1995), and Hartog, Plug, Diaz-Serrano and Vieira (2003).
constitutes by itself a substantial improvement over previous empirical literature. We allow for the fact that within a given schooling level, both returns and risk may vary across educational types. For example, it is plausible that earnings distributions within the fields of Economics and Law, which attract more students, differ from those in for instance Engineering.
Taking as baseline the work in Hartog and Vijberberg (2002), in this paper we attempt to provide new empirical evidence on risk compensation in wages using Danish data. In contrast to previous literature dealing with this subject that reports evidence mainly based on cross-section data, we use a panel consisting of a 10 percent sample of the whole Danish population aged 16 and above observed during 17 years (about 500,000 observations per year). Using such a big panel allows us to separate permanent from transitory shocks in earnings, and to test if risks arising from both types of shocks are compensated for and in what manner. At the same time, our dataset also allows to experiment with new measures of risk based on earnings mobility. Thus, our contribution is not only based on the use of a wide range of educational types in measuring risk, but also on introducing a new dynamic dimension in the estimation of risk compensating differentials. Our results confirm the existence of such compensation in wages. With the aims described above, the remainder of the paper is structured as follows. In section 2 we review the existing literature dealing with risk, education and wages. In section 3 we develop a simple model on risk compensating differentials. Section 4 provides a detailed description of the data used throughout this paper. Section 5 describes the risk measures used and reports the empirical results. Finally, section 6 presents a discussion on the main implications of our empirical results and concludes.
2. Previous literature
In the economic literature, earnings uncertainty (hereafter risk) has received considerable attention. Three different approaches have been proposed. The first and most widely used approach focuses on the effect of risk on human capital investment decisions. In their seminal work Levhari and Weiss (1974) use a two-period model of educational choice and find that earnings risk acts as a disincentive on the investment in human capital. Applying also a two-period model, Eaton and Rosen (1980) analytically confirm the results by
Levhari and Weiss, while Kodde (1986) rejects them empirically by observing the contrary effect. Using a the dynamic programming framework, Williams (1979) obtains that higher risk reduces the investment in human capital. Just the opposite conclusion is found by Hogan and Walker (2001) and Belzil and Hansen (2002). Hartog and Diaz-Serrano (2002) also analyse the effect of the stochastic post-school earnings on the optimal educational length. Their theoretical model predicts that increasing risk in future income should exert a negative effect on the individual’s educational length for risk-averse individuals and
positive for “risk-lovers”. These forecasts are validated by empirical findings using Spanish data.
The second approach establishes a link between the returns to schooling, as commonly defined in the Mincerian earnings equations, and risk. Low and Ormiston (1991) considered the firsts two moments (mean and variance) of the earnings distribution in the individual’s utility function, hence they allow the returns to education to vary with the individuals’ degree of risk aversion. They find that education has a positive impact on the variance of earnings, and the returns to education tend to decrease as the individual’s level of risk aversion increases. Their findings come close to the theory we maintain that individuals facing more risk in future incomes have greater expectations for higher earnings. Harmon, Hogan and Walker (2003) specify a Mincerian earnings equation and include a variation in the parameter associated to years of schooling. They consider returns to schooling as a random coefficient. Both works represent one step further in the estimation of the returns to schooling in a risky world, where individuals differ in their level of risk aversion. Neither Hogan et al nor Ormiston and Low attempt to measure risk compensation in wages, as we do here; moreover, Ormiston and Low use a very unattractive utility function, with the reservation premium for risk increasing in income and decreasing in risk.
The third approach, in which the present work can be inserted, deals with risk compensation in wages. Although the literature on this subject is scarce and mainly focused on the US labour market, the empirical results are very consistent. Weiss (1972) was the first to consider the variance of earnings by educational levels and to correct the estimated rates of returns to schooling for different degrees of risk aversion. In a paper by King (1974) the standard deviation and skewness of earnings, computed by occupations, are regressed on the average earnings. The author finds that riskier occupations (higher variance in earnings) are associated with higher mean incomes. Using a six- year panel on hourly wages,
Feinberg (1981) accounts for the existence of compensating differentials for increased earnings-risk, measured as the individual’s intertemporal variations in earnings. He calculates the intertemporal coefficient of variation of individual earnings, and includes it as a covariate in a cross-sectional regression (last year of the panel).
McGoldrick (1995) and McGoldrick and Robst (1996) also report significant compensating differentials for earnings uncertainty and penalty for skewness affection for men and women. McGoldrick’s (1995) work introduces an important novelty by distinguishing
between systematic and unsystematic earnings. She estimates a two-step model. First, unsystematic earnings are estimated as the residuals of a standard Mincerian earnings equation that uses as regressors those variables that tend to create systematic variations in earnings (years of schooling, age or geographical location). Second, once systematic variations (variations not associated with earnings risk) are removed from earnings, the variance and skewness of the first-step residuals are included as regressors in a Mincer
2equation. Applying this technique to Spanish data, Diaz-Serrano (2001) finds significant
risk compensation and skewness penalty. Hartog, Plug, Diaz-Serrano and Vieira (2003) obtain the same result for The Netherlands, Germany, Spain and Portugal.
Our point of departure is the research on risk compensating differentials developed by Hartog and Vijverberg (2002), who support the empirical findings with a formal theoretical model. They test risk compensation and skewness affection in wages for the US labour
3market using a wide variety of measures derived from their theoretical model by using both
reduced form and structural earnings equations. Christiansen and Nielsen (2002) analyse the risk-premium in wages using a Mean-Variance type of model, and thus establish a link between human capital and finance literature. They employ very detailed data on education (the same used here), which allows them to base the risk measure only on educational levels (110 cells). Using 11 years of Danish panel data, the authors find a positive and significant effect of risk on wages. However, they do not account for skewness affection, which is crucial in assessing the magnitude and the sign of the risk-premium. Using cross-country data, Pereira and Martins (2002) establish a positive link between risk as measured from quantile regressions and returns to education.
2 Similar to King (1974), this author also concludes that individuals coming from wealthier families tend to choose riskier occupations (decreasing risk-aversion). 3 All previous studies estimate risk using the standard formula of the variance in earnings or their estimated residuals from a Mincer equation.
3. Conceptual framework
Our framework is similar to that presented in Hartog and Vijverberg (2002). Individuals face several schooling options and will only undertake them if they are sufficiently compensated. The basic Mincer earnings function allows for compensation for earnings postponement, under strict assumptions implying a constant mark-up for every additional year of schooling. In our approach we allow for the fact that individuals considering an education generally do not face some fixed income after completing a certain education. Instead they face an entire income distribution depending on the exact education which has
been chosen. Thus, investing in schooling is a risky venture as an individual simply does not know where in this distribution she will end up. Risk averse individuals will want compensation for this risk. This risk premium will emanate from market supply reactions to the wage differential for options differing in earnings risk. Insufficient risk compensation will reduce supply of labour with that education and push up the wage, until equilibrium is established.
To be more specific, assume individuals can choose between educations, equal in length, intrinsic attractivity, etc. During an education individuals accumulate human capital, but upon entering the education they do not know how much, as they do not know their aptitude for this education. The accumulation of human capital differs between individuals. Individuals know the parameters of the probability distribution for the amount of human capital at the end of the schooling period. After leaving school, their amount of human capital is public knowledge.
There is a market for human capital that determines a market clearing price per efficiency unit of human capital for every education (human capital is heterogeneous across educations, homogeneous within educations). The supply of new human capital equals the probability distribution of human capital upon graduation, multiplied by the number of graduates. Total supply equals the supply of new human capital (new graduates) plus the predetermined stock of existing human capital. Demand, in units of human capital, is a declining function of the unit price. Equality of supply and demand of human capital determines the equilibrium unit price. The expected earnings in an education, at the moment of deciding on entering this education, are equal to expected level of human capital upon graduation multiplied by the unit price of human capital (actual earnings when graduating
are equal to realised level of human capital multiplied by the unit price). We can only have long run equilibrium if the difference in expected earnings in two educations matches the required compensation for differences in risk. This requires a particular supply of new entrants to an education.
To simplify the exposition, suppose there are two options open to a potential student. The two educations are identical in all relevant aspects except for the distribution of human capital at the end of the education. Say education 2 has a greater variance of human capital upon graduation. With market clearing through equilibrium unit price operating for both educations, this translates into different variances of earnings for individuals contemplating the direction of their education. Assume all individuals are equally risk averse, implying some desired risk premium in the expected wage for education 2 relative to education 1. The realised wage differential between the two educations is determined by relative supplies of workers with the two educations. A shift from education 2 to education 1 will increase the unit price (wage) in education 2 and reduce the unit price in education 1 (because both educations have declining demand curves for human capital), thus increasing the wage gap. A long-run equilibrium exists if supply is distributed over both educations in such a way that the bid prices from the demand curves generate a wage differential that individuals find exactly compensating for the difference in risk.
So far, we only consider risk due to uncertainty about the output of the schooling process. In terms of earnings distribution this is an individual fixed effect or permanent risk: human capital produced in school is given for the rest of working life. Now, let’s add intertemporal risk. Suppose, for individuals with a given education there is some process of accumulating human capital during working life. Again, within an educational category, human capital is homogeneous. So, the market clearing unit price is determined at the intersection of the total demand curve for human capital of a given type and total supply: number of new graduates multiplied by mean level of human capital produced in school plus number of workers of each experience class multiplied by their level of human capital. Suppose the demand curve is shocked every year: the equilibrium value of a unit of human capital fluctuates randomly over time. Assume the parameters of this process are public knowledge. Then individuals embarking on an education know how much intertemporal variation in earnings they must anticipate. As before, they will take that into account when choosing their education, and only enter when the compensation for risk is sufficient. With
a given stock of experienced workers, long-run equilibrium again obtains if the number of entrants leads to supplies that precisely uphold the wage gap requested as risk
We can derive the required compensation for risk from imposing equal expected lifetime utility for all educations. For the sake of exposition, we assume that there is one option that has fixed earnings in every year that an individual works. We ignore experience effects for individuals in all options. We will also ignore compensation for postponing earnings when going to school, as this is taken care of in the usual Mincer mark-up.
Consider first the permanent effect from risky human capital production. In the riskless alternative, annual earnings are given as Y, generating utility U(Y), where U( ) is a f f
concave utility function with U’ > 0, U” < 0 and U’” > 0 (the latter condition is necessary
for declining absolute risk aversion, see Tsiang, 1974 or Hartog and Vijverberg, 2002). In the risky option, income is a single draw for the rest of working life, written as Y+~ equal r
expected lifetime utility requires
TT(1) ？？))tt UYedtEUYedt()()，？~fr?? 00
where T is the length of working life and ) the time discount rate. We can write the left-
hand side as
T1？？))tT UYedteUY，？()1();；(2) ff?0)
For the stochastic term on the right-hand side we apply a third-order Taylor expansion
Yaround the expected value , one order up from Pratt’s original contribution (Pratt, 1964), f
T111??？？))23tT UYedteUYUYUY~??()1'()''()'''()？，？？？(3) ;；rrrara???026)??
4 Random fluctuation of the demand for human capital is only one way of generating intertemporal earnings risk. Stochastic production of human capital in on-the-job training and job search processes are alternatives. The precise underpinning of intertemporal risk is immaterial for our purpose, all we need is a foreseeable intertemporal earnings risk in an individual’s working life.
22where is the second moment (risk) and is the third moment (skewness) of ~ around ??aa
the expected value zero. Equating (2) and (3) and rewriting a little, after applying a first-
Yorder Taylor expansion around for (2), we get r
2323 YY？????1''1'''''11UUUrfaaaa ，？？，？YYYVVV(4) rrrrsr2323YUUU2'6'''26YYYY rrrrr
where V is Arrow-Pratt’s relative risk aversion and V is the similar definition for relative rs
skewness affection (we call it affection, because individuals like skewness; see Hartog and Vijverberg, 2002). With V and V positive by definition, we note from (4) that individuals rs
will only enter an education if the permanent effect from unknown human capital production is matched by a positive premium for the risk (variance), while they allow an earnings drop for skewness.
Let’s now consider the transitory component of risk. Again, let there be a riskless option, with earnings fixed at Y for the rest of working life, and a stochastic option given by f
2233E()0~，Ets()0,~~，?, , , E()~?，E()~?，tsttata
We now take Y as fixed: it’s the initial draw from the earnings distribution that contains the r
5permanent effect discussed above. Applying the same rules as above, we derive
23 YY？??11rfaa ，？VVV(6) rsr23Y26YY rrr
Just as for permanent shocks, individuals want compensation for the risk involved in the
23annual shocks and are willing to pay for the skewness in the annual shocks . So far, ??aa
we have assumed that individuals only know the parameters of the distributions of human capital production in school and shifts in demand (equilibrium unit prices) over time. It is this risk they need to be compensated for. But suppose they would have full information over their individual fixed effect: individuals can perfectly predict how much human capital
5 Instead of annual shocks coming from the same distribution every year, we might make the distribution conditional on time or experience. We have decided to leave such complications for later work.
they will get out of the education, or, less demanding, they perfectly predict their ranking in the human capital distribution. In that case, the individual fixed effect entails no risk as individuals themselves simply know the realized value and not only the distribution they draw from. Hence they would require no compensation. Thus, including the fixed effect in an empirical analysis is a test on information: if individuals are sure of their position in the distribution upon graduation, they will not be compensated for the dispersion in that distribution, if they don’t know it, it will be a risk for them and they need such compensation. More generally we can say that the extent of compensation for permanent variability relative to transitory variability will reflect the relative degree of information that individuals have on their prospects, i.e a relative measure of risk versus individual
6heterogeneity. Similarly, the correlation between the transitory and permanent variability would suggest whether the permanent variability might reflect foreseeable earnings risk. If the correlation is high, it is unlikely that the permanent variability just reflects individual heterogeneity.
4. The data
We use data collected by Denmark Statistics, which represents a 10 percent random sample of the Danish population aged between 16 and 75 over the period 1984-2000 (about 500,000 individuals per year). The data contains detailed information on the individuals’ labour situation, occupation, education, social and family status. The variables we use in this study are real gross yearly earnings, age, occupation, industry, and the highest level of education attained. The education variable contains 1,750 different categories. Nevertheless, in order to have a representative number of individuals in each education cell, we group this variable in a new one with 75 categories. In order to avoid selectivity problems on female labour force participation we restrict our sample to male wage earners. We start by selecting those cohorts of working men who were aged between 30 and 40 in 1984. There are three reasons for imposing this age restriction. First, we avoid selectivity problems due to early retirement decisions. Second, we ensure that the selected individuals have already completed their educational process. And third, by excluding young workers entering the
6 We owe this interpretation to Wim Vijverberg