Compensating Wage Differentials for Schooling Risk in Denmark

Compensating Wage Differentials for Schooling Risk in Denmark* Luis Diaz-Serrano National University of Ireland, Maynooth CREB, Barcelona Joop Hartog 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 JEL classification: D8, J3 Preliminary version, please do not quote.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 File: SchoolriskDK.doc * 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: [email protected].  Department of Economics. Universiteit van Amsterdam. Roetersstraat, 11. 1018WB Amsterdam. (The Netherlands). E-mail: [email protected]; Hartog is a Fellow of Tinbergen Institute, IZA and CESifo  Department of Economics, University of Aarhus, Ndr. Ringgade 1, DK-8000 Aarhus C (Denmark). Email: [email protected] 1 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 confirms this theory1. 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). 2 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 3 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 sixyear panel on hourly wages, 4 rns to education. 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 equation. Applying this technique to Spanish data, Diaz-Serrano (2001)2 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 market using a wide variety of measures derived from their theoretical model3 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 retu 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. 5 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 6 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 compensation.4 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 Yf , generating utility U(Yf ), where U( ) is a 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 Yr+  equal expected lifetime utility requires 7 00 () ( ) TT tt fr UY e dt E UY e dt      (1) where T is the length of working life and  the time discount rate. We can write the lefthand side as  0() 1 () TtT 1 f f UY e dt e UY      (2) For the stochastic term on the right-hand side we apply a third-order Taylor expansion around the expected value f Y, one order up from Pratt’s original contribution (Pratt, 1964), to  23 0 111 ( ) 1 '( ) ''( ) '''( ) 26 TtT rrrara UY e dt e U Y U Y U Y             (3) 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. 8 2 a2 a where  is the second moment (risk) and  is the third moment (skewness) of  around the expected value zero. Equating (2) and (3) and rewriting a little, after applying a firstorder Taylor expansion around Y for (2), we get r 23 23 1''1'''''1 1 rf aa aa YY UUU YYYVVV       rt r t YY 23 23 2' 6'''2 6 rr rrsr rrr rr YU UU YY YY (4) where Vr is Arrow-Pratt’s relative risk aversion and Vs is the similar definition for relative skewness affection (we call it affection, because individuals like skewness; see Hartog and Vijverberg, 2002). With Vr and Vs positive by definition, we note from (4) that individuals 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 Yf for the rest of working life, and a stochastic option given by  () 0 t E  , 22 () ta E   33 () ta E ,    ()0, ts Ets ,  (5)    We now take Yr as fixed: it’s the initial draw from the earnings distribution that contains the permanent effect discussed above5. Applying the same rules as above, we derive 23 23 11 26 rf aa rsr rrr YY VVV YYY   2 a3 a (6) Just as for permanent shocks, individuals want compensation for the risk involved in the annual shocks  and are willing to pay for the skewness in the annual shocks  . So far, 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. 15 instance, now using expression (13), in an education cell where R(4) is one unit higher wages rise a maximum around 43% (2000) and the minimum increase observed is around 20% (1987), reducing the spread between maximum and minimum to about a third of its level using R (2). An increase in one unit in K(4) causes a maximum depression in wages around 5% (2000) and a minimum around 0.7% (1987), cutting the spread in half. By using R(4) and K(4) the average effect on wages throughout the sample period are 28% and –2.5%, whereas by using R(2) and K(2) these average effects were 44.6% and –6.3% respectively. The intertemporal standard deviation of the risk-premium falls from 0.2 when R(2) is used to 0.05 for R(4). Such a remarkable fall of the dispersion also holds between K(2) and K(4) (see table 6). By applying the measures of R and K defined in (12) and (13) we observe a substantial improvement estimating the risk-premium and the skewness-penalty on wages, since they are more stable and homogeneous throughout time. The standard deviation of R(3), R(4), K(3) and K(4) is four times smaller than for R(1), R(2), K(1) and K(2). In future work we will dig deeper into the timing effects of compensation for earnings variability. For now, we just observe that the declining effects of R and K in the annual cross-sections may reflect a dominant settlement in early career years: over the sample period, the panel inevitable ages, and the early cross-sections are dominated by relatively inexperienced workers compensated for early earnings variability. The conceptual framework in section 3 pointed to supply reactions of entrants to educations and wage determination (per unit of human capital) when the entrants graduate. A relatively strong effect in early career years is compatible with this model. In later stages of the career other effects may become more important. However, precise testing requires a precise model of cohort and time effects and we will leave that for another occasion. The empirical results provided in this subsection are in accordance with the previous empirical evidence, thus we add Denmark to the selected list of countries for which the effects of risk and skewness on wages have been tested. However, in contrast to the previous literature, we base our measures of risk and skewness just on education cells, and not on occupations. This is an important improvement, as an education once completed is given and cannot be undone by selective exits as is the case with occupation cells.12.Our 12 McGoldrick (1995) uses occupation cells and cross-section data for the US data. Hartog, Plug, DiazSerrano and Vieira (2003) use occupation cells and cross-section data from Netherlands, Germany, Spain results are consistent, and at this point we can unambiguously confirm the existence of a compensating wage differentials for schooling risk in Denmark. However, there are still some issues related to the dynamics of earnings shocks and risk compensation that need to be disentangled. We face these issues in the next subsection. 5.2. Permanent and transitory shocks in earnings One of the problems associated with using annual measures on R and K as commonly done in the literature, and as indeed we did in last subsection, is their sensitivity to measurement errors. Our 17 years panel allows us to look for a long-term measure of risk13, which averages the possible measurement errors affecting the annual measures of risk over time, as we did in the previous section. On the other hand, using a big panel as ours also allows to test for compensating wage differentials for schooling risk controlling for individual heterogeneity. Hence, shocks in earnings (residuals) can be decomposed into a permanent and a transitory component. In this subsection, we estimate a Mincer earnings equation using panel data estimation, and hence we decompose residuals between transitory and permanent shocks. We then calculate separate measures of risk and skewness for both permanent and transitory shocks, and we include them in the pooled cross-section Mincer equation. Now, the model we use in the first stage is a panel data model with fixed-effects for individuals and education cells. The model is the following 16 ijtijtijt XY (14)    ln itjiijt u where the subscript i indicates individuals, and j indicates the educational cell the individual belongs to. Y is real gross yearly earnings, and X is a set of explanatory variables. In equation (14) we decompose the disturbance term as       where (15) and Portugal. And Hartog and Vijverberg (2002) use education-occupation cells and cross-section data for the US. 13 Hartog and Vijverberg (2002) emphasise the necessity of such a long-term measure to test risk compensation in wages in a more appropriate way. 2 () jh 0 j h E j h          17 2 2 it ()0 u ik ik Euu ik    E , , () 0 ks ikts otherwise        ,  222    u2 u  2)( j   The residual component ui is the time-invariant individual effect,  j is the time-invariant education cell effect, and  it is the time-variant residual effect. To our purpose controlling for heterogeneity across types of education is crucial. On one hand, this term picks up the effect of omitted variables that otherwise would “pollute”  it, and hence also our measures of R and K on transitory shocks. And on the other hand, by considering  j we ensure that total within-cell variance holds for each education cell, where is the variance of the permanent shocks and is the variance of the transitory shocks. It allow us to get consistent estimates of the variance of the transitory shocks in earnings for each education cell . We estimate  j by considering dummies for each education cell. To estimate model (14) we use the unbalanced panel design described in section 4. In order to isolate the time-invariant education effects  j, we include dummies for each education cell, thus they are added to the set of explanatory variables in X (years of schooling, age and age squared). 2   Once model (14) is estimated, we compute R and K separately for the exponential of the permanent shocks ui and the transitory shocks  it, and we include them in earnings equation (9). To estimate model (14) we restrict the sample period from 1985 to 1999, whereas we leave the samples corresponding to the first (1984) and the last (2000) year of our sample period to estimate equation (9). Define  i=exp(ui) and eit=exp(  it), hence R and K for the permanent shocks in earnings are computed as 2 1 1() j N p jijj i j RN      3 1 1() j N p jijj i j KN      (16) and for the transitory shocks 2 11 11 () j N T ijt jt ti j a j R ee    TN 3 11 () j N T ijt jt ti Kee    (17) 11 a j j TN where in both (16) and (17) the subscript j indicates the education cell the individual belongs to14. Notice that in (17) R and K are somewhat of a longitudinal schooling risk and skewness. Controlling for education cells fixed effects implies that E(  j)=0 but E(  jt)  0 since we do not control for time-specific effects. This is the reason E(  jt) enters in measures (17). In table 9 we report the basic results of the panel data estimation of equation (14)-(15). Table 10 reports some summary statistics on the distributions of Rp, Kp, Ra and Ka. These statistics reveal that once more R and K display sufficient variation across education types to look for effects on wages. Our first stage regression indicates that the variance of the permanent shock is much larger than the variance of the transitory shock. This is similar to what Chen (2003) reports for the United States 15. However, if we group the variances by education, we find that the average value of risk is smaller for permanent shocks than for transitory shocks, while the reverse holds for skewness. Insert table 9 Insert table 10 18 jjjj RK As we mentioned previously, one of the roles of the education time invariant effects in expression (15) is to control for the potentially devastating effect of omitted variables, which could bias the estimates of Rp, Kp, Ra and Ka., In the second stage estimation, we cannot include fixed education effects. However, we can test whether R and K just pick up fixed effects, and possibly represent something else than earnings variability by regressing the time-invariant education effects on R and K :     . If R and K just represent fixed effects we would find  =0 and  =0. Results reported in table 11 confirms the absence of this type of bias in Rp, Kp, Ra and Ka. Insert table 11 Insert table 12 14 We only use one specification for R (K), as table 5 shows perfect correlation between definitions (8) and (10). 15 In the literature we can find some evidence on the variance of the permanent and transitory shocks in earnings by education levels (see e.g. Olson, White and Shefrin, 1979). However, there is no evidence about these shocks using detailed education types as we do here. Thus, we cannot contrast our results for Denmark extensively with those found in other countries. Alvarez, Browning and Ejrnaes (2003) provide a detailed analysis of patterns of individual earnings residuals in Denmark and find a large amount of individual heterogeneity in parameters for residual structures. Their approach is much too refined for our purpose; and certainly one could not expect compensation for all such heterogeneity. Formatted 19 p p a a Estimations on equation (9) using R, K, R and K are reported in table 12. Model 1 and 2 estimate risk-premium and skewness affection separately for permanent and transitory shocks, whereas model 3 includes simultaneously R and K of transitory and permanent shocks. We find that in both years 1984 and 2000, our measures of risk and skewness for transitory and permanent shocks in earnings are significant and with the expected signs. This significance of R and K in both years separated by so wide an interval confirms that our findings are quite stable. Thus, they also confirm that risk is an intrinsic long-run feature of the human capital investments. For instance, taking the results in 2000 for model 1 and 2, we estimate that a one percent increase in risk is associated with 0.06% higher earnings when it comes from permanent shocks, and 0.19% higher earnings when it comes from transitory shocks. The effects of skewness for both types of shocks display a very similar intensity, and depression in wages are around 0.005% for both types of shocks. In model 3, all the effects are also very significant but with a small fall in their intensity, however these latter results have to be taken with caution due to the correlations between Rp, Kp, Ra and Ka, see table 13.16 The fact that the two types of variability are correlated may be seen as a further indication that the permanent component is not just individual heterogeneity. Why would educations with a high level of individual heterogeneity (e.g. ability) systematically also be characterized by a high level of transitory risk? It is more plausible that the high level of correlation reflects that some educations are affected by both permanent income shocks, for instance the scarring effect of graduating in a recession, and transitory business cycle effects on earnings. Insert table 13 Our results on compensating wage differentials for schooling risk reveal that transitory shocks in earnings play a more important role than permanent shocks. Permanent variability is less compensated for transitory shocks, which means that those shocks are partly associated with individual heterogeneity or ability. To the extent that this information is better known by an individual entering an education than the future transitory shocks, the required compensation for such type of risk should be smaller. Hence, the result of a smaller compensation for permanents shocks is consistent with individuals being better informed on 16 Using a rule of thumb that the correlation between regressors should not exceed 0.9, only the correlation between permanent risk and skewness constitutes a serious multicollinearity problem. permanent shocks, as they contain individual heterogeneity on which individuals are better informed than the researcher. 5.3. Earnings mobility and transitory risk Both in this paper and in earlier papers, we have established a premium on wages to compensate for the differential earnings risk associated with different educations. To measure earnings risk, we calculated statistics from earnings function residuals grouped by education. Thus we are vulnerable to the critique that such measures do not adequately measure risk. To meet this critique, we now deal with risk measures based on earnings mobility. We argue that the extent of movement of individuals through the earnings distribution is a good measure of transitory risk. In this subsection we use two different types of earnings mobility measures. The first set is based on earnings time-dependence (coefficient of rank correlation over time and minus-chi squared statistic), and the second one is based on individual earnings positional movement (quantile mobility ratio and percapita quantile movement). Define eit=exp(  it), where  it are the transitory shocks in earnings estimated from equation (14). We compute earnings mobility with a time gap of 5 years, 1985-1990, 1986-1991, and so on. The definition of the selected mobility measures applied over eit are: A. Time-dependence measures A1. We define the coefficient of rank correlation (  ) as  (18) )1( )5()(6 1)5,( 2 1 2      jj N iijij jNN trtr tt j  where the subscript j denotes the education cell the individual belongs to, rij(t) is the individual’s ranking position in the transitory earnings distribution at year t, and rij(t+5) is the individual’s ranking position at year t+5. The rank correlation determines timedependence, so that we take as time-independence 1-  j. After calculating the T-5 possible rank correlations for all our sample period we average them throughout time for each education cell 20 5 1 5 T T  1 1( ,5) j t tt       (19) Expression (19) increases with earnings mobility: a higher value represents greater earnings risk, as the ranking in a given year has less predictive power for the ranking five years later. A2. The minus chi-squared statistic is defined as   lk j p tt )1.0( )5,( 2 , 2 lk 1.0 (20) Where pk,l is the probability to move from quantile k in year t to quantile l in year t+5, and being k  l. To estimate pk,l we use a quintile transition matrix between t and t+5, averaged throughout time (21)      5 1 2)5,( 5 1T tjtt T In (21) we change the sign in order to reflect time-independence. Thus, the coefficient rises with earnings mobility: a higher value represents a higher risk, as there is more movement between the quantiles of the distribution. B. Positional mobility measures B1. We define the quantile mobility ratio Qk  l(t,t+5)=1-Qk=l(t,t+5), which is computed by a quantile transition matrix on earnings transitory shocks, as the fraction of individuals that do not remain in the same quantile between period t and t+5. This index reflects instability. We distinguish between upward fluctuations Qk<l(t,t+5) and downward fluctuations Qk>l(t,t+5), where k is the quintile where the individual is allocated in year t, and l is the same concept for year t+5. Once all the transition matrixes have been computed for each education cell we average these indexes throughout time. We use as quantiles the deciles and quartiles. B2. We define the per capita quantile mobility as (18)      5 11 )5()( 5 1T t N ij ijij j N tQtQ T 21 22 Where Qij(t) is the quantile of the earnings distribution where the individual is located in year t, and Qij(t+5) is his quantile location in year t+5. We compute these indices by each education cell and average them over time. We use deciles and the index rises with earnings mobility. In this subsection we follow the same strategy as before. Once all these movement measures on eij have been computed for each education cell, we include each of them separately in a Mincer wage equation to test for compensating wage differentials for schooling risk. To compute transition matrixes and intertemporal rankings on eit we use the panel covering the period 1995-1999, whereas to look for risk compensation we use again the first (1984) and last (2000) of our panel. As we mention above, the mobility and time-dependence measures used here are averaged over time. The results of the augmented Mincer equations are reported in table 13. Besides the earnings mobility measure, the earnings equations also include years of schooling, age, age squared, and dummies for occupation and industry. To make the results comparable we calculate the risk-wage elasticity for each mobility measure. Insert table 14 To make our results in accordance with theory, all coefficients should be positive, except those for immobility. Note first of all that all our new measures , with very similar magnitudes in both years 1984 and 2000. For instance, concerning the results in 2000, one percent increase in the rank correlation variable in a given education cell rises wages about 0.07%, whereas for the minus chi-squared and per-capita decile movement statistic such increment in wages is about 0.13% and 0.005%. The theoretical predictions are supported for the measures based on rank correlation, immobility (quartiles and deciles) and per capita decile movement. Disturbing results derive from the distinction between upward and downward movement: one would have expected the signs to be reversed, as downward movement is generally considered as undesirable and upward movement may be hailed as a boon. The negative sign for the chi-squared measure is also disturbing. These results necessitate further reflection on the extent to which they are damaging to the thesis that the labour market provides compensation for wage risk. 23 6. Conclusions In this paper we contribute with new empirical evidence to the emerging literature on risk compensation in wages. To do this we use a 17 years panel containing 10% of the Danish population, and with a very detailed description of the educational attainment of the Danes. The qualities of our data set allow an in-depth analysis of the intrinsic return-risk trade-off associated with schooling choices. Our main contribution relative to the previous literature is to focus on two aspects. First, we base our estimations on compensating wage differentials on risk measures that employ education cells only, whereas the previous evidence also relies on occupation cells. And second, we incorporate an intertemporal dimension to the post-schooling risks. We are able to distinguish transitory and permanent earnings risk. We find that both permanent and transitory risk are associated with compensationg differentials, but that transitory shocks in earnings is much more relevant for compensating wage differentials than the permanent shocks. Encouraged by this latter result and given the dynamic nature of the transitory shocks in earnings, we also experiment with tests of risk compensation using new measures of risk based on fluctuations in transitory earnings. So far, we find mixed results: support but also rejections. The new dynamic dimension introduced here fills a gap that previous evidence could not cover. We have experimented with permanent measures of risk rather than only contemporaneous ones. Clearly, these new permanent measures based on panel data catch the intrinsic long-run feature of the post-schooling risk and the required compensation for it. Our results are mostly in accordance with what theory predicts, though not for all risk measures. From our results we can derive some important implications. First, while some previous literature has revealed the important role of the length of education in the riskreturn trade-off, we find that not only the length but also the type of education plays a crucial role in this sense. And second, more risk-averse individuals facing a lower degree of risk will experience lower wage growth or even wage stagnation if they display strong preference for positively skewed wage distributions. This horizontal dimension in the schooling choices we introduce here should be taken in to account for a proper research on individuals’ curricula design and their returns. Hence, further research in this line is encouraged. Immediate extensions of our research would be to allow for selective choice of educations and test whether this is as important as many 24 believe, and to allow for the drop-out risk. There are also many new fields in this area waiting to be ploughed. 31 Table 5: Summary statistics for R(1), R(2), K(1) and K(2). Pearson Correlation R(1) R (2) K (1) K (2) R(1). R(2) K (1). K(2) Mean S. D. Mean S. D. Mean S. D. Mean S. D. 1984 0.999 0.999 0.103 0.075 0.094 0.063 0.127 0.265 0.108 0.210 1985 0.999 0.999 0.106 0.068 0.097 0.058 0.121 0.219 0.103 0.178 1986 0.999 0.998 0.114 0.078 0.103 0.066 0.147 0.288 0.123 0.226 1987 0.999 0.998 0.117 0.077 0.105 0.064 0.143 0.273 0.119 0.214 1988 0.999 0.998 0.117 0.077 0.106 0.064 0.146 0.263 0.122 0.204 1989 0.999 0.998 0.119 0.075 0.107 0.062 0.136 0.245 0.113 0.188 1990 0.999 0.999 0.122 0.091 0.109 0.074 0.165 0.443 0.135 0.326 1991 0.999 0.999 0.122 0.088 0.109 0.073 0.160 0.408 0.133 0.313 1992 0.999 0.996 0.130 0.102 0.116 0.082 0.202 0.487 0.165 0.363 1993 0.999 0.999 0.137 0.117 0.121 0.093 0.244 0.655 0.196 0.489 1994 0.999 0.999 0.150 0.142 0.132 0.112 0.310 1.140 0.241 0.805 1995 0.999 0.998 0.155 0.137 0.137 0.110 0.341 1.068 0.270 0.772 1996 0.996 0.996 0.160 0.145 0.139 0.113 0.352 1.148 0.276 0.820 1997 0.997 0.998 0.160 0.151 0.139 0.114 0.325 1.159 0.249 0.790 1998 0.998 0.997 0.164 0.141 0.144 0.110 0.350 0.987 0.276 0.692 1999 0.998 1.000 0.170 0.151 0.150 0.126 0.677 3.467 0.549 2.797 2000 0.998 0.997 0.179 0.128 0.157 0.105 0.433 0.878 0.353 0.701 Table 6: Summary of annual estimation of equation (9) Mean Std. dev Minimum Maximum R(1) 0.3806 0.1659 0.1641 0.7043 K(1) -0.0627 0.0534 -0.1663 -0.0051 R(2) 0.4466 0.1977 0.1705 0.8132 K(2) -0.0775 0.0672 -0.2018 -0.0067 R(3) 0.2412 0.0479 0.1626 0.3755 K(3) -0.0204 0.0106 -0.0448 -0.0067 R(4) 0.2813 0.0551 0.1944 0.4368 K(4) -0.0247 0.0126 -0.0541 -0.0089 Sample size 94,000 106,000 Figure 1: Annual estimation of risk premium and skewness affection using annual measures -0,4 -0,2 0 0,2 0,4 0,6 0,8 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 1 R(1) K(1) R(2) K(2) Figure 2: Annual estimation of risk premium and skewness affection using annual measures averaged over time. -0,1 -0,05 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 0,4 0,45 0,5 R(3) 32 K(3) R(4) K(4) 33 (1) (2) Table 7: Intertemporal correlations between R and R 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 1985 0.95 1986 0.95 0.96 1987 0.88 0.89 0.93 1988 0.88 0.87 0.91 0.96 1989 0.86 0.86 0.91 0.94 0.96 1990 0.88 0.84 0.88 0.90 0.91 0.94 1991 0.85 0.80 0.86 0.92 0.91 0.94 0.96 1992 0.76 0.71 0.79 0.88 0.89 0.92 0.93 0.97 1993 0.70 0.65 0.72 0.85 0.85 0.88 0.90 0.95 0.98 1994 0.74 0.68 0.75 0.82 0.85 0.88 0.93 0.94 0.96 0.96 1995 0.73 0.69 0.75 0.80 0.84 0.86 0.91 0.90 0.92 0.91 0.97 1996 0.78 0.72 0.78 0.85 0.86 0.88 0.92 0.92 0.91 0.90 0.94 0.94 1997 0.74 0.68 0.73 0.78 0.83 0.83 0.91 0.87 0.88 0.87 0.92 0.90 0.93 1998 0.77 0.73 0.76 0.82 0.85 0.84 0.91 0.89 0.86 0.84 0.90 0.88 0.90 0.94 1999 0.59 0.59 0.55 0.53 0.56 0.58 0.58 0.56 0.53 0.49 0.54 0.56 0.56 0.61 0.66 2000 0.66 0.69 0.67 0.63 0.69 0.65 0.65 0.60 0.56 0.51 0.57 0.61 0.60 0.64 0.77 0.61 Table 8: Intertemporal correlations between K(1) and K(2) 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 1985 0.95 1986 0.94 0.95 1987 0.90 0.92 0.96 1988 0.85 0.84 0.90 0.84 1989 0.87 0.84 0.90 0.85 0.92 1990 0.87 0.82 0.85 0.82 0.86 0.94 1991 0.85 0.78 0.85 0.83 0.86 0.94 0.98 1992 0.75 0.68 0.78 0.78 0.83 0.88 0.90 0.94 1993 0.80 0.75 0.82 0.86 0.81 0.89 0.92 0.95 0.94 1994 0.81 0.73 0.77 0.76 0.80 0.88 0.97 0.96 0.88 0.92 1995 0.79 0.73 0.77 0.76 0.78 0.87 0.94 0.93 0.85 0.89 0.97 1996 0.77 0.71 0.75 0.75 0.76 0.85 0.91 0.91 0.82 0.84 0.93 0.95 1997 0.80 0.73 0.74 0.72 0.77 0.84 0.94 0.92 0.83 0.88 0.97 0.93 0.92 1998 0.78 0.73 0.73 0.72 0.77 0.83 0.91 0.89 0.81 0.83 0.92 0.88 0.89 0.97 1999 0.15 0.16 0.09 0.09 0.11 0.15 0.12 0.13 0.12 0.09 0.11 0.10 0.13 0.17 0.23 2000 0.39 0.40 0.38 0.34 0.42 0.40 0.40 0.39 0.34 0.33 0.39 0.41 0.42 0.48 0.61 0.11 Table 9: Basic results for fixed-effects model (11) Coefficient t-statistic Years of schooling 0.0722 9.4 Age 0.0443 65.24 Age-squared -0.0004 -54.96 2 u  0.323 2 e 2    2 u2 e  0.161 u/( +) 0.67 R2 0.121 Number of individuals 39,399 Number of observations 458,204 Table 10: Summary statistics for R and K. Permanent shocks Transitory shocks R K R K Mean 0.1483 0.5195 0.3027 0.0372 Stand. Dev. 0.3080 3.1852 0.1086 0.1082 Percentiles 10th 0.0313 0.0044 0.1990 -0.0086 25th 0.0500 0.0137 0.2336 0.0020 50th 0.0737 0.0383 0.2810 0.0134 75th 0.1390 0.1215 0.3413 0.0348 90th 0.2634 0.4679 0.4444 0.0767 Table 11: Omitted variable bias test Model 1 Model 2 Risk (PS) -0.275 (-1.46) Skewness (PS) 0.017 (0.97) Risk (TS) 1.557 (0.74) Skewness (TS) -3.549 (-1.49) TS: Transitory shocks; PS=Permanent shocks 34 35 Table 12: Estimation of equation (9) using transitory and permanent shocks 1984 2000 Model 1 Model 2 Model 3 Model 1 Model 2 Model 3 Risk (PS) 0.3426 (16.85) 0.0485 0.2791 (10.93) 0.0395 0.4743 (20.10) 0.0672 0.2838 (9.41) 0.0403 Skewness (PS) -0.0256 (-10.01) -0.0041 -0.0132 (-3.50) -0.0021 -0.0362 (-11.96) -0.0058 -0.0218 (-4.83) -0.0035 Risk (TS) 3.8468 (13.59) 0.1142 1.4827 (4.18) 0.0445 6.3753 (20.21) 0.1912 4.0249 (10.00) 0.1207 Skewness (TS) -0.8047 (-2.33) -0.0027 -2.4304 (-3.86) -0.0082 -1.5514 (-3.64) -0.0053 -1.6788 (-2.26) -0.0057 TS: Transitory shocks; PS: Permanent shocks. t-values in parentheses Elasticity in italic Table 13: Correlations between risk and skewness for TS and PS Risk (PS) Skewness (PS) Risk (TS) Skewness (PS) 0.9192 Risk (TS) 0.5940 0.4790 Skewness (TS) 0.7521 0.7473 0.6490 TS: Transitory shocks; PS: Permanent shocks. 36 Table 14: Estimation of equation (9) using transitory earnings mobility measures 1984 2000 Coefficient Elasticity Coefficient Elasticity Rank correlation (1-) 0.0526 (4.94) 0.074 0.0496 (4.09) 0.070 Mobility quartile ratio Immobility: Qk=l(t,t+5) -0.0030 (-2.11) -0.083 -0,0102 (-6.33) -0.282 Downward mobility: 1-Qk>l(t,t+5) -0.0120 (-7.75) -0.420 -0.0062 (-3.49) -0.217 Upward mobility: 1-Qk<l(t,t+5) 0.0218 (11.95) 0.813 0.0275 (12.77) 1.026 Mobility decile ratio Immobility: Qk=l(t,t+5) -0.0058 (-2.85) -0.069 -0.0130 (-5.43) -0.156 Downward mobility: 1-Qk>l(t,t+5) -0.0108 (-7.76) -0.459 -0.0054 (-3.48) -0.229 Upward mobility: 1-Qk<l(t,t+5) 0.0170 (10.91) 0.773 0.0144 (8.02) 0.655 -2 -0.1094 (-4.62) 0.087 -0.1648 (-6.17) 0.131 Per-capita decile mobility 0.0114 (3.19) 0.006 0.0010 (2.29) 0.005 Sample size 31,504 29,226