Is thre a Risk-Return Trade-off accross Occupations? Evidence from Spain

Is there a Risk-Return Trade-off across Occupations? Evidence from Spain Luis Diaz-Serrano♣ National University of Ireland, Maynooth IZA, Bonn CREB, Universitat de Barcelona Joop Hartog♦ FEE-SCHOLAR, Universiteit van Amsterdam Abstract: We use data from Spain to test for an effect of earnings risk and skewness on individual wages. We carry out separate estimation for men, women, public and private sector employees. In accordance with previous evidence for the US we show the existence of a risk-return trade-off across occupations in the Spanish labour market. These results are in conformity with preferences of risk-averse individuals with decreasing absolute risk aversion. JEL code: J3, D8 Keywords: Risk-aversion, skewness affection, occupational choices, compensating wage differentials. ♣ 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: J.Har[email protected]. 1 1. Introduction In a riskless world, choosing an occupation should be, undoubtedly, an easy task. In such a case, individuals can make their choice just maximizing the earnings across occupations. However, in a risky world like ours, where the fact that workers are averse to fluctuations in their incomes is universally recognised, such a decision becomes much more complicated. Such a fluctuations in earnings is what we call earnings risk. Economic theory suggests that if these risks are foreseeable, they should be compensated for. In the empirical literature on compensating wage differentials there exist a wide variety of studies analysing the effect of different sources of risk in the job place on wages. However, this literature is mainly focused on injury or fatality risks. As Adam Smith we claim that in a competitive labour market there must exist a way of compensation in those occupations that entail a higher probability of failure (higher variance in earnings) in order to attract sufficient supply. While uncertainty in labour income is accounted for in most theoretical models it has been rarely tested apart from some exceptions in the US. Additionally, there is also a growing literature that shows the relevance of the skewness of the returns in many economic decisions. For example, Garret and Sobel (1999) and Golec and Tamarking (1998) find evidence that risk-averse individuals playing lottery games and betting in horse races in the US base their participation decision on the skewness of the prize distributions, respectively. Prackash et al. (2003) found empirical evidence from Latin American, US and European capital markets that investors do trade expected return of the portfolio for skewness. DiazSerrano (2004) empirically supports that positive skewness favour homeownership in Germany and Spain. And Hartog and Vijverberg (2002) in the US and Diaz-Serrano, 2 Hartog and Nielsen (2004) in Denmark shows that individuals appreciate positively skewed income distributions, and they incorporate this information into their educational choices. In this paper, we empirically test for the Spanish labor market whether risk-averse workers are compensated for earnings risks in their occupational choices, and whether there is a willingness to pay for positive skewness in their incomes. The remainder of the paper is structured as follows. In section 2 the existing literature in this issue is extensively reviewed. Section 3 presents the theoretical background. In section 4 we describe the empirical framework. In section 5 we describe the dataset. We carry out the empirical analysis in section 6. And section 7 summarizes and concludes. 2. Literature review In labour economics there is a growing literature dealing with earnings risk and its effects on individuals’ behaviour in the labour market. This literature considers three different approaches, the effect of risk on the human capital investment, on the occupational choices, and on the compensating wage differentials. 2.1. Earnings risk and schooling choices Levhari and Weiss (1974) built a two period model with the choice between working or studying during the first period, and stochastic earnings during the second period for those who attended education in the first period. In their theoretical model they obtain that increasing earnings risk reduces the investment in education. Kodde (1986) built on Levhari and Weiss model’: in his theoretical model he finds an ambiguous effect, but his empirical estimation suggests increasing demand for 3 education with increasing risk. Snow and Warren (1990) found that human capital decreases with increasing risk in its future returns if such investment is an inferior activity and individuals exhibit decreasing risk aversion. Williams (1979) applied dynamic programming to the education decisions, where production and depreciation of human capital and future wages are all stochastic. He concludes, under conditions, that higher risk in the production of human capital reduces investment in schooling. Belzil and Hansen (2002) and Hogan and Walker (2002) also used the dynamic programming framework, both models find that individuals prefer to stay at school longer with increasing risk in future earnings. The first argue that it is because while being at school they receive non risky parental income, the second attribute this result to the increased value of waiting for a good earnings draw. The work of Hartog and Diaz-Serrano (2002) constitutes one of the few empirical studies on this issue. They develop a human capital model for optimum schooling length with stochastic earnings and highlight the pivotal role of risk attitudes and the schooling gradient of earnings risk. Their empirical estimation uses Spanish data on high school graduates deciding on attending university education. They find that the basic response to increasing earnings risk is negative but that in households with lower risk aversion, the response will be dampened substantially and may even be reversed to positive. 2.2. Occupational choices Orazem and Mattila (1986) developed an empirical model of occupational choice under uncertainty. They considered the first two moments of the earnings distribution (mean and variance) within various alternative occupations. Their 4 empirical results confirm that increasing mean and decreasing variance of the earnings distribution increase the probability of choosing a given occupation. Siow (1984) estimated supply curves assuming uncertainty in the future wages and tenure of the occupational choice by a cohort of entrants into an occupation. This author used a sample of American lawyers. De Meza (1984) also analysed occupational choices under wage uncertainty, this author finds that increasing risk decreases individual’s utility. 2.3. Risk compensation in wages This literature starts with King (1974) using aggregated data regressed the variance and the skewness by occupation cells on average earnings, observing a positive effect for variance and negative for skewness in the US labour market. McGoldrick (1995) built on King’s work and using US microdata obtained the same results. McGoldrick and Robst (1996) studied the effect of workers mobility on compensating differentials for earnings risk. They observe that workers with high mobility receive smaller compensations for earnings risk, since they show preference for uncertain situations. Also in the context of the US labour market, Feinberg (1981a) estimated significant wage compensation for earnings risk using a 6-years panel. He estimated earnings-risk as the coefficient of variation of individual yearly earnings during the sample period. And Feinberg (1981b) also finds that workers experiencing employment instability in their occupations are compensated for. Hartog and Vijverberg (2002) were the first to provide a formal modelling on risk compensation in wages. Using US data they estimated structural equations measuring risk and skewness by occupation-education cells, and they observe a positive compensation for risk and a penalty for skewness in wages. Diaz-Serrano, 5 Hartog and Nielsen (2003) also estimated positive compensation for risk using Danish panel data. They estimated risk using just education cells and provide new estimates by experimenting with several dynamic measures of earnings risk and skewness. They also found a significant positive effect of the variance and negative for the skewness on wages. 3. Theoretical background As we mention in the previous section, there is a wide number of studies that considers an effect of earnings uncertainty in the educational an occupational choices. However, a little has been said yet about skewness. Tsiang (1974) found theoretical support that risk-averse individuals display preference for skewness, in addition to aversion to dispersion (risk), of the probability distribution of the returns in economic decisions that entail an uncertain outcome. This result suggests that since increasing absolute risk aversion is absurd, decreasing absolute risk aversion requires that individuals appreciate higher moments as e.g. skewness. Other well established theories also emphasize around this finding. For example, prospect theory (Kahneman and Tversky, 1979, 1991) states that the individual’s disutility caused by a loss is greater than the utility caused by a gain of the same size, which goes in the same direction as Tsiang’s findings. These arguments suggest that if we assume future earnings attached to an occupational/educational choice to be uncertain, both the variance and skewness of earnings, in addition to the mean, should be considered when analyzing how these choices are planned and achieved. To understand how such a compensation mechanism in wages may arise we follow Hartog and Vijvenberg (2002) and Diaz-Serrano et al. (2004). Assume that a riskaverse individual has to choose between two occupational options that only differ in risk. 6 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+ ε . Equal expected lifetime utility requires 00 () ( ) TT tt fr UY e dt E UY e dt ρρ ε −− =+ ∫∫ (1) where T is the length of working life and ρ the time discount rate. We can write the lefthand side as () 0 1 () 1 () TtT f f UY e dt e UY ρρ ρ −− =− ∫ (2) For the stochastic term on the right-hand side we apply a third-order Taylor expansion around the expected value r Y, one order up from Pratt’s original contribution (Pratt, 1964), to () 23 0 111 ( ) 1 ( ) ''( ) '''( ) 26 TtT rrrprp UY e dt e UY U Y U Y ρρ ε σκ ρ −− ⎡ ⎤ +=− + + ⎢ ⎥ ⎣ ⎦ ∫ (3) where 2 p σ is the second moment (risk) and 2 p κ is the third moment (skewness) of ε around the expected value zero. Equating (2) and (3) and rewriting a little, after applying a first-order Taylor expansion around r Y for (2), we get 23 23 23 23 1 '' 1 ''' '' 1 1 2'6'''2 6 rf p p p p rrrrsr rrr rr YY UUU YYYVVV YUUU YY YY σκ σκ −=− − = − (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 7 individuals only enter an occupation if the permanent effect from an unknown occupational outcome is matched by a positive premium for the risk (variance), while they allow an earnings drop for skewness. 3. Empirical framework Assume that earnings of an individual can be expressed as follows isj s ij YY η = , (5) where Yisj are the observed earnings of individual i with education S in occupation j, Ys= µ sY0 are the expected earnings of an individual with education level S, with Y0=exp(X β ), and η ij=exp(uij) is a term picking up specific effects on earnings of individuals’ occupation. This specification allows individuals with the same schooling to earn different wages. Appling logarithms in both sides of (5) we get log log ij s i ij YXu µ β = ++ , (6) where X are the observable determinants of Yij, log µ s is the fixed effect of education on wages, and uij is the effect on wages of occupation j for individual i. Expression (6) provides the familiar Mincer mark-up model. If wages include a compensation for risk in labour earnings, uij can be decomposed as follows 23 ij j j j i uu λασ γκ =+ + +, (7) where λ j are the occupation fixed-effects, 2 j σ is the variance of earnings within occupations, 3 j κ is the skewness, and ui is a random term normally distributed with 0 mean and constant variance across individuals. By substituting (7) in (6), the complete specification of individuals’ earnings can be expressed as 8 23 log log isjijji YX u µλ βασγκ =+++++ , (8) The existence of a risk compensation requires α >0, whereas the so called “skewness affection” that entails a penalty in wages requires γ <0. We take as suitable measures of 2 j σ (hereafter Rj) and 3 j κ (hereafter Kj) the variance and the skewness of the observed earnings by occupations cells, respectively. We decompose earnings according to the source of variation, i.e. systematic and unsystematic component. Systematic fluctuations in earnings are caused by supply variables (e.g. human capital), which are usually known by individuals, and therefore, have nothing to do with risk. However, unsystematic variations in earnings catch variations which are unknown by individuals when they have to make their choice of education and ensuing occupation. They reflect indeed the risk to the individual: their as yet unknown abilities, suitability for her job, and hence relative position in the occupations’ earnings distribution. They also reflect demand factors (e.g. business cycle or shocks in output demand) and they are expected to generate compensating wage differentials. Hence, suitable measures of risk and skewness in wages require that systematic variation in wages shall be purged from observed earnings, since otherwise the true relationship between risk and wages might be obscured. We use a two-step method to test for risk compensation in the earnings equation (8). 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(1979): “Uncertainty and the accumulation of human capital over the lifecycle”, Journal of Business 52, pp. 521-48. 18 Table 1: Sample descriptive statistics Full sample Women Men Public sector Private sector Mean STD Mean STD Mean STD Mean STD Mean STD Age 37,14 12,09 34,03 11,40 38,54 12,14 39,10 11,48 36,46 12,23 Women 0,31 0,46 0,38 0,49 0,29 0,45 Married 0,36 0,48 0,31 0,46 0,38 0,48 0,41 0,49 0,34 0,47 Household size 4,14 1,54 4,02 1,57 4,19 1,52 3,93 1,51 4,22 1,54 # of children 0,57 0,50 0,52 0,50 0,59 0,49 0,55 0,50 0,58 0,49 Years of schooling 8,39 4,29 9,21 4,40 8,03 4,19 10,78 4,65 7,56 3,83 Log(yearly wages) 13,87 0,83 13,55 0,89 14,01 0,75 14,19 0,74 13,76 0,83 Dummies industry Agriculture 0,08 0,26 0,05 0,21 0,09 0,28 0,01 0,12 0,10 0,30 Energy 0,02 0,14 0,00 0,07 0,03 0,16 0,02 0,14 0,02 0,14 Chemical 0,03 0,17 0,01 0,11 0,04 0,20 0,02 0,13 0,04 0,19 Mechanics 0,08 0,26 0,02 0,14 0,10 0,30 0,02 0,13 0,10 0,29 Other manufactures 0,13 0,33 0,13 0,34 0,12 0,33 0,01 0,11 0,16 0,37 Construction 0,10 0,30 0,01 0,11 0,14 0,35 0,02 0,14 0,13 0,34 Commerce 0,16 0,37 0,19 0,39 0,15 0,35 0,02 0,12 0,21 0,41 Transport 0,06 0,23 0,03 0,16 0,07 0,26 0,08 0,28 0,05 0,22 Banking 0,05 0,22 0,05 0,21 0,05 0,22 0,01 0,10 0,06 0,24 Other services 0,30 0,46 0,51 0,50 0,21 0,41 0,79 0,40 0,13 0,34 Dummies occupation Managerial 0,01 0,10 0,00 0,05 0,01 0,12 0,01 0,10 0,01 0,10 Professionals 0,09 0,29 0,13 0,33 0,08 0,27 0,23 0,42 0,04 0,20 Scientists 0,07 0,26 0,11 0,31 0,05 0,23 0,12 0,33 0,05 0,22 Technicians 0,13 0,33 0,20 0,40 0,09 0,29 0,19 0,39 0,10 0,31 Clerical 0,21 0,41 0,37 0,48 0,14 0,34 0,16 0,37 0,23 0,42 Qualified workers 0,06 0,24 0,00 0,07 0,08 0,28 0,04 0,18 0,07 0,25 Clerical 0,08 0,28 0,01 0,11 0,12 0,32 0,05 0,22 0,10 0,30 Manual workers 0,33 0,47 0,18 0,38 0,39 0,49 0,14 0,35 0,39 0,49 Other 0,02 0,14 0,00 0,07 0,03 0,16 0,06 0,24 0,01 0,08 Public workers 0,26 0,44 0,32 0,46 0,23 0,42 Dummies location Urban area 0,58 0,49 0,62 0,49 0,56 0,50 0,70 0,46 0,53 0,50 Region 1 0,40 0,49 0,39 0,49 0,40 0,49 0,40 0,49 0,40 0,49 Region 2 0,37 0,48 0,37 0,48 0,37 0,48 0,40 0,49 0,36 0,48 Region 3 0,23 0,42 0,24 0,43 0,23 0,42 0,20 0,40 0,24 0,43 Sample size 18132 5620 12512 4675 13457 19 Table 2: Probit estimates for female participation Coefficient Z-stat Constant Primary education Secondary education Higher education Age Age square Children Married Number of wage earners Urban area -3.6399 (-18.6) 0.1565 (2.5) 0.3684 (8.4) 1.0198 (4.3) 0.1098 (8.7) -0.0016 (-6.8) -0.2909 (-4.7) 0.3725 (7.1) 0.5089 (3.8) 0.1374 (4.2) 0 – Non-participant 1 – Participant 15569 5620 Sample size 21189 Notes: Endogenous variable is female participation. Estimates include dummies for region. 20 Table 3: Probit estimates for public-private sector choice Coefficient Z-stat Intercept Primary education Secondary education Higher education Actually studying Age Age square Female Children Married Urban Region 1 Region 3 Scientists Professionals Operators Administrative White-collars Blue-collars -4.1242 (-16.1) 0.3698 (4.6) 0.9197 (10.1) 1.6174 (16.0) 0.4602 (6.5) 0.0998 (7.9) -0.0008 (-7.3) 0.2351 (7.4) -0.1505 (-3.4) 0.1630 (3.7) 0.2127 (7.1) 0.0728 (1.6) -0.4938 (-9.7) 0.5552 (6.1) 0.1760 (2.1) 0.1258 (1.6) -0.3535 (-4.8) -0.6774 (-7.4) -0.9382 (-13.0) Public sector Private sector 4675 13417 Sample size 18092 Note: Endogenous variable is working in the private sector. 21 Table 4: OLS and two-step estimates of equation (2) used to purge systematic earnings. Full sample Males Females Females1Public2 Private2 Constant Schooling Exp. Exp. square Exp. cube Female Urban Region 1 Region 3 Correction term 12.2383 (397.8) 0.0969 (71.1) 0.0757 (18.2) -0.0014 (-7.2) 6.4·10-6 (2.5) -0.4507 (-41.2) 0.1319 (12.6) -0.0937 (-8.2) 0.1044 (7.9) 12.1515 (334.6) 0.0849 (57.8) 0.0937 (18.9) -0.0018 (-8.1) 8.9·10-6 (3.1) 0.1374 (11.9) -0.0963 (-7.6) 0.1105 (7.5) 11.6686 (212.2) 0.1182 (44.3) 0.0843 (11.3) -0.0025 (-6.7) 2.6·10-5 (4.9) 0.1274 (6.1) -0.0872 (-3.8) 0.1052 (4.1) 11.6906 (103.7) 0.1198 (41.1) 0.0835 (11.1) -0.0025 (-6.7) 2.5·10-5 (4.9) 0.1293 (6.2) -0.0860 (-3.7) 0.1079 (4.2) -0.0403 (-1.3) 13.0405 (110.1) 0.0658 (17.5) 0.0736 (10.4) -0.0017 (-7.4) 1.4·10-5 (3.4) -0.3178 (-17.9) 0.1263 (6.2) -0.0829 (-4.2) 0.1147 (4.6) -0.2856 (-7.1) 12.4335 (328.0) 0.0675 (24.8) 0.0613 (12.3) -0.0011 (-4.8) 2.6·10-6 (0.8) -0.5673 (-42.4) 0.1268 (10.4) -0.1006 (-7.4) 0.2034 (12.2) 0.3992 (9.9) Sample size 17919 12512 5251 5251 4675 13457 Notes: (1) Heckman’s selectivity correction (2) Lee’s selectivity correction 22 Table 5: Summary statistics for estimated R (risk) and K (skewness). Risk Skewness Mean STD Mean STD Total 0.631 0.867 3.502 3.140 Industry Agriculture 0.804 0.897 5.608 1.421 Energy 0.561 0.333 2.681 1.838 Chemical 0.588 0.887 2.255 1.999 Mechanics 0.500 0.935 2.653 1.952 Other manufactures 0.660 0.774 3.493 3.331 Construction 0.801 0.424 8.096 4.493 Commerce 0.809 1.506 2.976 1.810 Transport 0.791 0.549 4.100 2.959 Banking 0.492 0.694 2.529 1.811 Other services 0.457 0.505 2.143 2.070 Education Incomplete primary 0.666 0.572 4.973 3.738 Primary 0.678 0.835 3.955 3.421 Secondary 0.602 1.057 2.971 2.247 University 0.484 0.816 1.690 1.361 Job level Managerial 0.782 0.463 1.380 0.974 Professionals 0.421 0.094 1.284 0.453 Scientists 0.600 0.346 1.907 1.750 Technicians 0.419 0.024 3.081 1.230 Clerical 0.597 0.663 2.601 2.051 Qualified workers 1.813 2.807 5.840 2.683 Clerical 0.455 0.117 3.280 1.516 Manual workers 0.649 0.482 5.046 4.215 Other 0.240 0.151 1.153 0.487 Age 18 to 25 0.600 0.541 3.424 3.009 25 to 35 0.624 0.846 3.386 3.045 35 to 45 0.645 1.003 3.461 3.157 45 to 55 0.643 0.898 3.751 3.376 55 to 65 0.665 1.062 3.699 3.213 Sector Private 0.685 0.952 3.853 3.281 Public 0.476 0.525 2.492 2.427 Gender Men 0.676 0.974 3.993 3.418 Women 0.532 0.550 2.409 2.019 23 Table 6: Estimation of returns to schooling, returns to risk and skewness penalty for several workforce groups1. (t-statistics in parenthesis) Full sample Males Females Public2 Private2 Intercept Schooling Risk Skewness Correction term 12.4281 (227.6) 0.0686 (37.3) 12.4140 (227.5) 0.0682 (37.1) 0.0377 (6.3) 12.4250 (226.0) 0.0679 (36.8) 0.0390 (6.5) 0.0199 -0.0027 (-2.7) -0.0096 12.4033 (212.8) 0.0610 (30.3) 0.0401 (6.8) 12.4221 (213.1) 0.0601 (29.7) 0.0424 (7.4) 0.0246 -0.0045 (-2.8) -0.0155 11.5004 (154.3) 0.0784 (19.4) 0.0140 (1.5) 11.8744 (110.9) 0.0783 (19.4) 0.0528 (4.2) 0.0359 -0.0527 (-4.8) -0.1012 13.5375 (67.4) 0.0531 (8.8) 0.0127 (0.4) -0.3270 (-3.8) 13.5005 (61.5) 0.0513 (8.5) 0.2330 (3.2) 0.0862 -0.0890 (-3.4) -0.0898 -0.3403 (-4.0) 12.2944 (116.5) 0.0525 (16.9) 0.0240 (7.3) 0.3288 (4.5) 12.3326 (116.1) 0.0521 (16.8) 0.0278 (7.9) 0.0181 -0.0063 (-3.0) -0.0119 0.3273 (4.5) Sample size 17919 12512 5251 4675 13457 Notes: (1) Full model specification includes a cubic polynomial on years of experience, and dummy controls for gender, family status, geographical, industry and occupations (2) Lee’s selectivity correction