InterÞrm Mobility, Wages, and the Returns to Seniority and Experience in the U.S. † Moshe Buchinsky‡ Brown University, CREST—INSEE and NBER Denis Foug`re e CNRS, CREST—INSEE, and CEPR Francis Kramarz CREST—INSEE and CEPR and Rusty Tchernis Brown University May, 2001 † We thank Andrew Foster, Oded Galor, and Tony Lancaster for their comments and discussions. ‡ Correspondingauthor, Department of Economics, Brown University, Box B, Providence, RI 02912. Email: Moshe Buchinsky@Brown.edu. 1 Introduction Much of the research in labor economics during the 1980s and the early 1990s was devoted to the analysis of changes in the wage structure across many of the world’s economies. In particular, wage inequality has been one of the prime topics of investigation. Only recently, has research turned to the analysis of mobility in its various guises. A large share of this recent effort has linked mobility with instability (see Farber (1999) for a detailed assessment), while a smaller fraction has been devoted to the analysis of mobility of individuals through the wage distribution (see Buchinsky and Hunt (1999)). The shift in focus is not surprising, because measures of inequality alone are not sufficient to assess changes in the wage determination process. For example, it is vital that we have more information in order for us to be able to understand changes in the respective roles of general- and Þrm-speciÞc human capital. This is an especially important issue when examining, for example, technological changes induced by computerization and globalization. While wage inequality increased in the United States during most of the 1980s, in France and some other European countries it was generally stable. Nevertheless, during the same period almost all countries witnessed a sharp decrease in wage mobility.1 This decline in wage mobility indicates that changes in wage inequality may be worse than previously thought. Furthermore, workers are more likely to be in a worse situation if there is an increase instability of jobs, as has been documented in the United States for males (see, again, Farber (1999), for a discussion of the evidence). Decreased wage mobility and increased job instability makes increasing wage inequality (as in the U.S.) or a high unemployment rate (as in France) less tolerable than if mobility through the distribution were relatively high. In general, workers’ wages may change through two channels. Workers can stay in the same Þrm for some years and collect the return to their Þrm-speciÞc human capital (seniority), in that particular Þrm. Alternatively, they can switch to a different employer if their outside wage offer exceeds that of their current employer or when they become unemployed. These two possibilities can be empirically investigated. If Topel (1991) is right, then the Þrst scenario provides a more plausible explanation for understanding wage increases. However, if Altonji and Williams (1997) are correct, then interÞrm mobility is necessary for wage increases to 1 See, for example, Buchinsky and Hunt (1998) for the U.S. and Buchinsky, Foug`re, and Kramarz (1998) for e France. 1 occur. Some comparative results (which do not take selection biases into account) seem to show that interÞrm mobility is associated with larger absolute changes in wages (e.g. Abowd, Finer, Kramarz, and Roux, (1997)), but there are also considerable variations in the returns to seniority across Þrms (e.g. Abowd, Finer, and Kramarz, (1999) for the U.S., and Abowd, Kramarz, and Margolis, (1999) for France). The analysis of these two channels constitutes the prime motivation for this study, which lies at the intersection of two classical Þelds of labor economics: (a) the analysis of interÞrm and wage mobility; and (b) the analysis of returns to seniority. The basic statistical model gives rise to three equations: (1) a participation equation; (2) a wage equation; and (3) an interÞrm mobility equation. In this model the wage equation is estimated simultaneously with the two decision equations, namely the decision to participate in the labor force and the decision to move to a new Þrm. Each equation includes a person-speciÞc effect and an idiosyncratic component. The participation and mobility equations also include lagged decisions as explanatory variables. We use the Panel Study of Income Dynamics (PSID) to estimate the model for three edu- cation groups: (1) high school dropouts; (2) high school graduates with some post-high school education; and (3) college graduates. We adopt a Bayesian approach and employ methods of Markov Chain Monte Carlo (MCMC) to compute the posterior joint distribution of the model’s parameters. Our main Þnding is that returns to seniority are quite high for all education groups. In contrast, the returns to experience appear to be lower than previously thought. While we use a somewhat different sample than the one used by Topel (1991), the results we obtained regarding the return seniority are, qualitatively, similar to Topel’s results, while the results for the return to experience differ somewhat. Consequently, our estimate of total within-job growth is lower than Topel’s estimate, but closer to other analyses reported in the literature (e.g. Altonji and Shakotko (1987), Abraham and Farber (1987), and Altonji and Williams (1997)). The closest papers in the literature to our paper are Dustmann and Meghir (2001) and Neal (1995) who analyzed similar questions but took different routes. SpeciÞcally, they did not explicitly model the decisions of the individuals that are directly related to the observed endogenous variables. Nevertheless, Dustmann and Meghir (2001) employed data and econometric methods which allowed them to identify the various components of wage growth, namely general, sector-speciÞc, and Þrm-speciÞc human capital. In contrast to all previous studies, in the current study we explicitly model the participation and mobility decisions. We Þnd that the effects of seniority 2 and experience differ for all education groups. However, in this study, unlike other studies in the literature, our modeling strategy also allows us to examine the individuals’ “optimal” mobility patterns for maximizing their wage growth over their lifetime.2 We Þnd that the optimal job durations differ markedly across education groups. The remainder of the paper is organized as follows. In Section 2, we outline the model and the econometric speciÞcations. Here we also introduce the likelihood function, which makes it clear why the usual (“frequentist”) maximization routines are virtually impossible to imple- ment. Section 3 presents the details of our numerical techniques for computing the posterior distribution of the model’s parameters. A brief discussion of the data extract used in this study is provided in Section 4. Section 5 presents the empirical results of the estimation procedure. Section 6 follows with a brief conclusion. 2 The Model and the Likelihood Function 2.1 The Model We use a statistical model that is suited to the incorporation of key elements that are important to labor markets and wage setting outcomes. The model consists of three equations. The Þrst equation is a participation equation, reßecting the individual’s choice of whether or not to participate in the labor market. The second equation is a mobility equation describing the individual’s decision to switch from one Þrm to another. Finally, a log wage equation speciÞes individuals’ annual earnings function.3 In the Þrst two equations we distinguish between periods for t > 1 and period t = 1, for which we need to specify some initial conditions as will become clear from the speciÞcations below. The participation equation for date t, t > 1, is given by ∗ yit = 1(yit ≥ 0), (1) yit = x0 β0 + βy yi,t−1 + βm mi,t−1 + αyi + uit, ∗ yit ∗ where yit denotes a latent variable that depends on xyit , the observable characteristics for the ith individual at time t. Among other things xyit includes education and actual lagged labor market 2 By “optimal path” we mean that it is the path that would have maximized the wage growth, had it been followed. 3 A similar model, but without the mobility equation, was also considered by Kyriazidou (1997). 3 experience (and its square). This last variable is constructed from the individual sequence of yit. The term αyi is a person speciÞc random effect, while uit a contemporaneous error term. The notation 1(·) is the usual indicator function, that is, yit denotes whether worker i participated at date t. Note also that the equation includes the past realizations of the participation and the mobility processes.4 The interÞrm-mobility equation at any date t, t > 1, is given by mit = 1(m∗ ≥ 0) × 1(yi,t−1 = 1, yit = 1), it m∗ = x0 λ0 + λm mi,t−1 + αmi + vit , it mit (2) where m∗ denotes a latent variable that depends on xmit , the observable characteristics for it the ith individual at time t. Among other things xmit (which need not be the same as xyit in equation (1)) includes education, lagged labor market experience (and its square), and lagged seniority (or tenure) in the Þrm where he/she is employed (and its square). The term αmi is a person speciÞc random effect, while vit is a contemporaneous error term. An obvious implication of the above speciÞcations, in (1) and (2), is that, by deÞnition, one cannot be mobile at date t unless he/she participates at both dates t − 1 and t. The (log) wage equation for individual i at all dates t, is speciÞed as follows: ∗ wit = wit × 1(yit = 1), (3) wit = Jit + x0 δ0 + αwi + ξit , ∗ W wit ∗ where wit denotes a latent variable that depends on observable characteristics xwit . Among other things xwit includes education, labor market experience (and its square), seniority (or tenure) in the Þrm where he/she is employed (and its square). The term αwi is a person W speciÞc random effect, while ξit is a contemporaneous error term. Finally, the term Jit denotes the sum of all wage changes that resulted from the moves that occurred before date t. We include this term to allow for a discontinuous jump in one’s wage when he/she changes jobs. The jumps are allowed to differ depending on the level of seniority and total labor market experience at the point in time when the individual changes jobs. SpeciÞcally,   W X X³ Mit 4 ´ Jit = (φs + φe ei0 ) di1 + 0 0  φj0 + φs stl −1 + φe etl −1 djitl  . j j (4) l=1 j=1 4 As is common in the literature, we make no distinction in this speciÞcation between unemployment and non-participation in the labor force. 4 Suppressing the i subscript, the variable d1tl equals 1 if the lth job lasted less than a year, and equals 0 otherwise. Similarly, d2tl = 1 if the lth job lasted between 1 and 5 years, and equals 0 otherwise, d3tl = 1 if the lth job lasted between 5 and 10 years, and equals 0 otherwise, d4tl = 1 if the lth job lasted more than 10 years and equals 0 otherwise. The quantity Mit denotes the number of job changes by the ith individual, up to time t (not including the individual’s Þrst sample year). If an individual changed jobs in his/her Þrst sample then di1 = 1, and di1 = 0 otherwise. The quantities et and st denote the experience and seniority in year t, respectively. Our analysis departs from the existing literature on the return to seniority in a number of crucial ways.5 The most important deviation is that we explicitly model the participation and mobility decisions. Moreover, we explicitly model the discrete jumps in wages that may occur whenever an individual moves from one job to another. This allows us to directly examine two competing hypotheses in the current literature. On one side Topel (1991) claims that the returns to seniority are high, while on the other side Altonji and Williams (1997), who use essentially the same data as Topel, claim that these returns are small, and largely insigniÞcant. (see also Abraham and Farber (1987) for the U.S., and Abowd, Kramarz, and Margolis (1999) for France, who all seem to Þnd low returns to seniority). Both Topel, and Altonji and Williams use a (single) wage equation that controls for experi- ence and seniority, while allowing for a time- and job-varying unobserved heterogeneity of the form ²ijt = φijt + µi + νijt , (5) for individual i in job j at time t. Most of the focus in the studies mentioned above is then to control for the potential correlation between experience and seniority, and the stochastic term ²ijt. Our speciÞcation also captures this potential correlation, but does so in a more explicit way. First, the (log) wage equation includes a person-speciÞc effect, similar to the µi term W in (5). Furthermore, we include the jump function, Jit , which explicitly allows for differential wage compensations (i.e., jumps in the entry wage), when moving from one job to another, as a function of the level of experience and seniority at the last job as well as the entire history of job transitions. In particular, our speciÞcation encompasses Altonji and Williams’ (1997) interpretation of the µi component, as a measure of the individual’s turnover tendency, but also allows for other aspects of the dynamic nature of job mobility, that is, the dependence on the 5 In particular, see Farber (1999) for a comprehensive survey of evidence in the literature. 5 worker’s labor market history. Topel (1991) speciÞes the initial wage as w0ijt = e0ijt β1 + φij0 + µi + νijt , where e0ijt denotes the initial experience on the job, while φij0 denotes the constant at the entry level of the new job. Our model extends this speciÞcation and essentially allows φij0 to depend on the previous labor market characteristics. Obviously, a failure to control for the (possible) dependence of the initial wage at the new job on the worker’s labor market history will result in biased estimates of the returns to seniority. W The inclusion in the Jit function of seniority at the end of the last job is also motivated by the literature on displaced workers. For example, Addison and Portugal (1989) show that wage losses are larger for displaced workers with more tenure (see also Jacobson, LaLonde, and Sullivan (1993) as well as Farber (1999)). The inclusion of job market experience at the W previous job as a determinant of the earnings change in the Jit function allows us to distinguish between displaced workers, who went through a period of non-employment after displacement, W from workers who move directly from one job to another. Similarly, the inclusion in the Jit function of the number of past mobilities and the seniority at the end of each of the past jobs allows us to control for the quality of the previous job matches. The explicit modeling of the participation and mobility decision allows us to directly address the endogeneity of the experience and seniority variables. This is an alternative, more direct, strategy to the one employed by Topel (1991). 2.2 Stochastic Assumptions In this subsection, we specify the stochastic structure of the random terms in equations (1)—(3) and provide the distributional assumptions for the random terms. First, the individual speciÞc effects are stochastically independent of the time-varying shocks, that is (αyi , αmi , αwi ) ⊥ (uit , vit , ξit ). Furthermore, we assume that (αyi , αmi , αwi ) are correlated individual speciÞc effects, with (αyi , αmi , αwi ) ∼ N(0, Ω), 6 where   2 σαy ραy αm σαy σαm ραy αw σαy σαw     Ω =  ραy αm σαy σαm  2 σαm ραm αw σαm σαw  .    2 ραy αw σαy σαw ραm αw σαm σαw σαw 2 2 2 Here, we allow σαy , σαm , and σαw , and consequently Ω, to be heteroskedastic, i.e., the variances are allowed to depend on xyit, xmit , and xwit , that is, 2 σαy = exp (h1 (γy , xyi1 , ..., xyiT )) , 2 σαm = exp (h2 (γm , xmi1 , ...xmiT )) , and 2 σαw = exp (h3 (γw , xwi1 , ..., xwiT )) , (6) for some real valued functions h1 (·), h2 (·), and h3 (·). Note that this speciÞcation has direct implications on the correlation between the regres- sor vectors and the person speciÞc random effects. Consider for instance the distribution of (αyi , xit). This distribution is normal, that is, ˜ (αyi , xit ) ∼ N ((0, µx ), Ω) where   2 σαy ραy x σαy σx  ˜  Ω= , 2 ραy x σαy σx σx and the covariance between αyi and xit , is ραy x σαy σx = Cov(αyi , xit) = E(αyi xit ), is different from zero in general because of heteroskedasticity (assuming, for simplicity, that x is univariate). Since E(αyi xit) = Ex E(xit αyi |xit ) = Ex xitE(αyi |xit) 6= 0, one has E(αyi |xit ) 6= 0 as long as ραy x 6= 0. Hence, our model allows the person speciÞc random effects to be correlated with the explanatory variables. The idiosyncratic error components (uit, vit , ξit) are assumed to be contemporaneously cor- related white noises. SpeciÞcally, we assume that τit ≡ (uit , vit , ξit )0 ∼ N(0, Σ), (7) where    1 ρuv ρuξ σξ    Σ=  ρuv 1 ρvξ σξ  .  (8)   ρuξ σξ ρvξ σξ 2 σξ 7 Note that for identiÞcation reasons, we set σu = σv = 1.6 2 2 2.3 The Likelihood Function In this subsection, we present the likelihood function for our problem. We Þrst specify the likelihood function, conditional on the individual speciÞc effects, and then integrate it with respect to the distribution of the individual speciÞc effects. For convenience of notation, let α1 = (αyi , αmi , αwi ), and let xit = (xyit, xmit , xwit ). Conditional on the individual speciÞc i effects, the individual’s likelihood function is given by n o n ³ ´o 1 1 W l (yit , mit , wit)t=1,...T αi , xit = l (yiT , miT , wiT )| αi , xit , yiT −1 , miT −1 , JiT (9) n ³ ´o ×l (yiT −1 , miT −1 , wiT −1 )| α1 , xit , yiT −2 , miT −2 , JiT −1 i W n ¯ o ¯ ×... × l wi1 ¯(yi1 , mi1 ), α1 , xit × l {yi1 , mi1 } . i Note that the last term of the right hand side of (9) is the likelihood for the initial state (at time t = 1) of the ith individual, that is the likelihood of (yi1 , mi1 ). Following Heckman (1981), we approximate this part of the likelihood by a probit speciÞcation given by ∗ yi1 = 1(yi1 ≥ 0), with (10) yi1 = axi1 + α0 + ui1 , ∗ yi and mi1 = 1(m∗ ≥ 0) × 1(yi1 = 1), i1 with (11) m∗ = bxi1 + α0 + vi1 . i1 mi The random terms α0 and α0 are assumed to be normally distributed random variables, yi mi with mean 0. Furthermore, they are allowed to be correlated with the Þxed individual speciÞc components (αyi , αmi , αwi ). Consequently we assume that 0 0 αi ≡ (αyi , αmi , αwi , αyi , αmi ) ∼ N (0, Γ), where 6 One can allow, in fact, for (uit , vit , ξit ) to follow AR(1) processes, as in Lillard and Willis˜(1978). 8   2  σα0 ρα0 α0 σα0 σα0 y m y m ραw α0 σαw σα0 y y ραy α0 σαy σα0 y y ραm α0 σαm σα0  y y y     ρα0 α0 σα0 σα0 2 σα0 ραw α0 σαw σα0 ραy α0 σαy σα0 ραm α0 σαm σα0    y m y m m m m m m m m    Γ =  ραw α0 σαw σα0 ραw α0 σαw σα0 2 σαw ραy αw σαy σαw ραm αw σαm σαw .  y y m m     ρ 2   αy α0 σαy σα0 y y ραy α0 σαy σα0 m m ραy αw σαy σαw σαy ραy αm σαy σαm    2 ραm α0 σαm σα0 y y ραm α0 σαm σα0 ραm αw σαm σαw m m ραy αm σαy σαm σαm (12) 2 2 2 As for σαy , and σαm in (6) we allow σα0 and σα0 to be heteroskedastic, that is m y ³ ´ 2 σα0y = exp h4 (γy 0 , xyi1 , ..., xyiT ) , and 2 σα0 = exp (h5 (γm0 , xmi1 , ...xmiT )) , m (13) for some real valued functions h4 (·) and h5 (·). Note that each individual in the sample has (potentially) different Γ, say Γi , that is αi ∼ N(0, Γi ). (14) For convenience we rewrite Γ as Γ = D∆ρ D, (15) where D is a diagonal matrix of the form ³ ´ D = diag σα0 , σα0 , σαw , σαy , σαm y m (16) and    1 ρα 0 α 0 y m ραw α0 y ραy α0 y ραm α0  y    ρ 0 0 1 ραw α0 ραy α0 ραm α0   αy αm   m m m    ∆ρ =  ραw α0 ραw α0 1 ραy αw ρα m α w  . (17)  y m     ρ ρα y α 0 ρα y α w 1 ραy αm   αy α0y m    ραm α0 y ραm α0 ραm αw m ραy αm 1 Furthermore, we simplify the variances in (6) and (13) to be only a function of the average of the regressors over the sample years.7 In generic form we have then hj (γ, x1 , ..., xT ) = x0 γj , ¯ j = 1, ..., 5, (18) 7 Even though it applies to the variance, this simpliÞcation is reminiscent of Mundlak (1971) where the mean of Þxed effect was modelled. 9 PT where x = ( ¯ i=1 xt )/T . Also we deÞne γ = (γ1 , γ2 , γ3 , γ4 , γ5 )0 . 0 0 0 0 0 Given the above assumptions, the form of the individual’s conditional likelihood, given the individual observable characteristics and unobservable individual-speciÞc effects, is given by n ¯ o ¯ l (yit, mit , wit ) ¯α1 , yi,t−1 , mi,t−1 , Jit yi W = {1 − Φ(x0 β0 + βy yi,t−1 + βm mi,t−1 + αyi )}1−yit yit n oyit −1 −1 × σξ × ϕ(ξit × σξ ) × {Φ(Bit ) − Φ2 (Ait , Bit , R)}yit ×(1−mit ) × {1 − Φ (Ait ) − Φ (Bit) + Φ2 (Ait, Bit , R)}yit ×mit (19) for t = 2, ...T , where Φ and ϕ are the cdf and the density function, respectively, of a standard normal variable, ξit = wit − {Jit + x0 δ0 + αwi }, W wit à ! ρuξ q Ait = − x0 β0 + βy yi,t−1 + βm mi,t−1 + αyi + ξit yit / 1 − ρ2 , uξ σξ à ! ρvξ q Bit = − x0 λ0 mit + λm mi,t−1 + αmi + ξit / 1 − ρ2 , vξ σξ ZA ZB à ! 1 x2 − 2Rxy + y2 Φ2 (A, B, R) = √ × exp − dxdy, and 2π 1 − R2 2(1 − R2 ) −∞ −∞ ρuv − ρuξ × ρvξ R = r³ ´ ³ ´. (20) 1 − ρ2 uξ × 1− ρ2 vξ Note that for derivation of the likelihood in (20) we used the fact that      ξit ρuξ /σξ   1 − ρ2 ρuv − ρuξ ρvξ  (uit , vit ) | ξit ∼ N   , uξ  . ξit ρvξ /σξ ρuv − ρuξ ρvξ 1 − ρ2 vξ Similarly, the likelihood function for the initial state is given by n o1−yi1 n oyi1 −1 −1 l {wi1 |yi1 , mi1 , αi )} l {yi1 , mi1 } = 1 − Φ(x0 a + α0 ) yi1 yi σξ × ϕ(ξi1 × σξ ) × {Φ(Bi1 ) − Φ2 (Ai1 , Bi1 , R)}yi1 ×(1−mi1 ) × {1 − Φ (Ai1 ) − Φ (Bi1 ) + Φ2 (Ai1 , Bi1 , R)}yi1 ×mi1 , where ξi1 = wi1 − {Ji1 + x0 δ0 + αwi }, W wi1 10 à ! ρuξ q Ai1 = − x0 a + α0 yi1 yi + ξi1 / 1 − ρ2 , uξ and σξ à ! ρvξ q Bi1 = − x0 b mi1 + α0 mi + ξi1 / 1 − ρ2 . vξ σξ Thus the individual likelihood function, integrated over the individual speciÞc effects αi , is given by n o Z "Y T # l (yit , mit , wit )t=1,...T = l {(yit , mit , wit ) |αi , xit , (yit−1 , mi,t−1 , wi,t−1 ) } t=2 ×l {wi1 |(yi1 , mi1 ), αi , xit , } × l {yi1 , mi1 } h i × (2π)−5/2 |Γi |−1/2 exp −0.5 × (αi )0 Γ−1 (αi ) dαi . i In the analysis reported below we adopt a Bayesian approach whereby we computed the conditional posterior distribution of the parameters, conditional on the data, using Markov Chain Monte Carlo (MCMC) methods as explained below.8 3 Computation of the Posterior Distribution Since it is analytically impossible to compute the exact posterior distribution of the model’s parameter, conditional on the observed data, our goal here is to summarize the posterior distri- bution of the parameters of the model using a Markov Chain Monte Carlo (MCMC) algorithm. Let the prior density of the model’s parameters be denoted by π(θ), where θ contains all the parameters of the model, i.e., θ = {β, α, Σ, ∆ρ , γ}, as deÞned in detail below. The posterior distribution of the parameters would then be: π(θ|z) ∝ P r(z|θ)π(θ), where z denotes the observed data. This posterior density cannot be easily simulated due to the intractability of Pr(z|θ). Hence, we follow Chib and Greenberg (1998), and augment the parameter space to include the vector of latent variables, zit = (yit , m∗ , wit ), where yit , m∗ , ∗ ∗ it ∗ ∗ it ∗ and wit are deÞned in (1), (2), and (3), respectively. 8 One can also use an alternative (“frequentist”) approach such as Simulated Maximum Likelihood (SML) method (see, for example, Gouri´roux and Monfort (1996), McFadden (1989), and Pakes and Pollard (1989) for e an excellent presentation of this type of methodology). However, the maximization is rather complicated and highly time consuming. For comparison we estimated the model using the SML method only for one group, (the smallest one). 11 With this addition it is easier to implement the Gibbs sampler (e.g. Casella and George (1992)). The Gibbs sampler iterates through the set of the conditional distributions of z ∗ (conditional on θ) and θ (conditional on z ∗ ). Note that in matrix form we can write the model in (1), (2), and (3) as ∗ zit = xitβ + Lt αi + τit , ˜ (21) for t = 1, ..., T , where αi ∼ N (0, Γi ), as is deÞned in (14), τit ∼ N(0, Σ), as deÞned in (7),    xyi1 0 0 0 0    xi1 =  0 xmi1 ˜  0 0 0 ,    0 0 xwi1 0 0    0 0 0 xyit 0    xit =  0 0 ˜  0 0 xmit ,  for t > 1,   0 0 xwit 0 0    1 0 0 0 0    L1 =  0 1 0 0 0  ,   and   0 0 1 0 0    0 0 0 1 0    Lt =  0 0 0 0 1  ,   for t > 1.   0 0 1 0 0 For clarity of presentation we deÞne a few other quantities as follows. The parameter vector β consists of the regression coefficients in (1), (2), and (3), including the parameters from the W function Jit deÞned in (4), and the parameter vectors from the initial condition equations (10) and (11). The parameter vector γ consists of the coefficients in (18). Note that the covariance matrix for αi , Γi , is constructed from γ and ∆ρ deÞned in (15), (16), and (18). Let the vector α contain all the individuals speciÞc random effects, that is, α0 = (α0 , ..., α0 ). For convenience 1 N we use the notation Pr(t|θ−t ) to denote the distribution of t, conditional on all the elements in θ, not including t.9 Below we explain the sampling of each of the parts in θ (augmented by z ∗ ), conditional on all the other parts and the data. A key element for computing the posterior distribution of the parameters is the choice of the prior distributions for the various elements of the parameter space. In this study we 9 For a similar hierarchical model see also Chib and Carlin (1999). 12 use conjugate, but very diffused priors on all the parameter of the model, reßecting our lack of knowledge about the possible values of the parameters. In all cases we use proper priors (although very dispersed) to ensure that the posterior distribution is a proper distribution. A limited sensitivity analysis that we carried out shows that the choice of the particular prior distribution hardly affects the posterior distribution of the parameters. This indicates that the chosen prior distributions are not dogmatic, in the sense that they have virtually no effect on the resulting posterior distributions. In fact, while all the prior distributions for the 2 parameters are centered around zero (except for σw , which is centered around 4), with a very large variance, the posterior distributions (as is also clear from the results provided below) are centered away from zero, and have relatively small variance. This last result stems largely from the fact that the data set used is rather large. Additional evidence that the results are not dominated by the choice of the prior distribu- tions is the fact that the point estimates from the SML procedure were essentially the same as those for the method reported here. Nevertheless, with the SML method one needs to resort to the Þrst-order asymptotic results, which do not provide the exact small sample distribution for the estimated parameters. 3.1 Sampling the Latent Variables z ∗ There are three latent dependent variables: yit, m∗ , and wit . While yit and m∗ are never ∗ it ∗ ∗ it ∗ directly observed, wit is observed if the ith individual worked in year t. Conditional on θ, the distribution of the latent dependent variables is zit |θ ∼ N (˜∗ β + Lt αi , Σ). ∗ xit From this joint distribution we can infer the conditional univariate distributions of interest, that is Pr(yit|m∗ , wit, θ) and Pr(m∗ |yit , wit , θ), which are truncated univariate normals, with ∗ it ∗ it ∗ ∗ truncation regions that depend on the values of yit and mit , respectively. Note that mit and wit are observed only if yit = 1. Therefore, when yit = 1 we sample m∗ from the appropriate trun- it cated distribution. In contrast, when yit = 0, the distribution of m∗ is not truncated. Similarly, it we can infer the distribution of the unobserved (hypothetical) wages, Pr(wit |yit , m∗ , θ). ∗ ∗ it 13 3.2 Sampling the Regression Coefficients β It can be easily shown (see Chib and Greenberg (1998) for details) that if the prior distribution of β is given by β ∼ N (β0 , B0 ), then the posterior distribution of β, conditional on all other parameters is ˆ β|θ−β ∼ N (β, B), where à ! N T XX ˆ β=B −1 B0 β0 + x0 Σ−1 (zit ˜it ∗ − Ltαi ) i=1 t=1 and à N T !−1 XX −1 B= B0 + x0 Σ−1 xit ˜it ˜ . i=1 t=1 3.3 Sampling the Individuals’ Random Effects αi The conditional likelihood of the random effects for individual i is as follows ( T ) X −T /2 ∗ 0 −1 ∗ l(αi ) ∝ Σ exp −.5 (zit − xit β − Lt αi ) Σ ˜ (zit − xitβ − Lt αi ) . ˜ t=1 The prior distribution for the random effects is N(0, Γi ), so that the posterior distribution of αi is αi ∼ N(ˆ i , Vαi ), α where à T !−1 X Vα i = Γ−1 i + L0 Σ−1 Lt t , t=1 and T X αi = Vαi ˆ L0 Σ−1 (zt − xit β). t ∗ ˜ t=1 3.4 Sampling the Covariance Matrix Σ Recall that the covariance matrix of the idiosyncratic error terms, τit, is given in (8). Since the conditional distribution of Σ is not a standard, known distribution, it is impossible to sample from it directly. Instead, we sample the elements of Σ using the Metropolis-Hastings (M-H) 14 algorithm (see Chib and Greenberg (1995)). The target distribution here is the conditional posterior of Σ, that is, ∗ 2 p(Σ|θ−Σ ) ∝ l(Σ|θ−Σ , αi , zit )p(σξ )p(ρ). The likelihood component is given by ( N T ) XX ∗ −NT /2 l(Σ|θ−Σ , αi , zit ) = |Σ| exp A0 Σ−1 Ait it , i=1 t=1 where, Ait = zit − xit β − Lt αi . The prior distributions for ρ = (ρuv , ρuξ , ρvξ )0 and σξ are chosen ∗ ˜ 2 to be the conjugate distributions, truncated over the relevant regions. For ρ we have p(ρ) = N[−1,1] (0, Vρ ), 2 a truncated normal distribution between -1 and 1. For σξ we have 2 p(σξ ) = N(0,∞) (µσξ , Vσξ ), a left truncated normal distribution truncated at 0. The candidate generating function is chosen to be of the autoregressive form, q(x0 , x∗ ) = x∗ + vi , where vi is a random normal disturbance. 2 The tuning parameter for ρ and σξ is the variance of vi ’s. 3.5 Sampling the Elements of Γi , ∆ρ and γ Recall that the covariance matrix Γi has the form given by Γi = diag(gi1 , . . . , gi5 ) ∗ ∆ρ ∗ diag(gi1 , . . . , gi5 )0 , (22) where ³ ´1/2 gj = exp(¯0 γj ) xij and ∆ρ is the correlation matrix given in (17). As in the sampling of Σ, we have to use the M-H algorithm. The sampling mechanism is similar to the sampling of Σ. The only difference is that now we sample elements of γ and ∆ρ , conditional on each other, and the rest of the elements of θ. The part of the conditional likelihood that involves Γi is N X N l(Γi |αi ) ∝ |Γi |− 2 exp{ αi Γ−1 α0 }, i i i=1 15 and the prior distributions of γ and elements of ∆ρ are taken to be NK (0, Vγ ) and N[−1,1] (0, Vδ ), respectively. In all the estimations reported below we employed 10,000 repetitions after the initial number of 1,000, which were discarded. 4 The Data The data for this study comes from the Panel Study of Income Dynamics (PSID). The PSID is a longitudinal study of a representative sample of individuals in the U.S. and the family units in which they reside. The survey, begun in 1968, emphasizes the dynamic aspects of economic and demographic behavior, but its content is broad, including sociological and psychological measures. Two key features give the PSID its unique analytic power: (i) individuals are followed over very long time periods in the context of their family setting; and (ii) families are tracked across generations, where interviews of multiple generations within the same families are often conducted simultaneously. Starting with a national sample of 5,000 U.S. households in 1968, the PSID has re-interviewed individuals from those households every year, whether or not they are living in the same dwelling or with the same people. While there is some attrition rate, the PSID has had signiÞcant success in its recontact efforts. Consequently, the sample size has grown somewhat in recent years.10 The data used in this study come from 18 waves of the PSID from 1975 to 1992. The sample is restricted to all heads of households who were interviewed for at least three years during the period from 1975 to 1992 and who were between the ages of 18 and 60 in these survey dates. We include in the analysis all the individuals, even if they reported themselves as self-employed. We also carried out some sensitivity analysis, excluding the self-employed from our sample, but the results remained virtually the same. We excluded from the extract all the observations which came from the poverty sub-sample of the PSID. In the analysis reported below, the experience and tenure variables play a major role. Nev- ertheless, there are some crucial difficulties with these variables, especially with the tenure variable, that one needs to carefully address. As noted by Topel (1991), tenure on a job is often 10 There is a large number of studies that used this survey for many different research questions. For more detailed description of the PSID see Hill (1992). 16 recorded in wide intervals, and a large number of observations are lost because tenure is miss- ing. Moreover, there are a large number of inconsistencies in the data. For example, between two years of a single job, tenure falls (or rises) sometime by much more than one year. The are many years with missing tenure followed by years in which a respondent reports more than 20 years of seniority. In short there is tremendous spurious year-to-year variance in reported tenure on a given job. Since the errors can basically determine the outcome of the analysis, we reconstructed the tenure and experience variables along the lines suggested by Topel (1991). SpeciÞcally, for jobs that begin in the panel, tenure is started at zero and is incremented by one for each additional year in which the person works for the same employer. This procedure seems consistent. For those jobs that started before the Þrst year a person was in the sample a different procedure was followed. The starting tenure was inferred according to the longest sequence of consistent observations. If there was no such sequence then we started from the maximum tenure on the job, provided that the maximum was less then the age of the person minus his/her education minus 6. If this was not the case then we started from the second largest value of recorded tenure. Once the starting point was determined, tenure was incremented by one for each additional year with the same employer. The initial experience was computed according to similar principles. Once the starting point was computed, experience was incremented by one for each year in which the person worked. Using this procedure we managed to reduce the number of inconsistencies to a minimum. In addition to this procedure we also took some other cautionary measures. For example, we checked to see that: (i) the reported unemployment matches against change in the seniority level; and (ii) there are no peculiar changes in the reported state of residence and region of residence, etc.11 Summary statistics of the extract used are reported in Table 1. By the nature of the PSID data collection strategy, the average age of the sample individuals does not increase much over time. We do note that education is very stable, whereas experience and seniority tend to increase. The mobility variable indicates that in each of the sample years approximately 1/10 of the individuals changed jobs. Notice that the mobility is very large in the Þrst year of the sample, certainly because of measurement error; hence, the need for treating initial conditions 11 The resulting program, written in Matlab, contains a few thousand of lines of code. The programs are available from the corresponding author upon request. 17 as separate equations. As a result, the average seniority is only around 6 years, while the average experience is over 21 years. Consistent with other data sources, the average wage decreases over the sample years, the wage dispersion increases across years, and the participation rate decreases somewhat. Note that a signiÞcant fraction of the sample is non-whites. Approximately 20% of the sample have children who are two years old and below, although this fraction decreases somewhat over the sample years, as does the fraction of the sample that have children who are between the ages of 3 and 5. The total number of children remained quite stable over the sample years. A signiÞcant fraction of the sample resides in SMSA, but that fraction tends to decrease. Looking at the distribution of individuals across the various industries we note that it remains quite stable, even though the fraction of workers employed in manufacturing industries decreases. Looking at the changes in the distribution of cohorts in our sample period, we observe that the fraction of people in the youngest cohort increases steadily, in particular between 1988 and 1990, dates between which the number of observations in our sample increases quite strongly together with the fraction of Hispanics.12 In the meantime, the fraction of people in the oldest cohorts decreases over the sample years. It is therefore important to control for the cohort composition of the sample in the regression analysis. 5 The Results The estimation is carried out for three separate education groups. The Þrst group includes all the individuals with less than 12 years of education, i.e., those who are high school dropouts. The second group consists of those who have are high school graduates, who may have acquired some college education or who earned a degree higher than high school diploma, but have not completed a four-year college. Finally, the third group consists of those that are college grad- uates, i.e., those who have at least 16 years of education. We refer to these three education groups as the high school dropouts group, high school graduates group, and college graduates group, respectively. Below we present the results, for each group separately, from the simul- taneous estimation of the three equations, namely participation, mobility and wage equation (together with the initial conditions equations for participation and mobility). For brevity we 12 In fact, those in charge of the PSID made a special effort to collect information for those who left the sample in the previous years. The changes in the age and race structure are due to strong geographic mobility of these young workers. 18 do not report the estimates for the initial conditions’ equations. The participation equation includes the following right-hand-side variables: a constant, ed- ucation, lagged labor market experience and its square, a set of three regional dummy variables, a dummy variable for residence in an SMSA, other family income, two dummy variables for being an African American and Hispanic, county of residence unemployment rate, number of children in the family, number of children less than 2 years old, number of children between the ages of 2 and 5, a dummy variable for being married, a set of four dummy variables for the cohort of birth, namely being of age 15 or less in 1975, being of age 16 to 25, age 26 to 35, and 36 to 45. The excluded dummy variable is for those who were over 45 years old in 1975. Finally we include a full set of year dummy variables. The mobility equation includes all the variables that are included in the participation equa- tion. In addition it also includes: lagged seniority on the current job and its square, and a set of nine industry dummy variables, all of which are listed in Table 1. The (log) wage equation includes the following right-hand-side variables: a constant, edu- cation, experience and its square, seniority on the current job and its square, a set of variables and dummy variables giving rise to possible discrete jumps in the wage as a result of a job mobility as explained in equation (4) above, a set of three regional dummy variables, a dummy variable for residence in an SMSA, two dummy variables for being an African American and Hispanic, a set of nine industry dummy variables (the same as in the mobility equation), county of residence unemployment rate, a set of four dummy variables for the cohort of birth (as in the previous two equations), and a full set of year dummy variables. The dependent variable in this equation is the log of deßated annual wage. For individuals that worked less than a full year we annualize their earnings. Recall that the variance covariance matrix for the individual random effects αi is given in (22). In order to estimate this matrix for all individuals one needs to obtain estimates for ³ ´1/2 both the elements of ∆ρ and the coefficient vectors γj in gj = exp(¯0 γj ) xij (j = 1, ..., 5). As explained above, the numerical computation of the posterior distribution of the γj ’s is difficult to obtain, especially when the γj ’s are of a high dimension. Hence, instead of using xij , we only ¯ use the Þrst three principle components of xij , as well as a constant term.13 ¯ 13 The Þrst three principle components account for over 98% of the total variance of xij , so that there is ¯ almost no loss of information by doing so. On the other hand, this signiÞcantly reduces the computation time. 19 High School Dropouts Group: The results for this group are presented in Tables 2 through 4. Table 2 provides the results for the participation and mobility decisions, while Table 3 contains the results for the wage equation. Table 4 presents the results for the elements of the covariance matrices, namely Σ and ∆ρ (which is part of Γi ). For brevity we do not report the estimates for γj (j = 1, ..., 5). In the discussion below, we focus on the role of education, experience, and seniority in wage determination, when the participation and mobility decisions are endogenously determined. To better evaluate the results, we also provide graphs of the marginal posterior distributions for the variables of interest. In Figure 1 we depict the marginal distribution for the coefficients on education, experience and experience squared in the participation equation. To be able to better compare the results for the three education groups the results for all education group are included. Similarly, in Figure 2 we depict the marginal posterior distribution for the same coefficients and the coefficients on seniority and seniority squared in the mobility equation for all three education groups. Figures 3 through 5 provide the posterior distributions for the returns to education, expe- rience, and seniority, respectively. While the return to education is simply the coefficient on education, for experience and seniority we need to evaluate the return at some level of experi- ence and seniority, respectively, as indicated in the Þgures. Finally, in Figure 6 we present the W wage paths due to changes in seniority and jobs mobility (the Jit function). The graphs are depicted for a high school dropout worker with a particular mobility pattern for two levels of experience: (a) a new entrants (Figures 6a); and (b) a mid-career worker (Figure 6b). It is apparent from Table 2 that the education level is almost irrelevant in this group for either the participation or the mobility decisions. In contrast, all lagged variables are very important predictors of both participation and mobility. Lagged experience has a signiÞcant positive effect on participation decision and negative effect on mobility. The same is true for lagged mobility in the mobility equation. That is, high school dropout workers who moved in the recent past tend to stay at their current jobs. Consequently, the average seniority in the sample, over all participating individuals in all years, is about 5.6 years. The probability of a move, when evaluated at the mean level of the regressors, is .078. If seniority increases by 5 years, this probability decreases to .054, i.e., a decline of more than 30%. The probability for those with 15.6 years of seniority (i.e., 10 years above average) is only .044, that is almost half the value at the average seniority. These results are consistent with the results generally 20 obtained in the literature. The results also indicate that children have almost no effect on either decision.14 There is also no clear pattern for the effect of place of residence. Being an African American has a signiÞcant negative effect on the probability of participation, but there is almost no difference between African Americans and white individuals in terms of the mobility patterns. Also the younger cohorts are more likely to participate in the labor force. Nevertheless, those who do participate have similar mobility patterns to the other cohorts. Consistent with the general pattern described in Table 1, but somewhat more difficult to interpret, is the general decline in the coefficients on the time dummy variables over time. The decline in these time dummy variables is more pronounced for the participation decision than for the mobility decision. Note also that, as one would expect, mobility differs considerably across the various industries, being higher in industries such as Þnance and personal services than in industries such as public administration. Table 3 reports the results for the wage equation, the focus of our investigation. The results clearly indicate that once one controls for jumps in earnings that result from job changes, the effect of seniority is of great importance. This is very much in line with Topel’s (1991) results, and in contrast with the results found by Abraham and Farber (1987) and Altonji and Williams (1997). In fact, the point estimates in our study are almost identical to those obtained by Topel (1991).15 Our results indicate that 10 years of job seniority for a typical high school dropout worker increases his earnings by 59.5% (i.e., 100 · (exp(.467) − 1), where .467 is the implied cumulative return to job tenure). We also note that the range of this parameter in the marginal posterior distribution is rather small, namely .0455, to .0580. As noted above, the returns to education, experience, and seniority, are also presented in Figures 3 through 5, respectively. Figure 5 clearly indicates that the return to seniority is quite high at all levels of seniority, being approximately 4.6% per year at 5 years of seniority and dropping down to 3.7% at 15 years of seniority. In fact, comparing Figures 4 and 5 indicates that the return to seniority is much larger than that for experience at any comparable level of seniority and experience. This Þnding is somewhat at odds with the results obtained by Topel (1991): Topel’s total within-job wage growth is 0.126, larger than the 0.080 estimate obtained 14 The data includes only heads of households, who are mostly men. 15 In particular, see Table 3 of Topel (1991). Unlike Topel’s case, we Þnd greater effects at higher levels of seniority, but this can be largely explained by the fact that we do not include more than quadratic terms in seniority and experience. 21 here. However, we model both the participation and mobility, so that Topel’s estimates can be viewed as biased estimates due to the endogeneity of experience. The return to education, measured within the generally low-wage group, (see Figure 3) lies exactly between the returns to experience and the returns to seniority. W The estimates for the parameter of the “switching” function Jit are reported in lines 7-19 of Table 3. The estimates indicate that those workers who change jobs frequently, i.e. after less than a year, apparently do so in order to increase their wages. The lump sum gain is about 10%, while there is no loss in wages due to loss of seniority in the previous job. High school dropout workers who move after more than one year, lose approximately 5% for every year of seniority they accumulated on their last job due to the loss on the accumulated returns to seniority. On the other hand these workers gain about 10-24% for each move they had in the past (depending on how long they remained at the previous job), in addition to an increase of 2-3.5% per year of seniority in their last job. The net effect on the individual’s annual earnings is negative if the employment spell with the last employer exceeded 5 years. If the worker’s experience at the last job exceeded 10 years there is an additional decline 0.9% per year of experience. This feature is speciÞc to high school dropouts and may well relate to the fact that most of their acquired human capital is Þrm speciÞc. Figure 6 depicts the wage path of an individual with a particular history of job mobility, that is, it represents the part of the individual’s annual earning that resulted from the returns to W seniority (i.e., within-job change in wage due to seniority) and the changes in the Jit function due to job changes (i.e., between-job change in wage). Note that each time a worker moves to a new Þrm, he/she loses the seniority accumulated on the previous job, and gains a certain amount according to his/her speciÞc job history (i.e., the accumulated experience, level of seniority in W the job that was left, the number of past moves, etc.) through the Jit . In order to account for the constraints implied by the mobility and wage equations, we depict the wage path for a typical mobility pattern for workers who moved. This mobility path was calculated from the data, for workers with 0-2 years of experience and for workers with 10-12 years of experience at the start of their sample period.16 The high school dropout workers move rather frequently, particularly earlier in their career. 16 For the 0-2 experience group the mobility sequence used is 0,1,0,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1, while for the 10-12 experience group it is 0,1,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0, where 1 denotes a move and 0 denotes the person stayed in the same job as last year. Each of the sequences is for 18 years, the same length as the sample period. 22 For both experience groups, short employment spells induce positive between-jobs wage changes, whereas long employment spells induce negative changes. Most of the wage increases are due to within-job rather than between-jobs wage changes. As Figure 6 indicates, a typical path does have periods with wage losses, but the trend over the life cycle is of general increase in real annual earnings. Note also that inter-industry wage effects (see lines 31-39 in Table 3) are very much in line with what is known in the literature on low-wage employment; manufacturing is a high-wage industry whereas services are low-wage industries for the high school dropouts. Finally, in Table 4 we report the parameters of the covariance matrices. As the estimates indicate, the correlation between the errors across equations for the individual speciÞc effects are almost all signiÞcant, especially for those not in the equations controlling for initial conditions (see lines 12 to 14). For the idiosyncractic parts only some are signiÞcant. As expected, participation and wage equations are negatively correlated through the white noises (-.035), but are positively correlated through the individual speciÞc effects (.296). Clearly, the correlation between individual speciÞc effects is the more dominant one, and it indicates that individuals who tend to participate more also tend to have higher wages. Interestingly, mobility and wages are negatively correlated both through the idiosyncratic shocks and through the individual speciÞc effects of these two equations. This implies that a large negative unexpected change in wage is likely to induce workers to move to a new job. This is also true for the individual speciÞc effects, that is, high-wage workers are less likely to move than low-wage workers having the same observed characteristics. Also, for the participation and mobility, the correlation between idiosyncratic parts is posi- tive (.003), but insigniÞcantly different from zero, while the correlation between the individual speciÞc terms is negative (-.21), and statistically signiÞcant. That is, the results indicate that the type of individuals who tend to participate less also tend to move more, when they do participate. Overall, the results clearly demonstrate the importance of directly accounting for participation and mobility decision. A failure to do so is likely to lead to substantial bias in the estimated returns. High School Graduates Group: The results for the high school graduates group are reported in Tables 5 through 7. Table 5 provides the results for the participation and mobility equations, while Table 6 contains the 23 results for the wage equation. Table 7 presents the estimates for the elements of the covariance matrices. Similar to the previous group, Figures 1 through 5 also provide the marginal posterior distribution for some of the key parameters, as well as for the returns to education, experience, and seniority. In Figure 7 we present wage paths resulting from a typical mobility pattern for two experience groups, similar to the ones presented in Figure 6. Table 5 indicates that, in sharp contrast to the high school dropout group, the level of education is a very important factor in the participation decision. In fact, the results indicate that workers who have some university education can extract some beneÞts from their additional investment in human capital relative to those with only high school education. Furthermore, and in sharp contrast to the high school dropouts group, the geographical location variables are, in general, statistically important, and especially residency in an SMSA. Most other variables have similar effects on the participation and mobility decisions as for the high school dropouts group. In particular, there is a cumulative effect of participation, i.e., past participation has positive effect on future participation through lagged experience. On the other hand there is also the opposite effect of mobility, that is, higher seniority and lagged mobility reduce the probability of a job move. The probability of a job switch for workers in this education group is 0.0983, when it is evaluated at the mean level of the regressors. The value of seniority at the mean is approximately 4.7 years. The probability of mobility for a person with 9.7 years of seniority is only 0.0623, and for a person with 14.7 years of seniority, it decreases further to 0.0468. A closer look at the marginal posterior distributions for the coefficients on experience and seniority shows quite a dense distribution around the reported parameter estimates for both the participation and mobility equations. Next we turn to the results of the wage equation, which are reported in Table 6 and Figures 3 through 5. Note that the effect of seniority is smaller than for the high school dropout group, but the marginal return declines at a slower rate. As a result the mean return at low levels of seniority (say 5 years) is higher for the high school dropouts group (see Figure 5a), but at high levels of seniority (say 15 years) the relationship is reversed (see Figure 5c). In any case, the return to seniority is clearly large and statistically very signiÞcant, with a cumulative return that exceeds that for the high school dropouts group. Furthermore, for this group, the return to experience is twice as large as it is for the high school dropouts group, at all levels of experience as is clear from a comparison of the graphs depicted in Figure 4. Hence, the sum of the linear components of the returns to seniority and experience, 0.924, is larger than for high school 24 dropout workers, but somewhat smaller than Topel’s (1991) Þndings for the whole population. W Lastly, we describe the results for the Jit function. First, we observe that the number of job changes always has a strong positive effect on the individual’s wage in the new job, except for those jobs that lasted more than 10 years. Furthermore, if seniority at the last job change was between 6 and 10 years, about 35% of the loss is recovered as a lump sum, but not because of the level of accumulated seniority in the last job. In contrast, workers for whom seniority in the last job was either between 2 and 5 years or over 10 years recover roughly 3% for each year of seniority. It therefore appears that, in comparison with a high school dropout, an optimal move should take place before a person becomes too acquainted with the job (i.e., after 2-5 years on the job), or after acquiring a signiÞcant amount of experience on the job (i.e., after 10 years with the same employer). Note that, in contrast with high school dropout workers, experience at the last job does not have a negative effect on the wage change, at all levels of experience. This implies that job movements later in one’s career seems more beneÞcial for the high school graduate workers. As in Figure 6, Figure 7 depicts the wage path of an individual with a particular history of job mobility, that is, it represents the part of the individual’s annual earnings that resulted W from the returns to seniority and the changes in the Jit function due to job changes. As for the high school dropouts group we consider workers at two experience levels, namely 0-2 and 10-12 years of experience.17 In contrast with Figure 6, job mobility causes almost no loss in earnings. Furthermore, earlier in one’s career, job changes seems to induce larger wage increases than are obtained due to returns to seniority per se. Nevertheless, this effect attenuates through time. For example, for workers with 10-12 years of experience most of the wage increases are due to within-job increases, even though job changes do come with large lump sum increases. Also, the return to education for the high school graduates group is somewhat higher than for the high school dropouts, and, as apparent from comparison of graphs depicted in Figure 3, the posterior distribution is less spread than for the high school graduates group. Looking at the estimates of the correlations presented in Table 7, we note that most of the estimated correlation coefficients are highly signiÞcant. They are generally similar and they all have the same sign as for the high school dropouts group. However, some key correlation 17 For the 0-2 experience group the mobility sequence used is 0,1,0,1,0,0,1,0,0,1,0,0,0,0,0,0,1,0, while for the 10-12 experience group it is 0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0. As in Figure 6, 1 denotes a move and 0 denotes the person stayed in the same job as last year. Each of the sequences is for 18 years, the same length as the sample period. 25 coefficients are much larger; see especially the estimates in lines 12 to 14 of Table 7. As for the high school dropouts the individual speciÞc effects from the participation and wage equa- tions are positively correlated (.335) and the coefficient is only slightly larger. The correlation coefficients between the individual speciÞc effects for the mobility and wage, and participation and mobility, are much larger in absolute terms than the corresponding coefficients for the high school dropouts group. For the mobility and wage the correlation coefficient is -.523, while for the participation and mobility equations it is -.430. That is, qualitatively the two groups demonstrate similar characteristics, but the high school graduates who tend to have larger wages tend to move even less than the high school dropouts. Similarly, the results indicate that the type of individuals who tend to participate less also tend to move more, when they do participate, and even more so for the high school graduate than for the high school dropouts. College Graduate Group: The results for the college graduate group are provided in Tables 8 through 10. Table 8 presents the results for the participation and mobility equations, while Table 9 contains the results for the wage equation. Table 10 presents estimates of terms of the covariance matrices, similar to those presented in Tables 4 and 7, for the lower education groups. As indicated above, the results are also presented graphically in Figures 1 through 5 and Figure 8. In Figure1 we depict the marginal distribution for the coefficients on education, experience and experience squared in the participation equation, along with the results for the other two educational groups. Similarly, in Figure 2 we depict the marginal posterior distributions for the same coefficients, as well as the coefficients on seniority and seniority squared, in the mobility equation. In Figures 3 through 5 we provide the marginal posterior distributions of the returns to education, experience, and seniority, respectively. Finally, similarly to Figures 6 and 7, W Figure 8 presents the wage change due to changes in seniority and the Jit function. From the three education groups, the college-educated workers are most likely to have general, rather than Þrm-speciÞc human capital. In addition one would expect within-group heterogeneity to be larger for this group than for the other two groups because of more pro- nounced differences in career paths, hierarchical positions in the Þrm, etc. Table 8 indeed conÞrms that assertion: The effects of the various variables are larger for this group than for the other two education groups. For example, the probability of moving, conditional on a move in the preceding period, is much lower than for the other two groups, indication of a more stable 26 career attachment for the more highly educated workers. Estimates of the wage equation, presented in Table 9 display similar features. The within- group return to education is comparable to that for the high school graduates group. How- ever, we note that the constant, a measure of between-group wage differentials–attributed to education–is larger (8.3) than those for the other education groups (approximately 7.9). In addition, returns to experience, a measure of the returns to general human capital, is also much larger for the college graduate (5.8%) than for the other two groups (3.7% and 4.0%, for the high school dropouts and high school graduate groups, respectively). The return to seniority is larger than for the high school graduate, but almost the same as for the high school dropouts. Nevertheless, the career incentives, and therefore the observed mobility pattern, are very different across the three education groups, as is apparent from close examination of the W various components of the Jit function. First, frequent job-to-job mobility induces large wage increases, but not as large as those observed for longer spells. A job change after one year is associated with a wage increase (for the remainder of the individual’s career) of approximately 25%, a much larger increase than for the other two groups. A job move after 2 to 5 years is associated with a smaller increase in wage, i.e., 18%, but the increase is augmented by an additional increase of 5.8% for each year of seniority in the previous job. The results associated with moves after more than six years are markedly different from those obtained for the less educated individuals (see Tables 3 and 6 in comparison with Table 9). In particular, the wage compensation is not proportional to the wage loss due to loss of seniority. For instance, a person leaving his/her employer after 6 years would lose 30% due to the loss of accumulated seniority on that job, but will gain wage increase of almost 40% (i.e., 100 · (exp(.3231 +.0111) −1) = 39.7) due to that move. After 8 years of seniority, the equivalent numbers would be 40% and, as before 40%, respectively. In contrast, job movements that occur after spells that last more than 10 years entail wage losses. In Figure 8 we depict, similarly to Figures 6 and 7 for the other two education groups, the results for the wage path for an individual with a particular history of job mobility. As before, the implied changes in the annual earnings are due to the changes in the returns to W seniority and the changes in Jit function due to job changes. As for the other groups the wage path is computed for two experience levels, namely 0-2 and 10-12 years of experience.18 It is 18 For the 0-2 experience group the mobility sequence used is 0,1,0,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0, while for the 10-12 experience group it is 0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0. As in Figures 6 and 12, 1 denotes a move and 0 27 apparent that the results are similar to those obtained for the high school dropouts and high school graduates groups. One difference that is worth noting is that the size of the between-jobs jumps are somewhat smaller, whereas the within-job growth is larger than for the other two groups. In addition to the dynamic considerations discussed above, we also see that some markets offer high wages. For instance, there is a premium to those who live in the Northeast region or in an SMSA. In contrast, college graduate workers employed in the North Central region receive lower wages. Similar structure is also observed across the various industries. For example, the wholesale and retail trades and personal services industries are low-wage sectors for the college-educated, while the manufacturing and Þnance are high-wage industries. Table 10 provides the estimates for the various elements of the covariance matrices for the college graduate groups. As is clearly seen, many of the estimated correlations are very similar to those estimated for the high school graduates group. In particular, the correlation coefficients between the individual speciÞc terms are almost the same. Nevertheless, college- educated workers with a higher tendency to participate have even less tendency to move than the high school graduates. This is yet more evidence that career concerns are more important for the college-educated. 6 Summary and Conclusions The most fundamental prediction of the theory of human capital is that compensation, in the form of wage, rises with seniority in a Þrm. The existence of Þrm-speciÞc capital explains the prevalence of long-term relationships between employees and employers. Nevertheless, there is much disagreement about the empirical evidence, as well as disagreement above the appropri- ateness of the methods used, to assess such theories. In a seminal paper, Topel (1991) concludes that there is a signiÞcant return to seniority and hence strong support for the theoretical liter- ature on human capital. This Þnding was in stark contradiction to most previous studies in the literature that concluded that there is no evidence for return to seniority. One particular paper in the literature that criticized Topel’s (1991) work is Altonji and Williams’s (1997) study, which largely supports the earlier Þndings. Here we reinvestigate the interrelations between participation, mobility and wages, while denotes the person stayed in the same job as last year. Each of the sequences is for 18 years, the same length as the sample period. 28 examining several questions central to labor economics. SpeciÞcally, we model the joint decision of participation and job mobility, while allowing for potential sample selection bias to exist when estimating the equation of interest, namely the wage function. This allows us to address, in a more satisfactory way, a topic which has been in the center of attention over the past Þfteen years, namely the return to seniority in the United States. We provide new evidence on the returns to seniority, and experience, as well as some evidence on “optimal” job-to-job mobility patterns. To do so, we use data similar to that used by both Topel (1991) and Altonji and Williams (1997). There are two main differences between the current study and earlier studies. Here we explicitly model a participation and a mobility equation along with the wage equation. Fur- thermore, we explicitly specify a model which allows for accumulation of return to seniority within a job, as well as discrete changes in the starting wage at the beginning of a new job. The results clearly demonstrate the importance of this joint estimation of the wage equation and the participation and mobility decisions. These two decisions have signiÞcant effects on observed outcomes, namely the annual earnings. We resort to a Bayesian analysis, which extensively uses Markov Chain Monte Carlo methods, allowing one to compute the posterior distribution of the model’s parameters. Whenever possible we use uninformative prior distributions for the parameters and hence rely heavily on the data to determine the posterior distributions of these parameters. We examine three educational groups. The Þrst group consists of all those that acquired less than high school education. The second group consists of all those who acquired at least high school education, but have not completed four-year college. The third group is comprised of only college graduates. We Þnd very strong evidence supporting Topel’s (1991) claim. There are large, and statistically signiÞcant, returns to seniority for all groups considered, although some differences across groups do exist. However, the total wage growth is somewhat smaller than implied by Topel’s study. Our estimates of the returns to experience are lower than those estimated by Topel, but they are not uniform across education groups; they are much higher for the college graduates than for the other two education groups. In addition, we are able to uncover the optimal patterns of job-to-job mobility, patterns that differ markedly across education groups. In particular, we see that job changes are important elements of wage growth for the most educated group. Furthermore, wage losses after a job change is much less likely for college graduate group than for workers with lower education. Hence, mobility through 29 the wage distribution is achieved through a combination of wage increases within the Þrm and across Þrms. The former is the more important for wage growth of the high school dropouts, while the latter is more important for the college graduates. 30 7 References Abowd, J., Finer, H., and F. Kramarz (1999): “Individual and Firm Heterogeneity in Compen- sation: An Analysis of Matched Longitudinal Employer and Employee Data for the State of Washington,” in J. Haltiwanger, J. Lane, J. Spletzer, K. Troske, eds., The Creation and Analysis of Employer-Employee Matched Data, North-Holland, pp.3—24. Abowd, J., Finer, H., Kramarz, F., and S. 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(1991): “SpeciÞc Capital, Mobility and Wages: Wages Rise with Job Seniority,” Journal of Political Economy, 99, 145—76. 32 Table 1: Summary Statistics for the PSID Extract for Selected Years, 1975—1992 Variable Year 1975 1978 1980 1982 1984 1986 1988 1990 1992 Individual and Family Characteristics: Observations 3,385 4,019 4,310 4,423 4,451 4,569 4,668 5,728 5,397 1. Education 11.5894 11.7158 11.8872 12.0242 12.1550 12.4064 12.4820 12.0997 12.1077 (3.3173) (3.1556) (3.0371) (2.9673) (2.9293) (2.9643) (2.8865) (3.2887) (3.3082) 2. Experience 20.8083 20.7275 20.6316 21.0707 21.3302 21.5714 21.9206 22.5134 24.1688 (14.3636) (14.4777) (14.4416) (14.3433) (14.1476) (13.9300) (13.7175) (13.2659) (12.8766) 3. Seniority 5.4968 5.4141 5.1609 5.5538 5.7433 6.0163 6.2339 6.2294 6.8648 (7.6857) (7.5439) (7.3769) (7.3118) (7.1423) (7.2307) (7.4338) (7.3835) (7.5628) 4. Participation 0.9424 0.9211 0.9151 0.8965 0.8809 0.8796 0.8706 0.8785 0.8616 (0.2330) (0.2696) (0.2788) (0.3047) (0.3239) (0.3254) (0.3357) (0.3267) (0.3454) 5. Mobility 0.2355 0.1411 0.1406 0.0916 0.0865 0.0895 0.0848 0.0826 0.0650 (0.4243) (0.3481) (0.3477) (0.2884) (0.2811) (0.2855) (0.2787) (0.2753) (0.2466) 6. Log Wage 9.3009 9.1183 9.0478 8.8652 8.7232 8.7794 8.6725 8.7129 8.5501 (2.4239) (2.7819) (2.8645) (3.1292) (3.3113) (3.3359) (3.4271) (3.3237) (3.5153) 7. Black 0.3090 0.3269 0.3339 0.3242 0.3197 0.3193 0.3186 0.2627 0.2535 (0.4622) (0.4692) (0.4717) (0.4681) (0.4664) (0.4663) (0.4660) (0.4402) (0.4350) 8. Hispanic 0.0360 0.0351 0.0323 0.0335 0.0335 0.0320 0.0311 0.0690 0.0712 (0.1864) (0.1840) (0.1767) (0.1799) (0.1799) (0.1759) (0.1735) (0.2534) (0.2571) 9. Family other income 0.6709 0.9232 1.2189 1.7336 2.0422 2.3115 2.5908 2.6488 2.9604 (1.9259) (2.6099) (3.7967) (6.3152) (7.0928) (6.5999) (7.2393) (10.8527) (13.4377) 10. No. of children 1.3495 1.2070 1.1316 1.0757 1.0420 1.0230 1.0021 1.0918 1.1073 (1.2246) (1.1567) (1.1158) (1.0792) (1.0434) (1.0485) (1.0457) (1.1891) (1.1664) 11. Children 1 to 2 0.2160 0.2195 0.2311 0.2293 0.2096 0.1996 0.1877 0.1969 0.1731 (0.3254) (0.3477) (0.3756) (0.3769) (0.3637) (0.3622) (0.3541) (0.4012) (0.3697) 12. Children 3 to 5 0.2245 0.2152 0.2123 0.2037 0.2125 0.2020 0.1982 0.1903 0.1964 (0.3330) (0.3597) (0.3609) (0.3565) (0.3675) (0.3672) (0.3664) (0.3868) (0.3855) 13. Married 0.8541 0.8074 0.7947 0.7746 0.7890 0.7779 0.7652 0.7699 0.7771 (0.4821) (0.4923) (0.4958) (0.4958) (0.4971) (0.4977) (0.4979) (0.4964) (0.4989) Table 1: (Continued) Variable Year 1975 1978 1980 1982 1984 1986 1988 1990 1992 Geographical Location Characteristics: 14. Northeast 0.1285 0.0901 0.0935 0.0879 0.0919 0.0875 0.0831 0.0841 0.0715 (0.6766) (0.8811) (0.8434) (0.8671) (0.8665) (0.8884) (0.9207) (0.8586) (0.9130) 15. North Central 0.2106 0.1722 0.1842 0.1707 0.1681 0.1620 0.1510 0.1374 0.1301 (0.7156) (0.9148) (0.8814) (0.9018) (0.8985) (0.9193) (0.9485) (0.8824) (0.9383) 16. South 0.3956 0.3620 0.3740 0.3715 0.3691 0.3677 0.3721 0.3781 0.3634 (0.7648) (0.9620) (0.9278) (0.9514) (0.9489) (0.9705) (1.0025) (0.9462) (0.9993) 17. Living in SMSA 0.6821 0.6850 0.6842 0.6812 0.5704 0.5647 0.5495 0.5981 0.5905 (0.4657) (0.4646) (0.4649) (0.4661) (0.4951) (0.4959) (0.4976) (0.4903) (0.4918) 18. County unemp. rate 8.9048 5.5994 7.0618 9.6538 7.1143 6.6044 5.3981 5.5160 6.9594 (3.1052) (2.1196) (2.5924) (3.4391) (3.1559) (2.6720) (2.2687) (2.1410) (2.2664) Industry: 19. Construction 0.0827 0.0931 0.0877 0.0780 0.0820 0.0871 0.0853 0.0899 0.0878 (0.2755) (0.2905) (0.2829) (0.2682) (0.2744) (0.2820) (0.2793) (0.2861) (0.2831) 20. Manufacturing 0.2449 0.2508 0.2483 0.2412 0.2274 0.2162 0.2138 0.2163 0.2010 (0.4301) (0.4335) (0.4321) (0.4279) (0.4192) (0.4117) (0.4100) (0.4118) (0.4008) 21. Trans., Comm., etc. 0.0818 0.0801 0.0858 0.0848 0.0894 0.0814 0.0805 0.0800 0.0793 (0.2741) (0.2715) (0.2802) (0.2786) (0.2854) (0.2735) (0.2722) (0.2713) (0.2702) 22. Wholesale and Retail 0.1108 0.1152 0.1146 0.1180 0.1247 0.1337 0.1395 0.1372 0.1247 (0.3139) (0.3193) (0.3186) (0.3227) (0.3304) (0.3404) (0.3465) (0.3441) (0.3304) 23. Finance 0.0349 0.0323 0.0309 0.0305 0.0333 0.0322 0.0326 0.0344 0.0337 (0.1835) (0.1769) (0.1730) (0.1720) (0.1793) (0.1765) (0.1775) (0.1823) (0.1805) 24. Bus. & Repair Services 0.0381 0.0323 0.0336 0.0378 0.0407 0.0490 0.0480 0.0520 0.0504 (0.1915) (0.1769) (0.1803) (0.1906) (0.1975) (0.2159) (0.2138) (0.2221) (0.2188) 25. Personal Services 0.0304 0.0289 0.0309 0.0188 0.0189 0.0173 0.0225 0.0223 0.0224 (0.1718) (0.1674) (0.1730) (0.1357) (0.1361) (0.1304) (0.1483) (0.1478) (0.1481) 26. Professional 0.0916 0.0918 0.0949 0.0875 0.0869 0.0952 0.0975 0.0883 0.0947 (0.2885) (0.2888) (0.2931) (0.2826) (0.2818) (0.2935) (0.2966) (0.2838) (0.2928) 27. Public Administration 0.0801 0.0759 0.0691 0.0640 0.0694 0.0707 0.0679 0.0693 0.0654 (0.2714) (0.2649) (0.2537) (0.2448) (0.2542) (0.2563) (0.2516) (0.2540) (0.2473) Table 1: (Continued) Variable Year 1975 1978 1980 1982 1984 1986 1988 1990 1992 Cohort Effects: 28. Age 15 or less in 1975 0 0.0926 0.1564 0.2044 0.2557 0.3171 0.3680 0.5120 0.5157 (0) (0.2899) (0.3633) (0.4033) (0.4363) (0.4654) (0.4823) (0.4999) (0.4998) 29. Age 16 to 25 in 1975 0.2177 0.2613 0.2735 0.2745 0.2685 0.2519 0.2397 0.1861 0.1864 (0.4128) (0.4394) (0.4458) (0.4463) (0.4432) (0.4342) (0.4270) (0.3892) (0.3895) 30. Age 26 to 35 in 1975 0.2960 0.2478 0.2204 0.2028 0.1867 0.1725 0.1590 0.1231 0.1236 (0.4566) (0.4318) (0.4146) (0.4021) (0.3897) (0.3778) (0.3657) (0.3286) (0.3291) 31. Age 36 to 45 in 1975 0.1725 0.1421 0.1246 0.1139 0.1054 0.0974 0.0898 0.0697 0.0699 (0.3779) (0.3492) (0.3303) (0.3178) (0.3071) (0.2965) (0.2859) (0.2546) (0.2549) Table 2: Participation and Mobility Equations for High School Dropouts Participation Mobility Variable Mean St. Dev. Range Mean St. Dev. Range Min Max Min Max 1. Constant -0.5880 0.3064 -1.1951 0.0145 -1.0892 0.2139 -1.5020 -0.6618 2. Education 0.0167 0.0138 -0.0107 0.0437 -0.0109 0.0090 -0.0292 0.0065 3. Experience at t − 1 0.0345 0.0101 0.0143 0.0545 -0.0217 0.0059 -0.0336 -0.0102 4. Experience at t − 1 squared -0.0012 0.0002 -0.0016 -0.0008 0.0001 0.0001 -0.0001 0.0004 5. Seniority at t − 1 – – – – -0.0812 0.0115 -0.1007 -0.0605 6. Seniority at t − 1 squared – – – – 0.0018 0.0003 0.0011 0.0024 7. Participation at t − 1 1.7349 0.0660 1.5999 1.8530 – – – – 8. Mobility at t − 1 0.5295 0.1258 0.3043 0.7836 -0.7190 0.0738 -0.8544 -0.5807 Family Characteristics: 9. Family other income 0.0045 0.0066 -0.0068 0.0181 -0.0350 0.0071 -0.0486 -0.0213 10. No. of Children 0.0179 0.0256 -0.0319 0.0697 0.0019 0.0146 -0.0268 0.0310 11. Children 1 to 2 -0.0911 0.0637 -0.2103 0.0361 0.0403 0.0363 -0.0302 0.1106 12. Children 3 to 5 -0.0858 0.0671 -0.2171 0.0457 0.0176 0.0320 -0.0456 0.0802 13. Married 0.3186 0.0842 0.1590 0.4834 -0.0692 0.0458 -0.1586 0.0204 Geographical Location: 14. Northeast -0.1167 0.0695 -0.2459 0.0230 -0.0373 0.0331 -0.1013 0.0285 15. North Central -0.0198 0.0738 -0.1600 0.1239 -0.0166 0.0371 -0.0847 0.0551 16. South 0.1173 0.0808 -0.0314 0.2573 0.0416 0.0426 -0.0334 0.1157 17. Living in SMSA -0.0485 0.0646 -0.1766 0.0780 -0.0419 0.0306 -0.1008 0.0182 18. County unemp. rate -0.0324 0.0102 -0.0518 -0.0124 0.0074 0.0069 -0.0058 0.0204 Race: 19. Black -0.3337 0.0827 -0.5005 -0.1780 -0.0300 0.0489 -0.1207 0.0602 20. Hispanic -0.0865 0.2805 -0.5438 0.4295 -0.0090 0.0758 -0.1616 0.1380 Cohort Effects: 21. Age 15 or less in 1975 0.9856 0.2591 0.5460 1.5599 -0.0694 0.1171 -0.3072 0.1532 22. Age 16 to 25 in 1975 0.8421 0.2516 0.4063 1.3342 -0.1047 0.1079 -0.3179 0.1043 23. Age 26 to 35 in 1975 0.8560 0.1727 0.5269 1.1936 -0.0640 0.0942 -0.2527 0.1171 24. Age 36 to 45 in 1975 0.7081 0.1742 0.3731 1.0653 0.0007 0.0889 -0.1797 0.1723 Table 2: (Continued) Participation Mobility Variable Mean St. Dev. Range Mean St. Dev. Range Min Max Min Max Industry: 25. Construction – – – – 0.7489 0.0686 0.6161 0.8811 26. Manufacturing – – – – 0.5901 0.0570 0.4782 0.7047 27. Trans., Comm., etc. – – – – 0.6428 0.0694 0.5081 0.7796 28. Wholesale & Retail Trades – – – – 0.7124 0.0628 0.5946 0.8376 29. Finance – – – – 0.8242 0.1192 0.5898 1.0621 30. Business & Repair Services – – – – 0.7008 0.0914 0.5261 0.8783 31. Personal Services – – – – 0.7489 0.1090 0.5413 0.9701 32. Professional – – – – 0.7290 0.1172 0.5041 0.9441 33. Public Administration – – – – 0.5535 0.1086 0.3439 0.7528 Time Effects: 34. Year 1976 1.0338 0.2154 0.6334 1.4204 0.0220 0.1101 -0.1975 0.2311 35. Year 1977 0.8399 0.1479 0.5498 1.1354 0.4728 0.0879 0.3063 0.6443 36. Year 1978 0.9913 0.1369 0.7386 1.2741 0.3810 0.0915 0.2014 0.5594 37. Year 1979 0.8712 0.2301 0.4956 1.3014 0.3748 0.1126 0.1573 0.5892 38. Year 1980 0.8898 0.1356 0.6417 1.1699 0.3263 0.0991 0.1353 0.5143 39. Year 1981 0.7150 0.1444 0.4485 1.0144 0.1238 0.1045 -0.0774 0.3281 40. Year 1982 0.6566 0.1851 0.3308 1.0018 0.0730 0.0919 -0.1071 0.2565 41. Year 1983 0.4078 0.1472 0.1367 0.7005 0.0360 0.1191 -0.1929 0.2574 42. Year 1984 0.3594 0.1620 0.0627 0.6661 0.1093 0.0863 -0.0607 0.2759 43. Year 1985 0.3685 0.1167 0.1442 0.5987 0.0399 0.0974 -0.1552 0.2248 44. Year 1986 0.3775 0.1663 0.0607 0.6693 0.1243 0.0988 -0.0690 0.3182 45. Year 1987 0.3129 0.1104 0.1019 0.5372 0.1635 0.0855 -0.0075 0.3280 46. Year 1988 0.1356 0.1538 -0.1451 0.4216 0.1672 0.1372 -0.0862 0.4099 47. Year 1989 0.1268 0.1051 -0.0786 0.3347 0.1260 0.0873 -0.0455 0.2952 48. Year 1990 0.0739 0.1189 -0.1461 0.3143 0.1346 0.1039 -0.0672 0.3311 49. Year 1991 -0.0111 0.0880 -0.1852 0.1607 0.1206 0.1058 -0.0805 0.3158 Table 3: Wage Equation for High School Dropouts Variable Mean St. Dev. Range Min Max 1. Constant 7.9945 0.1519 7.7081 8.2797 2. Education 0.0366 0.0068 0.0238 0.0492 3. Experience 0.0283 0.0027 0.0229 0.0334 4. Experience squared -0.0007 0.0000 -0.0007 -0.0006 5. Seniority 0.0517 0.0034 0.0455 0.0580 6. Seniority squared -0.0005 0.0001 -0.0008 -0.0003 Job switch variables in Þrst sample year: 7. Dummy for job change job in 1st year -0.0336 0.0800 -0.1796 0.1108 8. Experience at t − 1 if variable 7=1 0.0152 0.0036 0.0082 0.0221 No. of switches of jobs that lasted: 9. Up to 1 year 0.0923 0.0144 0.0635 0.1203 10. 2 to 5 years 0.0958 0.0219 0.0526 0.1386 11. 6 to 10 years 0.1229 0.1027 -0.0569 0.3076 12. Over 10 years 0.2457 0.1078 0.0474 0.4606 Seniority at last job change that lasted: 13. 2 to 5 years 0.0293 0.0084 0.0127 0.0456 14. 6 to 10 years 0.0213 0.0109 0.0003 0.0422 15. Over 10 years 0.0350 0.0053 0.0238 0.0444 Experience at last job change that lasted: 16. Up to1 year 0.0009 0.0012 -0.0015 0.0033 17. 2 to 5 years -0.0007 0.0016 -0.0038 0.0024 18. 6 to 10 years 0.0007 0.0030 -0.0049 0.0060 19. Over 10 years -0.0090 0.0029 -0.0150 -0.0035 Geographical location: 20. Northeast 0.0505 0.0192 0.0131 0.0879 21. North Central 0.0283 0.0184 -0.0094 0.0624 22. South -0.0778 0.0184 -0.1135 -0.0424 23. Living in SMSA 0.0666 0.0164 0.0349 0.0993 24. County unemp. rate -0.0042 0.0023 -0.0087 0.0002 Race: 25. Black -0.2904 0.0368 -0.3596 -0.2213 26. Hispanic -0.0669 0.0458 -0.1532 0.0233 Cohort effects: 27. Age 15 or less in 1975 0.4504 0.0660 0.3224 0.5795 28. Age 16 to 25 in 1975 0.3308 0.0706 0.1943 0.4659 29. Age 26 to 35 in 1975 0.2756 0.0602 0.1581 0.3915 30. Age 36 to 45 in 1975 0.2183 0.0682 0.0883 0.3565 Table 3: (Continued) Variable Mean St. Dev. Range Min Max Industry: 31. Construction 0.2693 0.0190 0.2324 0.3065 32. Manufacturing 0.3707 0.0158 0.3398 0.4020 33. Trans., Comm., etc. 0.3554 0.0268 0.3034 0.4077 34. Wholesale and Retail Trades 0.2196 0.0185 0.1829 0.2553 35. Finance 0.1801 0.0407 0.0997 0.2601 36. Business and Repair Services 0.1532 0.0324 0.0934 0.2162 37. Personal Services 0.1600 0.0328 0.0966 0.2243 38. Professional 0.1970 0.0310 0.1371 0.2575 39. Public Administration 0.2484 0.0988 0.1087 0.3846 Time Effects: 40. Year 1975 0.5969 0.0365 0.5241 0.6679 41. Year 1976 0.5531 0.0347 0.4837 0.6201 42. Year 1977 0.5120 0.0417 0.4300 0.5929 43. Year 1978 0.4821 0.0344 0.4133 0.5506 44. Year 1979 0.4422 0.0314 0.3800 0.5039 45. Year 1980 0.3975 0.0292 0.3402 0.4550 46. Year 1981 0.3417 0.0285 0.2833 0.3965 47. Year 1982 0.3162 0.0276 0.2611 0.3704 48. Year 1983 0.2596 0.0321 0.1964 0.3210 49. Year 1984 0.2198 0.0291 0.1630 0.2754 50. Year 1985 0.2564 0.0263 0.2039 0.3074 51. Year 1986 0.2370 0.0238 0.1900 0.2825 52. Year 1987 0.1853 0.0297 0.1277 0.2409 53. Year 1988 0.1401 0.0333 0.0766 0.2009 54. Year 1989 0.1414 0.0231 0.0960 0.1864 55. Year 1990 0.0808 0.0225 0.0376 0.1260 56. Year 1991 0.0474 0.0202 0.0079 0.0875 Table 4: Estimates of the Stochastic Elements for Hifh School Dropouts Variable Mean St. Dev. Range Min Max Covariance Matrix of White Noises (element of Σ): 1. ρuv 0.0029 0.0077 -0.0117 0.0160 2. ρuξ -0.0346 0.0072 -0.0497 -0.0183 3. ρvξ -0.0055 0.0074 -0.0185 0.0072 4. 2 σξ 0.2448 0.0064 0.2331 0.2539 Correlations of Individual SpeciÞc Effects (elements of ∆ρ ): 5. ρα0 α0 y m -0.1020 0.1146 -0.2589 0.1067 6. ραw α0 y 0.3447 0.0351 0.2732 0.4142 7. ραy α0 y 0.7548 0.0566 0.6525 0.8747 8. ραm α0y 0.0278 0.2007 -0.2908 0.2281 9. ραw α0 m 0.0646 0.0505 -0.0061 0.1794 10. ραy α0m 0.1972 0.0746 0.0260 0.2971 11. ραm α0 -0.0573 m 0.1666 -0.2619 0.2194 12. ραy αw 0.2958 0.0282 0.2292 0.3560 13. ραm αw -0.2744 0.0799 -0.4083 -0.1348 14. ραy αm -0.2100 0.1053 -0.3832 -0.0429 Table 5: Participation and Mobility Equations for High School Graduates Participation Mobility Variable Mean St. Dev. Range Mean St. Dev. Range Min Max Min Max 1. Constant 0.3645 0.6728 -1.0401 1.7243 -1.6639 0.2736 -2.2260 -1.1390 2. Education 0.1068 0.0300 0.0494 0.1676 0.0156 0.0134 -0.0100 0.0430 3. Experience at t − 1 0.0518 0.0152 0.0225 0.0812 -0.0314 0.0073 -0.0457 -0.0172 4. Experience at t − 1 squared -0.0024 0.0003 -0.0030 -0.0017 0.0004 0.0002 0.0001 0.0008 5. Seniority at t − 1 – – – – -0.0910 0.0078 -0.1059 -0.0753 6. Seniority at t − 1 squared – – – – 0.0021 0.0003 0.0015 0.0026 7. Participation at t − 1 1.5108 0.0876 1.3431 1.6801 – – – – 8. Mobility at t − 1 0.4362 0.1317 0.1885 0.6832 -0.7715 0.0533 -0.8772 -0.6686 Family Characteristics: 9. Family other income -0.0105 0.0049 -0.0199 -0.0007 -0.0229 0.0045 -0.0314 -0.0145 10. No. of Children 0.0064 0.0427 -0.0827 0.0866 -0.0043 0.0183 -0.0409 0.0309 11. Children 1 to 2 -0.1098 0.0787 -0.2605 0.0409 0.0427 0.0352 -0.0262 0.1121 12. Children 3 to 5 0.0299 0.0894 -0.1438 0.2122 -0.0434 0.0365 -0.1148 0.0279 13. Married 0.3479 0.0975 0.1528 0.5460 -0.0408 0.0434 -0.1271 0.0425 Geographical Location: 14. Northeast 0.2372 0.1115 0.0239 0.4663 -0.0380 0.0323 -0.1015 0.0252 15. North Central -0.2235 0.0850 -0.4096 -0.0654 0.0264 0.0281 -0.0294 0.0828 16. South 0.0410 0.0738 -0.1130 0.1863 0.0190 0.0259 -0.0317 0.0689 17. Living in SMSA -0.2096 0.1013 -0.4106 -0.0093 0.0119 0.0348 -0.0556 0.0813 18. County unemp. rate -0.0163 0.0137 -0.0433 0.0099 -0.0045 0.0063 -0.0171 0.0078 Race: 19. Black -0.7999 0.1471 -1.0473 -0.4737 0.0540 0.0385 -0.0202 0.1292 20. Hispanic 0.2959 0.3183 -0.2943 0.9353 0.0411 0.0733 -0.1050 0.1831 Cohort Effects: 21. Age 15 or less in 1975 -0.0277 0.3661 -0.7951 0.6613 0.0280 0.1553 -0.2806 0.3258 22. Age 16 to 25 in 1975 -0.3305 0.3636 -1.0753 0.3345 0.0262 0.1507 -0.2762 0.3165 23. Age 26 to 35 in 1975 -0.0513 0.3293 -0.6915 0.5926 0.0450 0.1398 -0.2317 0.3140 24. Age 36 to 45 in 1975 0.1024 0.2887 -0.4651 0.6583 0.1373 0.1238 -0.1082 0.3765 Table 5: (Continued) Participation Mobility Variable Mean St. Dev. Range Mean St. Dev. Range Min Max Min Max Industry: 25. Construction – – – – 1.0302 0.0905 0.8493 1.2041 26. Manufacturing – – – – 0.8824 0.0817 0.7240 1.0454 27. Trans., Comm., etc. – – – – 0.8285 0.0891 0.6587 1.0064 28. Wholesale & Retail Trades – – – – 1.0256 0.0858 0.8608 1.1951 29. Finance – – – – 1.0473 0.1016 0.8452 1.2461 30. Business & Repair Services – – – – 0.9934 0.1032 0.7951 1.1990 31. Personal Services – – – – 1.0269 0.1145 0.7954 1.2569 32. Professional – – – – 1.0271 0.0948 0.8460 1.2243 33. Public Administration – – – – 0.7635 0.0889 0.5884 0.9475 Time Effects: 34. Year 1976 -0.0306 0.2117 -0.4403 0.3813 -0.2577 0.1215 -0.4953 -0.0247 35. Year 1977 0.3586 0.2180 -0.0604 0.7816 0.4856 0.1004 0.2935 0.6818 36. Year 1978 0.4981 0.2207 0.0713 0.9388 0.4142 0.0963 0.2266 0.6029 37. Year 1979 0.2731 0.2091 -0.1559 0.6720 0.4896 0.0950 0.3021 0.6723 38. Year 1980 0.4403 0.1966 0.0483 0.8079 0.3365 0.0933 0.1560 0.5180 39. Year 1981 0.5411 0.1857 0.1877 0.8843 0.0682 0.0953 -0.1185 0.2537 40. Year 1982 0.2613 0.1861 -0.0946 0.6417 0.0247 0.0992 -0.1749 0.2223 41. Year 1983 0.1105 0.1774 -0.2483 0.4542 0.0713 0.0915 -0.1072 0.2484 42. Year 1984 0.0574 0.1635 -0.2621 0.3818 -0.0233 0.0941 -0.2115 0.1589 43. Year 1985 0.1224 0.1558 -0.1809 0.4202 -0.0713 0.0936 -0.2556 0.1130 44. Year 1986 0.2696 0.1644 -0.0498 0.6010 0.0606 0.0877 -0.1098 0.2306 45. Year 1987 -0.1352 0.1569 -0.4468 0.1615 0.1641 0.0873 -0.0052 0.3343 46. Year 1988 -0.0784 0.1608 -0.4237 0.2132 0.0503 0.0851 -0.1205 0.2148 47. Year 1989 0.1526 0.1593 -0.1613 0.4585 0.0322 0.0892 -0.1430 0.2035 48. Year 1990 -0.0012 0.1462 -0.3028 0.2800 0.1633 0.0857 -0.0083 0.3306 49. Year 1991 0.0504 0.1400 -0.2229 0.3324 0.0901 0.0837 -0.0701 0.2534 Table 6: Wage Equation for High School Graduates Variable Mean St. Dev. Range Min Max 1. Constant 7.8848 0.1321 7.6266 8.1391 2. Education 0.0397 0.0056 0.0292 0.0510 3. Experience 0.0498 0.0030 0.0440 0.0555 4. Experience squared -0.0011 0.0001 -0.0013 -0.0010 5. Seniority 0.0426 0.0029 0.0369 0.0481 6. Seniority squared -0.0001 0.0001 -0.0002 0.0001 Job switch variables in Þrst sample year: 7. Dummy for job change job in 1st year -0.0205 0.0592 -0.1321 0.1021 8. Experience at t − 1 if variable 7=1 0.0140 0.0044 0.0054 0.0225 No. of switches of jobs that lasted: 9. Up to 1 year 0.1234 0.0143 0.0951 0.1519 10. 2 to 5 years 0.1671 0.0210 0.1251 0.2075 11. 6 to 10 years 0.3464 0.0667 0.2144 0.4783 12. Over 10 years 0.1079 0.0874 -0.0638 0.2826 Seniority at last job change that lasted: 13. 2 to 5 years 0.0271 0.0072 0.0131 0.0413 14. 6 to 10 years -0.0071 0.0090 -0.0247 0.0109 15. Over 10 years 0.0331 0.0059 0.0215 0.0447 Experience at last job change that lasted: 16. Up to1 year -0.0014 0.0015 -0.0044 0.0016 17. 2 to 5 years -0.0005 0.0016 -0.0036 0.0026 18. 6 to 10 years -0.0023 0.0026 -0.0072 0.0028 19. Over 10 years -0.0011 0.0039 -0.0086 0.0066 Geographical location: 20. Northeast 0.0425 0.0208 0.0009 0.0821 21. North Central -0.0333 0.0170 -0.0672 0.0009 22. South -0.0181 0.0139 -0.0450 0.0089 23. Living in SMSA 0.0526 0.0144 0.0236 0.0809 24. County unemp. rate -0.0032 0.0020 -0.0072 0.0008 Race: 25. Black -0.2640 0.0261 -0.3141 -0.2104 26. Hispanic -0.0078 0.0458 -0.0982 0.0781 Cohort effects: 27. Age 15 or less in 1975 0.4329 0.0855 0.2668 0.5982 28. Age 16 to 25 in 1975 0.2771 0.0833 0.1081 0.4354 29. Age 26 to 35 in 1975 0.2114 0.0810 0.0525 0.3677 30. Age 36 to 45 in 1975 0.2193 0.0809 0.0538 0.3799 Table 6: (Continued) Variable Mean St. Dev. Range Min Max Industry: 31. Construction 0.2266 0.0231 0.1814 0.2715 32. Manufacturing 0.3650 0.0188 0.3283 0.4006 33. Trans., Comm., etc. 0.3995 0.0231 0.3544 0.4440 34. Wholesale and Retail Trades 0.2377 0.0193 0.1996 0.2764 35. Finance 0.3095 0.0301 0.2523 0.3697 36. Business and Repair Services 0.1942 0.0258 0.1455 0.2463 37. Personal Services 0.2071 0.0313 0.1473 0.2687 38. Professional 0.2423 0.0248 0.1940 0.2901 39. Public Administration 0.3522 0.0234 0.3064 0.3985 Time Effects: 40. Year 1975 0.5761 0.0425 0.4930 0.6614 41. Year 1976 0.5659 0.0399 0.4880 0.6434 42. Year 1977 0.5258 0.0380 0.4524 0.6019 43. Year 1978 0.4780 0.0356 0.4088 0.5478 44. Year 1979 0.4382 0.0341 0.3717 0.5067 45. Year 1980 0.4212 0.0320 0.3580 0.4836 46. Year 1981 0.3788 0.0301 0.3190 0.4381 47. Year 1982 0.3263 0.0297 0.2684 0.3851 48. Year 1983 0.2777 0.0277 0.2229 0.3320 49. Year 1984 0.2357 0.0262 0.1853 0.2872 50. Year 1985 0.2647 0.0254 0.2150 0.3151 51. Year 1986 0.2199 0.0235 0.1741 0.2659 52. Year 1987 0.1468 0.0232 0.1026 0.1939 53. Year 1988 0.1231 0.0219 0.0799 0.1660 54. Year 1989 0.1056 0.0220 0.0632 0.1491 55. Year 1990 0.0578 0.0202 0.0185 0.0966 56. Year 1991 0.0348 0.0201 -0.0045 0.0739 Table 7: Estimates of the Stochastic Elements for High School Graduates Variable Mean St. Dev. Range Min Max Covariance Matrix of White Noises (element of Σ): 1. ρuv 0.0090 0.0099 -0.0143 0.0277 2. ρuξ -0.0472 0.0155 -0.0696 -0.0200 3. ρvξ -0.0282 0.0052 -0.0394 -0.0183 4. 2 σξ 0.2024 0.0024 0.1976 0.2073 Correlations of Individual SpeciÞc Effects (elements of ∆ρ ): 5. ρα0 α0 y m -0.0121 0.0662 -0.1731 0.0831 6. ραw α0 y 0.4193 0.0521 0.3123 0.5301 7. ραy α0 y 0.5843 0.0988 0.3482 0.7148 8. ραm α0 -0.0957 y 0.0865 -0.2260 0.0605 9. ραw α0 m 0.0114 0.0468 -0.1082 0.0981 10. ραy α0m -0.2517 0.1578 -0.4480 0.0641 11. ραm α0 -0.0560 m 0.0384 -0.1312 0.0243 12. ραy αw 0.3351 0.0315 0.2821 0.4046 13. ραm αw -0.5234 0.0860 -0.6179 -0.3495 14. ραy αm -0.4304 0.1516 -0.6418 -0.1613 Table 8: Participation and Mobility Equations for College Graduates Participation Mobility Variable Mean St. Dev. Range Mean St. Dev. Range Min Max Min Max 1. Constant -1.5795 0.5380 -2.6852 -0.5840 -1.0151 0.2494 -1.5113 -0.5269 2. Education 0.1146 0.0245 0.0690 0.1645 -0.0129 0.0100 -0.0329 0.0062 3. Experience at t − 1 0.0660 0.0152 0.0381 0.0959 -0.0368 0.0066 -0.0492 -0.0240 4. Experience at t − 1 squared -0.0021 0.0003 -0.0027 -0.0015 0.0005 0.0002 0.0002 0.0008 5. Seniority at t − 1 – – – – -0.0878 0.0074 -0.1024 -0.0734 6. Seniority at t − 1 squared – – – – 0.0020 0.0003 0.0015 0.0026 7. Participation at t − 1 2.0046 0.0944 1.8178 2.1978 – – – – 8. Mobility at t − 1 0.3336 0.1646 0.0111 0.6274 -0.9019 0.0552 -1.0133 -0.7953 Family Characteristics: 9. Family other income -0.0020 0.0018 -0.0052 0.0018 -0.0110 0.0021 -0.0152 -0.0071 10. No. of Children 0.1615 0.0605 0.0400 0.2737 -0.0673 0.0188 -0.1041 -0.0308 11. Children 1 to 2 -0.1562 0.1203 -0.3881 0.0822 0.0650 0.0337 -0.0014 0.1309 12. Children 3 to 5 -0.0880 0.1212 -0.3291 0.1468 -0.0138 0.0392 -0.0911 0.0631 13. Married 0.0892 0.1126 -0.1410 0.2959 -0.0771 0.0398 -0.1523 0.0006 Geographical Location: 14. Northeast 0.0152 0.0853 -0.1322 0.2038 -0.0121 0.0242 -0.0600 0.0348 15. North Central 0.0575 0.0879 -0.1250 0.2133 -0.0244 0.0237 -0.0705 0.0221 16. South -0.0301 0.0775 -0.1809 0.1237 0.0155 0.0235 -0.0291 0.0612 17. Living in SMSA -0.1068 0.0982 -0.2962 0.0876 0.0537 0.0333 -0.0123 0.1173 18. County unemp. rate -0.0034 0.0171 -0.0361 0.0311 -0.0009 0.0063 -0.0135 0.0113 Race: 19. Black -0.2672 0.1477 -0.5592 0.0328 0.0888 0.0439 0.0043 0.1764 20. Hispanic -0.6326 0.2704 -1.1633 -0.0897 -0.0444 0.1053 -0.2550 0.1553 Cohort Effects: 21. Age 15 or less in 1975 0.5290 0.2813 0.0050 1.1356 -0.0386 0.1256 -0.2892 0.2046 22. Age 16 to 25 in 1975 0.3074 0.3123 -0.2943 0.9407 -0.0346 0.1222 -0.2779 0.2015 23. Age 26 to 35 in 1975 0.8920 0.3007 0.3360 1.5230 -0.0380 0.1098 -0.2535 0.1751 24. Age 36 to 45 in 1975 0.5458 0.2543 0.0587 1.0604 -0.0039 0.0966 -0.1951 0.1879 Table 8: (Continued) Participation Mobility Variable Mean St. Dev. Range Mean St. Dev. Range Min Max Min Max Industry: 25. Construction – – – – 0.8457 0.1050 0.6367 1.0563 26. Manufacturing – – – – 0.9323 0.0920 0.7549 1.1143 27. Trans., Comm., etc. – – – – 0.9094 0.1010 0.7063 1.1087 28. Wholesale & Retail Trades – – – – 1.0468 0.0918 0.8676 1.2280 29. Finance – – – – 1.0297 0.0996 0.8408 1.2290 30. Business & Repair Services – – – – 1.0211 0.1009 0.8232 1.2238 31. Personal Services – – – – 0.9327 0.1199 0.6973 1.1652 32. Professional – – – – 0.9019 0.0896 0.7215 1.0770 33. Public Administration – – – – 0.7583 0.0973 0.5668 0.9428 Time Effects: 34. Year 1976 0.5046 0.2361 0.0446 0.9692 -0.1597 0.1104 -0.3817 0.0549 35. Year 1977 0.6716 0.2324 0.2115 1.1274 0.4063 0.0917 0.2310 0.5893 36. Year 1978 0.5539 0.2332 0.0952 0.9937 0.3363 0.0894 0.1613 0.5135 37. Year 1979 0.5600 0.2332 0.0959 1.0053 0.3315 0.0876 0.1618 0.5042 38. Year 1980 0.5975 0.2279 0.1564 1.0636 0.3545 0.0842 0.1880 0.5217 39. Year 1981 0.7175 0.2317 0.2705 1.1717 -0.0934 0.0900 -0.2730 0.0827 40. Year 1982 0.4096 0.1978 0.0132 0.7923 -0.0768 0.0872 -0.2448 0.0953 41. Year 1983 0.5422 0.2042 0.1365 0.9254 -0.1023 0.0871 -0.2716 0.0679 42. Year 1984 0.3945 0.1770 0.0440 0.7291 -0.0883 0.0850 -0.2500 0.0793 43. Year 1985 0.2879 0.1776 -0.0611 0.6262 0.0075 0.0838 -0.1615 0.1693 44. Year 1986 0.1038 0.1698 -0.2194 0.4463 -0.0259 0.0816 -0.1907 0.1325 45. Year 1987 -0.0052 0.1708 -0.3391 0.3365 -0.0763 0.0833 -0.2433 0.0868 46. Year 1988 0.1342 0.1645 -0.1795 0.4634 -0.0444 0.0805 -0.2004 0.1133 47. Year 1989 0.2361 0.1677 -0.1059 0.5560 -0.0272 0.0806 -0.1909 0.1299 48. Year 1990 0.0821 0.1613 -0.2671 0.3926 0.0485 0.0800 -0.1102 0.2020 49. Year 1991 -0.0336 0.1486 -0.3204 0.2702 0.0352 0.0770 -0.1159 0.1865 Table 9: Wage Equation for College Graduates Variable Mean St. Dev. Range Min Max 1. Constant 8.3258 0.1347 8.0614 8.5874 2. Education 0.0411 0.0054 0.0302 0.0516 3. Experience 0.0580 0.0032 0.0518 0.0643 4. Experience squared -0.0013 0.0001 -0.0015 -0.0012 5. Seniority 0.0518 0.0029 0.0460 0.0576 6. Seniority squared -0.0005 0.0001 -0.0007 -0.0004 Job switch variables in Þrst sample year: 7. Dummy for job change job in 1st year 0.0769 0.0673 -0.0519 0.2062 8. Experience at t − 1 if variable 7=1 0.0108 0.0044 0.0020 0.0192 No. of switches of jobs that lasted: 9. Up to 1 year 0.2240 0.0172 0.1905 0.2572 10. 2 to 5 years 0.1648 0.0189 0.1274 0.2018 11. 6 to 10 years 0.3231 0.0683 0.1861 0.4572 12. Over 10 years 0.4717 0.0869 0.3031 0.6425 Seniority at last job change that lasted: 13. 2 to 5 years 0.0567 0.0070 0.0432 0.0709 14. 6 to 10 years 0.0111 0.0097 -0.0079 0.0303 15. Over 10 years 0.0062 0.0055 -0.0050 0.0166 Experience at last job change that lasted: 16. Up to 1 year -0.0071 0.0016 -0.0102 -0.0040 17. 2 to 5 years -0.0058 0.0016 -0.0090 -0.0027 18. 6 to 10 years -0.0025 0.0025 -0.0073 0.0024 19. Over 10 years -0.0026 0.0033 -0.0090 0.0036 Geographical location: 20. Northeast 0.0497 0.0157 0.0188 0.0802 21. North Central -0.0501 0.0141 -0.0784 -0.0232 22. South -0.0114 0.0131 -0.0368 0.0140 23. Living in SMSA 0.0359 0.0128 0.0108 0.0616 24. County unemp. rate -0.0042 0.0020 -0.0082 -0.0003 Race: 25. Black -0.2343 0.0358 -0.3065 -0.1660 26. Hispanic 0.0079 0.0717 -0.1384 0.1478 Cohort effects: 27. Age 15 or less in 1975 -0.0172 0.0793 -0.1751 0.1323 28. Age 16 to 25 in 1975 -0.2371 0.0822 -0.3947 -0.0794 29. Age 26 to 35 in 1975 -0.1633 0.0743 -0.3038 -0.0145 30. Age 36 to 45 in 1975 0.0261 0.0735 -0.1132 0.1717 Table 9: (Continued) Variable Mean St. Dev. Range Min Max Industry: 31. Construction 0.3495 0.0285 0.2921 0.4050 32. Manufacturing 0.4559 0.0207 0.4154 0.4963 33. Trans., Comm., etc. 0.3875 0.0262 0.3360 0.4395 34. Wholesale and Retail Trades 0.2969 0.0215 0.2546 0.3391 35. Finance 0.3923 0.0272 0.3394 0.4458 36. Business and Repair Services 0.3172 0.0254 0.2688 0.3674 37. Personal Services 0.1864 0.0348 0.1187 0.2520 38. Professional 0.3774 0.0190 0.3401 0.4143 39. Public Administration 0.3935 0.0250 0.3438 0.4419 Time Effects: 40. Year 1975 0.3573 0.0430 0.2741 0.4417 41. Year 1976 0.3543 0.0407 0.2725 0.4332 42. Year 1977 0.3017 0.0380 0.2255 0.3759 43. Year 1978 0.2819 0.0365 0.2100 0.3533 44. Year 1979 0.2510 0.0345 0.1846 0.3200 45. Year 1980 0.2025 0.0329 0.1394 0.2675 46. Year 1981 0.1794 0.0304 0.1201 0.2390 47. Year 1982 0.1789 0.0292 0.1215 0.2362 48. Year 1983 0.1801 0.0272 0.1263 0.2335 49. Year 1984 0.1174 0.0253 0.0673 0.1678 50. Year 1985 0.1388 0.0242 0.0907 0.1865 51. Year 1986 0.1484 0.0231 0.1037 0.1935 52. Year 1987 0.1218 0.0219 0.0795 0.1640 53. Year 1988 0.0939 0.0209 0.0539 0.1348 54. Year 1989 0.0413 0.0196 0.0030 0.0800 55. Year 1990 0.0496 0.0191 0.0118 0.0861 56. Year 1991 0.0065 0.0183 -0.0298 0.0420 Table 10: Estimates of the Stochastic Elements for College Graduates Variable Mean St. Dev. Range Min Max Covariance Matrix of White Noises (element of Σ): 1. ρuv -0.0005 0.0113 -0.0217 0.0188 2. ρuξ -0.0496 0.0124 -0.0672 -0.0205 3. ρvξ 0.0013 0.0075 -0.0111 0.0161 4. 2 σξ 0.2062 0.0023 0.2016 0.2104 Correlations of Individual SpeciÞc Effects (elements of ∆ρ ): 5. ρα0 α0 y m 0.8040 0.0556 0.7024 0.9005 6. ραw α0 y 0.1335 0.0757 0.0169 0.2714 7. ραy α0 y 0.5716 0.0286 0.5190 0.6224 8. ραm α0 -0.6044 y 0.0773 -0.7595 -0.4892 9. ραw α0 m -0.1450 0.0884 -0.2586 0.0403 10. ραy α0m 0.2896 0.0429 0.2268 0.3845 11. ραm α0 -0.4234 m 0.0789 -0.5691 -0.2668 12. ραy αw 0.2174 0.0553 0.1066 0.3017 13. ραm αw -0.5352 0.0590 -0.6371 -0.4131 14. ραy αm -0.5061 0.0656 -0.6172 -0.3874 Figure 1: Participation Equation a. Education 0.35 HS Dropouts HS Grad. College Grad. 0.3 0.25 0.2 Density 0.15 0.1 0.05 0 -5 0 5 10 15 20 25 Coefficient b. Experience 0.4 HS Dropouts HS Grad. College Grad. 0.35 0.3 0.25 Density 0.2 0.15 0.1 0.05 0 0 2 4 6 8 10 12 14 Coefficient c. Experience Squared 20 HS Dropouts HS Grad. 18 College Grad. 16 14 12 Density 10 8 6 4 2 0 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 Coefficient Figure 2: Mobility Equation a. Education 0.45 HS Dropouts HS Grad. 0.4 College Grad. 0.35 0.3 0.25 Density 0.2 0.15 0.1 0.05 0 -6 -4 -2 0 2 4 6 8 Coefficient b. Experience 0.7 HS Dropouts HS Grad. College Grad. 0.6 0.5 0.4 Density 0.3 0.2 0.1 0 -7 -6 -5 -4 -3 -2 -1 0 1 Coefficient c. Experience Squared 35 HS Dropouts HS Grad. College Grad. 30 25 20 Density 15 10 5 0 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Coefficient Figure 2: (Continued) d. Seniority 0.7 HS Dropouts HS Grad. College Grad. 0.6 0.5 0.4 Density 0.3 0.2 0.1 0 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 Coefficient e. Seniority Squared 15 HS Dropouts HS Grad. College Grad. 10 Density 5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Coefficient Figure 3: Return of Wage to Education 0.8 HS Dropouts HS Grad. College Grad. 0.7 0.6 0.5 Density 0.4 0.3 0.2 0.1 0 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Return Figure 4: Return of Wage to Experience a. Return at 5 years of experience 1.8 HS Dropouts HS Grad. 1.6 College Grad. 1.4 1.2 1 Density 0.8 0.6 0.4 0.2 0 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 Return b. Return at 10 years of experience 2 HS Dropouts HS Grad. 1.8 College Grad. 1.6 1.4 1.2 Density 1 0.8 0.6 0.4 0.2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Return c. Return at 15 years of experience 2.5 HS Dropouts HS Grad. College Grad. 2 1.5 Density 1 0.5 0 0 0.5 1 1.5 2 2.5 3 Return Figure 5: Return of Wage to Seniority a. Return at 5 years of seniority 2 HS Dropouts HS Grad. 1.8 College Grad. 1.6 1.4 1.2 Density 1 0.8 0.6 0.4 0.2 0 3 3.5 4 4.5 5 5.5 Return b. Return at 10 years of seniority 3 HS Dropouts HS Grad. College Grad. 2.5 2 Density 1.5 1 0.5 0 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 Return c. Return at 15 years of seniority 2.5 HS Dropouts HS Grad. College Grad. 2 1.5 Density 1 0.5 0 2.5 3 3.5 4 4.5 5 Return Figure 6: High School Dropouts–Wage Change for Typical Mobility Pattern a. New Entrants (0-3 years of experience) 0.8 0.7 0.6 0.5 Log wage change 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 12 14 16 18 Year in sample b. Mid-Career Workers (10-12 years of experience) 0.8 0.7 0.6 Change in log wage 0.5 0.4 0.3 0.2 0.1 0 0 2 4 6 8 10 12 14 16 18 Year in sample Figure 7: High School Graduates–Wage Change for Typical Mobility Pattern a. New Entrants (0-3 years of experience) 1.2 1 0.8 Change in log wage 0.6 0.4 0.2 0 0 2 4 6 8 10 12 14 16 18 Year in sample b. Mid-Career Workers (10-12 years of experience) 1.2 1 0.8 Change in log wage 0.6 0.4 0.2 0 0 2 4 6 8 10 12 14 16 18 Year in sample Figure 8: College Graduates–Wage Change for Typical Mobility Pattern a. New Entrants (0-3 years of experience) 1.2 1 0.8 Change in log wage 0.6 0.4 0.2 0 0 2 4 6 8 10 12 14 16 18 Year in sample b. Mid-Career Workers (10-12 years of experience) 1.2 1 0.8 Change in log wage 0.6 0.4 0.2 0 0 2 4 6 8 10 12 14 16 18 Year in sample