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- A Labor Market Dynamics of Unemployment and the Search Literature The purpose of sections A, A.1, and A.2 is to show how studying unemployment dynamics contributes to two specific questions in the search literature. Namely, does the AKM model (Abowd, Kramarz, and Margolis, 1999) suffer a strong bias from endogenous labor mobility and what does unemployment dynamics say about the worker-specific contribution to wage dispersion in search models with piece-rate wages.
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- I start by considering a linear model of log-wages (wit), worker-specific capital (θi), firmspecific capital (ÈJ(i,t)) and a residual (εit) motivated by the AKM model (Abowd, Kramarz, and Margolis, 1999).
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- Sørensen and Vejlin (2011) estimate the AKM model using Danish data from 1980-2006. Since they have multiple observations for each worker they estimate a time-invariant worker effect (θAKM ) and a time-varying worker effect, i.e. experience (Xβ). In the wage correlation (see section A) there is only one observation per individual, so the worker effect is the sum of both of these effects (θ = θAKM + Xβ). The decomposition of the wage dispersion is reported for both Cov(w,θAKM ) V ar(w) and Cov(w,Xβ) V ar(w) , the sum of which is Cov(w, θAKM ) V ar(w) + Cov(w, Xβ) V ar(w) = Cov(w, θAKM + Xβ) V ar(w) = V ar(θAKM + Xβ) V ar(w) + Cov(È, θAKM + Xβ) V ar(w) = V ar(θ) V ar(w) + Cov(È, θ) V ar(w) = Corr(w0, w1) which is exactly what is being measured by the wage correlation (see equation 20).
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- The covariance between pre- and post-unemployment spell wages under these assumptions is Cov(wi0, wi1) = V ar(θi) + Cov(ÈJ(i,0), θi) (18) where the second term is zero if there is no sorting between workers and firms or if firm-specific human capital accumulation is independent of a worker’s human capital. The second term describes the covariance between human capital and firm-specific capital in the general labor market. The correlation is then Corr(wi0, wi1) = Ã(wi0)Ã(wi1) V ar(θi) + Cov(ÈJ(i,0), θi) (19) Finally, I make the assumption that the variance in wages of the job offer distribution is roughly equal to the variance of the wages in the labor market (Ã(wi,1) ≈ Ãw ≡ Ã(wi,0)), which is empirically supported in the Danish data by the findings in Christensen, Lentz, Mortensen, Neumann, and Werwatz (2005). The correlation is then Corr(wi0, wi1) = V ar(θi) V ar(wi) +
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