Online Appendix for “Productivity Shocks, Long-Term Contracts and Earnings Dynamics” Neele Balke∗, Thibaut Lamadon† September 25, 2020 W1 Model web appendix........................ W1 W1.1 Properties of equilibrium functions............ W1 W1.2 Existence of equilibrium................. W9 W2 Identification web appendix.................... W23 W2.1 Data............................ W24 W2.2 Identifying the choice probabilities............ W24 W2.3 Identifying the model parameters............ W26 W2.4 Proofs........................... W27 W3 Data web appendix......................... W43 W3.1 Institutional background................. W43 W3.2 Moments description................... W45 W4 Estimation web appendix..................... W46 W4.1 Numerical solution to the model............. W47 W4.2 Simulating moments.................... W48 W4.3 Optimization........................ W48 W4.4 Computing standard errors................ W49 ∗Kenneth C. Griffin Dept. of Economics, University of Chicago,
[email protected]. †Kenneth C. Griffin Dept. of Economics, University of Chicago,
[email protected], IFAU, IFS and NBER. W1 Model web appendix W1.1 Properties of equilibrium functions In this section, we define the set J of profit functions of the firm and then, taking an arbitrary J ∈ J as given, derive properties of the market tightness, job finding probability, and search and effort policy functions in equilibrium. Definition W1 (Definition of J). Let J be defined as the set of firms’ value functions J : S × V → R such that (J1) For all (x, z) ∈ S and all V1,V2 ∈ V with V1 ≤ V2, the difference J(x, z, V2)− J(x, z, V1) is bounded by −BJ (V2 − V1) and −BJ (V2 − V1) where BJ ≥ BJ > 0 are some constants. (J2) For all (x, z, V ) ∈ S × V, J(x, z, V ) is bounded in [J, J] where J = f(x,z)−u−1 v+c(e)−βv f(x,z)−u−1 v+c(e)−βv 1−β and J = 1−β .