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- B Numerical Appendix B.1 Preliminaries We calibrate the model such that t represents a month. Specifically, we set the discount rate β to 0.991/3 , the vacancy creation cost to 0.45 and employ a matching function given by m(u, v) = uv(uι + vι )â1/ι so that q(θ) = (1 + θι )1/ι , which is bounded between 0 and 1. We set ι = 0.9 by nonlinear least squares to match the empirical relationship between aggregate market tightness and job-finding rates. We set the exogenous separation rate s = 0.031 to the average monthly separation rate in the Current Population Survey (CPS) from 1951 to 2019. This implies that the pass-through parameter Ï equals 0.034. Separation rates and job-finding rates are both adjusted for time aggregation following Shimer (2005).
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- Step 3: Envelope Theorem We seek to apply of Theorem 1 of Marimon and Werner (2021), which relies on the following technical assumptions. Technical Assumptions: TA1. The set X of feasible allocations is convex, and f, u, Ï, ua, and Ïa are continuous functions of {a, w, z0} TA2. The constraint set G(z0) = {(w, a) â X : G(w, a; z0) ⤠0} is compact for every z â Z, a neighborhood of z0, and there exists a contract (w, a) such that the participation constraint (44) is slack. TA3. The set of optimal contracts is non-empty. We argue these conditions apply in our setting. X is convex as the product of segments.
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