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The Exact Likelihood Function for an Empirical Job Search Model

  • Computer Science
  • Economics
  • Mathematics


e"~~~R Discussion ceM for a erR ~mic Research 8414 1990 17 I 1J5 ~,~Q 1~~~JrJ, ' ' . II~INIII~N~II IIIhnyIIll~n~lAN ~ll No. 901~ THE EXACT LIKELIHOOD FUNCTION FOR AN EMPIRICAL JOB SEARCH MODEL f' y ~ by Bent Jesper Christensen and Nicholas M. Kiefer ~'~~'~ Z March 1990 ISSN 0924-7815 TFR; EXACT LIKELIHOOD FUNCI'ION FOR AN EMPIRIGAI. JOB SEARCH MODEL by Bent Jesper Christensen` and Nicholas M. Kiefer" ` Department of Finance, New York University, 40 West 4th Street, Room 922, New York, NY 10003. " Department of Economics, Cornell University, Uris Hall, 4th Floor, Ithaca, NY 14853-~601. We are grateful to seminar participants at several Universities - Amsterdam, Cornell, (3roningen, Rotterdam, end Tilburg - for comments. Part of the work on this paper was performed while the second author was visiting CentER. Research support was provided by a grant from the NSF. z ABSTRACT The exact Likelihood functions for a sequence of job search models are analyzed. The optimality condition implied by the dynamic programming framework is fully imposed. When unemployment duration and reemployment wage data are both available, using the optimality condition allows identification of an offer arrival probability separately from an offer acceptance pzobability. The estimation problem is nonstandard. The shape of the likelíhood function in finite samples is considered, along with asymptotic propertíes of the maximum likelihood estimator. 3 Estimatíon of dynamic programmíng models is an important new tool for empirical economícs. As computational capability increases dramatically - and perhaps as the mathematical level of our profession íncreases, although somewhat less dramatically - dynamíc programming methods once used only by theorists in carefully contrived environments are being used in data analysis. Recent applícations include Pakes (1986) on the decísion to hold or release a patent, Rust (1987b) on replacement investment, and Rust (1987a) on

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