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·	From Theory To Practice

The core analytical methodology builds on an earlier body of theoretical and empirical research that addresses the determinants of benefit and unemployment durations. (References to this literature are given in the Bibliography.) Theoretically, the interpretive framework derives from job search analysis, an approach widely used in labour economics, although in fact the nature of the empirical investigation is not limited to this theoretical approach.

The basic model of job search by an unemployed individual is set in continuous time and begins in a stationary environment, so there is no systematic tendency for the external situation facing a searcher to change. Thus, this basic model initially excludes change in circumstances associated with the exhaustion of UI or EI benefits. Extensions of the model incorporating such features are discussed below. In the core model, job offers arrive at random intervals (that are beyond the control of the individual searcher) according to a Poisson process with arrival rate d. If a job is located, it is permanent and yields a wage w forever. When individuals are unemployed, they receive the current level of UI/EI benefits, b. Job offers are independently drawn from a known distribution of wages (with finite mean and variance) and there is no recall of an offer if it is rejected. Individuals care about utility which is linear in income and future income streams are discounted at a constant rate r.

In such an environment, the value of accepting a job paying a wage w is given by

^e(w) = w/r

the present value of receipt of w forever. In contrast, the value of being unemployed over a period of length h is

^u = bh/(1+rh)+(dh/(1+rh))E[max{V^e(w),V^u}]+(1-dh)V^u/(1+rh)+o(h)

where the final term reflects the value of receiving more than one offer in the period of length h; this term vanishes in the limit as h shrinks to zero. Note that this second valuation is defined implicitly in terms of itself and the other valuation. Together, these two expressions yield a solution for the reservation wage w* since V^e(w) is increasing and continuous in w, while V^u is independent of w (depending only on its expectation). That is, w* is the unique value that solves the valuation equation ^e(w*)=V^u.

One can hence derive the main result which is:

(w*-b)r=d(1-F(w*))[E(w|w>w*)-w*]

The left hand side can be interpreted as the imputed interest income consequent upon the rejection of an offer of w* (and hence on receipt of b for another period); and hence, represents the marginal cost of rejection of w*. The three right hand side terms are, respectively, the offer receipt probability (i.e., the Poisson arrival rate), the region of the offer distribution in which offers are accepted, and the marginal expected benefit of a wage offer above w*. The reservation value that guides optimal behaviour equates the marginal cost and the expected marginal benefit of acceptance and/or rejection.

In practice, use of this search theoretic framework as a guide for empirical analysis requires some further modification. Specifically, the framework must take into account the fact that the reservation wage, the central construct in this analysis, is not typically observed (or, if reported or "observed" in some sense, may be observed with error). Thus, the model is extended to yield implications for observables such as unemployment durations or durations in receipt of UI/EI benefits, the distribution of acceptance wages in the next job found, or the joint distribution of such wages and durations analyzed together.

In addition, one must address the appropriate modification of the basic risk-neutral, stationary search model to incorporate more realistic and important institutional features. These features might include exhaustion of UI, potential asset depletion during a jobless spell, changes in overall economic conditions during a search spell, finite-lived jobs, time-varying search intensity, and firm behaviour that responds differently to applicants with different elapsed durations (either based on some real change that occurs with duration such as skill depletion or based on bias against the longer-term unemployed). Mortensen (1977), for example, addresses a number of these extensions and a discussion with related empirical analysis applied to UI exhaustion (using US data) is provided in Meyer (1990). In the context of the econometric analysis of durations, such extensions yield implications for duration dependence as the hazard out of unemployment — the conditional probability that a spell will end in a given period, given its continuation to this period — varies with the elapsed duration of unemployment.

Further discussion of these theoretical approaches is provided in the survey by Mortensen (1986), a reference that covers principally the theoretical model, and Devine and Kiefer (1991), a book that surveys both structural and reduced forms of econometric approaches. Moreover, other references, including some papers by the present principal investigator that illustrate the nature of the prospective investigation, are included in the selective bibliography.