【正文】 entation here will actually be very similar in many respects to those models. The Basic Model Consider a worker seeking to maximize 1 E X 175。 (1) t=0 7 1 where 175。 1) is the discount factor, yt is ine at t, and E denotes the expectation. Ine is given by y = w if employed at wage w and y = b if unemployed (hours worked are … xed to unity for now, but this will be relaxed below). Although we refer to w as the wage, more generally it could be interpreted as capturing some general measure of the desirability of the job, which could depend on things like location, prestige, etc. Similarly, although we will refer to b 0 as unemployment insurance, it can also be interpreted as including the value of leisure and home production, of any cost of The individual chooses a policy indicating whether to accept any given job o164。ers, characterized by the cdf F (w) = prob(w er is rejected the agent remains unemployed that period. Previously rejected o164。 then t hese ar e equivalent. However , the analysis can be int epreted m ore generally. If we assume risk aversion and plete marke ts, t he worker can ma ximize exp ect ed utility by … rst maximizing ine, which is the problem on which we focus, and t hen sm oothing his consumption throug h markets. Another inter pretatio n is that there are no markets for tr ansferring in e across time and states, so he must consume his ine at each date, i n which case one can s imply reinterpr et yt as current utility. The case of a risk a vers e ag ent facing s ome but not plete markets is more di162。 a recent versio n is BrowningCrossleyS mith (1999). Num er ical analyses wh en risk averse consumers can save but cannot insure against ine risk include Valdi via (1997) and Costain ( 1997). problem is stationary – an o164。er is accepted the worker keeps the job forever. Hence, W (w) = w=(1 161。 ) is the payo164。er (W for the value of working ), and U = b + 175。 U ] is the payo164。er w in hand, let’s call it O(w), satis… es the fol lowing Bellman’s equation: O(w) = max[W (w)。 175。 b + 175。 175。 175。 EO, which expresses wR in terms of the unknown function O. To eliminate E O, … rst use U = wR=(1 161。 ) to rewrite (2) as ( w O(w) = 1161。 for w 184。175。 wR)=(1 161。). Substitution into wR = (1 161。 )b + (1 161。 )175。 161。 1 wR = T (wR) 180。 175。 Z 1 max(w。erent expression for wR is derived as follows. First, rewrite U = b + 175。 175。 Z 1 [W (w) U ]dF (w): (4) wR Then use (1 161。 )U = wR and W (w) 161。 wR )=(1 161。) to get 175。 175。er, and is the form often seen in the literature. Sometimes one also integrates by parts to arrive at 175。 175。 hence, the res er vatio n wage increas es (the worker g ets m ore demanding) as the horizon g ets longer. 10 161。 U . In more plicated models, this may not be possible, so we need the following trick: … rst integrate (4) by parts to write wR = b + 175。 wR and then insert W 0 (w) = 1=(1 161。 ) to get (6). In any case, versions of (6) will be encountered frequently below. This very simple model already makes predictions about individual un employment sp ells. The probability of getting a job each period, called the hazard rate, is given by H = 1 161。 H )d161。 1+r162。1H = : d=1 H Notice, for example, that an increase in b – say, a more generous unemploy ment insurance policy – raises D because it raises wR. It should be obvious that even though he is unemployed longer after b increases, the individual is not worse o164。 wR]. Of course, not everything that leads to an increase in D makes him better o164。er while he is unem ployed. Actually, this subsumes the possibility of receiving no o164。ers, and of receiving more than one, since F can be reinterpreted as the distribution of the best o164。ers each period. In the context of this example we will also show how one can move neatly from discrete to continuous time (which is useful because in some contexts continuous or discrete time may be more convenient, so it is good to know b oth). We will also show how this extension leads naturally to endogenous search intensity. Following the presentation in Mortensen (1986), suppose the length of each period is given by 162。 = 1 . Let a(n。) be the probability of n o164。 n。) the distribution of the for a given worker, but that the workers with the long est sp ells of unemployment h ave t he lowest hazard rates (see, ., Wolpin [1995] for a discussion) . 8 For example, consider changes in F . An increas e (decrease) in all wages, either propor tionately or by a constant, will increas e (decrease) wR and exp ect ed utility f or a searcher, U . A mean pr es erving spread i n F also increases wR and U . Changes i n F have impli cat ions for the aver age wage wA , too, and somet imes counterintuitive result s can obtain. For instance, increasing all wages can actually reduce wA . Ho wever , this and many other counterintuit ive results can be ruled out by ass uming logconcavity – ., that log F 12 1 n=2 w 161。 1 U = b + X a(n。) Z 1[W (w) U ]dG(w。 162。 1 + r162。 It is natural and convenient to assume o164。: that is, a(1。) = 174。 + o(162。 162。), where o(162。)=162。 ! Inserting this into (7), rearranging, and taking the limit as 162。 Z 1 [W (w) U ]dF (w) (8) wR (an alternative derivation of this equation that some people may … nd easier follows from material presented below). The ?ow value of being employed at any w is rW (w) = w, and, in particular, U = W (wR) = wR =r. Hence, (8) implies 174。 wR )dF (w): (9) wR This, or the equation that results from integrating (9) by parts, is the continuous time reservation wage 0 The hazard rate is now H = 174。 F (wR )], the product of the exogenous arrival rate 174。er is accepted 1 161