Model specification - search and matching model, Managerial Economics

Model Specification 

We proceed with the model specification in the following steps.

1)  The economy is composed of competitive firms (F  in number) and identical workers  (N  in  number).  In  each  discrete time  period a fraction  6 of  the employed  is  laid  off  and joins the  unemployment pool.  The  fraction  6  is called the  'rate of separation'  in  the literature. Firms hire workers from the pool, not directly  from other firms. 

2)  The marginal  cost of  hiring  for each  firm is an increasing  fimction of its level of hiring. This captures the  idea that a high rate of hiring may  force firms to increase their  search intensity  or,  in  a more general model with heterogeneous workers,  to  accept poor matches between workers and jobs. The marginal cost is also a decreasing function of aggregate unemployment -  high aggregate unemployment makes it easier and cheaper for the firm to find willing and competent workers. 

3)  Since each firm chooses the rate of hiring by  equating the marginal  cost of hiring to the net marginal benefit of hiring,  it  is important to-determine,  in the model, the marginal benefit of hiring to the firm. Assuming a firm to be risk neutral, the marginal value to the firm of a worker hired in this period is the expected present value of his marginal product so long as  he works with the firm.  The marginal value, denoted by q,, is therefore an infinite sum of discounted  marginal  productivities  from  the  present period onwards to infinity. Two discounting factors are used  on  each term:  one, as usual, to take account of  time and the other to take account of the probability that a given worker will have left the job by time (t + i). 

4)  The net marginal benefit of hiring is equal to this marginal value minus the discounted present value  of wages  to be paid  to the worker who  is newly hired. It is in the spirit of search and matching models to assume that there is no labour market in which the wage is set -job  matches require an explicit search  process. The wage  is  set through bargaining  so  as  to  divide  the surplus from the job  between the worker and the firm. To simpli'fy matters, it is assumed in the present model that the worker experiences neither costs nor  benefits from unemployment, so that the  total  surplus from  the job is just the marginal value determined in paragraph 3 above. It  is assumed that the worker obtains a share 5 of the surplus and the firm gets (1 -  6)  with the size of 5 reflecting the bargaining power of  the worker. Thus the marginal benefit of hiring to the firm is given as a fraction of  the marginal value qt: 


5)  Each  firm chooses the rate of hiring, h,, by equating the marginal benefit of hiring specified  in  paragraph  4  above  with  the  marginal  cost of hiring determined in paragraph 2 above 

Posted Date: 10/26/2012 6:24:53 AM | Location : United States

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