Continuous Time Optimization, Reservation Wage Path and External Shocks

This paper studies how the nonstationarity in the reservation wage arises within a continuous time optimization framework. Assuming a Poisson distributed offer arrivals and a simple job search model with a finite search horizon, the solution of the optimization as summarized by a differential equation is examined. It is shown that the unique solution, i.e., the unique reservation wage path, exists and exhibits dynamic stability. As expected, the path presents decreasing reservation wage over time for the period of search, i.e., participation, in the labor market, under absence of external shocks. With introduction of external shocks which are unanticipated, it is shown that the reservation wage paths exhibit disjoint jumps at the times of the shocks but the paths are decreasing over time at the continuity points. With anticipated shocks, however, the reservation wage paths can have regions of increasing reservation wage. The analysis is extended to examine the reservation wage path along a business cycle. The case of the infinite search horizon is also examined.