How it Works
In the McCall (1970) job search model, an unemployed worker receives one wage offer per period drawn from distribution F(w). The worker decides each period whether to accept (earning that wage forever) or reject (receive benefit b, draw again next period).
The optimal policy is a reservation wage w*: accept if w ≥ w*, reject otherwise. The Bellman equation defines w* as the wage that makes the worker indifferent between accepting and continuing search:
The simulation plots the wage offer distribution with the reservation wage threshold. Each drawn offer is shown as a dot; rejected offers appear in red, the accepted offer in green. The histogram of offers accumulates as search progresses.
Frequently Asked Questions
What is the McCall job search model?
The McCall (1970) job search model describes an unemployed worker who receives one wage offer per period drawn from a known distribution F(w). The worker decides to accept (ending search) or reject and continue searching. The optimal strategy is a reservation wage rule: accept if w ≥ w*.
What is the reservation wage?
The reservation wage w* is the minimum wage a worker will accept. It is determined by the Bellman equation: the value of accepting w* equals the value of continuing to search. All offers above w* are accepted; all below are rejected.
What is the Bellman equation in job search?
The Bellman equation states: w*/(1-β) = b/(1-β) + β∫max(w, w*)dF(w), where b is unemployment benefit, β is the discount factor, and F is the wage offer distribution. This defines the optimal stopping point.
How does the discount factor affect search?
A higher discount factor β (closer to 1) means the worker is more patient and places more value on future wages. This raises the reservation wage and prolongs search. A very impatient worker (low β) accepts almost any offer.
How do unemployment benefits affect the reservation wage?
Higher unemployment benefits b increase the opportunity cost of accepting a low wage, raising the reservation wage. This extends unemployment duration but leads to better job matches — the classic efficiency-insurance trade-off.
What determines expected unemployment duration?
Expected duration = 1/(1-F(w*)). If the reservation wage is high, only rare good offers are accepted, and average duration grows. The model predicts that duration increases with benefits and with the dispersion of the wage distribution.
What is optimal stopping theory?
Optimal stopping is the mathematical problem of choosing the best time to take an action (accept an offer) given a sequence of random draws. The McCall model is a classic application: the optimal rule is a threshold (reservation wage) above which you stop.
What wage distribution does the model use?
The original McCall model uses any distribution F(w). Common choices include uniform, log-normal, and normal distributions. Log-normal captures the right-skew of real wage distributions. The reservation wage shifts with the mean and variance of F.
What is job matching theory?
Job matching theory (Mortensen, Pissarides) extends McCall by adding firms searching for workers. The equilibrium wage is determined by Nash bargaining over the joint surplus. This creates the matching function linking vacancies, unemployment, and hires.
Can the reservation wage change over time?
In the basic McCall model with infinite horizon, w* is constant. With finite unemployment benefit duration (benefit exhaustion), the reservation wage falls as the deadline approaches — workers become less choosy, consistent with empirical evidence on job finding spikes near benefit exhaustion.