Consider a simple model of career and job search. We assume a worker’s wage, wt, can be
decomposed into two components: career level (θt) and job quality (t):
At the beginning of each period, the worker has a certain career level denoted by θt and job quality
denoted by t. The only choice the individual has to make in very period is one of the following
• Option A: retain the current career and job; (θt;t) stays unchanged. This option is referred
to as “stay put”
• Option B: retain current career, θt, but redraw a new job, t. This option is referred to as “a
• Option C: redraw both a career θt and a job t. This option is referred to as “new life”
The draw of θ and are independent of each other and their past values. θt is drawn from a
distribution denoted by F and t is drawn from a distribution denoted by G. Notice that the worker
does not have the option to retain a job but redraw a career – starting a new career always requires
starting a new job.
A worker aims to maximize the expected sum of discounted wages
subject to the choice restrictions specified above. E is the expectation operator, β is the discount
factor, and wt is the wage at time t.
Let v (θ;) denote the value function, which is the maximum of expected sum of discounted
wages given initial state (θ;). The value function is represented as
v (θ;) = maxfA;B;Cg
Evidently A, B and C correspond to three possible options individual can choose in every period:
“stay put”, “new job” and “new life”, respectively.
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