Dynamic Labor Demand:
A Simple Implicit Contract Model
Imagine a group of
identical workers, all of whom are “permanently” attached to a firm.
The workers are
risk averse; the firm is risk neutral.
The future value of the workers’ labor to the firm,
, is unknown today,
but the workers and firm would like to come up with a Pareto-efficient arrangement today that stipulates,
for every possible
, how many workers will be hired and the incomes of every one of them “tomorrow”
The reason firms and workers might want to do this in advance is to take advantage of
some gains from trade (involving the provision of insurance by the risk-neutral firm to the risk averse
workers) that could not be realized in an ex-post spot market for labor services.
Once this arrangement (or “implicit contract”) is in place, the covariation of employment and wages we
observe will simply consist of the “playing out” of the rules of the contract in response to the realizations of
As we demonstrate below, this covariation can be very different from that generated by “spot” labor
markets which operate after
is realized (
can make both workers and firms better off).
1. The base-case model (“
In our initial treatment, we will imagine that there
the possibility of private UI (payments by the firm to
its unemployed workers), optimally chosen to be part of an efficient contract.
We will change this
our treatment here, we will assume that employment adjusts
on the “extensive” margin
(i.e. the number of people employed), so there is no variation in hours per worker. As a result, we can say
that each worker supplies one unit of labor to the firm if employed and zero units otherwise.
assumption is relaxed in the Burdett-Wright and van Audenrode papers on the reading list, which consider
the effects of short-time working and short-time-compensation.
We will also assume that, if some
workers are not employed in a given state of nature (
), these workers are chosen at random from the
Since all workers (by assumption) are permanently attached to the firm, we interpret these episodes
of nonwork as temporary layoffs.
The phenomenon of layoffs by inverse seniority, plus a more continuous
distinction between insiders and outsiders, is explored in my own paper on the reading list.
Finally, we will
assume that the realized value of the state,
, is sufficiently observable to firms, workers and outside
authorities that binding, contingent contracts can be based on it.
The cases of asymmetric information
, and of “nonverifiable”
’s, are considered, among others, by O. Hart, “Optimal Labor
Contracts Under Asymmetric Information:
In more detail, let the value of the firm’s output in state