Basic search analyses of the labor market for “normal times” proceed by taking the value of a worker to a firm as given primarily by technology; and the value to a worker of being without a job as given by preferences (and unemployment insurance). This is partial equilibrium modeling, leaving out the role of the output market. As a method of capturing labor market outcomes around turning points in the business cycle, analyses have examined the dynamics of an economy when these exogenous values shift. However, this still leaves the critical task of endogenizing the values of production and the costs of lack of work. That task is particularly important for times of high unemployment.
While commonly referred to both as changes in the “value of output” and as shocks to “productivity,” the broad range of changes around turning points is strongly supportive of an aggregate demand interpretation. While the term “productivity” may be useful metaphoric shorthand, we should not think that output per worker provides a reasonable measure of the value of additional output for business cycle analysis. With a Walrasian output market, productivity does measure the value of output, but with a search model of the output market, and so a limited ability to make sales, productivity is not necessarily a good measure of the value of output.
In other words, a labor market model is a partial equilibrium model, not a general equilibrium model. As such it can shed light on partial equilibrium questions and partial equilibrium aspects of general equilibrium issues, but can not, by itself, fully evaluate general equilibrium questions, such as the role of aggregate demand stimulation. Combining a frictional labor market with a Walrasian output market seems likely to miss some important links that matter for policy design for extended periods of high unemployment. While the bulk of search analyses have focused on the labor market per se, search also has been used to see how the presence of frictions affects the aggregate economy.