In very different fields of economics, economic inference and policy evaluation require economists to parametrize a production function that links measures of input factors to measures of output. While doing so,(strong) assumptions are
implicitly made about microeconomic variables such as the distribution of factors(see Houthakker (1955-1956)), the distribution of ideas (see Jones (2005)), the distribution of productivity (see Rosen (1978)) or the distribution of jobs(this paper). How stringent these assumptions are is not known unless we derive these production functions from more microfounded models.
For instance, in the skill-biased technology change and rising skill-premium literature, a standard assumption is that aggregate production is of the Constant Elasticity of Substitution (CES) type and technical change is skilled-labor augmenting. What the CES assumption implies for the distribution of jobs or what the skilled-labor augmenting technical change implies for the evolution of the distribution of jobs over time is not known. To answer this question, we derive the shape of the aggregate production
function from the assignment of heterogenous workers to heterogenous tasks.
In this model, the shape of the production function crucially depends on the distribution of workers and jobs and the type of technological changes crucially depends on the evolution of these distributions. The model therefore provides a way to evaluate how stringent assumptions about the type of production functions or technological change are by comparing the implied distribution of jobs and its evolution over time to observations of the distribution of jobs and its evolution over time.
For instance, the model indicates that the standard assumptions in the SBTC literature imply that the distribution of jobs is symmetric and constant over time. This is in sharp contrast with recent evidence provided by Autor et al.(2006) and Goos and Manning (2006) about the job polarization in the (US and UK) economy and suggests that the workhorse model in SBTC is too restrictive to capture the main features of the impact of technical change on the relative demand for skills.
We derive from the model the general Constant Ratio of Elasticities of Substitution production function that nests the CES production function. We then show through calibrations that although the CES production function with
changing elasticity of substitution parameter over time replicates some patterns of job polarization, only the CRES production function is able to replicate accurately the empirical magnitude of job polarization observed in the US.