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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 governing the shape of the aggregate production function. In this paper, I develop an assignment model that provides a microeconomic foundation for aggregate production functions. The shape of the production function depends crucially on the distribution of workers and jobs and the type of technological changes depends crucially on the evolution of these distributions. Sufficient and necessary conditions are provided for the production function to be of the Constant Ratio of Elasticities of Substitution form, a form nesting the broadly used Constant Elasticity of Substitution form. This model provides a way to evaluate how stringent assumptions about the type of production function 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. -- Microfoundations of production function ; tasks assignment ; technical change

This paper presents a general equilibrium assignment model of workers to tasks with endogenous supply of skills. In the model, skills are endogenous and multidimensional, and two types of assignment occur: workers self‐select the type of skills to supply, and firms assign workers to tasks. The model shows that the impact of any skill‐biased technical change on wage inequality is tightly related to the distribution of skills in the population. When the supply of skills is endogenous, productivity effects can be overestimated or underestimated by wage data, and Johnson's () distinction between intensive and extensive technical change is impossible.

This paper develops an assignment model of heterogeneous workers to heterogeneous tasks that provides a microeconomic foundation for aggregate production functions. The shape of the production function is shown to depend crucially on the distribution of tasks. Necessary and sufficient conditions are provided for the production function to be of the constant ratio of elasticities of substitution form, which nests the widely used constant elasticity of substitution (CES) form. For the CES production function, the elasticity of substitution between skill groups of workers is shown to depend only on the variance of tasks in the economy.

This article reviews the literature on two-sided atomless assignment
models of workers to tasks. Using simple parametric examples,
the fundamental differences between the comparative-advantage and
the scale-of-operations models are illustrated. Holding the distributions
of abilities and tasks and the production function of worker-task
pairs constant, the two principles are shown to produce different wage
distributions and wage inequality. These models are useful to evaluate
the general equilibrium effect of technical change on the wage structure.
In all models, Skill Biased Technical Change that impacts the
production function of worker-task pairs leads to rising wage inequality.

While the skill-premium has been rising sharply in the US and the UK for 20 years, the Dutch skill-premium decreased for much of that period and only started to rise in the early 90s. In this paper, we investigate whether the Dutch skill-premium will rise in the next decades. To answer this question, we forecasts the skill-premium using the Katz and Murphy (1992) and the Krusell et al. (2000) models. The Katz and Murphy model (KM) explains demand shifts by skill-biased technological change in unobservable variables captured by a time trend. In contrast, the Krusell et al. model (KORV) explains demand shifts by (observable) changes in the capital stock under a capital-skill complementarity technology. The results show that while the KM model predicts that the skill-premium will have increased by 30% in 2020, based on realistic predictions of the stock of capital, the KORV model predicts that the skill-premium will remain between -5% and +5% of its 1996 level.

We use a simple structural matching model with unobserved heterogeneity to produce counterfactual marriage patterns, and thus quantify the contribution of changes in marital patterns in rising income inequality. We propose an algorithm that allows us to fix the degree of assortative mating without changing the level of marital gains and hence isolate the intensive and extensive margins (i.e. isolate changes in assortative mating from changes in marriage rates). We apply this approach to US data from 1962 to 2017, and show that marital patterns can explain about a quarter of the rise in income inequality, the intensive margin contributing 7%, the extensive margin the remaining 93%. Our algorithm also allows us to show that the extensive margin is itself driven for three‐fifths by a change in the total number of singles and for two‐fifths by a change in the distribution of types among singles (in particular low‐educated women).