Teams: Heterogeneity, Sorting, and Complementarity

TL;DR

This paper develops an econometric framework to measure individual contributions to team output, accounting for heterogeneity, sorting, and complementarities, using observed team outputs over time.

Contribution

It introduces novel estimation methods for both additive and nonlinear production models, including a mixture approach for complementarity, applied to real-world data.

Findings

Economists' contributions to research output quantified.

Inventors' impact on patent quality measured.

New estimation techniques for team production models.

Abstract

How much do individuals contribute to team output? I propose an econometric framework to quantify individual contributions when only the output of their teams is observed. The identification strategy relies on following individuals who work in different teams over time. I consider two production technologies. For a production function that is additive in worker inputs, I propose a regression estimator and show how to obtain unbiased estimates of variance components that measure the contributions of heterogeneity and sorting. To estimate nonlinear models with complementarity, I propose a mixture approach under the assumption that individual types are discrete, and rely on a mean-field variational approximation for estimation. To illustrate the methods, I estimate the impact of economists on their research output, and the contributions of inventors to the quality of their patents.