This paper develops a new method for identifying econometric models with partially latent covariates . Such data structures arise naturally in URLanization and labor economics settings where data are collected using an "input-based sampling" strategy, e.g., if the sampling unit is one of multiple labor input factors. We show that the latent covariates can be nonparametrically identified, if they are  functions of a common shock satisfying some plausible monotonicity assumptions  . With the latent covariates identified, semiparametric estimation of the outcome equation proceeds within a standard IV framework that accounts for the endogeneity of the covariates. We illustrate the usefulness of our method using two applications. The first focuses on pharmacies: we find that production function differences between chains and independent pharmacies may partially explain the observed transformation of the industry structure. Our second application investigates education achievement functions and illustrates important differences in child investments between married and divorced couples.
This paper develops a new method for identifying and estimating production functions with partially latent inputs . Such data structures arise naturally when data are collected using an "input-based sampling" strategy, e.g., if the sampling unit is one of multiple labor input factors. We show that the latent inputs can be nonparametrically identified, if they are strictly monotone functions of a scalar shock a la Olley Pakes (1996) . With the latent inputs identified, semiparametric estimation of the production function proceeds within an IV framework that accounts for the endogeneity of the covariates. We illustrate the usefulness of our method using two applications. The first focuses on pharmacies: we find that production function differences between chains and independent pharmacies may partially explain the observed transformation of the industry structure. Our second application investigates skill production functions and illustrates important differences in child investments between married and divorced couples.
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econometric models
and estimating production functions
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covariates
inputs
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in URLanization and labor economics settings where
when
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covariates
inputs
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strictly monotone
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common shock satisfying some plausible monotonicity assumptions
scalar shock a la Olley
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Pakes (1996)
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covariates
inputs
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outcome equation proceeds within a standard
production function proceeds within an
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education achievement
skill production