Using Monotonicity Restrictions to Identify Models with Partially Latent Covariates / Minji Bang, Wayne Gao, Andrew Postlewaite, Holger Sieg.

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Bang, Minji

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Material type: Text

TextSeries: Working Paper Series (National Bureau of Economic Research) ; no. w28436.Publication details: Cambridge, Mass. National Bureau of Economic Research 2021.Description: 1 online resource: illustrations (black and white)Subject(s):

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Abstract: This paper develops a new method for identifying econometric models with partially latent covariates. Such data structures arise naturally in industrial organization 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.

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February 2021.

This paper develops a new method for identifying econometric models with partially latent covariates. Such data structures arise naturally in industrial organization 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.