How to Use One Instrument to Identify Two Elasticities

Abstract: 

In this paper we show that exogenous variation in the tax rate can be used to simultaneously estimate both demand and supply responses. Our result relies on two restrictions that play a central role in virtually all economic models of taxation since Ramsey (1927). First, we make a standard exclusion restriction stating that a tax that is levied on the demand side only affects supply through its impact on the price excluding the tax. Second, the same tax only appears in the demand equation through its impact on the price including the tax. We call the latter restriction the Ramsey Exclusion Restriction (RER). Together the standard exclusion restriction and the RER imply that we can estimate both the demand and supply elasticities with only one instrument. Our result extends to a supply-demand system with J goods and J independent tax rates, as well as a setting where the tax is levied on the supply side. We provide a simple TSLS estimator for both elasticities, as well as a test to assess instrument strength, and a method to test the RER when an additional instrument is available. We apply our method to the Norwegian labor market. We estimate the labor-supply and demand elasticity, using quasi-experimental variation in the payroll tax. Our data is a panel of exporting plants in Norway between 1996-2012. We find evidence of large labor demand and supply elasticities with the caveat that the instrument is rather weak.

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