Cournot Profitability and Measurement Error

Abstract

This paper tests whether firms compete by choosing quantities (Cournot competition) when quantities are measured with error. I extend Aguiar & Kashaev ( Citation: 2021 Aguiar, V. & Kashaev, N. (2021). Stochastic Revealed Preferences with Measurement Error. The Review of Economic Studies, 88(4). 2042–2093. https://doi.org/10.1093/restud/rdaa067 ) , who introduced measurement error into the Revealed Preference test ( Citation: Afriat, 1967 Afriat, S. (1967). The Construction of Utility Functions from Expenditure Data. International Economic Review, 8(1). 67–77. https://doi.org/10.2307/2525382 ) , to the deterministic Revealed Profitability (RP) test of the Cournot model ( Citation: Carvajal, Deb & al., 2013 Carvajal, A., Deb, R., Fenske, J. & Quah, J. (2013). Revealed Preference Tests of the Cournot Model. Econometrica, 81(6). 2351–2379. https://doi.org/10.3982/ecta10175 ) . The RP analysis derives a set of inequalities from the convexity of the firm’s profit-maximization problem. The convexity stems from the demand function and the firm’s cost function, which are both unknown, but the test does not require any parametric assumptions on either. Under the null hypothesis, firms compete in quantities, but observed quantities are mismeasured. To address the measurement error, the test needs only a centering condition, which fixes the location of the true quantities. If the test fails to reject the null hypothesis, it can then be inverted to answer counterfactual questions, such as how much firms would adjust their output in response to a change in price. I apply the method to the international crude oil market, where measurement error might arise from meter and gauge calibration, human recording errors, and the conversion of raw volumes to standard barrels. As the centering condition, I assume measured quantities are correct on average over each half-year. Unlike the deterministic test, the test allowing for measurement error no longer rejects the null hypothesis of Cournot competition at the 5 percent significance level. In this application, failing to account for measurement error thus leads to an over-rejection of the Cournot model.

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