A1625
Title: Log-OLS and mean elasticities: A specification test
Authors: Stanley Iat-Meng Ko - Tohoku University (Japan) [presenting]
Abstract: Log-linear regressions are widely used to estimate elasticities and proportional effects in applied economics. However, coefficients from log-OLS generally recover derivatives of the conditional expectation of the log outcome, whereas many empirical interpretations concern elasticities of the conditional mean. These two objects need not coincide. The aim is to study when log-OLS admits an elasticity interpretation for the conditional mean. It is shown that, under a multiplicative conditional mean benchmark, this interpretation requires an orthogonality restriction between regressors and the log regression error. A specification test of this restriction is developed using residuals implied by multiplicative mean estimators, and the relative asymptotic efficiency of log-OLS and standard multiplicative alternatives is characterized. Monte Carlo simulations illustrate the finite-sample behavior of the test, and applications to trade gravity equations, health expenditure models, and firm-level investment outcomes show that the distinction is empirically consequential. The results provide a practical diagnostic for assessing when log-linear regressions recover mean elasticities and when multiplicative estimators should be preferred.
