第36回統計科学セミナー（ 2026年1月5日開催）「When Does Log-Linearization Work? A Specification Test with Applications to Trade, Health, and Firm Investment」のご案内

講演概要：

　Applied researchers often estimate log-linear models for positive outcomes, implicitly assuming that the conditional mean of $\log(Y)$ equals the logarithm of the targeted quantity of conditional mean of $Y$. When the variance of the multiplicative error depends on regressors, this equality fails, rendering the log-OLS estimator inconsistent. This paper develops a simple specification test to determine when log-linearization provides a valid conditional mean representation within a multiplicative framework. The test compares the orthogonality condition implied by log-OLS with that of multiplicative pseudo–maximum likelihood estimators such as Poisson (PPML) and Gamma (GPML), offering a direct diagnostic of when the log transformation is appropriate. Monte Carlo evidence shows that log-OLS remains consistent and efficient under mild heteroskedasticity but fails when the error variance systematically depends on regressors. Empirical applications to international trade, health expenditures, and firm-level investment demonstrate that the test successfully distinguishes between valid and misspecified log-linear models. The
procedure provides a practical tool for assessing functional form and guiding model selection in multiplicative settings.