2026/01/05開催：第36回統計科学セミナー　「When Does Log-Linearization Work? A Specification Test with Applications to Trade, Health, and Firm Investment」

日時：2026年1月5日（月）16:30 - 17:30 
場所：東北大学大学院情報科学研究科2階大講義室
タイトル：When Does Log-Linearization Work? A Specification Test with Applications to Trade, Health, and Firm Investment
講演者：高 日明　准教授（東北大学 大学院経済学研究科）
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.

Ko Iat Meng (Graduate School of Economics and Management, Tohoku University)

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