Working Paper: CEPR ID: DP5311
Authors: João Santos Silva; Silvana Tenreyro
Abstract: Although economists have long been aware of Jensen's inequality, many econometric applications have neglected an important implication of it: the standard practice of interpreting the parameters of log-linearized models estimated by ordinary least squares as elasticities can be highly misleading in the presence of heteroskedasticity. This paper explains why this problem arises and proposes an appropriate estimator. Our criticism of conventional practices and the solution we propose extends to a broad range of economic applications where the equation under study is log-linearized. We develop the argument using one particular illustration, the gravity equation for trade, and apply the proposed technique to provide new estimates of this equation. We find significant differences between estimates obtained with the proposed estimator and those obtained with the traditional method.
Keywords: Elasticities; Gravity Equation; Heteroskedasticity; Jensen's Inequality; Poisson Regression
JEL Codes: C13; C21; F10; F11; F12; F15
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Using OLS (C51) | Estimated elasticity of GDP is close to one (E20) |
| Estimated elasticity of GDP is close to one (E20) | Contradicts empirical observations that smaller countries tend to be more open to trade (F14) |
| OLS exaggerates importance of geographical proximity (R12) | PML shows these effects to be statistically insignificant (C52) |
| Heteroskedasticity critically affects estimates from log-linearized models (C51) | Misleading policy implications (D78) |
| Heteroskedasticity (C21) | OLS estimates lead to significant biases in estimated elasticities (C51) |
| Using PML estimator (C51) | GDP elasticities are significantly smaller (E20) |
| PML method is consistent and robust (C52) | OLS leads to biased estimates (C51) |