Dynamic Biases of Static Panel Data Estimators

TL;DR

This paper uncovers a dynamic bias in fixed effects panel estimators caused by ignoring past outcomes, which can distort treatment effect estimates in dynamic settings like economic growth.

Contribution

It introduces a new fixed-T bias correction estimator to address dynamic bias in panel data analysis involving feedback effects.

Findings

Dynamic bias can be larger than Nickell bias.

Correcting for dynamic bias reduces estimated temperature effects on GDP.

The new estimator provides more accurate treatment effect estimates in dynamic panels.

Abstract

This paper identifies an important bias - termed dynamic bias - in fixed effects panel estimators that arises when dynamic feedback is ignored in the estimating equation. Dynamic feedback occurs if past outcomes impact current outcomes, a feature of many settings ranging from economic growth to agricultural and labor markets. When estimating equations omit past outcomes, dynamic bias can lead to significantly inaccurate treatment effect estimates, even with randomly assigned treatments. This dynamic bias in simulations is larger than Nickell bias. I show that dynamic bias stems from the estimation of fixed effects, as their estimation generates confounding in the data. To recover consistent treatment effects, I develop a flexible estimator that provides fixed-T bias correction. I apply this approach to study the impact of temperature shocks on GDP, a canonical example where economic theory points to an important feedback from past to future outcomes. Accounting for dynamic bias lowers the estimated effects of higher yearly temperatures on GDP growth by 10% and GDP levels by 120%.