Panel Local Projections without Fixed-Effects: A Cumulative-Difference OLS Estimator

Summary

Despite their popularity, the theoretical properties of panel local projections remain only partially understood. Recent work has shown that conventional fixed-effects estimators suffer from an incidental parameter bias. This paper proposes a new unbiased estimator based on pooled OLS and long-differences.

Key points

• Key points:
• We show that cumulative differencing asymptotically removes the individual effects, derive the appropriate lag-augmented local projection specification, and prove that the resulting pooled OLS estimator is unbiased under standard exogeneity and stationarity assumptions.
• Monte Carlo simulations covering alternative persistence structures, sample dimensions, and dynamic specifications demonstrate that the proposed estimator consistently exhibits the smallest finite-sample bias and coverage probabilities close to their nominal levels, while the performance of fixed-effects, random-effects, and split-panel jackknife estimators depends critically on the persistence of both shocks and outcomes.
• Empirical applications further illustrate that estimator choice can materially affect estimated impulse responses. The results suggest that many biases recently documented in panel local projections arise from the interaction between within transformations and dynamic persistence rather than from local projections themselves, providing a simple and robust alternative for empirical researchers.

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