Draft talk:Local Projections

This is a solid article, but I would suggest a few modifications. I'd be happy to discuss this article further as it progresses.

Cumulative IRFs

When the dependent variable is in log‑levels, you can express the left‑hand side as a simple long difference, y_t+h-y_t−1. This formulation simplifies both estimation and inference. Likewise, a fiscal multiplier can be estimated in a single step by regressing the cumulative series of the outcome on the cumulative series of government spending, using an appropriate government‑spending shock as an instrument.

Identification

Local projections (LPs) and vector autoregressions (VARs) are both tools for estimating dynamic treatment effects, but neither solves the identification problem on its own. The result by Plagborg‑Møller and Wolf shows that any identification strategy that works for one method will work for the other, because the impact estimate—once identified—is the same up to a scaling factor (see https://doi.org/10.3982/ECTA17813).

These papers also highlight a clear bias‑variance trade‑off between LPs and VARs. VARs tend to have larger bias but lower variance; reducing the bias requires adding enough lags so that VAR and LP estimates converge. Smoothed LPs and Bayesian VARs can be viewed as moving along this bias‑variance frontier.

Inference

The confidence bands usually reported for local projections do not capture the covariance of the estimates across horizons, so they are not a joint hypothesis test. Montiel‑Olea et al. (2025) review a sup‑t bootstrap estimator that constructs joint intervals with good coverage properties (see https://www.nber.org/books-and-chapters/nber-macroeconomics-annual-2025-volume-40/local-projections-or-vars-primer-macroeconomists).

Bias Correction

It is good practice to apply a bias‑correction procedure to local projections, especially in small samples (see https://doi.org/10.1016/j.jeconom.2024.105655). The idea mirrors the bias‑correction approach used for VARs (https://doi.org/10.1111/j.1467-9892.1990.tb00056.x).

State‑dependence

Best practice for state‑dependent LPs is to interact all control variables with the shock, not just the state indicator (http://www.nber.org/papers/w30971). Moreover, if the state variable is not orthogonal to the shock, the estimator becomes increasingly biased as the shock’s magnitude grows, with the bias vanishing only for infinitesimally small shocks (see https://doi.org/10.1016/j.jeconom.2024.105702).

Additional reference

https://doi.org/10.1146/annurev-economics-082222-065846 Quant-macro (talk) 22:15, 6 February 2026 (UTC)