Model-Free Impulse Responses
Oscar Jorda – 2003
VARs decompose the economy (or more literally, a vector of time series) into systematic/deterministic responses and random sources of variation.
The central benefit of local projections is that they do not require specifying and estimating an unknown multivariate dynamic system. This is especially relevant when the data may not in fact follow such a system, perhaps because certain variables are effectively exogenous to the subsystem of variables you are most interested in. Although they are most often used in macroeonomic studies, this feature makes local projections especially useful in micro settings, hence their adoption in the causal inference setting of LP-DiD (@dubeLocalProjectionsApproach).
VARs are in fact ideal for one-period ahead forecasting. While they can be used for longer horizon forecasting as well, this put them firmly in the realm of extrapolation, leading to bias. They are global approximations to the true dynamic multivariate system, which again, doesn’t necessarily even exist in the first place. Thus in using them you are actually making a significant assumption right off the bat, whether you realize it or not.
If the data do follow a VAR, then a VAR will be the most efficient estimator. However, if the data do not follow such a structure, local projections can be more robust, especially as the forecast horizon increases. There is a good argument that, unless you have strong theory which suggests the data follows a VAR, you should remain agnostic to the DGP and use a local projection to estimate impulse responses. The only caveat to this is that the two methods estimate the same impulse response up to the horizon corresponding to the chosen lag length , i.e. while (@plagborg-mollerLocalProjectionsVARs2021). After that horizon, however, all bets are off – they no longer estimate the same impulse responses unless the DGP is a VAR, which you can’t know for certain in applied settings. See Local projections vs. VARs and @liLocalProjectionsVs2023.
VARs are especially dangerous when the data is persistent or non-stationary, as the model misspecification biases imbued by the cross-horizon restrictions get amplified. These issues are less severe when the data is stationary, since no matter what the impulse responses need to trend toward zero with the horizon length. This will happen automatically in any reasonably accurate VAR estimated on stationary data.