Differences From Differencing: Should Local Projections With Observed Shocks Be Estimated in Levels or Differences?

Abstract

We show there are large finite‐sample estimation improvements from estimating local projections (LP) in a cumulated differences (long‐differenced) specification vs. a specification in levels when the impulse response of interest is to an externally identified (“observed”) shock. The long‐differenced specification substantially reduces, and in many cases eliminates, estimation bias, as well as significantly improves confidence interval coverage. These improvements increase for more persistent processes, at longer horizons, and for smaller sample sizes and extend to the instrumental variable LP (LP‐IV) setting where the observed shock is an instrument for an endogenous variable of interest. We demonstrate these results via simulations as well as illustrative analytic results.