Differences From Differencing: Should Local Projections With Observed Shocks Be Estimated in Levels or Differences?
研究发现，当脉冲响应针对外部识别的观测冲击时，使用累积差分（长差分）形式估计局部投影，相比水平值形式能大幅减少估计偏差、改善置信区间覆盖，对持久性强的过程、长预测期和小样本效果更显著。
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.