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Bias in Local Projections
Local projections (LPs) are a popular tool in applied macroeconomic research. We survey the related literature and find that LPs are often used with very small samples in the time dimension. With small sample sizes, given the high degree of persistence in most macroeconomic data, impulse responses estimated by LPs can be severely biased. This is true even if the right-hand-side variable in the LP is iid, or if the data set includes a large cross-section (i.e., panel data). We derive a simple expression to elucidate the source of the bias. Our expression highlights the interdependence between ...
When is the Fiscal Multiplier High? A Comparison of Four Business Cycle Phases
We synthesize the recent, at times conflicting, empirical literature regarding whether fiscal policy is more effective during certain points in the business cycle. Evidence of state dependence in the multiplier depends critically on how the business cycle is defined. Estimates of the fiscal multiplier do not change when the unemployment rate is above or below its trend. However, we find that the multiplier is higher when the unemployment rate is increasing relative to when it is decreasing. This result holds using both a long time-series at the U.S. national level and for a panel of U.S. ...
Assessing Macroeconomic Tail Risk
What drives macroeconomic tail risk? To answer this question, we borrow a definition of macroeconomic risk from Adrian et al. (2019) by studying (left-tail) percentiles of the forecast distribution of GDP growth. We use local projections (Jord, 2005) to assess how this measure of risk moves in response to economic shocks to the level of technology, monetary policy, and financial conditions. Furthermore, by studying various percentiles jointly, we study how the overall economic outlook-as characterized by the entire forecast distribution of GDP growth-shifts in response to shocks. We find that ...
Bias in Local Projections
Local projections (LPs) are a popular tool in macroeconomic research. We show that LPs are often used with very small samples in the time dimension. Consequently, LP point estimates can be severely biased. We derive simple expressions for this bias and propose a way to bias-correct LPs. Small sample bias can also lead autocorrelation-robust standard errors to dramatically understate sampling uncertainty. We argue they should be avoided in LPs like the ones we study. Using identified monetary policy shocks, we demonstrate that the bias in point estimates can be economically meaningful and the ...