Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments

Abstract

External sources of as‐if randomness — that is, external instruments — can be used to identify the dynamic causal effects of macroeconomic shocks. One method is a one‐step instrumental variables regression (local projections – IV); a more efficient two‐step method involves a vector autoregression. We show that, under a restrictive instrument validity condition, the one‐step method is valid even if the vector autoregression is not invertible, so comparing the two estimates provides a test of invertibility. If, however, lagged endogenous variables are needed as control variables in the one‐step method, then the conditions for validity of the two methods are the same.

From Data to Causes I: Building A General Cross-Lagged Panel Model (GCLM)

“…Thus, impulses act as a conceptual randomization device, with CLþCLMA terms showing the short-run effects of random interventions (see Dufour, Pelletier, & Renault, 2006;Dufour & Renault, 1998;Dufour & Tessier, 1993;Lütkepohl, 1993;Sims, 1980). Indeed, longitudinal methods that use planned or natural experiments can rely on this logic by using treatment variables as predictors of random impulses (i.e., putting a time-varying treatment variable "behind" each random impulse; Angrist & Kuersteiner, 2011;Bojinov & Shephard, 2017;Stock & Watson, 2018). Of course, not everyone endorses the idea that impulses approximate randomization, but the fact that cross-lagged models are common and can be shown to rely on past impulses (see Online Appendix B) may help readers appreciate this kind of thought experiment.…”

Does a Big Bazooka Matter? Central Bank Balance-Sheet Policies and Exchange Rates

“…We proxy the variables in the vector ω t−1,h that includes period-t − 1 values and period-t − 1 expectations of future values of the UIP fundamentals by lags of the policy rate, three-month money-market and two-year sovereign rate differentials, CIP deviations, the CitiGroup Macroeconomic Surprise indices, the VIX; moreover, as suggested by Stock and Watson (2018), we also include in the vector ω t−1,h the lags of our instruments given by the ECB and Federal Reserve QE announcements. For the respective policy rates we use the Federal Funds target rate as well as the ECB deposit facility rate (DFR).…”

“…To the extent that QE measures are a systematic response of central banks to adverse shocks, this requirement is unlikely to be satisfied. Although the derivation of our local projection regression equation from a structural equation for the exchange rate shows that in the particular context of this paper our estimation only requires that QE announcements are uncorrelated with contemporaneous and future structural shocks, we explore the robustness of our findings to the inclusion of variables as controls that proxy lagged structural shocks to which the QE announcements might respond to (Jorda et al, 2015;Stock and Watson, 2018). In particular, we include as additional controls the lags of the differential between euro area and US industrial production growth and consumer-price inflation.…”

“…Furthermore, Stock and Watson (2018) suggest that in order to improve efficiency one can include future values of the instruments as controls in the local projection regression. The underlying intuition is that the error term ζ t,h defined in Equation (26) of the second-stage regression in Equation (25) includes future QE shocks.…”

“…The use of external instruments was originally introduced in the VAR context byStock (2008), subsequently used byStock and Watson (2012) as well asMertens and Ravn (2013), and has recently gained prominence throughGertler and Karadi (2015) as well asCaldara and Kamps (2017). SeeStock and Watson (2018) for a survey and discussion.…”