Econometrics Seminar - Seojeong Lee (UNSW)

Title: What Impulse Response Do Instrumental Variables Estimate?

Abstract: Instrumental variables (IV) are often used to identify impulse responses of a shock to macroeconomic variables. While a macroeconomic shock is often a composite of various shock elements, each of which may well have heterogeneous correlation with the instrument, the correlation is conventionally assumed to be homogenous across elements, and so is the identified impulse response. By accommodating the macroeconomic variable’s heterogeneous responses to diverse shock elements in the structural vector moving average model, we show that the conventional IV estimand of the impulse response, in general, does not identify a meaningful quantity. Only under a sign restriction on the correlation between the instrument and the shock elements, the IV estimand identifies an instrument-specific weighted average of impulse responses of shock elements to the macroeconomic variable of interest, comparable to the local average treatment effect in microeconometrics. Furthermore, we provide conditions under which the component impulse responses are identified without the sign restriction. We illustrate our theory by extending the empirical work reported in Ramey and Zubairy (2018, Journal of Political Economy). By decomposing the IV estimates of the aggregate government spending multiplier, we estimate the defense and the non-defense spending multipliers and find that the non-defense spending multiplier gradually increases over time and can be larger than one after four years even when the aggregate and defense spending multipliers are well below one.