Control VAR: a counterfactual based approach to inference in macroeconomics

Abstract

A recursive VAR is read as causal whenever the policy is ordered first. I show that this ordering is not sufficient when the policy reacts to the economy it is meant to affect: the impulse response then combines the causal effect with a bias from the common trends that the policy reacts to and a bias specific to the treated unit. I develop the Control VAR (CVAR), which compares the treated unit with untreated controls that share its stochastic trends, and removes the first bias and, under exogeneity with respect to the counterfactual cycle, the second. The method allows repeated, continuous and multiple policies, separates the effect of a single policy change from that of its later values, measures the bias of a VAR without controls through the response of the controls, and bounds the remaining bias. I estimate the weights, derive bootstrap inference, show that the CVAR in changes remains valid when the treated unit has a stochastic trend of its own, test whether the more efficient CVAR in levels is supported, and characterise the bias of weights estimated in changes. I apply the CVAR to the Alaska Permanent Fund Dividend, extended unemployment benefits and California's Low Carbon Fuel Standard.

arXiv commentCode and data: https://github.com/Raimondo-P/Control-VAR