Controls, not shocks: estimating dynamic causal effects in macroeconomics

A common approach to estimating causal effects in macroeconomics involves constructing orthogonalised ‘shocks’ then integrating them into local projections or vector autoregressions. For a general set of estimators, we show that this two-step ‘shock-first’ approach can be problematic for identification and inference relative to a one-step procedure which simply adds appropriate controls directly in the outcome regression. We show this analytically by comparing one and two-step estimators without assumptions on underlying data-generating processes. In simple ordinary least squares (OLS) settings, the two approaches yield identical coefficients, but two-step inference is unnecessarily conservative. More generally, one and two-step estimates can differ due to omitted-variable bias in the latter when additional controls are included in the second stage or when employing non-OLS estimators. In monetary-policy applications controlling for central-bank information, one-step estimates indicate that the (dis)inflationary consequences of US monetary policy are more robust than previously realised, not subject to a ‘price puzzle’.