What do the VARs mean? Measuring the output effects of monetary policy

Cochrane argues that even once a VAR-based monetary policy shock is “correctly identified” – the focus of the extensive VAR literature on variable selection and shock orthogonalization – a further, purely theoretical identifying assumption is still required before the estimated impulse-response function can be read as the causal effect of that shock: whether anticipated monetary policy actions, not just unanticipated shocks, can themselves affect output. Using both a flexible linear model that weights anticipated and unanticipated money by a parameter lambda, and an explicit Rotemberg-style sticky-price model parameterized by a price-adjustment-cost parameter alpha, Cochrane shows that this single identifying choice moves the estimated output effects of monetary policy at least as much as, and typically more than, the variable-selection and orthogonalization assumptions the VAR literature usually debates. Applying both models to a standard M2 VAR and a federal-funds-rate VAR on 1959-1992 U.S. quarterly data, he finds that if anticipated money is assumed to have no effect on output – the implicit assumption behind treating the impulse-response function itself as the policy-invariant effect of a shock – the estimated output response to a shock not followed by the customary further monetary expansion is large, hump-shaped, and takes roughly five years to die out; but allowing anticipated money to matter even slightly shrinks this same estimated response dramatically, because most of the impulse-response function’s persistence then reflects the systematic further money growth that has historically followed such shocks, not the shock’s own lagged causal effect. The sticky-price model reproduces this result through a different mechanism and adds the counterintuitive finding that assuming stickier prices implies a smaller and shorter estimated output response to an unanticipated shock, since more of the VAR’s observed dynamics are then attributed to slow price adjustment. Cochrane concludes that data from a single policy regime cannot settle which identifying assumption is correct, but that circumstantial considerations – the otherwise-coincidental similarity in shape between the money and output impulse responses, and the alternative’s reliance on ad hoc multi-year delay and propagation mechanisms – favor giving at least some role to anticipated, systematic monetary policy, with direct implications for how VAR evidence is used to argue about the length and size of monetary policy’s real effects.

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What do the VARs mean? Measuring the output effects of monetary policy