A Sufficient Statistics Approach for Macro Policy

This 2023 American Economic Review paper by Régis Barnichon and Geert Mesters develops a theoretical framework, with an empirical application to U.S. monetary policy, for evaluating whether current macroeconomic policy is optimal without estimating or fully specifying a structural model of the economy. In a general linear environment with quadratic loss and a unique rational-expectations equilibrium (their Assumption 1), the authors show (Proposition 1) that current policy is optimal if and only if a weighted inner product of two directly observable objects vanishes: the impulse responses of outcomes to a hypothetical policy perturbation, and the forecasts of those outcomes under the current policy path. These two objects — forecasts and impulse responses, already standard outputs central banks produce and monitor — are the paper’s “sufficient statistics” for policy evaluation. When the condition fails, the authors construct the “Optimal Policy Perturbation” (OPP), a rescaled version of the gradient of the loss function with respect to the policy perturbation — formally analogous to a weighted-least-squares regression coefficient rather than a plain steepest-descent step (Eq. 24) — which in this linear-quadratic setting exactly attains the optimum in a single step (Proposition 2); they further decompose the OPP into a component reflecting a systematically nonoptimal policy rule and a component reflecting exogenous policy shocks, extend it to perturbations of only a subset of instruments (e.g., the short rate while holding the yield-curve slope fixed), and derive a “constrained OPP” that respects a policymaker’s precommitment. Empirically, they implement the OPP for U.S. monetary policy over 1990-2022 using inflation- and unemployment-gap forecasts spliced across three sources by sub-period — the Fed’s Monetary Policy Report (MPR, the SEP’s predecessor) plus Greenbook long-run estimates for 1990-2006, the FOMC’s Summary of Economic Projections (SEP, introduced October 2007) plus Greenbook long-run estimates for 2007-2009, and the SEP together with its own long-run estimates from 2009 on — and impulse responses from a six-variable Bayesian VAR (inflation, unemployment, the Fed funds rate, the 10-year bond–Fed funds rate spread, and two monetary-surprise series ordered first) identified with a high-frequency instrument (following Eberly, Stock, and Wright 2020, building on Kuttner 2001 fed funds futures surprises), estimated over 1990-2018, under a dual-mandate loss with equal weight on the inflation gap and unemployment gap and a five-year planning horizon. The short-rate OPP averages roughly 25 basis points over the full 1990-2022 sample, while the slope OPP falls below -1 percentage point during 2009 and remains significantly different from zero through 2009-2013; in illustrative case studies, an April 2008 short-rate OPP of -0.30 implies an additional roughly 25-basis-point cut would have lowered unemployment at the cost of a modest, delayed inflation overshoot, an April 2010 slope OPP of -0.90 implies nearly a full percentage point more accommodation at the long end, and around the September 2020 FOMC precommitment the unconstrained OPP calls for immediate liftoff by March 2021 (with over 90 percent probability that the funds rate is too low) while the constrained OPP — respecting that precommitment — is exactly zero, turning nonzero again by November 2021 once the precommitment’s own conditions had been met. The framework is exact only in the “general linear environment” the authors define; in nonlinear economies the OPP is valid only as a first-order local approximation, it evaluates perturbations around the current policy path rather than assessing the optimality of a precommitment itself, and the empirical implementation inherits the identifying assumptions of the high-frequency-instrument VAR and of taking the FOMC’s own median projections as the relevant forecast.

Geert Mesters | Macro Paper Warehouse

A Sufficient Statistics Approach for Macro Policy