Are Inflationary Shocks Regressive? A Feasible Set Approach

Research Question. The paper asks whether inflationary shocks are regressive, and demonstrates that the answer depends critically on the source of the shock. A single aggregate inflation statistic conceals radically different distributional consequences depending on whether inflation is driven by an oil supply contraction or by expansionary monetary policy.

Framework. The authors develop a “feasible set approach” grounded in the envelope theorem. They show that the first-order money-metric welfare effect of any macroeconomic shock on a household is summarized by the present discounted value of changes to five components of the household’s budget constraint: (1) consumption prices, (2) wage income, (3) asset dividends, (4) asset prices, and (5) government transfers. Because the envelope theorem implies that endogenous substitution responses are not welfare-relevant to a first order, no assumption about the utility function’s form or the economy’s general equilibrium structure is required. The framework is valid for generic stationary shocks that do not directly shift household preferences.

Double Robustness of Local Projections and Some Unpleasant VARithmetic

This paper provides formal theoretical results on the relative robustness of local projection (LP) and vector autoregression (VAR) confidence intervals for impulse response inference when the data generating process (DGP) is locally misspecified. The research question is whether the widely held belief that LP estimators are more robust to misspecification than VARs is theoretically justified, and if so, precisely under what conditions and with what consequences for VAR inference.

The analytical framework models the DGP as a stationary structural VARMA(1, ∞) that is local to an SVAR(1), of the form y_t = Ay_{t-1} + H[I + T^{-ζ}α(L)]ε_t, where the MA component T^{-ζ}α(L)ε_t represents misspecification that vanishes at rate T^{-ζ} as sample size T grows. The key rate parameter is ζ ∈ (1/4, 1/2), which corresponds to misspecification large enough to be detected with probability approaching 1 by conventional Hausman-type specification tests, yet small enough that the bias-variance trade-off between LP and VAR remains non-trivial asymptotically. The framework encompasses under-specification of lag length, omitted variables, temporal aggregation, measurement error, and failure of shock invertibility — essentially all sources of dynamic misspecification relevant to linearized DSGE models.

Eric Qian | Macro Paper Warehouse

Are Inflationary Shocks Regressive? A Feasible Set Approach

Double Robustness of Local Projections and Some Unpleasant VARithmetic