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.

When inequality matters for macro and macro matters for inequality

This paper argues that two standard excuses for relying on representative-agent macro models – that heterogeneous-agent models with aggregate shocks are computationally intractable, and that realistic household heterogeneity does not matter much for aggregate dynamics anyway – are both weaker than commonly believed. To address the first, the authors extend Michael Reiter’s discrete-time linearization approach to continuous time: they solve a model’s stationary equilibrium fully nonlinearly using the finite-difference methods of Achdou et al. (2015), take a first-order Taylor expansion of the full discretized equilibrium system around that steady state using automatic differentiation, and solve the resulting large linear system of stochastic differential equations by standard techniques, exploiting continuous time’s tendency to generate sparse transition matrices; a companion model-free dimensionality-reduction method, adapted from the engineering “model reduction” literature, lets the computer – rather than the researcher – identify the low-dimensional information in the cross-sectional distribution needed to forecast prices accurately, generalizing the “approximate aggregation” logic of Krusell and Smith (1998) beyond cases where a hand-picked set of moments happens to work. On the standard Krusell-Smith (1998) business-cycle model, the method is roughly 1,500 times faster and about three times more accurate (by Den Haan’s 2010 error metric) than the best-performing algorithm in the JEDC comparison project, though its accuracy – being a local, linear approximation – degrades as the size of aggregate shocks grows. To address the second excuse, the authors apply their (open-sourced) toolbox to a two-asset incomplete-markets model, calibrated to match the U.S. joint distribution of income, wealth, and marginal propensities to consume, in which “wealthy hand-to-mouth” households arise endogenously from a costly-to-access illiquid asset. This richer model jointly reproduces two features of aggregate consumption dynamics – sensitivity to predictable income changes and relative smoothness – that have long challenged representative-agent and simple spender-saver benchmarks, and, in an extension with capital-skill complementarity, shows that aggregate productivity shocks can generate substantial, shock-specific swings in income and consumption inequality, providing what the authors call “a striking counterexample to the main result of Krusell and Smith (1998).”

Christian Wolf | Macro Paper Warehouse

Double Robustness of Local Projections and Some Unpleasant VARithmetic

When inequality matters for macro and macro matters for inequality