Local Projections and VARs Estimate the Same Impulse Responses
with Mikkel Plagborg-Møller

Abstract: We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they belong to a spectrum of dimension reduction techniques with common estimand but different bias-variance properties. (ii) VAR-based structural estimation can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under non-invertibility. (iv) Linear VARs are as robust to non-linearities as linear LPs.

Instrumental Variable Identification of Dynamic Variance Decompositions
with Mikkel Plagborg-Møller

Abstract: Macroeconomists often estimate impulse response functions using external instruments (proxy variables) for the shocks of interest. However, existing methods are silent on the importance of the structural shocks for macroeconomic fluctuations. We provide tools for doing inference on variance decom- positions in a general semiparametric moving average model, disciplined only by the availability of external instruments. The share of the variance that can be attributed to a shock is partially identified, albeit with informative bounds. Point identification of most parameters, including historical decompositions, can be achieved under additional assumptions that are weaker than invertibility, a condition imposed in conventional Structural Vector Autoregressive analysis. In fact, we prove that invertibility is testable in the presence of external instruments. We illustrate the practical usefulness of our methods by obtaining a tight upper bound on the importance of monetary policy shocks for U.S. inflation dynamics.

SVAR (Mis-)Identification and the Real Effects of Monetary Policy Shocks
Revised & Resubmitted, American Economic Journal: Macroeconomics

Abstract: I argue that the seemingly disparate findings of the recent empirical literature on monetary policy transmission are in fact all consistent with the same standard macro models. Weak sign restrictions, which suggest that contractionary monetary policy boosts output, present as policy shocks what actually are expansionary demand and supply shocks. Classical zero restrictions are robust to such misidentification, but miss high-frequency effects. Two recent approaches – restrictions on Taylor rules and external instruments – instead work well. My findings suggest that empirical evidence is consistent with models in which the real effects of monetary policy are larger than commonly estimated.

Aggregation in Heterogeneous-Firm Economies: A Sufficient Statistics Approach
with Yann Koby

Abstract: We show that, in a large class of heterogeneous-firm models, the extent to which the production sector admits aggregation to a representative firm is governed by the elasticity of investment with respect to changes in the cost of and the return to investment. Under the near-infinite price elasticities typical of the standard neoclassical model of investment, real or financial micro frictions shape firm-level investment behavior, but become irrelevant for aggregate investment dynamics. Since we find standard calibration targets to be uninformative about these elasticities, we measure them directly through evidence on the firm-level responsiveness of investment to tax changes. Our estimated elasticities are an order of magnitude below the levels required for near-aggregation. To illustrate our results we show that, in heterogeneous-firm models consistent with dampened price elasticities, firm-level real and financial frictions lead to substantial state dependence in the aggregate effects of monetary and fiscal policy.


When Inequality Matters for Macro and Macro Matters for Inequality
with SeHyoun Ahn, Greg Kaplan, Benjamin Moll and Thomas Winberry

Abstract: We develop an efficient and easy-to-use computational method for solving a wide class of general equilibrium heterogeneous agent models with aggregate shocks, together with an open source suite of codes that implement our algorithms in an easy-to-use toolbox. Our method extends standard linearization techniques and is designed to work in cases when inequality matters for the dynamics of macroeconomic aggregates. We present two applications that analyze a two-asset incomplete markets model parameterized to match the distribution of income, wealth, and marginal propensities to consume. First, we show that our model is consistent with two key features of aggregate consumption dynamics that are difficult to match with representative agent models: (i) the sensitivity of aggregate consumption to predictable changes in aggregate income and (ii) the relative smoothness of aggregate consumption. Second, we extend the model to feature capital-skill complementarity and show how factor-specific productivity shocks shape dynamics of income and consumption inequality.