Missing Aggregate Dynamics: On the Slow Convergence of Lumpy Adjustment Models
The estimated persistence of macro aggregates involving lumpy microeconomic adjustment is biased downward when inferred from VAR estimates. The extent of this “missing persistence bias” decreases with the level of aggregation, yet convergence is very slow. Paradoxically, while idiosyncratic shocks smooth away microeconomic non-convexities and are often used to justify approximating aggregate dynamics with linear models, their presence exacerbates the bias. We propose a method to estimate the true speed of adjustment and illustrate its effectiveness via simulations and applications to real data.
The missing persistence bias is relevant for macroeconomists on many grounds. First, when calibrating or estimating models via simulation based methods, macroeconomists should pay attention to the number of agents used in simulations for otherwise they are likely to obtain systematic biases in their parameter estimates. Second, results purporting to find persistence measures that vary systematically with levels of aggregation should be examined with care since the differential speeds may disappear when using estimation methods robust to the missing persistence bias. To illustrate the latter, we show that the difference in the speed with which inflation responds to sectoral and aggregate shocks (Boivin et al 2009; Mackoviak et al 2009) disappears once we correct for the missing persistence bias.
We are grateful to Filippo Altissimo, Fernando Alvarez, Luigi Bocola, William Brainard, Jeff Campbell, Larry Christiano, Olivier Coibion, Ian Dew-Becker, Marty Eichenbaum, Xavier Gabaix, Pablo García, Marc Giannoni, Robert Hall, Fabiano Schiaverdi, Jon Steinsson, Eric Swanson, Yuta Takahashi, Harald Uhlig, Joe Vavra and seminar participants at Chicago Fed, Columbia University University of Chicago, FGV (Rio and Sao Paulo), Humboldt Universität, IEIS Stockholm, MIT, NBER SI (EFCE), PUC (Chile), Universidad de Chile (CEA and FEN), University of Maryland, University of Paris, University of Pennsylvania, Uppsala University, Yale University, NBER EFG Meeting, 2nd ECB/IMOP Workshop on Dynamic Macroeconomics, Hydra and the Central Bank of Chile’s "The Micro and the Macro of Price Rigidities” workshop for their comments on an earlier version of this paper. We thank Juan Daniel Díaz for outstanding research assistance. Financial support from NSF is gratefully acknowledged. This paper is an extensively revised version of “Adjustment is Much Slower than You Think," NBER WP #9898. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.