Abstract
This article presents a method to decompose the causal effects of U.S. defense spending on income into a local effect and a spillover effect using panel data. We estimate positive local and spillover multipliers. By construction, the sum provides an estimate of the aggregate multiplier, which is slightly greater than one in our benchmark specification. Using disaggregate data improves precision relative to using aggregate data alone. More generally, we provide a template to conduct inference on local, spillover, and aggregate causal effects in a unified framework.
Introduction
“No man is an island…”
—John Donne, 1624
Over the past few decades, there has been a movement in economics toward applying disaggregate—particularly regional—data to answer macroeconomic questions. For example, Chodorow-Reich (2020) cites 50 papers published between 2012 and 2018 in top economics journals that combine cross-regional variation in exogenous shocks and regional outcomes in an attempt to infer the macroeconomic effects of such shocks. For these papers, the statistical unit of observation is a region. This contrasts with the standard approach to causal inference in empirical macroeconomics, embodied in early work by Sims (1972), in which the unit of observation is an entire economy, which is sampled repeatedly over time. Variation in the treatment, which for Sims is an exogenous change in monetary policy, occurs along the time dimension.
When the treatment of interest is defined at the regional level, spillovers across regions must be considered—regions are not “islands.” If region A receives a treatment, region B may be affected by that treatment even if it receives no treatment on its own. A cross-region “spillover” might arise, for example, from regional trade in goods or movements in factors of production and constitutes a classic violation of the Stable Unit Treatment Value Assumption (SUTVA), which requires that potential outcomes be unaffected by the treatment status of other observational units. The local effect of a treatment need not equal the treatment’s aggregate effect in the presence of spillovers. For example, if there are negative spillovers across regions, then a positive local effect will overstate the aggregate effect of the treatment.
Using this panel-based estimate of the aggregate multiplier, we substantially improve precision relative to one based on aggregate data alone, without taking a stand on the form of the spillover. We develop a technique to estimate the local and spillover effects of region-level treatments. Our parameterization allows us to infer the effects of aggregate-level treatments from these region-level estimates. We illustrate this approach by studying how regional defense spending affects regional income, decomposing government defense spending into (i) a local (or direct) effect and (ii) a spillover (or indirect) effect.
