From a recent draft fiscal stimulus in a monetary union by Emi Nakamura and Jon Steinsson:
We exploit regional variation in military spending in the US to estimate the effect of government spending on output in a monetary union. We use the fact that when the U.S. embarks upon a military buildup, there is a systematic tendency for spending to increase more in some states than others. For example, when aggregate military spending in the US rises by 1 percent of GDP, military spending in California on average rises by about 3 percent of California GDP, while military spending in Illinois rises by only about 0.5 percent of Illinois GDP. Under the assumption that the US doesn’t embark upon military buildups like the Vietnam War because states like California are doing badly relative to states like Illinois, we can use regional variation associated with these buildups to estimate the effect of a relative increase in spending on relative output. We find that when relative spending in a state increases by 1 percent of GDP, relative state GDP rises by 1.5 percent.
At first glance, this multiplier estimate may seem quite large. However, it pertains to a different object than the conventional “close economy aggregate multiplier,” in that it measures the effect of a relative change in government spending in two different states on the relative change in output. We coin the term the “open economy relative multiplier” for this object and develop a theoretical frame- work for interpreting how it relates to the more commonly studied aggregate government multiplier. This framework is useful in interpreting the growing number of studies that attempt to use regional variation to measure the government spending multiplier (e.g., Acconcia et al., 2011; Chodorow-Reich et al., 2012; Clemens and Miran, 2012; Cohen et al., 2011; Fishback and Kachanovskaya, 2010; Serrato and Wingender, 2010; Shoag, 2010; Wilson, 2011).
We show that the open economy relative multiplier is a sharp diagnostic tool in distinguishing among alternative macroeconomic models. The closed economy aggregate multiplier is highly sensitive to how aggressively monetary and tax policy “lean against the wind” in response to a government spending shock, with the multiplier being larger if policy is more accommodative. In contrast, since the open economy relative multiplier focuses on relative changes in government spending and output, these aggregate factors are “differenced out,” allowing for much sharper theoretical predictions.
We show that our estimates are much more consistent with New Keynesian models in which “aggregate demand” shocks—such as government spending shocks—have potentially large effects on output than they are with the plain-vanilla Neoclassical model. In particular, our results suggest that government spending should have large output multipliers when the economy is in a liquidity trap, i.e., the nominal interest rate hits its lower bound of zero and becomes unresponsive to economic shocks. This scenario is particularly relevant in the context of the near zero nominal interest rates that have prevailed in many countries in recent years.