Fiscal Stimulus in a Monetary Union: Evidence from US Regions† By Emi Nakamura and Jón Steinsson*

American Economic Review 2014, 104(3): 753–792 http://dx.doi.org/10.1257/aer.104.3.753 Fiscal Stimulus in a Monetary Union:   Evidence from US Regions† By  Emi Nakamura and Jón Steinsson* We use rich historical data on military procurement to estimate the effects of government spending.  We exploit regional variation in military buildups to estimate an “open economy relative multiplier” of approximately 1.5.  We develop a framework for interpreting this estimate and relating it to estimates of the standard closed economy aggregate multiplier.  The latter is highly sensitive to how  strongly aggregate monetary  and tax  policy “leans  against the wind.” Our open economy relative multiplier “differences out” these effects because monetary and tax policies are uniform across the nation. Our evidence indicates that demand shocks can have large effects on output.  (JEL  E12, E32, E62, F33, H56, H57, R12)

 The effect of government spending on output is often summarized by a multiplier—the  percentage  increase  in  output  that  results  when  government  spending  is increased by 1  percent of GDP.  There is a wide range of views about this statistic in the literature. On the one hand, the recent  American Recovery and Reinvestment Act (ARRA)—perhaps  the  largest  fiscal  stimulus  plan  in  US  history—was  motivated  by a relatively high estimate of the multiplier of 1.6  (Romer and Bernstein 2009). Other studies argue that the multiplier is substantially smaller and potentially close to zero. In particular, if the determination of output is dominated by supply-side factors, an increase in government purchases to a large extent “crowds out” private sector consumption and investment. The wide range of views on the multiplier arises in part from the difficulty of measuring it. Changes in government spending are rarely exogenous, leading to a range of estimates depending on the estimation approach.1  Two  main  approaches have  been  used to  estimate  the multiplier  in  the academic literature.  The first  is to study the output effects of increases in military spending associated with wars, which are plausibly unrelated to prevailing macroeconomic conditions  (Ramey and Shapiro 1998; Edelberg, Eichenbaum, and Fisher 1999; Burnside, Eichenbaum, 

* Nakamura: Graduate School of Business, Columbia University, 3022 Broadway, New York, NY 10027  (e-mail: enakamura@columbia.edu); Steinsson: Department of Economics, Columbia University, 420  W 118 St., New York, NY 10027  (e-mail: jsteinsson@columbia.edu).  We thank Nicolas Crouzet, Shaowen Luo, and  Thuy Lan Nguyen for excellent research assistance.  We thank Steve Davis, Gauti Eggertsson, Jordi Galí, Erik Hurst, Karel Mertens, Marcelo Moreira, James Stock, Ivan  Werning, Michael  Woodford, Pierre  Yared, Motohiro  Yogo, and seminar participants at various institutions for helpful comments and conversations. †  Go to  http://dx.doi.org/10.1257/aer.104.3.753 to  visit the article  page  for additional  materials  and author  disclosure statement(s). 1 For surveys of the existing evidence, see, for example, Perotti  (2008), Hall  (2009), Alesina  and Ardagna (2010), and Cogan et al.  (2010). 753

754 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 and Fisher 2004; Ramey 2011; Barro and Redlick 2011; Fisher and Peters 2010). This approach faces  the  challenge  that large  wars  are relatively infrequent.  Another challenge is confounding variation associated with tax increases, price controls, patriotism, and other macroeconomic  shocks.2  The second main approach used to identify the multiplier is the structural  VAR approach  (Blanchard and Perotti 2002; Perotti 2008; Mountford and Uhlig 2009; Ilzetzki, Mendoza, and  Vegh 2013). This approach relies on structural assumptions about output and fiscal policy dynamics to estimate the multiplier. The wide range of views on the multiplier also arises from contrasting results in the theoretical literature.  The government spending multiplier is not a deep structural parameter like the elasticity of labor supply or the intertemporal elasticity of substitution. Different models, therefore, differ in their implications about the multiplier depending on what is assumed about preferences, technology, government policy, and various “frictions.” Simple versions of the Neoclassical model generally imply a small multiplier, typically smaller than  0.5  (see,  e.g., Baxter and King 1993). The multiplier  is  sensitive  to  how  the  spending  is  financed—smaller  if  it  is  financed  by distortionary taxes than lump sum taxes.3  In New  Keynesian models,  the size of the multiplier depends critically on the extent to which monetary policy “leans against the  wind.” Strongly  counter-cyclical  monetary  policy—such  as that  commonly estimated for the  Volcker-Greenspan period—can generate quite low multipliers—comparable to those for the Neoclassical model. However, when monetary policy is less responsive—e.g., at the zero lower bound—the multiplier can exceed two.4  Clearly, there is no “single” government spending multiplier.  This is likely one contributing factor for the wide range of empirical estimates of the multiplier discussed above, since different identification schemes implicitly put different weights on periods when different policy regimes were in place. We analyze the effects of government spending in a monetary and fiscal union— the  United  States.  We  estimate  the  effect  that  an  increase  in  government  spending in one region of the union  relative  to another has on  relative  output and employment.  We refer to this as the “open economy relative multiplier.”  We use variation in regional military procurement associated with aggregate military buildups and drawdowns to estimate these effects. The “open economy relative multiplier” we estimate differs conceptually from the more familiar “closed economy aggregate multiplier” that one might estimate using aggregate US data.  At first glance, this might seem to be a pure disadvantage, since much interest is focused on the closed economy aggregate multiplier.  We show, however, that the open economy relative multiplier has important advantages.  These advantages stem from the fact that  relative  policy is precisely pinned down across regions in the United States:  The Federal Reserve cannot raise interest rates in some states relative to others, and federal tax policy is common across states in the union. 

2 Most of the evidence from this approach derives from the United States’ experience during  WWII and the Korean  War, when changes in US military spending were largest and most abrupt as a fraction of total output. Hall (2009)  and Barro and Redlick  (2011)  emphasize that it is not possible to draw meaningful inference using aggregate data on military spending after 1955 because there is insufficient variation in military spending in this period. 3 See, e.g.,  Baxter and  King  (1993); Ohanian  (1997);  Corsetti, Meier, and Muller  (2012);  and Drautzburg and Uhlig  (2011). 4 At the zero lower bound, fiscal stimulus lowers real interest rates by raising inflation  (Eggertsson 2010; Christiano, Eichenbaum, and Rebelo 2011).

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 755 We show that this property makes the open economy relative multiplier a powerful diagnostic tool for distinguishing among competing macroeconomic models. Military  spending  is  notoriously  political  and  thus  likely  to  be  endogenous  to regional economic conditions  (see, e.g., Mintz 1992).  We, therefore, use an instrumental variables approach to estimate the open economy relative multiplier. Our instruments are based on two  characteristics of military  spending. First, national military spending is dominated by geopolitical events. Second, when national military spending rises by 1  percentage point of GDP, it rises on average by more than 3  percentage points in states that receive a disproportionate amount of military spending—such as California and Connecticut—but by less than one-half of one  percent in states that don’t—such as Illinois.  We use this heterogeneity in the response of regional spending to national military buildups and drawdowns to identify  the  effects  of  government  spending  on  output.5  Our  identifying  assumption is that the United States does not embark on military buildups—such as those associated with the  Vietnam  War and the Soviet invasion of  Afghanistan—because states that receive a disproportionate amount of military spending are doing poorly relative to other states.  This assumption is similar—but weaker than—the common identifying assumption in the empirical literature on the effects of national military spending, that variation in national military spending is exogenous to the United States business cycle. By including time fixed effects, we control for aggregate shocks and policy that affect all states at a particular point in time—such as changes in distortionary taxes and aggregate monetary policy. We estimate the open economy relative multiplier to be roughly 1.5. In other words, when relative per capita government purchases in a region rises by 1  percent of regional output, relative per capita output in that region rises by roughly 1.5  percent.  We develop a theoretical framework to help us interpret our estimate of the open economy  relative multiplier and  assess how it relates to the closed economy aggregate multiplier for the United States. Using this framework, we show that our estimate for the open economy relative multiplier favors models in which demand shocks can have large effects on output. Our estimates line up well with the open economy relative multiplier implied by an open economy New Keynesian model in which consumption and labor are complements.6  This model generates a large closed economy aggregate multiplier when monetary policy is unresponsive, such as when the nominal interest rate is at its zero lower bound.  The “plain-vanilla” Neoclassical model, however, yields a substantially lower open economy relative multiplier, regardless of the monetary response. The relative monetary policy across regions—fixed relative nominal rate and exchange rate—is more accommodative than “normal” monetary policy in the United States—which raises the real interest rate substantially in response to inflationary shocks such as government spending shocks. Our open economy relative 5 Since  regional variation in military  procurement  is much  larger than  aggregate  variation,  this  approach  allows us to overturn the conclusion from the literature that focuses on aggregate data that little can be learned about fiscal multipliers from the post-1960 data. Data from this period has the advantage that it is less affected by unusual factors such as price controls, rationing, patriotism, and large changes in taxes than data from the  WWII and Korean War experiences  (Perotti 2008). 6 Another potential approach to matching our multiplier estimate would be to consider a model with “hand-tomouth” consumers as in Galí, López-Salido, and  Valles  (2007).

756 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 multiplier is thus akin to a closed economy aggregate multiplier for a more accommodative monetary policy than the one seen in the United States under  Volcker and Greenspan.  This implies that our estimate of 1.5 for the open economy relative multiplier  is  perfectly  consistent  with  much  lower  existing  estimates  of  the  closed economy aggregate multiplier  (e.g., those of Barro and Redlick 2011). Since the nominal interest rate is fixed across regions in our setting, one might think that our open economy relative multiplier would be akin to the closed economy aggregate multiplier when nominal interest rates are fixed at the zero lower bound, in which  case  the  New  Keynesian  model  generates  large  multipliers  (Eggertsson  2010; Christiano, Eichenbaum, and Rebelo 2011).  We show that this is not the case.  This simple intuition ignores a crucial dynamic aspect of price responses in a monetary union. Since transitory demand shocks do not lead to permanent changes in relative prices across regions and the exchange rate is fixed within the monetary union, any increase in prices in the short run in one region relative to the other must eventually be  reversed  in  the  long  run.  This  implies  that  even  though  relative  short-term  real interest  rates fall  in response  to government spending  shocks in  our model, relative long-term  real  interest  rates  don’t  (in  contrast  to the  zero  lower  bound  setting). It is the fall in long-term real interest rates that generates a high multiplier in the zero lower bound setting.  The absence of such a fall in our setting explains why the open economy relative multiplier generated by the baseline New Keynesian model is much lower than the closed economy aggregate multiplier at the zero lower bound. The intuition for why the open economy relative multiplier is larger than the closed economy aggregate multiplier for normal monetary policy is similar to the intuition for why the government spending  multiplier is larger under a fixed than a f lexible exchange rate in the Mundell-Fleming model. In fact, we show that the open economy relative multiplier is exactly the same as the aggregate multiplier in a small open economy with a fixed exchange rate. Our estimate can, therefore, be compared with other estimates of multipliers in open economies with fixed exchange rates. Based on data from 44  countries, Ilzetzki, Mendoza, and  Vegh  (2013)  estimate a multiplier of 1.5 for countries that operate a fixed exchange rate regime, but a much lower multiplier for countries operating a flexible exchange rate regime.7 An important difference between our open economy relative multiplier and the closed economy aggregate multiplier is that the regions that receive spending don’t have to pay for it. Could this perhaps explain the “large” relative multiplier we estimate? In this respect, it is important to keep in mind that in a Neoclassical model, an increase in wealth shifts labor supply in and thus reduces the multiplier.  With sticky prices  and home bias, an  increase in  wealth also increases aggregate demand for home goods, which acts to increase the multiplier. In our baseline model, we assume that financial markets are complete across regions.  Thus any increase in wealth associated  with  the  government  spending  is fully  shared  with  the  rest  of  the economy. Following Farhi and  Werning  (2012), we  consider a version of our model in which f inancial markets are incomplete across  regions.  We use this model to compare  the effects of federally financed government spending and locally financed government 7 Kraay  (2012)  estimates a government spending multiplier of about 0.5 for 29 aid-dependent developing countries using variation in  World Bank lending.

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 757 spending. For our baseline parameters, the open economy relative multiplier is only slightly larger for federally financed spending than locally financed spending. The theoretical  framework we describe  helps to interpret recent and ongoing research on the effects of other forms of local government spending  (Acconcia, Corsetti, and Simonelli 2011; Chodorow-Reich et al. 2012; Clemens and Miran 2012; Cohen, Coval, and Malloy 2011; Fishback and Kachanovskaya 2010; Serrato and  Wingender 2010; Shoag 2010;  Wilson 2012). In general, these studies appear to estimate open economy relative multipliers of a similar magnitude as we do. There are, however, a few potentially important differences between our study and these. Some of these studies focus on windfall transfers rather than purchases.8  One advantage of our focus on military purchases is that it seems reasonable to assume that they are separable from other forms of consumption, as is typically assumed in macroeconomic models. Our empirical approach builds on previous work by Davis, Loungani, and Mahidhara  (1997), who study several drivers of regional economic fluctuations, including military procurement.9  Several other studies on the impact of regional defense spending are surveyed in Braddon  (1995).  The most important difference in  our  empirical  methodology  relative  to  these  studies  is  our  use  of  variation  in aggregate military spending in creating instruments to account for potential endogeneity of local procurement spending as well as measurement error. Our work is also related to Canova and Pappa  (2007), who study the price effects of fiscal shocks in a monetary union. Our theoretical analysis is related to earlier work on monetary and  fiscal policy in  a monetary  union by Benigno  and Benigno  (2003)  and  Galí and Monacelli  (2008). The  remainder  of  the  paper  is  organized  as  follows.  Section  I  describes  the  data we use. Section  II presents our empirical results. Section  III presents the model we use to interpret these empirical results. Section  IV presents our theoretical results. Section V concludes. I.  Data Relative to other forms of federal government spending, the geographical distribution of military spending is remarkably well documented, perhaps because of the intense political scrutiny surrounding these purchases. Our main source for military  spending  data  is  the  electronic  database  of  DD-350  military  procurement  forms available from the US Department  of Defense.  These forms document military purchases of everything from repairs of military facilities to the purchase of aircraft carriers.  They cover purchases greater than $10,000 up to 1983 and greater than 

8 Our open economy relative multiplier is not a “windfall” or “manna from heaven” multiplier. Rather, the spending  we  study  is  akin  to  a  foreign  demand  shock.  Agents  are  getting  paid  to  produce  goods  that  are  “exported” for use in defense of the union as a whole. 9 Similarly, Hooker and Knetter  (1997)  estimate the effects of military procurement on subsequent employment growth using a somewhat different specification.

758 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 $25,000 thereafter.10  These data are for the federal government fiscal year.11  We have used the DD-350 database to compile data on total military procurement by state and year for 1966 –2006.12 The DD-350 forms list prime contractors and provide information on the location where  the  majority  of  the  work  was  performed.  An  important  concern  is  the  extent of interstate subcontracting.  To help assess the extent of such subcontracting, we have compiled a new dataset on shipments to the government from defense oriented industries.  The source  of these  data  are  the  Annual  Survey  of  Shipments  by DefenseOriented Industries  conducted by the US Census Bureau from 1963 through 1983 (Census Bureau 1963–1983). In Section IIB, we compare variation in procurement spending with these shipments data. Our primary measure of state output is the GDP by state measure constructed by the US Bureau of Economic  Analysis  (BEA), which is available since 1963.  We also make use of analogous data by major SIC/NAICS grouping.13  We use the Bureau of Labor  Statistics  (BLS)  payroll  survey  from  the  Current  Employment  Statistics  (CES) program to measure state-level employment.  We also present results for the BEA measure of state employment which is available  since 1969.  We  obtain state  population data from  the Census Bureau.14  We  obtain  data on oil prices  (the annual  average spot price of  West  Texas Intermediate)  and the Federal Funds rate  (annual average) from the St. Louis Federal Reserve’s FRED database. Finally, to analyze price effects, we construct state and regional inflation measures from  several  sources.  Before  1995,  we  rely  on  state-level  inflation  series  constructed by Del Negro  (1998a, b)  for the period 1969–1995 using a combination of BLS regional inflation data and cost of living estimates from the  American Chamber of Commerce  Realtors Association  (ACCRA).15  After 1995, we construct state-level price indexes by multiplying a population-weighted average of cost of living indexes from the  ACCRA for each region with the US aggregate Consumer Price Index. Reliable annual consumption data are, unfortunately, not available at the state level for most of the time period or regions we consider.16 10 Purchases reported on DD-350 forms account for 90  percent of military purchases. DD-1057 forms are used to summarize smaller transactions but do not give the identity of individual sellers. Our analysis of census shipment data in Section  II suggests DD-350 purchases account for almost all of the time-series variation in total military procurement. 11 Since 1976, this has been from October 1 to September 30. Prior to 1976, it was from July 1 to June 30. 12 The electronic military prime contract data file was created in the mid-1960s and records individual military prime contracts since 1966.  This occurred around the time Robert McNamara was making sweeping changes to the procurement  process of the US  Department of Defense.  Aggregate statistics before this point do not appear to  be a reliable source of information on military purchases since large discrepancies arise between actual outlays and procurement for the earlier period, particularly at the time of the Korean  War. See the Department of Defense Greenbook  for aggregate historical series of procurement and outlays. 13 The data are organized by SIC code before 1997 and NAICS code after 1997.  The BEA publishes the data for both systems in 1997, allowing the growth rate series to be smoothly pasted together. 14 Between census  years,  population is  estimated  using a  variety of  administrative  data sources  including  birth and death records, IRS data, Medicare data, and data from the Department of Defense. Since 1970, we are also able to obtain population by age group, which allows us to construct estimates of the working age population. 15 See  Appendix  A of Del Negro  (1998a)  for the details of this procedure. 16 Retail sales estimates from  Sales and Marketing Management Survey of Buying Power  have sometimes been used as a proxy for state-level annual consumption. However, these data are constructed by using employment data to impute retail sales between census years, rendering them inappropriate  for our purposes. Fishback, Horrace,  and Kantor  (2005)  study the longer run effects of New Deal spending on retail sales using census data.

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 759 II.  Measurement of the Open Economy Relative Multiplier A.  Empirical Specification and Identification We use variation in military procurement spending across states and regions to identify  the  effects  of  government  spending  on  output.  Our  empirical  specification  is (1)    Y it  −   Y it−2  _ Y it−2    =   α i  +   γ t  +  β      G it  −   G it−2  _ Y it−2    +   ε it, where    Y it   is per capita output in region  i  in year  t,    G it   is per capita military procurement spending in region  i  in year  t, and    α i   and    γ t   represent state and year f ixed effects.17  The inclusion of state fixed effects implies that we are allowing for state specific time trends in output and military procurement spending.  The inclusion of time fixed effects allows us to control for aggregate shocks and aggregate policy—such as changes in distortionary taxes and aggregate monetary policy.  All variables in the regression are measured in per capita terms.18  We regress two-year changes in output on two-year changes in spending, as a crude way of capturing dynamics in the relationship between government spending and output.19  We  use annual panel data on state and regional output and spending for 1966 –2006 and account for the overlapping nature of the observations in our regression by clustering  the standard  errors by  state or  region.  The  regional data  are  constructed by aggregating state-level data within census divisions.  We make one adjustment to the census divisions.  This is to divide the “South  Atlantic” division into two  parts because of its large size.20  This yields ten  regions made up of contiguous states. Our interest focuses on the coefficient  β  in regression  (1), which we refer to as the “open economy relative multiplier.” An important challenge to identifying the effect of government spending is that government spending is potentially endogenous since military spending is notoriously political.21  We, therefore, estimate equation  (1)  using an instrumental variables approach. Our instruments are based on two  characteristics of the evolution of military spending. Figure  1 plots the evolution of military procurement spending relative to state output for California and Illinois, as well as military procurement 17 We  deflate  both  regional output  and  military  procurement  spending  using  the national  CPI  for  the United  States. 18 A potential concern with normalizing on both sides of the regression  by state-level output and population is that measurement error in these variables might bias our results. However, we use instrumental variables that are based on variation in national government spending and thus uncorrelated with this measurement error.  This should eliminate any bias due to measurement error.  We have also run a specification  where we regress the level of output growth on the level of government spending.  This yields slightly larger multipliers. 19 An alternative approach would be to use one-year changes in output and government spending and include lags and leads of government spending on the right-hand side.  We have explored this and found that our biannual regression  captures  the  bulk  of  the  dynamics  in a  parsimonious  way.  The  sum  of  the  coefficients  in  the  dynamic specification is somewhat larger.  This is mostly due to positive coefficients on the first three leads, suggesting that there may be some anticipatory affects. However, the standard errors on each coefficient in this specification are large and dynamic panel regressions with fixed effects should be analyzed with care since they are, in general, inconsistent. Also, there may be measurement error in the timing of the procurement spending variable we use and some of the work may actually be carried out in the year after  (or before)  the year the procurement spending is recorded. 20 We place Delaware, Maryland,  Washington DC, Virginia, and  West Virginia in one region, and North Carolina, South Carolina, Georgia, and Florida in the other. 21 See Mintz  (1992)  for a discussion of political issues related to the allocation of military procurement spending.

760 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 California National Illinois 1966 1970 1974 1978 1982  1986  1990 1994  1998 2002  2006 Figure 1. Prime Military Contract Spending as a Fraction of State GDP spending relative to total output for the United States as a whole.22  First, notice that most of the variation in national military spending is driven by geopolitical events— such as the  Vietnam  War, Soviet invasion of  Afghanistan, and 9/11. Second, it is clear  from  the  figure  that  military  spending  in  California  is  systematically  more  sensitive to movements  in national military spending than military spending in Illinois. The  1966 –1971  Vietnam  War  drawdown  illustrates  this.  Over  this  period,  military procurement in California fell by 2.5  percentage points  (almost twice the national average), while military procurement  in Illinois fell by only about 1  percentage point  (about 2/3 the national average).  We use this variation in the sensitivity of military spending across regions to national military buildups and drawdowns to identify the effects of government spending shocks. Our identifying assumption is that the United States does not embark on a military buildup because states that receive a disproportionate amount of military spending are doing poorly relative to other states.  This assumption is similar—but weaker than—the common identifying assumption in the empirical literature on the effects of national military spending, that variation in national military spending is exogenous to the US business cycle. We employ two  separate approaches to constructing instruments that capture the differential sensitivity of military spending across regions to national military buildups and drawdowns.23  Our baseline approach is to instrument for state or region military procurement using total national procurement interacted with a state or region dummy.  The “first stage” in the two-stage least squares interpretation of this procedure  is  to  regress  changes  in  state  spending  on  changes  in aggregate  spending and  fixed effects allowing for  different  sensitivities across different states.  This 22 Below,  we  will  sometimes  refer  to  spending  relative  to  GDP  simply  as  spending  and  the  change  in  spending divided by GDP simply as the change in spending, for simplicity. 23 Murtazashvili  and  Wooldridge  (2008)  derive conditions for consistency of the fixed effects instrumental variables estimator we employ for a setting in which the multiplier varies across states.

図

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 761 Table 1—States Most Sensitive to  Aggregate Military Buildups Missouri Connecticut Texas Vermont New Hampshire Massachusetts Kansas California Georgia Louisiana Note:  The  table  lists  the  ten states  for which log  state  military  procurement  spending  increases the most when log national military procurement spending increases in descending order. yields scaled versions of changes in national spending as fitted values for each state. Table  1 lists the states for which state procurement spending is most sensitive to variation in national procurement spending.  We also employ a simpler “Bartik” approach to constructing instruments  (Bartik 1991). In this case, we scale national spending for each state by the average level of spending in that state relative to state output in the first five years of our sample.24 We estimate the effects of military spending on employment and inflation using an analogous approach. For employment, the regression is analogous to equation  (1) except  that  the  left-hand-side  variable  is  ( L it  −   L it−2 )/ L it−2  ,  where    L it   is  the  employment rate  (employment divided by population). For the inflation regression, the left-hand-side variable is  ( Pit  −   Pit−2 )/ Pit−2  , where    Pit   is the price level. US  states  and  regions  are  much  more  open  economies  than  the  United  States  as a whole. Using data from the US Commodity Flow Survey and National Income and Product  Accounts, we estimate that roughly 30  percent of the consumption basket of the typical region we use in our analysis is imported from other regions  (see Section  IIID for details). Even though a large majority of goods are imported, the overall level of openness of US regions is modest because services account for a large fraction of output and are much more local.  This estimate suggests that our regions are comparable in openness to mid-sized European countries, such as Spain. B.  Subcontracting of Prime Military Contracts An important question with regard to the use of prime military contract data is to what extent the interpretation of these data might be affected by subcontracting to firms in other states. Fortunately, a second source of data exists on actual shipments to the government from defense oriented industries.  These data were gathered by the Census Bureau over the period 1963 –1983 as an appendage to the Annual Survey of Manufacturers.  They have rarely been used, perhaps because no electronic version previously existed.  We digitized these data from microfilm. 24 Nekarda and Ramey  (2011)  use a similar approach to instrument for government purchases from particular industries.  They use data at five year intervals to estimate the share of aggregate government spending from different industries.

762 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 35 30 25 Billion $ Billion $ 20 15 10 0 5 10 0123456789 California Prime military contracts Military shipments Massachusetts 10 Billion $ Billion $ 2002 2006 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 1966 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 1966 1970 1974 1978 1982 1986 1990 1994 1998 0123456789 30 25 20 15 10 0 5 2002 2006 1966 1970 1974 1978 1982 1986 1990 1994 1998 Connecticut Texas Figure 2. Prime Military Contracts and Military Shipments Figure  2 illustrates the close relationship between these shipment data and the military procurement data for several states over this period—giving us confidence in the prime military contract data as a measure of the timing and magnitude of regional military production.  To summarize this relationship, we estimate the following regression of shipments from a particular state on military procurement, (2)  MS it  =   α i  +  βMPS it  +   ε it, where  MS t   is the value of shipments from the Census Bureau data and  MPS it   is military procurement spending.  This regression yields a point estimate of  β  =  0.96, indicating that military  procurement moves on average  one-for-one with the value of  shipments.  The  small differences  between  the two  series  probably indicate that they both measure regional production with some error.  As we discuss below, one advantage of the instrumental variables approach we adopt is that it helps adjust for this type of measurement error. C.  Effects of Government Spending Shocks The first row of  Table  2 reports the open economy relative multiplier  β  in regression  (1)  for our baseline instruments. Standard errors are in parentheses and are clustered by states or regions.25  In the second  row of  Table  2, we present an analogous set of results using a broader measure of military spending that combines military procurement spending with compensation of military employees for each 25 Our standard errors thus allow for arbitrary correlation over time in the error term for a given state or region. They also allow for heteroskedasticity.

Vol. 104 No. 3state or region. We present results for output both deflated by national CPI and our measure of state CPI.26The point estimates of β for the output regression range from 1.4 to 1.9, while the point estimates of β for the employment regression range from 1.3 to 1.8. The estimates using regional data are, in general, slightly larger than those based on state data, though the differences are small and statistically insignificant. The standard errors for the state regressions range from 0.3– 0.4, while those for the region regres-sions range from 0.6– 0.9. As is clear from Figure 1, the variation we use to estimate the multiplier is dominated by a few military buildups and drawdowns.These results control for short-term movements in population associated with gov-ernment spending by running the regressions on per capita variables. The last column of Table 2 looks directly at population movements by estimating an analogous speci-fication to equation (1) where the left-hand-side variable is (Pop it  −  Pop it−2 )/Pop it−2and the right-hand-side government spending variable is constructed from the level of government spending and output rather than per capita government spending and output. We find that the population responses to government spending shocks are small and cannot be distinguished from zero for the two year time horizon we con-sider.27 We also present estimates of the effects of military spending on consumer prices. These are statistically insignificantly different from zero, ranging from close to zero to a small positive number.Figure 3 gives a visual representation of our main specification for output. The figure plots averages of changes in output against predicted military spending (based on our first-stage regression), grouped by 30 quantiles of the predicted military spending variable. Both variables are demeaned by year and state fixed effects. The 26 When deflating by our measure of state CPI in Table 2, we impute the state CPI’s for the first two years using our baseline instrumental variables regression of state CPI on procurement spending.27 Our estimates appear consistent with existing estimates of regional population dynamics. Blanchard and Katz (1992) show that population dynamics are important in determining the dynamics of unemployment over longer horizons.

図3

764 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 0.02 0.01 0 0.01 0.02 0.01 0.005 0 0.005 0.01 Figure 3. Quantiles of Change in Output versus Predicted Change in Military Spending Notes:  The figure shows averages of changes in output and predicted military spending  (based on our first-stage regression), grouped by 30  quantiles of the predicted military spending variable. Both variables are demeaned by year and state fixed effects. vast majority of points in the figure are located in the northeast and southwest quadrants, leading  to a positive coefficient in our IV regression.  To assess the robustness of our results to outliers, we have experimented with dropping states and regions with especially large or small estimated sensitivity of spending to national spending and this slightly raises the estimated open economy relative multiplier.28 In  Table  3, we report results for the simpler “Bartik” approach to constructing instruments. For output, this approach yields an open economy relative multiplier of roughly 2.5 for the states and 2.8 for the regions. For employment, this approach also yields larger open economy relative multipliers than our baseline specification—1.8 for states and 2.5 for regions. Our estimates using the Bartik-type instruments are somewhat less precise than those using our baseline instruments.  This arises because, in constructing this instrument, we use the level of spending in each state as a proxy for the sensitivity of state spending to national spending—but it is an imperfect proxy. Table  3  also  reports  a  number  of  alternative  specifications  for  the  effects  of  military procurement on output and employment designed to evaluate the robustness of our results.  We report the output multiplier when per capita output is constructed using a measure  of the  working age population  as opposed  to the  total population.29  We  add the price of oil interacted with state dummies as controls to our baseline regression. 28 Missouri and Connecticut have substantially higher estimated sensitivity of spending to national spending than other states and North Dakota has a substantially negative estimated  sensitivity  (alone  among the states). Dropping any combination of these states from our baseline regression slightly raises our multiplier estimate. Dropping all three yields 1.88  (0.57). 29 State-level measures of population by age group are available from the Census Bureau starting in 1970.  We define the working age population as the population between the ages of 19 and 64.

表3

Vol. 104 No. 3We add the real interest rate interacted with state dummies as controls to our baseline regression. We estimate the employment regression using the BEA’s employment series (available from 1969) instead of BLS payroll employment. Table 3 shows that these specifications all yield similar results to our baseline estimates.We have extensively investigated the small-sample properties of our estimation approach using Monte Carlo simulations. These simulations indicate that neither the regional regressions nor the regressions using the Bartik-type instruments suf-fer from bias associated with weak or many instruments. However, our estimates of the state regressions using our baseline instruments are likely to be conserva-tive in the sense of underestimating the open economy relative multiplier for states by roughly 10 percent (implying that the true state-level open economy relative multiplier is 1.65 rather than 1.43). Intuitively, this downward bias arises because instrumental variables does not fully correct for endogeneity in small samples when instruments are weak or when many instruments are used—i.e., IV is biased in the direction of OLS.30 Table 3 also reports results using the LIML estimator, which is 30 See Stock, Wright, and Yogo (2002) for an overview of this issue. The concern is that the first stage of the IV procedure may pick up some of the endogenous variation in the explanatory variable in the presence of a large num-ber of instruments. In contrast to the canonical examples discussed in Stock, Wright, and Yogo (2002), this actually 

766 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 not affected by the presence of many instruments.  This yields an output multiplier of roughly 2.0.31  Our Monte Carlo simulation also allows us to assess the small sample properties of the standard errors we report. Our simulations imply that the asymptotic  standard  errors  for the  region  regressions  are  slightly smaller than  their small-sample counterparts: the standard 95  percent confidence interval based on the  standard  errors  reported  in  Table  2  is,  in  fact,  a  90  percent  confidence  interval. This adjustment arises from the well-known small-sample bias in clustered standard errors in the presence of a small number of clusters.  This does not apply to the statelevel regressions for which the asymptotic standard errors almost exactly replicate the small sample results from our simulations. A potential concern with interpreting our results would arise if states receiving large  amounts of  military spending  were  more  cyclically  sensitive  than other  states. We have compared the cyclical  sensitivity of states  that receive large and small amounts of military spending.  The standard deviation of output growth is almost identical in states with above-median military spending and in states with belowmedian military spending, indicating that a difference in overall cyclical sensitivity is not driving our results.32 Davis, Loungani, and Mahidhara  (1997)  finds smaller employment multipliers when using data from the Current Population Survey  (CPS)  than when using CES data.  They  argue  that  this  may  be  due  to  shifts  in employment  between  the  selfemployed sector and more formal sectors, since self-employment is only measured in the CPS.  We have run regression  (1)  with CPS data. In this case, the sample period is 1976 –2006 and we use the Bartik-type instruments to avoid the difficulties associated with the many instrument problem discussed above given this short sample period.  The point estimates using CPS data are 1.4  (0.5). Using CES data for the same sample period yields 1.8  (0.4).  The estimate based on CPS data is, thus, smaller, though not significantly so.  This provides some suggestive evidence of shifts between self-employment and the more formal sector. Ramey  (2011)  argues that news about military spending leads actual spending by several quarters and that this has important implications for the estimation of fiscal multipliers.  When we add future spending as a regressor in regression  (1), the coeff icient  on this variable  is positive  and the sum  of the coefficients on  the government spending rises somewhat.  This suggests that our baseline specification somewhat

 biases us  away  from finding a statistically significant result in small samples, since the OLS estimates in our case are close to zero. Our Monte Carlo analysis is roughly consistent with the asymptotic results reported in Stock and Yogo  (2005). The  partial  R 2  of the excluded instruments, a statistic  frequently used to gauge the “strength”  of instruments, is 12  percent for the state regressions and 18  percent for the region regressions.  However, because we use a large number of instruments in our baseline case—one for each state or region—the Cragg-Donald  (1993)  first stage  F-statistic suggested by Stock and Yogo  (2005)  is roughly five for our baseline specification of the state-level regressions and eight for the region-level regressions. For the simpler Bartik-type instrument specification, it is 106 for the state-level regression and 53 for the region-level regression. Our Monte Carlo analysis indicates that, while the large number of instruments in the state-level specification leads to a slight downward-bias in the coefficient on government spending, the standard error on this coefficient is unbiased because of the high  R 2  of our instruments taken as a whole.  We thank Marcelo Moreira, James Stock, and Motohiro Yogo for generous advice on this issue. 31 See Stock and  Yogo  (2005)  for a discussion of the LIML estimator’s properties in settings with many instruments.  The disadvantage of LIML is that its distribution has fat tails and, thus, yields large standard errors. 32 Furthermore, suppose we regress state output growth  Δ Y it   on scaled national output growth    s iΔ Y t, where the scaling factor    s i   is the average level of military spending in each state relative to state output, as well as state and time fixed effects. If states with high    s i   are more cyclically sensitive, this regression should yield a positive coefficient on    s iΔ Y t. In fact, the coefficient is slightly negative in our data. In contrast, when    s iΔ Y t   is replaced with    s iΔ G t , this regression yields a large positive coefficient.

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 767 underestimates  the  multiplier by  ignoring output effects  associated  with anticipated future spending. Table  3 also presents OLS estimates of our baseline specification for output.  The OLS estimates are substantially lower than our instrumental variables estimates. One potential explanation for this is that states’ elected officials may find it easier to argue for spending at times when their states are having trouble economically. Another potential explanation is that our instruments correct for measurement error in the data on state-level prime military contracts that does not arise at the national level.  Such measurement  error  causes  an  “attenuation  bias” in  the OLS  coefficient toward  zero.  We  can  assess  the  importance  of  measurement  error  in  explaining  the difference between our IV and OLS estimates by using the shipments data discussed  in Section IIB  as an instrument  for the prime  military contract data.33  For the  1966 –1982 sample  period  for which  we have  the shipments  data,  this IV procedure  yields  an  open economy  relative multiplier  of  1.3  (0.5),  OLS yields 0.2  (0.2), and IV with the Bartik-type instrument yields 2.0  (0.4).  This suggests that measurement error explains a substantial fraction of the difference between our IV and OLS estimates. Table  4 presents the results for equation  (1)  estimated separately by major SIC/NAICS groupings.  An important point evident from  Table  4 is that increases in government sector output contribute negligibly to the overall effects we estimate. The table also shows that increases in relative procurement spending are not associated with increases in other forms of military output. Effects on measured output in the government sector are less easily interpretable than effects on output in the private sector since much of government output is measured using input costs. Transfers  associated  with  increases  in  public  sector  wages  are  therefore  difficult  to distinguish from changes in actual output. Statistically significant output responses occur in the construction, manufacturing, retail, and services sectors. D.  Government Spending at High versus Low Unemployment Rates We next investigate whether the effects of government spending on the economy are larger in periods when the unemployment rate is already high.  There are a variety of reasons why this could be the case. Most often cited is the idea that in an economy with greater slack, expansionary government spending is less likely to crowd out private consumption or investment.34  A second potential source of such differences is the differential response of monetary policy—central bankers may have less incentive to “lean against the wind” to counteract the effects of government spending increases if unemployment is high.  We show in Section  IV, however, that this second effect does not affect the size of the open economy relative multiplier since aggregate policy is “differenced out.” 33 Since the shipments data are an independent  (noisy)  measure of the magnitude of spending, they will correct for measurement error. But they will not correct for endogeneity due to countercyclicality of spending. 34 This might arise, for example, if unemployment leads to a higher labor supply elasticity  (Hall 2009)  or because of tighter capacity constraints in booms  (Gordon and Krenn 2010).

表4

768THE AMERICAN ECONOMIC REVIEWMARCH 2014To investigate these issues, we estimate the following regression:(3)    Y it  −  Y it−2  _  Y it−2  =  α i  +  γ t  +  β hG it  −  G it−2  _  Y it−2  + ( β l  −  β h )  I itG it  −  G it−2  _  Y it−2  +  ε it,where  I it  is an indicator for a period of low economic slack, and the effects of gov-ernment spending in high and low slack periods are given by  β h  and  β l  respectively. We define high and low slack periods in terms of the unemployment rate at the start of the interval over which the government spending occurs. We present two sets of results; one with slack defined using the national unemployment rate and the other with slack defined using the state unemployment rate.35Table 5 presents our estimates of equation (3). For output, the point estimates support the view that the effects of government spending are larger when unem-ployment is high. Depending on the specification, the open economy relative mul-tiplier lies between 3.5 and 4.5 in the high slackness periods, substantially above 35 When we base our low slack indicator  I it  on the national unemployment rate, we set  I it  = 1 for all states in years when the national unemployment rate is below its median value over our sample. When we base  I it  on the state unemployment rate, we set  I it  = 1 for state i in years when its unemployment rate is below its median over our sample period. When we define slack using the state unemployment rate, we interact the year and state fixed effects with the dummy.

表5

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 769 Table 5 —Effects of Military Spending in High versus Low Unemployment Periods Output Employment National slack State slack National slack State slack βh βl  −    β h 3.54 (1.55) − 2.80 (1.49) 4.31 (1.80) − 3.37 (1.84) 1.85 (0.87) − 0.75 (0.89) 1.32 (0.81) 0.03 (0.84) Notes:  A shorthand for the dependent variable is stated at the top of each column.  The dependent variable is a two-year change divided by the initial value in each case.   All variables are  per  capita.  Standard  errors  are  in  parentheses.  The  unit  of  observation  is  US  states  for  all regressions in the table.  The two regressors are  (i)  the two-year change in military spending and  (ii)  the two-year change in military spending interacted with a dummy indicating low slackness.  We employ two  different measures of slackness: “National slack” refers to whether  the  national  unemployment  rate  is  below  its  median  value  over  the  sample  period; “State slack” refers to whether the state unemployment rate is below its median value over the sample period.  This yields the effect of spending during high unemployment periods  (βh ) and the difference between the effect of spending during low and high unemployment periods (βl  −   β h ).  The national slack regressions include state and time fixed effects.  The state slack regressions include state and time fixed effects interacted with the low slackness dummy.  The regression are estimated by two-stage least squares.  The sample period is 1966 –2006. Output is state GDP. Employment is from the BLS payroll survey. our estimates for the time period as a whole. Given the limited number of business cycles  in our sample,  we are  not, however,  able to estimate  these effects  with much statistical precision.  The difference in the multiplier in the high and low spending periods  is  only  moderately  statistically  significant  (with  p-values  of  0.06  and  0.07). For employment, the multiplier estimates for the high slack periods are close to those for the period as a whole and the difference in the multiplier between the high and low spending periods is relatively small and statistically insignificant.36 III.  A Model of Government Spending in a Monetary Union In this section, we develop a framework to help us interpret the “open economy relative multiplier” that we estimate in Section  II, and relate is to the “closed economy aggregate multiplier,” which has been the focus of most earlier work on government spending multipliers. Many of the issues that arise in interpreting the open economy  relative  multiplier  also  arise  in  the  international  economics  literature.  The model  we  develop,  therefore,  draws  heavily  on  earlier  work  on  open  economy  business cycle models  (Obstfeld and Rogoff 1995; Chari, Kehoe, and McGrattan 2002), and, in particular, the literature on monetary unions  (Benigno and Benigno 2003; Galí and Monacelli 2008). Our model and some of our results are closely related to the analysis of Corsetti, Kuester, and Muller  (2011), who discuss government spending in a small open economy with a fixed exchange rate. The model consists of two  regions that belong to a monetary and fiscal union. We refer to the regions as “home” and “foreign.”  Think of the home region as the region in which the government spending shock occurs—a US state or small group 36 Other recent papers that find evidence for larger multipliers during recessions include  Auerbach and Gorodnichenko  (2012)  and Shoag  (2010).

770 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 of states—and the foreign region as the rest of the economy.  The population of the entire economy is normalized to one.  The population of the home region is denoted by  n. Household preferences, market structure, and firm behavior take the same form in both regions. Below, we describe the economy of the home region. A.  Households The home region has a continuum of household types indexed by  x. A  household’s type indicates the type of labor supplied by that household. Home households of type  x  seek to maximize their utility given by ∞ (4)  E 0   ∑ t=0 βtu( C t,  L t(x)), where  β  denotes the household’s subjective discount factor,    C t   denotes household consumption of a composite consumption good,    L t(x)  denotes household supply of  differentiated  labor  input  x.  There  are  an  equal  (large)  number  of  households  of each type. The composite consumption good in expression  (4)  is an index given by η _ (5) C t  =   [  ϕH1 _ η   CHtη−1 η     1 _ +   ϕF η−1 _ η CFt η     _ η−1 ] , where    C Ht   and    C Ft   denote the consumption of composites of home and foreign produced goods, respectively.  The parameter  η  >  0 denotes the elasticity of substitution between home and foreign goods and    ϕ H   and    ϕ F   are preference parameters that determine  the household’s relative preference  for home and foreign goods. It is analytically convenient to normalize    ϕ H  +   ϕ F  =  1. If    ϕ H  >  n, household preferences are biased toward home produced goods. The subindices,    C Ht   and    C Ft , are given by ] θ _ θ−1   (6)   C Ht  = [  ∫01   c ht (z ) θ−1 _ θ   dz  and   C Ft  = θ _ [  ∫01   c ft (z ) θ−1 θ   dz  ] _ θ−1 , where    c ht(z)  and    c ft(z)  denote  consumption of  variety  z  of  home and foreign  produced goods, respectively.  There is a continuum of measure one of varieties in each region.  The parameter  θ  >  1 denotes the elasticity of substitution between different varieties. Goods markets are completely integrated across regions. Home and foreign households thus face the same prices for each of the differentiated goods produced in the economy.  We denote these prices by    p ht(z)  for home produced goods and  p ft(z)  for foreign produced goods.  All prices are denominated in a common currency called “dollars.”

Vol. 104 No. 3Households have access to complete financial markets. There are no impediments to trade in financial securities across regions.37 Home households of type x face a flow budget constraint given by(7)   P t  C t  +  E t[  M t, t+1  B t+1 (x)] ≤  B t(x) + (1 −  τ t )  W t(x)  L t(x)  +  ∫01Ξ ht (z) dz −  T t,where  P t  is a price index that gives the minimum price of a unit of the consump-tion good  C t ,  B t+1(x) is a random variable that denotes the state contingent payoff of the portfolio of financial securities held by households of type x at the begin-ning of period t + 1,  M t, t+1  is the stochastic discount factor that prices these payoffs in period t,  τ t  denotes a labor income tax levied by the government in period t,  W t(x) denotes the wage rate received by home households of type x in period t,  Ξ ht(z) is the profit of home firm z in period t and  T t  denotes lump sum taxes.38 To rule out Ponzi schemes, household debt cannot exceed the present value of future income in any state of the world.Households face a decision in each period about how much to spend on consump-tion, how many hours of labor to supply, how much to consume of each differentiated good produced in the economy and what portfolio of assets to purchase. Optimal choice regarding the trade-off between current consumption and consumption in dif-ferent states in the future yields the following consumption Euler equation:(8)  u c( C t+j,  L t+j(x))  __   u c( C t,  L t(x))   =    M t, t+j  _ βj   P t+j  _  P t   ,as well as a standard transversality condition. Subscripts on the function u denote partial derivatives. Equation (8) holds state-by-state for all j > 0. Optimal choice regarding the intratemporal trade-off between current consumption and current labor supply yields a labor supply equation:(9)u ℓ  ( C t,  L t(x))  _   u c( C t,  L t(x))   = (1 −  τ t ) W t(x) _  P t    .Households optimally choose to minimize the cost of attaining the level of con-sumption  C t. This implies the following demand curves for home and foreign goods and for each of the differentiated products produced in the economy:(10)   C H, t  =  ϕ H  C t  ( P Ht  _  P t    )  −η  and  C F, t  =  ϕ F  C t  ( P Ft  _  P t    )  −η ,(11)   c ht(z) =  C Ht   ( p ht(z) _  P Ht    )  −θ  and  c ft (z) =  C Ft  ( p ft(z) _  P Ft    )  −θ ,37 Section IVD discusses a version of our model with incomplete financial markets across regions.38 The stochastic discount factor  M t, t+1  is a random variable over states in period t + 1. For each such state, it equals the price of the Arrow-Debreu asset that pays off in that state divided by the conditional probability of that state. See Cochrane (2005) for a detailed discussion.

772 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 where (12)   and (13) _ 1−θ  P Ht  = [  ∫01p ht(z ) 1−θ  dz ] 1 P t  =   [  ϕ H  PHt1−η  +   ϕ F  PFt1−η ] 1 _ _ 1 1−θ and   P Ft  = [  ∫01p ft(z ) 1−θ  dz ] 1−η   . , As we noted above, the problem of the foreign household is analogous.  We, therefore refrain from describing it in detail here. It is, however, useful to note that combining the home and foreign consumption Euler equations to eliminate the common stochastic discount factor yields (14) u c( Ct∗ ,  Lt∗ (x)) _ u c( C t,  L t(x))    =   Q t, where  Q t  =   Pt∗/P t  is the real exchange rate and  Pt∗  denotes the foreign price level. This is  the  “Backus-Smith”  condition  that  describes  optimal  risk-sharing  between  home and foreign households  (Backus and  Smith 1993). For simplicity,  we assume that all households—in both regions—initially have an equal amount of financial wealth. B.  The Government The economy has a federal government that conducts fiscal and monetary policy. Total government spending in the home and foreign region follow exogenous AR(1) processes. Let    G Ht   denote government spending per capita in the home region.  Total government  spending  in  the  home  region  is  then  nG Ht.  For  simplicity, we assume that  government  demand  for  the  differentiated  products  produced  in  each  region takes the same CES form as private demand. In other words, we assume that ) −θ (15)   g ht(z)  =   G Ht  (p ht (z) _ P Ht    and   g ft(z)  =   G Ft  ) −θ _ (p ft(z) P Ft    . The government levies both labor income and lump-sum taxes to pay for its purchases of goods. Our assumption of perfect financial markets implies that any risk associated with variation in lump-sum taxes and transfers across the two  regions is undone through risk-sharing.  (See Section IVD for an alternative case.)  Ricardian equivalence holds in our model.  We describe the policy for labor income taxes in Section IV. The federal government operates a common monetary policy for the two  regions. This policy consists of the following augmented  Taylor-rule for the economy-wide nominal interest rate:  rtn  =   ρ r      rt−1 n +  (1  −   ρ i )( ϕ π     πtag  +   ϕ y      ytag  +   ϕ g      gtag ),

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 773 where hatted variables denote percentage deviations from steady state.  The nominal interest rate is denoted         rtn. It responds to variation in the weighted average of consumer price inflation in the two  regions         πtag  =  n πt  +  (1  −  n) πt∗,  where  πt   is consumer price inflation in the home region and         πt∗   is consumer price inflation in the  foreign region. It also responds to variation in the weighted average of output in the two  regions  ytag  =  n y   t  +  (1  −  n) yt∗ . Finally, it may respond directly to the weighted average of the government spending shock in the two  regions         gtag  =  n g   t  +  (1  −  n) gt∗ . C.  Firms There is a continuum of firms indexed by  z  in the home region. Firm  z  specializes in the production of differentiated good  z, the output of which we denote    y ht (z). In our baseline model, labor is the only variable factor of production used by firms. Each firm is endowed with a fixed, nondepreciating stock of capital.39  The  production function of firm  z  is (17) y ht (z)  =  f ( L t(z)). The function  f  is increasing and concave. It is concave because there are diminishing marginal returns to labor given the fixed amount of other inputs employed at the f irm.  Labor  is immobile  across  regions.  Our  model  yields very similar  results  to  a model in which labor and capital are assumed to be equally mobile and the government spending shock is to per capita  spending.40  We  follow Woodford  (2003)  in assuming that each firm belongs to an industry  x  and that there are many firms in  each industry.  The goods in industry  x  are produced using labor of type  x  and all f irms in industry  x  change prices at the same time. Firm  z  acts to maximize its value, ∞ (18)   E t    ∑ j=0 M t, t+j[  p ht+j(z)  y ht+j(z)  −   W t+j(x) L t+j(z)]. Firm  z  must satisfy demand for its product.  The demand for firm  z’s product comes from three  sources: home consumers, foreign consumers, and the government. It is given by (19)   y ht(z)  =  (nC Ht  +  (1  −  n)  CHt∗   +  nG Ht ) 39 Section IVE discusses two extensions of our baseline model with investment. ) −θ (  p ht(z) _ P Ht    . 40 If labor and capital are equally mobile, factor movements simply affect the relative size of the regions. For example, a positive shock to the home region causes inward migration of both labor and capital and this makes the home region larger. But in per capita terms, the model is identical to a model without factor mobility  (save a slight change in home bias)  as long as the government spending shock is defined in per capita terms and the open economy relative multiplier is thus virtually identical. In contrast, if labor is more mobile then capital, inward migration in response to a positive government spending shock will lower the capital-labor ratio in the home region and, through this channel, lower the per capita government spending multiplier  (and vice versa if capital is more mobile than labor).

774 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 Firm  z  is therefore subject to the following constraint: ) −θ (20) (nC Ht  +  (1  −  n) CHt∗   +  nG Ht ) (  p ht(z) _ P Ht    ≤  f ( L t (z)). Firm  z  takes  its industry  wage    W t(x)  as  given. Optimal  choice of  labor  demand  by the firm is given by (21) W t (x)  =   f ℓ ( L t(z))  S t(z), where    S t(z)  denotes  the  firm’s  nominal  marginal  cost  (the  Lagrange  multiplier  on equation  (20)  in the firm’s constrained optimization problem). Firm  z  can reoptimize its price with probability 1  −  α  as in Calvo  (1983). With probability  α  it must keep its price unchanged. Optimal price setting by firm  z  in periods when it can change its price implies (22)   p ht (z)  =   θ _ ∞  α  j  M t, t+j  y ht+j(z) θ  −  1  E t  ∑ j=0 __ ∞ E t    ∑ k=0 α kM t, t+k  y ht+j(z) S t+j(z). Intuitively, the firm sets its price equal to a constant markup over a weighted average of current and expected future marginal cost. D.  Calibration of Preferences and  Technology We consider the following two forms for the utility function: (23)   (24) u ( C t,  L t(x))  =      Ct1−σ−1   _ 1  −   σ −1     −  χ    L t (x ) 1+ν−1   _ 1  +   ν −1     , u ( C t ,  L t(x))  =    ( C t  −  χ L t(x ) 1+ν−1  /(1  +   ν −1 ) ) 1−σ−1  ___ 1  −   σ −1  . In  the  first  utility  specification,  consumption  and  labor  enter  separably.  They  are therefore neither complements nor substitutes.  The second utility function is adopted from Greenwood, Hercowitz, and Huffman  (1988).  We refer to this utility function as representing GHH preferences. Consumption and labor are complements for households with GHH preferences. Recently, Monacelli and Perotti  (2008), Bilbiie (2011),  and Hall  (2009)  have emphasized  the  implications  of consumption-labor complementarities for the government spending multiplier. For  both specifications  of  utility,  we  must  specify  values  for  σ  and  ν  (χ  is irrelevant when utility is separable and determined by other parameters in the GHH case). In both cases,  ν  is the Frisch-elasticity of labor supply.  We set  ν  =  1.  This  value is somewhat higher than values estimated in microeconomic studies of employed workers, but relatively standard in macroeconomics.  The higher value is meant to capture variation in labor on the extensive margin—such as variation in unemployment and retirement  (Hall 2009, Chetty et al. 2011). As  Hall  (2009)  emphasizes, 

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 775 assuming a high labor supply elasticity raises the government spending multiplier. For the separable utility specification,  σ  denotes the intertemporal elasticity of substitution  (IES).  There is little agreement within the macroeconomics literature on the appropriate values for the IES. Hall  (1988)  estimates the IES to be close to zero,  while  Bansal  and  Yaron  (2004),  Gruber  (2006),  and  Nakamura  et  al.  (2013) argue for values above 1.  We set  σ  =  1, which yields balanced growth for the model with separable preferences,  σ  =  1.  We set the subjective discount factor equal to β  = 0.99, the elasticity of substitution across varieties equal to  θ  =  7 and the elasticity of substitution between home and foreign goods to  η  =  2.41  Larger values of η  yield more expenditure switching between regions in response to regional shocks and thus lower open economy relative multipliers. We assume the production function  f ( L t(z))  =   L t(z ) a   and set  a  =    2 _ 3 . Regarding the frequency with which firms can change their prices, we consider two  cases:  α  =  0 (i.e., fully flexible prices)  and  α  =  0.75  (which implies that firms reoptimize their prices on average once a year). Rigid prices imply that relative prices across regions respond sluggishly to regional shocks.  We set the size of the home region to  n  =  0.1. This roughly corresponds to the size of the average region in our regional regressions  (where we divide the United States into ten regions).  The value of the open economy relative multiplier in our model is relatively insensitive to the size of  n. We set the steady state value of government purchases as a fraction of output to 0.2.  We log-linearize the equilibrium conditions of the model and use the methods of Sims (2001)  to find the unique bounded equilibrium. By doing this we rule out the types of nonlinearities we find suggestive evidence for in Section IID. We use data from the US Commodity Flow Survey  (CFS)  and the US National Income and Product  Accounts  (NIPA)  to set the home-bias parameter    ϕ H. The  CFS reports data on shipments of goods within and between states in the United States. It covers shipments between establishments in the mining, manufacturing, wholesale, and retail sectors. For the average state in 2002, 38  percent of shipments were within state and 50  percent of shipments were within region. However, roughly 40  percent of all shipments in the CFS are from wholesalers to retailers, and the results of Hillberry and Hummels  (2003)  suggest that a large majority of these are likely to be within region. Since the relevant shipments for our model are those from manufacturers to wholesalers, we assume that 83  percent of these are from another region (50 of the remaining 60 percent of shipments). To  calculate  the  degree  of  home  bias,  we  must  account  for  the  fact  that  a  substantial fraction of output is services, which are not measured in the CFS. NIPA data  indicate  that goods  represent  roughly  30  percent  of  US GDP. If  all  inter-region trade were in goods—i.e., all services were local—imports from other regions would  amount  to  25  percent  of  total  consumption  (30  ×  0.83  =  25).  However,  for the United States as a whole, services represent roughly 20  percent of international trade.  Assuming that services represent the same fraction of cross-border trade for regions, total inter-region trade is 31  percent of region GDP  (25/0.8  =  31). We therefore set    ϕ H  =  0.69.  This makes our regions slightly more open than Spain and slightly less open than Portugal.  We set    ϕ H∗   so that overall demand for home

 41 This is the same value for  η  as is used by Obstfeld and Rogoff  (2005), and only slightly higher than the values used by Backus, Kehoe, and Kydland  (1994)  and Chari, Kehoe, and McGrattan  (2002).

776 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 products as a fraction of overall demand for all products is equal to the size of the home population relative to the total population of the economy.  This implies that  ϕ H∗  =  (n/(1  −  n)) ϕ F. We have so  far calibrated  the “fundamentals”—i.e.,  preferences and  technology— for our model economy.  We leave the detailed description of government policy to the next section.  We wish to draw a clear distinction between fundamentals and government policy.  The former determine constraints on the potential effects of government policy. In contrast, monetary and fiscal policy are under the government’s control and therefore “choice variables” from the perspective of an optimizing government, making it relevant to consider not only the policies that have persisted in the past but also the potential effects of alternative government policies. IV.  Theoretical Results In this section, we analyze the effects of government spending shocks in the model presented in Section  III.  We consider several different specifications for the economy’s “fundamentals”  (separable versus GHH preferences, flexible versus sticky prices)  as well as different specifications for aggregate monetary and tax policy. In the Neoclassical  (flexible price)  versions of the model, money is neutral, implying that the specification of monetary policy is irrelevant.  Tax policy is, however, important and we consider two  specifications for tax policy described below. In the New Keynesian  (sticky price)  versions of the model, monetary policy is important and we consider three  specifications of monetary policy within the class of interest rate rules described by equation  (16). The monetary policies we consider are:  (i)  a “Volcker-Greenspan” policy,  (ii)  a “fixed  real-rate”  policy,      and  (iii)  a  “fixed  nominal-rate”  policy.  These  policies  are designed  to  imply  successively  less  “leaning  against  the  wind”  by  the  central  bank in response to inflationary government spending shocks.  The “Volcker-Greenspan” policy is meant to mimic the policy of the US Federal Reserve during the  VolckerGreenspan period. For this case, we set the parameters in equation  (16)  to  ρ  =0.8, ϕ π  = 1.5,    ϕ y  =  0.5, and    ϕ g  =  0.42  This specification of monetary policy implies that the monetary  authority aggressively raises  the real  interest rate to curtail the inflationary effects of a government spending shock. Under the “fixed real-rate” policy, the central bank maintains a fixed real interest rate in response to government spending shocks. However, to guarantee price-level determinacy,  the  central  bank  responds  aggressively  to  the  inflationary effects  of all other shocks. Under the “fixed nominal-rate policy,” the central bank maintains a fixed nominal interest rate in response to government spending shocks. But as with  the  fixed  real-rate  policy,  it  responds  aggressively  to  the  inflationary  effects of all other shocks.  We describe the details of how the fixed real-rate and fixed nominal-rate policies are implemented in online  Appendix  A.  The fixed nominalrate policy is a close cousin of the zero lower bound scenario analyzed in detail in Eggertsson  (2010); Christiano, Eichenbaum, and Rebelo  (2011); and Mertens and Ravn  (2010). It is, in a sense, the opposite of the aggressive “leaning against 42 Many recent papers have estimated monetary rules similar to the one we adopt for the  Volcker-Greenspan period  (see, e.g.,  Taylor 1993 and 1999; Clarida, Galí, and Gertler 2000).

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 777 the wind” embodied in the  Volcker-Greenspan policy because an inflationary shock generates  a  fall in  real  interest rates  (since  nominal rates are held  constant).  The f ixed real-rate policy charts a middle ground. We consider two  specifications for tax policy. Our baseline tax policy is one in which government spending shocks are financed completely by lump-sum taxes. Under this policy, all distortionary taxes remain fixed in response to the government spending shock.  The second tax policy we consider is a “balanced budget” tax policy. Under this policy, labor income taxes vary in response to government spending shocks such that the government’s budget remains balanced throughout: (25) nP Ht  G Ht  +  (1  −  n) P Ft  G Ft  =   τ t    ∫  W t (x)  L t(x)  dx. This policy implies that an increase in government spending is associated with an increase in distortionary taxes.  We assume that the government spending shocks follow  an AR(1)  process and estimate the persistence of this process using data on aggregate  military  procurement  spending.  This  yields a  quarterly  AR(1)  coefficient of 0.933.43  We also in some cases consider the implications of more transitory government spending shocks. We present results for both the closed economy aggregate multiplier that has been studied in much of the previous literature and the open economy relative multiplier that we provide estimates for in Section  II and has been the focus of much recent work  using subregional  data  (Acconcia,  Corsetti,  and  Simonelli 2011; ChodorowReich et al. 2012; Clemens and Miran 2012; Cohen, Coval, and Malloy 2011; Fishback and Kachanovskaya 2010; Serrato and  Wingender 2010; Shoag 2010; Wilson 2012).  We begin in Sections  IVA and IVB by describing results for the case of additively separable preferences.  We then consider the case of GHH preferences in Section  IVC. Finally, in Section  IVE, we consider an extension of our model that incorporates investment. A.  The Closed Economy  Aggregate Multiplier We  define  the  closed  economy  aggregate  multiplier  analogously  to  the  previous literature on multipliers  (e.g., Barro and Redlick 2011)  as the response of total output  (combining home and foreign production)  to total government spending, i.e.,  β in the regression, agg (26)    Ytagg  −   Yt−2 _ Yt−2 agg    agg =  α  +  β Gtagg  −   Gt−2 _ Yt−2 agg    +   ε t, where    Ytagg   denotes aggregate output and    Gtagg   denotes aggregate government spending.  This  regression  is identical  to the  one we  use to measure the open economy relative multiplier—equation  (1)—except that we are using aggregate variables and have dropped the time fixed effects.  We calculate this object by simulating quarterly 

43 Our aggregate military procurement spending data is annual.  We use a simulated method of moments approach to estimate  the persistence of our  quarterly AR(1)  process. We  describe this  procedure in  detail in online Appendix  B.

778 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 Table 6—Government Spending Multiplier in Separable Preferences Model Closed economy   aggregate multiplier Open economy   relative multiplier Panel  A. Sticky prices Volcker-Greenspan monetary policy Constant real rate Constant nominal rate Constant nominal rate  (ρg  =  0.85) Panel B. Flexible prices Constant income tax rates Balanced budget 0.20 1.00 ∞ 1.70 0.39 0.32 0.83 0.83 0.83 0.90 0.43 0.43 Notes:  The table reports the government spending multiplier for output deflated by the regional CPI for the model presented in the text with the separable preferences specification. Panel  A presents  results  for the  model with  sticky  prices, while  panel  B presents  results  for  the model with flexible prices.  The first three  rows differ only in the monetary policy being assumed.  The fourth  row varies the persistence of the government spending shock relative to the baseline parameter values.  The fifth and sixth rows differ only in the tax policy being assumed. data from the model described in Section  III, time-aggregating it up to an annual frequency, and running the regression  (26)  on this data. The first column of  Table  6 reports results on the closed economy aggregate multiplier.  These results clearly indicate  that the closed economy aggregate multiplier is highly sensitive to aggregate monetary and tax policy—a point emphasized by Woodford  (2011); Eggertsson  (2010); Christiano, Eichenbaum, and Rebelo  (2011); and Baxter  and King  (1993). In the New Keynesian model with  a Volcker-Greenspan monetary policy, it is quite low—only 0.20.  The low multiplier arises because the monetary authority reacts to the inflationary effects of the increase in government spending by raising real interest rates.  This counteracts the expansionary effects of the  spending  shock.  For  monetary  policies  that  respond  less  aggressively  to  inflationary shocks, the closed economy multiplier can be substantially larger. For the constant real-rate  policy, the multiplier is  one  (Woodford 2011). Intuitively, since the real interest rate remains constant rather than rising when spending increases there is no “crowding out” of consumption, implying that output rises one-for-one with government spending. For the constant nominal-rate policy, the multiplier is larger than one and can  become very large depending on parameters. It is 1.70 if the government  spending  shock  is  relatively  transient  (half-life  of  one  year,    ρ g  =  0.85 ). With more persistent government spending shocks  ( ρ g  =  0.933 )  it becomes infinite. However, it should be kept in mind that the case we are considering is effectively assuming that the economy stays at the zero lower bound indefinitely. If the economy is expected to revert to, e.g., a  Volcker-Greenspan monetary policy before some fixed future point the multiplier is finite.44  The intuition for the large multipliers with a constant nominal-rate policy is that the government spending shock raises inflationary expectations, which lowers the real interest rate and thereby “crowds in” private demand. 44 Similar  issues  regarding  the  finiteness  of  the  zero  lower  bound  multiplier  arise  in  Eggertsson  (2010)  and Christiano, Eichenbaum, and Rebelo  (2011).

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 779 The second panel of  Table  6 presents results for the Neoclassical model.  These results clearly indicate that the closed economy aggregate multiplier also depends on the extent to which the government spending is financed by contemporaneous distortionary taxes. If the spending is financed by an increase in distortionary taxes in such a way as to maintain a balanced budget period-by-period  (as opposed to by lump-sum taxes), the multiplier falls by about a fourth to 0.32. If distortionary taxes are reduced in concert with an increase in government spending the aggregate multiplier can be substantially higher  (though we do not report this in the table). It is useful to pause for a moment to consider why price rigidity—the feature that distinguishes the New Keynesian and Neoclassical models we consider—matters so much in determining effects of government spending. For concreteness, consider a transitory shock to government spending at the zero lower bound.  This shock puts pressure on prices to rise. In the Neoclassical model with a constant money supply, prices  immediately  jump  up and  begin  falling.  This  implies  that the real  interest  rate rises  on impact  (because  prices  are  falling)  and  crowds  out private  spending.  In  the New  Keynesian  model,  however,  prices  rise  only  gradually  since  many  are  rigid  in the  short  run.  This  implies  that  the real  interest  rate  falls  on  impact  and  thus boosts private spending. It is this difference in the response of the real interest rate to government spending shocks—caused by a difference in the flexibility of prices—that explains the difference in the multiplier across these models. The sensitivity of the closed economy aggregate multiplier to aggregate monetary and tax policy probably explains some of the wide range of estimates in the empirical  literature.  Most  economists  agree  that  the  extent  to  which  the  Federal  Reserve has “leaned against the wind” has varied substantially over the last century  (see, e.g., Clarida, Galí, and Gertler 2000).  This sensitivity carries over to other variables. Much  recent  work  on  the  effects  of  fiscal  policy  has  focused  on  consumption,  real wages, and markups  (Ramey 2011, Perotti 2008). In our New Keynesian model with  Volcker-Greenspan  monetary  policy,  the  closed  economy  aggregate  multiplier is negative for all three of these variables, while it is positive for more accommodative monetary policy. The enormous variation in possible values for the closed economy aggregate multiplier depending on the policy environment underscores the difficulty of using the closed  economy aggregate multiplier  to distinguish among alternative views of how government spending affects the economy. Under “normal” monetary policy (i.e., the  Volcker-Greenspan  policy), it may be exceedingly difficult to distinguish between the Neoclassical and New Keynesian models. Both frameworks predict little effect of  government spending  on output. Yet  this does  not imply that  the models have similar implications overall.  While the Neoclassical model continues to generate  a low  aggregate multiplier  in the fixed  nominal rate scenario  that we use to proxy for the zero lower bound, the New Keynesian model can generate extremely large multipliers in this environment. In the next section, we illustrate that the open economy  relative  multiplier  has  important  advantages  when  it  comes  to  distinguishing between  different views of  how government spending affects the economy, because  it  is  not  sensitive  to  the  specification  of  aggregate  monetary  and  tax  policy but rather to the relative policies across regions—which are precisely pinned down in a monetary and fiscal union.

780 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 B.  The Open Economy Relative Multiplier Contrast the wide range of different closed economy aggregate multipliers produced  by  our  model  for  different  monetary  policies  with  the  complete  stability  of the open economy relative multiplier reported in the second  column of  Table  6.  The open  economy  relative  multiplier  is  calculated  by  estimating  equation  (1)  using  the regional data from the model—the same specification we use in our empirical analysis.45  For all three  specifications of monetary policy we consider, the open economy relative  multiplier  is 0.83.  Furthermore,  the  fifth  and sixth  rows  of  Table  6  present results for the different specifications of tax policy in the Neoclassical model and illustrate  that  the  open  economy  relative  multiplier  is  also  completely  insensitive  to aggregate tax policy.  The open economy relative multiplier  is  sensitive to economic fundamentals  (e.g., the degree of price rigidity)  and to region-specific policies  (e.g., the persistence of the regional government spending shock)  as we discuss below. Intuitively, the open economy relative multiplier is independent of aggregate policy because we “difference out” aggregate shocks and aggregate policy by including time fixed effects in the regression. In a monetary union, the monetary authority cannot respond to a shock in one region by making monetary policy tighter in that region alone.  The relative monetary policy between the two  regions is, therefore, held fixed by the monetary union in a very precise way, regardless of the stance of aggregate monetary policy. In this sense, the open economy relative multiplier is akin to the closed economy aggregate multiplier for a relatively accommodative aggregate monetary policy—more accommodative than US monetary policy under Volcker and Greenspan. The open economy relative multiplier is smaller than one for a wide range of parameters in our model.  This is most easily seen by considering the “Backus-Smith” risk-sharing condition    c t  −   ct∗  =  σ q t. An increase in home government spending will increase the relative price of home goods and therefore decrease the “real exchange rate”  ( Q t  =   Pt∗ / P t ). By the Backus-Smith condition, this implies that home consumption must fall relative to foreign consumption. In other words, government spending  “crowds  out”  private  spending  in  relative  terms  implying  a  relative  multiplier that is smaller than one. Since the relative nominal interest  rate is constant in response to a regional government spending shock, it is tempting to think that this situation is analogous to  the zero lower bound, where the nominal interest rate is fixed at zero in response to government spending shocks.  As in the zero lower bound case, an increase in relative government spending in the home region can raise expected inflation, lowering relative short-term real interest rates. However, unlike the zero lower bound case, the relative  long-term  real interest rate does not fall in response to a fiscal shock. The fiscal shock leads to an immediate rise in relative prices and expectations of further  increases  in  the  short term.  This lowers the  relative short  term  real interest rate.  However,  since  a  transitory shock  to  spending does  not  lead  to  a  permanent change in relative prices and the exchange rate is fixed within the monetary union, any short term increase in prices in one region relative to the other region must be 

45 Specifically, we take a linear approximation of the dependent and independent variables in equation  (1)  and run the regression using these approximate variables. See online  Appendix C for details.

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Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 781 0.25 0.20 0.15 0.10 0.05 0.00 0.05 0.10 Price level Real interest rate 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

80 Figure 4. Prices and Real Interest Rates after a Government Spending Shock Note:  The  figure  plots the  relative  price  level and  the relative real  interest  rate  in  the two  regions for the model with separable preferences after a positive government spending shock to the home region. undone by a fall in relative prices in that region later on.46  In fact, after their initial jump, relative prices are anticipated to fall more in the long run than they are anticipated to rise further in the short run.  This implies that the relative long-term real interest rate actually rises slightly in the home region in response to an increase in government spending.47 To more clearly see the intuition for this result, Figure  4 presents the impulse response of the price level and the real interest rate in the home region relative to the foreign region after a government spending shock in our model.  The home price level rises for several periods, but then falls back to its original level.  This movement in prices implies that the real interest rate in the home region initially falls, but then  rises  above  its  steady  state  level  for  a  prolonged  period.  Figure  5  shows  what happens to consumption in the home region relative to the foreign region after a government spending shock. Despite the short-run fall in the real interest rate, consumption falls.  This is because households anticipate  high real rates  in  the future— equivalently, they face a high current long-term real interest rate—and therefore cut their consumption. Since the relevant interest rate for consumption decisions—the long-term real interest rate—actually rises slightly in response to an increase in government spending irrespective  of the  persistence  of the  shock  and other  parameters,  the fixed  relative nominal interest rate policy in a monetary union is fundamentally different from 

46 Parsley  and Wei  (1996)  present evidence for rapid convergence  of relative prices following regional shocks using data for US regions. 47 Corsetti, Kuester, and Muller  (2011)  show that the same logic holds for the case of a small open economy with a fixed exchange rate.

図5

782 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 0.05 0.00 0.05 0.10 0.15 0.20 0.25 Consumption Real interest rate 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Figure 5. Consumption and Real Interest Rate after a Government Spending Shock Note:  The  figure  plots  the  relative  consumption  and  the  relative  real  interest  rate  in  the two  regions for the model with separable preferences after a positive government spending shock to the home region. a zero lower bound setting in a closed economy in which the long-term real interest rate falls in response to a government spending shock.  The response of relative longterm  real interest  rates  in our setting  is closest  to the  fixed  real  interest rate case  in the closed economy setting.  Table  6 shows that the open economy relative multiplier is, in fact, 0.83 for our baseline parameter values.  This is far below the zero lower bound  multipliers  emphasized  by  Eggertsson  (2010)  and  Christiano,  Eichenbaum, and Rebelo  (2011), but just slightly lower than the closed economy aggregate multiplier for a fixed real rate monetary policy. C.  Model with GHH Preferences The models we have considered so far have generated predictions for the open economy  relative  multiplier  substantially  below  the  point  estimate  of  roughly  1.5  that we obtained in Section  II.  We next consider a model with GHH preferences that is capable of fitting this feature of our empirical estimates.48  GHH preferences imply that consumption and labor are complements.  This complementarity is intended to represent  the extra  consumption on  food away  from  home,  clothing, gas,  and the  like that often arises in the context of work  (Aguiar and Hurst 2005 and  Aguiar, Hurst, and Karabarbounis 2013 present empirical evidence for such complementarities).49 

48 Models with hand-to-mouth consumers of the type studied by Galí, López-Salido, and  Valles  (2007)  may also have the potential to generate large open economy relative multipliers. 49 Schmitt-Grohe and Uribe  (2012)  estimate a rich business cycle model with Jaimovich and Rebelo  (2009) preferences—-which nests GHH and King, Plosser, and Rebelo  (1988)  preferences as special cases.  The values 

表7

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 783 Table 7–Government Spending Multiplier in GHH Model Closed economy   aggregate multiplier Open economy   relative multiplier Panel  A. Sticky prices Volcker-Greenspan monetary policy Constant real rate Constant nominal rate Constant nominal rate  (ρg  =  0.50) Panel B. Flexible prices Constant income tax rates Balanced budget 0.12 7.00 ∞ 8.73 0.00 − 0.18 1.42 1.42 1.42 2.04 0.30 0.30 Notes:  The table reports the government spending multiplier for output deflated by the regional CPI for the model presented in the text with the GHH preferences specification. Panel  A presents  results  for  the  model  with  sticky  prices,  while  panel  B  presents  results  for  the  model  with f lexible prices.  The first three  rows differ only in the monetary policy being assumed.  The fourth  row varies the persistence of the government spending shock relative to the baseline parameter values.  The fifth and sixth rows differ only in the tax policy being assumed. Previous work by Monacelli and Perotti  (2008), Bilbiie  (2011), and Hall  (2009) has shown that allowing for complementarities between consumption and labor can have powerful implications for the government spending multiplier.  The basic intuition is that, in response to a government spending shock, households must work more to produce the additional output.  This raises consumption demand since consumption is complementary to labor. But to be able to consume more, still more production must take place, further raising the effects on output. The second  column of  Table  7 presents estimates of the open economy relative multiplier  for the  model with  GHH  preferences.  The  New Keynesian model with GHH preferences can match our empirical findings in Section  II of an open economy multiplier of roughly 1.5  (assuming a quarterly persistence of    ρ g  =  0.933 as in the military spending data).  As in the model with separable preferences, this statistic is entirely insensitive to the specification of aggregate policies. For the case of more transitory government spending shocks  ( ρ g  =  0.5), the open economy relative multiplier rises to 2.0.  The Neoclassical model, however, continues to generate a low multiplier  (0.3)  in this model. Figure  6 plots relative output and consumption in the New Keynesian model with GHH preferences after a positive shock to home government spending. Both output and consumption rise on impact by a little more than twice the amount of the shock. They then both fall more rapidly than the shock.  The fact that the initial rise in consumption is as large as the rise in output—which is partly fulfilling increased orders from the government—implies that the home region responds to the shock by running a trade deficit in the short run. Consumption eventually falls below its steady state level for a period of time. During this time, the home region is running a trade surplus. Intuitively, the complementarity between consumption and labor implies that home households want to shift their consumption toward periods of high work effort associated with positive government spending shocks. 

that they estimate  for the  preference  parameters  of their  model are  those  for which  Jaimovich-Rebelo  preferences reduce to GHH preferences.

図6

784 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 2.50 2.00 1.50 1.00 0.50 0.00 0.50 Output Consumption Government spending 0 5 10 15 20 25 30 35 40 Figure 6. Output and Consumption after a Government Spending Shock in GHH Model Note:  The figure plots the relative output and consumption in the two  regions for the model with GHH preferences after a positive government spending shock to the home region. How does the introduction of GHH preference affect the closed economy aggregate multiplier?  The first column of  Table  7 reports the closed economy aggregate multiplier in our model with GHH preferences. Under certain circumstances—in particular,  the  case  of  a fixed nominal  rate  rule  meant  to proxy  for  the zero lower bound—this model can generate an extremely large closed economy aggregate multiplier. However, if monetary policy is highly responsive to output as in the case of Volcker-Greenspan  policy,  the  New  Keynesian  model  with  GHH  preferences  implies a low closed economy aggregate multiplier, just as the Neoclassical model does. Table  7 makes clear  that the introduction  of GHH  preferences does not generically increase  the closed economy aggregate multiplier. In the Neoclassical model, introducing GHH preferences lowers the closed economy aggregate multiplier  (to zero) by  eliminating  the  wealth  effect  on  labor  supply.50  The  introduction  of  GHH  preferences also lowers the closed economy aggregate multiplier in the New Keynesian model when monetary policy responds aggressively to the inflationary effects of government spending shocks—as in the case of the  Volcker-Greenspan policy rule. For this policy, the endogenous increase in real interest rates chokes off the chain of increases in output, employment, and consumption that otherwise generates a large  multiplier  in the  GHH  model.  A  key  reason  why  the  introduction of  GHH 

50 In the New Keynesian model, government spending shocks affect the markup of prices over marginal costs and, therefore, affect output by shifting labor demand. Similarly, the open economy relative multiplier in the Neoclassical model with GHH preferences is nonzero because the government spending shock shifts the labor supply curve as a function of the real product wage.

表8

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 785 Table 8 —Government Spending Multipliers in Incomplete Markets Model Closed economy aggregate multiplier Open economy relative multiplier Panel  A. Sticky prices Baseline model  (complete markets) Incomplete markets, locally financed Incomplete markets, federally financed Panel B. Flexible prices Baseline model  (complete markets) Incomplete markets, locally financed Incomplete markets, federally financed 0.20 0.18 0.18 0.39 0.39 0.39 0.83 0.84 0.90 0.43 0.41 0.40 Notes:  The table reports the government spending multiplier for output deflated by the regional CPI for a version of the model presented in the text with separable utility in which the only f inancial asset traded across regions is a noncontingent bond. Panel  A presents results for the model with sticky prices, while panel B presents results for the model with flexible prices. preferences  raises  the  open  economy relative multiplier  when  compared  to  the  case of separable preferences is thus that the monetary union implies an accommodative “relative” monetary policy—sufficiently accommodative not to choke off the increase in relative output. Summing up our results thus far, our estimates of equation  (1), based on the military procurement data, yield an open economy relative multiplier of roughly 1.5.  This lies far above the open economy relative multipliers for the Neoclassical model—which are below 0.5 for both separable preferences and GHH preferences. Our empirical estimate of 1.5 is also substantially higher than the open economy relative multiplier of 0.83 implied by the New Keynesian model with separable preferences.  The New Keynesian model with GHH preferences, however, is able to match the open economy relative multiplier we estimate in the data. Our results are thus consistent with a model in which demand shocks  can  have large effects on output— if monetary policy is sufficiently accommodative  (as it is at the zero lower bound). D.  Model with Incomplete Financial Markets The model we develop in Section  III features complete financial markets across regions of the economy.  This implies that all risk associated with differential taxes and labor income across regions—possibly arising from government spending shocks—is perfectly shared. In a recent paper, Farhi and  Werning  (2012)  have shown that  in a  monetary union  with incomplete  financial  markets  across regions,  regional government spending multipliers can differ substantially depending on whether the spending is financed by local taxes or federal taxes.  Table  8 presents open economy relative multipliers for a version of our model in which the only financial asset that is traded across regions is a  noncontingent bond. For this model, we present results for two  assumptions about how spending is financed: locally financed spending and federally financed spending. Table  8  shows  that  these  two  versions  of  the  incomplete  markets  model  yield similar results about the open economy relative multiplier to the baseline complete markets model. In the case of federally financed spending, the open economy relative  multiplier rises  to 0.90 when  prices  are  sticky.  The  intuition for  this is  that 

786 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 home agents are wealthier as a result of the government spending  (they receive labor income far in  excess of the extra taxes they must pay). Since their preferences are home-biased, their increased wealth increases home demand. In the long run,  the increased wealth reduces labor supply. But the first of these effects outweighs the latter, implying that the multiplier increases. What is perhaps more surprising is that even in the case of locally financed spending, the incomplete markets model yields a slightly larger open economy relative multiplier than the complete markets model when prices are sticky. In this case, home agents are not wealthier due to the government spending shock. However, they are  wealthier  than they would have been  had they  shared all risk.  The reason is that the government spending shock leads to an increase in the relative price of home goods. Since home households have a stronger preference for home goods than foreign households, it is efficient for them to purchase state contingent assets that pay out when home goods are cheap and require them to pay when home goods are  expensive.  A  home  government  spending  shock  therefore  leads  to  a  negative transfer for home agents under complete markets. When prices are flexible, the open economy relative multiplier is slightly lower in the incomplete markets model than it is with complete markets.  With flexible prices,  the increase in wealth associated with the government spending reduces labor supply, whereas it does not lead to a Keynesian increase in aggregate demand. This reduction in labor supply decreases the open economy relative multiplier. The effects of changes in wealth on the open economy relative multiplier are sensitive to the elasticity of substitution between home and foreign goods. Our baseline value for this parameter is 2. If we instead assume that this elasticity is 1, the open  economy  relative  multiplier  rises to  1.05  for federally financed  spending.  To be able to generate an open economy relative multiplier of 1.5, we must assume that this  elasticity  is  below  0.6.  This  is  a  substantially  lower  value  than  most  empirical studies suggest. 

E.  Models with  Variable Capital 

The model we develop in Section  III abstracts from investment and capital accumulation. In  Appendixes  F and G we incorporate investment and capital accumulation into our model in two  different ways.  The specification presented in online Appendix  G follows closely the setup in  Woodford  (2003, 2005). In this model, capital is firm-specific in that each firm owns its capital stock and faces convex investment adjustment costs  at the firm level. Our baseline model is a limiting case of  this  model  when  the  capital  share  goes  to  zero.  This  setup  has  been  used,  e.g.,  by Eichenbaum and Fisher  (2007)  and  Altig et al.  (2011).  The specification presented in online  Appendix  F largely mirrors Christiano, Eichenbaum, and Evans  (2005). In this case, households own the capital stock and firms rent capital on a period-byperiod basis in a frictionless regional capital market.  This specification also allows for variable capital utilization and investment adjustment costs at the regional level. Table  9 presents open economy relative multipliers for these models in the case when households have GHH preferences.  The output multiplier for the firm-specific capital model is slightly larger than for our baseline model. Since the government spending shock is persistent, firms expect a high marginal return on capital for some 

表9

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 787 Table 9—Open Economy Relative Multiplier in Models with Variable Capital Output CPI inflation Baseline model  (fixed capital) Firm-specific capital model Regional capital market model Firm-specific capital model, flexible prices 1.42 1.47 0.98 0.25 0.17 0.15 0.09 0.36 Notes:  The table reports the open economy relative government spending multiplier for output and CPI inflation for our baseline model with GHH preferences and the two  models with variable capital, also with GHH preferences. Output is deflated by the regional CPI. time and increase  investment when the  shock occurs.  In contrast, the  model with regional capital markets yields a smaller multiplier than the baseline model.  This occurs despite investment rising as in the firm-specific capital model.  The main reason for the fall in the multiplier is that the regional nature of the capital market reduces the degree of strategic complementarity of the price setting decisions across firms relative to the baseline model  (since firms that raise their price can costlessly  reduce the  amount of capital  they rent). Clearly,  the assumption that firms rent the capital that they use each period on frictionless regional capital markets is unrealistic. Eichenbaum and Fisher  (2007)  and  Altig et al.  (2011)  show that adopting the more realistic setting of firm-specific capital helps New Keynesian models with capital match the sluggish response of prices to aggregate disturbances without resorting to unrealistic assumptions about the frequency of price adjustment or the indexing of prices.  The final row of  Table  9 shows that, with flexible prices, the open economy relative multiplier  is close to zero  in the firm-specific capital model. Table  9 also presents open economy relative multipliers for CPI inflation.  The New Keynesian models generate small increases in relative inflation.  This lines up well with our empirical findings on relative inflation. In contrast, the model with flexible prices counterfactually implies a much sharper rise in relative inflation rates. F.  Welfare The welfare consequences of government spending depend not only on the multiplier, but also on the utility agents derive from the goods and services purchased by the government.  Woodford  (2011)  and Werning  (2012)  provide an extensive discussion of the welfare consequences of government spending.  To illustrate the main forces, suppose household utility can be represented by  U ( C t,   L t,   G t )  and the  production  function  is    Y t  =  f ( L t ).51  Household  utility  may  then  be  written  as U ( Y t  −   G t,   f−1( Y t ),   G t ).  Following Woodford  (2011), we can differentiate this and get (27)    dU _ dG    =   ( U C  −    −  U L  _ f L    _ )dY dG    +  ( U G  −   U C ). 51 For simplicity, we abstract from investment, heterogeneous labor markets, and price dispersion due to price rigidity.  And we assume that government spending is financed by lump-sum taxes.

788 THE  AMERICAN ECONOMIC REVIEW MARCH 2014 The first  term is the difference between the marginal utility of consumption and the marginal disutility of producing goods  ( U L   is negative), multiplied by the government spending multiplier. In a frictionless economy, this term is zero since output is chosen optimally to equate the two  terms in the bracket.  The second  term is the difference between the marginal value of government spending and the marginal value of  private spending. In  a  frictionless  economy,  thus,  the government should spend up to a point where the value of an extra dollar of government spending is equal to that of private spending. In an economy with frictions, output might, however, be below its optimal level making the first term positive. In this case, it may be desirable, other things equal, to increase spending beyond the point at which the second  term is equal to zero.  The extent of extra desirable spending will depend on the size of the multiplier, with a larger multiplier implying that more spending is desirable.  Woodford  (2011)  argues that monetary policy should be the tool of choice to eliminate such “output gaps” since there is no cost  to using  monetary policy, and this allows fiscal policy to focus on equalizing the marginal value of an extra dollar of government spending and private spending. If fiscal policy is used to eliminate output gaps, this may interfere with that second objective. Only when monetary policy is constrained—such as when the nominal interest rate is at its zero lower bound—should fiscal policy be used to eliminate output gaps. In an economy with price rigidity, welfare is also affected by the extent of inefficient price dispersion due to inflation and government spending can raise welfare to the extent it can help stabilize inflation.  Werning (2012)  decomposes optimal stimulus spending into an “opportunistic” part, which reflects  the  desire  of  the government  to  take  advantage  of low  prices during  recessions, and a true “stimulus” part, which reflects additional spending beyond this benchmark.  He  argues  that an  important  part  of optimal  stimulus at the  zero  lower bound is “opportunistic” and that “stimulus” spending may optimally be zero or close to zero. 

V.  Conclusion 

We exploit regional variation in military spending in the United States to estimate the effect of government spending on output in a monetary union.  We use the fact that when the United States 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 United States 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  United  States  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 “closed economy aggregate multiplier,” in that it measures the effect of a relative change in government spending 

Vol. 104 No. 3 Nakamura aNd SteiNSSoN: FiScal StimuluS  iN  a  moNetary  uNioN 789 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 framework for interpreting how it relates to the more commonly studied aggregate government spending 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,  Corsetti,  and Simonelli  2011; Chodorow-Reich et al. 2012; Clemens and Miran 2012; Cohen, Coval, and Malloy 2011; Fishback and Kachanovskaya 2010; Serrato and  Wingender 2010; Shoag 2010;  Wilson 2012). 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. 

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