Geographic Cross-Sectional Fiscal Spending Multipliers: What Have We Learned?

Transcription

1 Geograpic Cross-Sectional Fiscal Spending Multipliers: Wat Have We Learned? Gabriel Codorow-Reic Harvard University and NBER December 2017 Abstract A geograpic cross-sectional fiscal spending multiplier measures te effect of an increase in spending in one region in a monetary union. Empirical studies of suc multipliers ave proliferated in recent years. In tis paper, I review tis researc and wat te evidence implies for national multipliers. Based on an updated analysis of te American Recovery and Reinvestment Act and a survey of empirical studies, my preferred point estimate for a cross-sectional output multiplier is 1.8. Economic teory of ow to map tese multipliers into a national multiplier as also advanced. Drawing on te teoretical literature, te paper discusses conditions under wic te crosssectional multiplier provides a roug lower bound for a particular national multiplier, te closed economy zero lower bound multiplier. Putting tese elements togeter, te cross-sectional evidence suggests a national zero lower bound multiplier of about 1.7 or above, at te upper end of most studies based on time series evidence. Te paper concludes by offering suggestions for future researc on cross-sectional multipliers. Harvard University Department of Economics, Littauer Center, Cambridge, MA ( codorowreic@fas.arvard.edu). Te online appendix is available from te autor s webpage. I tank Arin Dube, Emmanuel Fari, Laura Feiveson, Josua Hausman, Emi Nakamura, four anonymous referees, David Romer, and Mattew Sapiro for elpful discussions and comments. Tzaci Raz provided excellent researc assistance. I acknowledge financial support from Te Frank N. Newman Fund in Economics. Disclosure: I was a staff economist on te Council of Economic Advisers from

2 1. Introduction A geograpic cross-sectional fiscal spending multiplier measures te effect of an increase in spending in one region in a monetary union. Te past several years ave witnessed a wave of new researc on suc multipliers. By definition, estimation uses variation in fiscal policy across distinct geograpic areas in te same calendar period. Tis approac as a number of advantages, most notably te potential for muc greater variation in policy across space tan over time and variation more plausibly exogenous wit respect to te no-intervention pats of outcome variables. At te same time, cross-sectional multipliers differ in important dimensions from te national government spending multiplier to wic tey are often compared. Recognition of tese differences as led to pessimism regarding weter cross-sectional multipliers provide any guidance for te effects of oter types of policies. 1 In tis paper, I assess wat we ave learned from tis researc wave. I find te retreat regarding te literature s informativeness for oter interventions to be premature. Drawing on teoretical explorations, I argue tat te typical empirical cross-sectional multiplier study provides a roug lower bound for a particular policy-relevant type of national multiplier, te closed economy, passive monetary policy, deficit-financed multiplier. Te lower bound reflects te ig openness of local regions, wile te roug accounts for te small effects of outside financing common in cross-sectional studies. I ten review empirical estimates and find a crossstudy mean of about 1.8. Putting tese two elements togeter, cross-sectional studies imply a 1 As part of er review article of fiscal multipliers, Ramey (2011a) concludes: More researc is needed to understand ow tese local multipliers translate to aggregate multipliers. In a more recently publised paper, Fisback and Kacanovskaya (2015, p. 126) write: Te state multipliers cannot be easily translated into a national multiplier because of spillover effects outside eac state s boundaries and because te same state multiplier can lead to a broad range of estimates of te national multiplier under a reasonable set of assumptions in a macroeconomic model. Many studies include similar caveats. 1

3 larger national multiplier tan often assumed. Te paper starts in section 2 by reviewing te econometrics of cross-sectional multipliers. I discuss a typical approac and compare wit te time series literature to igligt te possible advantages of relying on cross-sectional variation. Section 3 develops te lower bound argument, following closely teoretical results in Soag (2015), Nakamura and Steinsson (2014), and Fari and Werning (2016). Muc of te pessimism regarding cross-sectional studies arises because in te vast majority of cases, te spending does not affect te present value of local tax burdens (for example, te spending is paid for by te federal government). I terefore first consider ow te effects of outside-financed spending compare wit local deficit-financed spending. Standard economic teory postulates a small quantitative difference between te two wen te spending is transitory. Intuitively, Ricardian agents increase teir private spending by te annuity value of a transfer, wic for transitory spending implies only a small increase relative to te direct cange in government purcases. Spending by rule-of-tumb, myopic, or liquidity-constrained agents does not depend at all on te present value of te tax burden; instead, for non-ricardian agents te comparison of outside-financed spending wit local deficit-financed spending (rater tan wit local taxfinanced spending) is crucial, since oterwise tere is an offsetting decline in output caused by te contemporaneous iger taxes. Next, a cross-sectional deficit-financed government spending multiplier differs from a national multiplier because te cross-sectional multiplier differences out oter national policy responses suc as a monetary policy reaction and because of te greater openness of local regions. Te quantitative importance of te monetary policy reaction for national multipliers 2

4 is well known (Woodford, 2011; Cristiano et al., 2011). Comparing te local multiplier to a national multiplier wen monetary policy does not react, for example because of a binding zero lower bound, eliminates tis difference between te two multipliers. Greater expenditure switcing and income leakage reduce local multipliers relative to te relevant aggregate multiplier wile greater factor mobility can raise tem. Since fixed reallocation costs limit factor mobility in response to transitory spending canges, te balance of tese elements suggests te national zero lower bound multiplier exceeds te locally-financed local multiplier. Combining tese arguments, in empirically-relevant cases te cross-sectional multiplier provides a roug lower bound for te closed economy, passive monetary policy, deficit-financed aggregate multiplier. Section 4 deals wit an important tecnical issue. Largely for reasons of data availability, many empirical studies report employment multipliers rater tan output multipliers. Comparing across studies and to teoretical models requires a conversion between tese two concepts. I sow using a simple framework tat for te United States a roug translation from an employment to output multiplier is to divide output per worker by te cost-per-job. Sections 5 and 6 review empirical cross-sectional multipliers. In section 5 I provide an updated example drawn from tree papers studying te effects of te 2009 American Recovery and Reinvestment Act (ARRA). Te example illustrates many of te econometric concepts and provides a template for future studies. I also obtain new results. Applying a common econometric framework to instruments from eac of te tree studies, I consistently find a cost-per-job of te ARRA of rougly $50,000. Using newly available gross state product data, I estimate an output multiplier of

5 Section 6 reviews te recent empirical literature more broadly. Te first part of te section groups togeter a set of papers wic ave examined various components of te ARRA. Tese studies all exploit variation omogeneous along te dimensions of te outside nature of te financing and te sort persistence of te intervention, and also all focus on employment rater tan output effects of spending. Te cost-per-job across tese studies ranges from rougly $25K to $125K, wit around $50K emerging as a preferred number. Using te relationsip between employment and output multipliers developed in section 4, tis magnitude translates loosely into an output multiplier of about 2. Te central tendency of tese magnitudes closely matces te results from te example in section 5. I ten turn to papers using oter sources of variation, many quite creative. Te diversity of outcome variables and policy experiments makes reacing a syntesized conclusion across tese studies arder; noneteless, tose wic estimate a cost-per-job find numbers around $30K, and, wit one or two notable exceptions, tose wic estimate income or output multipliers find numbers in te range of Section 7 summarizes wat we ave learned. After adjusting for spending persistence, te mean cross-sectional output multiplier is 1.8. Applying te roug lower bound result, a cross-sectional multiplier of 1.8 implies a zero lower bound deficit-financed national multiplier of about 1.7 or above. Tis magnitude falls at te very upper end of te range found in a recent review article based mostly on time series evidence (Ramey, 2011a). Tus, crosssectional multiplier studies suggest te national multiplier can be larger tan often assumed. In addition, many studies find iger multipliers in periods and regions wit greater economic slack, pointing to te presence of forces suc as lower factor prices or congested labor markets in generating state-dependent multipliers. 4

6 Finally, section 8 offers suggestions to elp increase te impact of future cross-sectional multiplier studies, including ow to furter bridge te gap to te national multiplier. 2. Econometrics of Cross-Sectional Multipliers Consider te relationsip: D t,t+ Y s = α,t + β xs F s,t + γ X s,t + ɛ s,t+, (1) were Y s is an outcome suc as output or employment in geograpic area s, D t,t+ is a difference operator defined as D t,t+ Y s = Y s,t+ Y s,t, α,t is a time fixed effect, F s,t is a vector of components of fiscal policy suc as government spending and taxes, and X s,t is a vector of covariates. 2 Te coefficient vector β xs measures te orizon response of Y to F. Te time fixed effect α,t in equation (1) caracterizes β xs as a cross-sectional multiplier (xs for crosssection) because identification of β xs comes only from variation in fiscal policy across space witin te same calendar period. For te regression estimate ˆβ xs to consistently estimate te true β xs, tere must be variation witin a calendar period in F s,t uncorrelated (conditional on X s,t ) wit te trajectory of economic activity across areas. Tis requirement mirrors te parallel trends assumption of difference-in-difference estimation. 2 Te notation F s,t is meant to be quite general. For example, te vector could include expectations of future spending and taxes. Some studies drop te t subscript and implement equation (1) as a pure cross-sectional regression, wile oters drop te difference operator on te dependent variable but add an area fixed effect. Because te econometric issues involved wit panel fixed effects estimation are similar, I focus on equation (1) for clarity. 5

7 2.1. Typical Approac Te typical cross-sectional econometric study starts by identifying some vector of variables Z s,t wic satisfy te conditions for an excluded instrument: Z s,t is correlated wit fiscal policy and te researcer can make an a priori plausible case for te exclusion restriction E[Z s,t ɛ s,t+ X s,t ] = 0, or in words, tat te variables Z s,t are conditionally independent of local economic trends. 3 In some instances, Z s,t does not ave a monetary representation. Estimation proceeds by using Z s,t as an instrument. For example, Z s,t migt consist of a metric of te restrictiveness of state-level balanced budget requirements. Often owever Z s,t consists of some component of government spending. For example, suppose federal government spending per capita in state s, G s,t, consists of a part constant across states, Ḡ t, a part wic responds endogenously to a state s economy, Gs,t, and a part Ĝ s,t wic is as-good-as-randomly assigned, were witout loss of generality te cross-sectional means of Gs,t and Ĝs,t are equal to zero. Clearly, te common component Ḡt provides no variation across states, and by assumption E[ G s,t ɛ s,t+ ] 0. Terefore, a researcer migt set F s,t = G s,t and Z s,t = Ĝs,t. In te first stage regression of a 2SLS estimate (abstracting from included instruments oter tan te time fixed effect, i.e. setting X s,t to empty), G s,t = ΠĜs,t + ξ t + u s,t, (2) te coefficient Π as a probability limit of 1 because by assumption of as-good-as-random 3 Formally, if F s,t is a Kx1 vector of components of fiscal policy, Z s,t an Mx1 vector, and X s,t an Lx1 vector, (i) M K (order condition), (ii) rank{e[ ( Z s,t X s,t) ( F s,t X s,t) ]} = K + L (rank condition), and (iii) E[Z s,t ɛ s,t+ = 0] t, (exclusion restriction). Te last condition is stronger tan strictly necessary. 6

8 assignment E[Ĝs,t G s,t ] = 0. Wit a first stage coefficient of 1, te second stage estimate of β xs is asymptotically equivalent to te reduced form coefficient obtained from simply replacing F s,t wit Z s,t in equation (1). Many studies estimate tis reduced form relationsip instead of 2SLS. Alternatively, if Z s,t is not independent of te rest of spending F s,t Z s,t, ten te two approaces will yield different multipliers. 4 Finally, rater tan reporting te impulse response function traced by β xs, many studies collapse equation (1) into a single regression cumulating te effects across orizons: [ H ] [ H ] D t,t+ Y s = α t + β xs F s,t + γ X s,t + ɛ s,t+, (3) =0 =0 were α t = H =0 α,t, β xs = H =0 βxs,t, and γ = H =0 γ,t. Intuitively, te individual coefficient β xs gives te impulse response of variable Y at orizon ; summing over tese impulse responses gives te cumulative additional increase in Y. In many instances total output or total employment per $1 of government spending provides a convenient summary measure of te multiplier pat. Collapsing tese effects into a single dependent variable makes calculations of standard errors straigtforward. 4 If Z s,t, te component of spending wic satisfies te exclusion restriction, is correlated wit te rest of spending, tere may be reason for concern tat te variation underlying Z s,t is truly as-good-as-randomly assigned. In two cases suc concern is not warranted. First, oter categories of spending may endogenously respond to te randomly assigned part. Ten in te terminology of applied microeconomics, te reduced form coefficient measures te intent-to-treat and te 2SLS coefficient te effect of te treatment-on-te-treated. Second, te researcer may ave identified only a subset of te randomly assigned part of spending. Expanding te example in te text, let Ĝs,t = Ĝ1 s,t + Ĝ2 s,t, Z s,t = Ĝ1 s,t, and suppose Corr[Ĝ1 s,t, Ĝ2 s,t] = ρ > 0. Ten te first stage coefficient Π = 1 + ρ V ar(ĝ2 s,t)/v ar(ĝ1 s,t) > 1, te exclusion restriction remains valid, and only te 2SLS coefficient as a meaningful interpretation. 7

9 2.2. Comparison to Time Series Regression It is informative to compare equation (1) to a typical time series regression (ts for time series) used to estimate a fiscal multiplier: D t,t+ Y = α + β ts F t + γ X t + ɛ t+, (4) were Y t = s Y s,t, F t = s F s,t, and X t is a vector of covariates. Two main callenges arise in estimating equation (4). First, fiscal policy may adjust in response to a canging economic trajectory. Tis reverse causality affects bot discretionary fiscal policy and automatic stabilizers. Researcers must ten identify some subset of canges in F t wic are ortogonal to ɛ t. Popular approaces include war spending (Barro, 1981; Ramey and Sapiro, 1998; Hall, 2009), narrative cataloging of policy canges taken for reasons unrelated to business cycle management (Romer and Romer, 2010), and VAR recursive or sign restrictions (Blancard and Perotti, 2002; Mountford and Ulig, 2009). Te second callenge comes from policy variables wic coincide wit or respond to canges in te researcer s measure of fiscal policy. Te response of monetary policy and wat appens to oter spending or taxes provide leading examples. 5 Tus, an estimate of β ts to exogenous canges in government spending gives te average effect over te beavior of current and future monetary policy and taxes in te researcer s sample and may provide a poor out-of-sample guide to te effects of government spending under alternative monetary or fiscal regimes. Te cross-sectional approac impacts bot of tese issues. Te time effect α,t in equa- 5 Teories empasizing te co-determination of monetary and fiscal policy suggest tese two cases are one and te same (Leeper, 1991). In principle, F t could include te expected pats of government spending and taxes, but it rarely does. 8

10 tion (1) removes te direct concern of endogenous fiscal response at te igest (e.g. federal) level. Instead, te researcer need only find a valid reason wy F s,t varies across geograpic areas. Importantly, te time effect does not immediately absolve te researcer of all concerns of countercyclical federal fiscal policy; targeting of a federal intervention toward geograpic areas more impacted by te recession would violate te requirement tat te areas be oterwise on similar economic trajectories. Te time effect also absorbs any monetary policy response or cange in oter federal fiscal variables. Tis consequence of cross-sectional estimation creates bot opportunities and callenges. On te one and, removing te effect of te endogenous response of monetary policy or taxes makes te estimate of β xs more directly tied to primitives of te economic environment and ence potentially more stable across studies, a point empasized by Nakamura and Steinsson (2014). On te oter, it creates some distance between te cross-sectional multiplier β xs and te aggregate multiplier βts, an issue I turn to next. 3. Teory of Cross-sectional Multipliers Te objective of tis section is to develop a relationsip between te cross-sectional multiplier and a judiciously-cosen teoretical construct, te closed economy, zero lower bound, deficit-financed national multiplier. Many of te concepts arise in te static Old Keynesian model and its open economy counterpart Mundell-Fleming; oters affect intertemporal budget constraints and arise only in more modern treatments. Te discussion in te text focuses on key economic concepts wic do not depend on a particular model environment. Online appendix A presents an example of a complete algebraic model of a cross-sectional multiplier 9

11 based on Fari and Werning (2016). 6 Soag (2015) and Nakamura and Steinsson (2014) also develop many of tese points formally. I start by introducing a convenient teoretical counterpart to β xs in equation (1). To fix ideas, consider te following setting. A closed national economy consists of a unit continuum of local areas wic sare a common currency. At time t a new pat of government spending is announced for a single local area s wit deviation at orizon of G s,t+. I defer for te moment discussion of te financing of te new pat of spending. Te pat of government spending in te rest of te economy remains uncanged. Because area s is infinitesimal, canges in spending in s do not measurably affect te wole economy. Te difference-in-difference in outcomes at orizon is terefore (Y s,t+ Y s,t ) (Y t+ Y t ) = D t,t+ Y s D t,t+ Y were now Y t = s Y s,tds is te average value of Y in te economy. Again letting F s,t denote some measure of te increase in spending (for example te contemporaneous increase G s,t or a present value), te counterpart to equation (1) is: β xs = D t,t+y s D t,t+ Y F s,t. (5) I argue tat in empirically-relevant cases β xs provides a lower bound for te effect of increasing spending in te entire economy wen monetary policy remains passive. I proceed in two steps. First, I sow wen an outside-financed local multiplier approximately coincides wit a deficit-financed local multiplier. Second, I review standard economic cannels familiar to te open economy literature wic make local deficit-financed multipliers a lower bound for te passive monetary policy aggregate multiplier. 6 Relative to tat paper, te presentation in online appendix A makes a few functional form assumptions at te outset and provides sufficient algebraic detail to allow an uninitiated reader to follow along wit minimal interruption. 10

12 3.1. Relationsip to Deficit-financed Currency Union Spending Multiplier Te multiplier defined in equation (5) as a close relationsip to deficit-financed stimulus policies by individual states or countries operating inside a monetary union. For example, te consequences of fiscal austerity by members of te euro area as received a great deal of attention. Te possible difference between suc policies and te cross-sectional multipliers reviewed below arises because in te vast majority of cases te spending used to identify cross-sectional multipliers does not require iger contemporaneous or future local taxes. For example, wen te federal government directs additional igway funds into a particular state, te tax burden associated wit paying for te additional spending falls on residents of all states equally. I refer to suc examples as financed by outside transfers, altoug in practice tey may also involve windfalls generated by oter factors suc as pension fund abnormal returns as in Soag (2015). To understand te difference between multipliers financed by outside transfers and deficitfinanced spending, it elps to furter fix some terminology. Let β xs,transfer denote te crosssectional multiplier at orizon wen te spending is financed by external transfers and β xs,deficit te cross-sectional multiplier wen spending is locally deficit-financed. One can tink of outside-financed spending as comprising an increase in a pat of spending wic is locally deficit-financed by issuance at date t of a perpetuity bond and te immediate purcase and cancellation of te perpetuity by te central government. Te present value of te increase in spending, or equivalently te present value of te transfer from te central government to cancel te iger debt, is equal to V = 0 e rj G s,t+j dj, were r is te real interest rate. Let 11

13 β transfer denote te multiplier associated wit te resources used by te central government to cancel te locally-issued debt. It follows tat: β xs,transfer F s,t = β xs,deficit F s,t + β transfer V. (6) I next consider te two cases of an economy inabited by fully rational agents wo can borrow and lend freely and were Ricardian equivalence olds, and economies dominated by non-ricardian agents. In te first, β transfer V is small as long as te increase in spending is transitory and te local economy is not too closed. In te second, β transfer V can go to zero. Tese cases clarify te conditions under wic a transfer-financed cross-sectional spending multiplier closely or exactly resembles a deficit-financed cross-sectional multiplier. Wen Ricardian equivalence olds. If Ricardian equivalence olds, te wedge between te outside-financed multiplier and te local deficit-financed multiplier depends on te size of te transfer, wic in turn depends on its persistence, and on te region s openness. A simple calculation elps to illustrate. Suppose spending increases by G s,t on announcement and ten decays exponentially at rate ρ, G s,t+j = e ρj G s,t, and is financed by te federal government. Ten te present value of te transfer is V = G s,t 1/(r +ρ). Te annuity value, equal to te per period interest payment on a perpetuity bond wit face value V, is rv = G s,t r/(r +ρ). For a log utility permanent income agent, te partial equilibrium effect of a wealt transfer on consumption expenditure equals tis annuity value. 7 Wen te transfer is transient (ρ is large), te annuity value rv is small relative to te 7 Tat is, for an agent wit intertemporal preferences over consumption c given by U t = e rj ln(c 0 t+j )dj and a budget constraint e rj p 0 t+j c t+j dj = W, optimization requires p t+j c t+j = rw j. Te annuity value is also te required per period transfer from te federal government to te local region to absolve te local region of ever needing to raise taxes to pay for te spending. 12

14 increase in government purcases. Te small partial equilibrium response to a transfer to pay for transient spending explains wy te term β transfer V can be small in te Ricardian case. Conversely, te partial equilibrium effect of a permanent increase in outside-financed spending (ρ 0) is to immediately raise expenditure by local agents by fully te amount of te increase in government spending. Openness matters because in general equilibrium te local output multiplier depends on te extent to wic local residents concentrate teir expenditure on locally-produced output. Online appendix A derives a simple expression combining tese elements for te increase in nominal expenditure on local output, β transfer,nominal, in a fully intertemporal, Ricardian setting: β transfer,nominal V = ( 1 α α ) ( ) r G s,t, (7) r + ρ were α is te sare of purcases from oter regions in local expenditure (see equation (A.39)). Equation (7) as te following interpretation. Te transfer causes a direct, partial equilibrium increase in expenditure on local output of (1 α)rv, te product of te ome expenditure sare and te total partial equilibrium expenditure increase. Te resulting increase in local income of (1 α)rv causes a second round increase in expenditure on local output of (1 α) 2 rv, and so on. In general equilibrium, terefore, expenditure on domestic output rises in response to te transfer by [ (1 α) + (1 α) ] rv = [(1 α) /α] rv = [(1 α) /α r/ (r + ρ)] G s,t. 8 Tus, nominal expenditure jumps upon announcement of te transfer and remains at te 8 Equivalently, te increase in domestic nominal income (denominated in te national price level) equals rv + [(1 α) /α] rv = (1/α)rV, exactly te amount required for domestic agents to purcase an additional rv of output produced in oter regions and keep te current account balanced. Te difference between outside and locally financed multipliers vanises as te economy becomes fully open, since ten private spending by local agents does not fall disproportionately on local products. 13

15 same iger level tereafter. Wit sticky prices te local price level does not jump, so te impact transfer multiplier on real output is also given by equation (7). Coosing for illustrative purposes α = 1/3, r = 0.03, and ρ = 0.8 (te last implies about 80% of te increased spending occurs by date t = 2), te fact tat te spending is outside financed raises local output on impact by only 0.07 G s,t. Setting F s,t = G s,t in equation (6), in tis example β xs,transfer =0 = β xs,deficit = , a small difference relative to empirical estimates of β xs,transfer discussed below. As te price of local output rises in response to te iger demand, te transfer exerts an ever smaller and, wit wealt effects on labor supply, eventually negative effect on local output (see equation (A.35)). Tus, te impact effect of 0.07 gives te maximum increase in te cross-sectional spending multiplier due to outside financing at any orizon in tis calibrated example. Failures of Ricardian equivalence. Failures of Ricardian equivalence can drive β transfer 0 suc tat te outside-financed and locally deficit-financed multipliers exactly coincide. Te reason stems crucially from te comparison of outside-financed spending wit deficit-financed rater tan tax-financed spending. For non-ricardian agents, tere is an exact analog between aving agents in future periods pay for current spending and aving agents in oter areas pay for current spending. It is informative to consider tree leading reasons for te failure of Ricardian equivalence. In te first, private agents do not internalize te prospect of iger future taxes to pay for current spending into teir budget constraints due to life cycle considerations and non-altruistic motives (Weil, 1987). If agents do not incorporate future tax liability into teir private intertemporal budget constraints, ten te outside-financed and locally deficit-financed multipliers coincide. 14

16 Liquidity constraints provide a second leading reason Ricardian equivalence may fail. 9 If ouseolds consume and firms invest based on current income rater tan permanent wealt, ten β transfer = 0 and an increase in temporary income resulting from a deficit-financed stimulus package will ave equivalent effects to an outside-financed increase in spending. A tird failure stems from myopic or boundedly rational beliefs (Gabaix, 2015). If agents ignore te intertemporal aspect of teir spending problem, ten te outside-financed and locally deficit-financed multipliers again coincide. Similarly, if agents do not know teir region as received an outside transfer, ten teir private spending cannot react to te transfer. Te low salience case appears plausible in many instances. In te context of studies of national increases in spending wit differential increases across regions, ouseolds would ave to know te geograpic spending pattern in order to react to any transfer component. Tese examples make clear tat in te non-ricardian case te coincidence result requires comparing outside-financed spending to a deficit-financed stimulus package. Oterwise, tere is an offsetting decline in private spending from te contemporaneously iger taxes wic does not occur in te outside-financed case. Quantitative magnitude. How muc could te transfer component matter quantitatively? In models similar to tat of online appendix A in wic private agents internalize all future taxes into teir budget constraints and calibrated to matc approximately te openness and persistence of government spending in many of te studies reviewed below, Nakamura and Steinsson (2014, table 8) and Fari and Werning (2016, table 1) bot find outside financing 9 Evidence for liquidity constraints comes from ouseolds responses to one-time stimulus payments (Jonson et al., 2006; Sam et al., 2012; Parker et al., 2013; Hausman, 2016), from direct examination of ouseolds liquidity positions (Lusardi et al., 2011; Kaplan et al., 2014), and from firms responses to to temporary cas flows (Fazzari et al., 1988; House and Sapiro, 2008; Maon and Zwick, 2015). 15

17 raises multipliers by less tan 0.1, tat is, a locally deficit-financed multiplier of 1.2 would become a multiplier of about 1.25 if outside-financed. Tis magnitude matces te illustrative calculation reported above. Intuitively, low persistence of stimulus spending and fairly open local regions mean tat te increase in purcases of local output in response to te transfer component is small. Fari and Werning (2016) find tis difference remains small even in te presence of non-ricardian and-to-mout agents as long as te comparison remains to a local deficit-financed multiplier Relationsip to Closed Economy Zero Lower Bound Multiplier Multipliers associated wit spending by one entity in a currency union differ from closed economy multipliers. Tis section discusses te most important reasons wy: absence of te possibility of a reaction by monetary policy; relative price effects wic cause agents to expenditure-switc toward output produced in oter regions; canges in private spending by local agents fall partly on output produced in oter regions; and factor mobility. I conclude tat te balance of tese forces likely makes te local deficit-financed multiplier a lower bound for a particular national multiplier, te closed economy zero lower bound multiplier. Monetary policy reaction. Te first difference offsetting interest rate canges by monetary policy makers wic reduce te national multiplier can matter substantially. However, tere exists a leading case wen monetary policy does not react to national fiscal policy: at te zero lower bound. Indeed, determining te national fiscal multiplier wen monetary policy cannot react is of particular interest to policy-makers. I call tis multiplier te zero lower bound or passive monetary policy multiplier, altoug in reality te equivalence is not exact as monetary policy can coose not to react to fiscal policy even outside te zero lower bound and central 16

18 banks ave tools (forward guidance, quantitative easing, negative interest rates) even after te policy rate reaces zero. Expenditure switcing. By purcasing local output, government spending may cause te price of local output to rise relative to goods produced in oter regions. Suc price increases could reflect increases in factor prices, markups, or diminising returns to scale. As a result of tis terms of trade effect, bot local and external consumers and businesses sift expenditure toward output produced in oter regions causing total private purcases of locally-produced output to fall. Tis effect makes te cross-sectional multiplier smaller tan te closed economy multiplier. Its magnitude depends on factors suc as te nature of price and wage setting, te degree of segmentation between goods purcased by government and te private sector, and te substitutability between locally-produced and externally-produced goods. 10 I elaborate briefly ere on tree elements were future researc migt contribute to a better quantitative understanding. Online appendix A provides algebraic detail. First, te expenditure-switcing cannel requires tat iger government spending actually cause local prices to rise. Absence of ig frequency, ig quality local price measures as made estimating te relative price effect difficult. In te context of spending multipliers, Nakamura and Steinsson (2014) find no evidence of local consumer prices responding to government spending. Te stability of inflation trougout te Great Recession as also led to some suggestions 10 Te magnitude does not depend monotonically on te openness of te local region (see equation (A.44) or Fari and Werning (2016, p. 2446)). On te one and, wen local agents purcase a large sare of teir consumption from local producers, teir desire to reduce total consumption wen te price of a unit of utility (i.e. te real interest rate) is temporarily ig causes a larger direct reduction in demand from local producers. On te oter and, tis reduction in demand by local purcasers mitigates te rise in te relative price of locally-produced output, wic in turn mitigates te decline in demand from external purcasers. As a result, te increase in te relative real interest rate empasized by Nakamura and Steinsson (2014) is not strictly necessary to generate a reduction in private demand for local goods. In fully open regions wit a private sector ome bias sare of zero, consumption baskets and consumer price indexes of local and external consumers coincide, and ence real interest rates coincide, but total private demand for local output still falls because of te relative rise in te local producer price index. 17

19 of a recent divorce between output and inflation dynamics (Hall, 2011). On te oter and, using geograpic variation in local demand caused by factors oter tan government spending, Fitzgerald and Nicolini (2014), Stroebel and Vavra (2016), and Beraja et al. (2016) all find evidence of local prices responding to local demand conditions. Second, by assumption government spending concentrates on goods and services from te local region; oterwise te cross-sectional multiplier experiment lacks variation in treatment across regions. Even if te iger government demand for local goods increases teir relative price, owever, tis price increase must spillover into goods and services purcased by private agents to affect teir spending. Suc spillovers can appen eiter troug competition in output markets (for example, if government and private agents purcase te same goods), or troug competition in input markets (for example, due to labor mobility across sectors and a common wage). Segmentation on eiter dimension will dampen te amount of expenditure switcing. Tird, te transmission from relative price canges to expenditure switcing depends on te elasticity of substitution between locally-produced and externally-produced goods. For temporary government spending socks, te sort-run elasticity is most relevant. Income effects. Te local multiplier also depends on total private spending by local agents, as any increase in demand leaks into oter areas. For example, liquidity-constrained workers wose labor income rises in response to te increase in government spending increase teir consumption of bot locally-produced and external goods. Complementarity in te utility function between consumption and ours worked would induce te same effect. For firms, excess sensitivity of investment to cas flow or increased purcases of intermediate inputs may 18

20 cause local firms to increase purcases from bot local and external suppliers. Tis cannel is distinct from expenditure switcing because it does not require any cange in relative prices to occur. Once again, owever, leakage makes te cross-sectional multiplier a lower bound for te aggregate closed economy multiplier. Te importance of income effects depends on bot te rise in purcases by domestic agents and te openness of te local area. For example, wit rigid relative prices and a mecanical marginal propensity to consume (mpc) and to import (mpm), te local government spending multiplier equals 1/(1 (mpc mpm)). In most settings, te smaller te local area te larger te sare of purcases from outside te region. Terefore, tis effect suggests te cross-sectional multiplier may increase in te level of te geograpic unit, i.e. it is larger for states tan for counties. Recognizing tis fact, some cross-sectional studies wic examine variation at a county level enlarge te region covered by te dependent variable to capture some of te spending leakage. Factor mobility. In contrast to te expenditure switcing and income cannels, ig factor mobility may pus up local multipliers relative to national multipliers. For example, as local government spending causes local labor demand to rise, workers may move in from oter areas. Te population influx furter raises local employment and output as te immigrants consume non-tradeable output and pus down wages in tradeable sectors. More generally, supply constraints may be less likely to bind at te local level. Because of fixed costs of moving, te importance of te migration cannel rises wit te persistence of te spending. Likely for tis reason, none of Fari and Werning (2016), Soag (2015), or Nakamura and Steinsson (2014) allows for net migration in teir teoretical model of 19

21 cross-sectional multipliers. In contrast, studies of longer run canges or more persistent policies treat population spatial equilibrium as a key force. 11 Wit fixed costs te importance of factor mobility also depends on te size of te local geograpic unit, as migration of workers or capital across neigboring counties engenders smaller costs tan migration across states. Soag (2015) and Nakamura and Steinsson (2014) eac estimate te cross-state population response to local government spending and find economically and statistically insignificant responses. Tus, for temporary increases in local government spending, te empirical relevance of te migration cannel appears small. Oter cannels. Oter potential differences between local currency union and national multipliers are ard to quantify or even sign. Confidence provides one example. By passing a countercyclical fiscal stimulus, a national government migt raise consumer and business confidence in te government s competence or more nebulously trigger animal spirits. Alternatively, if private agents view te spending as an insufficient response to te circumstances or contaminated by political favoritism, confidence migt fall. Looking furter aead, te political reaction to national spending migt affect outcomes of future elections and ence a ost of oter policies. Because tese cannels ave ambiguous sign and vary wit specific circumstances, tey resist incorporation into a general framework. Put differently, local multipliers can inform only about a national multiplier for wic cannels suc as confidence in te 11 See e.g. Moretti (2010) for analysis of long-run employment multipliers and Glaeser and Gottlieb (2008) for a formal spatial equilibrium model. Moretti (2010) estimates te additional aggregate local employment caused by an additional job in different sectors, at decadal frequency. Assuming tat immigration makes te local labor supply elasticity larger tan te national, e argues tat te employment multiplier of an additional job in a non-traded sector provides an upper bound of te national spending multiplier and te multiplier of an additional job in a traded sector provides a lower bound. Tis argument also implicitly assumes canges persistent enoug to induce migration and tat output and employment are not demand-constrained. Wile possibly reasonable assumptions for te decadal frequency Moretti examines, failure of tese assumptions at sorter orizons make te bounds inapplicable to sort-run spending multipliers. 20

22 national government do not play a role Summary and discussion As described in section 3.1, multipliers for transitory increases in local spending not financed locally map rougly into locally deficit-financed currency union multipliers. Section 3.2 argued tat locally-financed currency union spending multipliers provide a lower bound for closed economy zero lower bound multipliers due to te dominance of te expenditure-switcing and leakage effects. Combining tese two results, standard teory suggests tat in empiricallyrelevant cases cross-sectional multipliers provide a roug lower bound for deficit-financed zero lower bound closed economy multipliers. 12 Wile sared by Nakamura and Steinsson (2014) and Fari and Werning (2016), tis conclusion is sarply at odds wit muc of te conventional wisdom extant at te start of tis wave of researc. 13 I conclude tis section wit a brief discussion of issues related to te size of te local region and te openness of te national economy. Te assumption tat spending occurs in a single 12 A recent literature as questioned te plausibility of some of te forward-looking elements of te New Keynesian model wic give rise to potentially very large closed economy zero lower bound multipliers (McKay et al., 2016; Kaplan et al., 2016). Te roug lower bound result does not depend on tese particular features. Indeed, aspects wic make te New Keynesian model less forward-looking also rule out one case discussed by Fari and Werning (2016) in wic closed economy zero lower bound deficit-financed spending may generate a contemporaneous multiplier of less tan te locally-financed currency union multiplier, werein te presence of liquidity constrained agents results in expectations of a recession in te future at te time taxes rise, tereby generating in te closed economy case a deflationary spiral wic reduces current expenditure by unconstrained agents. Enoug price rigidity also rules out tis outcome. 13 For example, Giavazzi (2012, p. 144) writes tat local multipliers deliver an upward biased estimate of total spending multipliers (empasis mine). Ramey (2011a, p. 681) provides a widely-cited example were tis conclusion olds. In Ramey s example, all agents ave a mecanical marginal propensity to consume (mpc) of 0.6 and ouseolds in Mississippi receive a government transfer of $1 financed by a contemporaneous lump sum tax levied on ouseolds in oter states. Ten, as Ramey points out, te increase in output in Mississippi and ence te local multiplier equals mpc/(1 mpc) = 1.5 but te national multiplier is 0. (Following Ramey, tis calculation assumes tat all consumption is of locally-produced output.) Canging te example sligtly, owever, suppose instead tat Mississippi financed te transfer by issuing debt purcased by foreigners. Ten te local deficit-financed multiplier also equals 1.5, te same as te outside-financed multiplier and te national deficitfinanced multiplier. Tus, te roug lower bound result differs from Ramey s conclusion because it compare local multipliers to national deficit-financed multipliers wereas er example compares te local multiplier to a national tax-financed multiplier. 21

23 area s of infinitesimal size igligts an important difference between te issues wic affect te mapping from β xs to βts and te no-interference stable unit treatment value assumption (SUTVA) often made in analyses of clinical trials and oter randomized experiments. SUTVA states te condition tat for te difference between treated and untreated units to provide a valid estimate of te causal effect of treatment, treatment of one unit must not affect outcomes of te non-treated units. Wen s is infinitesimal te spillovers from iger local spending, arising inter alia from expenditure switcing, income effects, and migration, are infinitesimal relative to te rest of te economy and SUTVA olds. Noneteless, te local multiplier estimated from te difference in outcomes between te single region s and te wole economy may differ from te effects of spending in te entire economy because economic integration as first order effects on outcomes in s. 14 Tis discussion makes clear two additional issues. First, wen s is not infinitesimal SUTVA will not old and β xs measures te effects of spending on outcomes in s relative to te effects in oter areas. Tus, if te cross-sectional multiplier based on spending in one local area understates te national zero lower bound multiplier, te cross-sectional multiplier based on increasing spending in a randomly cosen alf of all U.S. states would furter understate te national multiplier. In practice, owever, most studies consider sufficiently small geograpic units tat te infinitesimal assumption likely provides a reasonable approximation. Second, wile adding spending in oter areas to equation (1) can potentially incorporate some of te spillovers, it does not turn β xs into a national multiplier. 14 Formally, suppose te national economy as population normalized to 1 and consists of N equally sized regions. Te effects of economic integration on te local region s and te rest of te economy are bot of order 1/N. As N, te effect of spending in s on te national economy vanises but te effect on te local region remains of te same order of magnitude as te region s size, 1/N. Note also tat wile related empirically, te concepts of region size and openness are teoretically distinct; a region of size 1/N may sell an arbitrary fraction α of its output to oter regions. 22

24 Finally, wat if te national economy is not closed? Openness of te national economy does not affect te local multiplier wen s is infinitesimal because te national economy does not respond to canges in s. However, as international macroeconomists ave known since Mundell (1963) and Fleming (1962), national multipliers do depend on te openness of te national economy for reasons similar to tose discussed in section 3.2. Te comparison to a closed economy multiplier simply reflects te absence of information from a cross-sectional multiplier for te difference between te multiplier in national closed versus open economies. 4. Relationsip Between Employment and Output Multipliers Many geograpic cross-sectional studies report employment multipliers rater tan output multipliers. Tis outcome reflects necessity as muc as coice; te Bureau of Economic Analysis only began in December 2015 to publis real gross state product (GSP) at a quarterly frequency and measures of output at te county level remain in development. In contrast, te Bureau of Labor Statistics publises montly employment by state or county based on ig quality administrative payroll tax data. Te availability of ig quality employment but not output data at a local level olds true in many oter countries as well. Before turning to te empirical studies, terefore, I derive a mapping between employment and output multipliers. Let β Y denote te output multiplier and βe te employment spending multiplier. Tat is, for a deviation in spending of G t, by definition: Y t+ = β Y G t, 23

25 E t+ = β E G t, were Y t is GDP, E t is employment, G t is government spending, denotes te deviation from some baseline pat, and I drop te geograpic subscript for simplicity. Let e t+ = E t+ /E t denote te percent cange in employment caused by te spending, y t+ = Y t+ /Y t te percent cange in output, and g t = G t /Y t te deviation of spending as a sare of output. It will be useful to write: e t+ = β E Y t E t g t. I assume a production function relating outputs and inputs Y t = A (N t E t ) 1 ξ, were N t denotes ours per worker. Implicitly, tis functional form assumes capital does not adjust in te sort run. Let n t = N t+ /N t. Ten: β Y = y t+ g t = y t+ e t+ e t+ g t (1 ξ) (1 + χ) Y t E t β E, (8) were χ = n t /e t denotes te elasticity of ours per worker to total employment. For te United States, ξ 1/3 and χ 0.5, yielding a combined multiplicative factor of (1 ξ) (1 + χ) As an alternative, Nakamura and Steinsson (2014) report estimates of bot β Y and te combined factor β E Y/E, te latter being te coefficient from a regression of e t on g t. Reassuringly, te ratio of tese two estimates is close to unity. Terefore, for te United States a roug translation from employment to output multipliers is to divide output per worker Y/E by te cost-per-job 1/β E, taking care to make sure tat Y/E and β E correspond to te same 15 Te estimate of ξ = 1/3 based on factor income sares is standard. Okun (1962) provides an early estimate of te relative movement of ours per worker and employment and Elsby et al. (2010) an updated estimate. 24

26 calendar lengt of time. 5. Example of a Cross-Sectional Multiplier I illustrate te cross-sectional approac by presenting a unified set of results based on crossstate variation generated by te American Recovery and Reinvestment Act (ARRA). Enacted in February 2009, te ARRA included new spending, transfers, and tax reductions totaling rougly $800 billion. As legislation proposed by te incoming president wit te explicit intent of mitigating te recession already underway, te ARRA offers little useful time series variation for assessing te consequences of fiscal policy. 16 Instead, researcers ave identified aspects of te spending allocation wic resulted in geograpic variation plausibly exogenous to economic trends. Crucially, more tan alf of te budgetary outlays went eiter to contractors directly or to subnational governments, and an unusual provision of te bill, section 1512, tracked suc spending by requiring federal agencies to report outlays in eac state and all prime recipients to report te funds received. Te combination of te variation in geograpic entitlement in many of te act s programs and te detailed data collection facilitated researc efforts Econometric Coices I implement equation (3) as a purely cross-sectional 2SLS regression: [ H ] (Y s,t+ Y s,t ) = α + β xs F s + γ X s + ɛ s, (9) =0 F s = Π 0 + Π 1Z s + Π 2X s + ν s, (10) 16 A few papers ave used istorical time series patterns to study te ARRA (Romer and Bernstein, 2009; Cogan and Taylor, 2012; Carlino and Inman, 2014). 25