Global Imbalances and Structural Change in the United States*

Transcription

1 Federal Reserve Bank of Minneapolis Research Deparmen Saff Repor 489 Revised: June 2014 (Firs version: Aug 2013) Global Imbalances and Srucural Change in he Unied Saes* Timohy J. Kehoe Universiy of Minnesoa, Federal Reserve Bank of Minneapolis, and Naional Bureau of Economic Research Kim J. Ruhl Sern School of Biness, New York Universiy Joseph B. Seinberg Universiy of Torono ABSTRACT Since he early 1990s, as he Unied Saes has borrowed from he res of he world, employmen in he U.S. goods-producing secor has fallen. We consruc a dynamic general equilibrium model wih wo mechanisms ha could generae declining goods-secor employmen: foreign lending and differenial produciviy growh across secors. We find ha 18 percen of he decline in goods-secor employmen from 1992 o 2012 follows from U.S. rade deficis. Mos of he decline in employmen in he goods secor can be accouned for by differences in produciviy growh across secors. As he Unied Saes repays is deb, is rade balance will reverse, bu goods-secor employmen will coninue o fall. Keywords: Global imbalances; Real exchange rae; Srucural change JEL classificaion: E13, F34, O41 *We hank David Back, David Sras, Frank Warnock, Kei-Mu Yi, and Vivian Yue for helpful discsions. Kehoe and Ruhl graefully acknowledge he suppor of he Naional Science Foundaion under gran SES We are graeful o Jack Rossbach for exraordinary research assisance. The daa ed here are available a hp:// The views expressed herein are hose of he auhors and no necessarily hose of he Federal Reserve Bank of Minneapolis or he Federal Reserve Sysem.

2 1. Inroducion Beween 1992 and 2012, hoeholds and he governmen in he Unied Saes borrowed heavily from he res of he world, and he U.S. ne inernaional invesmen posiion deerioraed by $4 rillion. A commonly held view in policy circles, expressed, for example, by Bivens (2006) and Sco, Jorgensen, and Hall (2013), is ha he U.S. rade deficis generaed by his borrowing have played an imporan role in he decline of employmen in he U.S. goods-producing secor and ha an end o hese deficis will reverse a large par of his rend. We e a dynamic general equilibrium model of he Unied Saes and he res of he world o address he quesions: To wha exen are rade deficis responsible for he loss of U.S. goods-secor employmen? Will employmen reurn o goods-producing secors when U.S. borrowing ends and rade deficis become rade surples? Our framework combines an open economy model of foreign lending and a model of srucural change he secular shif of employmen from goods-producing indries o services-producing indries ha has been ypically sudied in a closed economy. Srucural change in our model is driven by differenial produciviy growh across secors as in Ngai and Pissarides (2007). Faser produciviy growh in he goods-producing secor, combined wih a low elasiciy of subsiuion beween goods and services, generaes he srucural change in he composiion of employmen. We e his model o quaniaively assess he relaive conribuions of asymmeric labor produciviy growh and he saving glu o he decline in goods-secor employmen in he Unied Saes. Our calibraed model of srucural change and rade imbalances accouns for 78 percen of he decline in goods secor employmen from 1992 o (Noably, we do no model he U.S. recession in excep hrough is impac on he rade balance.) In he model, U.S. rade deficis accouned for 17.7 percen of he decline in he goods-producing secor s employmen beween 1992 and 2012, wih mos of he remainder aribued o faser produciviy growh in he goods secor relaive o oher secors. This implies ha eliminaing he rade defici will no generae a significan increase in goods-secor employmen. We find ha, if he rade defici gradually changes o a surpl, U.S. borrowing in he 1990s and 2000s has been welfare improving. If he rade balance reverses quickly and unexpecedly a sudden sop, like ha in Mexico in hen welfare would be greaer if he Unied Saes had no borrowed. 1

3 I is easy o see why some view rade deficis as derimenal o goods-secor employmen. Figure 1 shows ha he share of employmen in he goods secor agriculure, mining, and manufacuring has fallen dramaically as he rade defici has grown. The inuiion for his idea is simple: Impored goods are subsiues for domesically produced goods. As he Unied Saes rades bonds for foreign goods, labor shifs away from domesically produced goods and is reallocaed o producing services and consrucion, which are less subsiuable for foreign goods. When he deb has o be repaid, labor will flow back ino he goods secor o produce he exra goods needed o repay he deb. The imporance of his channel for U.S. goods-secor employmen is he quaniaive quesion a he cener of our sudy. In consrucing he model, we need o specify he driving force behind U.S. borrowing. A common explanaion is ha foreign demand for saving increased, making foreigners more willing o rade heir goods for U.S. bonds. Bernanke (2005) coined he erm global saving glu o refer o his idea, and we adop Bernanke s global-saving-glu hypohesis. Several explanaions have been proposed for he increased demand for saving in he res of he world, such as a lack of financial developmen in he res of he world (Caballero, Farhi, and Gourinchas, 2008; Mendoza, Quadrini, and Ríos-Rull, 2009), differences in biness cycle or srucural growh properies (Back e al., 2006; Perri and Fogli, 2010; Jin 2012), and demographic differences (Du and Wei, 2013). We do no ake a sand on which of hese explanaions, if any, are correc. Insead, we ake he saving glu as given and calibrae a process for he preferences of hoeholds in he res of he world over curren vers fuure consumpion so ha our model maches exacly he pah of he U.S. rade balance beween 1992 and We include four feaures in he model ha make i well suied o address hese issues. Firs, we model an economy wih hree secors: goods, services, and consrucion. Goods and services can be raded, which allows o capure he fac ha he Unied Saes consisenly runs a subsanial rade surpl in services. Inernaional macroeconomic models ually rea goods as he only radable secor and lump all oher secors ino a single nonradable secor. This assumpion is a odds wih he daa: Services are a large componen of U.S. expors. Consrucion is he only nonradable secor and is ed almos enirely o produce invesmen goods, which means ha consrucion is more sensiive han he oher secors o he effecs of capial flows and economic flucuaions in general. Second, we build a deailed inpu-oupu srucure ino he producion side of he model. This allows o model he elasiciy of 2

4 subsiuion beween goods, services, and consrucion in producion as well as consumpion. Third, we allow he elasiciy of subsiuion beween foreign and domesic inpus o differ across secors. Our calibraion assigns a higher elasiciy of subsiuion beween domesic and foreign inpus in he goods secor o mach he fac ha he goods rade balance is more volaile han he services rade balance, as seen in figure 6. Fourh, and perhaps mos imporan, we allow labor produciviy o grow a differen raes across secors, maching he fac ha labor produciviy in he goods secor grew a a faser pace han in oher secors over he pas wo decades, as seen in figure 2 The srucural change lieraure emphasizes asymmeric produciviy growh as an imporan driver of he long-run reallocaion of labor across secors. Recen sudies embed his mechanism, originally due o Baumol (1967), ino closed-economy models ha are consisen wih aggregae balanced growh (Ngai and Pissarides, 2007; Buera and Kaboski, 2009). We ake a similar approach in an open economy model. Several oher recen papers sudy srucural change in open economies (Echevarria, 1995; Masuyama, 1992, 2009; Sposi, 2012; Uy, Yi, and Zhang, 2013). Wih he excepion of Sposi (2012), hese sudies e models of balanced rade, absracing from inernaional capial flows. Allowing for unbalanced rade, we can assess he relaive conribuions of radiional srucural change forces and he saving glu o he dynamics of he U.S. economy. Buera and Kaboski (2012) idenify hree possible sources of srucural change: differenial secoral produciviy growh and a low elasiciy of subsiuion beween secors (Ngai and Pissarides, 2007); nonhomoheic preferences (Kongsamu, Rebelo, and Xie, 2001); and capial deepening and secor-specific capial shares (Acemoglu and Guerrieri, 2008). As argued by Buera and Kaboski (2012), nonhomoheic preferences are mos relevan a low levels of income and are h unlikely o be imporan for he Unied Saes. We allow for secorspecific capial shares in our model, bu hey do no play a quaniaively imporan role in our resuls. We calibrae our model so ha i maches exacly he naional accouns and inpu-oupu able for he Unied Saes in 1992 and he U.S. rade balance during As figures 5 7 show, our calibraed model endogenoly generaes oucomes ha mach several key facs abou he U.S. economy during his period: We mach he magniude of he real exchange rae 3

5 appreciaion and subsequen depreciaion, he dynamics of he disaggregaed goods and services rade balances, and he changes in secoral employmen shares. We e he model o conduc wo kinds of exercises: hisorical counerfacuals and predicions abou he fuure. In our counerfacual scenario, we urn off he saving glu, which allows o answer quesions abou he pah he U.S. economy would have aken had he saving glu never occurred. In our model wihou a saving glu, he goods secor s employmen share falls from 19.7 percen in 1992 o 15.1 percen in 2012 compared wih 14.1 percen in he model wih he saving glu and o 12.5 percen in he daa. Looking o he fuure, our benchmark model predics ha he goods secor s employmen share will coninue o decline in he long run, and ha he rade balance reversal required o repay he deb he Unied Saes incurred during he saving glu will have lile impac on goods-secor employmen. The goods secor s employmen share is 13.1 percen in 2024 in our benchmark, vers 12.6 percen in he counerfacual scenario in which he saving glu never occurs. Our model allows o ask: To wha exen has he saving glu been good for U.S. hoeholds? We consruc a measure of he real income of U.S. hoeholds in 1992, and compare he welfare of U.S. hoeholds in he baseline model o a counerfacual in which he saving glu did no occur. The saving glu iself improves welfare: The lifeime real income of U.S. hoeholds in 1992 would have been almos $700 billion lower (abou 11 percen of 1992 GDP) if he saving glu had no happened. In our baseline model, we assume ha he ransiion from a rade defici o a surpl will happen gradually. In an exension, we consider he effecs of a sharp reversal of he rade balance a sudden sop as suggesed in Obsfeld and Rogoff (2005, 2007). Our resuls indicae ha a sudden sop in he Unied Saes in would look similar o hisorical episodes in emerging economies: a large real exchange rae depreciaion, a subsanial produciviy-driven oupu conracion, and a sharp reallocaion of facors across secors (Calvo, Izquierdo, and Mejía, 2004; Calvo and Talvi, 2005; Kehoe and Ruhl, 2009). As in sudden sops of he pas, hese effecs would be shor-lived; several years afer he sudden sop ends, he U.S. economy would be on almos he same pah on which i would have been if he sudden sop had never happened. Any emporary reallocaion of labor o he goods-producing secor during he sudden sop would be quickly reversed and have no long-erm effec. 4

6 In he sensiiviy analysis of our model, we find ha our main resuls are rob o a range of modeling choices, such as alering our assumpions abou he pah of governmen spending and abandoning perfec foresigh in favor of a sochasic model wih raional expecaions. The inpu-oupu producion srucure and he radabiliy of services, however, play imporan quaniaive roles in our model s predicions for goods-secor employmen. Removing he inpu-oupu srucure raises he elasiciy of subsiuion beween goods and services in gross oupu, which caes our model o capure a significanly smaller fracion of he decline in goods-secor employmen we observe in he daa during This change also leads our model o oversae he role of he saving glu in reducing goods-secor employmen during his period; making services nonradable has a similar effec. To jify our assumpion ha he U.S. rade defici has been driven by he res of he world s demand for saving raher han domesic facors, we sudy a version of our model in which we aler he preferences of U.S. hoeholds raher han hose in he res of he world o mach he U.S. rade balance. This domesic-saving-drough experimen does no significanly affec our main resuls abou goods-secor employmen, bu i leads o predicions for invesmen and consrucion employmen ha are sharply a odds wih he daa: The foreign-saving-glu hypohesis fis he daa beer. 2. The U.S. economy, This secion presens our approach o analyzing U.S. daa over he pas wo decades. We view he massive foreign borrowing and he differenials in produciviy growh across secors as exogeno driving forces ha we ake as inpus ino he model. Below, we presen hree key facs abou U.S. daa ha we view as ess for our model. I is our model s abiliy o replicae hese hree facs in response o he exogeno driving forces ha gives confidence in ing he model o make predicions abou he fuure of he U.S. economy. Exogeno driving force 1: Foreign borrowing increased, hen decreased Figure 3 illraes j how much borrowing hoeholds and he governmen in he Unied Saes have done. The curren accoun balance measures he exac magniude of capial flows ino he Unied Saes, bu we see ha he rade balance racks he curren accoun balance almos exacly. Since our model is no designed o accuraely capure he difference beween hese wo 5

7 series, and he rade balance has an exac model analogue, we e he rade defici as our measure of U.S. borrowing. Figure 3 shows ha beween 1992 and 2006, he rade defici grew seadily, reaching 5.8 percen of GDP, afer which i began o shrink. In 2012, he rade defici remained a 3.6 percen of GDP. We view he pah of he rade balance as wha defines he saving glu in our model. Our hypohesis is ha he U.S. economy is currenly in he process of emerging from he saving glu. Capial flows are imporan o our analysis in wo ways. Firs and foremos, he imbalanced flow of goods ino he Unied Saes direcly affecs he need o produce goods domesically and, h, he labor needed in ha secor. The rade balance is he mos appropriae measure of his force. Second, he accumulaed deb evenually needs o be repaid, which could affec he fuure employmen needed o produce goods in he Unied Saes. In he model, accumulaed rade balances are he measure of his accumulaed deb, which differs from he U.S. ne foreign asse posiion by any revaluaion effecs. These revaluaion effecs have, a imes, played a significan role in he value of he U.S. ne foreign asse posiion (Lane and Milesi-Ferrei, 2008; Gourinchas and Rey, 2007). To he exen ha revaluaion has been in he favor of he Unied Saes, he smaller fuure deb burden would decrease he need o reallocae labor back ino he goods-producing secors. Exogeno driving force 2: Labor produciviy grew fases in he goods secor During , labor produciviy in he goods secor increased by an average of 4.2 percen per year, while i increased by only 1.3 percen per year in he services secor and fell by 1.2 percen per year in consrucion. Wha is essenial in our model is he differenial beween produciviy growh in he goods secor and ha in he services secor. As he daa in figure 2 show, his differenial has been close o consan since 1980, wih average produciviy growh of 4.1 percen per year in goods during , compared wih 1.3 percen in services. Excep for he produciviy slowdown of he 1970s, he differenial has been persisen since Our hypohesis is ha his produciviy differenial persiss unil a leas Fac 1: The real exchange rae appreciaed, hen depreciaed Figure 3 presens he firs key fac ha we ask our model o replicae. The figure shows ha he U.S. real exchange rae was volaile and racked he rade balance closely during

8 We consruc our measure of he U.S. real exchange rae by aking a weighed average of bilaeral real exchange raes wih he Unied Saes 20 larges rading parners, wih weighs given by hese counries shares of U.S. impors in (Oher weighing schemes do no significanly affec our resuls.) This approach forms he basis of our concep of he res of he world in our model. The real exchange rae appreciaed by 27.9 ( 100 (100 / ) ) percen beween 1992 and 2002, afer which i depreciaed by 22.1 percen beween 2002 and The inuiion for why he real exchange rae and rade balance should move closely is sraighforward: As foreign goods and services become cheaper, U.S. hoeholds buy more of hem. Noice, however, ha he iming is off: The maximum appreciaion of he real exchange rae occurred in 2002, whereas he larges rade defici occurred in Fac 2: The goods secor drove aggregae rade balance dynamics Figure 6 presens our second key fac. Here we disaggregae he rade balance, ploing he rade balances for goods and services separaely. We see ha he goods rade balance generaes mos of he flucuaions in he aggregae rade balance, whereas he services rade balance flucuaes in a band beween 0.5 and 1.2 percen of GDP. Tha he Unied Saes has consisenly run a rade surpl in services moivaes one of he key feaures of our modeling framework. Sandard modeling convenions in inernaional macroeconomics lump services ogeher wih consrucion ino a nonradable secor, reaing goods as he only secor ha produces oupu ha can be raded inernaionally. By conras, we allow boh goods and services o be raded in our model, and we calibrae home bias parameers he share parameers in he Armingon aggregaors for each secor separaely o capure he fac ha he Unied Saes consisenly runs a surpl in services and a defici in goods. Fac 3: Employmen in goods declined seadily; consrucion employmen rose, hen fell Figure 7 presens our hird fac: Beween 1992 and 2012, he fracion of oal labor compensaion paid o he goods secor fell from 19.7 percen o 12.5 percen. The fracion of oal labor compensaion is our preferred measure of he goods secor s employmen share becae i maps direcly ino our model, where we measure labor inpus in erms of effecive hours worked, raher han raw hours worked. As figure 1 shows, his measure moves closely wih more common measures like he share of employees in he goods secor; he same is rue for 7

9 he consrucion secor. The consrucion secor s share of labor compensaion rose from 4.4 percen in 1992 o 5.7 percen in 2006, as consrucion boomed prior o he financial crisis in Employmen in consrucion hen sared o fall, and by 2012 he consrucion secor s share of labor compensaion was again 4.4 percen. 3. Model We model an economy wih wo counries, he Unied Saes and he res of he world (RW). We e he superscrips and rw o denoe prices, quaniies, and parameers in he Unied Saes and he res of he world. The lengh of a period is one year. Each counry has a represenaive hoehold ha works, consumes, and saves o maximize uiliy subjec o a sequence of budge consrains. The model begins in 1992, is subjec o ransiory hough decades long changes in secoral produciviy growh raes and he res of he world s willingness o lend, and evenually seles ono a long-run balanced growh pah. Each counry produces commodiies ha serve boh inermediae and final es. We model he U.S. producion srucure in deail, ing an inpu-oupu srucure ha we calibrae o he U.S. inpu-oupu marix. We model producion in he res of he world in a simpler fashion, absracing from invesmen and domesic inpu-oupu linkages. We model he U.S. governmen in a reduced-form fashion as well he governmen s spending and deb are specified exogenoly, and he governmen levies lump-sum axes on U.S. hoeholds o ensure ha is budge consrains are saisfied. Financial asses The U.S. governmen, hoeholds in he Unied Saes, and hoeholds in he res of he world have access o a one-period, inernaionally raded bond, b, ha is denominaed in unis of he U.S. consumer price index (CPI). U.S. hoeholds can also save by invesing in he U.S. capial sock, bu will be indifferen beween holding capial and bonds becae hey boh pay he same reurn in equilibrium. We model a single bond, bu he equilibrium of our baseline model is equivalen o one in which boh governmens and hoeholds issue deb. The deerminisic naure of he model gives rise o Ricardian equivalence (excep a he onse of he savings glu), so he spli beween public and privae deb is essenially irrelevan. In secion 6 we presen a 8

10 sochasic version of he model in which public and privae deb are disinc, bu we find his change o be quaniaively insignifican. Producion The Unied Saes produces four commodiies: goods y, services y, consrucion y, and g s c invesmen y i. The res of he world produces is own goods rw y and services y. Prices are rw g s denoed analogoly. All commodiies are sold in perfecly compeiive markes. Each U.S. commodiy j cgs,, is produced ing capial k and labor j, along wih inermediae inpus j of U.S. goods z gj, U.S. services z, U.S. consrucion sj z cj, and impors m j purchased from he same secor j in he res of he world: z z z 1 j j j. gj sj cj j 1 j (1) y j M j j min,,, Aj kj j j (1 j ) mj a a a gj sj cj This nesed producion funcion embeds a Leonief inpu-oupu srucure in an Armingon aggregaor. The parameers of he producion funcions are: M j and A j, he consan scaling facors ed o faciliae calibraion; j, which governs he share of impors in producion;, j which governs he elasiciy of subsiuion beween domesic and impored inpus; a,, gj a sj acj, which govern he shares of goods, services, and consrucion in gross oupu; j, he secorspecific labor produciviy; and, capial s share of value added. j Our assumpion of zero subsiuabiliy beween inermediae inpus is sandard in he inpu-oupu lieraure, consisen wih empirical findings ha direc requiremen coefficiens vary lile over ime (Sevaldson, 1970; Miller and Blair, 2009). This assumpion implies ha he elasiciy of subsiuion beween goods and services in boh inermediae and final es is lower han he same elasiciy in final es alone. In secion 6, we show ha his assumpion plays an imporan role in our model s abiliy o capure he reallocaion of labor across secors ha we observe in he daa. We allow he Armingon elasiciies 1/(1 ) o differ across secors o capure he fac ha he goods rade balance is more volaile han he services rade balance (see figure 6). We j 9

11 also allow labor produciviy j o grow a differen raes across secors o capure he fac ha produciviy in he goods secor has grown faser han in oher secors. This differenial produciviy growh is he driving force behind he srucural change mechanism in he model. U.S. producers in all hree secors j g, sc, choose inpus of inermediaes and facors o minimize coss, which implies sandard marginal produc pricing condiions for capial and labor. The U.S. invesmen good is produced ing inpus z gi, z si, and z of goods, services, ci and consrucion according o (2) yi G zgi zsi zci g s c, g s c 1. This specificaion is consisen wih evidence repored by Bems (2008) ha expendiure shares on invesmen inpus are approximaely consan over ime across a range of counries. We model he res of he world s producion srucure in less deail, absracing from invesmen and inpu-oupu linkages. Goods and services in he res of he world are produced ing labor rw j and impored inermediae inpus rw m j from he same secor j in he Unied Saes. The producion funcions are simpler nesed Armingon aggregaors of he form 1 j j rw rw rw rw rw j rw rw (3) y j M j j j j (1 j ) mj Hoeholds. Each counry is populaed by a coninuum of idenical hoeholds. We draw a disincion beween he oal and working-age populaions so ha our model can capure he impac of demographic changes on hoeholds incenives o borrow and save. We denoe he oal U.S. populaion by n and he working-age populaion by. We evaluae consumpion per capia on an adul-equivalen basis, defining he U.S. adul-equivalen populaion as n ( n )/2. The res of he world s demographic variables are defined analogoly. We normalize he amoun of ime available for work and leisure by a U.S. working-age person o one and denoe oal U.S. labor supply by. U.S. hoeholds choose labor supply, 10

12 consumpion of composie goods and services c h g h b o maximize uiliy h and c s, invesmen i, and bond holdings (4) h (1 ) h c h g h c s (1 ) 0 n n 1 subjec o he budge consrains h h h h (5) p c p c p i qb 1 w p ( p, p ) b (1 ) r k T, g g s s i he law of moion for capial g s k k (6) k 1 (1 ) k i, appropriae non-negaiviy consrains, iniial condiions for he capial sock and bond holdings h k and 0 b 0, and a consrain on bond holdings ha rules ou Ponzi schemes bu does no oherwise bind in equilibrium. We e he superscrip h for U.S. hoeholds consumpion and bond holdings o disinguish hem from hose of he U.S. governmen, for which we e he superscrip g. Hoeholds pay consan proporional axes on capial income and a lump- k sum ax or ransfer T. We e he capial income ax o obain a sensible calibraion for he iniial capial sock and depreciaion rae. We also allow he ax rae on capial income in 1993 o differ from he consan rae in order o mach he level of invesmen in Bonds are denominaed in unis of he U.S. CPI, defined as (7) p c p c p ( pg, ps ). P h h g g1992 s s1992 h h g1992cg1992 Ps1992cs 1992 We model discoun bonds, so he price q represens he price in period of one uni of he U.S. CPI baske in period 1. The real ineres rae in unis of he U.S. CPI is given by (8) 1 1 p ( p, p )/ q. r g s During he sudden sop episode ha can occur in 2015, bond holdings are fixed and he inernal real ineres rae is deermined endogenoly in each counry separaely. The marke clearing condiion for bonds is 11

13 (9)(9) b g b h b rw 0. The res of he world s hoeholds solve a simpler problem. We absrac from invesmen dynamics in he res of he world, so he only way he res of he world s hoeholds can save is by buying U.S. bonds. We can easily allow for res-of-he-world bonds as well wihou changing he equilibrium of he model. Labor supply is endogeno and he res of he world s hoeholds have a uiliy funcion similar o ha of U.S. hoeholds: (10) 0 rw (1 ) rw rw rw c rw rw g rw c s (1 ) rw rw rw n n 1. The only differences from he U.S. hoeholds uiliy funcion are he share parameer he uiliy weigh rw rw and. The laer is an ineremporal demand shifer, which we calibrae o mach he U.S. rade balance during During his period rw falls, reflecing a reducion in uiliy gained from consumpion a compared wih fuure consumpion. This is he driving force behind he saving glu. The res of he world s represenaive hoehold chooses labor supply rw, consumpion of goods and services c rw g and c rw maximize uiliy subjec o he budge consrains, rw rw rw rw r (11) w rw rw rw p c p c qb 1 w p ( p, p ) b, g g s s g s s, and bond holdings b rw o and non-negaiviy and no-ponzi consrains similar o hose ha U.S. hoeholds face. The res of he world s CPI is defined analogoly o he U.S. CPI in (7). The real exchange rae is (12) rer p rw ( p rw, p rw )/ p ( p, p ). g s g s U.S. governmen The governmen in he Unied Saes levies axes and sells bonds o finance exogenoly required expendiures on consumpion of goods and services. The budge consrain is g g g g (13) p c p c qb 1 r K T p ( p, p ) b. g g s s k k g s We specify exogeno ime pahs for oal governmen consumpion expendiures and deb as fracions of GDP, ing hisorical daa for and Congressional Budge Office (CBO) 12

14 projecions for he fuure. We e and o denoe hese ime series. We allow he lumpsum ax T o vary as necessary o ensure ha he governmen s budge consrain is saisfied. To allocae is oal expendiure beween goods and services, in each period, he governmen chooses g c and c o maximize g g g g g (14) cg c s s subjec o he consrain ha he governmen makes is required oal expendiures. We assume ha governmen spending does no ener he hoehold s uiliy funcion (or equivalenly, eners in a separable fashion), nor does i ener any of he producion funcions. Becae of he lump sum ax, our model exhibis near-ricardian equivalence. Tha is, he iming of axes and governmen borrowing is almos irrelevan. Ricardian equivalence breaks down only when we inroduce unexpeced evens he saving glu and he sudden sop. Unanicipaed changes in he ime pah of governmen deb ha accompany hese evens do affec he model s equilibrium dynamics, paricularly in he shor run. Equilibrium An equilibrium in our model, for a given sequence of ime-series parameers { rw,, } and 0 iniial condiions ( b h 0, b g 0, k 0 ), consiss of a sequence of all model variables such ha hoeholds in he Unied Saes and he res of he world maximize heir uiliies subjec o heir consrain ses, prices and quaniies saisfy marginal produc pricing condiions for all commodiies, prices and quaniies are such ha all producion aciviies earn zero profis, all commodiy, facor, and bond marke clearing condiions are saisfied, and he U.S. governmen solves is consumpion-spending allocaion problem in each period. When we solve he model numerically, we require ha equilibria converge o balanced growh pahs afer 100 years. There are an infinie number of possible balanced growh pahs indexed by he sum of public and privae U.S. deb bu our model s equilibrium is unique, becae he iniial condiions deermine ono which balance growh pah he economy seles. 4. Calibraion We calibrae he model s parameers and iniial condiions so ha he equilibrium replicaes he U.S. inpu-oupu marix and naional accouns for We do his for a model in which he 13 g

15 agens do no foresee he savings glu. We view his as he mos naural way o hink abou he agens expecaions in he early 1990s: We do no hink ha U.S. hoeholds in 1992 foresaw he kind of borrowing he Unied Saes would do over he subsequen wo decades. Table 2 liss our calibraed parameer values. More deails are provided in he online appendix a hp:// U.S. producion parameers We choose unis so ha U.S. GDP is equal o 100 and all prices are equal o 1 in We compue he parameers in he Leonief porion of he U.S. producion funcions in (1) direcly from he inpu-oupu marix shown in able 1. For example, o compue a gc, he amoun of goods needed o produce one uni of gross oupu in he consrucion secor, we divide he value in he goods row and consrucion column (3.7) by gross oupu in consrucion (10.7). We e a similar procedure o calculae facor shares in value added for each secor. For he Armingon aggregaors in (1), we firs specify values for he elasiciies of subsiuion beween domesic and impored inpus. There is some debae over his elasiciy becae biness cycle models end o imply a low elasiciy, whereas analysis of rade policy changes ofen suggess a much higher elasiciy; see Ruhl (2008) for a deailed discsion. Becae he services rade balance is less volaile han he goods rade balance, we choose a lower elasiciy of subsiuion beween domesic and foreign inpus in he services secor. We se he elasiciy in goods 1/(1 g ) o 3 and ha in services 1/ (1 s ) o 1. We hen e equilibrium condiions (marginal produc pricing and zero profis) o calibrae j from he inpu-oupu marix. The scale facors are se so ha equilibrium oupus mach heir respecive enries in he inpu-oupu able. We e a similar procedure o calibrae he producion funcion for invesmen. Hoehold and governmen parameers We se he elasiciy of ineremporal subsiuion 1/(1 ) o 0.5. We se he long-run ineres rae o 3 percen (U.S. Congress, Congressional Budge Office, 2012) and he discoun facor so ha his ineres rae is consisen wih balanced growh. We se he elasiciy of subsiuion beween goods and services in consumpion, 1/(1 ), o 0.5, as in Sockman and Tesar (1995). We calibrae he parameers h and of he hoeholds preferences ing privae M j 14

16 consumpion daa from he inpu-oupu able and daa on hours worked. A similar procedure yields he governmen s share parameer U.S. iniial condiions g. To calculae he iniial capial sock, we se he 1992 real ineres rae o 4 percen. The real ineres rae in 1992 is no an equilibrium objec in our model; i would have been deermined in 1991, bu 1992 is our iniial model year. The real ineres rae on 10-year U.S. Treasury bonds was approximaely 4 percen in Given a ax rae on capial income, we can compue k our iniial capial sock ing daa on depreciaion from he 1992 naional income accouns and daa on paymens o capial in he inpu-oupu able. We choose 0.4, which implies a depreciaion rae of 6.6 percen per year, well wihin he sandard range of annual depreciaion raes found in he lieraure. Our resuls are no sensiive o alernaive approaches o calibraing he iniial capial sock. U.S. governmen deb was 48.1 percen of GDP in 1992, and we e his g value direcly o se he level of governmen deb in 1992, b We hen se privae bond h h g holdings, b, so ha oal ne foreign asses 1992 b 1992 b 1992 are 7.8 percen of GDP as repored in Lane and Milesi-Ferrei (2007). k Calibraing he res of he world To calibrae he remaining parameers, we need o define he res of he world. We selec he Unied Saes op 20 rading parners, ranked by average annual bilaeral rade (expors pl impors) beween 1992 and 2012, and weigh hem by heir average share of U.S. oal annual rade during his period. We e hese counries weighs o consruc a composie rading parner, hinking of he res of he world as being composed of 20 idenical counries ha all look like his composie. To calculae he size of he res of he world relaive o he Unied Saes, we ake a weighed average of goods and services consumpion of hese 20 counries and muliply hese figures by 20 o ge oal consumpion of goods and services in he res of he world. We e equilibrium condiions in a similar manner as before o calibrae he res of he world s Armingon aggregaors and preference parameers. 15

17 Exogeno processes We e hisorical daa and fuure projecions from he World Populaion Prospecs: 2010 Revision (Unied Naions, 2011) o consruc ime series for he demographic parameers for boh he Unied Saes and he res of he world (ing he same 20 counries and weighs as before). The Unied Saes and he res of he world are projeced o grow a differen raes well pas he 100-year erminal dae in our model, so o ensure balanced growh, we assume ha he populaions in boh counries begin o converge o consan levels afer Our model s equilibrium dynamics during , he period on which we foc, are no sensiive o his assumpion. We calculae secor-level produciviy growh raes ing daa on value added and labor compensaion by secor from he BEA for We find ha he average growh raes of labor produciviy over his period are 4.3 percen in goods, 1.3 percen in services, and 1.2 percen in consrucion. We e hese values in he model beween 1992 and 2030, and in he years following we assume ha all of he secor-level growh raes converge slowly o 2 percen per year, o ensure ha he equilibrium converges o a balanced growh pah. We need o specify he exogeno ime pahs for governmen expendiure and governmen deb. We e hisorical daa on governmen consumpion and deb for he years From 2012 onward, we e CBO projecions and make adjmens o reain consisency wih he naional income accouns and o allow for balanced growh in he long run. Some of he CBO projecions made for he pah of governmen deb are implaible, however; he CBO s exended baseline scenario predics ha governmen deb will drop below zero by 2070, and he CBO s exended alernaive scenario predics ha deb will surpass 250 percen of GDP by We herefore assume ha governmen deb as a fracion of GDP will remain consan a he 2023 value of 77.0 percen of GDP in 2024 and beyond. More deails abou he consrucion of he governmen s variables are available in he appendix. Recall ha we are calibraing he model under he assumpion ha he savings glu was unforeseen in Formally, his means ha we calibrae he res of he world s preference rw parameer o mach he U.S. rade balance in 1992, and we assume ha i converges 1992 gradually o a consan value of 1 hereafer. 16

18 The saving glu A his poin, we have calibraed and solved he model in which agens believe ha he ineremporal rae of subsiuion in he res of he world will remain relaively consan. To calibrae he savings glu, we need o calibrae he values of rw for so ha he equilibrium replicaes exacly he aggregae U.S. rade balance during his period. Noe ha his is he only ime series from he daa ha we e in he calibraion. We assume ha gradually converges o 1 afer We refer o he model s pos-2012 dynamics in his scenario as a gradual rebalancing, represening he oucome of a slow, orderly end o he forces driving he saving glu. The saving glu, which manifess in our model as emporarily reduced uiliy from consumpion and leisure in he res of he world, is an unanicipaed even: Model agens in 1992 do no expec i o occur, bu hey have perfec foresigh hereafer. In our sensiiviy analysis, we relax he perfec foresigh assumpion and allow for agens o be uncerain abou he lengh of he saving glu. 5. Quaniaive resuls This secion presens he baseline quaniaive resuls and demonsraes ha he model replicaes our hree key facs. We hen compare he oucomes of he baseline model wih hose from a model in which he savings glu does no occur. Replicaing he hree key facs Prices, quaniies, and he rade balance from 1992 onward are endogeno oucomes of he model. Here we show ha he equilibrium of he calibraed model maches he U.S. daa in he hree key dimensions laid ou in secion 2. As figure 4 shows, our calibraion procedure implies ha he U.S. rade balance maches exacly he daa from In his figure we have also ploed he rade balance from he model in which he saving glu never occurs. Noice ha, in his counerfacual scenario, rade is approximaely balanced hroughou he period. In he baseline model, however, he saving glu has occurred, so he Unied Saes m repay is deb in he long run. The figure shows ha he U.S. rade balance will swich from a defici o a surpl in 2018, and will reach a surpl of more han 1 percen of GDP by Even hough goods-secor produciviy growh is rapid, here is lile incenive for he agens o borrow o smooh consumpion in he absence of he savings glu. The weighed- rw 17

19 average produciviy growh rae in he economy in is very close o he long-run produciviy growh rae of 2 percen: In he aggregae, here is lile reason for ineremporal rade. The small amoun of ineremporal rade in figure 4 is due o diffences in populaion growh raes beween he Unied Saes and he res of he world. Figure 5 plos he model s real exchange rae in he baseline model agains he daa and he no-saving-glu counerfacual. Our model does a good job of maching he magniude of he appreciaion during : The real exchange rae appreciaed by 27.9 percen in he daa and 26.1 percen in he model before beginning o depreciae. The model, however, fails o capure he iming of he depreciaion. In he daa, he real exchange rae begins o depreciae in 2002, four years before he rade defici begins o shrink. In our model, he real exchange rae moves in andem wih he rade balance, so i does no begin o depreciae unil In our model, consumers and firms begin o impor fewer foreign goods and services only once hey begin o become more expensive. Figure 5 also shows ha if he saving glu had never occurred, he U.S. real exchange rae would appreciae slowly over he long run, due in large par o he increase in he relaive price of services, in which he Unied Saes has a comparaive advanage. The saving glu did occur, however, and becae he Unied Saes m run a rade surpl in he long run, is goods and services m become cheaper. Our model predics ha he real exchange rae will coninue o depreciae for several years, evenually converging o a level ha is 5.9 percen higher ha is, more depreciaed han ha in he no-saving-glu counerfacual. Figure 6 plos he secor-level rade balances in he model and he daa. The model maches boh he goods and services rade balances closely beween 1992 and This aspec of he model s performance is mosly due o our choice of Armingon elasiciies. Had we ed he same elasiciy in boh secors, he goods rade balance would no have moved enough, while he services rade balance would have been oo volaile. The figure also shows ha in he absence of he saving glu, he services rade balance would no have been subsanially differen, while he goods rade balance, refleced in he aggregae rade balance, would have been almos fla. In he long run, he model predics ha he goods rade balance will be 1.4 percen of GDP higher by 2024 han i would have been if he saving glu had never occurred. Despie his, he model predics ha he goods rade balance will be negaive in he balanced growh pah: The services secor will be he source of he enire long-run rade surpl. 18

20 Figure 7 plos he employmen shares for goods and services in he model and he daa. The baseline model maches he daa closely beween 1992 and 2001, afer which he goods employmen share falls more in he daa han in he model. For , our baseline model capures 78.0 percen of he decline in he goods secor s employmen share ha we observe in he daa. In he no-saving-glu counerfacual, however, he model sill capures 64.2 percen of he decline. The figure suggess ha, while he saving glu did emporarily accelerae he decline in goods-secor employmen, he bulk of he decline is aribuable o he fac ha labor produciviy has grown faser in he goods secor han in he res of he economy. This resul implies ha ha he end of he saving glu will have lile impac on employmen in he goods secor. By 2024, he goods secor s share of employmen will be almos exacly he same regardless of wheher or no he saving glu happened. Even hough he U.S. economy m run a rade surpl in he long run o repay is deb, he goods secor s employmen share will coninue o decline once he saving glu ends. There are wo main reasons for his resul. Firs, labor produciviy coninues o grow faser in goods han in oher secors in our model even afer he saving glu ends. This aspec of srucural change has been a consisen force in he U.S. economy since he 1960s, and we see no reason ha i should end when he saving glu does. Second, he Unied Saes can repay is deb wih he rade surpl generaed by he services secor; our model predics ha he Unied Saes will coninue o run a defici in goods rade once he saving glu ends and he aggregae U.S. rade balance reverses. Figure 7 also shows ha he model capures several aspecs of he consrucion secor s employmen share beween 1992 and Beween 1992 and 2006, he consrucion secor s employmen share rises in boh he model and he daa, alhough our model generaes a larger increase. Our model overexplains he boom in consrucion secor employmen j by inroducing he saving glu. The subsequen b is smaller in he model han in he daa primarily becae we have no inroduced he financial crisis of in any form oher han he way in which i affeced he rade balance. If we were o inroduce addiional feaures o he model o more accuraely model he crisis, we would undoubedly do beer in his regard, bu his is no he foc of our sudy. As he figure shows, our model suggess ha he effecs of he saving glu on he consrucion secor will largely dissipae by 2016; as in he goods secor, he consrucion secor s long-run employmen share dynamics will be driven primarily by produciviy growh raher han he rebalancing process. 19

21 Welfare implicaions of he saving glu Did he saving glu make U.S. hoeholds beer off? To answer his quesion, we consruc a measure of real income in 1992 denominaed in 1992 U.S. dollars. This real income index is he cos of achieving he equilibrium sequence of uiliy from 1992 onward in unis of he U.S. CPI in 1992:. 1 h h (15) 1992 q ( ) s 1992 s pgcg pscs w The prices and quaniies in (15) represen equilibrium objecs in our benchmark model. To conver his objec o 1992 dollars, we scale i so ha consumpion expendiures in he model are equal o 1992 privae consumpion in he naional income and produc accoun (NIPA) ables. We e he resuling scaling facor o calculae real income in alernaive scenarios, like he counerfacual in which he saving glu does no occur or he scenario in which boh he saving glu and a sudden sop occur. In our baseline model we assume ha, in 1992, model agens expec governmen consumpion expendiures o remain fixed a he 1992 level of 16.6 percen of GDP, bu when he saving glu begins, an unforeseen change in governmen spending policy occurs: Governmen spending as a fracion of GDP racks he daa beween 1993 and 2012, hen rises o 22.9 percen over ime. This reflecs policy changes ha have occurred over he pas wo decades, such as increased healh care and defense spending, ha people likely did no anicipae in he early 1990s. This increase in governmen consumpion gives U.S. hoeholds an incenive o save for he fuure. We repor our welfare resuls under an alernaive assumpion: In 1992, agens expec governmen consumpion, as a fracion of GDP, o follow he pah i acually ook beween 1992 and 2012, and hen follow he same rajecory o 22.9 percen ha we ed in he saving-glu scenario in our main exercise. In he saving-glu scenario, we require ha governmen consumpion, in erms of acual quaniies of goods and services, say consan in all hree sages of he exercise: he no-saving-glu counerfacual, he saving glu wih gradual rebalancing, and he sudden sop. This modificaion has virually no impac on any of he resuls repored above, and i allows for direc welfare comparisons across he hree scenarios even if governmen spending eners he uiliy funcion as long as i eners in an addiively separable fashion allowing o ask wheher he saving glu is good or bad, and j how cosly a sudden sop would be. 20

22 The firs column of able 3 presens our resuls on he welfare impac of he saving glu for our baseline model. In row 1, column 1, we repor real income of U.S. hoeholds in 1992 relaive o he gradual rebalancing scenario. Our model indicaes ha he real income of U.S. hoeholds in 1992 would have been $689 billion lower if he saving glu had never occurred: 10.9 percen of U.S. GDP in Tweny years of increased consumpion of foreign impors have made U.S. hoeholds subsanially beer off as long as he saving glu ends in gradual rebalancing. 6. Sensiiviy analysis We have performed exensive sensiiviy analysis wih our model. Our main resuls abou he reallocaion of labor across secors are rob o all he modeling alernaives ha we have ried. In his secion, we discs five modeling alernaives in deail: (1) We allow he savings glu o end abruply in a sudden sop. (2) We relax our baseline model s assumpion of perfec foresigh by sudying a version of our model in which he duraion of he saving glu is uncerain now follows a sochasic process and agens have raional expecaions. (3) We remove he inpu-oupu relaionships beween secors. (4) We do no allow services o be raded inernaionally. (5) We calibrae he preferences of U.S. hoeholds, raher han hose of hoeholds in he res of he world, o generae observed U.S. borrowing a domesic saving drough insead of a global saving glu. Alernaive endings o he savings glu In he baseline model, he rebalancing process is gradual and orderly. In his secion, we e our model o explore he implicaions of a sudden end o he savings glu. We model a sudden sop o capial inflows in as a surprise. Agens in he model have perfec foresigh before and afer he sudden sop, bu when he sudden sop occurs, i is compleely unexpeced. We model he sudden sop as a surprise becae U.S. ineres raes currenly indicae ha financial markes do no assign a significanly posiive probabiliy o a U.S. deb crisis j as hey did no assign significanly posiive probabiliies o a crisis in Mexico in 1995 or o he currenly ongoing deb crises in he Eurozone. (See, for example, Arellano, Conesa, and Kehoe, 2012.) We hink of he possibiliy of a deb crisis sriking he rw 21

23 Unied Saes as he sor of self-fulfilling crisis modeled by Cole and Kehoe (2000) and Conesa and Kehoe (2012). We model a sudden sop as a wo-year period during which he Unied Saes is resriced from borrowing furher from he res of he world, afer which foreigners are again willing o purchase U.S. bonds. We assume ha he res of he world s preference parameer converges o is long-run value of 1 more quickly han in he previo scenario o capure he idea ha a sudden sop is associaed wih a faser end o he forces ha drove he saving glu. Furhermore, we assume ha a sudden sop generaes a disorderly adjmen in financial markes ha caes oal facor produciviy (TFP) in all hree producion secors o fall by 10 percen in 2015, o recover half of his drop in 2016, and o fully recover in This TFP drop capures he sor of disrupion and rapid recovery ha occurred in sudden sop episodes like ha in Mexico in We also assume ha he U.S. governmen s deb as a fracion of GDP falls o a lower long-run level (60 percen) han in he baseline model, represening he idea ha a sudden sop is associaed wih, or perhaps riggers, a long-erm change in U.S. governmen deb policy. The sudden sop riggers an immediae reversal in capial flows and a large real exchange rae depreciaion. The rade balance rises from 1.5 percen of GDP o 2.8 percen on impac, and he real exchange rae depreciaes by 12.7 percen. The rade balance reversal induces he goods secor s labor compensaion share o rise from 14.3 percen o 15.1 percen on impac. These effecs, however, would be shor-lived. By 2024 he rade balance and real exchange rae would be almos idenical o heir levels in he gradual rebalancing scenario. Alhough a sudden sop involves quicker deb repaymen, he effec on he long-erm need o repay is small in our model. The Unied Saes has borrowed so much from he res of he world in he las wo decades ha wo years of rapid repaymen do no make much of a den in he overall sock of deb. We repor he welfare effecs of a sudden sop in able 3. If he savings glu ends in a sudden sop, he real income of U.S. hoeholds will fall by $1,019 billion compared wih he baseline model: If he saving glu ends in a sudden sop raher han gradual rebalancing, U.S. hoeholds would have been beer off if he saving glu had never occurred. We also repor welfare in a version of our model in which a sudden sop occurs bu TFP does no fall. In his case, welfare falls by only $386 billion a sudden sop wihou an accompanying TFP shock rw 22