EMERGING MARKET FLUCTUATIONS: THE ROLE OF INTEREST RATES AND PRODUCTIVITY SHOCKS

EMERGING MARKET FLUCTUATIONS: THE ROLE OF INTEREST RATES AND PRODUCTIVITY SHOCKS Mark Aguiar Universiy of Rocheser Gia Gopinah Harvard Universiy Business cycles in emerging markes are characerized by high levels of volailiy in income, invesmen, and ne expors. Consumpion is more volaile han income, and ne expors are highly counercyclical (see Aguiar and Gopinah, 2007). Furhermore, he ineres raes faced by hese economies are highly volaile and negaively correlaed wih income, as described in Neumeyer and Perri (2005). In his paper, we adop a sandard sochasic business cycle model of a small open economy and allow he economy o be driven by produciviy shocks ha have permanen and ransiory componens, as well as by shocks o he ineres rae process. We hen esimae he role of he differen processes in explaining he business cycle behavior of emerging markes. In Aguiar and Gopinah (2007), we examine an economy driven exclusively by shocks o produciviy. Produciviy shocks in his conex may be viewed as manifesaions of deeper fricions in he economy, such as changes in moneary, fiscal, and rade policies. For insance, Resuccia and Schmiz (2004) provide evidence of a 50 percen drop in produciviy in he peroleum indusry in Venezuela wihin five years of is naionalizaion in 1975. Similarly, Schmiz and Teixeira (2004) documen almos a doubling of produciviy in he Brazilian iron ore indusry following is privaizaion in 1991. We view such dramaic changes in produciviy following reforms and he undoing of reforms as characerisic of emerging markes. Several emerging markes also experience erms-of-rade shocks ha display Curren Accoun and Exernal Financing, edied by Kevin Cowan, Sebasián Edwards, and Rodrigo O. Valdés, Saniago, Chile. 2008 Cenral Bank of Chile. 345

346 Mark Aguiar and Gia Gopinah a high degree of persisence. In his se-up, we provide a mehodology for idenifying he role of ransiory versus rend shocks in explaining business cycles. The procedure relies on using he inuiion behind he permanen income hypohesis. In Aguiar and Gopinah (2007), we adop he sandard small open economy assumpion and model he ineres rae as an exogenous inernaional risk-free rae, which we hold consan. The economy always repays is deb, and here is never any defaul. In Aguiar and Gopinah (2006), we explicily allow for defaul in an Eaon and Gersoviz (1981) se-up. Tha paper specifies an endowmen economy driven by rend and saionary shocks. We show ha incorporaing rend shocks is imporan in generaing empirically plausible raes of defaul, as well as simulaneously maching key correlaions beween he ineres rae, oupu, and he curren accoun. In his paper, we exend Aguiar and Gopinah (2007) o allow for a sochasic ineres rae process. We consider hree specificaions. The firs models he case of exogenous ineres rae shocks ha are independen of he produciviy shocks. In he second specificaion, he ineres rae responds o ransiory produciviy shocks in addiion o independen shocks. In he hird case, he ineres rae also responds o rend produciviy shocks. We assume a reducedform specificaion for all hese processes and provide inuiion for he naure of he process. We esimae he ineres rae process from he Euler equaions and do no use observed ineres raes. This mirrors our reamen of produciviy shocks, for which we do no use he Solow residual series o direcly idenify he underlying produciviy process. We do his for wo reasons. Firs, he observed raes are no risk-free raes given he probabiliy of defaul. The promised rae observed in he daa herefore may no be he relevan real rae governing behavior. 1 Second, agens may be consrained in heir access o financial markes. In ha case, an implici Lagrange muliplier, raher han he observed marke rae, governs he consumpion/invesmen decision. Our esimaion will pick up flucuaions in his muliplier. This approach is differen from he work of Neumeyer and Perri (2005), who ake he observed ineres rae process and feed i ino he economy. This assumes ha he Euler equaion wih repaymen is always saisfied a he observed ineres raes. We show ha he model wih ineres rae shocks ha are orhogonal o produciviy shocks does poorly in maching he 1. For explici models of defaul, see Aguiar and Gopinah (2006); Arellano (2006).

Emerging Marke Flucuaions 347 feaures of he daa for emerging marke counries. Movemens in he ineres rae affec consumpion and invesmen by seing he price for ineremporal subsiuion. An increase in he ineres rae reduces consumpion relaive o he fuure, as i increases he incenive o save. I also reduces invesmen in physical capial, since he reurn from he bond is higher. Because ineres rae shocks are orhogonal o produciviy shocks in his exercise, he induced correlaions beween consumpion and income, and invesmen and income are low, which is conrary o he daa. The response of oupu, on impac, o a rise in he ineres rae will be small, as produciviy has no changed and capial akes ime o adjus. Moreover, when consumpion and leisure are inseparable, labor supply rises in response o a drop in consumpion, which generaes an increase in oupu; his is counerfacual, given ha periods of high ineres raes have been associaed wih large declines in oupu. Ineres rae shocks ha are no associaed wih movemens in produciviy will clearly perform poorly in maching he facs for emerging markes. This poin is similar in spiri o he work of Neumeyer and Perri (2005) and Chari, Kehoe, and McGraan (2005). We nex allow he ineres rae o respond o produciviy shocks, including boh ransiory and rend shocks. The daa sugges ha a high level of produciviy should be associaed wih a lower ineres rae. A posiive shock o produciviy raises consumpion, and he increase is amplified by he conemporaneous decline in ineres raes. This increases he relaive volailiy of consumpion for a given income process. Invesmen also increases following he rise in produciviy and he decline in ineres raes. This implies ha ne expors decrease, inducing a negaive correlaion beween ne expors and income. The precise momens of he saionary disribuion will depend on he persisence in he income and ineres rae processes. For reasons explained below, he model performs beer when he ineres rae primarily responds o he ransiory income shock. Finally, we use generalized mehod of momens (GMM) and daa from Mexico o esimae he parameers of a model ha allows for boh exogenous ineres rae shocks and produciviy shocks and for he ineres rae shock o respond o he ransiory income shock. In he benchmark case, in which he model allows only for produciviy shocks, he random walk componen of he Solow residual is esimaed a 1.02. In Aguiar and Gopinah (2007), we esimae a far lower random walk componen for Canada, a 0.5. When we allow for he richer specificaion wih ineres rae shocks, we esimae he random

348 Mark Aguiar and Gia Gopinah walk componen o be essenially he same, a 1.01. This suppors he conclusions in Aguiar and Gopinah (2007) ha emerging markes are subjec o more volaile rend shocks han developed markes. We also find evidence of a small negaive covariance beween produciviy shocks and he implied ineres rae. The differences in he Solow residual processes beween developed and emerging markes may well be a manifesaion of deeper fricions in he economy. Chari, Kehoe, and McGraan (2007), for insance, show ha many fricions, including financial fricions, can be represened in reduced form as Solow residuals. From he perspecive of privae agens in our economy, hese shocks appear as exogenous shifs in produciviy. Our analysis provides suppor for models wih fricions ha are refleced in he persisence of Solow residuals, raher han fricions ha disor he response of invesmen and consumpion o underlying produciviy. Guajardo (in his volume), for insance, finds ha his model wih financial fricions fis he daa bes when procyclical exogenous labor financing wedges affec hiring decisions. Tha is, financing working capial requiremens is easier in booms han in recessions. These financing wedges behave like produciviy shocks. Our analysis shows ha ineres rae shocks ha only affec he Euler equaion add lile o maching he facs in he daa for emerging markes. One could clearly argue ha ineres rae movemens can inerac wih underlying financial fricions o generae shocks ha look like produciviy shocks. Our analysis is compleely consisen wih such a model. We also presen evidence ha Chile has feaures similar o oher emerging markes documened in Aguiar and Gopinah (2007). 2 The correlaion beween Hodrick-Presco-filered ne expors as a raio of gross domesic produc (GDP) and he HP-filered log of GDP is 0.82 for Chile. Quarerly series on privae consumpion are no available before 1996. For he en years from 1996 2006, he volailiy of he HP-filered log GDP is 1.63, compared wih a volailiy of 1.89 for he HP-filered log of privae consumpion. This is similar o oher emerging markes, in which consumpion volailiy generally exceeds he volailiy of income and ne expors are highly counercyclical. The nex secion describes he sochasic growh model. Secion 2 hen oulines he idenificaion sraegy and provides inuiion hrough impulse responses o various shocks. Secion 3 presens he resuls from a GMM esimaion of he model. 2. We hank David Rappopor for providing us wih his daa.

Emerging Marke Flucuaions 349 1. STOCHASTIC GROWTH MODEL The model here is based on Aguiar and Gopinah (2007) and augmened o include a sochasic ineres rae process. Technology is characerized by a Cobb-Douglas producion funcion ha uses capial, K, and labor, L, as inpus z 1 Y e K L, (1) where (0, 1) represens labor s share of oupu. The parameers z and represen produciviy processes. The wo produciviy processes are characerized by differen sochasic properies. Specifically, z follows an AR(1) process, z z z z 1, (2) wih z < 1, and z represens independen and idenically disribued (i.i.d.) draws from a normal disribuion wih zero mean and sandard deviaion z. The parameer represens he cumulaive produc of so-called growh shocks. In paricular, e g 1 s0 e gs and g g g, 1 g g g 1 where z < 1, and g represens i.i.d. draws from a normal disribuion wih zero mean and sandard deviaion g. The erm g represens he long-run mean growh rae of produciviy. We loosely refer o he realizaions of g as growh shocks, as hey consiue he sochasic rend of produciviy. We use separae noaion for shocks o he level of produciviy (z ) and he growh of produciviy (g ) o simplify exposiion and calibraion. Given ha a realizaion of g permanenly influences, oupu is nonsaionary wih a sochasic rend. For any variable x, we inroduce a ha o denoe is derended counerpar: ˆx x. 1

350 Mark Aguiar and Gia Gopinah We normalize by rend produciviy hrough period 1. This ensures ha if x is in he agen s informaion se as of ime 1, hen so is ˆx. The soluion o he model is invarian o he choice of normalizaion. Period uiliy is Cobb-Douglas: u C 1 L 1 1 1, (3) where 0 < < 1. If is he subjecive ineremporal discoun facor, a well-behaved seady sae of he deerminisic linearized model requires * 1 r 1 1 g. The equilibrium is characerized by maximizing he presen discouned value of uiliy subjec o he producion funcion (equaion 1) and he per-period resource consrain: K g C K Y K 1 1 1 e K B qb 2 K 2 1. (4) Capial depreciaes a he rae, and changes o he capial sock enail a quadraic adjusmen cos of (/2)[(K +1 /K ) e g ] 2 K. We assume ha inernaional financial ransacions are resriced o oneperiod, risk-free bonds. The level of deb due in period is denoed B, and q is he ime price of deb due in period + 1. We focus on flucuaions in he price of deb, q. We assume ha he ineres rae is poenially driven by an exogenous process, r, as well as he domesic oal facor produciviy (TFP) shocks. Specifically, he price of deb, q, is given by he following expression: 1 q r azzagg g * B 1 b 1r e e 1, (5) where r r r 1. (6) r

Emerging Marke Flucuaions 351 The world ineres rae is held consan a r*. The counry-specific shock o he ineres rae is given by r, which is orhogonal o z and g. The induced process, r, has an auocorrelaion coefficien of r and a long-run mean of zero. The parameers a z and a g capure he sensiiviy of he ineres rae o he ransiory produciviy shock and he rend produciviy shock, respecively. Correlaion beween he ineres rae and produciviy does no imply a direcion of causaion beween he wo, however. Aguiar and Gopinah (2006) describe a model in which exogenous domesic produciviy shocks drive an endogenous ineres rae, while Neumeyer and Perri (2005) presen a model in which exogenous (foreign) ineres rae shocks drive domesic TFP. The variable b represens he seady-sae level of deb, and > 0 governs he elasiciy of he ineres rae o changes in indebedness. This sensiiviy o he level of ousanding deb akes he form used in Schmi-Grohé and Uribe (2003). 3 When choosing he opimal amoun of deb, he represenaive agen does no inernalize he fac ha he or she faces an upward-sloping supply of loans. In normalized form, he represenaive agen s problem can be saed recursively: 1 1 Cˆ 1 L VKˆ, Bˆ, z, g, r max 1, CLK ˆ,, ˆ, Bˆ (7) g 1 e EVKˆ, Bˆ, z, g, r such ha ˆ ˆ g ˆ ˆ ˆ g C e K Y K e K ˆ ˆ ˆ Kˆ e g K B e g 1 q B. (8) 2 The evoluion of he capial sock is given by g e Kˆ K Kˆ Xˆ ˆ K e g e g 1 ˆ K ˆ. (9) 2 3. This adjusmen is ypically moivaed by he need o make asses saionary in he linearized model. An alernaive is o recognize ha we are linearly approximaing a nonlinear economy for which a saionary disribuion exiss (for example, as a resul of borrowing consrains and a world equilibrium ineres rae ha is lower han he discoun rae, as in Aiyagari, 1994). Quaniaively, since he elasiciy of he ineres rae o changes in indebedness is se close o 0 (0.001 o be exac), here is a negligible difference beween he wo approaches in erms of he HP-filered or firs-differenced momens of he model. 2 2

352 Mark Aguiar and Gia Gopinah Given an iniial capial sock, ˆK 0, and deb level, ˆB 0, he behavior of he economy is characerized by he firs-order condiions of he problem (equaion 7), he echnology and budge consrains (equaions 1 and 8, respecively), and he ransversaliy condiions. We solve he normalized model numerically by log-linearizing he firs-order condiions and resource consrains around he deerminisic seady sae. Given a soluion o he normalized equaions, we can recover he pah of he nonnormalized equilibrium by muliplying hrough by 1. We also compue he heoreical momens of he model from he coefficiens of he linearized soluion. 2. IDENTIFICATION The primary goal of his paper is o assess he relaive imporance of ineres rae shocks, ransiory produciviy shocks, and permanen shocks o produciviy in explaining he behavior of emerging markes. In Aguiar and Gopinah (2007), we describe he mehodology of exploiing decisions by informed, opimizing agens for idenifying he underlying shock process. This paper exends ha mehodology o accommodae a richer process for he ineres rae. The mehodology we employ selecs parameers of he model o mach key momens of he daa. Below, we discuss which momens are paricularly useful in idenifying he parameers of ineres. We do no use marke ineres raes on sovereign deb, however, because hose ineres raes represen he price of a defaulable bond. This is a differen asse han ha modeled above. To see his, consider he Euler equaion for bonds from he above model: q E u c 1. (10) u c While consumpion is sochasic, he ineres rae paid (condiional on informaion a he ime of borrowing) is deerminisic. In a model wih defaulable deb, he consumer pays he ineres rae condiional on no defaul and pays zero (or some fracion) if defaul occurs. Therefore, he observed marke ineres rae canno be used direcly in a simple Euler equaion, bu mus be combined wih a full specificaion of he saes in which defaul occurs and he paymens o be made condiional on defaul. Our ineres rae process, q, can be viewed as a wedge in he Euler equaions for consumpion and invesmen. Our esimaion

Emerging Marke Flucuaions 353 will hen back ou he parameers governing he sochasic process of his wedge, similar o he exercise of Chari, Kehoe, and McGraan (2007). I also capures unobserved fricions (o a linear approximaion) such as addiional borrowing coss or consrains beyond he marke ineres rae. 2.1 Ineres Rae Shocks Orhogonal o Produciviy Shocks We begin wih an exploraion of uncorrelaed ineres rae shocks ha is, shocks o he ineres rae ha are orhogonal o oal facor produciviy. Changes in he ineres rae induce changes in consumpion and invesmen for a given pah of income owing o ineremporal subsiuion. This will raise he relaive volailiy of consumpion and invesmen. Such shocks herefore have he poenial o explain he relaively high volailiy of consumpion in emerging markes. However, inroducing shocks ha move consumpion and invesmen independenly of income reduces he covariance of consumpion and invesmen wih income. This generaes counerfacual implicaions for he cyclicaliy of ne expors. Figure 1 plos he impulse responses of consumpion, invesmen, ne expors, and income o a one percen shock o r. We se r = 0.9. As expeced, an increase in he ineres rae leads o a drop in consumpion, wih an iniial decline of roughly 3 percen. Invesmen declines even more dramaically. Oupu remains seady, declining slighly over ime as a resul of he lagged declines in invesmen. This leads o a jump in ne expors. Figure 1. Impulse Response o Ineres Rae Shock a Source: Auhors compuaions. a. Impulse response of consumpion, invesmen, ne expors, and income o a one percen shock o r ; we se r = 0.9.

354 Mark Aguiar and Gia Gopinah To explore how orhogonal ineres rae shocks affec key momens of he simulaed model, we se a z = a g = 0, bu se r sandard deviaion ( r ) > 0. To be precise, we consider models wih various values of r, ranging from zero o one percen. For each environmen, we compue key momens of he simulaed economy and plo hem in figure 2. We fix all oher parameers. We also se =1, so ha labor supply is fixed. All momens refer o HP-filered variables. Panel A of figure 2 illusraes how he relaive (o income) variance of consumpion, invesmen, and ne expors increases as we increase r. This corresponds o he above inuiion. Panel B shows ha ne expors become more procyclical as r increases. This akes us furher from he daa. A he same ime, consumpion and invesmen become less correlaed wih income, because a posiive ineres rae shock lowers consumpion and invesmen. Since TFP has no changed, his reduces he correlaion wih income. When consumpion and leisure are inseparable, he decreased consumpion is associaed wih higher labor and herefore higher income, inducing a negaive correlaion beween consumpion and income. In his se-up, a crisis associaed wih a large increase in ineres raes will reduce consumpion bu raise oupu, which is compleely counerfacual. Exogenous ineres rae shocks clearly do poorly in explaining he behavior of emerging markes. Such a model is unable o generae he large counercyclicaliy in he curren accouns and he much larger responsiveness of consumpion relaive o income. This argumen is in line wih he resuls in Neumeyer and Perri (2005) and Chari, Kehoe, and McGraan (2005). A model in which he ineres rae process does no affec produciviy has lile hope of maching momens of he business cycle. 2.2 Ineres Raes ha Covary wih Produciviy Shocks The previous secion confirms ha we need o inerac he ineres rae shock wih he produciviy shock. Since we have wo produciviy processes, we can link he ineres rae and produciviy along wo dimensions. We begin by seing a g = 0 and considering he link beween ransiory produciviy shocks and he ineres rae. We hen se a z = 0 and assume he ineres rae responds only o he permanen shock, g.

Emerging Marke Flucuaions 355 Figure 2. Business Cycle Momens and r a A. Sandard deviaion of invesmen, consumpion, and ne expors B. Cyclicaliy of invesmen, consumpion, and ne expors Source: Auhors compuaions. a. Panel A shows he sandard deviaion of (HP-filered, log) consumpion, invesmen, and ne expors relaive o income as a funcion of r. Panel B shows he correlaion of (HP-filered, log) consumpion, invesmen, and ne expors wih income as a funcion of r. Figure 3 plos he impulse response funcions of consumpion and income o a shock o z when a z = 0 and when a z = 0.1. The laer case generaes a fall in he ineres rae when produciviy increases. This could be an implicaion of an Eaon-Gersoviz model of defaul, in which defaul occurs during low income realizaions (see Aguiar and Gopinah, 2006; Arellano, 2006). Wih persisen shocks, a high shock oday implies, on average, high shocks omorrow and a correspondingly low probabiliy of defaul, resuling in a negaive relaionship beween produciviy and he ineres rae.

356 Mark Aguiar and Gia Gopinah Figure 3. Impulse Response o z Shock a Source: Auhors compuaions. a. Impulse response of consumpion, invesmen, ne expors, and income o a one percen shock o z. Benchmark model ses a z = 0; az model ses a z = 0.1. For he benchmark case of a z = 0, we find he sandard consumpion-smoohing resul: consumpion increases, bu income increases much more. The case of a z < 0 combines he income response wih a subsiuion response ha favors iniial consumpion. This generaes a larger iniial jump in consumpion and a subsequen decline. Given he ransiory naure of he shock, he ne effec is ha consumpion racks he shape of he income impulse response. The response of invesmen (no depiced) has a similar inuiion as consumpion. The impulse responses indicae ha allowing he ineres rae and produciviy o comove overcomes some of he limiaions of ransiory produciviy. Namely, consumpion and invesmen respond more srongly o income and in a way ha makes ne expors negaively associaed wih income. To illusrae how his exension affecs business cycle momens, we plo he key momens as a funcion of a z in figure 4. As a z becomes increasingly negaive, he volailiy of consumpion rises relaive o income. A posiive produciviy shock lowers ineres raes, generaing an increase in consumpion above and beyond he income effec. In conras wih he orhogonal ineres rae process of figure 2, he addiional consumpion volailiy increases he correlaion of consumpion and income. This effec is driven by he fac ha he ineres rae moves one-for-one wih produciviy. A similar sory holds for invesmen. These effecs make ne expors counercyclical, a key feaure of he daa for emerging markes.

Emerging Marke Flucuaions 357 Figure 4. Business Cycle Momens and a z a A. Sandard deviaion of invesmen, consumpion, and ne expors B. Cyclicaliy of invesmen, consumpion, and ne expors Source: Auhors compuaions. a. Panel A shows he sandard deviaion of (HP-filered, log) consumpion, invesmen, and ne expors relaive o income as a funcion of a z. Panel B shows he correlaion of (HP-filered, log) consumpion, invesmen, and ne expors wih income as a funcion of a z. As noed above, an alernaive approach is o allow he ineres rae o respond o permanen produciviy shocks, ha is, o se a g < 0. Figure 5 plos he impulse response funcions o a shock o g in he benchmark case and in he case of a g = 1. Given ha g has a permanen effec on income, consumpion responds srongly o he iniial shock in he benchmark case, exceeding he iniial response of income. Allowing he ineres rae o respond as well heighens he iniial response of consumpion. The ineres rae falls back quickly o is iniial level,

358 Mark Aguiar and Gia Gopinah however, as g is nearly i.i.d. This generaes a sharp fall in consumpion and hen a leveling ou, bu income jumps and hen coninues o rise in response o a growh shock. Allowing a g < 0 hus lowers he correlaion of consumpion wih income, aking us furher from he daa. This effec is clearly demonsraed in figure 6. As we increase a g (in absolue value), he variance of consumpion and invesmen increase, while he correlaions wih income a business cycle frequencies fall. This reduces he cyclicaliy of ne expors, drawing us furher from he daa. Figure 5. Impulse Response o g Shock a Source: Auhors compuaions. a. Impulse response of consumpion, invesmen, ne expors, and income o a one percen shock o g. Benchmark model ses a g = 0; ag model ses a g = 0.1. Figure 6. Business Cycle Momens and a g a A. Sandard deviaion of invesmen, consumpion, and ne expors

Emerging Marke Flucuaions 359 Figure 6. (coninued) B. Cyclicaliy of invesmen, consumpion, and ne expors Source: Auhors compuaions. a. Panel A shows he sandard deviaion of (HP-filered, log) consumpion, invesmen, and ne expors relaive o income as a funcion of a g. Panel B shows he correlaion of (HP-filered, log) consumpion, invesmen, and ne expors wih income as a funcion of a g. The poor performance of he model wih a g < 0 is due o he fac ha growh raes are no very persisen, generaing ineres raes ha similarly flucuae. Alernaively, ineres raes could be a funcion of he level of he sochasic rend,, bu his would imply a nonsaionary ineres rae. 2.3 Produciviy Shocks Alone Aguiar and Gopinah (2007) consider a model in which a z = a g = 0. Here, we briefly summarize he inuiion behind he idenificaion of he relaive variance, g / z. In response o a ransiory shock o produciviy, agens increase consumpion by less han he increase in income, since hey expec income o fall in he fuure and herefore save o smooh fuure consumpion. On he oher hand, if he economy is hi by a growh shock ha implies permanenly higher income and (depending on he persisence of he growh shock) an upward-sloping profile of income, he agens will increase consumpion by a leas as much as he increase in income. Therefore consumpion is more volaile relaive o income under permanen shocks han under ransiory shocks. This difference in he response of (c)is shown in figure 7. By observing he behavior of consumpion, we can infer he relaive imporance of rend versus ransiory shocks. I follows ha given he response of consumpion and income, we should expec ne expors o

360 Mark Aguiar and Gia Gopinah Figure 7. Business Cycle Momens and g / z a A. Sandard deviaion of invesmen, consumpion, and ne expors B. Cyclicaliy of invesmen, consumpion, and ne expors Source: Auhors compuaions. a. Panel A shows he sandard deviaion of (HP-filered, log) consumpion, invesmen, and ne expors relaive o income as a funcion of g / z. Panel B shows he correlaion of (HP-filered, log) consumpion, invesmen, and ne expors wih income as a funcion of g / z. be far more counercyclical for he economy wih rend shocks, and he momen on ne expors can be used o idenify he underlying produciviy shock. 2.4 Idenificaion Sraegy Given he above resuls, we resric r = a g = 0. Tha is, we consider a model in which he ineres rae covaries wih ransiory produciviy shocks, and we allow for boh ransiory and rend

Emerging Marke Flucuaions 361 shocks o produciviy. The paerns depiced in figures 4 and 7 indicae how we can idenify he key parameers. Increases in he magniude of a z and g / z have a similar impac on he cyclicaliy of he curren accoun. However, while boh raise he relaive volailiy of consumpion, ne expors, and invesmen, he relaionships differ. Figure 4 indicaes ha a z has an almos linear effec on he relaive variances, while figure 7 shows ha he impac of g / z evenually dies ou. In paricular, for a large enough a z, he relaive volailiy of ne expors exceeds ha of consumpion. This reflecs he differenial sensiiviy of invesmen and consumpion o ineres rae shocks. Therefore, he empirical momens of (c) and (nx), combined wih he empirical covariance of ne expors wih oupu, pin down he relaive magniudes of a z and g / g. Given he relaive variance of rend and ransiory shocks, he level of income volailiy hen idenifies he level of z and g. 3. ESTIMATES In his secion, we follow he above idenificaion sraegy o esimae g, z, and a z by maching he following (HP-filered) momens of he daa: he sandard deviaions of income, consumpion, and ne expors; and he covariance of ne expors wih income. We use daa from Mexico as a represenaive emerging marke and Canada as a represenaive developed open economy. We fix oher parameers a he values lised in able 1. Table 1. Benchmark Parameer Values Parameer Symbol Value Time preference rae 0.98 Coefficien of relaive risk aversion 2 Cobb-Douglas uiliy parameer 1, 0.36 Raio of seady-sae deb o GDP b 0.10 Coefficien on ineres rae premium 0.001 Labor exponen (producion) 0.68 Depreciaion rae 0.05 Capial adjusmen cos 1.5 Persisence in z process z 0.95 Persisence in g process g 0.01 Source: Auhors esimaions.

362 Mark Aguiar and Gia Gopinah For each se of esimaes, we repor he relaive imporance of he random walk componen of produciviy. Beveridge and Nelson (1981) show ha any I(1) series can be decomposed ino a random walk componen (denoed ) and a saionary componen. A naural measure of he imporance of he random walk componen is he raio of he variance of he growh rae of he rend componen o he growh rae of oal TFP: 2 2 TFP 2 2 g 2 1 g 2 TFP 2 2 2 g 1 g. (11) 2 2 2 2 2z 1 z g 1 g We repor he esimaes for g, z, and a z in able 2. In he columns labeled benchmark, we resric a z = 0. This corresponds o he benchmark model of Aguiar and Gopinah (2007). The remaining columns esimae a z. The firs wo columns consider a model for Mexico in which labor is supplied exogenously. This corresponds o seing he Cobb-Douglas preference parameer on consumpion () o one, so ha leisure does no ener uiliy. The nex wo columns allow labor supply o vary endogenously, seing = 0.36. The final wo columns esimae he model using Canadian daa and assuming endogenous labor supply. For he benchmark model using Mexican daa (column 1), g is larger han z, and he relaive conribuion of he random walk componen o TFP is 1.02. This is similar o he resuls repored in Aguiar and Gopinah (2007). In he second column, we esimae a z along wih z and g. We find ha a z < 0, alhough we canno rejec a z = 0 a sandard significance levels. Even allowing for ineres rae shocks, we esimae a relaively large g, wih an esimaed conribuion of he random walk componen of 1.01. Allowing labor supply o vary endogenously does no overurn his paern. In boh specificaions, he random walk componen of produciviy is esimaed o be roughly 1.0. The coefficien a z is esimaed o be small. The case of Canada indicaes a relaively small random walk componen. In boh specificaions, he esimaed relaive random walk componen is 0.4. The esimaed coefficien a z is also small and no significanly differen from zero.

Table 2. Esimaes for z, g, and a z a Mexico Canada Exogenous labor Endogenous labor Endogenous labor Parameer Benchmark Wih a z Benchmark Wih a z Benchmark Wih a z z 0.13 0.16 0.13 0.24 0.72 0.69 (2.42) (0.79) (0.66) (1.06) (0.09) (0.16) g 2.78 2.70 2.69 2.68 0.84 0.89 (0.44) (0.33) (0.00) (0.31) (0.15) (0.09) a z 0.40 0.01 0.01 (1.85) (0.55) (0.02) Random walk componen 1.02 1.01 1.01 1.00 0.39 0.44 (0.18) (0.08) (0.05) (0.15) (0.07) (0.13) Source: Auhors esimaions. a. Esimaes were obained from maching empirical momens of Mexico and Canada for respecive columns. The momens used were he sandard deviaion of he HP-filered log of income, he log of consumpion, and ne expors/gdp, as well as he covariance of HP-filered ne expors/gdp and he log of income. Exogenous labor model ses = 1; endogenous labor model ses = 0.36. In he columns labeled benchmark, we resric a z = 0; he remaining columns esimae a z. Sandard errors are in parenheses

364 Mark Aguiar and Gia Gopinah Table 3 repors he implied business cycle momens from he esimaed models, ogeher wih he corresponding empirical momens from Mexico and Canada. In he case of Mexico, boh models perform well in maching key feaures of he daa. The empirical relaive volailiy of consumpion is 1.3, while he models wih and wihou ineres rae shocks boh generae relaive variances of 1.1. The cyclicaliy of ne expors is 0.8 in he daa and 0.7 and 0.6 in he models wihou and wih ineres rae shocks, respecively. In general, allowing for ineres rae shocks does no markedly improve he fi of he model. A similar sory holds for Canada, as repored in he final hree columns of able 3. The specificaion wih ineres rae shocks reveals ha ineres raes are counercyclical in Mexico and procyclical in Canada. The variance of he implied ineres raes is negligible, however. This reflecs he fac ha while consumpion is volaile in emerging markes, i is driven no by ineremporal subsiuion, bu raher by income shocks. 4. DISCUSSION AND CONCLUSION Emerging markes are characerized by large volailiy in heir income and consumpion and large counercyclicaliy in ne expors relaive o developed small open economies. They also face a volaile ineres rae process ha is negaively correlaed wih heir GDP level. A large lieraure aemps o explain hese feaures of he daa and infer he imporance of produciviy and ineres rae shocks in explaining he paerns observed in he daa. In his paper, we have performed a similar exercise by exending he framework in Aguiar and Gopinah (2007), which only allows for produciviy shocks, o allow for boh, a richer specificaion of ineres rae shocks and ineracion beween produciviy and ineres rae shocks. One finding, which suppors oher evidence in he lieraure, is ha ineres rae shocks ha do no effec produciviy canno be he main explanaion for business cycles in emerging markes. These markes are characerized by large movemens in oupu a business cycle frequencies, which are associaed wih large movemens in he Solow residual. Ineres rae shocks alone do lile o explain hese large movemens in oupu. I is imporan o uncover channels hrough which ineres rae shocks affec produciviy. If ineres raes are negaively correlaed wih he produciviy shock, hey can explain, a leas qualiaively, boh counercyclical ne

Table 3. Implied Momens of he Business Cycle a Mexico Canada Parameer Daa Model I Model II Daa Model I Model II (y) 2.40 2.69 2.63 1.55 1.56 1.55 (c) / (y) 1.26 1.09 1.10 0.74 0.71 0.72 (nx) / (y) 0.90 0.74 0.84 0.57 0.59 0.60 (i) / (y) 4.15 3.52 3.81 2.67 3.23 3.13 (r) n.a. 0.08 n.a. 0.01 (y,y 1 ) 0.82 0.78 0.78 0.90 0.79 0.79 (c,y) 0.92 0.98 0.98 0.87 0.87 0.85 (nx,y) 0.75 0.68 0.61 0.12 0.17 0.13 (i,y) 0.91 0.86 0.82 0.74 0.85 0.84 (r,y) n.a. 0.01 n.a. 0.90 Source: Auhors esimaions. n.a. No applicable. a. Empirical momens and implied momens are from alernaive models. Model I and model II for Mexico correspond, respecively, o he firs wo columns of esimaes of able 2 (ha is, he exogenous labor supply model). For Canada, model I and model II correspond o he respecive columns of esimaes for Canada in able 2.

366 Mark Aguiar and Gia Gopinah expors and a consumpion process ha is more volaile han income. When we esimae he model o allow for he ineracion beween ineres raes and produciviy, we find a small negaive correlaion beween produciviy and ineres raes. We also find ha, even in his framework, rend shocks play a large role, which suppors he main resul in Aguiar and Gopinah (2007) namely, ha an imporan characerisic of emerging markes is ha shocks o rend produciviy are a predominan facor in explaining movemens a business cycle frequencies, in conras o developed markes. In his paper, we have aken a reduced-form approach o modeling boh he ineres rae process and produciviy shocks. Fuure work should examine he srucural feaures of emerging markes ha give rise o he paricular form of hese processes. In Aguiar and Gopinah (2006), we explore a model wih Eaon-Gersoviz-syle endogenous defaul. While his approach does generae defaul in equilibrium and can generae a counercyclical ineres rae process, i fails o generae sufficien volailiy in he marke ineres rae process. Furher research is required o uncover he source of volailiy in he ineres rae process.

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