NBER WORKING PAPER SERIES SUDDEN STOPS, SECTORAL REALLOCATIONS, AND THE REAL EXCHANGE RATE Timohy J. Kehoe Kim J. Ruhl Working Paper 14395 hp://www.nber.org/papers/w14395 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachuses Avenue Cambridge, MA 02138 Ocober 2008 This paper has benefied from discussions wih George Alessandria, David Backus, Michael Devereux, Parick Kehoe, Enrique Mendoza, Carlos Végh, and he paricipans a he Micro Foundaions of Real Exchange Raes Conference a he Carnegie Bosch Insiue, he Workshop on Srucural Analysis of Business Cycles in he Open Economy a he Sveriges Riksbank, he XXXI Simposio del Análisis Económico, he New Perspecives on Financial Globalizaion Conference a he Inernaional Moneary Fund, and seminars a Arizona Sae Universiy, UCLA, MIT, and Washingon Universiy in S. Louis. This work was underaken wih he suppor of he Naional Science Foundaion under gran SES-0536970. All of he daa used in his paper are available a www.econ.umn.edu/~kehoe. The views expressed herein are hose of he auhors and no necessarily hose of he Federal Reserve Bank of Minneapolis, he Federal Reserve Sysem, or he Naional Bureau of Economic Research. NBER working papers are circulaed for discussion and commen purposes. They have no been peerreviewed or been subjec o he review by he NBER Board of Direcors ha accompanies official NBER publicaions. 2008 by Timohy J. Kehoe and Kim J. Ruhl. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.
Sudden Sops, Secoral Reallocaions, and he Real Exchange Rae Timohy J. Kehoe and Kim J. Ruhl NBER Working Paper No. 14395 Ocober 2008 JEL No. E13,F34,F41 ABSTRACT A sudden sop of capial flows ino a developing counry ends o be followed by a rapid swich from rade deficis o surpluses, a depreciaion of he real exchange rae, and decreases in oupu and oal facor produciviy. Subsanial reallocaion akes place from he nonraded secor o he raded secor. We consruc a mulisecor growh model, calibrae i o he Mexican economy, and use i o analyze Mexico's 1994-95 crisis. When subjeced o a sudden sop, he model accouns for he rade balance reversal and he real exchange rae depreciaion, bu i canno accoun for he decreases in GDP and TFP. Exending he model o include labor fricions and variable capial uilizaion, we sill find ha i canno quaniaively accoun for he dynamics of oupu and produciviy wihou losing he abiliy o accoun for he movemens of oher variables. Timohy J. Kehoe Universiy of Minnesoa Deparmen of Economics 1925 Fourh Sree Souh Minneapolis, MN 55455-0462 and NBER and Federal Reserve Bank of Minneapolis kehoe@umn.edu Kim J. Ruhl NYU Sern School of Business Deparmen of Economics 44 Wes Fourh Sree New York, NY 10012-1126 kruhl@sern.nyu.edu
1. Inroducion A sudden sop of capial flows ino a developing counry ends o be followed by a swich from rade deficis o surpluses, a depreciaion of he real exchange rae, and decreases in oupu and oal facor produciviy. Subsanial reallocaion akes place from he nonraded secor o he raded secor. We consruc a simple dynamic general equilibrium model and calibrae i o Mexico in 1988. We find ha he model can capure he large capial inflows ino Mexico following is financial opening in 1989 90, boh because Mexico was iniially capial poor and because is working age populaion was growing rapidly. When we subjec he model o a sudden sop he deb crisis in 1994 95 i can reproduce he movemens of he rade balance, he real exchange rae, and he relaive price of nonraded goods. When he sudden sop is he only exogenous shock, he model canno reproduce he observed decreases in oupu and TFP. We hen quaniaively assess wo frequenly menioned mechanisms ha, a leas qualiaively, could accoun for he decline in oupu and TFP, fricions in reallocaing labor and variable capial uilizaion. We find ha hese mechanisms canno accoun for he observed behavior of oupu and TFP wihou causing he model o generae wild movemens of he rade balance, he real exchange rae, and he relaive price of nonraded goods. There have been numerous heories of why sudden sops occur; see, for example, Calvo (1988, 1998), Kaminsky and Reinhar (1999), Cole and Kehoe (2000), and Mendoza (2006). The models consruced o analyze a governmen s decision o defaul on is deb or a foreign lender s willingness o lend ypically ake he effecs of he defaul on oupu as exogenous. This is done o mainain racabiliy. In conras, a second line of research has focused on he effecs of sudden sops, aking he sudden sop as given, which is our approach. Chari, Kehoe, and McGraan (2005), Cook and Devereux (2006), and Meza and Quinin (2007) exogenously impose sudden sops and sudy heir effecs on aggregae variables. The empirical lieraure regarding sudden sops has mainly focused on aggregae variables. Calvo and Talvi (2005), Guidoi, Surzenegger and Villar (2004), Chari, Kehoe and McGraan (2005), and Meza and Quinin (2007) documen he declines in GDP and TFP ha accompany sudden sops. Our findings regarding aggregae oupu and produciviy are similar o heirs. 1
This paper focuses on he effecs of a sudden sop on he disaggregaed economy. When credi is resriced, we find ha raded oupu falls by less han nonraded oupu and ha labor and invesmen move from he nonraded secor o he raded secor, as is also emphasized by Tornell and Wesermann (2002). We also find ha he movemen in he relaive price of nonraded o raded goods accouns for abou 20 percen of he movemen in real exchange raes. We documen hese characerisics for he sudden sop in Mexico in 1994 95. Our findings are in line wih Bursein, Eichenbaum, and Rebelo (2005) and Mendoza (2005), who sudy he real exchange rae depreciaions ha accompany sudden sops and also find ha nonraded goods prices play a large role in hese depreciaions. Accouning for he declines in GDP and TFP ha coincide wih sudden sops is challenging. Chari, Kehoe, and McGraan (2005) show ha equilibrium models wih sandard preferences predic no an oupu decrease, bu an increase because of a decrease in he consumpion of leisure following a reversal of he curren accoun balance. They noe ha generaing an oupu decrease requires fricions ha have negaive effecs on oupu large enough o overcome he naural response o a decrease in credi. Our analysis follows he analysis of grea depressions of Cole and Ohanian (1999) and Kehoe and Presco (2002, 2007) in insising ha he model generaes growh accouning ha maches ha in he daa. The growh accouning in he daa indicaes ha mos of he drop in oupu during he sudden sop is due o a drop in TFP. We sar by explaining ha he negaive erms of rade shock generaed by he sudden sop canno resul in drops in TFP if oupu is measured as real GDP in base period prices as in he daa. We hen exend our baseline model o incorporae wo mechanisms ha could generae his drop in TFP. The firs is coss o adjusing he amoun of labor used in producion in each secor. These coss are modeled as drops in oupu, so he reallocaion of labor beween he wo secors generaes a decrease in TFP. In our calibraed model, however, hese coss canno accoun for he observed decrease in TFP; increasing hese coss beyond a cerain poin jus resuls in less reallocaion. The second is variable capial uilizaion, as in Greenwood, Hercowiz, and Huffman (1988) and Meza and Quinin (2007). To he exen ha he aggregae capial sock does no change bu he amoun of oupu falls, he drop in uilizaion during he sudden sop appears as a 2
decrease in TFP. In our model, however, while capial in he nonraded secor is underuilized during he sudden sop, capial in he raded secor is overuilized. Consequenly, we find ha variable capial uilizaion alone canno accoun for he observed decrease in TFP. Combining he labor adjusmen coss and variable capial uilizaion and pushing hese fricions owards heir limis, we find ha he model is able o generae he observed decrease in TFP. Doing so, however, produces wild movemens of he rade balance, he real exchange rae, and he relaive price of nonraded goods. Oher researchers have suggesed ha financial consrains are imporan for undersanding sudden sops: see, for example, Calvo (1998), Mendoza and Smih (2004), Neumeyer and Perri (2005), and Schneider and Tornell (2004). We absrac from he financial secor in our model o quaniaively assess how far a sandard model can go in explaining he effecs of sudden sops. As discussed above, our simple model can go a long way in accouning for he effecs of a sudden sop, alhough he effecs of a sudden sop may work hrough he financial secor in generaing declining TFP. I is worh noing ha he papers in exising lieraure on financial consrains and sudden sops generae decreases in oupu largely hrough a decrease in labor, however, raher han hrough he observed decrease in TFP. As a final exension, we consider a specificaion of our model in which he economy is subjec o an aggregae negaive TFP shock. We find ha he exended model can also accoun for a large share of he decline in oupu wihou disoring our abiliy o accoun for prices and rade flows. Alhough we do no view modeling he decrease in TFP as an exogenous shock as an appealing explanaion for he observed decrease in oupu, we consider i an imporan robusness check. 2. The 1994 95 Mexican deb crisis In his secion, we presen he properies of Mexico s opening o foreign capial in 1989 90 and is sudden sop in 1994 95. The successes and failures of our model depend on is abiliy o accoun for hese properies. The properies ha we idenify are ypical of sudden sop episodes in a large sample of counries; see Tornell and Wesermann (2002). Figure 1 plos Mexico s rade balance as a share of GDP. (All of he daa used in his paper are available a www.econ.umn.edu/~kehoe.) As Mexico opened is capial 3
markes, he counry wen from being a ne lender o a ne borrower. In 1994, he rade defici was 4.83 percen of GDP. In he final weeks of 1994, he sudden sop began as he governmen had rouble rolling over is deb. (See, for example, Kehoe 1995b.) The rade defici became rade surpluses of 2.66 and 2.06 percen of GDP in 1995 and 1996. When he sudden sop ended in 1997, he rade balance reurned o a defici, reaching 2.14 percen of GDP in 1998. The rade balance reversal is a robus feaure of sudden sops; see Guidoi, Surzenegger, and Villar (2004). To address he naural quesion of wheher here were foreseeable condiions in Mexico ha led o he sudden sop, consider he ineres rae on Mexican dollar denominaed deb. (Our measure of his ineres rae is he J.P. Morgan Emerging Marke Bond Index spread on Mexican Brady Bonds, compued afer sripping ou he collaeralized principal.) We decompose his ineres rae ino wo pars: The firs is he U.S. Treasury bill rae, which is our proxy for he risk free rae. The second is he Mexico-specific ineres rae spread, which is commonly used o measure he counry specific ineres rae premium. We find ha he ineres premia on Mexican deb did no increase before he crisis. In November 1994, he ineres premium on Mexican deb was 4.56 percen, less han he average premium from 1991 hrough November 1994. No unil December, he firs monh of he crisis, did he premium increase o 8.90 percen and hen peak a 16.37 in March 1995. We ake his behavior of ineres premia as evidence ha he sudden sop was sudden and largely unforeseen. The sudden sop was accompanied by a large depreciaion of he real exchange rae. We define he real exchange rae for Mexico, vis-à-vis he Unied Saes, as (1) RER = NER mex, us, mex, us, P P us, mex, NER is he peso-dollar exchange rae and P j, is he price level in counry j, where mex, us, as measured using gross oupu deflaors. We plo he naural logarihm of he real exchange rae for Mexico in figure 2. Afer he opening o foreign capial, he real exchange rae appreciaed; a he onse of he sudden sop, he real exchange rae depreciaed by 31.49 percen from 1994 o 1995 and appreciaed again as he sudden sop ended, approaching is 1994 level in 2000. 4
To decompose he movemens of he real exchange rae ino secoral componens, we follow Sockman and Tesar (1995) and Bes and Kehoe (2001) in defining agriculure, mining, and manufacuring as he raded goods secor and consrucion and services as he nonraded goods secor. We rewrie (1) as (2) RER NER P P P RER RER T T us, mex, mex, T N mexus,, = mexus,, = mexus,, T T mexus,, P mex, Pus, P us,, T where he price of raded goods, P, is he gross oupu deflaor for agriculure, mining, and manufacuring. The firs erm in he decomposiion measures he raded good real exchange rae. The second erm in he decomposiion is he price of nonraded goods in N he Unied Saes relaive o ha in Mexico. We plo he log of RER in figure 2. When Mexico opened o foreign capial, he price of nonraded goods increased by 15.84 percen from 1988 o 1994. This accouns for 42.24 percen of he appreciaion of he real exchange rae. During he sudden sop, he price of nonraded goods decreased by 6.19 percen, accouning for 19.66 percen of he real exchange rae depreciaion. We plo real GDP per working age (age 16 54) person and oal facor produciviy in figure 3. The figure shows he sharp conracion of oupu during he firs year of he sudden sop. Real GDP per working age person fell by 9.05 percen in 1995. To measure TFP we use he aggregae producion funcion, (3) Y = AK L, α 1 where Y is real GDP, A is oal facor produciviy, 5 K is capial, and L is hours worked in period. We choose a capial share of α = 0.38, in line wih he esimaes of García-Verdú (2005). We compue TFP as Y (4) A = 1 K α L. α The capial sock is consruced from invesmen daa using he perpeual invenory mehod, and labor is measured as oal hours worked. TFP fell by 7.89 percen in 1995, almos maching he decline in oupu. We have seen ha he sudden sop was accompanied by a decline in oupu. The secoral daa allow us o say more. In figure 4, we plo real value added for he raded
and nonraded secors in Mexico. During he crisis, value added in he nonraded secor fell more han in he raded secor and hen recovered a a much slower rae. This shif in producion is he focus of our analysis and a key ingredien in our model below. In response o a sudden sop, he relaive price of raded o nonraded goods increased, leading o a shif of resources away from he nonraded secor and ino he raded secor. In he nex secion, we consruc a general equilibrium model o help us accoun for he feaures of he daa we have highlighed here. 3. Baseline model We model Mexico as a semi-small open economy wih perfec foresigh over he pahs of ineres raes, TFP, populaion, and ariffs. Mexico is a small open economy in he sense ha i akes world ineres raes as exogenous, bu Mexico is no small in he goods marke. The price of Mexico s expored good changes in order o clear he marke. In 1988 and 1989, he economy is closed o foreign capial. The economy opens o foreign capial in 1990; five years laer, here is a sudden sop when foreign invesors unexpecedly sop lending o he counry in 1995 and 1996. From 1989 o 1993, Mexico liberalized is financial markes, inernally and exernally; see, for example, Kehoe (1995a). We choose 1990 as he dae o model he financial opening because, as figure 1 shows, i was he firs year in which Mexico had a large rade defici. Our model combines elemens of he mulisecor, saic applied general equilibrium models used o sudy NAFTA (see, for example, Kehoe and Kehoe 1994), he models of Fernández de Córdoba and Kehoe (2000) and Bems and Jönsson Harelius (2006) used o sudy financial liberalizaion in small open economies, and he models in he collecion of Kehoe and Presco (2007) used o sudy grea depressions. 3.1 Producion There are 5 ypes of goods in he model: a domesically produced raded good, y D, an impored good, m, a composie raded good, y T made up of he domesic raded good and impors, a nonraded good, y N, and an invesmen good, i. All goods markes are perfecly compeiive. 6
The domesic raded good is produced using capial, k D, labor, D composie raded good, z TD, and he nonraded good, z ND, according o α D y =min D ztd / atd, znd / and, AD kd g D. α (5) ( ) 1 D, he The producer chooses capial, labor, and inermediae inpus o minimize coss, which implies marginal produc pricing condiions for capial and labor of he form 1 α D D TD T ND N D D D D α (6) ( ) ( ) 1 D r p a p a p α A k g and similarly for he wage =, ha he producer earns zero profis in equilibrium: w. Perfec compeiion and consan reurns o scale imply (7) p y rk w p z p z = 0. D D D D T TD N TN The producion funcion for he nonraded good and he corresponding profi maximizaion condiions are defined analogously. We assume ha produciviy in each secor grows a he same, consan rae g 1. The composie raded good is made up of impors and he domesic raded good using an Armingon aggregaor: ( ) 1 ζ ζ ζ (8) μ ( 1 μ) y = M x + m. T D The impored good is he numeraire in his model, making is f.o.b. price equal o 1, bu impors are subjec o domesically levied ariffs, τ. The invesmen good is produced using a Cobb-Douglas producion funcion: (9) y = Gz z. γ 1 γ I TI NI Mexico is a semi-small open economy in he sense ha i faces a downward sloping demand curve for is expors. Foreign demand for he domesic raded good is ( ) 1 1 (10) ( 1 τ ) x = D + p ζ, F F T 7
where τ F is he ariff imposed by he res of he world on is impors. This expor demand funcion implies ha he res of he world has an Armingon aggregaor ha is analogous o he one in Mexico (8). The facor D grows over ime, reflecing he increasing demand for he goods produced in Mexico. This growh is driven by populaion growh in he res of he world as well as by echnological progress. 3.2 Households The economy is populaed by a coninuum of idenical households. We differeniae he oal populaion from he working age populaion. We denoe he working age populaion and mach i o he evoluion of he populaion aged 15 64 in Mexico. Leing n denoe oal populaion, we calculae he adul equivalen populaion as (11) n = + ( n ) 1 2 o evaluae consumpion per capia. We normalize he amoun of ime available for work by a working age person o be 1 and denoe he oal labor supply in period as. Households choose his labor supply,, consumpion of raded goods and nonraded goods, c T and c N, invesmen in capial i, and bond holdings, b, o maximize uiliy, (12) ( ) = 1988 subjec o he budge consrain, ηψ ρ ρ ρ ( 1 η) ψ c T c N β ε + 1 ε 1 / ψ n n (13) ( ) he law of moion for capial, p c p c qi b w r b r k T, T T + N N + + + 1 = + 1+ + K + (14) ( δ ) k = 1 k 1 + + i, he appropriae nonnegaiviy consrains, iniial condiions for he capial sock, k 1988, and bond holdings, b 1988, and a condiion on bond holdings, 8
(15) b, ng B where B is chosen large enough so ha his consrain rules ou Ponzi schemes bu does no oherwise bind in equilibrium. If he economy is open o foreign capial, so ha consumers can buy and sell foreign bonds, he firs order condiions for b and k imply he arbirage condiion (16) ( δ ) ( ) 1 1+ r = 1 q + r / q. K When he economy is closed o foreign capial, he ineres rae r is endogenously deermined by he reurn o domesic capial and paymens on deb, b, are made a an exogenous rae r. When he economy is open o foreign capial r = r* + σ, where he world ineres rae is consan a r * and he ineres rae premium is σ. Bonds are denominaed in unis of he impored good, which implies ha a real depreciaion makes deb more expensive in erms of domesically produced goods. Households receive a lump sum ransfer, T, of ariff revenues colleced on impors. In our calibraion, we also impose a ax on ne capial income in 1989 o accoun for he low level of invesmen in 1988 relaive o fuure periods, replacing r K1989 in he budge consrain (13) by ( τ ). The revenue from his ax is also rebaed in he lump sum ransfer T 1989. 1 r K1989 K1989 3.3 Marke clearing and equilibrium The marke clearing condiions are (17) x = y (18) cn + zni + znd + znn = yn (19) ct + zti + ztd + ztn + xf = yt (20) i = yi (21) kd + kn = k (22) D + N =. D D 9
The balance of paymens condiion is (23) ( ) Here ( ) m + b = p x + + r b. + 1 T F 1 pdxf m = b+ 1 1+ r b is he balance of rade and b 1 b = ptx F m + + rb is he balance of paymens. In he model wihou a sudden sop, an equilibrium consiss of sequences of all relevan variables such ha households maximize uiliy subjec o he budge consrains and oher consrains, he prices and quaniies saisfy he profi maximizaion condiions for producers, he res of he world demands Mexican expors according o is demand funcion, he marke clearing condiions and balance of paymens condiions hold, and ariff and ax revenues equal he lump sum rebae in each year. The economy is closed o foreign capial flows in 1988 and 1989, and we assume ha ne foreign bond holdings say consan a b1990 = b1989 = b1988 and ha paymens on he deb b are made a he rae r1990 = r1989 = r1988. In he model wih a sudden sop in 1995, he equilibrium is ha of he model wihou he sudden sop up unil 1995. The equilibrium in 1995 and hereafer is ha of a model saring in 1995, wih iniial capial and foreign bond holdings given by he model wihou a sudden sop, bu in which he economy is closed o foreign capial flows in 1995 and 1996, and in which ne foreign bond holdings say consan a b1997 = b1996 = b1995 and ha paymens on he deb b are made a he rae r1997 = r1996 = r1995. In oher words, we model he equilibrium as one of perfec foresigh, excep ha he sudden sop is compleely unexpeced. The period in he model is one year. To compue he equilibrium of he model, we runcae he model afer 100 years, requiring he equilibrium o converge o a balanced growh pah in 2088. See Conesa, Kehoe, and Ruhl (2007) for informaion abou how o do his sor of compuaion, including an algorihm. 4. Calibraion As in he mulisecor, saic applied general equilibrium models analyzed by Kehoe and Kehoe (1994), mos of he model s parameers are calibraed so ha he equilibrium of he model in 1988 replicaes he daa in an inpu-oupu marix. Table 1 presens such a 10
marix for Mexico in 1988. We ake he Unied Saes o sand in for he res of he world; in 1994, he Unied Saes accouned for 68.97 percen of oal merchandise impors o Mexico and 84.22 percen of oal merchandise expors from Mexico. The dynamic naure of he model makes several oher feaures of he calibraion of crucial imporance. The iniial capial sock k 1988 and he iniial ax on capial incomeτ K1989 are calibraed so ha Mexico is capial poor. (We could impose a ax τ K1988, bu i is irrelevan since k 1988 is fixed and ax revenues are rebaed o consumers.) In 1990, Mexico no only opens iself o foreign capial flows, bu also underakes reforms o domesic financial markes ha we model as an eliminaion of τ K1989. Also of crucial imporance o he dynamics of he model are he calibraion of he pahs for working age populaion and adul equivalen populaion, and n, and he growh in hese variables compared o growh in he Unied Saes, capured by D. When Mexico opens o capial flows, i borrows, no only because i is capial poor, bu also because i has a rapidly growing working age populaion. The rapidly growing populaion causes his borrowing o persis over ime. The ineres premia σ play an imporan role in deermining he pah of borrowing, in paricular, slowing i iniially. Of less imporance are he pahs for Mexican ariffs τ and U.S. ariffs τ F. We summarize he baseline model s calibraion in able 2. 4.1 Producion parameers The parameers in he producion funcions for he domesic raded and nonraded goods are compued from he inpu-oupu marix in able 1. We choose quaniies for he model so ha all prices and he wage rae are equal o 1 in 1988. Quaniy unis have been normalized so ha GDP is 100. Since prices have been normalized o 1, his means ha every quaniy is expressed as a percen of 1988 GDP. Using he profi maximizaion condiions for producers, we calibrae he parameers of he producion funcions so ha he quaniies in he inpu-oupu marix are equilibrium values in 1988. Consider, for example, he producion funcion for he invesmen good (9). The firs order condiions for profi maximizaion imply ha 11
γ z = (1 γ ) z T1988 NI1988 (24) p p N1988 TI1988. Seing p 1988 = p 1988 = 1 and plugging in he values z 1988 = 10.158 and z 1988 = 12.403, T N we obain γ = 0.450, which is in line wih he esimaes of Bems (2008). We calculae TI NI y 22.561 G = = = 1.990. z z I (25) γ 1 γ 0.450 0.550 TI NI 10.158 12.403 To calibrae he Armingon aggregaor, we mus choose he elasiciy of subsiuion beween impors and domesic raded goods, 1 ( 1 ζ ). As discussed in Ruhl (2008), here is debae over his elasiciy since business cycle models end o imply low elasiciies while analysis of rade policy episodes suggess elasiciies much higher. We choose ( ζ ) 1 1 = 2. The firs order condiions for profi maximizaion imply ha (26) μ p D1988 m 1988 = 1 μ 1+ τ1988 xd 1988 ζ 1. Wih prices normalized o 1 in he base year, μ can be calculaed using he daa on impors and domesic raded goods. The parameer M is chosen so ha he oupu of he composie raded good in equaion (8) is ha observed in he daa. We choose he growh rae g 1 o be 2 percen, which is he growh rae of U.S. GDP per working age person during he wenieh cenury, and which Kehoe and Presco (2007) argue is he growh rae implied by echnological progress. Our resuls indicae ha his value may be a lile oo high for Mexico, a leas during 1988 2000. We se r 1988 = 0.1574. This value comes from seing r * = 0.0400 and from our daa on ineres premia and is similar o ha obained by he calculaion of how much of he income difference beween Mexico and he Unied Saes can be accouned for by differences in capial socks by Kehoe (1995b). Given ha depreciaion was 10.566 percen of GDP in 1988 while gross capial earnings were 37.295, we can calculae (27) 1988 k 37.295 10.566 = = 169.817 0.1574 12
(28) 10.566 δ = = 0.062. 169.817 4.2 Household parameers We se he ineremporal elasiciy of subsiuion ( ψ ) 1 1 = 0.5. Following McGraan and Presco (2003), we se he world ineres rae in he balanced growh pah r * = 0.040. Requiring his ineres rae o be consisen wih balanced growh implies 1 ψ ha β g ( r ) = 1 + * = 0.987. Following Kravis, Heson, and Summers (1982) and Sockman and Tesar (1995), we se he elasiciy of subsiuion beween raded and nonraded goods in consumpion as 1/ (1 ρ) = 0.5. The firs order condiions from he household s problem yields he condiion (29) ε p T1988 c T1988 = 1 ε pn1988 cn1988 1 ρ, which can be used o calibrae ε. Given he value of / = 0.267 from he daa se of Bergoeing, Kehoe, Kehoe, and Soo (2002), we can similarly calibrae η. In 1989, Mexico ran a rade surplus of 1.390 percen of GDP. We se he iniial sock of bonds held by he consumer, b 0, so ha he model replicaes his saisic. To accoun for he level of invesmen in 1989 in he inpu-oupu marix, we se τ K1989 = 0.201 in he baseline numerical experimen. Since he reurn o capial in 1989 varies in our oher numerical experimens, we need o recalibrae τ K1989 in each one. 4.3 Exogenous processes To accoun for any changes ha migh be due o he Norh American Free Trade Agreemen, we include falling ariffs in he model. We model Mexican ariffs on U.S. goods as being 10.00 percen unil 1994, a which ime hey fall o 5.00 percen. From 1994 o 2004 he ariff raes fall by 0.50 percenage poins a year, unil hey are 0. U.S. ariffs on Mexican goods are 3.00 percen unil 1994, a which ime hey fall o 1.50 percen. From here, ariffs fall by 0.15 percenage poins per year unil hey reach 0 in 13
2004. Boh ariffs remain a 0 forever afer 2004. (See Kehoe 1995a for informaion on he Mexican rade reform.) As can be seen in figure 5, he ineres premium on Mexican deb fell from 11.74 percen in December of 1990 o 4.56 percen in November of 1994. These higher ineres raes are usually regarded as counry specific risk premia, and he gradual eliminaion of hese premia reflec he idea ha Mexico gradually gained credibiliy as i insiued srucural changes. Since we do no model he srucural changes aking place in he Mexican economy, we ake as exogenous a ime varying ineres premium on he rae a which Mexico can borrow from he res of he world. This approach is also used in Bems and Jönsson Harelius (2006) and Cook and Devereux (2006). We use he J.P. Morgan Emerging Marke Bond Index spread on Brady Bonds as our measure of he Mexican ineres premia, as discussed previously in secion 2. The premia spike in 1995, reflecing he increase in he perceived counry risk following he sudden sop. Since he pos-1994 premia would no have evolved in he same way if he counry had no experienced he crisis, we assume ha agens believed he pah of ineres premia o be ha same as in he daa up o 1994, and ha he premia gradually decline o zero by 2005. These anicipaed premia are graphed in figure 5. Once he sudden sop has occurred, agens perfecly foresee he pah of ineres raes ha are he same as in he daa unil 1998, a which poin hey gradually decline o zero by 2015. Our daa sar in 1991, and we assume ha he premia for 1988 90 are he same as in 1991. Populaion growh raes for he Unied Saes and Mexico are exogenous o he model. These populaion growh raes are consruced from he observed daa for 1988 2005 and from populaion projecions made by he Unied Naions for 2005 50. (See he daa appendix available a www.econ.umn.edu/ ~kehoe.) We deermine he series for D using he calibraed value for D 1988, he growh facor g = 1.020, and he growh of working age populaion in he Unied Saes. I is worh noing ha he consan ineres rae r * = 0.040 is no consisen wih varying populaion growh, bu we do no inend o carefully model he dynamics of U.S. ineres raes. In he formula for he real exchange rae in (1) and ha for he relaive price of T nonraded goods in (2), we need a series for he relaive price P, P,. We ake his us us 14
series from he daa. Given our modeling of Mexico as a semi-small open economy, his series plays no role in our model, only in he comparison of he resuls wih he daa. 5. Resuls Before subjecing he model o a sudden sop, i is useful o sudy briefly he model wihou a sudden sop. When Mexico opens o capial flows, is capial-oupu raio is lower han i will be in he balanced growh pah. Figure 6 plos he capial-oupu raio for he model wihou a sudden sop. Mexico accumulaes capial unil i reaches he balanced growh pah. To smooh consumpion over he ransiion, he counry borrows from abroad iniially, running rade deficis. The deficis swich o surpluses as he counry pays back he deb. 5.1 Baseline model When he sudden sop occurs, he raded good, whose use was being financed by a rade defici, becomes relaively scarce and is price increases. Since he sudden sop is unexpeced, capial and labor are no efficienly allocaed across he wo secors, so hey are reallocaed from he nonraded o he raded good secor. The resuls of he baseline numerical experimen are summarized in figure 7 and able 3. Figure 7(a) plos he rade balance in he model and he daa. As in he graphs ha follow, he daa are ploed as a solid line and he model resuls are ploed as a dashed line. The model does a good job of reproducing he shape of he rade balance. The rade balance goes negaive when he counry opens o capial flows and sharply reverses when he sudden sop occurs. As he sudden sop ends, he rade balance reurns o a defici, hough i akes longer in he model, no urning negaive unil 2002. In he model, Mexico does no reurn o borrowing immediaely following he sudden sop because he ineres premia, shown in figure 5, remain high unil 1999. Figure 7(b) plos he real exchange rae. The real exchange rae in he model does no appreciae as quickly as in he daa, bu i displays he same sharp depreciaion as he daa during he sudden sop. In he model, he real exchange rae depreciaes by 41.36 percen compared o he 31.49 percen in he daa. As he sudden sop ends, he real exchange rae appreciaes, as in he daa, alhough less so. During he sudden sop, he 15
price of nonraded goods in Mexico decreases. This can be seen in figure 7(b), which displays he relaive price of nonraded goods, log RER N. From 1994 o 1995 he price of nonraded goods in he model falls by 6.10 percen, compared o 6.19 percen in he daa. T N Mendoza (2000) and ohers show ha changes in RER and hose in RER are negaively correlaed in periods of managed exchange raes and posiively correlaed oherwise. The period 1988 2000 sraddles a regime change; Mexico allowed he peso o floa saring in 1995. In he daa, he correlaion beween firs differences in T RER and N hose in RER is 0.30 for 1988 94 and 0.79 for 1995 2000. Our real model canno address issues of nominal exchange rae managemen. Neverheless, i capures 36 percen of he difference beween he wo correlaions. The relevan correlaion is 0.54 for 1988 94 and 0.93 for 1995 2000, suggesing ha he relevan differences beween he wo subperiods involve more han jus differences in exchange rae managemen. Our model depars from he small open economy framework by assuming ha he erms of rade, which are ploed in figure 7(d), are no exogenous. The erms of rade in he model depreciae much more han hose in he daa; he boom in expors ha accompanies he sudden sop drives he raded good price oo low relaive o he daa. Some of his is a resul of model specificaion. In he model, all domesically produced raded goods are expored, in conras o a model where he good ha is expored differs from he baske of all raded goods. Daa ha are more closely relaed o our model s erms of rade are he raded good real exchange rae, T RER. Figure 7(d) shows ha he T depreciaion in RER is larger han ha in he erms of rade and is almos idenical o ha in model. In secion 5.5, we sudy a model wih exogenous erms of rade. Much of he model s failure o capure he speed a which he rade balance reurned o a defici and he real exchange rae appreciaed is due o he high ineres premia in 1998 and 1999, due o he Asian crisis and he Russian crisis. A model in which he jump in hese premia is sudden and unforeseen could do beer in capuring he rade deficis and he real exchange rae depreciaion. So could a model in which a period is a quarer raher han a year noice ha, in figure 5, he ineres premia are no high during all of 1998 or 1999. 16
Figure 7(c) shows ha he model reproduces he shif of producion from he nonraded o he raded secor, bu i fails o capure he falling oupu in he raded secor. Oupu in he nonraded secor does fall, bu no by as much as i does in he daa. Figure 7(f) compares GDP per working age person and TFP in he model and in he daa. The model does a poor job of generaing he decline in oupu and TFP ha we see in he daa. We discuss his feaure of he model in deail in secion 6. The qualiaive feaures of our resuls come from having wo goods, one of which is nonraded, and an iniial capial sock ha is below is balanced growh levels. The quaniaive feaures of our resuls are deermined by many facors, bu he mos imporan wo are he specificaions of he ineres rae premia and of he populaion growh raes. In exensive sensiiviy analysis no repored here, we have found ha i is hese sors of facors hose relaed o he model s dynamics ha are mos imporan o our resuls. The specificaions of he saic feaures are far less imporan. When we model he combinaion of inermediae goods and value added in he producion funcions for goods in (5) as being Cobb-Douglas raher han fixed proporions, for example, we find ha he resuls change by negligible amouns. 5.2 Model wihou ineres rae premia To see how he ineres premia deermine our resuls, we consider a model wihou hem. We recalibrae parameers o mach he same arges as in he baseline model. Table 3 summarizes he model s resuls. The resuls for he model wihou ineres premia are qualiaively similar o hose of he baseline model, bu are far more volaile, as can be seen in figure 8(a). Wihou he gradually falling premia, Mexico immediaely runs large rade deficis, quickly accumulaing deb. When he sudden sop occurs, he curren accoun reversal is much larger han in he baseline model. When he sudden sop ends, he counry immediaely reurns o borrowing. Immediaely being able o borrow a he world ineres rae leads o a larger movemen ou of he raded good secor in he early 1990s. This increases he price of he domesic raded good and drives he sharp real exchange rae appreciaion in figure 8(b). During he sudden sop, he real exchange rae depreciaes even more so han in he baseline model as he larger deb ha has been accumulaed requires larger ineres 17
paymens, which brings abou a larger boom in expors. As is clear from able 3, he ineres premia have lile effec on he aggregae quaniies. 5.3 Model wihou populaion growh Mexico is experiencing a demographic ransiion; he populaion of age 15 64 is growing faser han he oal populaion. The growing working age populaion increases he demand for capial, creaing a greaer incenive o borrow abroad. In his secion, we consider he baseline model, bu wihou populaion growh. The resuls are summarized in able 3. Figure 9(a) plos he rade balance. I is clear from he figure ha populaion growh is a key driver of he model. Wihou populaion growh, Mexican households quickly accumulae enough capial o make borrowing unnecessary, which can be seen by comparing figure 9(b) o 7(f). In fac, afer he sudden sop, agens would like o lend o he res of he world in order o ake advanage of he high ineres rae premia in 1998. 5.4 Model wihou rade liberalizaion During he period we sudy, Mexico was liberalizing is rade, boh unilaerally and hrough he Norh American Free Trade Agreemen. To capure his in he baseline model, we have ariffs falling over ime, as described in secion 4. We es he sensiiviy of he model o his assumpion by solving he model wih ariffs se o zero in every period. The recalibraion o 1988 requires us o modify he inpu-oupu marix o eliminae he iniial ariff. The resuls of his model are summarized in able 3. Besides speeding up impor growh in he early 1990s and slighly increasing he overall volailiy of our resuls, removing rade liberalizaion has lile effec. 5.5 Exogenous erms of rade In he baseline model, Mexico faces an expor demand funcion (10). This specificaion, alhough sandard in saic applied general equilibrium rade models, is a deparure from he common assumpion ha he expor price is an exogenous variable in open economy macro models. The erms of rade in he baseline model depar significanly during he sudden sop, as was seen in figure 7(d). In his version of he model, we allow he erms of rade o be endogenous in all periods excep for 1995. We adjus D, he scale 18
parameer in he expor demand funcion, (10), in 1995 and hereafer by he facor of 1.638, so ha he increase in he erms of rade in he model is exacly he same as i is in he daa. This is an increase in U.S. demand for Mexican expors resuling from NAFTA, bu no capured by our Armingon specificaion (10). We can hink of Ruhl (2008) as providing a jusificaion, bu we should noe ha we assume ha he increase is no foreseen. The resuls are summarized in able 3 and figure 10. In able 3, he resuls from he model wih exogenous erms of rade differ from he baseline resuls in wo significan ways: during he sudden sop, he real exchange rae does no depreciae enough, and impors increase. The smaller depreciaion of he real exchange rae is, again, he produc of he model specificaion; he erms of rade are T RER, so dampening he erms of rade dampens T RER, which dampens he response of he real exchange rae. Given he specificaion ha he expored good is he same as he raded good, he model accouns eiher for he erms of rade or he real exchange rae, bu no boh. To do boh, we would need o model expors as having a differen price han he baske of all raded goods. 6. Oupu and produciviy The baseline model can accoun for he rade balance, real exchange raes, and relaive prices. Ye, as seen in figure 7(f), i canno reproduce he oupu dynamics in Mexico. We decompose he growh of GDP using an accouning framework based on he neoclassical growh model. Following Hayashi and Presco (2002) and Kehoe and Presco (2002), we wrie he producion funcion in (3) in erms of oupu per working age person and measures of facor inpus ha are consan along a balanced growh pah, (30) α 1 1 α 1 α = A, Y K L N Y N where N is he working age populaion. We ake he logarihm of (30) and use i o decompose changes in oupu per working age person ino changes in labor, capial accumulaion, and TFP. The growh accouning is presened in able 3. In 1988 94 oupu per working age person grew a a rae of 1.06 percen per year, more han half of which came from an 19
increase in hours worked. During he sudden sop, oupu per working age person fell by 8.89 percen, he TFP facor, 1 1 A α K Y α α, fell by 12.69 percen, he capial facor, ( ) 1, increased by 6.18 percen, and hours worked per working age person fell by 2.38 percen. Since he end of he crisis, oupu per working age person grew a 3.16 percen per year, mosly accouned for by growh in TFP and hours worked. Our resuls are similar o hose in Meza and Quinin (2007) who also use a growh accouning framework o sudy sudden sops in Mexico and counries affeced by he Asian crisis in he lae 1990s. Growh accouning makes i clear ha any heory ha hopes o explain he drop in oupu following a sudden sop mus also deliver a sharp decline in aggregae TFP. Our growh accouning provides discipline as in he papers in Kehoe and Presco (2007) o our search for a model of oupu dynamics. In wha follows, we consider candidae explanaions for he oupu drops ha have been suggesed in he lieraure: he increased price of inermediae inpus, fricions in he labor marke, variable capial uilizaion, and quasilinear uiliy funcions. In analyzing he resuls from our model, we do growh accouning using equaion (30), reaing he daa generaed by our model jus as he Mexican saisical agency, he Insiuo Nacional de Esadísica, Geografía, e Informáica, and we rea he daa from Mexico. We calculae real oupu, Y in equaion (30), as GDP in 1993 base year prices: (31) α 1 D 1 ( 1993 1993 1993 ) ( ) α N 1 ( ) ( ) Y = p a p a p A k g D TD T ND N D D D 1 α N + p a p a p A k g + τ m N1993 TN T1993 NN N1993 N N N 1993 α D. Similarly, we calculae he invesmen ha goes ino calculaing he capial sock in equaion (30) by dividing invesmen expendiures in curren prices pt zti + pn zni by he GDP deflaor formed by dividing GDP in curren prices by consan prices in equaion (31). Noice ha he resuling measure of he capial sock differs from ha in he model in equaions (9) and (14). This is rue especially in he model wih variable capial uilizaion and allows he model o accoun for some of he changes in measured TFP. 20
6.1 Impored inermediae goods A he onse of he sudden sop, he erms of rade urned agains Mexico. Consequenly, he expors ha Mexico was producing now bough fewer impored inermediae goods. Thus, negaive erms of rade shocks have an effec similar o a negaive TFP shock. Was he deerioraion in he erms of rade imporan for undersanding Mexico s oupu and TFP? Quaniaively, he answer is no. The erms of rade in he baseline model depreciae even more so han in he daa ye here is no noiceable drop in eiher oupu or TFP. No only do erms of rade changes no quaniaively affec oupu in he model, bu, when oupu is measured as real GDP in (31), he erms of rade shocks canno qualiaively effec oupu eiher. This is because he erms of rade ener GDP calculaions as a price. As discussed in Kehoe and Ruhl (2008), he naional accouning procedures imply ha erms of rade shocks can rarely affec real GDP. 6.2 Labor fricions In his secion, we inroduce a cos o firms ha adjus heir labor inpus. During he sudden sop he economy wans o move workers from he nonraded secor o he raded secor. In doing so, some oupu is los. Qualiaively, his creaes a drop in GDP and a drop in TFP. In his secion, we assess he quaniaive relevance of his fricion. The model is idenical o he baseline model excep ha firms lose some oupu if hey adjus employmen. The adjusmen funcion akes he quadraic form used by Sargen (1978). The producion funcion for domesic raded goods becomes 2 1 =min /, /, D α D D D TD TD ND ND D D D θ 1 D 1 D 1 y z a z a A k g g. The producion funcion for nonraded goods changes similarly. We assume ha he α (32) ( ) coss grow a he same rae as produciviy, g 1, so ha he coss are nonrivial in he model s balanced growh pah. We assume ha labor in each secor has grown proporionaely beween 1987 and 1988. No imposing some sor of adjusmen cos in 1988 resuls in a sharp drop in oupu in 1989. The adjusmen coss in 1988 require us o recalibrae all of he parameers of each producion funcion so ha he equilibrium replicaes he 1988 inpu-oupu marix. 21
The labor adjusmen cos funcion adds a new parameer, θ, ha we calibrae o mach he reallocaion of labor across he wo secors ha we find in he daa. In Mexico, as in mos indusrialized counries, he share of labor used in he raded secor has a negaive rend. During he sudden sop, labor sops moving ou of he raded secor and even increases by a small amoun; his amouns o relaive o he rend a significan reallocaion of workers o he raded secor. We could model his by specifying differen raes of growh of echnological progress, gd > gn, in he producion funcions. Insead, we absrac from he secular rend in employmen, so we remove a leas-squares linear ime rend boh from he daa and from he model. Figure 11(a) plos he derended raio of raded labor o oal labor. We se θ = 6.468 so ha he reallocaion from 1994 o 1997 is he same in he model as in he daa. The resuls for he model wih labor fricions are summarized in able 4. Labor fricions have heir larges impac on he price of nonraded goods, as shown in figure 11(b). The fricions resric he amoun of raded goods ha can be produced, leading o higher raded good prices in his model relaive o he baseline model. The bilaeral price of nonraded goods in Mexico falls 31.38 percen, more han five imes ha in he baseline model. The large movemen in he relaive price of nonraded goods causes he real exchange rae o depreciae during he sudden sop by 61.30 percen compared o 41.36 in he baseline model. Reurning o he original argumen for including hese coss, we can see from able 4 ha GDP rises by abou half as much as in he baseline model and TFP falls by 0.26 percen; he movemens are nowhere near as large as hose in he daa. I is worh noing ha movemens in TFP are no monoonic in he cos parameer θ : seing θ very high resuls in very lile movemen of labor and very low coss incurred. 6.3 Variable capial uilizaion Our hird candidae explanaion is variable capial uilizaion. Firms choose how much o uilize he capial sock, bu he more ha capial is used, he higher is he depreciaion rae. The rade-off implies ha when he marginal produc of capial is low, he agens will choose no o use i as much. In he eyes of he saisician, hough, capial is 22
measured he same way regardless of uilizaion, which is unobserved. This measuremen issue implies ha a decrease in uilizaion will appear as low produciviy. The law of moion for capial in he domesic raded secor is (33) 1 ( 1 δ ( )) where k = D ud k + + D i, D χ = +. ω (34) δ ( ud ) δ ( u ω D 1) α α D D D D Value added in he producion funcion (5) is now ( ) ( ) 1 D D A u k g. We assume ha he raded secor has he same uilizaion echnology. Here capial uilizaion is u ; he parameer ω governs he curvaure of he depreciaion funcion; and δ and χ are parameers calibraed so ha depreciaion in 1988 is equal o ha in he daa and so ha u D1988 un1988 1 = =. This specificaion ness our baseline specificaion in he limiing case where ω ends o infiniy and he specificaion of Greenwood, Hercowiz, and Huffman (1988) in he case where χ / ω = δ. We firs consider he case where we calibrae ω = 3.751 so ha χ / ω = δ. The resuls are summarized in able 4. The model can generae abou one-hird of he drop in he TFP facor, bu GDP sill increases during he sudden sop. This is because uilizaion is anoher margin on which o adjus. During he sudden sop, raded capial uilizaion increases and nonraded capial uilizaion decreases, as in figure 12(b). This allows he economy o produce more raded oupu han i could in he baseline model. If we combine he labor fricions and variable capial uilizaion, we can accoun for he observed fall in TFP. We se ω = 6.510 and θ = 8.964, producing boh he drop in TFP and he reallocaion of labor observed in he daa. In his specificaion, χ / ω < δ. The labor fricion makes i more difficul o move labor across he secors, so he change in capial uilizaion is larger, creaing he larger drop in TFP. The model wih boh fricions also decreases GDP almos as much as in he daa. Noice, however, ha he oher resuls generaed by he model are sharply a odds wih he daa: he rade balance, real exchange rae, and relaive price of nonraded goods flucuae wildly. By limiing 23
he movemens in labor, he model forces adjusmens o ake place elsewhere. While combining fricions can mach he observed drop in TFP, i desroys he model s abiliy o accoun for oher pars of he daa. 6.4 Quasilinear uiliy When he baseline model is hi wih a sudden sop, he labor inpu increases because he wealh effec of he sudden sop overwhelms he subsiuion effec. Households prefer o work more during he sudden sop and o consume less leisure o make up for he loss of income. In some small open economy models, however, he period uiliy funcion is specified as a quasilinear funcion, as in Greenwood, Hercowiz, and Huffman (1988), 1 ψ ρ ρ η 1 ρ c c u c,, T 1 N T cn = ε + ε λg 1, ψ n n (35) ( ) ( ) so ha here is no wealh effec on labor supply. As Chakrabory (2006) poins ou, using his uiliy funcion in a one secor model of sudden sops eliminaes he increase in labor because of he wealh effec generaed by a sandard uiliy funcion. We consider a model wih a uiliy in which ψ = 0, ha is, in which ineremporal uiliy is logarihmic, because we canno calibrae a value of β less han 1 if ψ = 1. We se η = 3 and calibrae λ o mach hours worked in 1988. Table 5 repors he resuls. These resuls are very similar o he baseline model, excep he increase in labor during he sudden sop is less han half of ha in he baseline model. Labor sill increases because of he increase in working age populaion. Labor per working age person declines slighly because of a small drop in he wage relaive o he prices of consumpion goods. One problem wih he quasilinear uiliy funcion is ha i produces a large posiive rend in labor as he economy increases is capial-oupu raio. 6.5 Exogenous decrease in TFP Our simple model, in which a sudden sop acs on an economy hrough he ineracion of raded and nonraded goods, is successful in reproducing many feaures of he Mexican crisis, bu is unable o accoun for he change in GDP. In his secion, we consider a 24