NBER WORKING PAPER SERIES MANAGING CURRENCY PEGS. Stephanie Schmitt-Grohé Martín Uribe. Working Paper

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1 NBER WORKING PAPER SERIES MANAGING CURRENCY PEGS Steanie Scmitt-Groé Martín Uribe Working Paer tt:// NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massacusetts Avenue Cambridge, MA May 2012 Te views exressed erein are tose of te autors and do not necessarily reflect te views of te National Bureau of Economic Researc. NBER working aers are circulated for discussion and comment uroses. Tey ave not been eerreviewed or been subject to te review by te NBER Board of Directors tat accomanies official NBER ublications by Steanie Scmitt-Groé and Martín Uribe. All rigts reserved. Sort sections of text, not to exceed two aragras, may be quoted witout exlicit ermission rovided tat full credit, including notice, is given to te source.

2 Managing Currency Pegs Steanie Scmitt-Groé and Martín Uribe NBER Working Paer No May 2012 JEL No. F41 ABSTRACT Te combination of a fixed excange rate and downward nominal wage rigidity creates a real rigidity. In turn, tis real rigidity makes te economy rone to involuntary unemloyment during external crises. Tis aer resents a graical analysis of alternative olicy strategies aimed at mitigating tis source of inefficiency. First- and second-best monetary and fiscal solutions are analyzed. Second-best solutions are found to be rudential, wereas first-best solutions are not. Steanie Scmitt-Groé Deartment of Economics Columbia University New York, NY and NBER steanie.scmittgroe@columbia.edu Martín Uribe Deartment of Economics Columbia University International Affairs Building New York, NY and NBER martin.uribe@columbia.edu

3 Wen confronted wit te current crisis in erieral Euroe, many secialists in emergingmarket macroeconomics feel tat it is déjà vu all over again. An imlication of tis feeling is tat in order to understand te current situation in soutern Euroe, one sould dust off te teories of excange-rate crises tat were motivated by te economic exerience under fixed excange rates in Latin America in te 1980s and 1990s. We quarrel wit tis view. Te models of te 1980s and 1990s were built around te remise tat te fixed excange-rate regime was unsustainable in te long run, rimarily because of structural fiscal deficits. Celebrated examles of tis body of work are Krugman s (1979) model of balance-of-ayments crises and Calvo s (1986) temorariness yotesis. In bot of tese models te emasis is on te macroeconomic dynamics during te initial and terminal stages of finite-lived excange-rate egs. In our view, te world is currently witnessing an entirely new breed of currency egs. Unlike in te Latin American exerience, in te Euroean one countries joined a currency union as art of a muc larger olitical and economic integration rogram wit a grou of countries tat includes two of te largest and most develoed economies in te globe, namely, Germany and France. As a consequence, for many of te emerging countries tat are art of te eurozone, and for reasons tat may exceed economic considerations, breaking away from te currency union may not be a viable otion. Te olicy callenges arising for tis new generation of eggers call for at least tree ieces of new teory. One iece is concerned wit te caracterization of economic fluctuations in emerging countries wit fixed excange rate regimes tat are exected to be ermanent. 1 In te resence of rigidities in nominal roduct or factor rices, tese fluctuations are bound to be inefficient. For te combination of rice rigidity and a fixed excange rate amounts to two nominal rigidities, and, consequently, to a real rigidity. Tis real rigidity motivates te need for a second iece of new teory concerned wit ow to attain te first-best allocation wen 1 Tere exists an earlier literature on ermanent egs for emerging countries known as te suly-side yotesis of excange-rate-based stabilization (see Roldós, 1995; Uribe, 1997; and Lairi, 2001). However, te scoe of tis literature is limited to te initial dynamics of ermanent currency egs. 1

4 te central bank s ands are tied by a currency eg. Finally, because te olicy instruments necessary to acieve te first-best allocation may not always be available to te olicymaker, te tird iece of teory needed is te study of second-best olicy interventions tat can be realistically imlemented witin a currency union. In tis aer, we summarize recent contributions of ours to tese tree teoretical issues (Scmitt-Groé and Uribe, 2011 and 2012). For edagogical reasons, ere we emloy a simle graical aroac. 1 Te Teoretical Framework Consider a small oen economy tat roduces tradable and nontradable goods. Te suly of exortable goods, denoted TOT t q t, is exogenous and stocastic. It reresents a source of aggregate fluctuations wic can be interreted as disturbances eiter to te terms of trade, denoted TOT t, or to te ysical abundance of te tradable endowment, denoted q t. Nontraded goods are roduced using labor wit te roduction function F ( t ), were F is increasing and concave, and t denotes labor inut. Let t Pt N /Pt T rice of nontradables in terms of tradables, were P N t and P T t denote te relative denote, resectively, te domestic-currency rices of nontraded and traded goods. We assume tat te law of one rice olds for traded goods and tat te foreign-currency rice of traded goods is constant and normalized to unity. Ten, we ave tat P T t = E t, were E t denotes te nominal excange rate, defined as te domestic-currency rice of foreign currency. Te labor cost faced by te firm, in terms of tradables, is given by w t W t /E t, were W t denotes te nominal wage rate. Te firm is a rice taker in roduct and factor markets. It cooses te amount of labor inut to maximize rofits, given by, t F ( t ) w t t, taking t and w t as given. Te first-order otimality condition of te firm s rofit maximization roblem is t = Wt/Et F ( t). Figure 1 resents a graical reresentation of tis otimality condition in te sace ( t, t ). An increase in te relative rice of nontradables raises te value of te 2

5 Figure 1: Te Suly Scedule W 0 /E 0 marginal roduct of labor, inducing firms to exand emloyment. Suose now tat te government devalues te domestic currency by increasing te nominal excange rate from E 0 to E 1 >E 0. Suose also tat te nominal wage is eld fixed at W 0. Ten, firms exerience a decline in te real cost of labor from W 0 /E 0 to W 0 /E 1, wic gives tem an incentive to exand emloyment for any given level of te relative rice t. Figure 2 illustrates tis effect wit a dased line. In resonse to te devaluation, te suly scedule sifts down and to te rigt. Te desired aggregate absortion of nontradables, denoted c N t, can be derived from te ouseold s otimization roblem. It is summarized by te exression c N t = A( t ; r t,d t,tot t q t,...), were r t and d t denote, resectively, te country s interest rate and external debt. Te function A is decreasing in t, reflecting substitutability between tradable and nontradable goods in consumtion. Any factor tat canges te ouseold s erceived ermanent income or intertemoral rice of consumtion will in general affect te desired consumtion of nontradables. In articular, te demand for nontradables is decreasing in r t (assuming tat te country is a net external debtor) and in d t and increasing in TOT t q t. Combining tis demand function wit te market clearing condition in te nontraded sector, given by c N t = F ( t ), 3

6 Figure 2: A Devaluation Sifts Te Suly Scedule Down and To te Rigt W 0 /E 0 W 0 /E 1 (E 1 >E 0 ) we obtain te relationsi t = D( t ; r t,d t,tot t q t,...), were, like A, te function D is decreasing in t, r t, and d t, and increasing in TOT t q t. We will refer to D, somewat imroerly, as te demand scedule. Figure 3 dislays a downward sloing locus, indicating tat, as te relative rice of nontradables increases, ouseolds reduce teir demand for tis tye of goods. In turn, te diminised absortion of nontradables requires fewer ours of work to be roduced. Suose now tat te country exeriences an increase in te interest rate carged by foreign lenders from r 0 to r 1 >r 0. Under our maintained assumtion tat te country is a net external debtor, te increase in te country remium causes te ermanent income of ouseolds to fall. Because consumers feel oorer, tey cut teir demand for nontradables. As a result, te demand scedule sifts down and to te left as sown wit a dased line in figure 4. Te central friction in te resent model is downward nominal wage rigidity. Secifically, we assume tat W t γw t 1, were γ 0 is a arameter measuring te degree of downward wage rigidity. Te iger is γ, te iger is te downward rigidity in nominal wages. In 4

7 Figure 3: Te Demand Scedule D(; r 0,...) Figure 4: An Increase in te Interest Rate Sifts te Demand Scedule Down D(; r 0,...) D(; r 1,...) r 1 >r 0 5

8 Figure 5: Adjustment Under Otimal Excange-Rate Policy D(; r 0,...) 0 bust D(; r 1,...) B A W 0 /E 0 1 C W 0 /E 1 bust Scmitt-Groé and Uribe (2011), we resent emirical evidence suggesting tat nominal wages are downwardly rigid and tat, for business-cycle analysis, a conservative value for γ is 0.99 wen te lengt of a eriod is one quarter. We assume tat workers suly >0units of labor inelastically eac eriod. However, worker will sometimes find tat tey cannot sell all of te ours and terefore in tose eriods, tey will be involuntarily underemloyed. Tus, we ave tat te constraint t must old at all times. Finally, te labor market closes wit te slackness restriction ( t )(W t γw t 1 ) = 0. Tis condition states tat if in any given eriod tere is underemloyment ( t < ), ten te lower bound on nominal wages must bind. Te slackness condition also states tat if tis constraint is not binding (W t >γw t 1 ), ten te economy must be at full emloyment. 2 Pegs and Crisis Amlification Having introduced te demand and suly scedules and described ow te labor market closes, we can analyze te macroeconomic effects of negative external socks. Figure 5 illustrates te adjustment rocess. Te original osition is at oint A, were te suly and demand scedules intersect and te economy is oerating at full emloyment ( t = ). Now 6

9 suose tat te country interest rate increases from r 0 to r 1 >r 0. As discussed above, tis causes te demand scedule to sift down and to te left as sown by te downward sloing dased line. Because te nominal excange rate is egged and because nominal wages are downwardly rigid (we are assuming for simlicity tat γ = 1), te suly scedule does not move. As a result, te new intersection occurs at oint B. At tis oint, involuntary unemloyment emerges in te magnitude bust. At te level of te individual firm, te roblem is tat it exeriences a fall in te rice of te good it sells (from 0 to bust ), but no cange in labor cost (te real wage remains constant at W 0 /E 0 ). To avoid losses, te firm must reduce emloyment, tereby cutting marginal costs (from (W 0 /E 0 )/F ( ) to (W 0 /E 0 )/F ( bust )). Te combination of a fixed excange rate and downwardly rigid wages causes a sillover effect by wic an external crisis, wic could ave been circumscribed to te traded sector, sreads its deleterious effects to te nontraded sector. A natural question is wat olicies can el te economy ameliorate tese negative sillover effects. In our analysis, we take te downward rigidity in nominal wages as given. Of course, if te government could someow imlement olicies tat render te nominal wage fully flexible, ten full emloyment would obtain at all times. Te related emirical and teoretical literature, owever, suggests te existence of imortant nonolicy factors, suc as morale, causing downward rigidity in nominal wages (see, for instance, Bewley, 1999). 3 First-Best Policy Interventions We consider four olicies tat can acieve te Pareto otimal allocation. One is monetary in nature and te oter tree are fiscal. 7

10 3.1 Otimal Excange-Rate Policy In Scmitt-Groé and Uribe (2011), we sow tat in te resent model tere exists an otimal excange-rate olicy tat acieves te Pareto otimal allocation. Tis olicy calls for a devaluation wenever te real wage consistent wit full emloyment in any eriod t falls below γw t 1 /E t 1. Figure 5 illustrates ow te otimal devaluation rate ensures full emloyment at all times. As exlained earlier, in te absence of a devaluation, te increase in te interest rate uses te economy from oint A, were te labor market oerates at full emloyment, to oint B, were involuntary unemloyment equals bust. Suose now tat te government devalues te domestic currency from E 0 to E 1 >E 0. Te devaluation sifts te suly scedule down and to te rigt as sown by te dased uward sloing line. If te size of devaluation is at least as large as te vertical fall in te demand scedule measured at t =, ten full emloyment reemerges. Te new equilibrium is at oint C. At tis oint, firms voluntarily coose to continue to ire units of labor because altoug te rice of te good tey sell fell (from 0 to 1 ), teir labor cost falls by exactly te same roortion (from W 0 /E 0 to W 0 /E 1 ). 3.2 Otimal Fiscal Policy For emerging countries tat are art of a currency union, suc as tose in te eriery of te eurozone, devaluations are not an otion. In Scmitt-Groé and Uribe (2011), we sow tat tere is an array of fiscal olicies tat can bring about te Pareto otimal allocation witout aving to resort to movements in te nominal excange rate. One suc instrument is a labor subsidy. Suose tat te government decides to subsidize emloyment at te firm level at te roortional rate s t er our emloyed. In tis case, te firm s otimality condition becomes t =(1 s t ) Wt/Et F ( t). Tis exression states tat for a given relative rice, t, and for a given real wage, W t /E t, te larger is te subsidy s t, te lower is te marginal cost of labor erceived by te firm, and terefore te larger te amount of ours it is willing to ire. 8

11 Figure 6: Adjustment Under Otimal Labor Subsidy Policy D(; r 0,...) 0 bust D(; r 1,...) B A W 0 /E 0 1 C (1 s )W 0 /E 0 bust Figure 6 sows ow labor subsidies can bring about te efficient allocation. Again, we consider a situation in wic an external sock (in te examle, an interest-rate increase from r 0 to r 1 ) brings te economy from an initial situation wit full emloyment (oint A) to one wit involuntary unemloyment in te amount bust (oint B). Te labor subsidy causes te labor suly scedule to sift down and to te rigt, as sown by te dased uward sloing line. Te new intersection of te demand and suly scedules is at oint C, were full emloyment is restored. We note tat, unlike wat aens under te otimal devaluation olicy, te real wage does not fall during te crisis under te otimal labor subsidy. Secifically, te real wage received by te ouseold remains constant at W 0 /E 0. Once te negative external sock dissiates (i.e., once te interest rate falls back to r 0 ), te fiscal autority can safely remove te subsidy, witout comromising its full emloyment objective. Anoter fiscal alternative to acieve an efficient allocation at all times is to subsidize sales in te nontraded sector. Let s yn t be a roortional subsidy on sales in te nontraded sector. An increase in te sales subsidy increases te marginal revenue of te firm. Te rofit-maximization condition of te firm becomes t = 1 1+s yn t W t/e t F ( t). Like a wage subsidy, a sales subsidy sifts te suly scedule down and to te rigt. Te graical analysis is 9

12 Figure 7: Adjustment Under Otimal Taxation of Nontradable Consumtion D(; r 0,...)=D((1 s cn ); r 1,...) 0 bust D(; r 1,...) B A W 0 /E 0 bust terefore qualitatively identical to tat used to exlain te workings of te otimal wage subsidy sown in figure 6. A tird fiscal instrument tat can be used to ensure full emloyment at all times in a egging economy wit downward nominal wage rigidity is a roortional subsidy to te consumtion of nontradables. Secifically, assume tat te after-subsidy rice of nontradable goods faced by consumers is (1 s cn t ) t. Te nontraded-consumtion subsidy makes nontradables less exensive relative to tradables. It can terefore be used by te government during a crisis to facilitate an exenditure switc toward nontraded consumtion and away from tradable consumtion. Wit nontraded-consumtion taxes, te demand scedule is given by D( t (1 s cn t ); r t,...). Figure 7 illustrates ow te consumtion subsidy can be otimally used to ensure te efficient functioning of te labor market. Again, te increase in te interest rate from r 0 to r 1 sifts te demand scedule down and to te left. As discussed before, in te absence of any intervention, our egging economy would be stuck at te inefficient oint B. Te introduction of te nontraded-consumtion subsidy sifts te demand scedule back u and to te rigt. If te magnitude of te subsidy is cosen aroriately, te demand scedule will cross te suly scedule exactly at oint A, were 10

13 te labor market returns to full emloyment. A criticism tat can be made against all tree of te fiscal alternatives considered ere is tat te imlied tax olicies inerit te stocastic roerties of te underlying sources of uncertainty (e.g., r t, q t TOT t, etc.). Tis means tat tax rates must cange at business-cycle frequencies. To te extent tat canges to te tax code are subject to legislative aroval, te long and uncertain lags involved in tis rocess migt render te imlementation of te otimal tax olicy imossible. 4 Second-Best Policy Intervention We now consider caital controls as a way to mitigate te inefficient adjustment of economies wit fixed excange rates and downward nominal wage rigidity. Te resent analysis draws from Scmitt-Groé and Uribe (2012). Suose tat te government imoses a tax τ d t on external borrowing. Negative values of τ d t corresond to a subsidy to external borrowing. Tis tye of caital control raises te effective interest rate on external debt from r t to r t + τt d. Te demand scedule ten becomes D( t; r t + τt d,...). In rincile, te government could use caital controls to fully offset any canges in te interest rate wit canges in τ d t. In tis case, te effective interest would be constant, and te demand scedule would not sift in resonse to disturbances in r t. Consequently, full emloyment in te nontraded sector would be reserved at all times. Suc a olicy, owever, would not be otimal. For te effective interest rate r t + τ d t governs te intertemoral rice of tradable consumtion. Tus, te caital control rate τ d t reresents a wedge in te relative rice of future and resent consumtion tat distorts te intertemoral allocation of exenditure. In determining te otimal value of τt d, te benevolent government, terefore, faces a trade off between an intertemoral distortion in consumtion and a static distortion in te labor market. As a result of tis tradeoff, te tax rate τ d t will adjust over te business cycle but will not fully stabilize te effective country interest rate. 11

14 Figure 8: Otimal Caital Controls and an Interest Rate Increase B D A W 0 /E 0 D(; r 0,...) D(; r 1 + τ d,...) D(; r 1,...) bust occ Figure 8 illustrates te role of otimal caital controls. As in te revious olicy exeriments, te starting oint is A, were te economy enjoys full emloyment. Under free caital mobility, an increase in te country interest rate from r 0 to r 1 sifts te demand scedule down and to te left and brings te economy to oint B, were te unemloyment rate is bust. Suose now tat te fiscal autority subsidizes external borrowing by setting τt d at a negative value. Tis olicy move incentivates external borrowing and aggregate absortion, causing te demand scedule to sift u and to te rigt as sown by te dased-dotted line. Te new intersection is at oint D. At tis oint, te level of emloyment is iger tan at oint B (corresonding to te outcome associated wit free caital mobility), but still less tan at oint A, indicating tat some unemloyment remains even under otimal caital controls. In Scmitt-Groé and Uribe (2012), we stress te fact tat te otimal caital control olicy is rudential. Tat is, unlike wat aens under te oter fiscal and monetary instruments considered earlier in tis aer, under te otimal caital control olicy te government acts reemtively during booms to curb aggregate sending via caital controls. Figure 9 illustrates te use of otimal caital controls during booms. In te gra, a fall 12

15 Figure 9: Otimal Caital Controls and an Interest Rate Decrease (b) An decrease in r from r0 to r2 D(; r 2,...) D(; r 2 + τ d 1,...) D(; r 0,...) D W 1/E 0 F W 0/E 0 A in te country interest rate from r 0 to r 2 <r 0 sifts te demand scedule u and to te rigt, as sown wit a dased line. Under free caital mobility, te new equilibrium is at oint D, were te economy is at full emloyment. As a result of te boom, te nominal wage increases from W 0 to W 1. Tis wage adjustment materializes frictionlessly, because nominal wages are assumed to be uwardly flexible. Te reason wy te government as an incentive to ut sand in te weels of exenditure in tis ase of te cycle is tat wen te sock dissiates and aggregate demand falls back to its normal level, te required fall in real wages will not occur quickly enoug because of te downward rigidity of nominal wages and te fixity of te nominal excange rate. Te government terefore imoses caital controls (τ d 1 > 0), wic cause te demand scedule to sift down and to te left, as sown wit a dased-dotted line. Te new intersection is oint F, were te unemloyment rate is zero, te nominal wage is lower tan at oint D, but iger tan at oint A, and te aggregate absortion of tradables is smaller tan under free caital mobility. Wile acieving only a second-best allocation, caital controls ave te advantage over income or consumtion taxes tat in many countries tey can be muc more swiftly imlemented. 13

16 5 Conclusion An imortant olicy issue is ow to finance te various subsidies discussed in tis and te revious section. In Scmitt-Groé and Uribe (2011, 2012), we sow tat tey can be financed in a nondistorting fasion wit a roortional tax on labor income of ouseolds. Te reason wy labor income taxes are nondistorting in a crisis is tat in tese circumstances ouseolds find temselves off teir suly scedule (i.e., tey are willing to work longer ours at te going wage tan tey are actually working). To conclude, we would like to stress tat because te central friction in te resent model is nominal (downward nominal wage rigidity), te natural instrument to correct it is monetary olicy. All of te fiscal alternatives discussed above (including caital controls) are likely to be significantly arder to imlement in ractice for te simle reason tat te monetary autority as te caacity to intervene at a seed far exceeding tat at wic te fiscal autority can alter te tax code or imose caital controls. Finally, wile an individual country in te eriery of te eurozone is owerless wen it comes to canging monetary olicy, te union s monetary autority could el te unemloyment roblem of ailing members by engineering an increase in te eurozone s overall rate of inflation. References Bewley, Truman F., Wy Wages Don t Fall During A Recession, Cambridge, MA: Harvard University Press, Calvo, Guillermo A., Temorary Stabilization: Predetermined Excange Rates, Journal of Political Economy 94, December 1986, Krugman, Paul, A Model of Balance-of-Payments Crises, Journal of Money, Credit and Banking 11, August 1979, Lairi, Amartya, Excange-Rate-Based Stabilizations Under Real Frictions: Te Role of Endogenous Labor Suly, Journal of Economic Dynamics and Control 25, August 14

17 2001, Roldós, Jorge, Suly-Side Effects of Disinflation Programs, IMF Staff Paers 42, Marc 1995, Scmitt-Groé, Steanie and Martín Uribe, Pegs and Pain, working aer, Columbia University, Scmitt-Groé, Steanie and Martín Uribe, Prudential Policy For Peggers, Columbia University, Uribe, Martín, Excange-Rate-Based Inflation Stabilization: Te Initial Real Effects of Credible Plans, Journal of Monetary Economics 39, June 1997,