Are Shocks to the Terms of Trade Shocks to Productivity?

Transcription

1 Federal Reserve Bank of Minneapolis Research Deparmen Saff Repor 39 Revised April 2008 (Firs version May 2007) Are Shocks o he Terms of Trade Shocks o Produciviy? Timohy J. Kehoe Universiy of Minnesoa, Federal Reserve Bank of Minneapolis, and Naional Bureau of Economic Research Kim J. Ruhl* Universiy of Texas a Ausin ABSTRACT Inernaional rade is frequenly hough of as a producion echnology in which he inpus are expors and he oupus are impors. Expors are ransformed ino impors a he rae of he price of expors relaive o he price of impors: he reciprocal of he erms of rade. Cas his way, a change in he erms of rade acs as a produciviy shock. Or does i? In his paper, we show ha his line of reasoning canno work in sandard models. Saring wih a simple model and hen generalizing, we show ha changes in he erms of rade have no firs-order effec on produciviy when oupu is measured as chain-weighed real GDP. The erms of rade do affec real income and consumpion in a counry, and we show how measures of real income change wih he erms of rade a business cycle frequencies and during financial crises. *We would like o hank Narayana Kocherlakoa, Ellen McGraan, Edward Presco, Kaheryn Russ, and an anonymous referee for helpful advice and commens. This work was underaken wih he suppor of he Naional Science Foundaion under gran SES The daa used in his paper are available a and a The views expressed herein are hose of he auhors and no necessarily hose of he Federal Reserve Bank of Minneapolis or he Federal Reserve Sysem.

2 . Inroducion The erms of rade he price of impors relaive o he price of expors vary grealy over ime and counry. This variaion makes he erms of rade a naural candidae for explaining counry performance. Inuiively, we can hink abou foreign rade as a producion echnology: a counry s expors are he inpus o he echnology, and hese inpus are urned ino oupus ha are recorded as a counry s impors. Expors are ransformed ino impors a he rae ha is he raio of he price of expors o he price of impors, which is jus he reciprocal of he erms of rade. Viewed in his way, an increase in he erms of rade acs much like a echnology shock: he same amoun of expors now produces a smaller amoun of impors. In his paper, we show ha sandard models do no suppor his line of reasoning when we measure echnology shocks using oal facor produciviy (TFP) where oupu is measured using real gross domesic produc (GDP). The problem lies in he consrucion of real GDP. The effec of a shock o he erms of rade on real GDP is no he same as he effec of a produciviy shock and is dependen upon he mehod used o consruc real GDP. When real GDP is consruced using he chain-weighing mehod specified in he Unied Naions Sysem of Naional Accouns, erms of rade shocks have no firs-order effecs if inpus of facors are consan. When real GDP is consruced using fixed base year prices, he effec of a erms of rade shock is ambiguous: in some cases a deerioraion of he erms of rade can even increase real GDP! In his paper, we bring his accouning o bear on he relaion beween he erms of rade and produciviy. As produciviy is compued using real GDP as he measure of oupu, he erms of rade canno have a direc effec on a counry s TFP. If facors of producion can vary, changes in he erms of rade can cause real GDP o vary, bu, even so, here is no firsorder effec on TFP. An increase in he erms of rade lowers he purchasing power of he counry, which can be painful in erms of consumpion and welfare, bu does no impac TFP. The relaion beween changes in he erms of rade and changes in real GDP is well undersood by economiss ineresed in index numbers and naional income accouning. Diewer and Morrison (986) and Kohli (983, 2004), for example, explain ha changes in he erms of rade are considered a price phenomenon, no a real phenomenon, in he consrucion of real GDP. These researchers also propose oher measures of real income ha rea erms of rade shocks as if hey were echnology shocks. We discuss hese measures laer in he paper.

3 This paper explores he relaion beween TFP shocks and erms of rade shocks in models and conrass his relaion wih he relaion in he daa. In paricular, we focus on TFP measured using real GDP, raher han on real GDP iself. When we examine daa for he Unied Saes and Mexico over he pas several decades, we see ha sharp deerioraions in he erms of rade are accompanied by drops in real GDP and ha mos of hese drops in real GDP are driven by drops in TFP, no drops in facor inpus. Since sandard models canno accoun for hese drops in TFP, our paper idenifies a puzzle and poses a challenge for researchers working wih open economy models: If we hink ha erms of rade shocks cause TFP flucuaions, we need o develop a new mechanism for generaing his causal relaion and build i ino our models. Oherwise, we need o come up wih some oher reasoning o explain why sharp deerioraions in he erms of rade and drops in TFP are highly correlaed in he daa, especially during financial crises in developing counries like Mexico. The empirical lieraure on growh is replee wih examples of he associaion of he erms of rade wih oupu growh and wih produciviy growh. Easerly, Kremer, Priche, and Summers (993) sudy a large panel of counries o uncover he sources of long-run growh and aggregae volailiy. They conclude ha shocks, especially o he erms of rade, play a large role in explaining variance in growh. In seing ou a framework for sudying developing counry growh, Easerly, Islam, and Sigliz (200) find ha volailiy in he erms of rade is more srongly correlaed wih volailiy in oupu han are he sandard deviaions of many of he usual suspecs: money growh, fiscal balance, and capial flows, o name a few. Becker and Mauro (2005) use a large panel of counries o sudy how oupu drops are relaed o various exernal shocks and, using he likelihood of he shock and he associaed oupu drop, compue he cos of he differen shocks. They find ha he coslies shocks, paricularly for developing counries, are erms of rade shocks. The idea underlying many of hese conclusions is succincly summarized by Easerly, Islam, and Sigliz (200), who wrie, For small open economies, adverse erms of rade shocks can have much he same effec as negaive echnology shocks, and his is one of he imporan differences beween macroeconomics in hese economies and ha which underlies some of he radiional closed economy models. In line wih he above reasoning, we show ha, in sandard models, a shock o he erms of rade has an effec on consumpion and welfare ha is similar o a TFP shock. The analogy beween he erms of rade and produciviy breaks down when we calculae heir effecs on real 2

4 GDP and on TFP. When real GDP is measured a base period prices and domesic facors of producion are held fixed, he effec of a erms of rade shock on real GDP is deermined by he curren erms of rade relaive o he base period erms of rade. If he curren impor price is he same as he base period price, hen he shock has no effec. If he curren price is higher han he base period price, he effec is negaive, and, conversely, if he curren price is lower, he effec is posiive. Wih base period price weighing, a change in he erms of rade can have a firs-order effec on GDP, bu his resul follows from an arifac of he deflaion mehod and no from an underlying srucural relaionship. When we consider real GDP calculaed as a chain-weighed index as is now he sandard for many counries hese arifacs disappear. Changes in he erms of rade do no have a firs-order impac on real GDP, and TFP remains unchanged. We expand he simple examples o show ha our resuls easily generalize o richer environmens. We show ha a shock o he erms of rade can affec he supply of producive facors like labor and ha he effecs of hese shocks, as in he simple examples, also have an ambiguous impac on real GDP a base period prices. Wih chain-weighed GDP he ambiguiy disappears and he effec on GDP comes only hrough facor supplies, implying ha TFP is no affeced by he erms of rade. A hird se of resuls shows how he effec of a erms of rade shock on real GDP and consumpion varies wih he elasiciy of subsiuion beween he domesic facors and he impored inpu. As he elasiciy of subsiuion decreases, changes in he erms of rade have larger impacs on consumpion bu smaller impacs on real GDP. When he producion funcion uses domesic and impored inpus in fixed proporions, changes in he erms of rade have a large impac on consumpion, bu no impac on real GDP. If he erms of rade do no have a clear effec on measures of real GDP and TFP, where are heir effecs visible? In naional accouning measures, he erms of rade affec gross domesic income (GDI). In a closed economy, real GDI and real GDP are he same, bu in an open economy hey are no. In secion 7, we discuss alernaive measures of real income, including he concep of command basis GDP used by he U.S. Bureau of Economic Analysis. These measures do respond o changes in he erms of rade and reflec how he purchasing power of an economy changes as foreign prices change. The problems highlighed in his paper are par of a much larger issue faced by quaniaive researchers. Developing good inuiion is paramoun in undersanding how models work, and consrucing analogies, such as he one beween he erms of rade and produciviy, 3

5 can be very helpful in developing inuiion. When evaluaing he quaniaive properies of a model, however, he saisics aken from he model mus be consruced in he same way as hey are in he daa. As we show below, i is exacly in his dimension ha he analogy beween he erms of rade and produciviy breaks down. In comparing models o daa, he researcher is faced wih wo choices. Eiher he saisics can be colleced from he model as hey are by he economiss a he saisical agencies, or he daa can be reconfigured o mimic he consrucs in he model. We ake he firs approach in secions 3 hrough 6 and show how he model s GDP as i would be consruced by a naional income accounan behaves in unexpeced ways. In secion 7, we ake he second approach and use he daa ha underlie GDP o consruc a measure of naional income ha corresponds o he analogy beween erms of rade shocks and produciviy shocks. This paper idenifies a puzzle. In he nex secion, we show ha deerioraions in he erms of rade are frequenly accompanied by declines in produciviy. We hen show ha sandard models do no generae his relaion. If here is a causal mechanism ha links shocks o he erms of rade o movemens in produciviy, researchers need o idenify i. 2. Terms of rade and produciviy in Mexico and he Unied Saes The daa ploed in figure show ha conracions in real GDP in he Unied Saes accompanied he sharp increases in he erms of rade caused mosly by he rise in peroleum prices ha followed he OPEC oil embargo in 973 and he Iranian Revoluion in 979. (All of he daa used in his paper are available a and a In his figure, he erms of rade are calculaed as he raio of he impor price deflaor and he expor price deflaor. Consequenly, he upward spikes in he erms of rade in 974 and 980 are deerioraions. The correlaion beween changes in he erms of rade and changes in real GDP over he enire period is only 0.2, bu we wan o focus on he comovemen during he wo periods wih he large deerioraions in he erms of rade, where he wo series move sharply in opposie direcions. Hamilon (983) has poined ou ha all bu one of he pos World War II economic downurns in he Unied Saes, from , were accompanied by an upward spike in he price of impored oil. Figure 2 presens he analogous daa for Mexico, which in 982 and 994 enered severe financial crises ha brough wih hem sharp increases in he price of impors. The large 4

6 deerioraions in he erms of rade in 983, 986, and 995 were accompanied by large conracions in real GDP. The correlaion coefficien for changes in real GDP and changes in he erms of rade is 0.7 for Mexico. To examine he relaion beween changes in he erms of rade and changes in produciviy, we calculae TFP as A = Y K L. () α α Here Y is real GDP, K is a measure of he real capial sock consruced using he perpeual invenory mehod, and L is a measure of aggregae hours worked. (See Conesa, Kehoe, and Ruhl 2007 for a discussion of he issues involved in he consrucion of his sor of daa.) There are wo hings worh noicing abou he daa for TFP in figures and 2: Firs, changes in he erms of rade have he same sor of relaion wih changes in TFP as hey do wih changes in real GDP. In paricular, he correlaion coefficien is 0.42 for he Unied Saes and 0.7 for Mexico. Furhermore, he deerioraions in he erms of rade in 974 and 980 in he Unied Saes and in 983, 986, and 995 in Mexico were accompanied by sharp drops in TFP. Second, he drops in TFP in boh counries ha occur during he years associaed wih large deerioraions in he erms of rade were even larger han he drops in real GDP, leaving no room for drops in facor inpus o play a role. 3. A simple model We begin by considering a simple model in which he single facor of producion, labor, is supplied inelasically, and in which here are no disorions or rigidiies. We subsequenly show how our resuls exend o models wih variable labor supply and o models wih disorions. We begin wih he case where real GDP is measured in erms of base year prices because he calculaions are simpler. We hen show how he resuls can be exended o he case where real GDP is calculaed wih chain-weighed prices. 3.. Closed economy We firs consider a closed economy and show ha a fall in produciviy in he inermediae goods secor produces a fall in GDP and in TFP, a resul ha does no carry over 5

7 when we reinerpre he model as ha of an open economy in which inermediae goods are impored. There are wo goods produced in his economy a each dae. The firs good, he y good, is consumed and is used in he producion of he second good, he m good. The y good is produced using labor and inermediae inpus of he m good according o he producion funcion y = f(, m ). (2) We assume he producion funcion, f, has consan reurns o scale, is concave, and is coninuously differeniable. We laer analyze he case where f is a fixed proporions producion funcion. The m good is produced using only inermediae inpus of he y good, which we denoe x. The producion funcion is m x a =, (3) where a is a uni oupu requiremen ha can vary. We assume ha he m good is sold in compeiive markes a price p. The m good producer chooses and o earn zero profis. The condiion ha equilibrium profis be zero is m and x o minimize coss p = a. (4) The feasibiliy condiion is c + x = y = f(, m ). (5) We normalize he price of he y good o be. Expendiure on final goods in he closed economy is only consumpion, so on he expendiure side, real GDP, Y, is Y = c = y x. (6) On he oupu side, real GDP is calculaed as he base period value of gross oupu minus he base period value of inermediae inpus: ( ) ( ) Y = y + p m p m + x = y x, (7) 0 0 where p0 = a0 is he base period price of he m good. 6

8 To calculae he impac of an increase in a, a decline in produciviy in he m good secor, we noe ha a compeiive economy chooses m o solve max f (, m ) am. (8) Labor is inelasically supplied, so we have se = ime. The firs-order condiion for his problem is, where is he household s endowmen of f (, m ) = a. (9) m Using he implici funcion heorem, we obain m ( a ) = < 0. (0) f (, m( a )) mm Suppose ha a + > a increases, ha is, ha produciviy in he inermediae goods secor falls. How does real GDP change? The firs-order change is where dy ( a ) Ya ( ) Ya ( ) ( a a), () + + da + Ya ( ) = f(, ma ( )) a ma ( ) (2) and where dy ( a)/ da + in equaion () denoes he derivaive of Ya ( + ) in equaion (2) evaluaed a a = + a. Differeniaing Ya ( + ), we use he firs-order condiion (9) o obain dy ( a ) = fm(, ma ( )) m ( a) am ( a) ma ( ) = ma ( ) < 0. (3) da + Real GDP and produciviy decline. Equaion () provides an expression for firs-order changes in real GDP when he producion funcion f is coninuously differeniable. When f is a fixed proporions funcion, ha is, where [ ] y = min, m / b, (4) we can obain exac expressions. In his case, ma ( ) = b and real GDP is 7

9 which implies ha he firs-order expression in () is exac. Ya ( ) = ab, (5) 3.2. Open economy Now consider an open economy wih he same srucure as ha of he closed economy, bu where m is now an impored inermediae inpu, x are expors of he y good, and p is he erms of rade. To make he analysis idenical o ha in he closed economy, we assume for he momen ha here is balanced rade, p m = x. (6) By comparing (6) o (3), we see how he erms of rade in he open economy, p, and he produciviy parameer in he closed economy, a, are similar. Noice ha we are also assuming ha all impors are being used as inermediae goods. We do his for simpliciy. I is easy o exend all of he resuls ha follow o a model where some impors are used direcly in consumpion and, in a model wih capial, in invesmen. Nohing of subsance changes. Real GDP is now Y = c + x p m = y p m = f(, m ) p m, (7) where p 0 is price of impors (relaive o expors) in he base year. A compeiive economy coninues o choose m o solve max f (, m ) pm (8) wih he corresponding firs-order condiion defining an implici funcion mp: ( ) f (, m ) = p (9) m m ( p ) = < 0. (20) f (, m( p )) mm An increase in p a deerioraion in he erms of rade has he idenical impac on consumpion and welfare as he decline in produciviy in he closed economy. Bu wha happens o real GDP and produciviy? 8

10 Y( p ) = f(, m( p )) p m( p ) (2) dy ( p ) = fm(, mp ( )) m ( p) pm 0 ( p) = ( p p0) m ( p). (22) dp + To he exen ha he erms of rade in he period before he deerioraion akes place, p, are close o he erms of rade in he base period, p 0, here is no firs-order change in measured real GDP or in produciviy. Noice ha, if p < p0, real GDP may even increase in response o a negaive erms of rade shock. Our calculaions in equaion (22) imply ha a change in he erms of rade can have eiher a posiive or negaive effec on GDP, depending on he value of he erms of rade in he prior period. As an example, consider he crises in Mexico in 983 and 995, episodes ha we will explore furher in secion 7.2. For he crisis in 983, we use real daa in which he base year is 980. Using he analogue o equaion (), we can calculae he firs-order approximaion o he change in real GDP: dy ( p ) Y( p ) Y( p ) ( p p ) (23) dp + Y( p ) Y( p ) ( p p ) m ( p )( p p ), (24) where equaion (24) is obained by subsiuing (22) ino (23). Approximaing m ( p982) by he raio of he change in real impors o he change in he erms of rade, we obain m m Y( p ) Y( p ) ( p p ) ( p p ) p983 p982 (25) Y( p ) Y( p ) ( p p )( m m ). (26) In 982, he erms of rade were 3.2 percen higher han in he base year 980. From 982 o 983, real impors fell by 43 billion 980 pesos. Using equaion (26), we can calculae he base period price effec Y( p ) Y( p ) 0.032( 43) = 4.6, (27)

11 which implies ha he change in real GDP due o he change in he erms of rade is 4.6 billion 980 pesos, which is 0.09 percen of GDP in 982. From 982 o 983, real GDP fell by 4.3 percen; so he base period price effec conribues o he fall in real GDP, bu is very small. An analogous calculaion for he crisis in 995 reveals he reverse. In 994 he erms of rade were lower han in he base period, which was 993 in his case, and he change in real GDP from he base period price effec ha we calculae using he analogue o equaion (25) is 0.02 percen, ha is, he deerioraion in he erms of rade acually caused measured real GDP o increase. Real GDP fell by 6.2 percen from 994 o 995; so he base period price effec moves in he opposie direcion from he change in real GDP, alhough, again, i is very small. There are wo cases in which he base period prices do no affec he calculaion of real GDP in an open economy. The firs, which we discuss in he nex secion, is he use of chained real GDP indices. The second is when f is he fixed proporions funcion (4), so ha real GDP is Y( p ) = p b, (28) which does no change a all as he erms of rade change. Noice ha he fixed proporions case is where consumpion, 0 c( p ) = ( pb), (29) and herefore welfare, falls he mos in response o a deerioraion in he erms of rade. The inuiion for our resuls is simple. A deerioraion in he erms of rade causes domesic oupu o fall, bu i also causes impors valued a base period prices o fall. Real GDP is he difference beween he wo, (2), and he envelope heorem says ha he wo effecs cancel o firs-order. Wih fixed proporions producion, he wo effecs are exacly equal Unbalanced rade In he previous secion, we have assumed in equaion (6) ha rade is balanced. In his secion, we argue ha our resuls exend o models in which rade is no balanced. This case is of obvious ineres because, in he daa, changes in he erms of rade are ofen accompanied by changes in he rade balance and because many dynamic open economy models endogenize he rade balance. 0

12 Suppose ha we have a dynamic model in which he budge consrain in period is c + b+ = w + ( + r) b, (30) where b is ne borrowing from abroad and r is he ineres rae and where We can rewrie he budge consrain as w = f (, m ) = f(, m ) pm. (3) c = f(, m) pm + ( + r) b b +. (32) The feasibiliy condiion remains he same as in equaion (5): c + x = f(, m ). Subracing his feasibiliy condiion from he budge consrain (32), we obain he rade balance condiion b ( + r) b = x + pm. (33) (Recall ha b + b is he curren accoun balance, which differs from he rade balance by rb.) In he dynamic model, he sequence of foreign borrowing and, possibly, he ineres rae are deermined endogenously. We do no have o specify he deails of his model, however, because hese deails make no difference o our resuls for real GDP. Real GDP remains equal o he expression in equaion (7), and, as long as he firs-order condiion p = f (, m ) holds, we m can obain he resul in equaion (22). The deerminaion of consumpion depends on he rade balance as seen in equaion (32) and is considerably more complicaed han in he saic model. In wha follows, we wan o compare he effecs of changes in erms of rade on consumpion and welfare wih heir effecs on real GDP and TFP. To keep his comparison simple, we assume ha rade is balanced when we calculae consumpion. 4. Chain-weighed real GDP Currenly, he U.S. Bureau of Economic Analysis in is Naional Income and Produc Accouns (NIPA) and he U.N. Saisics Division in is Sysem of Naional Accouns (SNA) recommend he use of chain-weighed price indices o deflae GDP. In his secion we show how he resuls of he previous secion carry over o chain-weighed real GDP. Alhough he calculaions are a lile more complicaed, an advanage of using chain-weighed real GDP is ha he annoying erms involving base period prices disappear.

13 The Unied Saes NIPA accouning uses Fisher chain-weighs. So does Saisics Canada. Mos counries ha follow he U.N. SNA accouning use Laspeyres chain-weighing of quaniies, alhough boh Fisher weighing and Paasche weighing are allowed. We sar by showing ha Fisher chain-weighing eliminaes he erms involving p0 p and hen briefly discuss how his resul exends o oher indices. Fisher chain-weighed real GDP is Y f (, mp ( + )) p+ mp ( + ) ( p ) =, (34) P + + where he Fisher chain-weighed price index is he geomeric average of he Paasche and he Laspeyres index beween he curren period and he previous period: + P f(, m( p+ )) p m( p ) + + f(, m( p)) p m( p) + f(, m( p+ )) pm ( p+ ) f(, m( p)) pm ( p) = where P 0 = in he reference period. P, (35) We can subsiue (35) ino (34), which yields he Fisher chain-weighed quaniy index f(, m( p )) p m( p ) f(, m( p )) pm( p ) Y( p + ) = Y( p ). (36) f(, m( p )) p m( p ) f(, m( p )) pm( p ) + I is easier o work wih he logarihm of chain-weighed GDP and calculae he firs-order change as ( ) log ( ) ( ) ( ) dlogy p logy p Y p p p. (37) + + dp + The naural logarihm of chain-weighed real GDP is log Y( p+ ) = log f(, m( p+ )) p+ m( p+ ) log f(, m( p)) p+ m( p) 2 2 ( ) ( ) + log ( f(, m( p+ )) pm ( p+ )) + log 2 2 ( f(, m( p)) pm ( p) ) 2 P (38) Differeniaing, we obain 2

14 dlog Y( p+ ) fm(, m( p )) m + ( p+ ) p m + ( p+ ) m( p+ ) = dp + 2 ( f(, m( p+ )) p+ m( p+ ) ).(39) mp ( ) fm(, mp ( )) m + ( p+ ) pm ( p+ ) (, ( )) ( ) 2 (, ( )) ( ) Since fm(, mp ( + )) = p+, his simplifies o ( f m p p+ m p ) ( f m p+ pm p+ ) dlog Y( p+ ) m( p+ ) m( p) = + dp + 2 f (, mp ( )) pmp ( ) 2 f(, mp ( )) p+ mp ( ) ( p+ p) m ( p+ ) + 2 (, ( )) ( ) ( ) ( ) ( f m p+ pm p+ ) Evaluaing his expression a p+ = p, we obain. (40) dlog Y( p ) = 0, (4) dp + which implies ha any effec of changes in he erms of rade on chain-weighed real GDP is of second order. Suppose ha, insead of Fisher weighing, he naional saisics agency uses Laspeyres weighing of quaniies. The relaion ha corresponds o (36) is Y p f(, m( p )) pm( p ) = + + ( + ) Y( p) f(, m( p)) pm ( p) Noice ha, in his case, he deflaor in (35) is = f(, m( p+ )) pm ( p+ ) P. (42) f(, m( p )) p m( p ) P, (43) ha is, a Paasche price index. In he case where he prices in (42) are hose of he second period, p + ha is, where he quaniy index is Paasche he deflaor in (43) uses he quaniy weighs in he firs period, f (, mp ( )) and mp ( ) ha is, he price index is Laspeyres. In eiher case, a simple argumen ha follows ha in equaions (38) (4), bu wih less algebra, proves ha he firs-order effec of a change in he erms of rade on chain-weighed real GDP is zero. 3

15 We could have used oher funcional forms in our calculaions. The Törnqvis index, for example, whose chain-weighed price index is of he form ( ) ( ( )) ( ) + ( + ) ( ( + ) ) + ( + ) pm p p m p + 2 p f, m p pm p f, m p p m p + + = p P P, (44) has a srong heoreical foundaion and has gained some use among boh economics researchers and saisical agencies. All of hese funcional forms chain-weighed Fisher, Laspeyres, Paasche, and Törnqvis indices share he propery ha changes in he erms of rade do no affec GDP o he firs-order. The inuiion for his resul is simple: in a chain-weighed index, he base period is always he preceding period. I is his propery of chain weighing, and no a paricular funcional form, ha eliminaes he dependency on base period prices. 5. Exensions of he simple model In his secion, we add variable labor supply and disorions o he model. To he exen ha shocks o he erms of rade change he labor supply, hey can change real GDP, bu no produciviy. Real GDP can even rise in response o a negaive erms of rade shock, alhough welfare falls. The model wih disorions is more complicaed. We analyze a model wih ariff disorions and show ha an increase in ariffs acs like a shock o he erms of rade bu has no firs-order effecs on GDP if iniial ariffs are zero. 5.. Variable labor supply z = Suppose ha here is a represenaive consumer who values boh consumpion and leisure. The uiliy funcion of his consumer is ucz (, ), and he consumer solves max uc (, ) (45) s.. c = w, where w = f (, m ). The firs-order condiion for his problem is which implicily defines he funcion ( w) : wu ( c, ) = u ( c, ), (46) c z wu ( w ( w), ( w)) = u ( w ( w), ( w)) (47) c z 4

16 u ( c, ) + u ( c, ) w u ( c, ) ( w ) = u c v w u c w u c c cc cz 2 cc (, ) 2 cz (, ) + zz (, ) Consider he consan elasiciy of subsiuion case, where Here ρ ρ ( c z ). (48) + γ γ / ρ for ρ, ρ 0 ucz (, ) =. (49) log c+ γ log z for ρ = 0 ρ ρc ( w) = ( ρ) + ( ) Noice ha ( w) has he same sign as ρ. 2 ρ 2 ρ 2 ( wc γ ). (50) How do w and m vary wih p? We can use he firs-order condiions for profi maximizaion o define implici funcions wp ( ) and mp ( ) Differeniaing, we obain f ( ( wp ( )), mp ( )) = wp ( ) (5) f ( ( wp ( )), mp ( )) = p. (52) m f (, m) ( w) w ( p) + f (, m) m ( p) = w ( p) (53) m f m(, m) ( w) w ( p) fmm(, m) m + ( p) =. (54) We can solve his sysem of wo equaions in he wo unknowns w ( p) and m ( p) o obain w ( p) = f m(, m) f (, m) f (, m) f (, m) f (, m) ( w) 2 ( ) mm mm m (55) m ( p) = f (, m) ( w). (56) f (, m) f (, m) f (, m) f (, m) ( w) 2 ( ) mm mm m As long as he denominaor of hese expressions is negaive, real wages fall wih an increase in p, a deerioraion of he erms of rade. If f (, m) ( w) is posiive, impors fall. Noice ha we can consruc examples where ρ < 0 implies ha ( w) < 0, so ha deerioraions o he erms of rade force he consumer o work more. 5

17 Leing c( p) = f( ( w( p)), m) pm( p), we can use he envelope heorem o show ha he change in consumer welfare induced by a change in he erms of rade is d ucp (( ), ( wp ( ))) = u c( c, ) m < 0. (57) dp Wha happens o real GDP and produciviy when he erms of rade change? Firs consider real GDP: Y( p ) = f( ( w( p )), m( p )) p m( p ) (58) dy ( p ) = f (, m) '( w) w'( p) + fm(, m) m ( p) p0m ( p) (59) dp + dy ( p ) = f (, m) ( w) w ( p) + ( p p0) m ( p). (60) dp + The firs erm on he righ-hand side of equaion (60) is he change in real GDP induced by he change in labor supply, and he second erm is he same as in he model wih inelasic labor supply. Noice ha real GDP can eiher rise or fall wih an increase in he erms of rade, bu, if ( w ) > 0, which implies ha w ( p ) < 0, and if ( p p0) m ( p) is small, real GDP falls. When real GDP is measured using a chain-weighed index and ( ) > 0, real GDP always falls. Now consider produciviy Y( p ) / ( w( p )) : 2 + ( ( )) ( ) d Y( p ) ( w) Y ( p ) Y( p ) ( w) w ( p ) =. (6) dp w p w Subsiuing in he expressions Y( p ) in (58) and for Y ( p ) in (60), we obain d dp Y( p ) w ( ) ( p p ) m( p ) m ( w) w( p ) = ( w( p)). (62) Once again, his erm is close o zero if p p0 is close o zero. When real GDP is measured wih a chain-weighed index, all of he change in GDP comes from a change in labor effor, so here is no effec on TFP. In he fixed coefficiens case, real GDP is 6

18 Y( p ) = ( p b) ( w( p )), (63) 0 and produciviy does no change as he erms of rade change. As our C.E.S. example shows, he impac of a change in he erms of rade on he labor supply is very sensiive o he specificaion of he consumer s uiliy funcion. In a model in which he rade balance varies, a change in he rade balance generaed by a change in he erms of rade can induce an addiional change in he labor supply. The response of he labor supply o a change in he rade balance is also sensiive o he specificaion of he consumer s uiliy funcion, as poined ou by Chakrabory (2006). Unforunaely, here is lile agreemen among economiss on how o specify consumers uiliy for leisure. See Blundell and MaCurdy (999) for a classic reference and Rogerson and Wallenius (2007) for a recen aemp o reconcile esimaes of labor supply elasiciies obained by microeconomiss wih hose obained by macroeconomiss. Forunaely, in erms of he issue addressed in his paper, his uncerainy abou he specificaion of labor supply is no very relevan. If we wan o sudy evens like he sharp deerioraions in he erms of rade ha have occurred in Mexico and he Unied Saes over he pas few decades, he growh accouning in secion 2 has shown us ha he corresponding drops in real GDP were generaed mosly by drops in TFP, no by drops in he labor supply Tariffs In his secion, we consider a model wih ariff disorions. We model ariff revenues as a lump-sum rebae o he represenaive consumer. In he presence of ariff disorions, changes in he erms of rade can have firs-order effecs on real GDP and produciviy because he firsorder condiion (9) is disored, alhough hese effecs are small o he exen ha ariffs are small or he producion funcion f is close o fixed coefficiens. We also exend our resuls o ariff changes and show ha hey are much like erms of rade shocks, excep ha ariff revenues are spen domesically. Once again, a useful benchmark is provided by he closed economy model. We assume ha he governmen imposes an ad valorem ax τ on inermediae inpus. To keep he discussion simple, assume again ha he labor supply is fixed. A compeiive economy chooses m o solve max f (, m ) ( +τ ) am. (64) 7

19 In he case where f is coninuously differeniable, he firs-order condiion is f (, m ) = ( +τ ) a. (65) m We firs consider he case where τ is fixed and a flucuaes. The implici funcion heorem implies ha + τ m ( a ) = < 0. (66) f (, m(( + τ ) a )) mm How do real GDP change and consumpion change? Ya ( ) = ca ( ) = f(, m(( + τ ) a )) a m(( + τ ) a ) (67) dy ( a) dc( a) = = τam (( + τ) a) m(( + τ) a) (68) da da + + Noice ha he ax disorion inroduces an addiional erm ino (3). We now consider he case where a is fixed and τ flucuaes: a m ( τ ) = < 0 f (, m(( + τ ) a )) mm (69) Y( τ ) = c( τ ) = f(, m(( + τ ) a )) a m(( + τ ) a ) (70) dy ( τ ) dc( τ ) = = τ am ( τ ) (7) dτ dτ + + To he exen ha he ax before he increase, τ, is close o zero, he firs-order impac of increasing τ is small. In he fixed coefficiens case, where m ( τ ) = 0, real GDP does no change. In he calculaions in he open economy case, where τ is an ad valorem ariff on impors, flucuaions in ariffs have he same impac on real GDP as do flucuaions in he erms of rade: Y( p ) = Y( τ ) = f(, m(( + τ ) p )) p m(( + τ ) p ) (72) dy ( p ) = (( + τ ) p p0) m ( p) (73) dp + 8

20 dy ( τ ) = (( + τ ) p p0) m ( τ ) (74) dτ + Noice ha he effec on real GDP of an increase in he erms of rade, or of an increase in he ariff, is close o zero o he exen ha eiher ( + τ ) p p0 is close o zero or o he exen ha f is close o a fixed proporions funcion. In erms of he impac on consumpion and welfare, he wo cases are very differen, however: c( p ) = c( τ ) = f(, m(( + τ ) p )) p m(( + τ ) p ) (75) dc( p ) = τpm (( + τ) p) m(( + τ) p) (76) dp + dc( τ ) = τpm (( + τ) p) (77) dτ + Consumpion falls much more in he case of a deerioraion of he erms of rade han i does when ariffs are increased because he revenue generaed is rebaed o he represenaive consumer. 6. Elasiciy of subsiuion Excep for he case where he producion funcion f combines domesic inpus and impored inpus in fixed proporions where here are analyical formulas for real GDP we have relied on he implici funcion heorem and firs-order approximaions o deermine he impac of erms of rade shocks on real GDP. In his secion, we invesigae he impacs of large shocks for he case where f is consan elasiciy of subsiuion: (, ) ( β) ( ) β f m = + m, (78) ρ ρ ρ where he parameer β deermines he share of impors in producion. Again, for simpliciy, we consider he case in which labor is fixed, =. The elasiciy of subsiuion beween impored inermediaes and labor which corresponds o all domesic inpus in a more general model is σ ( ρ ) =. This elasiciy is frequenly referred o as he Armingon elasiciy. Like he elasiciy of labor supply, he Armingon elasiciy is he subjec of considerable disagreemen 9

21 among reseaerchers. Trade economiss esimae his elasiciy o be large, on he order of 5 2, while open economy macroeconomiss esimae i o be small, on he order of 0 2. See Ruhl (2005) for a recen aemp o reconcile hese esimaes. Producers choose m o minimize coss, min p m (79) (( ) ) β βm ρ ρ s.. + ρ y. We can use he firs-order condiion o obain he demand for impors ρ ρ ρ ( ) = ( β ) ( β β) m p p ρ ρ ρ. (80) This allows us o express real GDP in base period prices as ρ ( ) ( β) β ( ) ρ ρ ( ) 0 ( ) Y p = + m p p m p. (8) Before sudying how real GDP changes are relaed o he elasiciy of subsiuion, we mus choose a value for β. The firs-order condiion for he producers problem (79) implies ha m ρ ρ ρ β (( β) + βm ) p = ρ. (82) The lef-hand side of he equaion is he share of impors in gross oupu. For each value of ρ we choose he parameer β so ha impors make up 8 percen of gross oupu when he impor price is one. This value is consisen wih U.S. daa, where impors average 7.8 percen of gross oupu in he NAICS classified daa over he period In figure 3, we plo he changes in real GDP ha resul from changes in he erms of rade for several values of he elasiciy of subsiuion. In his example, we have assumed ha he erms of rade in he period prior are he same as hose in he base year, so he firs-order effec is zero in equaion (22). The absence of a firs-order effec can be seen in he figure, where he change in real GDP from a small change in he erms of rade is negligible. The figure also shows he impac of larger changes in he erms of rade. The elasiciy of subsiuion beween 20

22 domesic and foreign inpus is commonly specified a or around 2.0 in inernaional real business cycle models. The average annual change in absolue value of he erms of rade for OECD counries is abou 3.5 percen. A 3.5 percen increase in he relaive price of impors leads o a percen decrease in real GDP when he elasiciy of subsiuion beween domesic and foreign facors is 2.0. When he elasiciy of subsiuion is 6.67, he same deerioraion of he erms of rade causes a percen decrease in real GDP, and, when he elasiciy is 0.33, a 3.5 percen increase in he erms of rade decreases real GDP by percen. Alhough an increase in he erms of rade has lile effec on real GDP, is effec on consumpion can be significan. In figure 4, we plo he change in consumpion ha resuls from changing he erms of rade. The less subsiuable impors are in producion, he more painful are increases in he price of impors. In he fixed proporions case, in which real GDP does no change a all wih he erms of rade, he consumpion and welfare effecs of a change in he erms of rade are he larges. 7. Alernaive income measures If real GDP does no accuraely reflec he real purchasing power of an open economy, are here measures ha do? In his secion we discuss measures of real domesic income ha incorporae he erms of rade. GDP in curren prices represens he curren value of boh producion and income in boh open and closed economies. (Alhough, in some circumsances, we may wan o use gross naional produc [GNP] as a measure of income because i adjuss for income earned abroad.) Real GDP and real income, hough equivalen in a closed economy, are no necessarily equivalen in an open economy. The difference beween real GDP and real gross domesic income in he open economy arises from he deflaion of he rade balance. Real GDP is compued by deflaing he curren value of he componens of GDP by heir respecive implici price deflaors, P, C I G X M GDP = + + +, (83) C I G X M P P P P P while one mehod of compuing real income is 2

23 GDI C I G X M = (84) C I G M P P P P Noice ha real GDP, as a measure of producion, values expors as an oupu and impors as an inpu, while real GDI values he nominal rade balance in erms of he amoun of impors ha i purchases. The U.S. Bureau of Economic Analysis (2006) refers o he income measure in equaion (84) as command-basis GDP, raher han as real gross domesic income as i is defined in he Unied Naions 993 Sysem of Naional Accouns (200). (I is acually command-basis GNP, raher han GDP, ha is ypically repored.) The Unied Naions (200) also allows for several definiions of real GDI ha differ by he index used o deflae X M, including he expor price index and he domesic absorpion price index. The Unied Naions (200) allows for various definiions of he GDI because here is no naural way o deflae he proceeds from foreign rade. The debae over he real rade balance in he naional income and produc accouns is a long one, going back o he early era of naional income accouning. Working wihin he NIPA framework, Nicholson (960), Bjerke (968), and ohers proposed differen mehods of deflaing he income from rade, wih mos of hem arguing for eiher he impor or he expor price deflaor, hough some (Burge and Geary 957) propose using one deflaor when he rade balance is posiive and anoher when he rade balance is negaive. As index number heory progressed, prominen researchers in he field developed alernaive indices of welfare and produciviy (Diewer and Morrison 986) and real domesic income (Kohli 2004) ha accouned for he erms of rade. Which mehod should we use? Mahdavy and Silver (989) compare hese mehods and find ha, for mos indusrial counries, he choice of deflaor is no imporan. They find he choice of deflaor can be imporan for non-indusrial counries. For simpliciy, and o be consisen wih he mehods used by he BEA, we will use he command-basis GDP measure (84) in wha follows. Command GDP offers an alernaive way of viewing a counry s performance. For counries in which eiher he erms of rade have been sable or rade is no an imporan facor in oupu, real GDP and command GDP are similar. The Unied Saes is a good example of his case. In figure 5 we plo real GDP and command GDP for he Unied Saes, as well as he erms of rade. The erms of rade have sayed fairly seady over he las 20 years, and command GDP and real GDP are almos indisinguishable. In conras, Swizerland s erms of rade have 22

24 seadily improved, falling 2.4 percen since 98, as can be seen in figure 6. The figure also shows how command GDP has grown significanly faser han real GDP in Swizerland; from command GDP grew 0.2 percen more han real GDP. Command GDP grew a.8 percen per year over his period, compared o he.5 percen per year growh in real GDP. Some Swiss economiss, noably Kohli (2004), have used measures similar o command GDP o help explain why hey do no believe he Swiss economy is doing poorly, despie he lack of growh in real GDP since 973. For furher discussion of Swizerland s economic performance, including he impac of he erms of rade, see Kehoe and Ruhl (2003, 2005). Recenly, Feensra, Heson, Timmer, and Deng (2004) have proposed adding he purchasing power pariy equivalen of he SNA concep of GDI o he Penn World Table, where he domesic absorpion price index is used o deflae he rade balance. They argue ha i is his concep of naional income ha should be used when researchers are ineresed in sudying welfare, while he radiional concep of real GDP should be used when researchers are ineresed in sudying producion. The Penn World Table now provides daa on boh real GDP and real GDI. Wha concep of real GDP was provided in he Penn World Table previously? Feensra, Heson, Timmer, and Deng (2004) argue ha inconsisencies in he GDP calculaions make i neiher one nor he oher and ha hese inconsisencies need o be eliminaed and boh variables need o be repored. 7.. Business cycle frequencies I is appropriae o model some counries as small open economies. These counries are small in he sense ha hey do no influence world prices, and hus he counry s erms of rade are exogenously given. I is easy o imagine one of hese small open economies being buffeed by shocks o is erms of rade and his in urn affecing he couny s GDP. Alhough erms of rade shocks canno have much of an effec on real GDP, paricularly given he magniude of hese shocks and he low level of subsiuabiliy usually assumed in hese models, we can use he command GDP measure o calculae how real income changes over he business cycle. Figures 7 and 8 plo Hodrick-Presco filered log real GDP and log command GDP for he Unied Saes and Swizerland. We use he sandard quarerly smoohing parameer of 600 in consrucing hese daa. For he Unied Saes, he wo measures are nearly idenical, bu his 23

25 is no rue for Swizerland. Command GDP in Swizerland is 6.8 percen less volaile han real GDP. The series do no move as closely eiher; he correlaion coefficien is Crises A crisis in a developing economy may be accompanied by deerioraions of he counry s erms of rade. Mexico, for example, has weahered wo crises in he las 30 years, he firs in , and he second in As repored in able, he erms of rade increased by 26.4 percen from 982 o 983 and by 8.7 percen from 994 o 995. These periods were also periods of significan declines in oupu: from 982 o 983, real GDP fell by 4.3 percen, and from 994 o 995, real GDP fell by 6.2 percen. We have seen in he previous secions ha he change in he erms of rade canno be he cause of he declines in real GDP. How does he siuaion change when he rising erms of rade are also aken ino accoun? During he firs crisis, real GDP fell by 4.3 percen, bu command GDP real domesic income fell by 6.5 percen. Command GDP fell by more during he second crisis as well, declining 7.8 percen from 994 o 995 compared o he 6.2 percen decline in real GDP over he same period. The oupu drops associaed wih financial crises like he ones in Mexico are frequenly used as evidence of he painful naure of he wihdrawal of credi o a counry. The evidence on real domesic income suggess ha hese sudden sop episodes are even more painful han he GDP evidence suggess! 8. Concluding remarks In sandard models, an adverse shock o he erms of rade acs like an adverse shock o produciviy along many dimensions: income and consumpion fall. In one crucial dimension, however, a erms of rade shock acs nohing like a produciviy shock: real GDP, he mos common measure of a counry s oupu, is ofen unchanged in sandard models. In reurning o our original quesion, if we are o use real GDP as a measure of producion, hen oal facor produciviy also remains unchanged. Alhough he erms of rade are shocks o a counry s income, hey are no shocks o a counry s produciviy. So how can we accoun for he relaions in figures and 2? This paper shows ha we canno expec sandard models o do so. One line of promising research argues ha here are oher responses o erms of rade shocks. The change in relaive prices may induce reallocaions 24

26 across goods and secors ha involve nonproducive aciviies like reraining, or capial may go idle, boh conribuing o lower oupu and measured TFP. The lieraure on developing counry crises is one area in which progress is being made in modeling he fricions ha may help accoun for he relaion beween he erms of rade, real GDP, and produciviy. Beginning wih sandard models, Meza and Quinin (2007) inroduce labor hoarding and variable capial uilizaion, Mendoza (2006) inroduces financial marke fricions, and Kehoe and Ruhl (2006) inroduce fricions in reallocaing labor across secors. These papers have had some success in replicaing he relaions discussed above, bu he exac specificaion and he quaniaive imporance of hese fricions remains a quesion for fuure research. Our ineres in large deerioraions in he erms of rade has led us o focus on he negaive correlaion beween he erms of rade and TFP ha is eviden in he daa: In figures and 2 when he erms of rade deeriorae sharply, so does produciviy. Figure 9, however, presens some daa ha should serve as a cauion o researchers. In conras o he paerns in figures and 2, in Swizerland over he period , improvemens in he erms of rade have been associaed wih declines in real GDP and in TFP, wih correlaion coefficiens of 0.54 and 0.55, respecively. 25

27 References Becker, T. and P. Mauro (2005), Oupu Drops and he Shocks ha Maer, IMF Working Paper Bjerke, K. (968), Some Reflecions on he Terms of Trade, Review of Income and Wealh, 4, Blundell, R. and T. MaCurdy (999), Labor Supply: A Review of Alernaive Approaches, in O. Ashenfeler and D. Card, ediors, Handbook of Labor Economics, Volume 3. Elsevier Science, Bureau of Economic Analysis (2006), A Guide o he Naional Income and Produc Accouns of he Unied Saes, hp:// Burge, R. W. and R. C. Geary (957), Balancing of a Sysem of Accouns in Real Terms, A Sysem of Price and Quaniy Indexes for Naional Accouns. Unied Naions. Chakrabory, S. (2006), Modeling Sudden Sops: he Role of Preferences, Baruch College, Ciy Universiy of New York. Conesa, J. C., T. J. Kehoe, and K. J. Ruhl (2007), Modeling Grea Depressions: The Depression in Finland in he 990s, Federal Reserve Bank of Minneapolis Quarerly Review, 3:, Diewer, W. E. and C. J. Morrison (986), Adjusing Oupu and Produciviy Indexes for Changes in he Terms of Trade, Economic Journal, 96, Easerly, W., R. Islam, and J. E. Sigliz (200), Shaken and Sirred: Explaining Growh Volailiy, in B. Pleskovic and N. Sern, ediors, Annual World Bank Conference on Developmen Economics The World Bank, 9 2. Easerly, W., M. Kremer, L. Priche, and L. H. Summers (993), Good Policy or Good Luck? Counry Growh Performance and Temporary Shocks, Journal of Moneary Economics, 32, Feensra, R. C., A. Heson, M. P. Timmer, and H. Deng (2004), Esimaing Real Producion and Expendiures across Naions: A Proposal for Improving he Penn World Tables, NBER Working Paper Hamilon, J. D. (983), Oil and he Macroeconomy since World War II, Journal of Poliical Economy, 9, Kehoe, T. J. and K. J. Ruhl (2003), Recen Grea Depressions: Aggregae Growh in New Zealand and Swizerland, , New Zealand Economic Papers, 37, Kehoe, T. J. and K. J. Ruhl (2005), Is Swizerland in a Grea Depression? Review of Economic Dynamics, 8,

28 Kehoe, T. J. and K. J. Ruhl (2006), Sudden Sops, Secoral Reallocaions, and Real Exchange Raes, Universiy of Minnesoa and Universiy of Texas a Ausin. Kohli, U. (983), Technology and he Demand for Impors, Souhern Economic Journal, 50, Kohli, U. (2004), Real GDP, Real Domesic Income, and Terms of Trade Changes, Journal of Inernaional Economics, 62, Mahdavy, K. and M. Silver (989), The Measuremen of a Naion s Terms of Trade Effec and Real Naional Disposable Income wihin a Naional Accouning Framework, Journal of he Royal Saisical Sociey, 52, Mendoza, E. G. (2006), Endogenous Sudden Sops in a Business Cycle Model wih Collaeral Consrains: a Fisherian Deflaion of Tobin s Q, Universiy of Maryland. Meza, F and E. Quinin (2007), Financial Crises and Toal Facor Produciviy, The B.E. Journal of Macroeconomics, 7: (Advances), aricle 33. Nicholson, J. L. (960), The Effecs of Inernaional Trade on he Measuremen of Real Naional Income, Economic Journal, 70, Rogerson, R. and J. Wallenius (2007), Micro and Macro Elasiciies in a Life Cycle Model wih Taxes, NBER Working Paper 307. Ruhl, K. J. (2005), The Elasiciy Puzzle in Inernaional Economics, Universiy of Texas a Ausin. Unied Naions (200), Sysem of Naional Accouns 993, Inerne Access Sysem, hp://unsas.un.org/unsd/sna993/inroducion.asp. 27

29 Table Comparison of real GDP and command GDP during he crises in Mexico Real GDP (percen change) Command GDP (percen change) Terms of Trade (percen change)

30 Figure Unied Saes erms of rade growh rae real GDP oal facor produciviy Figure 2 Mexico erms of rade growh rae real GDP -0.0 oal facor produciviy