Federal Reserve Bank of Chicago

Transcription

1 Is he Unied Saes an opimum currency area? An empirical analysis of regional business cycles Federal Reserve Bank of Chicago By: Michael A. Kouparisas WP

2 Is he Unied Saes an opimum currency area? An empirical analysis of regional business cycles Michael A. Kouparisas Federal Reserve Bank of Chicago P.O. Box 834 Chicago IL December 2001 Absrac This paper develops a saisical model o sudy he business cycles of he eigh U.S. BEA regions. By combining unobserved componen and VAR echniques I idenify no only common and idiosyncraic sources of innovaion, bu also common and idiosyncraic responses o common shocks. Using his model, I show, a he usual levels of saisical significance, ha U.S. regions deviae significanly from Mundell s noion of an opimum currency area. I idenify five core regions ha have similar sources of disurbances and responses o disurbances (New England, Mideas, Grea Lakes, Rocky Mounains and Far Wes) and hree non-core regions ha differ significanly from he core in heir sources of disurbances and/or responses o disurbances (Souheas, Plains and Souhwes), a business cycle frequencies. JEL Classificaion: E32; E52; R11. Key Words: VAR; Unobserved Componens; Moneary Union;. I would like o hank Charles Evans for helpful discussions and Carrie Jankowski for excellen research assisance. All errors and omissions are mine. The views expressed herein are hose of he auhor and no necessarily hose of he Federal Reserve Bank of Chicago or he Federal Reserve Sysem.

3 1 Inroducion There was a grea deal of doub over he long-run viabiliy of he U.S. Federal Reserve Sysem in 1913, largely because i followed wo previously unsuccessful aemps a esablishing a U.S. cenral bank. 1 Similarly, here is widespread skepicism oday surrounding he long-run viabiliy of he EMU. Alhough, he debae over he viabiliy of he EMU is more focused han he earlier FRS debae. This is due in large par o seminal work on currency areas by Mundell (1961). Mundell argued ha he survival of a currency union depends on how close i comes o he noion of an opimum currency area (OCA). According o his heory, if a moneary union is no an OCA, hen some of is members will incur macroeconomic coss (persisen high unemploymen and low oupu) ha will ouweigh he microeconomic benefis of a single currency (lower ransacion and hedging coss), forcing hem o abandon he union. Many commenaors argue ha common moneary policy acions will be damaging o some member counries because he EMU is a long way from an OCA. 2 Since Mundell s work, economiss have basically agreed ha four crieria mus be me for a group of regions/counries o consiue an opimal currency area: (i) regions should be exposed o similar sources of economic disurbance (common shocks); (ii) he relaive imporance of hese shocks across regions should be similar (symmeric shocks); (iii) regions should have similar responses o common shocks (common responses); and (iv) if regions are subjec o regionspecific economic disurbances (idiosyncraic shocks), hey need o be capable of quick adjusmen. The basic idea is ha regions saisfying (i)-(iv) will have similar business cycles, so a common moneary policy response would be opimal. 1 The Firs Bank of he Unied Saes was disbanded in 1811, and he naional charer of he Second Bank of he Unied Saes expired in 1836 afer is renewal was veoed four years earlier by Presiden Andrew Jackson. 2 See, for example, Euro brief: The meris of one money The Economis, Ocober 28, 1998, pp

4 How far he EMU is from an OCA is an open quesion for research. A firs glance, he daa seem o suppor he skepics view ha he EMU is no an OCA. Firs, EMU counries have experienced frequen and ofen large idiosyncraic shocks over recen years. A well-known example is German reunificaion. Second, persisen high unemploymen raes hroughou Europe sugges ha EMU economies are slow o adjus o all economic disurbances. These observaions have spawned a small, bu growing body of formal empirical research ha assesses he long-run viabiliy of poenial European currency unions. These papers ypically approach he issue of wheher a region will be a viable moneary union by comparing he region wih a well-funcioning moneary union (he U.S.) along OCA crieria. 3 The basic idea is ha if he moneary union is as close as he U.S. is o an OCA, hen here can be no presumpion ha he moneary union will no be viable in he long run. Alernaively, if he moneary union is less like an OCA han he U.S., hen here is some doub abou he long-run viabiliy of he moneary union. Implici in his hypohesis is he criical join assumpion ha saisfying OCA crieria is sufficien for a moneary union o be viable and ha he U.S. is an OCA. This paper examines he usefulness of his research o he EMU debae by formally invesigaing wheher he U.S. is an OCA. I do so, by esimaing a quarerly srucural vecor auoregression (VAR) ha allows me o examine wheher he eigh U.S. Bureau of Economic Analysis (BEA) regions saisfy (i)-(iv). The VAR includes he growh raes of real personal income in he BEA regions, he relaive price of oil, and a moneary policy variable (federal funds rae). The esimaion period is 1969:Q1 o 2002:Q1. Model based forecas error decomposiions sugges ha U.S. regions are largely subjec o common sources of innovaion. The relaive imporance of common shocks differs somewha across regions. However, he main influence on regional aciviy appears o be a common shock 3 See for example Eichengreen (1992), Eichengreen and Bayoumi (1993), and Kouparisas (1999). 2

5 o income ha is no explained by shocks o he relaive price of oil or moneary policy. Impulse responses funcions esimaed from he VAR sugges ha, wih he excepion of he Plain and Souhwes regions, U.S. regions have similar responses o common shocks. Variance decomposiions sugges ha here is a grea deal of variaion in he share of income flucuaions explained by region specific shocks. While, he model s impulse response funcions suggess ha regions adjus quickly o region specific disurbances, wih mos of he adjusmen o hese shocks occurring in he firs year afer he shock. The remainder of he paper is organized as follows. Secion 2 inroduces he daa by way of he second-momen properies of he business cycle componens of U.S. regional income. Secion 3 describes in deail he srucural VAR and esimaion sraegy. The empirical findings of he paper (deails of forecas error decomposiions, variance decomposiions and impulse response funcions) are repored in secion 4. Secion 5 concludes by summarizing he paper s main findings. 2 Business cycle properies of U.S. regional income A simple and direc way of making a preliminary assessmen of wheher he U.S. is an OCA is o calculae he correlaion beween U.S. regional business cycles. A high correlaion implies common sources of disurbances and similar responses o disurbances across U.S. regions, while a low correlaion indicaes differences in he sources of disurbances and/or differen responses o disurbances across U.S. regions. Regional cyclical flucuaions are esimaed by applying a Baxer and King (1999) business cycle band-pass filer o U.S. Deparmen of Commerce, Bureau 3

6 of Economic Analysis (BEA) quarerly sae personal income from 1969:Q1 o 2001:Q1, deflaed by he naional consumer price index. 4,5 Esimaes repored in firs column of he upper panel of Table 1 indicae a high level of comovemen across U.S. regions, wih he conemporaneous correlaion beween regional and aggregae U.S. income ranging from 0.77 for he Souhwes o 0.99 for he Souheas. A similar picure emerges for he inerregional correlaion saisics. Regions ha are geographically close end o have correlaion coefficiens ha are higher han regions ha are no geographically close. For example, he correlaion of New England and Mideas business cycle flucuaions is 0.94, while he correlaion beween New England and Souhwes business cycle flucuaions is The lower panel of Table 1 repors he correlaion coefficiens for leads and lags of regional income. The main diagonal describes he persisence of regional flucuaions. Regional cycles are roughly as persisen as he aggregae cycle, wih own-lag-correlaion coefficiens of beween 0.92 and The remaining cells of his panel do no indicae a srong lead/lag relaionship for U.S. regional business cycles a one quarer: here are only a few cases where he lead/lag correlaion exceeds he conemporaneous correlaion and he differences are no saisically significan. The lead/lag relaionship is considerably weaker a longer horizons of wo o four quarers. Overall, hese resuls sugges ha U.S. regions have common sources of innovaion and common responses o hese disurbances. On he basis of hese findings he U.S. can no be ruled ou as an OCA. An obvious weakness of his simple approach is ha i does no allow for a comparison of he sources of disurbances or responses o disurbances across regions. 4 Gross sae produc (GSP) is an alernaive measure of regional aciviy. The main drawback of GSP is ha i is colleced annually, which makes i less able o pick business cycle urning poins wih any precision. 5 The Baxer-King business cycle filer isolaes frequencies of he daa ha occur a 18 monhs o 8 years. I use his filer in large par because hese frequencies are arguably of more ineres o policymakers. 4

7 3 Empirical mehod One way of overcoming he limiaions of he simple correlaion analysis is o use a srucural vecor auo regression (VAR). Wih appropriae parameer resricions a VAR can idenify common and idiosyncraic sources of innovaion, and idenify he shape of common and idiosyncraic responses o common shock. 3.1 The model I approach he problem of idenifying shocks and responses o shocks by classifying hem as eiher being common or idiosyncraic. Common shocks affec all regions, while idiosyncraic shocks only affec one region. Similarly, a common response is a response o common shock ha is he same across regions, while an idiosyncraic response is a response o a common shock ha is region specific. Working oward ha end, I assume ha he log-firs-difference of real regional income in region i a ime, y i, is he sum of wo unobserved componens, a common componen of regional oupu x and an idiosyncraic (or region specific) componen x i. I permi regions o have differen sensiiviy o he common componen governed by a parameer γ i, so ha, y = γ x + x, (1) i i i for all i = 1,...,8. In his seing, if U.S. regions had no idiosyncraic componen x i, hen regional income yi would simply be proporional o he common componen x, heir business cycles would be perfecly correlaed and hey would easily saisfy he OCA crieria, (i)-(iv). I follow he lieraure on regional business cycles by allowing for wo oher sources of economic disurbance o affec real regional income. In addiion o shocks o he common and 5

8 region-specific income componens, regions are affeced shocks o moneary policy and energy prices. Following many ohers, I use he firs-difference of he level of he federal funds rae as my explici indicaor of moneary policy. While, energy prices are measured as he log-firs difference of he price of oil relaive o he CPI. From here I divide he ime series ino common and idiosyncraic variables. The common variables include x, he moneary policy indicaor m, and he relaive price of energy he idiosyncraic componens are he x s. I idenify shocks o he common variables by i following he approach of he VAR lieraure on idenifying shocks o U.S macroeconomic variables. I do so by reaing he common regional income componen in he same way macroeconomic sudies rea aggregae U.S. income. My approach is mos closely relaed o Chrisiano, Eichenbaum and Evans (1994) in heir work on idenifying and measuring he aggregae effecs of U.S. moneary policy shocks. To be more specific he common componens block of he model focuses on he dynamic behavior of a 3 1 vecor, Z = [ p, x, m ] The dynamics of Z are represened by a VAR, p, while AZ = B( L) Z + e 1 (2) where A is a 3 3marix of coefficiens describing he conemporaneous correlaion among he variables; BL ( ) is a 3 3marix of polynomials in he lag operaor L ; and e = [ ε, ε, ε ] is a 3 1 vecor of orhogonal srucural disurbances. p x m Addiional srucure mus be placed on A o idenify he elemens of e. Following Chrisiano, e al. I resric A o be a unique lower riangular marix wih ones along he diagonal. 6

9 The implicaions of ha assumpion are ha: innovaions o x and m ; innovaions o x have a conemporaneous effec on and innovaions o m have a lagged effec on p have a conemporaneous effec on m and a lagged effec on p ; p and x. The underlying assumpion is ha in seing policy he U.S. Federal Reserve boh reacs o and affecs he economy. This is implemened by assuming ha he moneary auhoriies feedback rule can be wrien as a linear funcion, Ψ, defined over a vecor, moneary policy is compleely described by, 33 m Ω, of variables observed a or before dae, so ha m =Ψ( Ω ) + A ε, (3) where ΨΩ ( ) is described by he hird row of BL ( ) and A 33 is he (3,3) elemen of he marix A. I model Ω as conaining lagged values (dae -1 and earlier) of all variables in he common componen block, as well as ime values of hose variables ha he moneary auhoriy looks a conemporaneously in seing policy (energy prices and he common income componen). In accordance he assumpions of he feedback rule, an exogenous shock o moneary policyε m canno conemporaneously affec ime values of he elemens of Ω. However, lagged values of ε m can affec variables in Ω. The idiosyncraic block of he model focuses on he dynamic behavior of a 8 1vecor of idiosyncraic componens of regional income, X = [ x, x,..., x ] I assume ha he relaive price of energy and moneary policy affec he idiosyncraic componen of regional income in a similar way in which hey affec he common componen. In paricular, I assume ha innovaions o p have a conemporaneous effec on x i, while innovaions o have a lagged effec on x i. In conras o he common income componen, innovaions o he m 7

10 idiosyncraic componen are assumed o have no effec on oil prices or moneary policy, eiher conemporaneously or lagged. Underlying his assumpion is he idea ha aggregae energy prices only respond o aggregae income shocks, while he Federal Reserve only reacs o common income flucuaions. I also assume for parsimony ha innovaions o x i do no affec x j for i j, eiher conemporaneously or wih a lag. Under hese assumpions he dynamics of region i s idiosyncraic componen is explained by, x = D( L) x + E ( L) W + ε, (4) i i i 1 i i for all i, where Di ( L) is a scalar polynomial in he lag operaor L ; Ei ( L ) is a 1 2 marix of polynomials in he lag operaor L ; W = [ p, m] ; and ε i is an orhogonal srucural disurbance (ha is, εi ε for all i j). j Following from his, he dynamics of he idiosyncraic componen vecor X are represened by, X = D( L) X + E( L) W + v (5) 1 where DL ( ) D1 ( L) D ( L) 0 L, M M O D8 ( L) 2 = EL ( ) E1 ( L) E ( L), M E8 ( L) 2 = v ε1 ε M ε 8 2 = and e v. Wih his model in hand, I assess he similariy of U.S. regional business cycles along wo dimensions. Firs, by sudying he sources of regional economic disurbances I can deermine he exen o which flucuaions are caused by common and region-specific shocks. Common shocks include unanicipaed changes o energy prices ε p, unanicipaed shocks o moneary policy variable ε m and unanicipaed shocks o he residual common income shock ε x ha capures innovaions o common oupu no capured by he oher common shocks. Idiosyncraic shocks 8

11 include unanicipaed flucuaions in region i s incomeε i. The relaive imporance of he various sources of disurbance is revealed by raios of he sandard deviaions of innovaions and he model s one-sep ahead forecas error decomposiions. Second, by sudying he model s impulse response funcions, I can assess wheher regions have similar responses o common shocks and deermine he ime i akes a region o adjus o idiosyncraic shocks. 3.2 Previous approaches o modeling regional income flucuaions The mos closely relaed sudy is Carlino and Defina (1998), hereafer (CD). 6 They use a srucural VAR o esimae he effecs of U.S. moneary policy on he eigh BEA regions. My approach o idenifying shocks and responses o shocks differs from CD in hree significan ways. Firs, hey assume ha here is no common income componen across he eigh BEA regions. In heir model common shocks o he relaive price of energy and moneary policy affec regional oupu wih a one period lag, while he residual shocks o regional incomes are region specific. This is a major shorcoming of heir sudy since my analysis suggess ha a large share of he variaion regional income across he eigh BEA regions is explained by innovaions in he common income componen. Second, following heir earlier paper Carlino and Defina (1995) hey allow region specific income shocks o spillover o oher regions. However, he approaches of he wo sudies are quie differen. The earlier paper conrols for common shocks by removing a common componen from regional income growh equal growh rae of aggregae income. This is similar o my approach, wih he main difference being ha I allow for he common componen o be esimaed in he model. The saed objecive of allowing for spillovers in he laer paper is so ha here is an 6 Carlino and DeFina (1998) provide an exensive lieraure review of empirical sudies of regional business cycles. 9

12 aggregae income shock affecing regional income in he model. In oher words, his is mean o capure common income flucuaions across regions. CD esimae heir model using firs differences of he log of regional oupu. While here is a very srong correlaion beween curren and lagged regional incomes a business cycle frequencies (see Table 1) he correlaion coefficiens are significanly lower for firs-difference daa, which means ha lagged aggregae regional oupu fails o capure he conemporaneous comovemen of regional income across BEA regions. My model does no allow for spillovers of region specific shocks, since he impulse responses of region specific shocks from oher regions were found o be no significanly differen from zero. Finally, CD allow region-specific shocks o affec he moneary policy variable conemporaneously, while my model only allows he common income shock o affec he moneary policy variable conemporaneously. My approach is arguably more appropriae, since i says ha cenral banks do no respond o idiosyncraic shocks, which is he poin of he debae surrounding he ECB moneary policy. Using his approach CD find ha unanicipaed shocks o U.S. moneary policy have very differen effecs on he income of he eigh BEA regions. They idenify a core group of regions including New England, Mideas, Plains, Souheas and Far Wes and a non-core group including he Grea Lakes, Souhwes and Rocky Mounains. Regions in he core group have very similar responses o moneary policy shocks, while regions in he non-core have very differen responses o moneary policy shocks. Their analysis implies ha he U.S. is no an OCA, since i fails o mee he common response crieria due o he very differen responses of he non-core regions. One of he drawbacks of heir analysis is ha hey do no provide a formal saisical es of he hypohesis ha he responses of regional income incomes o moneary policy vary significanly, 10

13 so i remains an open quesion for research o es if regions respond differenly o moneary policy shocks. 3.3 Daa I esimae he model using quarerly daa from 1969:Q1 o 2001:Q1. Regional income is measured by real personal income across eigh BEA regions. Real incomes are calculaed by deflaing each region s nominal income wih he naional consumer price index (CPI). The relaive price of energy is he Inernaional Moneary Fund s U.S. dollar world crude oil price index deflaed by he U.S. CPI. Following he wealh of empirical research on idenifying moneary policy, I use he federal funds rae as my indicaor of moneary policy. I use maximum likelihood o esimae he model s parameers, so he variables used in he esimaion mus be saionary. Table 2 repors he resuls of Augmened Dickey-Fuller uni roo ess applied o he log-levels and log-firs-differences of real regional income and he relaive oil price, and he levels and firs-difference of he federal funds rae. The null of a uni roo canno be rejeced for any of he log-level daa series a he 5 percen level of significance. However, he null of a uni roo is rejeced for he log-firs-difference daa a he same level of significance. In ligh of his, I specify and esimae he model using he log-firs-differences of real regional income and he relaive oil price, and he firs-difference of he federal funds rae. Finally, I muliply he log-firs-difference daa is by 100 so ha sandard deviaions of disurbances and impulse response funcions are expressed as percenages of regional income. 3.4 Esimaion sraegy The model described by (1)-(5) is a varian of Wason and Engle s (1983) general dynamic muliple indicaor-muliple cause (DYMIMIC) model. This framework allows unobserved variables o be dynamic in naure as well as be associaed wih observed variables. This laer 11

14 feaure is an imporan par of he presen sudy, since one he goals is o see how much of he variaion in he common income componen is explained by shocks o observed variables (moneary policy and energy prices). DYMIMIC models are esimaed using maximum likelihood. Likelihood funcions are evaluaed by using he Kalman filer on he model s sae space represenaion. In my case he sae space represenaion of he model is described by he following: measuremen equaion, 081 I8 8 0 Y Y I Γ X ε 0 p W = 2 8 A 02 8 B( L) W C( L) ε m (6) and ransiion equaion, DL ( ) 0 EL ( ) v X = X 1 W 0 Dx( L) + + Ex( L) ε x (7) where Y = [ y1, y2,..., y8] ; A is an 2 2 lower riangular marix; BL ( ) is an 2 2 marix of polynomials in he lag operaor L; Γ= [ γ1, γ2,..., γ8] ; CLis ( ) an 2 1 marix of polynomials in he lag operaor L; X = [ X, x ] ; D ( L ) is a scalar polynomial in he lag operaor L; E ( L ) is x an1 2 marix of polynomials in he lag operaor L. These parameer marices map ino he model specified in (1)-(5) in he following way, x A= E x (0) , while A21 C(0) 12 1 BL ( ) 11 CL ( ) 11 BL ( ) 12 BL ( ) = Ex( L) 11 Dx( L) Ex( L) 12 BL ( ) 21 CL ( ) 21 BL ( ) 22 for all L 1 Idenifying he parameers ha govern he common income componen, idiosyncraic responses and srucural disurbances requires addiional normalizaion resricions. The variance of he common income componen s srucural disurbance is idenified by normalizing γ i o 12

15 uniy for one of he eigh regions. The idiosyncraic responses of regional income o unanicipaed shocks o he relaive oil price and moneary policy are idenified by normalizing one region s idiosyncraic responses o be he same as he common income componen s responses. In oher words, he idiosyncraic responses are idenified by resricing Ei ( L ) = 0 for one of he eigh regions. I use he Souheas as he normalizing region since i is has he highes correlaion wih aggregae U.S. income and i has virually he same ampliude as aggregae U.S. income, a business cycle frequencies. The lag lengh of he model is deermined by changes in he value of he likelihood funcion. The number of lags of all variables was increased up o he poin where he likelihood raio saisic could no rejec he null ha he addiional parameers were joinly equal o zero. Using his crierion he model was resriced o wo lags in all variables. I esimae he DYMIMIC model using he recursive EM algorihm described in Wason and Engle (1983). To avoid local opimizaion problems I examined a wide range of saring values and impose severe convergence crieria on he parameer space of Sandard errors of he parameers are esimaed using a sandard gradien search algorihm o evaluae he marix of second derivaives of he likelihood funcion a he EM parameer esimaes. 3.5 Variance decomposiions a business cycle frequencies A goal of his paper is o decompose he variance of regional income a business cycle frequencies according o he various common and idiosyncraic sources of innovaion. I do his by way of a linear filer GLha ( ) allows me o map from he covariance of he firs-difference of he regional income o he covariance of he business cycle componens of regional income. The precise form of he filer is, GL ( ) = BP ( ) 6,32 L, where 6,32 1 L BP ( L ) is he Baxer-King approximae band-pass filer for quarerly daa; and L is he lag operaor. The mapping of covariance of he 13

16 firs-difference daa o covariance of he business cycle frequency daa is carried using sandard specral/fourier analysis ools. 4 Empirical resuls Wih esimaes of he model in hand, I assess he similariy of U.S. regional business cycles along wo dimensions. Firs, by sudying he sources of regional economic disurbances I deermine he exen o which flucuaions are caused by common and region-specific shocks. Second, by sudying he model s impulse response funcions, I assess wheher regions have similar responses o common shocks and deermine he ime i akes a region o adjus o idiosyncraic shocks. 4.1 Sources of variaion The upper panel of Table 3 describes he level of he esimaed sandard deviaion of he model s eleven srucural disurbances, while he lower panel of Table 3 describes he relaive volailiy of region-specific shocks, using he Souheas as he normalizing region. Focusing on he upper panel, we see ha innovaions o he common income componen are esimaed o have a sandard deviaion ha is more han more han wice as large are he sandard deviaion of region specific shock o he Souheas. This implies ha common shocks are an imporan source of variaion in he Souheas. While, he lower panel reveals ha here is a grea deal of saisically significan variaion in he relaive size of he sandard deviaions of regionspecific shocks. Esimaes range from 1.29 for he Grea Lakes up o 2.85 for he Plains, which, holding oher hings consan, suggess ha region specific shocks are more imporan source of income variaion in he Plains han in he Grea Lakes. Decomposiions of he forecas errors of regional income repored in Table 4, provide a more complee picure of he relaive imporance of disurbances. These decomposiions indicae he share of he forecas error aribuable o a paricular disurbance for a given horizon. The one- 14

17 sep-ahead errors are informaive abou he similariy of he sources of disurbances across regions, while sep lenghs of greaer han one conain join informaion abou he similariy of disurbances and responses o disurbances. Table 4 reveals ha a large share of he disurbance o U.S. regions is due o common shocks (ha is, unanicipaed shocks o oil prices, moneary policy, and common income componen). For example, common disurbances explain a large share of he Souheas s one-sep-ahead forecas error, 87 percen. The Plains appear o have he larges region-specific influences, wih only 47 percen of he variaion in heir one-sep-ahead forecas error explained by common disurbances. The six oher regions fall in beween, wih common disurbances explaining roughly 58 o 76 percen of he variaion in heir one-sep-ahead forecas errors. The relaive imporance of differen common disurbances is similar across regions. Shocks o he common income componen are considerably more imporan han shocks o oil prices and moneary policy a all forecas horizons. Wih he excepion of he Souheas and Plains, hese resuls sugges ha U.S. regions have similar sources of economic disurbances. Table 4 also provides some indicaion of he similariy of responses o disurbances. Looking a horizons of greaer han one quarer, he relaive imporance of common and idiosyncraic disurbances is similar across regions. This suggess ha responses o common and idiosyncraic shocks are similar. A common finding is ha unanicipaed shocks o he common income componen are less imporan a longer horizons. 4.2 Impulse response funcions Figures 1 o 6 describe in deail he cumulaive responses of he log-firs-difference of income of he eigh BEA regions o common shocks. These impulse response funcions describe he way ha he level of regional income responds over ime o a permanen one-sandard deviaion shock o he relaive price of oil, he federal funds rae, and common componen of income. The 15

18 responses are presened in wo ways. Firs, I plo he regional responses agains each oher o esablish differences across he regions. Nex, I plo he individual responses wih heir 95 percen confidence inerval. 7 Figure 1 shows ha an unanicipaed rise in he relaive price of oil has a negaive effec on income in all eigh regions. Regions can be broken up ino hree groups. The Plains response is much larger han in he Souheas, while he responses in he Souhwes, Rocky Mounains and Far Wes are much weaker han in he Souheas. Responses of he remaining regions are similar o hose of he Souheas. Figure 2 reveals ha wih he excepion of he weak response group, he response funcions of he regions are all significanly differen from zero. Figure 3 reveals ha an unanicipaed shock o moneary policy (an unexpeced rise in he federal funds rae) also has a negaive effec on regional income in all eigh regions. Regions fall ino wo groups. New England, Mideas, Souhwes and Far Wes have weaker responses han he Souheas, while he Grea Lakes, Plains and Rocky Mounains have responses ha are sronger han he Souheas. The responses are shown in Figure 4 o be significanly differen from zero across all regions wo o hree quarers afer he shock, which reflecs he well known lagged effec of moneary policy. Responses o an unanicipaed increase in he common income componen are described in Figure 5. Regions fall ino hree groups. The Plains, Souhwes, and Rocky Mounains have sronger responses han he Souheas, while he Mideas has a weaker response han he Souheas. New England, Grea Lakes and Far Wes have responses ha are similar o he Souheas. Figure 6 reveals ha hese responses are all significanly differen from zero a all lags. 7 Confidence inervals are calculaed by Mone Carlo mehods. Following Hamilon (1994) secion 11.7, I randomly draw from he esimaed disribuion of he model s parameers. For each draw of parameers I generae an impulse response funcion. I repea his process 10,000 imes. A each lag I calculae he 2500 h lowes and 9750 h highes value across all 10,000 simulaed response funcions. The boundaries of he confidence inervals in he figures correspond o hese values. 16

19 Overall, he response funcions sugges ha regions respond o common sources of disurbance in a similar way. However, here is some variaion across regions in he sensiiviy of he responses o hese common disurbances. The objecive of he nex wo secions is es if he differences in response funcions are saisically significan. I do his by breaking down he responses ino heir common and idiosyncraic componens 4.3 Common responses Differences in common responses o common shocks across regions merely reflec differences in he sensiiviy o he common componen measured by γ i. Regions wih a γ i > 1 have greaer sensiiviy o flucuaions of he common componen, while regions wih γ i < 1 are less sensiive o flucuaions of he common componen. Table 5 repors he maximum likelihood esimaes of hese parameers along wih heir sandard errors and -saisics for he null hypohesis ha γ = 1. These saisics sugges ha he null of a common response o he common componen i across all regions canno be rejeced a he 5 percen level of significance. A he 10 percen level, he null is rejeced for he Plains and Far Wes. 4.4 Idiosyncraic responses The model developed in he previous secion is flexible enough o allow for differen regional responses o common shocks. These so-called idiosyncraic responses capure he difference beween he region s oal and common response o a common shock. Figure 7 shows ha he idiosyncraic responses of regional income o an unanicipaed rise in he relaive price of oil is no significanly differen from zero in New England, he Mideas and Grea Lakes. The idiosyncraic response funcions of he Souhwes, Rocky Mounains and Far Wes are significanly greaer han zero, while he response funcion of he Plains is significanly less han zero. This reflecs he fac ha he Souhwes, Rocky Mounains and Far Wes are oil 17

20 producing and disribuion regions. The Plains, on he oher hand, has a large agriculure secor, which is highly sensiive o oil price flucuaions. Idiosyncraic responses o unanicipaed shocks o moneary policy are ploed in Figure 8. They reveal ha idiosyncraic responses o moneary policy shocks are no saisically differen from zero in all eigh BEA regions. This finding sands in conras o he general conclusion of Carlino and Defina (1998) ha moneary policy has a greaer effec on he income of more manufacuring oriened regions, such as he Grea Lakes. There is, however, some evidence in suppor of heir conclusion ha he Souhwes is less sensiive o moneary policy. This is revealed by he fac ha he idiosyncraic response of he Souhwes is very close o being saisically differen from zero a he 5 percen level. Figure 9 reveals he effecs of an unanicipaed shock o he common income componen on he idiosyncraic componens of regional income. Shocks o he common componen of income affec he idiosyncraic componen hrough he lagged responses of oil prices and moneary policy. Wih he excepion of he Souhwes, he idiosyncraic responses o common income shock are no saisically differen o zero. This reflecs he fac ha posiive shocks o he common income componen have a posiive effec on oil prices and he federal funds rae, o which he Souh has a significan posiive idiosyncraic response. Responses o unanicipaed region-specific shocks are repored in Figure 10. All eigh regions have significan responses o heir region-specific shocks. Regions generally complee heir adjus o a region specific disurbance wihin a year of he shock. However, adjusmen is slower in New England, Souhwes and Far Wes, wih adjusmen lags of almos wo years. In mos cases he cumulaive effec exceeds he impac effec. The main excepions o his rule are Souheas and Plains. The main implicaion of his observaion is ha he relaive imporance of region-specific 18

21 disurbances is relaively smaller a longer horizons in he Souheas and Plains, when compared o New England, Souhwes and Far Wes (see Table 4). 4.5 Variance decomposiion a business cycle frequencies Panel A of Table 5 ies ogeher he sources of disurbances and responses by decomposing he variance of regional oupu a business cycle frequencies. Each column breaks down he variance of regional income by source of shock. For example, he firs elemen of he firs column reveals ha innovaions o oil prices explain 16 percen of he business cycle flucuaions in Souheas income. The nex enry reveals ha a similar percenage is explained by moneary policy shocks, while common income shocks explain 64 percen of he variaion in Souheas income. Moving on down he column, we see ha common shocks explain 96 percen of he variaion in Souheas income, wih he remaining 4 percen of he variaion in Souheas income explained by region specific shocks. The remaining columns of he upper panel reveal ha a large share of he business cycle flucuaions of U.S. regions is due o common shocks. Regions fall ino hree groups. A he upper end of he range common shocks explain more han 86 percen of he variaion in regional income of he Souheas and Grea Lakes, while a he lower end common shocks accoun for 56 and 63 percen of he income variaion in New England and Souhwes regions, respecively. The oher regions fall in beween wih common shocks accouning for 68 o 74 percen of income flucuaions in he Mideas, Plains, Rocky Mounains and Far Wes. Panel B highlighs differences in he idiosyncraic responses of regions by breaking down he relaive imporance of he common sources of variaion. The residual common-incomecomponen shock is he mos imporan source of disurbance explaining on average 70 percen of he variaion explained by all hree common shocks. While, moneary policy and relaive oil price shocks accoun on average for 15 percen of he variaion in regional income explained by 19

22 common shocks. The variaion across regions is greaes for oil price shocks, wih oil price shocks explaining 4-5 percen of he variaion in he Souhwes, Rocky Mounains and Far Wes on up o 32 percen in he Plains. This reflecs he relaively weaker responses in he former regions and he relaively srong response in he laer region. The relaive imporance of moneary policy shocks is more uniform across regions, wih he main oulier being he Souhwes, where shocks o moneary policy accoun for 8 percen of he variaion explained by common shocks. I assess he overall similariy of he regional business cycles by a simple disance measure ha compares he variance decomposiion of each region wih he average across all regions. These saisics are repored a he boom of Panel A (hey are disribued as a 2 χ wih 3 degrees of freedom). A he 5 percen level of significance I can rejec he null of common sources of innovaion and/or responses o innovaions a business cycle frequencies in he Souheas, Plains and Souhwes. This implies he U.S. regions can be divided ino a core group of New England, Mideas, Grea Lakes, Rocky Mounains and Far Wes, ha mee Mundell s OCA crieria described by (i)-(iv), and a non-core group of he Souheas, Plains and Souhwes ha fail o mee his crieria. 8 In he case of he Plains and Souheas hese findings largely reflec differences in he relaive volailiy of region-specific disurbances when compared o he core group. In paricular, regionspecific disurbances accoun for a relaively small share of he business cycle volailiy of Souheas income and a relaively large of he business cycle volailiy of Plains income. On he oher hand, hese findings reflec he fac ha he Souhwes has very differen responses o boh common and idiosyncraic shocks, when compared o he core group. 8 Relaxing he level of significance o he 1 percen level expands he opimum currency area o include he Souheas and Souhwes. 20

23 5 Conclusion This paper develops a saisical model o sudy he business cycles of he eigh U.S. BEA regions. By combining unobserved componen and VAR echniques I idenify no only common and idiosyncraic sources of innovaion, bu also common and idiosyncraic responses o common shocks. I use formal saisical ess o show ha he eigh U.S. BEA regions deviae from Mundell s ideal of an opimum currency area, a ypical levels of significance. Based on hese resuls, I idenify five core regions ha have similar sources of economic disurbance and similar responses o hese disurbances (New England, Mideas, Grea Lakes, Rocky Mounains and Far Wes) and hree non-core regions ha differ significanly from he core in heir sources of disurbance (Souheas and Plains) and responses o disurbances (Souhwes), a business cycle frequencies. References Baxer, M. and R.G. King, 1999, Measuring business cycles: Approximae band pass filers for economic ime series, Review of Economics and Saisics, Vol. 81, pp Carlino, G.A. and R. Defina, 1995, Regional income dynamics, Journal of Urban Economics, Vol 27, pp Carlino, G.A. and R. Defina, 1998, The differenial regional effecs of moneary policy, The Review of Economics and Saisics, Vol. 80, pp Chrisiano, L.J., M. Eichenbaum and C.L. Evans, 1994, Idenificaion and he effecs of moneary policy shocks, Federal Reserve Bank of Chicago, working paper, No Eichengreen, B.J., 1992, Is Europe an opimum currency area?, reprined in European Moneary Unificaion: Theory, Pracice, and Analysis, B.J. Eichengreen (ed.), Cambridge: MIT Press, pp

24 Eichengreen, B.J., and T. Bayoumi, 1993, Shocking aspecs of European moneary unificaion, reprined in European Moneary Unificaion: Theory, Pracice, and Analysis, B.J. Eichengreen (ed.), Cambridge: MIT Press, pp Hamilon, J.D., 1994, Time Series Analysis, Princeon: Princeon Universiy Press. Kouparisas, M.A., 1999, Is he EMU a viable common currency area? A VAR analysis of regional business cycles, Federal Reserve Bank of Chicago, Economic Perspecives, Vol 23, pp Mundell, R.A., 1961, A heory of opimum currency areas, American Economic Review, Vol. 51, pp Sims, C., 1972, Money, income, and causaliy, American Economic Review, Vol. 62, pp Wason, M.W., and R.F. Engle, 1983, Alernaive algorihms for he esimaion of dynamic facor, MIMIC and varying coefficien models, Journal of Economerics, Vol. 23, pp

25 Table 1: Regional business cycle comovemen and persisence A. Conemporaneous correlaion Income a ime Income a ime US SE NE ME GL PL SW RM FW Unied Saes Souheas New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes B. Lead/lag correlaion Income a ime +1 Income a ime US SE NE ME GL PL SW RM FW Unied Saes Souheas New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes Noes: US=Unied Saes, SE=Souheas, NE=New England, ME=Mideas, GL=Grea Lakes, PL=Plains, SW=Souhwes, RM=Rocky Mounains, and FW=FarWes. Regional and aggregae income daa filered using he quarerly business cycle band-pass filer described in Baxer and King (1999). Sources: Auhor s calcuaions using daa from he Bureau of Economic Analysis.

26 Table 2: Uni roo ess Variable Log level Log firs difference Souheas income New England income Mideas income Grea Lakes income Plains income Souhwes Income Rocky Mounains income Far Wes income Relaive price of oil Federal funds rae Noes: Wih excepion of funds rae all ess of uni roos in log-levels include include an inercep erm and ime rend, funds rae es only has an inercep. Uni roo ess of log-firsdifferences include an inercep erm. Source: Auhor s calculaions using regional income daa from Bureau of Economic Analysis, oil price daa from he Inernaional Moneary Fund and federal funds rae daa from he Board of Governors of he Federal Reserve Sysem.

27 Table 3: Esimaed volailiy of srucural disurbances Srucural disurbance Sandard deviaion Sandard error -saisic (σi=0) Common Oil price Common income Moneary policy Region specific Souheas New England 9 Mideas 0.55 Grea Lakes 2 Plains 0.92 Souhwes 8 Rocky Mounains 4 Far Wes 2 Srucural disurbance Relaive sandard deviaion Sandard error -saisic (σi/σ1=1) Region specific Souheas 1.00 New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes

28 Table 4: Sensiiviy o common shock Region Coefficien (γi) Sandard error -saisic (γi=1) Souheas 1.00 New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes

29 Table 5: Variance decomposiion of U.S. regional income a business cycle frequencies A. All sources of innovaion Percenage of oal variaion due o innovaion Source of innovaion: SE NE ME GL PL SW RM FW Average Relaive oil prices Moneary policy Common income Toal common Region-specific income Toal all shocks Chi squared es (sources are common) B. Common sources of innovaion Percenage of common variaion due o innovaion Source of innovaion: SE NE ME GL PL SW RM FW Average Relaive oil prices Moneary policy Common income Toal common Noes: SE=Souheas, NE=New England, ME=Mideas, GL=Grea Lakes, PL=Plains, SW=Souhwes, RM=Rocky Mounains, and FW=FarWes.

30 Figure 1: Cummulaive impulse response of regional income o oil price shock Souheas New England Mideas Grea Lakes Plains Souheas Souhwes Rocky Mounains Far Wes

31 Figure 2: Cummulaive impulse response of regional income o oil price shock (wih 95 percen confidence inerval) Souheas New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes

32 Figure 3: Cummulaive impulse response of regional income o moneary policy shock - - Souheas New England Mideas Grea Lakes Plains - - Souheas Souhwes Rocky Mounains Far Wes

33 Figure 4: Cummulaive impulse response of regional income o moneary policy shock (wih 95 percen confidence inerval) Souheas New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes

34 Figure 5: Cummulaive impulse response of regional income o common income shock Souheas New England Mideas Grea Lakes Plains Souheas Souhwes Rocky Mounains Far Wes

35 Figure 6: Cummulaive impulse response of regional income o common income shock (wih 95 percen confidence inerval) Souheas New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes

36 Figure 7: Cummulaive impulse response of idiosyncraic regional income o oil price shock Souheas New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes

37 Figure 8: Cummulaive impulse response of idiosyncraic regional income o moneary policy shock Souheas New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes

38 Figure 9: Cummulaive impulse response of idiosyncraic regional income o aggregae oupu shock Souheas New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes

39 Figure 10: Cummulaive impulse response of idiosyncraic regional income o region-specific oupu shock Souheas New England Mideas Grea Lakes Plains Souhwes Rocky Mounains Far Wes