The S-Curve Revisited: The Terms, Volume and Balance of Trade over the Business Cycle

Transcription

1 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), The S-Curve Revisied: The Terms, Volume and Balance of Trade over he Business Cycle Jon Nadenichek* California Sae Universiy - Norhridge Absrac This paper examines he abiliy of a dynamic general equilibrium model o replicae rade balance movemens seen in he daa. Specifically, he S-curve paern found in he crosscorrelaion beween he erms of rade and he rade balance is evaluaed. This paper exends earlier work in his area by examining he behavior of he rade balance in greaer deail, focusing on he cross-correlaion beween oupu, he erms of rade, he volume of rade, and he rade balance a differen leads and lags. Models driven by produciviy shocks are found o replicae mos of he cross-correlaion funcions esimaed from he daa. These resuls suppor he proposiion ha he S-curve and J-curve paerns seen in he daa are generaed by he endogenous responses of boh he erms of rade and he balance of rade o produciviy shocks raher han by he response of he rade balance o exogenous erms of rade innovaions. Keywords: S-curve, rade balance, erms of rade JEL Classificaion: F31, F32, F41 1. Inroducion The ineracion beween he erms of rade and he rade balance is an imporan opic in he field of inernaional economics. In he popular press, rade deficis are generally described as unfavorable and are assumed o be a primary cause of domesic job loss. Poliicians and oher policy makers face pressure o reduce rade deficis eiher by increasing he barriers o rade or by changing policy variables. Allowing or encouraging he exchange rae o depreciae is a soluion ofen employed o worsen he erms of rade in order o improve he rade balance. Because rade deficis can influence imporan policy decisions, a greaer undersanding of he causes of rade flucuaions is desirable. Much of he analysis of he ineracion beween he erms and balance of rade has aken place hrough an examinaion of wheher or no a J-curve paern exiss in he daa. The J-curve paern is characerized by an iniial worsening and laer improvemen of he rade balance following a erms of rade depreciaion. Following a worsening of he erms of rade, he decreased value of expors and increased value of impors ends o cause he rade balance o deeriorae. However, over ime, he higher relaive price of impors should cause he volume of expors o increase and he volume of impors o decrease. If he goods are sufficienly elasic, hese volume movemens evenually produce a ne improvemen of he balance of rade.

2 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Over he years, he J-curve has been analyzed for a wide variey of counries and daa ses using an assormen of economeric echniques. This area of research has me wih decidedly mixed resuls. Examples of papers finding suppor for he J-curve include Marwah and Klein (1996), Bahmani-Oskooee and Alse (1994) and Hacker and Hamani (2003). Evidence of a weak or delayed J-curve has also been found by several auhors such as Moffe (1989), Rosensweig and Koch (1988), Yusoff (2007) and Bahmani-Oskooee and Bolhasani (2011). Oher auhors such as Rose and Yellen (1989), Rose (1991), Hsing (2009), Hsing and Savvides (1996), and Mehme and Mushag (2010) have no found any evidence of a J-curve in he daa. A closely relaed area of research, focused on in his paper, has been direced a capuring he cross correlaion beween he erms of rade and he rade balance a various leads and lags. Backus e al. (1994) find ha he rade balance is negaively correlaed, in general, wih curren and fuure movemens in he erms of rade, bu posiively correlaed wih pas movemens. They describe his cross-correlaion paern as resembling an S-curve, similar o he J-curve paern commonly described in he lieraure. They also find ha his S-curve paern is replicaed by a general equilibrium model driven by produciviy shocks. Research ino he S- Curve coninues o be an acive area of research. Recen papers such as Senhadji (1998), Parikh and Shibaha (2004), Bahmani-Oskooee e al (2008), and Bahmani-Oskooee and Raha (2007, 2008, 2010), have coninued he discussion. A comprehensive review of he empirical invesigaions ino he exisence of boh he J-curve and he S-curve can be found in Bahmani- Oskooee and Hegery (2010). In his paper, I revisi he S-curve paern and is original inerpreaion as he endogenous movemens of boh he erms and balance of rade generaed by produciviy shocks. The area under invesigaion is expanded o include an esimaion of he cross-correlaion funcions beween oupu, he erms of rade, he balance of rade, and he volume of impors and expors a differen leads and lags. The esimaed relaionships are hen compared o hose obained from a general equilibrium model. This allows he daa o be evaluaed wihin a heoreical framework and serves as an informal es of he model s economic relevance. Examinaion of he daa from he original G-6 counries over a hiry year period resuls in empirical regulariies similar o hose repored in previous research. The rade balance is found o be negaively correlaed wih oupu. Addiionally, an S-curve paern is found in he crosscorrelaion funcion beween he rade balance and erms of rade. Empirical analysis also reveals several empirical relaionships beyond hose previously repored. Boh he volume of expors and he volume of impors are posiively correlaed wih oupu. The erms of rade is posiively correlaed wih he volume of expors and negaively correlaed wih fuure impor volumes. Also, increases in oupu are associaed wih erms of rade depreciaions. A wo-counry general equilibrium model driven by produciviy innovaions is able o replicae mos of he regulariies found in he rade daa. A posiive produciviy innovaion leads o an increase in oupu and a deerioraion of he erms of rade. Because he produciviy innovaion is persisen, here is an inflow of invesmen goods leading o an iniial rade balance defici. Laer, he rade balance improves as goods are expored o he foreign counry. This allows he model o replicae he counercyclical behavior of he rade balance. Following a produciviy

3 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), shock, he increased volume of boh impors and expors leads o posiive correlaions beween oupu and boh of hese variables. The erms of rade depreciaion coupled wih he iniial rade balance defici generaes he S-curve paern in he relaionship beween hose variables. Also, he model replicaes he posiive correlaion beween he erms of rade and impor volume. The remainder of he paper is organized as follows. Secion 2 inroduces he daa and repors he empirical findings. Secion 3 inroduces a wo-counry general equilibrium model and secion 4 repors impulse response funcions and cross-correlaion funcions generaed by he model simulaions. Secion 5 concludes. 2. Properies of he Daa Quarerly daa from he Inernaional Moneary Fund s Inernaional Financial Saisics over he period 1980.i hrough 2010.i are used o examine he relaionships beween oupu and he various componens of rade for he original G-6 counries. 1 The rade balance, denoed by TB, is defined as he raio of he ne expor of goods and services o oupu. The erms of rade, denoed by TOT, is defined as he raio of impor prices o expor prices, where an increase in his variable corresponds o a depreciaion of he erms of rade. Oupu is defined as real gross domesic produc and is denoed by Y. The volume of impors and expors are symbolized by VEX and VIM respecively. In order o focus on he behavior of hese variables over he business cycle, he daa is derended using he Hodrick and Presco filer wih a smoohing parameer of The focus of his paper is on he correlaion beween he various rade variables and oupu a differen leads and lags. Figures 1 hrough 7 conain he cross-correlaion funcions from he G-6 counries a leads and lags of up o eigh quarers. The correlaions are repored on he verical axis and k, he lead or lag of he second variable, is repored on he horizonal axis. The crosscorrelaion beween he erms of rade and he rade balance, TOT and TB +k, for k beween -8 and 8 replicaes he S-curve paern described in Backus e al. (1994). The resuls repored in Backus e al. (1994) are found o be consisen wih hose repored in his paper using an addiion 15 years of daa. Lagged and conemporaneous values of he rade balance are negaively correlaed wih he erms of rade while fuure rade balance values are posiively correlaed wih he erms of rade. This cross-correlaion paern is similar o he J-curve paern commonly discussed in he lieraure. The cross-correlaion funcion beween oupu and he rade balance, Y and TB +k, is generally negaive, reaching a minimum a conemporaneous values of boh oupu and rade. Over he business cycle, increases in oupu are associaed wih a worsening of he rade balance. The cross-correlaion beween oupu and he erms of rade, Y and TOT +k, is posiive, indicaing ha increases in oupu are associaed wih a depreciaion of he erms of rade. Boh he crosscorrelaion funcions beween oupu and he volume of expors, Y and VEX +k, and beween oupu and he volume of impors, Y and VIM +k, are posiive and hump-shaped, reaching a maximum a k=0. A rise in oupu is associaed wih boh an increased ouflow and inflow of goods and services.

4 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), The cross-correlaion funcions beween he erms of rade and he volume of expors and beween he erms of rade and impor volume are boh posiive, reaching a maximum a k=0. A erms of rade depreciaion is associaed wih increases in he volume of boh impors and expors. The erms of rade appears o be negaively correlaed wih fuure impor volumes and posiively correlaed wih curren and pas impor volumes. 3. A General Equilibrium Model In his secion, a wo-counry, wo-good inernaional real business cycle model similar o ha used in Backus e al. (1994) is described. In each counry, goods are produced using capial and labor as inpus. A represenaive agen in each counry maximizes uiliy under complee markes by consuming and invesing an aggregae good creaed by combining goods from boh counries. The represenaive agen in he domesic counry chooses leisure, L, and consumpion, c, in order o maximize expeced lifeime uiliy, subjec o he consrains lised below. The momenary uiliy funcion faced by he domesic agen is given by, 1 Ψ 1 ( ) = ( L ) σ U c, L c (1) 1 σ where (1 σ ) is he ineremporal elasiciy of subsiuion. In each counry, final goods, y, are produced using capial, k, and labor, N, according o he Cobb-Douglas producion funcion, y = a α α k N 1 (2) where a is a sochasic produciviy shock and α is labor s share in producion. 2 The represenaive agen in each counry consumes and invess an aggregae good composed of final goods from boh counries. 3 In he domesic counry, he aggregae good is produced by μ μ 1 μ [( η)( y ) + (1 η)( y ) ] x (3) = h f where x is he amoun of aggregae final goods available o he domesic agen for consumpion and invesmen, y h is he amoun of domesic final goods which remain in he domesic counry and y f is he amoun of foreign final goods which are raded o he domesic counry. Corresponding variables represening he foreign counry are denoed wih an aserisk. The agen in each counry faces several consrains on resources. The agen mus allocae a fixed amoun of ime beween labor and leisure, he producion and use of final goods mus be equal, and oal invesmen and consumpion by he domesic agen mus be equal o he amoun of aggregae goods available. These consains are, respecively, 1 N = 0 L (4) y y + y h * h = (5)

5 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), x c + i + g = (6) i where is invesmen in domesic counry capial goods and represens governmen consumpion. Also, new capial is creaed by invesing aggregae final goods, ( ) k 1 δ k + i γ (7) + = (1 ) g where δ is he capial sock depreciaion rae. The parameer values used o calibrae he sandard model are similar o hose used in oher inernaional real business cycle papers and are summarized in Table Properies of he Theoreical Economy In his secion, he paern of movemen generaed from he heoreical economy is compared o he previously discussed empirical regulariies. Impulse response funcions are compued in order o undersand more fully he ineracion beween he model variables. The model is simulaed o obain heoreical cross-correlaion funcions. These simulaed funcions are hen compared o hose esimaed from he daa. This comparison is used o evaluae he model s overall abiliy o replicae he daa and serves o highligh any componens of he model which fail o accuraely reflec realiy Impulse Response Funcion The paern of movemen caused by a one-percen innovaion in produciviy as variables deviae from and reurn o heir seady-sae levels is graphed in Figure 8. Following such a shock, oupu increases, boh direcly due o he produciviy increase and o increased labor paricipaion. This high level of producion causes a depreciaion of he domesic erms of rade ha reach is maximum poin several quarers afer he produciviy shock. The subsanial increase in invesmen demand following he shock moderaes he iniial depreciaion of he erms of rade, creaing a lag beween he shock and he poin of maximum erms of rade depreciaion. Because here is a high degree of persisence in he driving process, following a produciviy shock, invesmen goods flow ino he counry in order o ake advanage of he expeced high fuure level of produciviy. This leads o an increased level of impored goods. This inflow, combined wih he depreciaed erms of rade, causes he balance of rade o worsen. In laer periods, he balance of rade improves as he volume of impors decreases and he volume of expors begins o increase. The increased producion in he domesic counry is evenually expored once demand for new domesic capial has been reduced. Iniially, however, expor volume does no increase and i is only afer he huge increase in invesmen demand has waned ha he increased oupu is expored abroad. 4.2 Model Simulaion The model is simulaed in order o generae heoreical cross-correlaion funcions. 6 Figures 9 hrough 15 conain he cross-correlaion funcions generaed from he model. The mean crosscorrelaions from he G-6 daa are also included for comparison.

6 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), The model is able o replicae many aspecs of he cross-correlaion funcions esimaed from he daa. The erms of rade is negaively correlaed wih curren and lagged values of he rade balance and posiively correlaed wih fuure values. This general paern is also seen in he daa and has been described as resembling an S-curve. Following a produciviy innovaion, he erms of rade depreciaion reaches is larges level a few quarers afer he maximum deerioraion of he balance of rade. This leads o a negaive correlaion beween he erms of rade and curren and pas values of he rade balance. In laer periods, he balance of rade improves as expors increase, leading o a posiive correlaion beween he erms of rade and fuure values of he balance of rade The model is also able o replicae he negaive cross-correlaion funcion beween oupu and he rade balance, Y and TB +k. Increases in oupu caused by produciviy shocks are associaed wih rade balance deerioraions. Following a produciviy shock, he inflow of invesmen goods iniially ouweighs he increase in expors. However his cross-correlaion becomes posiive for k larger han wo or hree due o he evenual rade balance improvemen caused by persisen produciviy increases. Evenually, as invesmen demand decreases, he volume of goods expored surpasses impors, leading o a rade surplus. The model generaes posiive cross-correlaion funcions beween oupu and boh he volume of expors and impors similar o hose seen in he daa. In he case of expor volume, however, he model predics a lag of wo quarers, wih a maximum correlaion occurring beween oupu and fuure expor volume. In he model, an increase in oupu generally precedes he maximum increase in expors by a few quarers, causing fuure expor volume o remain posiively correlaed wih curren oupu The posiive correlaion seen in he daa beween he erms of rade and pas impor volume and he negaive correlaion beween he erms of rade and he fuure volume of impors are also generaed by he model. The cross-correlaion funcion beween TOT and VIM +k reaches a minimum a abou k=4. The iming of he correlaion beween he erms of rade and expor volume prediced by he model does no replicae ha seen in he daa. In he model, he erms of rade is negaively correlaed wih he volume of expors and posiively correlaed wih fuure expor volumes. This correlaion reaches is maximum a k=4 quarers. This lag is similar o ha seen beween oupu and expor volume. In boh insances he lag prediced by he model is no replicaed in he daa. The model is also able o replicae he relaionship beween oupu and he erms of rade, Y and TOT +k. In he daa his cross-correlaion funcion is posiive, paricularly for negaive values of k. Increases in oupu are correlaed wih erms of rade depreciaions. In he model, produciviy shocks cause susained increases in oupu and depreciaions of he erms of rade, leading o a posiive correlaion beween hese variables. This posiive correlaion would generally no be found in models driven primarily by demand shocks or exernal, exogenous erms of rade innovaions. 7

7 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Conclusions The basic dynamic general equilibrium model examined in his paper is able o generally replicae he paern of comovemen found beween oupu and he erms, balance and volume of rade. Consisen wih earlier work, an S-curve is found in he daa. Addiionally, mos of he oher cross-correlaions beween oupu and he various componens of he rade balance are prediced by he model. The finding ha boh he erms and balance of rade are driven by produciviy shocks and ha he subsequen behavior generaes an S-curve paern, reminiscen of he J-curve, is given addiional suppor. The fac ha produciviy shocks would generae a paern similar o he J-curve underscores he imporance of properly idenifying he shocks generaing movemens in he rade balance in he broader J-curve lieraure. The resuls sugges wo avenues for furher research. This paper has idenified several new paerns exhibied by he cross-correlaion funcions generaed by he inernaional rade daa. Addiional empirical work, looking a he more deailed correlaions for a wider se of counries, including lesser developed counries is suggesed. I is possible ha rade in smaller economies is driven more by exernal shocks, such as erms of rade shocks, raher han by inernal produciviy innovaions. This would poenially generae a differen paern of correlaions han ha seen in he larger economies examined in his paper. A second area of fuure research would be o refine he empirical models o beer replicae he daa. In recen years, a lieraure has grown, focused on improving he abiliy of dynamic general equilibrium models o replicae he inernaional rade daa. A small sample of hese improvemens include adding variable facor uilizaion raes in works such as Baxer and Farr (2004), asse marke resricions as in Baxer and Crucini (1995), and expecaion shocks and asse bubbles as represened in Xiao (2004). These augmenaions have improved he abiliy of he models o replicae he rade daa along dimensions oher han hose examined in his paper. Fuure work could include an evaluaion of hese augmened models and heir abiliy o replicae he cross-correlaion funcions discussed in his paper. Endnoes *Deparmen of Economics, College of Business and Economics, California Sae Universiy Norhridge, Nordhoff Sree, Norhridge. CA, jon.nadenichek@csun.edu. 1. These counries represen he larges indusrialized economies over his period and include France, Germany, Ialy, Japan, UK and US. 2. The sochasic produciviy shock evolves according o A = ρa -1 + ε, where A = [a a *], and he auocorrelaion marix,ρ, describes he degree of persisence of he echnology innovaions. The innovaion vecor ε is assumed o be normally disribued wih a variance-covariance marix given by Ω. The driving process is similar o ha used in Backus e al. (1994), esimaed using Solow residuals generaed from he daa.

8 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), This aggregaion funcion from Armingon (1969) is a sandard feaure of inernaional real business cycle models. In his aggregaor funcion, he elasiciy of subsiuion beween domesic and foreign final goods is conrolled by he parameer μ such ha σ x = 1 ( 1+ μ). 4. Following Sockman and Tesar (1995), he ineremporal elasiciy of subsiuion, 1/σ, is se equal o 0.5. Governmen consumpion is se equal o one-fifh of oal producion. Also, he elasiciy of subsiuion beween domesic and foreign final goods in forming he aggregae goods, σ x, is fixed a 1.5. The mehod of King e al. (1988) is used o solve and simulae he model. 5. For a discussion of he abiliy of his ype of model o mach oher aspecs of he daa such as he relaive volailiies of hese and oher variables, see Baxer and Crucini (1995) or Sockman and Tesar (1995). 6. These funcions are generaed from 1000 model simulaions, each of 120 periods in lengh. 7. As found in Backus e al (1994) and Senhadji (1998), he produciviy shocks are he key o generaing he S-curve paern. As seen in hese models, demand shocks will generae a posiive, hump-shaped cross-correlaion funcion beween he erms of rade and he rade balance. References Armingon, Paul S A Theory of Demand for Producs Disinguished by Place of Producion, Inernaional Moneary Fund Saff Papers, 16(1), Backus, David K., Parick J. Kehoe, and Finn E. Kydland Dynamics of he Trade Balance and he Terms of Trade: The J-Curve? American Economic Review, 84(1), Bahmani-Oskooee, Mohsen and Janardhanan Alse Shor-run verses long-run effecs of devaluaions: error correcion modeling and coinegraion, Easern Economic Journal, 20(4), Bahmani-Oskooee, Mohsen and Marzieh Bolhasani How Sensiive is U.S.-Canadian Trade o he Exchange Rae: Evidence from Indusry Daa, Open Economies Review, 22(1), Bahmani-Oskooee, Mohsen, Gour Goswami and Bidyu Kumar Talukdar The Bilaeral J-Curve: Canada verses her 20 rading parners, Inernaional Review of Applied Economics, 22, Bahmani-Oskooee, Mohsen and Sco W. Hegery The J- and S-curves: a survey of he recen lieraure, Journal of Economic Sudies, 37(6), Bahmani-Oskooee, Mohsen and Ararana Raha Bilaeral S-Curve beween Japan and her rading parners, Japan and he World Economy, 19(4),

9 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Bahmani-Oskooee, Mohsen and Ararana Raha S-Curve a he indusry level: evidence from US-UK commodiy rade, Empirical Economics, 35(1), Bahmani-Oskooee, Mohsen and Ararana Raha S-Curve dynamics of rade beween U.S. and China, China Economic Review, 21, Baxer, Mariane and Mario J. Crucini Business Cycles and he Asse Srucure of Foreign Trade, Inernaional Economic Review, 36(4), Baxer, Marianne and Dorsey D. Farr. 2004, Variable capial uilizaion and inernaional business cycles, Journal of Inernaional Economics, 65(2), Hacker, Sco and Abdulnasser Haemi Is he J-Curve Effec Observable for Small Norh European Economies? Open Economies Review, 14(2), Hsing, Yu Tes of he J-curve for six seleced new EU counries, Inernaional Journal of Economic Policy in Emerging Economies, 2(1), Hsing, Han-Min and Andreas Savvides Does a J-curve exis for Korea and Taiwan? Open Economies Review, 7(2), King, Rober G., Charles I. Plosser, and Sergio T. Rebelo Producion, Growh, and Business Cycles I: The Basic Neoclassical Model, Journal of Moneary Economics, 21, Marwa, Kana and Lawrence Klein Esimaion of J-curves: Unied Saes and Canada, Canadian Journal of Economics, 29(3), Mehme, Yazici and Ahmad Klasra Mushag Impor conen of expors and he J- curve effec, Applied Economics, 42(6), Moffe, Michael H The J-Curve Revisied: An Empirical Examinaion for he Unied Saes, Journal of Inernaional Money and Finance, 8, Parikh, Ashok. and Myuki Sibaha Dynamics of he relaionship beween he erms of rade and he rade balance in developing counries of Asia, Africa and Lain America, Journal of Quaniaive Economics, 2, Rose, Andrew The role of exchange rae in a popular model of inernaional rade: Does he Marshall-Lerner condiion hold? Journal of Inernaional Economics, 30, Rose, Andrew K. and Jane L. Yellen Is There a J-Curve? Journal of Moneary Economics 24, Rosensweig, Jeffery A. and Paul D. Koch The U.S. Dollar and he Delayed J-Curve. Alana Federal Reserve Bank of Alana, Economic Review, 2-15.

10 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Senhadji, Abdelhak Dynamics of he rade balance and he erms of rade in LDCs: The S-curve, Journal of Inernaional Economics, 46(1), Sockman, Alan C. and Linda L. Tesar Tases and Technology in a Two-Counry Model of he Business Cycle: Explaining Inernaional Comovemens, American Economic Review 85(1), Xiao, Wei Can indeerminacy resolve he cross-counry correlaion puzzle? Journal of Economic Dynamics and Conrol, 28(12), Yusoff, Mohammed The Malaysian real rade balance and he real exchange rae, Inernaional Review of Applied Economics, 21(5),

11 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Table 1 Model Calibraion Variable Symbol Calibraion ime discoun facor (quarerly) β 0.99 rae of echnological progress (quarerly) γ ineremporal elasiciy of subsiuion 1/σ 0.5 labor s share of oupu α 0.66 capial depreciaion rae (quarerly) δ elasiciy of subsiuion beween σ x =1/(1+μ) 1.2 home and foreign goods rade as a share of oupu expors/gdp 0.15 leisure preference parameer a Ψ Armingon aggregaor parameer b η Auocorrelaion Marix ρ Variance-Covariance Marix Ω ( ) 1*10 5 * a Calibraed o se he seady-sae leisure a 4/5 of oal ime available. b Calibraed o se rade as a share of oupu equal o 0.15.

12 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Figure 1. S-Curve: Cross-Correlaion Beween (TOT, TB +k ) Figure 2. Cross-Correlaion Funcion: (Y, TB +k )

13 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Figure 3. Cross-Correlaion Funcion: (Y, TOT +k ) Figure 4. Cross-Correlaion Funcion: (Y, VEX +k )

14 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Figure 5. Cross-Correlaion Funcion: (Y, VIM +k ) Figure 6. Cross-Correlaion Funcion: (TOT, VEX +k )

15 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Figure 7. Cross-Correlaion Funcion: (TOT, VIM +k ) Figure 8. Model Impulse Response Funcion

16 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Figure 9. S-Curve: Cross-Correlaion Beween (TOT, TB +k ) Figure 10. Cross-Correlaion Funcion Beween (Y, TB +k )

17 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Figure 11. Cross-Correlaion Funcion Beween (Y, TOT +k ) Figure 12. Cross-Correlaion Funcion: (Y, VEX +k )

18 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Figure 13. Cross-Correlaion Funcion: (Y, VIM +k ) Figure 14. Cross-Correlaion Funcion: (TOT, VEX +k )

19 Nadenichek, Inernaional Journal of Applied Economics, Sepember 2012, 9(2), Figure 15. Cross-Correlaion Funcion: (TOT, VIM +k )