Purchasing Power Parity (PPP) in the Long-Run: A Cointegration Approach. Md. Nisar Ahmed Shams * S. M. Woahid Murad **

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1 Purchasing Power Pariy (PPP) in he Long-Run: A Coinegraion Approach Md. Nisar Ahmed Shams * S. M. Woahid Murad ** Absrac: This paper inends o es he long-run purchasing power pariy (PPP) in Bangladesh economy during he period 1971/ /08. The coinegraion ess using exchange rae and price indices from annual observaions rejec he PPP proposiion for Bangladesh. The resuls indicae ha deviaions in domesic and foreign price levels are no refleced in nominal exchange rae movemens. Insead of considering PPP as a complee model of exchange rae deerminaion, i should be used in providing a guideline in seing exchange raes in he presence of moneary disurbances. 1. Inroducion The Purchasing Power Pariy (PPP) docrine saes ha he exchange rae beween wo currencies should be equal o he raio of he price levels in wo counries so ha a given commodiy has he same price in boh counries when expressed in erms of he same currency. The inellecual origins of he docrine can be aribued o he works of Whealey (1807) and Ricardo (1821), where i appears as an exension of he quaniy heory of money. Is laes revival owes much o Gusav Cassel s wriings hroughou he 1920s o explain he behaviour of he dislocaed European exchanges during World War I (Humphrey and Kelehar, 1982). The emergence of he floaing exchange rae sysem afer 1973 inspired an enormous resurrecion of ineres in PPP heory. Numerous sudies have been carried ou in esing he validiy of he PPP heory. Early sudies of PPP cenered on he European and Unied Saes economies during he 1920s. The resuls suppor he PPP hypohesis as exchange raes could no be separaed from he price levels. On he conrary, PPP collapsed during he 1970s due o various srucural changes in he Unied Saes economy wih is rade parners (Frenkel, 1976, 1980; Krugman, 1978). In hese sudies, esimaions were carried ou wihou examining he ime series properies of he variables. If he variables are nonsaionary, we can sudy heir behaviour only for he ime period under consideraion wihou generalizing i o oher ime periods. Provided ha he variables are saionary as well as coinegraed, we may consider a long-run relaionship among hem. Besides, a number of sudies were conduced on he basis of coinegraion ess o idenify he long-run relaionship beween exchange rae and price levels. Basher and Mohsin (2004) es he PPP hypohesis using panel coinegraion framework for en Asian counries. The resuls did no indicae any evidence in favor of PPP. The sudies underaken by Corbae and Ouliaris (1988) and Eazaz e al. (2002) on US and Pakisan economies respecively, did no find any evidence in favor of he PPP hypohesis. * Associae Professor, Deparmen of Economics, Jahangirnagar Universiy, Savar, Dhaka. ** Lecurer, Deparmen of Economics, Asian Universiy of Bangladesh, Uara, Dhaka.

2 Purchasing Power Pariy (PPP) in he Long-Run: A Coinegraion Approach This aricle aims a assessing he long-run PPP relaionship in Bangladesh economy. Insead of regressing exchange rae on relaive prices, he coinegraion approach is adoped in esing PPP hrough analyzing he ime series properies of he variables. Unless he wo variables are coinegraed, one canno show ha here exiss a long-run relaionship beween hem. In such a case, he observed relaionship may be enirely spurious. The ouline of his paper is as follows. Secion 2 presens he heoreical framework, while secion 3 discusses he economeric mehodology. Secion 4 repors he daa sources and empirical resuls. Finally, he concluding remarks are provided in secion Theoreical Framework The absolue version of he purchasing power pariy (PPP) saes ha he equilibrium exchange rae equals he raio of domesic o foreign general price levels. If E is he nominal exchange rae measured as he domesic currency price of a uni of foreign currency and P d and P f are he domesic and foreign price indexes respecively, hen PPP can be wrien as: E = P d / P f (2.1) The logarihmic version of he PPP is as follows: Ln E = α 0 + α 1 Ln (P d / P f ) + ω (2.2) where, E is he nominal exchange rae (Taka per US dollar), P d and P f are he price indexes in Bangladesh and Unied Saes (US) respecively, α s are he coefficiens o be esimaed and ω is he disurbance erm represening shor-run deviaions from PPP. Two common price indexes used in he empirical verificaion of PPP are he consumer price index (CPI) and he wholesale price index (WPI). However, here exiss a grea deal of debae over he choice of he price index. One of he views emphasizes on commodiy arbirage in he deerminaion of exchange raes and considers WPI o be he appropriae price index which represens he prices of radable goods (Pigou, 1920). On he conrary, proponens of asse equilibrium in he deerminaion of exchange raes, relies on CPI which covers a broad range of commodiies (Cassel, 1928). However, WPI has been criicized o assign oo much weigh o raded goods. This sudy considers CPI o be he appropriae price index o be used in he empirical verificaion of he PPP hypohesis which has a greaer represenaion of nonraded goods. This aricle aemps o es of he absolue version of he PPP hypohesis. Various disurbances from moneary shocks may no lead o he equilibrium relaionship beween exchange rae and he raio of domesic o foreign general price levels in he shor-run. A necessary condiion for PPP o hold requires ω o follow a saionary process. In such a case, he deviaions from he equilibrium value are correced over ime. A coinegraed sysem offers a srong evidence for he absolue version of PPP heory. 2

3 3. Mehodology 3.1 Uni Roos The economeric mehodology firs examines he saionariy properies of he ime series. Two procedures for deecing a uni roo in exchange rae and price level daa are used in our analysis: (i) The Dickey-Fuller (DF) es (Dickey and Fuller, 1979), and (ii) he Augmened Dickey-Fuller (ADF) es (Dickey and Fuller, 1981). The DF es is derived from he regression equaion: X γ + u 1 δ 1 (3.1) = 0 + γ 1 + δx 1 where, X is a random walk wih drif around a sochasic rend and u is a whie noise error erm which is assumed o be uncorrelaed. Ifδ = 1, hen X is nonsaionary. Alernaively, we can esimae he model: X = γ + γ + X + u (3.2) 0 1 ϕ 1 where ϕ = ( δ 1) and is he firs-difference operaor, and es he null hypohesis ha ϕ = 0. If ϕ = 0, δ =1, we have a uni roo, implying ha he ime series under consideraion is nonsaionary. The ADF es is underaken by adding lagged values of he dependen variable X if he error erms are correlaed. Thus, he following regression is esimaed for uni roo esing: X = γ + γ + ϕx + α X + ε p j j (3.3) j= 1 In model (3.3) X is a random walk wih drif around a sochasic rend, is he firsdifference operaor, ε is a whie noise error erm and p is he number of lags in he dependen variable. The null hypohesis of a uni roo implies ha he coefficien of X 1 is zero i.e., ϕ = 0. Rejecion of he null hypohesis implies ha he series is saionary and no differencing in he series is necessary o induce saionariy. The number of lags in he dependen variable is chosen by he Akaike Informaion Crierion (AIC). Uni roo es idenifies wheher he variables are saionary or nonsaionary. The es is applied on boh he original series (in logarihmic form) and o he firs differences. In addiion, boh models wih and wihou rend are ried. The DF and ADF ess are carried ou by replacing X wih LnE and Ln(P d /P f ) in equaions (3.2) and (3.3) respecively. 3.2 Coinegraion Tess Time series should o be checked for coinegraion. For wo or more variables o be coinegraed, he ime series mus have similar saisical properies i.e., hey mus be inegraed of he same order. The Engle-Granger wo-sep mehod (Engle and Granger, 1987) is used for his purpose. The order of inegraion of he variables are idenified in he firs sep while in he second sep he residuals are esimaed from he Ordinary Leas Squares 3

4 Purchasing Power Pariy (PPP) in he Long-Run: A Coinegraion Approach (OLS) regression on he levels of he variables from equaion (2.2). Thus, according o he Engle-Granger mehod, wo variables, exchange rae (LnE ) and relaive price [Ln(P d /P f ) ] are considered o be coinegraed if hey are inegraed of he same order i.e., I(d) and he residuals in he regression of LnE on Ln(P d /P f ) (or vice versa) is inegraed of order less han d. The presence of a long-run equilibrium relaionship beween exchange rae and relaive price is also esed hrough Johansen (1988) maximum likelihood procedure. In Johansen s procedure, exchange rae and relaive price are assumed o follow he firs order Vecor Auo Regressive (VAR) represenaion as follows: E = Π E + R Π 12 1 ε E R = Π E + R Π 22 1 ε R (3.4) (3.5) Subracing lagged dependen variables from he respecive equaions, he sysem can be wrien in marix noaion as follows: E R = E R ε ε E R where 11 = Π 11-1, 22 = Π 22-1, 12 = Π 12 and 21 = Π 21 and E and R are firs difference saionary i.e., I(1). The exisence of a coinegraing relaionship depends on he rank of he marix which mus be equal o one as here can be up o one linearly independen coinegraing vecors. Johansen s procedure gives wo likelihood raio ess for he number of coinegraing vecors (r) which are found by he race and he maximum eigen value ess as follows: λ = N ln (1 ) race ( r ) λ i k i = r + 1 ˆ (3.6) λ max( + λ = N ln( 1 ˆ ) (3.7) r, r + 1) r 1 where, λ i 's are he characerisic roos of he marix and N is he sample size. The null hypohesis of a mos r coinegraing vecors is esed in boh he race es as well in he maximum eigen value es. In he race es, he alernaive hypohesis is ha he number of coinegraing vecors is equal o or less han r+1, whereas i is equal o r+1 in he maximum eigen value es. The Johansen s maximum likelihood procedure is carried ou by replacing E wih LnE and R wih Ln(P d /P f ) in equaions (3.4) and (3.5) respecively. 4. Daa Sources and Empirical Resuls The sudy is based on annual daa for he period 1971/ /08. Nominal exchange raes (period average) are expressed as unis of local currency (Taka) per US dollar. Daa on exchange raes have been gahered from various issues of Economic Trends, published by he 4

5 Bangladesh Bank. The relaive price is he domesic price index divided by a similar US price index. The CPI (Base: =100) has been used as he appropriae price index. Daa on CPI for Bangladesh and US have been obained from differen publicaions of Saisical Yearbook of Bangladesh and IMF Inernaional Financial Saisics (IFS) Yearbook, respecively. Economeric esimaions have been performed using STATA (version 9.2). The resuls in Table-1 indicae ha in all cases, he level of he logarihm of exchange rae and relaive price (measured by consumer price index) are nonsaionary. Thus o achieve saionariy he variables mus be firs-differenced. The DF and ADF saisics are significan only for he firs-differenced series. Thus, exchange rae and relaive price series appear o be I(1). Table-1: Uni Roo Tess wih DF and ADF for he period 1971/72 o 2007/08 DF Wih Trend ADF Variables Levels Firs Difference Levels Firs Difference Ln E *** (2) -4.67*** (2) Ln (P d /P f ) *** (1) -4.91*** (1) DF Wihou Trend ADF Variables Levels Firs Difference Levels Firs Difference Ln E *** (2) -3.11** (2) Ln (P d /P f ) *** (1) -5.28*** (1) Noes: i) Figures wihin parenheses indicae lag lenghs chosen by he Akaike informaion crierion (AIC); ii) *** and ** denoe rejecion of he null hypohesis of uni roo a he 1% and 5% levels respecively. Table 2: Uni Roo Res for he Residuals ω Wih Trend Wihou Trend Coinegraing Regressions DF ADF DF ADF Ln E = Ln (P d /P f ) (1) (1) Ln (P d /P f ) = Ln E (1) (1) Noes: i) Figures wihin parenheses indicae lag lenghs chosen by he Akaike informaion crierion (AIC); ii) The null hypohesis of uni roo in he residuals canno be rejeced a he 1%, 5% and 10% levels respecively. 5

6 Purchasing Power Pariy (PPP) in he Long-Run: A Coinegraion Approach The resuls repored in Table-1 provide he basis for he es of coinegraion. The DF and ADF saisics for he coinegraion ess are presened in Table-2. The resuls show ha exchange rae and relaive price series for Taka-US Dollar are no coinegraed. The residuals of he coinegraing regressions are nonsaionary indicaing ha deviaions beween exchange rae and relaive price coninue indefiniely wihou reconciling ogeher in he long-run. Table-3: Johansen s Maximum Likelihood Procedure Trace λ-max Null r = 0 r 1 r = 0 r = 1 Number Alernaive r 1 r 2 r = 1 r = 2 of lags (k) Ln E, Ln (P d /P f ) Noes: i) The lag lenghs are chosen by Akaike s Final Predicion Error (FPE) crieria; ii) r denoes he number of coinegraing vecors; iii) The null hypohesis of no coinegraion canno be rejeced a he 1% and 5% levels. Table-3 provides he resuls of he Johansen s maximum likelihood procedure for deermining he number of coinegraing vecors r. The resuls show ha he null hypohesis of no coinegraion (r = 0 ) canno be rejeced. Therefore, i can be confirmed ha exchange rae and relaive price are no coinegraed i.e., PPP does no hold for he Bangladesh economy. 5. Conclusion The aim of his paper has been o es he absolue version of he PPP hypohesis in Bangladesh Economy for he period 1971/ /08. Exchange rae and relaive price were nonsaionary in levels, bu saionary in firs difference i.e., hey are inegraed of order one, I(1). The sudy applies coinegraion echnique of economic ime series o verify he exisence of a sable relaionship beween exchange rae and relaive price. The resuls indicae ha here is no coinegraing relaionship beween he variables i.e., deviaions in domesic and foreign prices due o disurbances are no refleced in nominal exchange rae movemens in Bangladesh. Thus, PPP should no be considered as a complee heory of exchange rae deerminaion. Insead of providing a general rend, he PPP heory may be used as a guide for fixing exchange rae in he even of any moneary disurbance. References Basher, A. and M. Mohsin, 2004, PPP Tess in Coinegraed Panels: Evidence from Asian Developing Counries, Applied Economic Leers, Vol. 11, pp Cassel, G., 1928, Pos-War Moneary Sabilizaion, Columbia Universiy Press, New York. 6

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