- Email: [email protected]
The real exchange rate: an alternative approach to the PPP puzzle
Journal of Policy Modeling 24 (2002) 533–538
The real exchange rate: an alternative approach to the PPP puzzle Minsoo Lee a,∗ , Mudziviri Nziramasanga b , Sung K. Ahn c a Economics
Department, Commerce Division, Lincoln University, Canterbury, New Zealand of Economics, Washington State University, Pullman, WA 99164-4741, USA c Department of Management and Decision Sciences, Washington State University, Pullman, WA 99164-4736, USA
b Department
Received 2 December 2001; accepted 27 February 2002
Abstract We use a reduced form model to empirically examine the relative importance of nominal (relative money supply and current account) and real variables (terms of trade and industry productivity) in determining the bilateral real exchange rate between New Zealand and Australia. Our results show that real variables have a long-term impact on the real exchange rate, while shocks to monetary variables have only a short-term effect. Our results from time series support the Balassa–Samuelson effect. We also show that New Zealand and Australia bilateral real exchange rate with Japan as a base country shares a common stochastic trend, which can be interpreted in terms of optimum currency area. © 2002 Society for Policy Modeling. Published by Elsevier Science Inc. All rights reserved. Keywords: Exchange rate; Productivity; Purchasing power parity
1. Introduction The concept of purchasing power parity (PPP) is derived directly from international trade theory’s law of one price. This law states in bilateral trade there will be one price (excepting for tariffs, transportation costs and non-tariff barriers), ∗
Corresponding author. Tel.: +64-33253627; fax: +64-33253847. E-mail address: [email protected] (M. Lee).
0161-8938/02/$ – see front matter © 2002 Society for Policy Modeling. PII: S 0 1 6 1 - 8 9 3 8 ( 0 2 ) 0 0 1 6 1 - 8
534
M. Lee et al. / Journal of Policy Modeling 24 (2002) 533–538
Pi = ePf . The domestic price of commodity i, Pi equals the foreign price Pf converted to the domestic currency through the use of the exchange rate, e. Conversely, the exchange rate between bilateral trading countries reflects the barter terms of trade. In addition, the relative factor proportions as well as relative factor prices are supposed to converge. Deviations from the long-run PPP can be of a short-term nature or of long-run duration. Monetary theory advocates argue that monetary variables are the major determinants of the exchange rate. The long-term neutrality of money would result in a decay over the long run of any monetary shocks on the exchange rate, even if prices were sticky downward (Rogoff, 1996). However, Froot and Rogoff (1995) have shown that monetary shocks could have a long-run effect through their impact on the balance of payments on the current account. Relative differences in the rate of technological change can result in an imbalance in the relative factor proportions and factor prices, and deviations from PPP. Balassa (1964) and Samuelson (1964) show that such shocks may have the effect of raising the price level in the smaller country. Technological change in the tradable goods sector that would increase the capital–labor ratio, given world prices for the exports, would raise wages in that sector. Assuming full employment, the non-tradable goods sector would face cost push pressures on prices in the developing country. Such pressures would be minimal in the more developed countries because of the relatively higher productivity of the non-tradable sector. The deviations from PPP would thus be long lasting because of this Balassa–Samuelson effect. A collorary is that fast growing countries would tend to see their exchange rate appreciate relative to their trading partners, assuming that technological change is spurred more often in the tradable goods sector as the result of intense international competitiveness (Rogoff, 1996). The majority of empirical studies have not been able to reject the null hypothesis of the existence of a unit root in bilateral exchange rate series. That means they are not able to prove convergence toward PPP in the long run due to the existence of real variables that cause permanent deviations from PPP, i.e., the Balassa–Samuelson effect (Rogoff (1996), Murray and Papell (2002)). Murray and Papell contend the point estimate results are consistent with anything from models with nominal rigidities to models where PPP does not hold and the confidence intervals of half-lives of PPP deviations are too wide to place any credence in the point estimates. The persistence of the long-run disturbances makes the PPP approach incomplete as it fails to capture the effects of major changes in economic policies. In an economic reform program, new policies are introduced and implemented sequentially and real prices are supposed to adjust to new equilibrium values. However, it would be difficult to use the PPP approach to forecast what the new equilibrium values would be, or how long it would take to converge to the new equilibria, if indeed there is ever any convergence. This is of particular importance to countries where the likelihood of changes in the fundamentals is particularly high because of the implementation of significant economic reform measures.
M. Lee et al. / Journal of Policy Modeling 24 (2002) 533–538
535
2. Model An alternative approach would be to estimate the equilibrium exchange rate as a function of both structural and monetary variables and then use impulse response analysis to gauge their relative importance and persistence of the disturbances on the equilibrium rate. In this paper, we use the reduced form model to empirically examine the relative importance of nominal (relative money supply and current account) and real variables (terms of trade and industry productivity) in determining the bilateral real exchange rate fundamentals between New Zealand and Australia. Since the variables are non-stationary we estimate the reduced form by using the error correction representation of the structural vector autoregressive (VAR) model (Johansen, 1988 and Ahn & Reinsel, 1990). Cointegration analysis allows us to examine the deviation from long-run equilibrium conditions for a stationary group of dynamic variables, which individually are non-stationary. If a policy change is introduced at some point, economic forces should drive the cointegrating variables toward the new long-run equilibrium conditions. The analysis is therefore ideal for the study of the effects of an economic reform program. We then use the error correction VAR estimates to derive the impulse response analysis. The full model and econometric estimates are available in our more comprehensive paper (Lee, Ahn & Nziramasanga, forthcoming). The determinants of the real exchange rate (Rt ) between Australia and New Zealand are the ratio of the index of industrial production (Dt ), terms of trade (Tt ), the ratio of money supply (Mt ), and the balances on current account (Xt ). In all cases, the Australian values are the numerator. An improvement in the terms of trade in favor of New Zealand is expected to lead to an appreciation in the equilibrium exchange rate. Assuming full employment, a positive terms of trade shock leads an increase in demand for imported manufactured goods but causes the output in the non-tradable goods to decline. This in turn will create excess demand in the non-tradable goods sector. An increase in the productivity of the tradable goods sector relative to the non-tradable goods sector results in an expansion of the tradable goods sector at the expense of the non-tradable goods sector. Therefore, it improves the trade balance, which will cause a real appreciation to keep the trade account at a sustainable level. Hence, a positive shock on the relative productivity in the tradable sector will cause the real exchange rate to depreciate. A positive shock on current account will lead the real exchange rate to depreciate. On the other hand, a positive shock on the relative money supply will lead the real rate to appreciate in the short run.
3. Empirical results From the estimated cointegration combination vector we obtain the estimated long-run equilibrium relation along with adjustment coefficients ␣
536
M. Lee et al. / Journal of Policy Modeling 24 (2002) 533–538
given by Rt = 1.651 − 1.645Dt + 0.119Mt + 3.873Tt − 0.175Xt , ␣ = (Rt , Dt , Mt , Tt , Xt ) = (−0.187, −0.096, 0.371, 0.113, −0.615). The long-run equilibrium estimates can be interpreted as real exchange rate misalignment and the speed of adjustment coefficients can be interpreted as the weights that measure the average speed of adjustment towards the estimated equilibrium state (Johansen & Juselius, 1990). Current account adjusts fastest to economic reform measures. On the other hand, the real exchange rate and index of industry production ratio responded much more slowly. A deviation from the equilibrium due to positive shock in the bilateral real exchange rate affects negatively the changes in the productivity ratio, and the current account, while positively affects the changes in the money supply ratio and the terms of trade. We investigate the response of each of the five variables to a positive, one standard deviation shocks in the residuals. The reader is referred to our comprehensive paper for the estimates (Lee, Ahn, & Nziramasanga, forthcoming). Our results show that the relative money supply has a small impact on the real exchange rate, and the half-life of the disturbance is about 3.5 years, in line with other studies. Money supply does, however, have a persistent effect on the terms of trade. The terms of trade in turn have the largest, long-lasting positive impact on the real exchange rate. In an indirect way, therefore, monetary shocks also have a persistent effect on the real exchange rate. Both relative industrial production and the balance on current account have the expected effects on the real rate, but the magnitudes are less than that of terms of trade. We next examine the existence of co-movements of bilateral real exchange rates of New Zealand and Australia with Japan and the United States as base countries. If their fundamental variables are sufficiently interrelated and their economies are highly integrated each other, then the non-stationary bilateral real exchange rates can share the common stochastic trend (Enders & Hurn, 1994), which is known as the generalized purchasing power parity (G-PPP) theory. The generalized purchasing power parity can be interpreted in terms of optimum currency areas (Mundell, 1961). We define the bilateral real exchange rates of NZ and AUS with Japan as a base country in the following way: RtNZ = E(YEN/NZD) × (PNZ /PJP ) and RtAUS = E(YEN/AUD) × (PAUS /PJP ), where E(YEN/NZD) and E(YEN/AUD) are the spot nominal exchange rates and Pi is the CPI of country i. We take a logarithm on these real rates and then we normalize them so that the logs of real rates in 1975:Q1 are equal to zero. When G-PPP holds, there exists a long-run equilibrium relationship between two real rates such that, rtNZ + brAUS = t a + εt , where rtNZ and rtAUS are the logarithms of RtNZ and RtAUS , and εt is the ˆ = stationary equilibrium error. The normalized cointegrating vector is ˆ = (1, b) (1, −0.57) and the speed of adjustment vector is ␣ˆ = (−0.118, 0.169). As Enders and Hurn (1994) emphasize, the magnitudes of the coefficients in the cointegrating vector are related to the aggregate demand parameters in such a way that the more
M. Lee et al. / Journal of Policy Modeling 24 (2002) 533–538
537
similar are a country’s demand parameters, the smaller are the parameters of the cointegrating vector. One possible explanation on the magnitude of 0.57 when related to the demand parameters is the difference between the percentage of total Australian exports that go to New Zealand since 1975 as compared to the percentage of total New Zealand exports to Australia during the same period. The relatively small speed of adjustment coefficients can imply that there will be a persistent long-run deviation from G-PPP. A deviation from the equilibrium due to positive shock in the real exchange of New Zealand negatively affects the changes in its own real exchange rate, while it affects more positively the changes in the real exchange of Australia. Impulse responses analysis of the real exchange rates of New Zealand and Australia to innovations on the real exchange rates of Australia and New Zealand indicates the fluctuations in Australia exchange rate with Japan as a base country will have a greater impact on the New Zealand exchange rate with Japan as a base county. Since there is cointegration relation between the two rates, they share a common stochastic trend. We obtain a common trend that represents a weighted-average of the two real exchange rates with the ratio of the weights between New Zealand and Australia being approximately 1 to 1.75. This weighted-average ratio between two rates is compatible with the openness ratio of the two economies which fluctuates around 1.7 with an average of 1.62. 4. Conclusions Our time series analysis shows that an asymmetric positive shock on the productivity in favor of Australia results in a depreciation of the bilateral real exchange rate. Our results support the ‘commodity currencies’ phenomena and show that an improvement in the New Zealand terms of trade relative to Australia results in an appreciation of the bilateral real exchange rate. In the long term, our time series results validate the Balassa–Samuelson effect. It takes long term for two dynamic economies to achieve a long-term convergence of their real exchange rate. This begs the question of whether attaining this convergence is of primary or even secondary importance if the technological change that stimulates the divergence also generates growth. For the country on the ‘losing’ side of relative productivity changes, a greater payoff may be generated by paying attention to the structural variables that determine terms of trade and industrial exports than by concentrating on monetary policy to achieve exchange rate equilibrium. Our results show that terms of trade had a persistent impact on the current account balance. A policy option for a price taker like New Zealand would be to use tariffs as a way of alleviating the impact of the cost-push effect in the non-tradable sector. References Ahn, S. K., & Reinsel, G. C. (1990). Estimation for partially nonstationary multivariate autoregressive models. Journal of the American Statistical Association, 85(411), 813–823.
538
M. Lee et al. / Journal of Policy Modeling 24 (2002) 533–538
Balassa, B. (1964). The purchasing power parity doctrine: A reappraisal. Journal of Political Economics, 72(6), 584–596. Enders, W., & Hurn, S. (1994). Theory and tests of generalized purchasing-power parity: Common trends and real exchange rates in the Pacific Rim. Review of International Economics, 2(2), 179– 190. Froot, K. A., & Rogoff, K. (1995). Perspectives on PPP and long-run real exchange rates. In G. Grossman & K. Rogoff (Eds.), The handbook of international economics (vol. 3, Chap. 32). Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12, 231–254. Johansen, S., & Juselius, K. (1990). Maximum likelihood estimation and inference of cointegration— with applications to the demand for money. Oxford Bulletin of Economics and Statistics, 52, 169– 210. Lee, M., Ahn, Sung K., & Nziramasanga, M. (forthcoming). Real exchange rate determination and common currency between New Zealand and Australia, EconModels.com. Mundell, R. (1961). A theory of optimum currency area. Papers and Proceedings of the American Economic Association, 51, 657–664. Murray, C. J., & Papell, D. H. (2002). The purchasing power parity persistence paradigm. Journal of International Economics, 56(1), 1–20. Rogoff, K. (1996). The purchasing power parity puzzle. Journal of Economic Literature, 34(2), 647– 668. Samuelson, P. (1964). Theoretical notes on trade problems. Review of Economics Statistics, 46(2), 145–154.
The real exchange rate: an alternative approach to the PPP puzzle Minsoo Lee a,∗ , Mudziviri Nziramasanga b , Sung K. Ahn c a Economics
Department, Commerce Division, Lincoln University, Canterbury, New Zealand of Economics, Washington State University, Pullman, WA 99164-4741, USA c Department of Management and Decision Sciences, Washington State University, Pullman, WA 99164-4736, USA
b Department
Received 2 December 2001; accepted 27 February 2002
Abstract We use a reduced form model to empirically examine the relative importance of nominal (relative money supply and current account) and real variables (terms of trade and industry productivity) in determining the bilateral real exchange rate between New Zealand and Australia. Our results show that real variables have a long-term impact on the real exchange rate, while shocks to monetary variables have only a short-term effect. Our results from time series support the Balassa–Samuelson effect. We also show that New Zealand and Australia bilateral real exchange rate with Japan as a base country shares a common stochastic trend, which can be interpreted in terms of optimum currency area. © 2002 Society for Policy Modeling. Published by Elsevier Science Inc. All rights reserved. Keywords: Exchange rate; Productivity; Purchasing power parity
1. Introduction The concept of purchasing power parity (PPP) is derived directly from international trade theory’s law of one price. This law states in bilateral trade there will be one price (excepting for tariffs, transportation costs and non-tariff barriers), ∗
Corresponding author. Tel.: +64-33253627; fax: +64-33253847. E-mail address: [email protected] (M. Lee).
0161-8938/02/$ – see front matter © 2002 Society for Policy Modeling. PII: S 0 1 6 1 - 8 9 3 8 ( 0 2 ) 0 0 1 6 1 - 8
534
M. Lee et al. / Journal of Policy Modeling 24 (2002) 533–538
Pi = ePf . The domestic price of commodity i, Pi equals the foreign price Pf converted to the domestic currency through the use of the exchange rate, e. Conversely, the exchange rate between bilateral trading countries reflects the barter terms of trade. In addition, the relative factor proportions as well as relative factor prices are supposed to converge. Deviations from the long-run PPP can be of a short-term nature or of long-run duration. Monetary theory advocates argue that monetary variables are the major determinants of the exchange rate. The long-term neutrality of money would result in a decay over the long run of any monetary shocks on the exchange rate, even if prices were sticky downward (Rogoff, 1996). However, Froot and Rogoff (1995) have shown that monetary shocks could have a long-run effect through their impact on the balance of payments on the current account. Relative differences in the rate of technological change can result in an imbalance in the relative factor proportions and factor prices, and deviations from PPP. Balassa (1964) and Samuelson (1964) show that such shocks may have the effect of raising the price level in the smaller country. Technological change in the tradable goods sector that would increase the capital–labor ratio, given world prices for the exports, would raise wages in that sector. Assuming full employment, the non-tradable goods sector would face cost push pressures on prices in the developing country. Such pressures would be minimal in the more developed countries because of the relatively higher productivity of the non-tradable sector. The deviations from PPP would thus be long lasting because of this Balassa–Samuelson effect. A collorary is that fast growing countries would tend to see their exchange rate appreciate relative to their trading partners, assuming that technological change is spurred more often in the tradable goods sector as the result of intense international competitiveness (Rogoff, 1996). The majority of empirical studies have not been able to reject the null hypothesis of the existence of a unit root in bilateral exchange rate series. That means they are not able to prove convergence toward PPP in the long run due to the existence of real variables that cause permanent deviations from PPP, i.e., the Balassa–Samuelson effect (Rogoff (1996), Murray and Papell (2002)). Murray and Papell contend the point estimate results are consistent with anything from models with nominal rigidities to models where PPP does not hold and the confidence intervals of half-lives of PPP deviations are too wide to place any credence in the point estimates. The persistence of the long-run disturbances makes the PPP approach incomplete as it fails to capture the effects of major changes in economic policies. In an economic reform program, new policies are introduced and implemented sequentially and real prices are supposed to adjust to new equilibrium values. However, it would be difficult to use the PPP approach to forecast what the new equilibrium values would be, or how long it would take to converge to the new equilibria, if indeed there is ever any convergence. This is of particular importance to countries where the likelihood of changes in the fundamentals is particularly high because of the implementation of significant economic reform measures.
M. Lee et al. / Journal of Policy Modeling 24 (2002) 533–538
535
2. Model An alternative approach would be to estimate the equilibrium exchange rate as a function of both structural and monetary variables and then use impulse response analysis to gauge their relative importance and persistence of the disturbances on the equilibrium rate. In this paper, we use the reduced form model to empirically examine the relative importance of nominal (relative money supply and current account) and real variables (terms of trade and industry productivity) in determining the bilateral real exchange rate fundamentals between New Zealand and Australia. Since the variables are non-stationary we estimate the reduced form by using the error correction representation of the structural vector autoregressive (VAR) model (Johansen, 1988 and Ahn & Reinsel, 1990). Cointegration analysis allows us to examine the deviation from long-run equilibrium conditions for a stationary group of dynamic variables, which individually are non-stationary. If a policy change is introduced at some point, economic forces should drive the cointegrating variables toward the new long-run equilibrium conditions. The analysis is therefore ideal for the study of the effects of an economic reform program. We then use the error correction VAR estimates to derive the impulse response analysis. The full model and econometric estimates are available in our more comprehensive paper (Lee, Ahn & Nziramasanga, forthcoming). The determinants of the real exchange rate (Rt ) between Australia and New Zealand are the ratio of the index of industrial production (Dt ), terms of trade (Tt ), the ratio of money supply (Mt ), and the balances on current account (Xt ). In all cases, the Australian values are the numerator. An improvement in the terms of trade in favor of New Zealand is expected to lead to an appreciation in the equilibrium exchange rate. Assuming full employment, a positive terms of trade shock leads an increase in demand for imported manufactured goods but causes the output in the non-tradable goods to decline. This in turn will create excess demand in the non-tradable goods sector. An increase in the productivity of the tradable goods sector relative to the non-tradable goods sector results in an expansion of the tradable goods sector at the expense of the non-tradable goods sector. Therefore, it improves the trade balance, which will cause a real appreciation to keep the trade account at a sustainable level. Hence, a positive shock on the relative productivity in the tradable sector will cause the real exchange rate to depreciate. A positive shock on current account will lead the real exchange rate to depreciate. On the other hand, a positive shock on the relative money supply will lead the real rate to appreciate in the short run.
3. Empirical results From the estimated cointegration combination vector we obtain the estimated long-run equilibrium relation along with adjustment coefficients ␣
536
M. Lee et al. / Journal of Policy Modeling 24 (2002) 533–538
given by Rt = 1.651 − 1.645Dt + 0.119Mt + 3.873Tt − 0.175Xt , ␣ = (Rt , Dt , Mt , Tt , Xt ) = (−0.187, −0.096, 0.371, 0.113, −0.615). The long-run equilibrium estimates can be interpreted as real exchange rate misalignment and the speed of adjustment coefficients can be interpreted as the weights that measure the average speed of adjustment towards the estimated equilibrium state (Johansen & Juselius, 1990). Current account adjusts fastest to economic reform measures. On the other hand, the real exchange rate and index of industry production ratio responded much more slowly. A deviation from the equilibrium due to positive shock in the bilateral real exchange rate affects negatively the changes in the productivity ratio, and the current account, while positively affects the changes in the money supply ratio and the terms of trade. We investigate the response of each of the five variables to a positive, one standard deviation shocks in the residuals. The reader is referred to our comprehensive paper for the estimates (Lee, Ahn, & Nziramasanga, forthcoming). Our results show that the relative money supply has a small impact on the real exchange rate, and the half-life of the disturbance is about 3.5 years, in line with other studies. Money supply does, however, have a persistent effect on the terms of trade. The terms of trade in turn have the largest, long-lasting positive impact on the real exchange rate. In an indirect way, therefore, monetary shocks also have a persistent effect on the real exchange rate. Both relative industrial production and the balance on current account have the expected effects on the real rate, but the magnitudes are less than that of terms of trade. We next examine the existence of co-movements of bilateral real exchange rates of New Zealand and Australia with Japan and the United States as base countries. If their fundamental variables are sufficiently interrelated and their economies are highly integrated each other, then the non-stationary bilateral real exchange rates can share the common stochastic trend (Enders & Hurn, 1994), which is known as the generalized purchasing power parity (G-PPP) theory. The generalized purchasing power parity can be interpreted in terms of optimum currency areas (Mundell, 1961). We define the bilateral real exchange rates of NZ and AUS with Japan as a base country in the following way: RtNZ = E(YEN/NZD) × (PNZ /PJP ) and RtAUS = E(YEN/AUD) × (PAUS /PJP ), where E(YEN/NZD) and E(YEN/AUD) are the spot nominal exchange rates and Pi is the CPI of country i. We take a logarithm on these real rates and then we normalize them so that the logs of real rates in 1975:Q1 are equal to zero. When G-PPP holds, there exists a long-run equilibrium relationship between two real rates such that, rtNZ + brAUS = t a + εt , where rtNZ and rtAUS are the logarithms of RtNZ and RtAUS , and εt is the ˆ = stationary equilibrium error. The normalized cointegrating vector is ˆ = (1, b) (1, −0.57) and the speed of adjustment vector is ␣ˆ = (−0.118, 0.169). As Enders and Hurn (1994) emphasize, the magnitudes of the coefficients in the cointegrating vector are related to the aggregate demand parameters in such a way that the more
M. Lee et al. / Journal of Policy Modeling 24 (2002) 533–538
537
similar are a country’s demand parameters, the smaller are the parameters of the cointegrating vector. One possible explanation on the magnitude of 0.57 when related to the demand parameters is the difference between the percentage of total Australian exports that go to New Zealand since 1975 as compared to the percentage of total New Zealand exports to Australia during the same period. The relatively small speed of adjustment coefficients can imply that there will be a persistent long-run deviation from G-PPP. A deviation from the equilibrium due to positive shock in the real exchange of New Zealand negatively affects the changes in its own real exchange rate, while it affects more positively the changes in the real exchange of Australia. Impulse responses analysis of the real exchange rates of New Zealand and Australia to innovations on the real exchange rates of Australia and New Zealand indicates the fluctuations in Australia exchange rate with Japan as a base country will have a greater impact on the New Zealand exchange rate with Japan as a base county. Since there is cointegration relation between the two rates, they share a common stochastic trend. We obtain a common trend that represents a weighted-average of the two real exchange rates with the ratio of the weights between New Zealand and Australia being approximately 1 to 1.75. This weighted-average ratio between two rates is compatible with the openness ratio of the two economies which fluctuates around 1.7 with an average of 1.62. 4. Conclusions Our time series analysis shows that an asymmetric positive shock on the productivity in favor of Australia results in a depreciation of the bilateral real exchange rate. Our results support the ‘commodity currencies’ phenomena and show that an improvement in the New Zealand terms of trade relative to Australia results in an appreciation of the bilateral real exchange rate. In the long term, our time series results validate the Balassa–Samuelson effect. It takes long term for two dynamic economies to achieve a long-term convergence of their real exchange rate. This begs the question of whether attaining this convergence is of primary or even secondary importance if the technological change that stimulates the divergence also generates growth. For the country on the ‘losing’ side of relative productivity changes, a greater payoff may be generated by paying attention to the structural variables that determine terms of trade and industrial exports than by concentrating on monetary policy to achieve exchange rate equilibrium. Our results show that terms of trade had a persistent impact on the current account balance. A policy option for a price taker like New Zealand would be to use tariffs as a way of alleviating the impact of the cost-push effect in the non-tradable sector. References Ahn, S. K., & Reinsel, G. C. (1990). Estimation for partially nonstationary multivariate autoregressive models. Journal of the American Statistical Association, 85(411), 813–823.
538
M. Lee et al. / Journal of Policy Modeling 24 (2002) 533–538
Balassa, B. (1964). The purchasing power parity doctrine: A reappraisal. Journal of Political Economics, 72(6), 584–596. Enders, W., & Hurn, S. (1994). Theory and tests of generalized purchasing-power parity: Common trends and real exchange rates in the Pacific Rim. Review of International Economics, 2(2), 179– 190. Froot, K. A., & Rogoff, K. (1995). Perspectives on PPP and long-run real exchange rates. In G. Grossman & K. Rogoff (Eds.), The handbook of international economics (vol. 3, Chap. 32). Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12, 231–254. Johansen, S., & Juselius, K. (1990). Maximum likelihood estimation and inference of cointegration— with applications to the demand for money. Oxford Bulletin of Economics and Statistics, 52, 169– 210. Lee, M., Ahn, Sung K., & Nziramasanga, M. (forthcoming). Real exchange rate determination and common currency between New Zealand and Australia, EconModels.com. Mundell, R. (1961). A theory of optimum currency area. Papers and Proceedings of the American Economic Association, 51, 657–664. Murray, C. J., & Papell, D. H. (2002). The purchasing power parity persistence paradigm. Journal of International Economics, 56(1), 1–20. Rogoff, K. (1996). The purchasing power parity puzzle. Journal of Economic Literature, 34(2), 647– 668. Samuelson, P. (1964). Theoretical notes on trade problems. Review of Economics Statistics, 46(2), 145–154.