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Productivity shocks and real exchange rates
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Journal of Monetary Economics 52 (2005) 555–566 www.elsevier.com/locate/jme
Productivity shocks and real exchange rates$ Annika Alexius Department of Economics, Uppsala University, 751 20 Uppsala, Sweden Received 12 January 2001; received in revised form 31 January 2003; accepted 15 July 2004 Available online 15 April 2005
Abstract Previous studies have concluded that productivity shocks have negligible effects on real exchange rate fluctuations. This paper shows that when long-run equilibrium relationships between real exchange rate levels and fundamental variables are taken into account, relative productivity shocks account for most of the long-run movements in the real exchange rates. This can be interpreted as empirical support for the Balassa (1964. Journal of Political Economy 72, 584–596) and Samuelson (1964. Review of Economics and Statistics 46, 145–154) model where differences in relative productivity is the main source of long-run deviations for purchasing power parity. r 2005 Elsevier B.V. All rights reserved. JEL classification: F31 Keywords: Real exchange rates; Productivity shocks; Variance decompositions
1. Introduction As purchasing power parity (PPP) is typically rejected in empirical test, equilibrium real exchange rates appear to be changing over time. Previous studies $ I am grateful to Per Jansson, Anders Vredin, Anders Warne, and an anonymous referee for comments and suggestions. Financial support from the Knut and Alice Wallenberg Foundation is gratefully acknowledged. Tel.: +46 18 471 15 64; fax: +46 18 471 14 78. E-mail address: [email protected].
0304-3932/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2004.07.003
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of the sources of real exchange rate fluctuations have concluded that real demand shocks account for most of the movements in the long-run as well as in the short-run (Clarida and Gali, 1994; Weber, 1997; Chadha and Prasad, 1997). Diverging results are presented by Rogers (1999) and Eichenbaum and Evans (1995), who document a larger relative influence of monetary shocks. However, all these studies conclude that the effects of productivity shocks on real exchange rates are negligible at all horizons. This is surprising in light of the related literature on long-run real exchange rate determination, where versions of the Balassa–Samuelson model dominate and exchange rates are modelled primarily as functions of relative productivity (Canzoneri et al., 1999; Chinn and Johnston, 1996). Another notable feature of the variance decomposition literature is that virtually all studies model only changes in real exchange rates and the fundamental variables. The presence of long-run relationships between the levels of the variables is either rejected (as in Clarida and Gali, 1994 and Rogers, 1999) or not investigated (as in Weber, 1997).1 Again, there is a gap between this empirical literature and related studies of long-run real exchange rate determination. Most papers in the latter field do find long-run equilibrium relationships between real exchange rates and various fundamental variables. There is ample documentation of cointegration between levels of real exchange rates and, for instance, relative productivity (see MacDonald, 1998, for a survey). Hence, previous studies of the sources of real exchange rate fluctuations (i) invariably conclude that productivity shocks have a negligible impact and (ii) do not find cointegration between real exchange rates and fundamental variables (or do not investigate whether they are cointegrated). After confirming the presence of cointegration, this paper demonstrates that relative productivity shocks dominate the long-run variance decompositions of real exchange rates when long-run equilibrium relationships are taken into account. The result is robust across a number of alternative empirical specifications.
2. Statistical methods If real exchange rates are cointegrated with fundamental variables, models using only differenced data are misspecified and do not utilize the information contained in the levels of the data. In particular, the absence of cointegration implies that it is not possible to model a time varying equilibrium level of the real exchange rate as function of the included fundamental variables. The VAR models used by Clarida and Galı´ (1994) and others to identify structural shocks and obtain variance decompositions can however incorporate long-run equilibrium relationships between the levels of the variables. Following King et al. (1991), structural shocks are 1
Actually, Clarida and Gali (1994) find cointegration for one of the four bilateral systems studied, but this is ignored in the subsequent empirical analysis. In Rogers (1999), the null hypothesis of cointegration would not be rejected if the 90% critical values of the Johansen (1988) tests were used instead of the 95% critical values.
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identified by imposing long-run restrictions of their effects within a cointegrated VAR model: Dxt ¼ m þ Pxt1 þ
P X
Gi Dxti þ tþ1 .
(1)
i¼1
The n-dimensional error-correction representation in (1) can be re-written as a common trends model (see e.g. Stock and Watson, 1993): xt ¼ x0 þ Att þ fðLÞvt ,
(2)
where tt ¼ m þ tt1 þ jt .
(3)
The number of cointegrating vectors r in (1) determines the number of independent stochastic trends k in the common trends model (2) as k ¼ n r: tt are the k stochastic trends with the drifts m and the innovations jt : The loading matrix A determines how the variables in xt are affected by the stochastic trends in the long run. In order to identify the structural shocks, kðk 1Þ=2 restrictions are imposed on the impact matrix A.
3. Empirical results We estimate the common trends model in (1)–(3) for each bilateral real exchange rate and the corresponding time-series on relative real output, relative government spending and relative price levels. Bilateral real exchange rates between the United States, the United Kingdom, Germany and Japan are constructed from nominal exchange rates (units of domestic currency per unit of foreign currency) and CPI price levels. Corresponding data on relative real output (volume indices), yt ; relative government consumption as share of output, gt ; and relative (CPI) price levels, pt ; are defined as the domestic variable minus the foreign variable. The data are collected from the OECD database Main Economic Indicators. All variables are in logarithms of the levels of the time series and the sample period is 1960Q1 to 1998Q4. As in previous studies, the ADF unit root test (not reported) indicates that the time-series are I(1). 3.1. Cointegration and identification The Johansen (1988) cointegration tests indicate that there is one cointegrating vector in all cases. There is more evidence of two cointegrating vectors than of no cointegration as two of the second largest trace statistics are significant. Given that the presence of cointegration between real exchange rates and fundamental variables is a controversial issue, the results have been confirmed using alternative methods.2 2
Additional tests for cointegration (Stock and Watson, 1988 and Park, 1992) also indicate that there is cointegration in four of the six bilateral systems. At least two of the three tests indicate cointegration for
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Table 1 Johansen (1988) tests for cointegration Currency
lð1Þ
lð2Þ
lð3Þ
lð4Þ
trð1Þ
trð2Þ
trð3Þ
trð4Þ
# lags
USD/DEM USD/JPY USD/GBP JPY/DEM JPY/GBP GBP/DEM Critical values
28.57 31.70 24.93 30.81 41.01 31.82 24.73
13.40 12.48 14.92 11.03 15.54 17.11 18.60
865 8.80 10.21 9.30 8.94 6.84 12.07
1.48 2.97 1.02 4.28 3.92 5.32 2.69
52.10 55.94 49.09 55.42 69.41 61.09 43.95
23.52 24.24 26.16 24.62 28.40 29.27 26.79
10.13 11.76 11.23 13.59 12.86 12.16 13.33
1.48 2.97 1.02 4.28 3.92 5.32 2.69
6 6 3 3 5 5
lð1Þ denotes the largest l-max statistic and lð2Þ denotes the second largest. 90% critical values are taken from Osterwald-Lenum (1992). While information criteria indicate that one to three lags are appropriate, three to six lags are required to remove residual autocorrelation.
According to the estimated cointegrating vectors, countries with high relative real GDP and high relative government consumption have stronger real exchange rates in the long-run (Table 1). The structural shocks are identified by imposing restrictions on their long-run effects. Given one cointegrating vector and four variables, there are three stochastic trends, identified as a relative productivity shock, a government spending shock, and a monetary shock. All three shocks are allowed to affect the real exchange rate and the relative price level in the long-run. Monetary shocks are identified by the assumption that they do not affect relative output or government spending in the long-run. One additional restriction is needed for exact identification. In the baseline model, following Rogers (1999), government spending shocks are allowed to affect output but changes in productivity are assumed not to affect government spending in the long-run. The identification of structural shocks within VARs has been questioned by e.g. Faust and Leeper (1997). Several empirical studies have however confirmed that VAR models identify productivity shocks that closely resemble classic and refined Solow residuals (Kiley, 1998; Alexius and Carlsson, 2002).In Section 4, we check whether the results are robust to variations in the empirical specification and the identifying assumptions. Fig. 1 illustrates that the stochastic relative productivity trends closely tracks relative real GDP. The short-run responses of output and prices to productivity shocks and government spending shocks have the expected signs in all empirical models. Most of these impulse-response functions are however not significant. More interestingly, all six real exchange rates appreciate significantly in response to increases in relative productivity both in the short- and long-run. This is consistent with the Balassa
(footnote continued) each real exchange rate, i.e. the different tests reject cointegration for different pairs of countries. Three of the four rejections of cointegrations however concern US bilateral real exchange rates.
ARTICLE IN PRESS A. Alexius / Journal of Monetary Economics 52 (2005) 555–566 Relative productivity trend
559
Relative real GDP, US-UK
0.05 0.00 -0.05 -0.10 -0.15 -0.20 -0.25 60
65
70
75
80
85
90
95
Fig. 1. Relative productivity trend and relative real GDP for the U.S. versus the U.K.
(1964) and Samuelson (1964) approach but not with the Obstfeld (1985) model or other models without a distinction between tradable and non-tradable goods. 3.2. Finite horizon variance decompositions Table 2 shows forecast error variance decompositions as the horizon is increased from 1 to 40 quarters. Three of the six real exchange rates behave roughly as expected: The DEM/JPY, USD/JPY and GBP/DEM. Transitory shocks dominate the short-run movements as they account for about half of the forecast error variance at the quarterly horizon. The relative influence of transitory shocks then declines as the forecasting horizon is extended. At the 10-year horizon, they only account for 15–20% of the variance. The remaining 80–85% of the 10-year fluctuations in these three real exchange rates can hence be explained by movements in the included fundamental variables. Monetary shocks are slightly more important to the first three real exchange rates than what is typically found. Since 20–30% of the 10-year fluctuations are due to monetary shocks, their effects are also rather persistent. Government spending shocks, on the other hand, are negligible. The influence of productivity shocks increases continuously with the horizon, from 15–20% of the forecast error variance at the first quarter to about 50% at the 10-year horizon. Productivity is hence much more important here than what has been found in the previous studies. For the second group of real exchange rates, the GBP/USD, USD/DEM, and GBP/JPY, transitory shocks dominate the variance decompositions even at forecasting horizons of 10 years. The share of the variance due to transitory shocks actually increases with the forecasting horizon in case of the USD/DEM real exchange rate. The finding that more than 80% of its 10-years fluctuations are transitory can be interpreted as the common trends model’s way of indicating that the USD/DEM real exchange rate is close to stationary over the sample period (see Fig. 2). This is an undesirable situation given that the statistical model is designed to handle non-stationary data. PPP is however formally rejected in all six cases.
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Table 2 Forecast error variance decompositions at one to 40 quarters Currency
Horizon
Productivity
DEM/JPY
1 4 8 12 20 40
14.31 29.48 38.00 42.64 48.55 56.82
USD/JPY
1 4 8 12 20 40
GBP/DEM
Government
Monetary
Transitory
1.70 2.22 2.26 2.74 3.80 5.77
18.84 30.21 30.78 29.57 26.93 22.19
65.15 38.09 29.95 25.05 20.72 15.21
21.23 17.34 21.97 26.89 34.11 45.27
0.20 0.67 0.40 0.82 3.81 9.41
41.54 44.78 44.59 43.28 38.39 29.07
37.21 37.20 33.04 29.01 23.67 16.25
1 4 8 12 20 40 1
17.36 25.70 36.49 38.21 40.56 48.47 3.67
2.85 1.81 0.99 1.05 2.65 3.88 0.13
27.88 31.21 33.29 34.18 32.40 27.17 20.59
51.92 41.28 29.23 26.55 24.39 20.48 75.60
GBP/USD
4 8 12 20 40 1
9.38 13.55 17.62 21.48 23.37 2.87
0.45 1.43 2.11 2.83 12.71 18.68
11.20 9.36 9.44 9.15 10.74 22.79
78.98 75.66 70.82 66.54 53.29 55.66
USD/DEM
4 8 12 20 40 1
1.96 4.74 6.34 7.39 6.24 7.50
10.51 7.91 6.67 5.01 3.99 30.13
20.16 16.46 13.2 9.81 7.51 2.22
67.38 70.90 73.79 77.80 82.25 60.15
GBP/JPY
4 8 12 20 40
6.25 4.72 3.80 3.77 23.9
27.81 27.25 27.32 28.02 23.24
8.12 6.41 5.46 5.77 4.61
57.82 61.67 63.42 62.43 48.21
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Real exchange rate, USD/GBP
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 60
(a)
65
70
75
Productivity driven part
80
85
90
95
Real exchange rate, USD/DEM
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 60
(b)
65
70
75
80
Productivity driven part
85
90
95
Real exchange rate, USD/JPY
1.2 0.8 0.4 0.0 -0.4 -0.8
(c)
60
65
70
75
80
85
90
95
Fig. 2. (a) The real exchange rate and its productivity driven part for the US versus the UK; (b) the real exchange rate and its productivity driven part for the US versus Germany; (c) the real exchange rate and its productivity driven part for the US versus Japan.
Another notable feature of the short- to medium-run variance decompositions for the second group of real exchange rates is that while the influence of productivity shocks increases with the horizon, they are much less important here than for the
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first group. Productivity shocks cause less than 25% of the movements in the GBP/ USD and GBP/JPY real exchange rates also at the 10-year horizon and their share never exceeds 8% in case of the USD/DEM. This is consistent with previous findings; it is the large influence of productivity shocks documented for the first group of real exchange rates that is atypical. 3.3. Infinite horizon variance decompositions Long-run forecast error variance decompositions reveal what structural shocks have caused the permanent movements in the real exchange rates. As shown in the second column of Table 4, relative productivity shocks account for most of the longrun variance, 63–90% for all the real exchange rates except the GBP/USD (where the share is only 26%). These results contrast blatantly with the typical finding that supply shocks only account for a minuscule share of the movements in real exchange rates. The largest influence of supply shocks previously documented for major currencies is one-third of the forecast error variance (Weber, 1997). Government spending shocks typically account for 20–30% of the long-run movements. They are more important to the GBP/USD (55%) and less important to the GBP/JPY (4%). As expected from long-run monetary neutrality, monetary shocks are unimportant in the long-run.
4. Historical decompositions By feeding the identified productivity shocks into the estimated systems, the productivity driven components of the real exchange rates can be extracted. Figs. 2a–c show the USD/DEM, USD/GBP and USD/JPY real exchange rates and their respective productivity components. Several observations can be made in light of these figures and the variance decompositions in Tables 2 and 3. Above all, the USD/DEM real exchange rate displays a weak relationship to its productivity driven part. At the same time, 64% of the infinite horizon forecast error variance is due to productivity shocks. The key to reconciling these two results can be found in the finite horizon variance decomposition, which shows that more than 80% of its 10-year fluctuations are transitory. Productivity shocks cause most of the permanent Table 3 Long run variance decomposition for the levels Currency
Productivity
Government
Monetary
USD/DEM USD/JPY GBP/USD DEM/JPY GBP/JPY GBP/DEM
63.7 72.2 26.3 80.1 76.4 90.6
30.3 20.0 54.9 11.7 22.2 4.1
6.0 7.8 18.9 8.2 1.2 5.0
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movements, but the non-stationary component of the USD/DEM real exchange rate is small relative to the stationary fluctuations. This case demonstrates that infinite horizon variance decompositions can provide different answers to the question about the causes of fluctuations than both finite horizon variance decomposition and historical decompositions when transitory shocks are important at long but finite horizons. The historical decomposition of the USD/JPY real exchange rate, on the other hand, is more consistent with the finding that productivity shocks explain most (72%) of the permanent movements. There are however also considerable deviations from the productivity driven trend. The finite horizon variance decomposition is not at odds with the infinite horizon results in this case as 45% of the 10-year movements are caused by productivity shocks and only 16% are transitory. The productivity driven component of the USD/GBP real exchange rate appears to track the permanent real exchange rate movements reasonably well. The infinite horizon variance decomposition however only attribute 26% of the permanent movements to productivity shocks, a number that squares well with the results for the 10-year horizon but appears low, given Fig. 2b. The finding that transitory shocks cause more than half of the 10-year movements is in line with the large and persistent deviations from the non-stationary equilibrium observed in the graph.
5. Robustness of the results The results from VAR models where the structural shocks are identified using restrictions on their long-run effects may vary considerably with the exact formulation of the empirical model. We therefore, study the robustness of the results with respect to changes in the identifying assumptions and the included variables. Five alternative empirical models are estimated. Three of them incorporate long-run equilibrium relationships between the real exchange rates and the fundamental variables. First, the baseline model is re-estimated using data on relative money supply instead of relative price levels to capture monetary developments (model A).3 Second, the identifying assumption that productivity shocks do not affect government spending is replaced by the alternative assumption that government spending does not affect output in the long-run (model B). This implies full crowding out of government spending in the long-run and a possible feed-back from real output to government spending. For instance, richer countries may have higher government spending relative to GDP. In model C, the government spending variable is excluded. Hence, this is the Clarida and Galı´ specifications with cointegration. The two final models ignore the presence of long-run equilibrium relationships between the variables. Model D is the original Clarida and Gali model including only the first differences of real exchange rates, relative output and relative prices. Model E is the baseline model of this paper re-estimated under the assumption of no 3
Data on money supply (M2) are taken from the OECD data base Main Economic Indicators.
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Table 4 The share of the long-run forecast error variance due to productivity shocks in alternative empirical models Currency
Model A
Model B
Model C
Model D
Model E
USD/DEM USD/JPY GBP/USD DEM/JPY GBP/JPY GBP/DEM
50.1 36.8 43.5 99.9 71.5 73.0
67.5 33.6 26.9 49.4 92.9 29.6
39.6 74.3 14.5 91.7 91.3 99.7
16.04 9.63 4.95 2.42 17.68 6.86
13.81 9.34 6.10 4.69 15.72 4.18
Model A is the original model with relative money supply rather than price levels. Model B is the original model with a different distinction between supply shocks and real demand shocks. Model C is a threevariable model including the levels of qt ; pt pt ; and yt yt : Model D is the Clarida and Gali model using only the first differences: [Dqt ; Dðpt pt Þ; and Dðyt yt Þ]. Model E is the model of this paper but without cointegration, i.e. [Dqt ; Dðyt yt Þ; Dðgt gt Þ; Dðpt pt Þ].
cointegration, i.e. a four variable VAR containing the first differences of the real exchange rate, relative output, relative prices and relative government expenditure. Table 4 shows the shares of the long-run variances due to supply shocks in the five alternative empirical specifications. In models A to C, productivity shocks account for a much larger share of the long-run variance than what has been found in previous studies. The GBP/USD real exchange rate is an exception as the share of the long-run variance due to supply shocks is below 30% in two of the specifications. For models D and E, productivity shocks are unimportant to the long-run real exchange rate movements, as is typically found when only changes in the variables are modelled. Hence, when long-run equilibrium relationships between the variables is taken into account, productivity shocks cause most of the long-run movements in real exchange rates. Without cointegration, there are no long-run equilibrium relationships between relative output levels and real exchange rate levels. To the extent that productivity shocks affect real exchange rates through these long-run relationships and the adjustment to equilibrium, excluding the cointegration term in Eq. (1) cuts the link between productivity and real exchange rates. It is however also clear that the identifying assumptions matter as the results in Table 4 vary considerably between the empirical specifications. Rogers (1999) also estimates a number of alternative empirical models. Supply shocks typically account for less than 10% of the long-run variance of real exchange rates in his study and the largest share is 25.2%. However, none of his nine alternative specifications includes cointegration between real exchange rates and the fundamental variables.
6. Conclusions Previous studies of the causes of fluctuations in real exchange rates conclude that the impact of productivity shocks is negligible. This paper uses a statistical approach where long-run equilibrium relationships between real exchange rates and
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fundamental variables are explicitly taken into account. Contrary to previous studies, relative productivity shocks are found to be the dominating source of longrun movements in real exchange rates. For five of the six real exchange rates, 60–90% of the permanent movements are due to productivity shocks. In the cases where transitory shocks are important at long horizons, historical decompositions are however more consistent with the finite horizon variance decomposition than with the infinite horizon results. Productivity shocks account for about half of the ten-year movements of the USD/JPY, DEM/JPY, and GBP/DEM, but are less important to the remaining three exchange rates. The documented real effects of money are slightly larger and more persistent in this paper than what is typically found. For three of the six real exchange rates, 20–30% of the 10-year movements are due to monetary shocks. Long-run monetary neutrality however appears to hold at the infinite horizon. To check the robustness of the results, five alternative empirical specifications using other identifying assumptions and/or variables are estimated. The exact formulation of the VAR model matters as the share of the long-run variance due to supply shocks varies considerably between the different models. However, in the cases where long-run equilibrium relationships between the levels of the real exchange rates and the fundamental variables is allowed, relative productivity shocks is a much more important source of long-run movements in real exchange rates than what has been documented in previous studies. This result can be interpreted as empirical support for the relative productivity approach of Balassa (1964) and Samuelson (1964). References Alexius, A., Carlsson, M., 2002. Measures of technology and the business cycle. Review of Economics and Statistics 87 (2), to appear. Balassa, B., 1964. The purchasing power parity doctrine: a reappraisal. Journal of Political Economy 72, 584–596. Canzoneri, M., Cumby, R., Diba, B., 1999. Relative labor productivity and the real exchange rate in the long-run: evidence for a panel of OECD countries. Journal of International Economics 47, 245–266. Chadha, B., Prasad, E., 1997. Real exchange rate fluctuations and the business cycle: evidence from Japan. International Monetary Fund Staff Papers 44, 328–355. Chinn, M., Johnston, L., 1996. Real exchange rate levels, productivity and demand shocks: evidence from a panel of 14 countries. NBER Working Paper No. 5709. Clarida, R., Gali, J., 1994. Sources of real exchange rate fluctuations: how important are nominal shocks? Carnegie Rochester Series on Public Policy 41, 1–56. Eichenbaum, M., Evans, C., 1995. Some empirical evidence of the effects of shocks to monetary policy on exchange rates. Quarterly Journal of Economics 110, 975–1010. Faust, J., Leeper, E., 1997. When do long-run identifying restrictions give reliable results? Journal of Business and Economics 15, 345–353. Johansen, S., 1988. Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control 12, 231–254. Kiley, M., 1998. Labor productivity in U.S. manufacturing: does sectoral co-movements reflect technology shocks? Mimeo, Federal Reserve Board. King, R., Plosser, C., Stock, J., Watson, M., 1991. Stochastic trends and economic fluctuations. American Economic Review 81, 819–840.
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MacDonald, R., 1998. What do we really know about real exchange rates? Working Paper No 28, Oesterreichische Nationalbank. Obstfeld, M., 1985. Floating exchange rates: experience and prospects. Brookings Papers on Economic Activity 2, 369–450. Osterwald-Lenum, M., 1992. A note with quantiles of the asymptotic distribution of the maximum likelihood cointegration rank test statistics. Oxford Bulletin of Economics and Statistics 54, 461–472. Park, J., 1992. Canonical cointegrating regressions. Econometrica 60, 119–143. Rogers, J., 1999. Monetary shocks and real exchange rates. Journal of International Economics 49, 269–288. Samuelson, P., 1964. Theoretical notes on trade problems. Review of Economics and Statistics 46, 145–154. Stock, J., Watson, M., 1993. A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61, 783–820. Weber, A., 1997. Sources of purchasing power disparities between the G3 economies. Journal of the Japanese and International Economies 11, 548–583.
Journal of Monetary Economics 52 (2005) 555–566 www.elsevier.com/locate/jme
Productivity shocks and real exchange rates$ Annika Alexius Department of Economics, Uppsala University, 751 20 Uppsala, Sweden Received 12 January 2001; received in revised form 31 January 2003; accepted 15 July 2004 Available online 15 April 2005
Abstract Previous studies have concluded that productivity shocks have negligible effects on real exchange rate fluctuations. This paper shows that when long-run equilibrium relationships between real exchange rate levels and fundamental variables are taken into account, relative productivity shocks account for most of the long-run movements in the real exchange rates. This can be interpreted as empirical support for the Balassa (1964. Journal of Political Economy 72, 584–596) and Samuelson (1964. Review of Economics and Statistics 46, 145–154) model where differences in relative productivity is the main source of long-run deviations for purchasing power parity. r 2005 Elsevier B.V. All rights reserved. JEL classification: F31 Keywords: Real exchange rates; Productivity shocks; Variance decompositions
1. Introduction As purchasing power parity (PPP) is typically rejected in empirical test, equilibrium real exchange rates appear to be changing over time. Previous studies $ I am grateful to Per Jansson, Anders Vredin, Anders Warne, and an anonymous referee for comments and suggestions. Financial support from the Knut and Alice Wallenberg Foundation is gratefully acknowledged. Tel.: +46 18 471 15 64; fax: +46 18 471 14 78. E-mail address: [email protected].
0304-3932/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmoneco.2004.07.003
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of the sources of real exchange rate fluctuations have concluded that real demand shocks account for most of the movements in the long-run as well as in the short-run (Clarida and Gali, 1994; Weber, 1997; Chadha and Prasad, 1997). Diverging results are presented by Rogers (1999) and Eichenbaum and Evans (1995), who document a larger relative influence of monetary shocks. However, all these studies conclude that the effects of productivity shocks on real exchange rates are negligible at all horizons. This is surprising in light of the related literature on long-run real exchange rate determination, where versions of the Balassa–Samuelson model dominate and exchange rates are modelled primarily as functions of relative productivity (Canzoneri et al., 1999; Chinn and Johnston, 1996). Another notable feature of the variance decomposition literature is that virtually all studies model only changes in real exchange rates and the fundamental variables. The presence of long-run relationships between the levels of the variables is either rejected (as in Clarida and Gali, 1994 and Rogers, 1999) or not investigated (as in Weber, 1997).1 Again, there is a gap between this empirical literature and related studies of long-run real exchange rate determination. Most papers in the latter field do find long-run equilibrium relationships between real exchange rates and various fundamental variables. There is ample documentation of cointegration between levels of real exchange rates and, for instance, relative productivity (see MacDonald, 1998, for a survey). Hence, previous studies of the sources of real exchange rate fluctuations (i) invariably conclude that productivity shocks have a negligible impact and (ii) do not find cointegration between real exchange rates and fundamental variables (or do not investigate whether they are cointegrated). After confirming the presence of cointegration, this paper demonstrates that relative productivity shocks dominate the long-run variance decompositions of real exchange rates when long-run equilibrium relationships are taken into account. The result is robust across a number of alternative empirical specifications.
2. Statistical methods If real exchange rates are cointegrated with fundamental variables, models using only differenced data are misspecified and do not utilize the information contained in the levels of the data. In particular, the absence of cointegration implies that it is not possible to model a time varying equilibrium level of the real exchange rate as function of the included fundamental variables. The VAR models used by Clarida and Galı´ (1994) and others to identify structural shocks and obtain variance decompositions can however incorporate long-run equilibrium relationships between the levels of the variables. Following King et al. (1991), structural shocks are 1
Actually, Clarida and Gali (1994) find cointegration for one of the four bilateral systems studied, but this is ignored in the subsequent empirical analysis. In Rogers (1999), the null hypothesis of cointegration would not be rejected if the 90% critical values of the Johansen (1988) tests were used instead of the 95% critical values.
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identified by imposing long-run restrictions of their effects within a cointegrated VAR model: Dxt ¼ m þ Pxt1 þ
P X
Gi Dxti þ tþ1 .
(1)
i¼1
The n-dimensional error-correction representation in (1) can be re-written as a common trends model (see e.g. Stock and Watson, 1993): xt ¼ x0 þ Att þ fðLÞvt ,
(2)
where tt ¼ m þ tt1 þ jt .
(3)
The number of cointegrating vectors r in (1) determines the number of independent stochastic trends k in the common trends model (2) as k ¼ n r: tt are the k stochastic trends with the drifts m and the innovations jt : The loading matrix A determines how the variables in xt are affected by the stochastic trends in the long run. In order to identify the structural shocks, kðk 1Þ=2 restrictions are imposed on the impact matrix A.
3. Empirical results We estimate the common trends model in (1)–(3) for each bilateral real exchange rate and the corresponding time-series on relative real output, relative government spending and relative price levels. Bilateral real exchange rates between the United States, the United Kingdom, Germany and Japan are constructed from nominal exchange rates (units of domestic currency per unit of foreign currency) and CPI price levels. Corresponding data on relative real output (volume indices), yt ; relative government consumption as share of output, gt ; and relative (CPI) price levels, pt ; are defined as the domestic variable minus the foreign variable. The data are collected from the OECD database Main Economic Indicators. All variables are in logarithms of the levels of the time series and the sample period is 1960Q1 to 1998Q4. As in previous studies, the ADF unit root test (not reported) indicates that the time-series are I(1). 3.1. Cointegration and identification The Johansen (1988) cointegration tests indicate that there is one cointegrating vector in all cases. There is more evidence of two cointegrating vectors than of no cointegration as two of the second largest trace statistics are significant. Given that the presence of cointegration between real exchange rates and fundamental variables is a controversial issue, the results have been confirmed using alternative methods.2 2
Additional tests for cointegration (Stock and Watson, 1988 and Park, 1992) also indicate that there is cointegration in four of the six bilateral systems. At least two of the three tests indicate cointegration for
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Table 1 Johansen (1988) tests for cointegration Currency
lð1Þ
lð2Þ
lð3Þ
lð4Þ
trð1Þ
trð2Þ
trð3Þ
trð4Þ
# lags
USD/DEM USD/JPY USD/GBP JPY/DEM JPY/GBP GBP/DEM Critical values
28.57 31.70 24.93 30.81 41.01 31.82 24.73
13.40 12.48 14.92 11.03 15.54 17.11 18.60
865 8.80 10.21 9.30 8.94 6.84 12.07
1.48 2.97 1.02 4.28 3.92 5.32 2.69
52.10 55.94 49.09 55.42 69.41 61.09 43.95
23.52 24.24 26.16 24.62 28.40 29.27 26.79
10.13 11.76 11.23 13.59 12.86 12.16 13.33
1.48 2.97 1.02 4.28 3.92 5.32 2.69
6 6 3 3 5 5
lð1Þ denotes the largest l-max statistic and lð2Þ denotes the second largest. 90% critical values are taken from Osterwald-Lenum (1992). While information criteria indicate that one to three lags are appropriate, three to six lags are required to remove residual autocorrelation.
According to the estimated cointegrating vectors, countries with high relative real GDP and high relative government consumption have stronger real exchange rates in the long-run (Table 1). The structural shocks are identified by imposing restrictions on their long-run effects. Given one cointegrating vector and four variables, there are three stochastic trends, identified as a relative productivity shock, a government spending shock, and a monetary shock. All three shocks are allowed to affect the real exchange rate and the relative price level in the long-run. Monetary shocks are identified by the assumption that they do not affect relative output or government spending in the long-run. One additional restriction is needed for exact identification. In the baseline model, following Rogers (1999), government spending shocks are allowed to affect output but changes in productivity are assumed not to affect government spending in the long-run. The identification of structural shocks within VARs has been questioned by e.g. Faust and Leeper (1997). Several empirical studies have however confirmed that VAR models identify productivity shocks that closely resemble classic and refined Solow residuals (Kiley, 1998; Alexius and Carlsson, 2002).In Section 4, we check whether the results are robust to variations in the empirical specification and the identifying assumptions. Fig. 1 illustrates that the stochastic relative productivity trends closely tracks relative real GDP. The short-run responses of output and prices to productivity shocks and government spending shocks have the expected signs in all empirical models. Most of these impulse-response functions are however not significant. More interestingly, all six real exchange rates appreciate significantly in response to increases in relative productivity both in the short- and long-run. This is consistent with the Balassa
(footnote continued) each real exchange rate, i.e. the different tests reject cointegration for different pairs of countries. Three of the four rejections of cointegrations however concern US bilateral real exchange rates.
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559
Relative real GDP, US-UK
0.05 0.00 -0.05 -0.10 -0.15 -0.20 -0.25 60
65
70
75
80
85
90
95
Fig. 1. Relative productivity trend and relative real GDP for the U.S. versus the U.K.
(1964) and Samuelson (1964) approach but not with the Obstfeld (1985) model or other models without a distinction between tradable and non-tradable goods. 3.2. Finite horizon variance decompositions Table 2 shows forecast error variance decompositions as the horizon is increased from 1 to 40 quarters. Three of the six real exchange rates behave roughly as expected: The DEM/JPY, USD/JPY and GBP/DEM. Transitory shocks dominate the short-run movements as they account for about half of the forecast error variance at the quarterly horizon. The relative influence of transitory shocks then declines as the forecasting horizon is extended. At the 10-year horizon, they only account for 15–20% of the variance. The remaining 80–85% of the 10-year fluctuations in these three real exchange rates can hence be explained by movements in the included fundamental variables. Monetary shocks are slightly more important to the first three real exchange rates than what is typically found. Since 20–30% of the 10-year fluctuations are due to monetary shocks, their effects are also rather persistent. Government spending shocks, on the other hand, are negligible. The influence of productivity shocks increases continuously with the horizon, from 15–20% of the forecast error variance at the first quarter to about 50% at the 10-year horizon. Productivity is hence much more important here than what has been found in the previous studies. For the second group of real exchange rates, the GBP/USD, USD/DEM, and GBP/JPY, transitory shocks dominate the variance decompositions even at forecasting horizons of 10 years. The share of the variance due to transitory shocks actually increases with the forecasting horizon in case of the USD/DEM real exchange rate. The finding that more than 80% of its 10-years fluctuations are transitory can be interpreted as the common trends model’s way of indicating that the USD/DEM real exchange rate is close to stationary over the sample period (see Fig. 2). This is an undesirable situation given that the statistical model is designed to handle non-stationary data. PPP is however formally rejected in all six cases.
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Table 2 Forecast error variance decompositions at one to 40 quarters Currency
Horizon
Productivity
DEM/JPY
1 4 8 12 20 40
14.31 29.48 38.00 42.64 48.55 56.82
USD/JPY
1 4 8 12 20 40
GBP/DEM
Government
Monetary
Transitory
1.70 2.22 2.26 2.74 3.80 5.77
18.84 30.21 30.78 29.57 26.93 22.19
65.15 38.09 29.95 25.05 20.72 15.21
21.23 17.34 21.97 26.89 34.11 45.27
0.20 0.67 0.40 0.82 3.81 9.41
41.54 44.78 44.59 43.28 38.39 29.07
37.21 37.20 33.04 29.01 23.67 16.25
1 4 8 12 20 40 1
17.36 25.70 36.49 38.21 40.56 48.47 3.67
2.85 1.81 0.99 1.05 2.65 3.88 0.13
27.88 31.21 33.29 34.18 32.40 27.17 20.59
51.92 41.28 29.23 26.55 24.39 20.48 75.60
GBP/USD
4 8 12 20 40 1
9.38 13.55 17.62 21.48 23.37 2.87
0.45 1.43 2.11 2.83 12.71 18.68
11.20 9.36 9.44 9.15 10.74 22.79
78.98 75.66 70.82 66.54 53.29 55.66
USD/DEM
4 8 12 20 40 1
1.96 4.74 6.34 7.39 6.24 7.50
10.51 7.91 6.67 5.01 3.99 30.13
20.16 16.46 13.2 9.81 7.51 2.22
67.38 70.90 73.79 77.80 82.25 60.15
GBP/JPY
4 8 12 20 40
6.25 4.72 3.80 3.77 23.9
27.81 27.25 27.32 28.02 23.24
8.12 6.41 5.46 5.77 4.61
57.82 61.67 63.42 62.43 48.21
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Real exchange rate, USD/GBP
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 60
(a)
65
70
75
Productivity driven part
80
85
90
95
Real exchange rate, USD/DEM
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 60
(b)
65
70
75
80
Productivity driven part
85
90
95
Real exchange rate, USD/JPY
1.2 0.8 0.4 0.0 -0.4 -0.8
(c)
60
65
70
75
80
85
90
95
Fig. 2. (a) The real exchange rate and its productivity driven part for the US versus the UK; (b) the real exchange rate and its productivity driven part for the US versus Germany; (c) the real exchange rate and its productivity driven part for the US versus Japan.
Another notable feature of the short- to medium-run variance decompositions for the second group of real exchange rates is that while the influence of productivity shocks increases with the horizon, they are much less important here than for the
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first group. Productivity shocks cause less than 25% of the movements in the GBP/ USD and GBP/JPY real exchange rates also at the 10-year horizon and their share never exceeds 8% in case of the USD/DEM. This is consistent with previous findings; it is the large influence of productivity shocks documented for the first group of real exchange rates that is atypical. 3.3. Infinite horizon variance decompositions Long-run forecast error variance decompositions reveal what structural shocks have caused the permanent movements in the real exchange rates. As shown in the second column of Table 4, relative productivity shocks account for most of the longrun variance, 63–90% for all the real exchange rates except the GBP/USD (where the share is only 26%). These results contrast blatantly with the typical finding that supply shocks only account for a minuscule share of the movements in real exchange rates. The largest influence of supply shocks previously documented for major currencies is one-third of the forecast error variance (Weber, 1997). Government spending shocks typically account for 20–30% of the long-run movements. They are more important to the GBP/USD (55%) and less important to the GBP/JPY (4%). As expected from long-run monetary neutrality, monetary shocks are unimportant in the long-run.
4. Historical decompositions By feeding the identified productivity shocks into the estimated systems, the productivity driven components of the real exchange rates can be extracted. Figs. 2a–c show the USD/DEM, USD/GBP and USD/JPY real exchange rates and their respective productivity components. Several observations can be made in light of these figures and the variance decompositions in Tables 2 and 3. Above all, the USD/DEM real exchange rate displays a weak relationship to its productivity driven part. At the same time, 64% of the infinite horizon forecast error variance is due to productivity shocks. The key to reconciling these two results can be found in the finite horizon variance decomposition, which shows that more than 80% of its 10-year fluctuations are transitory. Productivity shocks cause most of the permanent Table 3 Long run variance decomposition for the levels Currency
Productivity
Government
Monetary
USD/DEM USD/JPY GBP/USD DEM/JPY GBP/JPY GBP/DEM
63.7 72.2 26.3 80.1 76.4 90.6
30.3 20.0 54.9 11.7 22.2 4.1
6.0 7.8 18.9 8.2 1.2 5.0
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movements, but the non-stationary component of the USD/DEM real exchange rate is small relative to the stationary fluctuations. This case demonstrates that infinite horizon variance decompositions can provide different answers to the question about the causes of fluctuations than both finite horizon variance decomposition and historical decompositions when transitory shocks are important at long but finite horizons. The historical decomposition of the USD/JPY real exchange rate, on the other hand, is more consistent with the finding that productivity shocks explain most (72%) of the permanent movements. There are however also considerable deviations from the productivity driven trend. The finite horizon variance decomposition is not at odds with the infinite horizon results in this case as 45% of the 10-year movements are caused by productivity shocks and only 16% are transitory. The productivity driven component of the USD/GBP real exchange rate appears to track the permanent real exchange rate movements reasonably well. The infinite horizon variance decomposition however only attribute 26% of the permanent movements to productivity shocks, a number that squares well with the results for the 10-year horizon but appears low, given Fig. 2b. The finding that transitory shocks cause more than half of the 10-year movements is in line with the large and persistent deviations from the non-stationary equilibrium observed in the graph.
5. Robustness of the results The results from VAR models where the structural shocks are identified using restrictions on their long-run effects may vary considerably with the exact formulation of the empirical model. We therefore, study the robustness of the results with respect to changes in the identifying assumptions and the included variables. Five alternative empirical models are estimated. Three of them incorporate long-run equilibrium relationships between the real exchange rates and the fundamental variables. First, the baseline model is re-estimated using data on relative money supply instead of relative price levels to capture monetary developments (model A).3 Second, the identifying assumption that productivity shocks do not affect government spending is replaced by the alternative assumption that government spending does not affect output in the long-run (model B). This implies full crowding out of government spending in the long-run and a possible feed-back from real output to government spending. For instance, richer countries may have higher government spending relative to GDP. In model C, the government spending variable is excluded. Hence, this is the Clarida and Galı´ specifications with cointegration. The two final models ignore the presence of long-run equilibrium relationships between the variables. Model D is the original Clarida and Gali model including only the first differences of real exchange rates, relative output and relative prices. Model E is the baseline model of this paper re-estimated under the assumption of no 3
Data on money supply (M2) are taken from the OECD data base Main Economic Indicators.
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Table 4 The share of the long-run forecast error variance due to productivity shocks in alternative empirical models Currency
Model A
Model B
Model C
Model D
Model E
USD/DEM USD/JPY GBP/USD DEM/JPY GBP/JPY GBP/DEM
50.1 36.8 43.5 99.9 71.5 73.0
67.5 33.6 26.9 49.4 92.9 29.6
39.6 74.3 14.5 91.7 91.3 99.7
16.04 9.63 4.95 2.42 17.68 6.86
13.81 9.34 6.10 4.69 15.72 4.18
Model A is the original model with relative money supply rather than price levels. Model B is the original model with a different distinction between supply shocks and real demand shocks. Model C is a threevariable model including the levels of qt ; pt pt ; and yt yt : Model D is the Clarida and Gali model using only the first differences: [Dqt ; Dðpt pt Þ; and Dðyt yt Þ]. Model E is the model of this paper but without cointegration, i.e. [Dqt ; Dðyt yt Þ; Dðgt gt Þ; Dðpt pt Þ].
cointegration, i.e. a four variable VAR containing the first differences of the real exchange rate, relative output, relative prices and relative government expenditure. Table 4 shows the shares of the long-run variances due to supply shocks in the five alternative empirical specifications. In models A to C, productivity shocks account for a much larger share of the long-run variance than what has been found in previous studies. The GBP/USD real exchange rate is an exception as the share of the long-run variance due to supply shocks is below 30% in two of the specifications. For models D and E, productivity shocks are unimportant to the long-run real exchange rate movements, as is typically found when only changes in the variables are modelled. Hence, when long-run equilibrium relationships between the variables is taken into account, productivity shocks cause most of the long-run movements in real exchange rates. Without cointegration, there are no long-run equilibrium relationships between relative output levels and real exchange rate levels. To the extent that productivity shocks affect real exchange rates through these long-run relationships and the adjustment to equilibrium, excluding the cointegration term in Eq. (1) cuts the link between productivity and real exchange rates. It is however also clear that the identifying assumptions matter as the results in Table 4 vary considerably between the empirical specifications. Rogers (1999) also estimates a number of alternative empirical models. Supply shocks typically account for less than 10% of the long-run variance of real exchange rates in his study and the largest share is 25.2%. However, none of his nine alternative specifications includes cointegration between real exchange rates and the fundamental variables.
6. Conclusions Previous studies of the causes of fluctuations in real exchange rates conclude that the impact of productivity shocks is negligible. This paper uses a statistical approach where long-run equilibrium relationships between real exchange rates and
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fundamental variables are explicitly taken into account. Contrary to previous studies, relative productivity shocks are found to be the dominating source of longrun movements in real exchange rates. For five of the six real exchange rates, 60–90% of the permanent movements are due to productivity shocks. In the cases where transitory shocks are important at long horizons, historical decompositions are however more consistent with the finite horizon variance decomposition than with the infinite horizon results. Productivity shocks account for about half of the ten-year movements of the USD/JPY, DEM/JPY, and GBP/DEM, but are less important to the remaining three exchange rates. The documented real effects of money are slightly larger and more persistent in this paper than what is typically found. For three of the six real exchange rates, 20–30% of the 10-year movements are due to monetary shocks. Long-run monetary neutrality however appears to hold at the infinite horizon. To check the robustness of the results, five alternative empirical specifications using other identifying assumptions and/or variables are estimated. The exact formulation of the VAR model matters as the share of the long-run variance due to supply shocks varies considerably between the different models. However, in the cases where long-run equilibrium relationships between the levels of the real exchange rates and the fundamental variables is allowed, relative productivity shocks is a much more important source of long-run movements in real exchange rates than what has been documented in previous studies. This result can be interpreted as empirical support for the relative productivity approach of Balassa (1964) and Samuelson (1964). References Alexius, A., Carlsson, M., 2002. Measures of technology and the business cycle. Review of Economics and Statistics 87 (2), to appear. Balassa, B., 1964. The purchasing power parity doctrine: a reappraisal. Journal of Political Economy 72, 584–596. Canzoneri, M., Cumby, R., Diba, B., 1999. Relative labor productivity and the real exchange rate in the long-run: evidence for a panel of OECD countries. Journal of International Economics 47, 245–266. Chadha, B., Prasad, E., 1997. Real exchange rate fluctuations and the business cycle: evidence from Japan. International Monetary Fund Staff Papers 44, 328–355. Chinn, M., Johnston, L., 1996. Real exchange rate levels, productivity and demand shocks: evidence from a panel of 14 countries. NBER Working Paper No. 5709. Clarida, R., Gali, J., 1994. Sources of real exchange rate fluctuations: how important are nominal shocks? Carnegie Rochester Series on Public Policy 41, 1–56. Eichenbaum, M., Evans, C., 1995. Some empirical evidence of the effects of shocks to monetary policy on exchange rates. Quarterly Journal of Economics 110, 975–1010. Faust, J., Leeper, E., 1997. When do long-run identifying restrictions give reliable results? Journal of Business and Economics 15, 345–353. Johansen, S., 1988. Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control 12, 231–254. Kiley, M., 1998. Labor productivity in U.S. manufacturing: does sectoral co-movements reflect technology shocks? Mimeo, Federal Reserve Board. King, R., Plosser, C., Stock, J., Watson, M., 1991. Stochastic trends and economic fluctuations. American Economic Review 81, 819–840.
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MacDonald, R., 1998. What do we really know about real exchange rates? Working Paper No 28, Oesterreichische Nationalbank. Obstfeld, M., 1985. Floating exchange rates: experience and prospects. Brookings Papers on Economic Activity 2, 369–450. Osterwald-Lenum, M., 1992. A note with quantiles of the asymptotic distribution of the maximum likelihood cointegration rank test statistics. Oxford Bulletin of Economics and Statistics 54, 461–472. Park, J., 1992. Canonical cointegrating regressions. Econometrica 60, 119–143. Rogers, J., 1999. Monetary shocks and real exchange rates. Journal of International Economics 49, 269–288. Samuelson, P., 1964. Theoretical notes on trade problems. Review of Economics and Statistics 46, 145–154. Stock, J., Watson, M., 1993. A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61, 783–820. Weber, A., 1997. Sources of purchasing power disparities between the G3 economies. Journal of the Japanese and International Economies 11, 548–583.