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Commodity Currencies and Empirical Exchange Rate Equations by Yu-chin Chen (Harvard University) and Kenneth Rogoff (International Monetary Fund) September 25, 2001 This paper was prepared for the November 15-16 Conference on Understanding Exchange Rates in Amsterdam, The Netherlands. The authors are grateful to Andra Ghent, Tracy Chan, and John Murray at the Bank of Canada, Faith Darling and Joseph Gagnon at the Board of Governors of the Federal Reserve System, Ximena Cheetham, Hali Edison and Paul Nicholson at the International Monetary Fund and to Anne-Marie Brook at the Reserve Bank of New Zealand. The views expressed in this paper are the authors’ own and do not necessarily represent those of the International Monetary Fund. 1. Introduction While there do not appear to be any robust exceptions to the Meese-Rogoff (1983) result for major OECD currencies (and certainly the advent of the euro has not changed that assessment), there are some purported exceptions among some of the smaller OECD currencies.1 Researchers at the Bank of Canada have claimed for many years that in fact, not only do standard empirical exchange rate equations fit out-of-sample, one can even use variants to successfully predict the exchange rate, both unconditionally and in response to policy alternatives.2 A key element of the Canadian equation involves augmenting the standard model by a terms of trade variable reflecting the volatile movements in world prices of Canadian commodity exports, particularly non-energy commodities. Researchers at the Reserve Bank of Australia have at times been even more ebullient, finding that over the 1990’s, one could have earned a substantial excess profit in trading on the Australian dollar by properly incorporating forecastable terms of trade movements into exchange rate forecasts.3 Finally, a similar framework has also been extended to the New Zealand dollar.4 It has long been recognized that if one could find a missing real shock that were sufficiently volatile, one could potentially go a long ways towards resolving major empirical exchange rate puzzles such as the Meese-Rogoff puzzle and the purchasing power parity (PPP) puzzle.5 For most OECD economies, it is hard to know what that shock might be, much less measure it.6 In Canada, Australia and New Zealand, however, because commodities constitute a significant component of their export, world commodity price fluctuations – generally exogenous to these small countries for all but a few goods – potentially explain a major component of their terms of trade fluctuations.7 Therefore, for the three “commodity currencies,” a potential key missing real shock is both easy to measure and to incorporate. 1 See Frankel and Rose (1995) for a comprehensive survey of the empirical research on exchange rates. See, for example, Amano and van Norden (1993) and Djoudad, Murray, Chan and Dow (2000). 3 See, for example, Gruen and Kortian (1996). 4 See again Djoudad, Murray, Chan and Dow (2000); the connection is also explored in Brook (1994). 5 See, for example, Rogoff (1996) for a discussion of the PPP puzzle. 6 Oil prices certainly have the volatility and there is some evidence that they impact the terms of trade (Backus and Crucini, 2000), but adding these variables to standard monetary equations does not seem to do the trick. 7 Simply incorporating the terms of trade as an explanatory variable would not be meaningful for most OECD countries, since the terms of trade contain a large component that moves mechanically with the exchange rate (see Obstfeld and Rogoff, 2000). This is most likely due to a combination of wage and price rigidities interacting with at 2 1 Our paper aims to address the following two questions. Is it true that commodity price shocks explain a significant share of exchange rate movements for these currencies? And if so, does the introduction of commodity prices more broadly “fix” standard monetary empirical exchange rate models? Affirmative answers here might encourage researchers to try harder to search for corresponding real shocks to the major currencies. In addition, understanding the effects of commodity price shocks on exchange rates is also of broad interest to developing countries, particularly as some open up their capital markets and adopt more flexible exchange rates. If commodity prices can indeed be shown to be a consistent and empirically reliable factor in empirical exchange rate equations, the finding would have important implications across a variety of policy issues, not least concerning questions such as how to implement inflationtargeting in developing countries.8 The outline of this paper is as follows. In section 2 of the paper, we give a brief overview of the economic environment in the three countries we are studying. We then proceed to give some simple, but striking, evidence on just how closely movements in these currencies seem to track the corresponding world price indices of their commodity exports. The strong correlations come through not only for cross rates against the U.S. dollar, but also for cross rates against the pound and against a broad index of non-US-dollar currencies. In section 3, we go on to see whether the visual evidence stands up to closer scrutiny, focusing on the simplest empirical models, not least because the data sample is limited and richer dynamic models would lack credibility. We find that for New Zealand and Australia, the correlation between commodity prices and exchange rates holds up remarkably well, and seems robust to alternative assumptions about the underlying time series processes. Though there is some evidence of structural breaks, especially at the time these countries switched to formal inflation targeting, the general size of the contemporaneous correlation between commodity prices and exchange rates nevertheless seems relatively consistent, both across time and across countries. The commodity price elasticity estimate is roughly 0.5 for Australian and 1.0 for New Zealand. For Canada, the least partial pass-through. Our main explanatory variable here is not the terms of trade but indices of world commodity prices, which presumably do not move automatically with these small countries exchange rates. 8 There has been related work for developing countries that looks at cross-country panel data. For example, Mendoza (1995) finds that terms of trade shocks account for a significant portion of variation in output in developing countries, whereas Bidarkota and Crucini (2000) find a strong connection between shocks to commodity prices and the terms of trade. 2 evidence is more mixed, with the correlation between exchange rates and commodity prices much more sensitive to detrending. We go on in section 4 to ask whether the relationship might result from the countries having market power in their commodities, and we find that this is not the case. A structural interpretation of the estimates is offered in the appendix, in light of two relatively standard exchange rate models. We argue that the quantitative size of our estimates is quite plausible. Having found a robust connection between commodity export prices and exchange rates, we extends the analysis in section 5 to look at commodity price-augmented standard empirical exchange rate equations. By controlling for this major source of real shocks, one might hope the standard exchange rate equations - adjusted for commodity price shocks - might perform better for "the commodity currencies" than they have been found to perform for the major currencies. However, our results do not offer very strong encouragement for this point of view. The final section concludes. 2. Background and Graphical Evidence 2.1. Background From a macroeconomic perspective, Australia, Canada, and New Zealand are near perfect examples of well-developed, small open economies. All three are highly integrated into global capital markets and active participants in international trade. Moreover, to varying degrees, all three countries can plausibly be described as “commodity economies”, given the large share primary commodities occupy in their production and exports. For at least the past decade, commodities have maintained a 60% share of Australia's total exports, with wool, wheat, and various metals as examples of leading exports. In New Zealand, while the share has declined from a hefty two-thirds in the late 1980s, commodities continue to account for more than half of total exports in recent years. Canada, albeit having a larger industrial base, still has more than a quarter of its exports in commodities such as base metals, forestry products, crude oil, and natural gas. 3 Given the major role primary commodities play in generating export earnings for these countries, it is perhaps no coincidence that, despite the relatively small size of their overall economies, these countries hold significant market power for a few of their products. In New Zealand, for instance, 46 million sheep cohabit with 3.8 million people. Not surprisingly, only 20 percent of its meat production are consumed domestically, and New Zealand supplies close to half of the total world exports of lamb and mutton. Canada similarly dominates the world market in forestry products, and Australia holds significant shares of the global exports in wool and iron ore. However, while each country has some market power for a few key goods, they are, on the whole, price takers in world markets for the vast majority of their commodity exports. In terms of monetary and exchange rate policies, all three countries have been operating under a flexible exchange rate regime for a considerable length of time. Shortly after the collapse of Bretton Woods, Canada began floating its currency, and as part of the economic reform efforts to revitalize their economies, Australia and New Zealand abandoned their exchange rate pegs in 1983 and 1985 respectively. In addition, Australia, Canada, and New Zealand all adopted some variant of inflation targeting in the early 1990s.9 2.2. Graphical Evidence [INSERT FIGURES 1a-c to 3a-c HERE] Figures 1a through c show the Australian real exchange rate relative to three reference currencies – the U.S. dollar, the British Pound, and a non-US-dollar currency basket – plotted alongside the world price of Australia’s major non-energy commodities, aggregated using Australian production weights. The corresponding graphs for Canada and New Zealand are shown in Figures 2 and 3. For all three countries, the sample period starts roughly a year after the float of the particular home currency. To abstract away from the issue of non-stationarity in nominal prices, we focus on real exchange rate behavior in this paper. The real exchange rates in these graphs (and in all the subsequent analyses) are end-of-quarter nominal rates, expressed as the foreign 4 exchange values of the domestic currency, adjusted by the relevant CPIs. An increase in the real rates thus represents a rise in the relative price of home goods or, a real appreciation for the home country. The non-dollar basket is adopted from the Broad Index of the Federal Reserve. It is a composite of over 30 non-US-dollar currencies, covering all major trading partners of the United States each weighted by their respective trade shares.10 By measuring the relevant home currencies against different anchors, especially the broad index covering many developing countries, we hope to insulate our analysis from being driven by shocks to the U.S. economy and the movements in the U.S. dollar. The country-specific commodity price indices cover non-energy commodities only, and they are fixed-weight geometric averages of the world market prices for the major commodities produced in each country, weighted by their corresponding domestic production share. Individual real commodity prices are quarterly averages of the world market transaction prices in U.S. dollars, deflated by the U.S. CPI. The commodities included in each index and their corresponding weights are listed in the data appendix.11 Looking at these sets of graphs, three features especially stand out. First, the correlations between the various exchange rates and the commodity prices are strikingly apparent. Not only do the series appear to mirror each other in movement, the magnitude of their swings are also similar. In addition, the exchange rates, some more than others, appear to be highly persistent, and possibly non-stationary. Lastly, the long-term decline of global commodity prices seems clearly reflected in these country-specific series as well. In the following section, we explore further just how strong and robust the apparent correlations are, and the role common trends may play in explaining the co-movements of real exchange rates and commodity prices. 9 We refer the reader to Zettelmeyer (2000) for a more thorough discussion of the conduct of monetary policy in these three countries in the 1990s. 10 It does not matter that the home-country currency appears in our non-dollar index (the New Zealand and Australia weights are zero/very small), since it essentially factors out when we construct the exchange rate of the non-dollar index against the home currency. There is no particular significance to using U.S. trade weights in our analysis; we adopt the broad index of the Federal Reserve as a convenient check for the robustness of our results. 11 The weights for individual commodities are drawn from Djoudad, Murray, Chan, and Daw (2000) and represent the average domestic production value of the commodity over the 1982-90 period. Certain commodities in the original Djoudad et al indices are excluded as we were unable to extend the price series. The excluded commodities amount to less then 5% of the original production weight in each instance (see the Data Appendix). However, Australia and Canada, respectively, do hold significant global export market shares in barley and sulphur. 5 3. Some Empirical Evidence We first focus extensively on testing very simple correlations, which seems an appropriate starting point in light of earlier empirical failures. In subsequent sections, we will explore richer dynamics, address potential endogeneity, and also test whether the inclusion of commodity prices can help provide stronger empirical support for canonical exchange rate models. Results in Table 1 capture the simple contemporaneous correlations we observe in the figures. The similarity of coefficient estimates across currency pairings is remarkable; a one percent improvement in the world price of their commodity export is associated with an appreciation of the home currency by around 40 to 50 basis points for all three countries, regardless of the anchor currency. Table I Commodity Price Elasticities of Real Exchange Rates Dependent Variable: Log of Real Exchange Rate, relative to Different Anchor Currencies ln(Real Exchange Rate)t = α + β*ln(Real Commodity Price)t + εt Australia National Currency vs. U.S. Dollar vs. British Pound Ln(Real 0.40 * Commodity Canada vs. U.S. Dollar vs. British Pound 0.51 * vs. NonDollar Basket 1 0.36 * 0.40 * (0.08) (0.09) (0.06) 0.39 0.55 0.51 New Zealand vs. U.S. Dollar vs. British Pound 0.50 * vs. NonDollar Basket 0.36 * 0.53 * 0.61 * vs. NonDollar Basket 0.41 * (0.07) (0.14) (0.09) (0.17) (0.10) (0.10) 0.56 0.34 0.34 0.30 0.45 0.36 Prices) 2 Adj. R2 N Obs. 70 114 62 Sample Period 1984Q1 - 2001Q2 1973Q1 - 2001Q2 1986Q1 - 2001Q2 Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors in parentheses. 1. “Non-dollar Basket” is a U.S. trade-weighted average of over 30 currencies, excluding the U.S. dollar, of major U.S. trading partners. It is based on the broad real index from the Federal Reserve. 2. Real commodity price index is the base country production-weighted average of world commodity prices in U.S. dollars, deflated by the U.S. CPI. See the data appendix for country-specific production weights. 6 3.1. Detrending The simple regressions in Table I are suggestive, but there is an issue of how best to address a small sample of data with (near) unit-root behavior.12 Since our small sample size precludes any meaningful test of stationarity, we instead rely on the considerable empirical evidence suggesting that real exchange rates are stationary, possibly with a trend, as theory would predict. (See Froot and Rogoff, 1995, who find that the half life of real exchange rate shocks is roughly 3-4 years across a wide variety of historical data, at least in linear models.). The same is arguably true for commodity prices.13 Ruling out non-stationarity/stochastic trends a priori, detrending the data seems an appropriate strategy to consider next.14 We employ three different types of detrending methods – linear trend, Hodrick-Prescott filter, and first differencing – to test the robustness of the positive correlations we observed earlier.15 Since results based on different anchor currencies are very similar, to conserve space, we only report results for the U.S. dollar exchange rates in this section. Table II shows the commodity price elasticity estimates under these filters. For Australia and New Zealand, the commodity price elasticity estimates show up slightly higher, but in general appear consistent with the previous findings. The estimates also seem robust to the three detrending methods, even first differencing, which admittedly would be more appropriate with non-cointegrated unit root series. Results for the other anchor currencies are similar. For Canada, under the full sample period of 1973 to 2001, detrending appears to render all previously observed correlations 12 In addition to the figures which hint at unit roots in these series, we cannot reject the null of non-stationarity using the augmented Dickey-Fuller or the Phillips-Perron tests for the exchange rate and commodity price series. The null of stationarity is rejected under the Kwiatkowski, Phillips, Schmidt, and Shen (1992) unit root test as well. 13 See Borensztein and Reinhart (1994) and Cashin, Liang and McDermott (2000). One might argue that even though most real exchange rates appear to be stationary, the commodity currencies might be an exception if commodity prices themselves have a unit root. However, it should be noted that over the very long run, countries can substitute out of commodity production into manufactures if the relative price of commodities drifts too low. Korea today exports primarily manufactured goods, but in 1960 almost 90% of exports were commodities. 14 Note that this assumption notwithstanding, the methodologies discussed in this section do cover the econometric techniques appropriate for I(1) processes, namely first-differencing and dynamic OLS. 15 We recognize the limitation and potential problems associated with each of these filters. For example, should the series be difference-stationary, linear detrending will result in spurious cycles. While the HP filter does not assume a stable trend process over time, it suffers from the well-documented end-point problem, as well as the drawback mentioned in Cogley and Nason (1991) should the exchange rate and commodity price series be cointegrated. First difference filter removes long term trend but also potentially important information contained in the levels of the series; it is mainly relevant when commodity prices and real exchange rates are non-cointegrated I(1) series. 7 between real commodity prices and the Canadian real exchange rates insignificantly different from zero, and in several cases, it produces negative commodity price elasticity estimates. We note that one cannot entirely dismiss the significance of the common long-term trend between the Canadian dollar and commodity export prices. Indeed, the downward drift in both series may be intimately connected; we simply cannot statistically demonstrate any such connection here. In addition, we suspect the elusiveness of this correlation for Canada may be related to its ambiguous status as a “true commodity economy”. After all, commodities are clearly the minority in its export base, compared to the case of New Zealand and Australia. However, structural breaks occurring somewhere over the thirty year period is certainly another possibility.16 Indeed, looking at the Canadian-U.S. rates since mid-1980s (as we do for Australia and New Zealand), we obtain significant positive coefficient estimates of around 0.3 under the linear and the hp filters. However, perhaps not surprisingly, such significant correlation disappears when its exchange rate is measured relative to the other two anchor currencies. We will return to the issue of parameter stability later. Table II: Detrending Series Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar Detrended ln(Real Exchange Rate)t = α + β*Detrended ln(Real Commodity Price)t + εt Australia Detrending Filter: Ln(Real Linear HP 0.81 * Commodity Canada st New Zealand Linear HP 0.09 1 Difference 0.05 1.10 * 0.73 * 1st Difference 0.59 * (0.15) (0.07) (0.06) (0.32) (0.20) (0.26) 0.05 0.03 -0.00 0.27 0.25 0.10 Linear HP 0.58 * 1 Difference 0.47 * 0.21 (0.12) (0.12) (0.14) 0.53 0.37 0.07 st Prices) Adj. R2 N Obs. Sample Period 70 114 62 1984Q1 - 2001Q2 1973Q1 - 2001Q2 1986Q1 - 2001Q2 Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors in parentheses. 16 It is important to emphasize that we focus here only on non-energy commodities. In gross terms at least, Canada is a significant exporter of coal and natural gas. Our explorations with including energy prices separately did not significantly change our results for the Canadian dollar, but the issue needs to be investigated more thoroughly than we take up here. 8 As different detrending techniques seem to yield similar results, we will continue the rest of our analysis with the linear trend. Figures 4 through 6 show the linearly detrended data. Again, note how closely the detrended commodity price and exchange rate series seem to track each other. [ INSERT FIGS 4-6 HERE] 3.2. Serial Correlation Given the persistence of the series, it is perhaps no surprise that even with the inclusion of a linear trend, the error structure in the linear regressions still exhibit significant serial correlation.17 We will examine more fully in section 5 how this serial correlation may reflect the nature of the missing shocks. In this section, we focus on correcting the biased standard errors estimates under serial correlation. Up to this point, we have been reporting the kernel-based nonparametric GMM estimator of Newey-West (1987). Because such non-parametric estimators are known to have poor small sample properties, we now also consider a parametric specification where the error terms are assumed to follow a first order autoregressive process. As can be seen from Table III, the AR(1) specifications effectively bring the Durbin-Watson statistics back towards 2, and while lowering the coefficients slightly, still give elasticity estimates of around 0.5, consistent with our earlier findings.18 Alternatively, if these series were non-stationary, the estimates and significance tests performed above based on classical statistical methods would be invalid. As a robustness check, we consider the alternative assumption that real exchange rates and real commodity prices are cointegrated I(1) series.19 In Table III, we present results from the dynamic OLS specifications of Stock and Watson (1993), where leads and lags of the first-differenced log commodity prices 17 The Durbin-Watson statistics for the regressions presented in Table 1 and 2 are all well below 2, and autocorrelograms show clear evidence of autoregressive error structures. (Note the HAC consistent GMM standard errors reported in these tables account for this serial correlation.) 18 The autocorrelation coefficient estimates are in the range of 0.88 to 0.96, broadly similar to what we see in PPP regressions (See Froot and Rogoff 1995). This is suggestive of why it is unlikely that commodity prices will indeed be the panacea for the monetary models, despite being able to explain a significant portion of the exchange rate volatility for these countries. We will come back to this point in Section 5. 19 We are aware of the inference problem put forth by Elliott (1998), that applying cointegration methods on nearunit root processes may introduce biases and inefficiencies. Here, we are simply using it as a robustness check. 9 are included in the regressions as well. Under the alternative assumption that real exchange rates and real commodity prices are cointegrated I(1) processes, the dynamic OLS approach produces the correct standard errors for the “superconsistent” point estimates which are robust to the presence of endogeneity.20 As evident in Table III, our small sample sizes notwithstanding, the elasticity estimates for Australia and New Zealand from the dynamic OLS are not far off from those obtained under the assumption of stationarity, and still produce estimates significantly different from zero.21 As in Table I, the elasticity estimate for the Canadian-U.S. real exchange rate shows up as significant under dynamic OLS, likely reflecting the common trend discussed earlier.22 As the coefficient estimates appear robust to these alternative assumptions on the underlying data generating process, we will continue with the Newey-West standard error correction procedure, in accordance with our view that these series are stationary. 20 See Hamilton (1994), Ch. 19. While asymptotically, the Stock-Watson dynamic OLS procedure yields the same parameter estimates as conventional OLS, this may not be the case in finite samples. We experimented with longer lead and lag lengths, and the estimation results are similar. 22 Stock (1987) shows that OLS estimators for cointegrating parameters converge faster than parameter estimates in OLS models using stationary variables, as the effect of common trend dominates that of the stationary component. 21 10 Table III: Alternative Specifications Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar Australia Ln(Real Comm Prices) NeweyWest 1 0.81* AR(1) (0.12) AR(1) root Durbin- 2 Canada NeweyWest 0.21 AR(1) 0.54 * Dynamic OLS 3 0.39 * (0.14) (0.06) (0.15) New Zealand NeweyWest 1.10 * AR(1) 0.04 Dynamic OLS 0.40 * 0.51 * Dynamic OLS 0.58 * (0.07) (0.03) (0.32) (0.21) (0.09) 0.88 * 0.96 * 0.95 * (0.05) (0.03) (0.05) 0.36 2.15 0.57 0.86 0.10 1.92 0.06 0.96 0.19 1.99 0.37 0.90 Watson stat Adj. R2 Sample Period 0.36 1984Q1 - 2001Q2 0.56 1973Q1 - 2001Q2 0.40 1986Q1 - 2001Q2 Note: * indicates significance at the 5% level. 1. ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt 2. using non-parametric GMM Newey-West approach to correct for the biased standard errors estimate ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt where εt follows an AR(1) 3. ln(Real Exchange Rate)t = α + γ*ln(Real Commodity Price)t + γ1*∆ln(Real Commodity Price)t+1 + γ0*∆ln(Real Commodity Price)t + γ-1*∆ln(Real Commodity Price)t-1 + εt, where ∆ is the first difference operator. Here real exchange rates and real commodity prices are assumed to be non-stationary and cointegrated, so DOLS produces super-consistent estimators (Stock and Watson 1993). 3.3. Parameter Stability As we mentioned earlier, all three countries adopted inflation targeting in the early 1990s. Together with our findings in Section 3.1 that the estimates for the Canadian dollar appear qualitatively different when we look at a shorter sample beginning in 1985, testing for the possibility of structure breaks seems warranted. While there are various parameter stability tests available, the applicability of some of these tests is constrained by our small sample sizes.23 Here we perform the classic Chow test on pre-selected potential breakpoints, and the Hansen (1992) test for structural break of unknown timing. Table III presents the results of these two structural break tests on the commodity price elasticity estimates for the three U.S.-dollar 23 See Hansen (2001) for a lucid summary of recent developments in the econometrics of structural change. 11 exchange rates. 24 As we are interested in possible instability in the commodity price elasticities but not so much in shifts in underlying trend, we use detrended variables for this analysis. The Chow test, designed to test the null hypothesis of constant parameters against an alternative of a one-time shift at some known time, suffers several well-known criticisms.25 In particular, because the pre-selected candidate breakpoint is often endogenous, the Chow test is likely to falsely indicate a break when none in fact exists. In our analysis, for example, we choose as candidate break-dates the year each of these countries adopted formal inflation targets (1990 for New Zealand, 1991 for Canada, and 1993 for Australia). It is easy to make a case that these regime shifts were endogenous. Nevertheless, the Chow test results do no show clear indication of parameter shifts pre- and post-inflation targeting, despite a likely bias towards doing so.26 The Hansen procedure, adopted from his 1992 paper, is approximately the Lagrange multiplier test of the null of constant parameters against the alternative of structural breaks of unknown timing and/or random walk parameters.27 The critical value for the stability of individual parameter is drawn from Hansen (1992). As is apparent from Table IV, the Chow test, which requires an a priori determination of the timing for the structural change, and the Hansen test, which tests for parameter instability over the full sample period, do not always produce consistent conclusions, such as in the case of the linearly detrended New Zealand data. We note that the Hansen test relies on asymptotic properties our small data samples may not adequately satisfy. Nevertheless, the conclusion we draw from these tests is that while there 24 It is evident from the figures 1-6 that although commodity prices and exchange rates have been remarkably correlated over the sample, the relationship notably breaks down over the past two years, especially for the U.S. dollar cross rates. Thus, any out-of-sample test, particularly one that focuses on the last few years, is likely to lead to fairly negative results. We acknowledge this, but given the striking correlation over the longer sample – far more striking than for typical empirical exchange rate equations – we will focus here mainly on in-sample parameter stability tests. The reader should interpret our results accordingly. 25 See Hansen (1992). 26 For Australian dollar against the non-dollar basket, there is similarly no evidence of parameter instability based on both the Chow break point test and the Hansen test. However, both tests reject parameter stability for the Australian-UK exchange rate, showing small and insignificant coefficient estimate before the break date and 0.65 (S.E. 0.25) after. Estimates for Canada remain negative and insignificant for the other two currencies. For New Zealand, neither the Chow nor the Hansen test indicates parameter instability when the exchange rate is measured against the other anchor currencies. 27 This particular version of the Hansen test does require stationary regressors, or else a different distributional theory applies. So, these results are valid only under the assumption that our series are trend-stationary. 12 may have been some parameter shifts over time, the basic sign and magnitude of the coefficients are notably stable for this kind of data.28 Table IVa: Parameter Stability Tests using Detrended Variables: Australia Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar Detrended ln(Real Exchange Rate)t = α + dt + (β + γ*dt)* Detrended ln(Real Commodity Price)t + εt, where dt = 1 if t ≥ Breakpoint; dt = 0 otherwise Australia Detrending Filter: Linear 0.81* Linear + Break Dummy 0.74 * Ln(Real Commodity Prices): β 0.58 * HP + Break Dummy 0.60 * (0.12) (0.17) (0.12) (0.15) Dummy* Ln(Real Commodity Prices): γ Breakpoint tested Hansen test 2 2 Adj. R 1 NA HP 0.18 -0.05 (0.26) (0.26) 1993Q1 NA 0.37 1993Q1 0.49 * 0.53 0.52 N Obs. 0.37 0.36 70 Sample Period 1984Q1 - 2001Q2 Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors in parentheses. 1. The breakpoint is the starting year for the use of formal inflation targets in the country. 2. The 5% asymptotic critical value for the Hansen individual parameter test is 0.47 (see Hansen 1992, Table 1). 28 Given this conclusion, it is natural to examine the out-of-sample performance of this apparent correlation, especially for Australia and New Zealand. Comparing the root mean square errors (RMSEs) of various commodity price-augmented exchange rate specifications against the RW, we do not observe significant out-of-sample gain. This is likely due to the divergent of exchange rate and commodity price series in the past 2 years, as evident in Figures 1-6. 13 Table IVb: Parameter Stability Tests using Detrended Variables: Canada Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar Detrended ln(Real Exchange Rate)t = α + dt + (β + γ*dt)* Detrended ln(Real Commodity Price)t + εt, where dt = 1 if t ≥ Breakpoint; dt = 0 otherwise Canada Detrending Filter: Ln(Real Commodity Prices): β Linear HP HP + Break Dummy 0.21 Linear + Break Dummy 0.38 * 0.09 0.13 (0.15) (0.16) (0.07) (0.09) Dummy* Ln(Real Commodity -0.60 * -0.09 Prices): γ (0.29) (0.13) Breakpoint tested 1 Hansen test NA 1991Q1 NA 0.49 * 2 Adj. R 1991Q1 0.38 0.05 0.14 0.03 N Obs. 0.02 114 Sample Period 1973Q1 - 2001Q2 Table IVc: Parameter Stability Tests using Detrended Variables: New Zealand New Zealand Detrending Filter: Ln(Real Commodity Prices): β Linear HP HP + Break Dummy 1.10 Linear + Break Dummy 2.13 * 0.72 1.23 * (0.32) (0.38) (0.20) (0.45) Dummy* Ln(Real Commodity -1.14 * -0.66 Prices): γ (0.50) (0.50) Breakpoint tested 1 NA Hansen test 0.39 2 Adj. R 1990Q1 NA 1990Q1 0.47 0.27 0.37 N Obs. 0.25 0.26 62 Sample Period 1986Q1 - 2001Q2 Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors in parentheses. 1. The breakpoint is the starting year for the use of formal inflation targets in the country. 2. The 5% asymptotic critical value for the Hansen individual parameter test is 0.47 (see Hansen 1992, Table 1). 14 4. Endogeneity and Instrumental Variables Although we have treated the commodity export prices as exogenous in the analysis above, we consider here two possible channels of endogeneity that could bias our estimates. First of all, as alluded to earlier, certain omitted variables related to cycles and shocks in the United States, or even the global economy, might affect both the exchange rate and the commodity markets independently. For example, a boom in the U.S. economy is likely to affect all dollar cross rates as well as the world price of the commodities Australia exports.29 However, it seems unlikely that the Australian cross rates against the British pound or a broad set of currencies would be similarly affected in response to events in the U.S. economy, generating the similar coefficient estimates we observe. A broad boom affecting all industrial countries (except Australia) would also drive up commodity prices, of course, and might exert an independent effect on the exchange rate. We note, however, that most models would predict that the independent effect would tend to depreciate rather than appreciate the Australian currency, so the fact that our coefficient estimates are consistently positive tends to mitigate against this source of bias.30 Another source of endogeneity can operate through the significant market power these countries exert in certain commodity markets. As mentioned above, New Zealand controls a near majority of the global sheep market. As such, the world sheep price may be set or significantly influenced by New Zealand’s exchange rate value. To address this potential form of endogeneity, we use the world price index of all non-energy commodities, each weighted by their global export earning shares, as an instrument for the country-specific, production-weighted commodity price index.31 Table V compares the results of single-variable GMM-IV regressions with their OLS counterparts. We employ a GMM procedure to optimally weight the orthogonality conditions 29 See Borensztein and Reinhart (1994) Although the Canadian dollar regressions occasionally show negative significant estimates, in the most cases the coefficient is insignificantly different from zero. We don’t observe any consistent pattern in the Canadian analysis. 31 We want to reiterate the point that despite having significant market power in a few commodities, these three countries are relatively small in the overall global commodity market. In 1999, for example, Australia represents less than 5 percent of the total world commodity exports, Canada about 9 percent, and New Zealand 1 percent. (For non-energy commodities only: the shares are 6.7%, 10%, and 1.6% respectively.) 30 15 and automatically correct the standard errors for serial correlation. As we have nine domesticanchor currencies combinations, we report three representative results in Table V. (We note that while the unreported results for Australia and New Zealand are similar to the ones in the table, the other Canadian results are all insignificantly different from zero, unlike one reported here under the IV specification.) As evident from the table, the world commodity price series works well as an instrument for the country specific commodity prices, and the IV estimations corroborate the least-squares findings. Namely, for Australia and New Zealand, world commodity price movements are associated with large and significant real exchange rate responses, while the effects are much smaller and mostly insignificant for Canada. Table V: Representative Univariate Regressions with Instrumental Variables Dependent Variable: Log Real Exchange Rate ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt Australian vs. U.S. Dollar Ln(Real Comm 0.81 * GMM IV1: World Commodity Price2 0.90 * Price) (0.12) (0.17) OLS OLS: Adj. R2 IV: 1st Stage R2 N Obs. Sample Period 0.57 Canadian Dollar vs. NonDollar Basket OLS GMM IV: World Commodity Price -0.31 -0.69 * New Zealand Dollar vs. British Pound OLS GMM IV: World Commodity Price 1.25 * 1.97 * (0.21) (0.24) (0.23) 0.46 0.55 0.91 0.89 70 1984Q1 – 2001Q2 (0.40) 0.79 85 1980Q1 – 2001Q1 62 3 1986Q1 – 2001Q2 Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors in parentheses. 1. Instrumental variable estimations are performed under 2SLS with GMM standard errors, using Bartlett kernel and variable Newey-West bandwidth. 2. The world commodity price index of all commodities is used as an instrument for the country-specific commodity price in the IV specifications. The world price index is the “non-fuel primary commodity price index” from the IMF. It consists of the US dollar prices of about 40 globally traded commodities, each weighted by their 1987-98 average world export earnings. 3. The Canadian sample here is limited to 1980Q1 to 2001Q1, the period over which world commodity price data is available. 16 5. Solving the Puzzle? Dornbusch’s (1976) overshooting monetary model seemed to broadly fit the facts for the 1970s and the early 1980s. However, as inflation gradually stabilized in major OECD countries over the ensuing period, it became clear that monetary instability alone could not possibly explain the persistent volatility in the exchange rates that remains even to this date. The failing of the monetary models is further resonated in the related purchasing power parity (PPP) puzzle. Solving the purchasing power parity (PPP) puzzle entails reconciling the extremely slow rate at which deviations from PPP seem to die out (half life of 3-4 years), with the enormous observed short-term volatility in the real exchange rates.32 Conventional shocks to the real economy, such as taste or technology shocks, while capable of generating the observed slow adjustment, are simply not volatile enough to account for the short-term variation in the exchange rates. Monetary or financial shocks, on the other hand, may help explain this short-term volatility, but the long half-lives of the shocks are simply incompatible with long-run monetary neutrality. After all, nominal rigidities, through which monetary shocks can temporarily impact the real economy, are believed to fully adjust within a much shorter time span (1-2 years). Therefore, a potential solution to this puzzle, it seems, lies in finding a real shock that is sufficiently volatile. The success of our univariate regressions suggests that commodity prices may be this missing shock. In this section, we explore whether the Dornbusch-type monetary models would work better in these rare country cases where certain real shocks are observable and can be substantially controlled for.33 We approach this first by including commodity prices into the standard monetary-type regressions. We then look at whether their inclusion can sufficiently remove the persistence in the data in order for monetary factors to play a role. Finally, we look at the interaction of these variables in a VAR setup. 5.1. The Augmented Monetary Model We do not propose any particular structural identification framework here, but aim to explore how the inclusion of commodity prices affects the role certain macroeconomic variables 32 See Rogoff (1996) for a full account of the PPP puzzle. 17 play in real exchange rate estimations.34 Specifically, we consider the following regression, focusing on real output differentials and real interest differentials between home and the anchor country,35 ln(Real Exchange Rate)t = α + β*t + γ1*ln(Real Commodity Price)t + γ2* (Real Interest Differential)t + γ3*(Real Output Differential)t + εt Again, we face possible endogeneity problem in the above contemporaneous specification. To address it, we use the world price index of all commodities to instrument for country-specific commodity prices, as explained earlier in Section 4. For the other contemporaneous regressors, we resort to notably cruder options – the one period lagged output and interest rate – as instruments.36 The regression results for the three national currencies against the British pound are reported in tables VIa-c below. We first note that even with the inclusion of these macro variables, the exchange rate-commodity price connection remains a strong “Down Under” phenomenon. However, even for these countries, commodity prices appear no Deus ex Machina. While it shows some promise in the Australian regressions by bringing out the output differentials, no significant results are found when the cross-currency is the U.S. dollar (Table VId), as in the case for New Zealand. These estimates seem only to corroborate further the “fickleness” of the monetary-type models documented extensively in the literature, and do not provide much evidence in favor of an augmented-Dornbusch type model. 33 While there have been previous efforts to incorporate terms of trade shocks into empirical exchange rate estimations of major currencies, sluggish nominal price adjustments and minimal pass-throughs typically make proper identification close to impossible. 34 See, for example, Obstfeld and Rogoff (1996) ch. 9, for structural models supporting such monetary-type regression specifications and their variants. 35 Real interest rate is measured by three-month Treasury bill rates adjusted by annualized quarter-by-quarter CPI inflation. 36 Lag real interest rate is an especially weak instrument, and mechanically does not always work well in all combinations of country vs. anchor currency regressions. Here we present a few examples where they do provide sensible results, despite the notably larger standard errors. We do not pretend the IV specification provides the correct identification, and therefore present the VAR analysis in the next section to better capture the dynamic interactions among these variables. 18 Table VIa : Specifications with Macro Variables: Australian Dollar vs. British Pound Dependent Variable: Log Real Exchange Rate, vs. British Pound ln(Real Exchange Rate)t = α + β*t + γ1*ln(Real Commodity Price)t + γ2* (Real Interest Differential)t + γ3*(Real Output Differential)t + εt Australia Australian Dollar vs. British Pound (1) OLS: Basic Monetary (2) OLS: 4 Variable Baseline (3) GMM IV 1: Lagged Macro Vars (4) GMM IV: World Comm. Price & Lagged Macro Vars Ln(Real 0.65 * 1.05 * Commodity Prices) (0.17) (0.26) Real Interest 0.79 * 0.45 -1.32 0.16 Differential (0.26) (0.28) (1.87) (1.06) Real Output 0.11 3.25 * -1.05 5.51 * Differential (1.08) (1.26) (1.35) (1.84) 0.50 0.62 2 Adj. R N Obs. 69 Sample Period 1984Q1 – 2001Q1 Table VIb: Specifications with Macro Variables: Canadian Dollar vs. British Pound Canada Canadian Dollar vs. British Pound (1) OLS: Basic Monetary (2) OLS: 4 Variable Baseline (3) GMM IV 1: Lagged Macro Vars (4) GMM IV: World Comm. Price & Lagged Macro Vars Ln(Real -0.41 -0.49 Commodity Prices) (0.32) (0.34) Real Interest -0.04 0.23 1.58 -0.92 Differential (0.31) (0.34) (2.92) (1.63) Real Output -0.17 -0.42 0.58 0.43 Differential (1.45) (1.27) (2.02) (1.17) 0.31 0.36 2 Adj. R N Obs. 85 Sample Period 1980Q1 – 2001Q1 Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors in parentheses. Instrumental variable estimations are performed under 2SLS with GMM standard errors, using Bartlett kernel and variable Newey-West bandwidth. 19 Table VIc: Specifications with Macro Variables: New Zealand Dollar vs. British Pound Dependent Variable: Log Real Exchange Rate, vs. British Pound ln(Real Exchange Rate)t = α + β*t + γ1*ln(Real Commodity Price)t + γ2* (Real Interest Differential)t + γ3*(Real Output Differential)t + εt New Zealand New Zealand Dollar vs. British Pound (1) OLS: Basic Monetary (2) OLS: 4 Variable Baseline (3) GMM IV 1: Lagged Macro Vars (4) GMM IV: World Comm. Price & Lagged Macro Vars Ln(Real 1.29 * 1.82 * Commodity Prices) (0.24) (0.50) Real Interest 0.61 * 0.21 -4.89 -0.22 Differential (0.28) (0.16) (7.98) (1.23) Real Output -0.14 -0.52 -2.77 -1.20 Differential (0.60) (0.41) (5.14) (0.96) 0.23 0.58 2 Adj. R N Obs. 60 Sample Period 1986Q1 – 2001Q1 Table VId : Specifications with Macro Variables: Australian Dollar vs. U.S. Dollar Australia Australian Dollar vs. U.S. Dollar (1) OLS: Basic Monetary (2) OLS: 4 Variable Baseline (3) GMM IV 1: Lagged Macro Vars (4) GMM IV: World Comm. Price & Lagged Macro Vars Ln(Real 0.72 * 0.66 * Commodity Prices) (0.09) (0.22) Real Interest 1.98 * 1.37 * 8.10 * 5.96 Differential (0.34) (0.28) (4.05) (3.59) Real Output 1.41 -0.36 0.85 -0.52 Differential (2.42) (1.49) (4.39) (2.51) 0.26 0.65 Adj. R2 N Obs. 69 Sample Period 1984Q1 – 2001Q1 Note: * indicates significance at the 5% level. Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors in parentheses. Instrumental variable estimations are performed under 2SLS with GMM standard errors, using Bartlett kernel and variable Newey-West bandwidth. 20 5.2. “The Nagging Persistence” Although commodity prices appear quite important in the exchange rate equations for these commodity economies, the above results suggest little evidence that their introduction can otherwise resuscitate the monetary approach to the exchange rate, at least from an empirical perspective. This section looks further at why the monetary fundamentals in the Dornbusch model may indeed be powerless in explaining the remaining variation in our augmented exchange rate equations. In the analysis below, we assume that real exchange rate shocks follow an AR(1) process and focus on the magnitude of this serial correlation.37 While we recognize that our small sample sizes may preclude very precise estimates of the autocorrelation coefficients, the analysis nevertheless provides meaningful insight to the nature of the “puzzle” at hand. The AR(1) columns in Table VII below demonstrate the persistence side of the PPP puzzle for the three commodity currencies. We note that the estimated serial correlation of the residuals appear broadly similar to what we see in the PPP literature, indicating half-lives much longer than what monetary factors can explain.38 Having established the PPP puzzle in our specific currencies, we then control for the effects of commodity prices, and further instrument them with the world commodity price index to address potential endogeneity. The next two columns in Table VII report the results. As evident from the AR(1) root estimates, after controlling for one major source of real shocks – commodity price shocks- the residuals still exhibit a generally similar degree of persistence as before! These implied half-lives are far longer than one can justify if the main source of the remaining shocks is monetary. Therefore, it is no surprise that the performance of our commodity price augmented Dornbusch-type equations is mixed at best. Furthermore, while we have peeled off one layer of the empirical exchange rate mystery by providing one explanation for the exchange rate movements in these commodity currencies, we find ourselves staring at the same PPP puzzle yet again. 37 See Froot and Rogoff (1995) and Rogoff (1996) for discussions of previous literature using this specification and other variants. 21 Table VII: Persistence in the Real Exchange Rates Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar Australia AR(1) + AR(1) 1 Comm Price 2 Canada AR(1) + IV 3 AR(1) + AR(1) Comm Price New Zealand AR(1) + IV AR(1) + AR(1) Comm Price AR(1) + IV Ln(Real 0.54 * 0.97 * 0.04 -0.27 0.51 * 0.72 * Comm Prices) (0.14) (0.35) (0.08) (0.16) (0.21) (0.35) 0.94 * 0.88 * 0.84 * 0.97 * 0.96 * 0.97 * 0.92 * 0.95 * 0.95 * (0.04) (0.05) (0.08) (0.03) (0.03) (0.03) (0.04) (0.05) (0.06) 2.03 2.15 2.06 1.98 2.01 1.67 2.03 1.99 1.92 0.84 0.86 0.95 0.95 0.90 0.90 AR(1) root DurbinWatson stat Adj. R2 1st Stage R2 Sample Period 0.94 0.89 0.92 70 86 62 1984Q1 - 2001Q2 1980Q1 - 2001Q2 1986Q1 - 2001Q2 Note: * indicates significance at the 5% level. 1. ln(Real Exchange Rate)t = α + β*t + εt, where εt follows an AR(1) 2. ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt, where εt follows an AR(1) 3. ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt, where εt follows an AR(1) and ln(World Commodity Price Index) is used as an IV 5.3. Vector Autoregressions Despite the failure of the single equation specifications, we look at the dynamic interactions of these variables in a VAR set up. As demonstrated in the Appendix, the effects of commodity price shocks on the exchange rate can be extremely long lasting, if not quite permanent. In the canonical Dornbusch (1976) sticky-price model where the exchange rate does not enter the deflator for real balances, a permanent shock to the steady state terms of trade leads to an immediate and permanent adjustment of the exchange rate. VARs provide a natural 38 See Froot and Rogoff (1995) for a comprehensive survey of the estimated half-lives for PPP deviations. 22 framework to capture richer dynamics in a multivariable setting.39 As can be seen below, the results, via both impulse responses and variance decompositions, provide further support for the relevance of commodity prices in understanding real exchange rate behavior in these economies. In a 4-variable VAR setup, we examine the dynamic interactions among the Australian-US dollar real exchange rate, the world price index of Australia’s major commodities, and the real output and interest differentials between Australian and the United States. Each of these variables enters the VAR with one lag, which is optimally selected based on the Schwarz information criterion. To orthogonalize the shocks in the VAR, a simple Cholesky decomposition is used. Consistent with our view that world commodity prices are exogenous to events in the home small open economy, log of real commodity price is ordered first, followed by real output differential, real interest differential, and the log of real exchange rate.40 The impulse responses in Figure 7 clearly show the long-lasting effect real commodity price shocks have on the real exchange rates.41 A one standard deviation shock takes, for example, over 80 quarters (20 years) to fully die out. Interest differentials, on the other hand, do not have much impact on the real exchange rate. The same impression is conveyed by the forecast error variance decomposition, shown in Table VII below. Here we observe the short- and long-term relative relevance of individual shocks in affecting the volatility of the real exchange rate. Again, commodity prices clearly play a consequential role. The VAR results are broadly supportive of our empirical estimating equation, in which we implicitly assume that the impact of commodity price shocks is the dominant effect. However, they also suggest that further research, allowing for richer intrinsic and extrinsic dynamics, is warranted. 39 In this section, the VARs are set up under the assumption that all series are stationary. No detrending is done on the data, allowing the VAR to more closely mimic the true data-generating process. 40 The results are not sensitive to the order of real interest differentials and real output differentials. 41 Impulse responses for other variables as well as other country-currency pairs are available upon request. 23 Table VII. Variance Decompositions from 4-Variable VAR Ordered as ln(Com. P), dY, dR, ln(Q) 1. Forecast Forecast Horizon Standard (Quarters) Error 1 0.034 9.0 0.1 3.6 87.3 4 0.066 18.6 6.6 2.6 72.2 8 0.093 29.1 17.9 1.7 51.3 12 0.112 35.8 20.9 1.5 41.9 16 0.128 39.8 19.6 1.5 39.2 20 1 0.141 41.6 18.3 1.5 38.5 Variance Decomposition for Log Real Exchange Rate (Percentage Points) log (Real Real Output Real Interest log (Real Commodity Price) Differential Differential Exchange Rate) The evolution of the distribution of variances begins to stabilize roughly at period 20 (5 years). 6. Conclusion The world real prices of commodity exports do appear to have a strong and relatively stable influence on the real exchange rates of New Zealand and Australia. For Canada, the relationship is somewhat less robust, especially to detrending. Thus, despite the fact that these countries had open capital markets and floating exchange rates over the sample period, one can identify an important real explanatory variable. Moreover, the quantitative size of the coefficient is broadly consistent with the predictions of standard theoretical models of optimal monetary policy. Though perhaps relatively modest, this is a significant result in a literature largely populated by negative findings. One might hope that, by being able to control for a major source of real shocks, standard exchange rate equations - adjusted for commodity price shocks - might perform better for "the commodity currencies" than they have been found to perform for the major currencies. Unfortunately, our results do not offer very strong encouragement for this point of view. The performance of our commodity price augmented Dornbusch-type equations is mixed at best, corroborating the well-known unreliability of such models. In addition, the substantial persistence that remains in the commodity price-adjusted exchange rates left us facing the same 24 PPP puzzle again, where neither standard monetary nor real shocks seems suitable for explaining the remaining variations that is both so volatile and persistent. Nevertheless, one may view the glass as half full rather than half empty; at least something works! Moreover, the findings here may be of more general interest. Although Australia, Canada and New Zealand are fairly unique among OECD countries, commodity price shocks (both export and import) have long been recognized as of great importance to many developing countries. Thus exchange rate equations for many such currencies may hold more promise than for cross exchange rates among the major currencies. 25 References Amano, R. and S. Norden, 1993, A forecasting equation for the Canada-U.S. dollar exchange rate, in The exchange rate and the economy, 201-65 (Bank of Canada, Ottawa) Backus, D. and M. Crucini, 2000, Oil prices and the terms of trade, Journal of International Economics 50, 185-213. Bidarkota, P. and M. Crucini, 2000, Commodity prices and the terms of trade, Review of International Economics 8(4), 647-66. Borensztein, E. and C. Reinhart, 1994, The macroeconomic determinants of commodity prices, IMF staff paper 41(2). Brook, A., 1994, Which bilateral exchange rates best explain movements in export prices, Reserve Bank of New Zealand Discussion Paper No. G94/2. Cashin, P., H. Liang and C.J. McDermott, 2000, How persistent are shocks to world commodity prices? IMF Staff Papers (47), 177-217. Djoudad, B., J. Murray, T. Chan, and J. Daw, 2000, The role of chartists and fundamentalists in currency markets: the experience of Australia, Canada, and New Zealand. Elliott, G., 1998, The robustness of cointegration methods when regressors almost have unit roots, Econometrica 66, 149-58. Frankel, J., and A. Rose, 1995, Empirical Research on Nominal Exchange Rates, in Handbook of International Economics vol. 3, Gene Grossman and Kenneth Rogoff (eds.), (Amsterdam: Elsevier Science Publishers B.V., 1995): 1689-1729. Froot, K., and K. Rogoff, 1995, Perspectives on PPP and long-run real exchange rates, in Handbook of International Economics vol. 3, Gene Grossman and Kenneth Rogoff (eds.), (Amsterdam: Elsevier Science Publishers B.V., 1995): 1647-88. Gruen, D. and T. Kortian, 1996, Why does the Australian dollar move so closely with the terms of trade, Reserve Bank of Australia Research Discussion Paper No. 9601. Hansen, B., 2001, The new econometrics of structural change: dating breaks in U.S. labor productivity, mimeo (University of Wisconsin) Hansen, B., 1992, Testing for parameter instability in linear models, Journal of Policy Modeling 14(4), 517-533. Hayashi, F., 2000, Econometrics (Princeton University Press, Princeton and Oxford). 26 Meese, R. and K. Rogoff, 1983a, Empirical exchange rate models of the Seventies: Do they fit out of sample, Journal of International Economics 14, 3-24. Mendoza, E., 1995, The terms of trade, the real exchange rate and economic fluctuations, International Economic Review 36(1), 101-137. Obstfeld, M. and K. Rogoff, 1996, Foundations of international macroeconomics (MIT Press, Cambridge, MA). Obstfeld, M. and K. Rogoff, 2000, New directions for stochastic open economy models, Journal of International Economics 50, 117-53. Rogoff, K., 1996, The Purchasing Power Parity Puzzle, Journal of Economic Literature 34, 647668. Stock, J. and M. Watson, 1993, A simple estimator of cointegrating vectors in higher order integrated systems, Econometrica 61(4), 783-820. Zettelmeyer, J., 2000, The impact of monetary policy on the exchange rate: evidence from three small open economies, IMF Working Paper WP/00/141. 27 Appendix: A Structural Interpretation of the Coefficients Given the remarkable consistency in the estimated sign and size of the elasticity of the real exchange rate with respect to real commodity prices, it is worth briefly considering the predictions of a simple theoretical model. Consider the following extension of the version of the Belassa-Samuelson model exposited in Obstfeld and Rogoff (1996, ch. 4). Suppose Home agents consume three goods, nontraded goods, exports and imports, but only produce the first two. Assume that labor is perfectly mobile across industries, and that physical capital can be freely imported from abroad at real interest rate r, measured in importables. The production function for the exportables is yX = AXf(kX), where y and k are output and capital per unit labor, and yN = ANf(kN), is the analogous function for nontraded goods production. Let px be the world price of exportables, which is given exogenously to the small country, and let pN be the home price of nontradables, both measured in terms of importables. Then, assuming that labor mobility leads to a common wage across the two home industries, and following steps analogous to pages 205206 in Obstfeld and Rogoff, one can derive the approximate relation: µ $ $ p$ N = LN (A + p$ X ) − A N µ LX X where a “hat” above a variable represents logarithmic derivatives, and 6LN and 6LX are the labor’s income share in the nontraded and export goods sectors, respectively. Thus, the effects of a rise in the relative price of exportables is the same as a rise in traded goods productivity in the standard Belassa-Samuelson model. If 6LN = 6LX, a rise in the price of exportables leads to a proportional rise in the price of nontraded goods. The impact on the real exchange rate depends, of course, on the utility function. Assume a simple logarithmic (unit-elastic) utility function: U = CN) CI* CX(1-)-*) 28 and normalizing the price of importables to one, the consumption-based consumer price index is then given by pN)pX(1-)-*) Therefore, as p$ N moves proportionately in response to p$ X , the effect of an export price shock on the utility-based real CPI is then given by p$ X (1-*) Assuming that importables account for 25% of consumption, then the elasticity of the CPI with respect to a unit change in the price of exportables would then be 0.75, which is broadly consistent with our estimated coefficients. (If 6LN > 6LX – it is standard to assume that nontraded goods production is labor intensive -- one gets a larger effect). What if the price of nontraded goods is sticky? Than a simple model of optimal monetary policy would predict that the exchange rate should be adjusted one for one with changes in the world price of exportables, in order to accommodate the requisite rise in the relative price of nontradable goods. (This assumes that export prices are flexible with complete pass-through, as otherwise a larger change in the exchange rate would be needed.) Of course, if the central bank is mechanically trying to stabilize CPI inflation, and if its rule does not allow any offset for export price shocks, then the authorities would not allow the nominal exchange rate to move by the amount required to mimic the flexible-price equilibrium, but instead only by a smaller amount. We have only offered one model, but many others can give parallel results. For example, the classic model of Dornbusch (1976) would also prescribe a one-for-one movement of the exchange rate in response to terms of trade shocks, in order to mimic the real allocation of the flexible price equilibrium. Whereas we have no illusions that the simple model presented here fully describes the data, it still provides a useful benchmark for assessing the estimated coefficients. 29 Data Appendix: Exchange Rates: - End of period quarterly nominal exchange rates are taken from IMF’s International Financial Statistics (IFS) and Global Financial Database for 1973Q1 to 2001Q2. Real exchange rates are nominal rates adjusted by the CPI ratios. To construct the real rates against the nondollar basket, we use the broad (real) index published by the Federal Reserve to adjust the country real rates against the U.S. dollar. The broad index measures the foreign exchange value of the U.S. dollar against the currencies of a large group of U.S. trading partner. CPI and Real Output: - Quarterly consumer prices and GDP volume (1995 = 100) are taken from the IFS. Inflation rates are calculated as annualized quarterly changes of the CPI. Short Term Interest Rates: - We use three-month Treasury bill rates as a measure of short-term interest rate. The sources are IFS and Global Financial Database. The real rates are the nominal rates adjusted for expected inflation, which we proxy with lagged inflation rate, calculated as the annualized quarterly change of the CPI from the previous quarter. Commodity Prices: - The country specific commodity export price index is constructed by geometrically weighting the world market prices in U.S. dollar of each country’s major non-energy commodity exports. The weights, taken from Djoudad, Murray, Chan, and Daw (2000), represent the average production value of the commodity over the 1982-90 period and are listed in Table A. The following commodities from the original Djoudad et al indices are excluded, as we were unable to update the price series. Their original weights in the relevant countries are in the parentheses: barley (2.4% in Australia, 1.8% in Canada), sulphur (1.4% in Canada), cod (0.01% in Canada), lobster (0.5% in Canada), and salmon (0.6% in Canada). - The world price index of all non-energy commodities is the “non-fuel primary commodity price index” of the IMF. It comprises the U.S. dollar prices of about 40 globally traded commodities, each weighted by their 1987-98 average world export earnings. 30 - The world market price of individual commodities is taken from various sources (see Table A). They are quarterly average spot or cash prices in U.S. dollars. The commodities in general are traded in different markets, including NYMEX, IPE, CBT, CME, KCB, ASX and SFE, and the prices are considered "world prices". A. Composition of Non-Energy Commodity Price Index World Market Price in U.S. Dollar Australia Canada New Zealand 1983Q1 – 2001Q2 1972Q1 - 2001Q2 1986Q1 - 2001Q2 Product Wt. Source Aluminum 9.1% IMF Beef 9.2% Copper Product Wt. Source Aluminum 4.8% BOC IMF Beef 9.8% 3.2% BOC Canola Cotton 3.4% IMF Gold 19.9% Iron Ore Wt. Source Aluminum 8.3% ANZ GFD Apples 3.1% ANZ 2.1% BOC Beef 9.4% ANZ Copper 4.7% BOC Butter 6.5% ANZ IMF Corn 1.3% BOC Casein 6.7% ANZ 10.9% IMF Gold 4.5% GFD Cheese 8.3% ANZ Lead 1.3% IMF Hogs 5.1% GFD Fish 6.7% ANZ Nickel 2.6% BOC Lumber 14.4% IMF Kiwi 3.7% ANZ Rice 0.8% IMF Newsprint 13.4% IMF Lamb 12.5% ANZ Sugar 5.9% GFD Nickel 3.9% BOC Logs 3.5% ANZ Wheat 13.5% BOC Potash 2.1% IMF Pulp 3.1% ANZ Wool 18.3% ANZ + Pulp 19.7% IMF Sawn 4.6% ANZ IMF Zinc 1.8% BOC Product Timber Silver 0.9% GFD Skim MP 3.7% ANZ Wheat 8.9% BOC Skins 1.6% ANZ Zinc 4.4% BOC Wholemeal 10.6% ANZ 7.7% ANZ MP Wool Note: BOC (Bank of Canada); ANZ (Australia-New Zealand Bank); GFD (Global Financial Database) 31 Impulse Responses of Australian - US Real Exchange Rate Response of log(Real Exchange Rate) to log(Real Comm. Price) Response of log(Real Exchange Rate) to Real Output Differential .05 .05 .04 .04 .03 .03 .02 .02 .01 .01 .00 .00 -.01 -.01 -.02 -.02 25 50 75 100 25 Response of log(Real Exchange Rate) to Real Interest Differential 50 75 100 Response of log(Real Exchange Rate) to log(Real Exchange Rate) .05 .05 .04 .04 .03 .03 .02 .02 .01 .01 .00 .00 -.01 -.01 -.02 -.02 25 50 75 100 25 50 75 100