Commodity Currencies and Empirical Exchange Rate Puzzles
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

Contributor Notes

Author’s E-Mail Address: ychen@kuznets.harvard.edu; Krogoff@imf.org

This paper re-examines empirical exchange rate puzzles by focusing on three OECD economies (Australia, Canada, and New Zealand) where primary commodities constitute a significant share of their exports. For Australia and New Zealand especially, we find that the U.S. dollar price of their commodity exports (generally exogenous to these small economies) —has a strong and stable influence on their floating real rates, with the quantitative magnitude of the effects consistent with predictions of standard theoretical models. However, after controlling for commodity price shocks, there is still a PPP puzzle in the residual. Nevertheless, the results here are relevant to many developing country commodity exporters, as they liberalize their capital markets and move towards floating exchange rates.

Abstract

This paper re-examines empirical exchange rate puzzles by focusing on three OECD economies (Australia, Canada, and New Zealand) where primary commodities constitute a significant share of their exports. For Australia and New Zealand especially, we find that the U.S. dollar price of their commodity exports (generally exogenous to these small economies) —has a strong and stable influence on their floating real rates, with the quantitative magnitude of the effects consistent with predictions of standard theoretical models. However, after controlling for commodity price shocks, there is still a PPP puzzle in the residual. Nevertheless, the results here are relevant to many developing country commodity exporters, as they liberalize their capital markets and move towards floating exchange rates.

I. Introduction

The connection between economic fundamentals and exchange rate behavior has been one of the most controversial issues in international finance, manifesting itself in various major empirical puzzles such as the Meese-Rogoff (1983) puzzle and the purchasing power parity (PPP) puzzle (Rogoff 1996).2 Recent research efforts to confront these challenges have explored new approaches in both theoretical and empirical fronts, including incorporating non-linearity in modeling exchange rate dynamics.3 Alternatively, it has also been recognized that if one could find a real shock that were sufficiently volatile, one could potentially go a long ways towards resolving these major empirical exchange rate puzzles. For most OECD economies, however, it is hard to know what that shock might be, much less measure it.4 In this paper, we focus on three OECD economies where a potential dominant real shock may be identified, and explore how controlling for this real shock may help shed light on empirical exchange rate puzzles.

In Canada, Australia and New Zealand, because primary commodities constitute a significant component of their exports, 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.5 In fact, researchers at the Bank of Canada have claimed for many years that not only do their 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.6 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.7 Finally, a similar framework has also been extended to the New Zealand dollar.8

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 solve the PPP puzzle, opening the door to salvation of standard monetary exchange rate models for these currencies? Affirmative answers here might encourage researchers to try harder to search for corresponding real shocks to the major currencies. More broadly, from a policy stand-point, understanding the effects of commodity price shocks on exchange rates is of considerable interest to developing countries, particularly as they liberalize capital market controls 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 inflation-targeting in developing countries.9

The outline of this paper is as follows. In Section II of the paper, we give a brief overview of the economic environment in the three countries, and provide some simple, but striking, evidence on just how closely movements in these currencies seem to track the corresponding world price of their commodity exports. The strong correlations come through not only for cross rates against the U.S. dollar, but also when the British pound and a broad index of non-US-dollar currencies are used as the numeraire. In Section III, we go on to see whether the visual evidence stands up to closer scrutiny, focusing on simple 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 connection between commodity prices and exchange rates holds up remarkably well, and appears quite robust to alternative assumptions on the underlying time series properties. 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 typically in the neighborhood of 0.75 for both Australia and New Zealand. For Canada, the evidence is more mixed, with the correlation between exchange rates and commodity prices much more sensitive to detrending. We go on in Section IV to consider two potential forms of misspecifications. We first ask whether the relationship might result from the countries having market power in their commodity exports, and find that this is not the case. In addition, we use commodity price indices as instruments for standard measures of terms of trade, and conclude that world commodity prices in fact better capture exogenous shocks to these countries’ terms of trade than standard measures do. Section V then offers a structural interpretation of the estimates in light of 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 extend the analysis in Section VI to ask whether the inclusion of commodity prices can help provide stronger empirical support for canonical exchange rate models. 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. In fact, we show that standard monetary variables are unlikely to work well in explaining exchange rate behavior, at least in linear models, because real exchange rates remain extremely persistent. The final section concludes.

II. Background and Graphical Evidence

A. Background

To effectively explore the temporal relationship between exchange rate behavior and commodity price shocks, we focus on developed economies where internal and external markets operate with little intervention, and where floating exchange rate regimes have been implemented for a sufficiently long period of time.10 From a macroeconomic perspective, Australia, Canada, and New Zealand are near perfect examples of such well-developed, small open economies. All three are highly integrated into global capital markets and are active participants in international trade. And in terms of monetary and exchange rate policies, they have all been operating under a flexible exchange rate regime for well over a decade. Canada began floating its currency before the collapse of Bretton Woods, in 1970. Australia and New Zealand abandoned their exchange rate pegs in 1983 and 1985 respectively, as part of the economic reform efforts to revitalize their domestic economies. Moreover, around 1990, all three adopted some variant of inflation targeting monetary policy.11

To varying degrees, all three countries can plausibly be described as “commodity economies”, because of the large share primary commodities occupy in their production and exports. For at least the past decade, commodities have maintained a 60 percent share of Australia’s total exports, with wool, wheat, and various metals examples of its 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 its total exports in recent years. By comparison, Canada has a larger and more developed industrial base, but still, it continues to rely more than a quarter of its exports on commodities such as base metals, forestry products, and crude oil. Despite the relatively small size of their overall economies, these countries retain a significant share of the global market for a few of their export products. In New Zealand, for instance, 46 million sheep cohabit with 3.8 million people. Not surprisingly, only 20 percent of its meat production is 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 may have 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.

B. Graphical Evidence and Data Description

Figure 1B through D show the value of Australian dollar 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. As a means of comparison, Figure 1A plots the Australian-US real exchange rate with a couple standard macroeconomic variables: the real income differentials and the real interest rate differentials between the two countries. The corresponding graphs for Canada and New Zealand are shown in Figures 2 and 3.

Fig. 1a:
Fig. 1a:

US - Australian Real Exchange Rate, Real interest Differential, Real Output Differential, 1984q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 1b:
Fig. 1b:

US -Australian Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 1c:
Fig. 1c:

Non-Dollar Basket - Australian Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 1d:
Fig. 1d:

UK - Australian Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 2a:
Fig. 2a:

US - Canadian Real Exchange Rate, Real Interest Differential, Real Output Differential, 1973q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 2b:
Fig. 2b:

US - Canadian Real Exchange Rate, Real Commodity Price 1973q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 2c:
Fig. 2c:

Non-Dollar Basket - Canadian Real Exchange Rate, Real Commodity Price, 1973q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 2d:
Fig. 2d:

UK - Canadian Real Exchange Rate, Real Commodity Price, 1973q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 3a:
Fig. 3a:

US - New Zealand Real Exchange Rate, Real Interest Differential, Real Output Differential, 1986q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 3b:
Fig. 3b:

US - New Zealand Real Exchange Rate, Real Commodity Price, 1986q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 3c:
Fig. 3c:

Non-Dollar Basket - New Zealand Real Exchange Rate, Real Commodity Price, 198Sq1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 3d:
Fig. 3d:

UK - New Zealand Real Exchange Rate, Real Commodity Price, 1986q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

For all three countries, the sample period starts shortly after the float of the particular home currency.12 The real exchange rates in these graphs (and in all the subsequent analyses) are end-of-quarter nominal rates, expressed as the foreign exchange values of the domestic currency, adjusted by the relative 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.13 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 are geometric averages of the world market prices of the major commodities produced in each country, weighted by their corresponding domestic production share.14 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.

Looking at these sets of graphs, three features especially stand out. First, whereas the two standard monetary exchange rate variables—interest rate and output differentials— exhibit no obvious visual correlation with the exchange rates, the correlations between commodity prices and various exchange rates are strikingly apparent. The commodity price and exchange rate series not only appear to mirror each other in movement, the magnitude of their swings are also similar. (This observation is confirmed by the contemporaneous regression results presented in Table 7 of the Appendix. Comparing across various currency pairings, we note the remarkable similarity in the coefficient estimates.) Secondly, these real exchange rates appear highly persistent and possibly non-stationary, a point we will address in more details in Section III. Lastly, the well-documented long-term decline of global commodity prices seems clearly reflected in these country-specific series as well. In the following section, we explore former just how strong and robust the apparent correlations are, and the role common trends (stochastic or not) may play in explaining the co-movements of real exchange rates and commodity prices.

III. Empirical Analysis

While establishing simple correlations seems an appropriate starting point in light of earlier empirical failures, formal empirical analysis cannot avoid addressing the issue of how best to model a small sample of data with near unit root behavior. Our short samples of fewer than 100 quarterly observations simply preclude any meaningful test of stationarity, a well-documented problem that has stimulated numerous innovative studies using long-horizon time series or panel data, coupled with various econometric techniques. In this paper, we rely on the considerable empirical evidence suggesting that real exchange rates are stationary, possibly with a trend.15 For example, Froot and Rogoff (1995) present evidence that the half-life of real exchange rate shocks in linear models is roughly 3–4 years across a wide variety of historical data. Culver and Papell (1999) and Wu (1996), among others, show mean-reversion in the post-Bretton Woods real exchange rates of most industrialized countries.16 In addition, using a century of annual data, Bleaney (1996) demonstrated that the trade-weighted Australian real exchange rate, along with the world price of primary commodities (relative to that of manufacturer), are both trend-stationary.

Ruling out non-stationarity/stochastic trends a priori, we mainly focus on the case where real exchange rates and real commodity prices are treated as stationary, possibly with trends.17 However, in the first subsection below, we consider several alternative underlying data-generating processes, including I(1) processes, as robustness checks for our results. We find that for Australia and New Zealand, the connection between real exchange rates and the world price of their commodity exports is quite strong and stable (whether or not we exclude unit roots), while that for the Canadian dollar seems less robust, especially to detrending. We then examine the stability of these parameter estimates in Section III.B.

A. Trends, Serial Correlations, and Non-Stationarity

We first present estimates for the commodity price elasticity of real exchange rate for the three countries, treating both series as stationary with a linear trend (see Figures 46 for the linearly detrended series). The OLS coefficient estimates are reported in the first column of Tables 1A-1C below. Since results based on different anchor currencies are similar, to conserve space, only results for the U.S. dollar rates are reported here. For Australia and New Zealand, we note that the elasticity estimates show up slightly higher but in general consistent with those obtained without the time trend (see Table 7 in the Appendix). From the second and the last columns, we see that these estimates also appear robust to alternative detrending methods: Hodrick-Prescott filtering and first differencing.18 For Canada, the positive correlation between commodity price and exchange rate does not seem to survive detrending, an issue we will discuss further.

Fig. 4a:
Fig. 4a:

Detrended US - Australia Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 4b:
Fig. 4b:

Detrended Non-Dollar Basket - Australian Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 4c:
Fig. 4c:

Detrended UK - Australia Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 5a:
Fig. 5a:

Detrended US - Canadian Real Exchange Rate, Real Commodity Price, 1973q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 5b:
Fig. 5b:

Detrended Non-Dollar Basket - Canadian Real Exchange Rate, Real Commodity Price, 1973q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 5c:
Fig. 5c:

Detrended UK - Canadian Real Exchange Rate, Real Commodity Price, 1973q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 6a:
Fig. 6a:

Detrended US - New Zealand Real Exchange Rate, Real Commodity Price, 1986q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 6b:
Fig. 6b:

Detrended Non-Dollar Basket - NZL Real Exchange Rate, Real Commodity Price, 1986q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 6c:
Fig. 6c:

Detrended UK - New Zealand Real Exchange Rate, Real Commodity Price, 1986q1 to 2001q2

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Table 1.A:

Real Exchange Rates and Commodity Prices: Different Assumptions on the Data Generating Processes Australia - Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar Sample Period: 1984Q1 – 2001Q2

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Note: * indicates significance at the 5 percent level. Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors in parentheses (except for the AR(1) specification).

ln(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + ε1 using non-parametric GMM Newey-West approach to correct for the biased standard errors estimate.

Hodrick-Prescott Detrended ln(Real Exchange Rate)t = α + β* HP Detrended ln(Real Commodity Price)t + εt. 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)

In(Real Exchange Rate)t = α + β*ln(Real Commodity Price)t + γ1*Δln(Real Commodity Price)t+1 + γ0*Δln(Real Commodity Price)t+ γ-1*Δln(Real Commodity Price)t-1, + εt, where Δ is the first difference operator. Here real exchange rates and real commodity prices are assumed to be non-stationary, so DOLS procedure is used to obtain super-consistent estimators for the cointegrating vector (Stock and Watson 1993). T-ratios, which are asymptotically standard normal, are reported.

Δln(Real Exchange Rate)t = α + β* Δln(Real Commodity Price)t + εt using non-parametric GMM Newey-West approach to correct for potential serial correlation in the standard errors estimate

Table 1.B:

Real Exchange Rates and Commodity Prices: Different Assumptions on the Data Generating Processes (Continued) Canada - Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar Sample Period: 1973Q1 – 2001Q2

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Table 1.C:

Real Exchange Rates and Commodity Prices: Different Assumptions on the Data Generating Processes (Continued) New Zealand - Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar Sample Period: 1986Q1 – 2001Q2

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The Durbin-Watson statistics in these regressions indicate that significant positive serial correlations remain in the residuals, even after detrending. Leaving its economic implication to Section VI, here we address alternative methods for correcting the biased standard errors estimates. For the majority of the analysis in this paper, the kernel-based nonparametric GMM estimator of Newey-West (1987) is used to account for the serial correlation. However, because such non-parametric estimators have poor small sample properties, the third columns in Tables 1A-1C present estimation results from an alternative parametric specification, where the error terms are assumed to follow a first order autoregressive process. The AR(1) specifications effectively bring the Durbin-Watson statistics back towards 2, and while lowering the coefficients slightly, still give estimates consistent with earlier findings.19

As already noted, tests of unit roots or cointegration have little statistical power in short time series. In fact, Blough (1992), Cochrane (1991), and Faust (1996) contend that in finite samples, a stationary process can always be arbitrarily well approximated by a non-stationary process (and vice versa).20 Following up on this observational equivalence idea, Engel (2000) further argues that the rejections of unit-root null in long horizon real exchange rate data may be the result of size distortions. If our real exchange rate and commodity price series are indeed non-stationary, the estimates and significance tests performed so far, based on classical statistical methods, would be invalid. Therefore, a robustness check we consider next takes up the alternative assumption that real exchange rates and real commodity prices follow unit root processes.

If the real exchange rate and commodity price series are non-stationary but not cointegrated, the estimation needs to be done in first-differences to avoid spurious regression. We have already seen that the first differenced series produce similar estimates as under the linear-trend specification (last columns of Tables 1A-1C). However, if we instead assume that the two series are cointegrated, the first-differencing approach would no longer be appropriate. The fourth columns in Tables 1A1C present results from dynamic OLS (DOLS) of Stock and Watson (1993), a specification designed to estimate cointegrating relations.21 The DOLS approach produces the correct standard errors for the “superconsistent” point estimates of the cointegrating vectors. Importantly, these estimates are robust to the potential endogeneity of commodity prices, an issue we discuss in Section IV.22 Our small sample sizes notwithstanding, the elasticity estimates for Australia and New Zealand from DOLS are not far off from those obtained under the assumption of stationarity, and still produce estimates significantly different from zero.23 As the coefficient estimates for Australia and New Zealand appear robust to various assumptions on the underlying data generating processes, we will proceed with the linear trend model, in accordance with our view that these series are trend-stationary.

For Canada, however, unlike in the trend-stationary models, commodity price shows up as significant under DOLS, likely reflecting common trends. We note that one cannot entirely dismiss the significance of the common long-term trend between Canadian dollar and its commodity export prices. Indeed, the downward drift in both series may be intimately connected; we simply cannot statistically demonstrate any such connection here. On the other hand, this elusive correlation may reflect Canada’s ambiguous status as a “true commodity economy”. After all, commodities are the minority in its export base, especially compared to the case of New Zealand and Australia.24 Structural breaks occurring somewhere over the thirty-year period is certainly another possibility. Indeed, looking at the Canadian-U.S. rate post-1985 only (a sample period comparable to those used for Australia and New Zealand), we obtain significant positive coefficient estimates of around 0.3 under both the linear and the hp filters. However, unlike the robustness we observed in the Australian and New Zealand estimates, the significant correlation disappears when the Canadian rate is measured relative to other anchor currencies.

B. Parameter Stability

As mentioned earlier, all three countries adopted inflation targeting policy in the early 1990s. Together with our findings in Section III. A that the estimates for the Canadian dollar appear qualitatively different when we look at a shorter sample, testing for possible structural breaks seems warranted. Table 2 below present results from the classic Chow test on pre- selected potential breakpoints and the Hansen (1992) test for structural break of unknown timing. As we are interested in possible instability in the commodity price elasticities, but not so much in shifts in underlying time trends, we use HP-filtered variables for this analysis.

Table 2:

Representative Parameter Stability Tests under HP Filter Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar Defended 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

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Note: * indicates significance at the 5 percent level. Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors in parentheses.

The breakpoint is the starting year for the use of formal inflation targets in the country.

The 5 percent asymptotic critical value for the Hansen individual parameter test is 0.47 (see Hansen 1992, Table 1).

As discussed in Hansen (1992), because pre-selected candidate breakpoints are often endogenous, the Chow test is likely to falsely indicate a break when none in fact exists. In our analysis, for example, the candidate break-dates are chosen to be 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 coefficients on the time dummies in the Chow test provide little indication of parameter shifts pre- and post-inflation targeting, despite a likely bias towards doing so. The Hansen (1992) procedure is approximately the Lagrange multiplier test for the null of constant parameters, against the alternative of structural breaks of unknown timing and/or random walk parameters.25 It similarly does not provide strong indication of parameter instability over the full sample periods.26 We note that the Hansen test relies on asymptotic properties our small sample size may not adequately satisfy. Nevertheless, the conclusion we draw from these tests is that while there may have been some parameter shirts over time, the basic sign and magnitude of the coefficients are notably stable for this kind of data.

Given the stability of the elasticity estimates, it is natural to explore the out-of-sample forecast performance of these contemporaneous correlations, especially for Australia and New Zealand.27 Simple rolling forecast regressions in the spirit of the original Meese-Rogoff (1983) are conducted across different forecast horizons and base currencies to predict the levels of exchange rate. In Table 9 of the Appendix, we present ratios of the root mean squared forecast errors between a commodity price-augmented exchange rate equation and the Random Walk. We do not observe significant out-of-sample gains over the Random Walk specification, especially across benchmark currencies. However, we note that the usefulness of commodity prices in exchange rate forecasts, even for these commodity currencies, requires much more in-depth analysis than our simple specification here offers. In particular, as pointed out by Diebold and Killian (2000), unit-root formulations, such as the vector error correction framework, may be a more appropriate specification for forecasting regardless of the true nature of the data generating processes.28 In addition, the statistical significance of any apparent forecast improvements would need to be evaluated.29

IV. Some Possible Misspecifications

A. Endogeneity of Commodity Prices

We have thus far treated commodity prices as exogenous in the exchange rate equation. In this section, we consider two possible channels of endogeneity that could potentially bias our estimates, and show that neither is likely to be dominating our results. First, as alluded to earlier, 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.30 However, a boom in the U.S. would seem unlikely to have a first order impact on the Australian cross rates against the British pound or a broad set of non-U.S. dollar currencies. Yet in these non-dollar regressions, we observe similar coefficients for the commodity price variable (see, for example, Table 7 in the Appendix). One also has to allow for the possibility of a broad boom that affects all industrial countries (except Australia), drives up commodity prices, and simultaneously exerts an independent effect on the Australian exchange rate. We note, however, that most models would predict that this independent effect (from high world growth relative to Australian growth) should tend to depreciate rather than appreciate the Australian currency. So, the fact that our coefficient estimates are consistently positive and of similar magnitudes across currency pairings tends to mitigate against this source of bias.31

A second source of endogeneity can operate through any market power these countries may hold in commodity markets. For instance, since New Zealand controls a near majority of the global sheep market, the world price of sheep may be significantly influenced by the value of New Zealand dollar. To address this potential form of endogeneity, we use a price index that incorporates all non-energy commodities, each weighted by their global export earning shares, as an instrument for the country-specific production-weighted price index that we have been using.32

Table 3 reports three representative results comparing GMM-IV regressions, using world price of all commodities as instruments, with their uninstrumented OLS counterparts. We employ a GMM procedure to optimally weigh the orthogonality conditions and automatically correct the standard errors for serial correlation. 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.33

Table 3.

Representative 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

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Note: * indicates significance at the 5 percent 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.

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.

The Canadian sample here is limited to 1980Q1 to 2001Ql, the period over which world commodity price data is available.

B. Do Commodity Prices Better Capture Exogenous Terms of Trade Shocks Than Conventional Measures?

While previous studies have tried 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. That is, in the case of sticky producer prices and perfect pass-throughs, the terms of trade and the real exchange rate will move one-to-one mechanically with no causal interpretation. The same is true when all goods are priced in local currencies, though the correlation will be of the opposite sign. When a mixture of the two pricing behavior co-exists, any sign is possible, and the dynamics are likely to be complex (see Obstfeld-Rogoff 2000). For these large commodity exporters, however, because commodity trading is mostly conducted in a few global exchange markets using U.S. dollars, world commodity price fluctuations can help us get around the identification problem to better capture the exogenous component in the variation of their terms of trade. We here consider an alternative specification: using world commodity prices as an instrument for the standard terms of trade measures. Results presented in Table 4 below indicate that this idea, while theoretically sound, does not appear to have much merit empirically. From the OLS regressions, we see that (again with Canada being the exception) terms of trade indeed appear well correlated with real exchange rates. To address the endogeneity issue, country-specific world market price indices of both energy and non-energy commodities are used as instruments for terms of trade, capturing potential shocks through both import and export channels. For New Zealand, even though over half of its exports are in commodities, the low Wald statistic in the first stage regression shows that standard terms of trade measure doesn’t seem to respond much to movements in the two commodity price indices.34 For Australia, despite valid first stage regression results connecting terms of trade movements to commodity prices, the Hansen (1982) J-test rejects the over-identification restrictions, indicating that the instruments are not orthogonal to the second stage residuals, and invalidating the estimated model. We take both of these findings as support for our original specifications and our view that world commodity prices appear much better at capturing the theoretical concept of exogenous terms of trade shocks for these countries. These results also suggest that standard terms of trade measures should be used with caution in empirical exchange rate estimations, despite their conceptual importance.

Table 4:

Real Exchange Rates, Terms of Trade, and Commodity Prices Dependent Variable: Log Real Exchange Rate vs. U.S. Dollar ln(Real Exchange Rate)t = α + β*t + γ*ln(Terms of Trade)t + εt

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Note: * indicates significance at the 5 percent 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. Both country-specific energy and non-energy commodity price indices are used as instruments.

The J-stanstics of Hansen (1982) test the null hypothesis that the GMM over-identification restrictions are satisfied/valid.

V. A Structural Interpretation of the Coefficients

Given the remarkable consistency in the estimated sign and size of the commodity price elasticity of real exchange rate, 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). Let Home be a small economy whose 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),(1)

where y and k are output and capital per unit labor, and

yN=ANf(kN),(2)

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 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 205-206 in Obstfeld and Rogoff, one can derive the approximate relation:

P^N=(μLNμLX)(A^X+p^X)A^N(3)

where a “hat” above a variable represents logarithmic derivatives, and μLN and μLX 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 μLN= μLX, 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=CNαCIβCX(1αβ)(4)

Normalizing the price of importables to one, the consumption-based consumer price index is then given by

PNαPX(1αβ)(5)

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(1β)(6)

Assuming that importables account for 25 percent 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 μLN> μLX – 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? Then 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.

VI. Empirical Exchange Rate Puzzles

While canonical exchange rate models such as Dornbusch’s (1976) overshooting model seemed to broadly fit the facts for the 1970s and the early 1980s, 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 exchange rate volatility that remains even to this date. The failure of standard monetary models further resonates in their inability to reconcile the extremely slow rate at which deviations from PPP seem to die out, with the enormous short-term volatility observed in real exchange rates. As exposited in Rogoff (1996), conventional shocks to the real economy such as taste or technology shocks, while capable of generating slow adjustment, are simply not volatile enough to account for the short-term variation in the exchange rates. Models based on monetary or financial shocks may explain this short-term volatility, but the long half-lives of shocks observed in the data are incompatible with the concept of long-run monetary neutrality under these models. Hence, a potential solution to this PPP puzzle may lie in identifying a shock that is both sufficiently volatile and persistent.

The success of our univariate regressions suggests that commodity prices may indeed be this missing shock. Would the Dornbusch-type monetary variables work better in these rare country cases where certain real shocks can be substantially controlled for? An affirmative answer would require sufficiently removing the persistence in real exchange rate shocks, so as to allow monetary variables to account for the remaining variations.35 By examining the degree of persistence in real exchange rate shocks, we show in this section that commodity prices are no Deus ex Machina; that is, although they are found to be a strong and consistent explanatory variable in exchange rate equations, their introduction does not otherwise resuscitate the monetary approach to exchange rate determination, at least from an empirical perspective.36

A. “The Nagging Persistence”

To examine the degree of persistence in real exchange rates, we assume real exchange rate shocks to follow an AR(1) process and focus on the magnitude of the autoregression coefficients.37 We have already seen in Table 1 that the AR roots are very large in the commodity price equations; Table 5 below presents a more systematic analysis. The AR(1) columns in Table 5 demonstrate the persistence side of the standard PPP puzzle (sans commodity prices) for the three commodity currencies. The estimated autocorrelations in the residuals appear broadly similar to what we see in the PPP literature, indicating half-lives much longer than what monetary factors can explain. We note that OLS estimates of the AR coefficients are well known to have substantial bias, especially when the autocorrelation is close to unity and the sample size is small.38 Work by Andrews (1993) and Fair (1996), among others, examine this bias extensively and propose various methods of correction.39 Furthermore, the direction of the bias has also demonstrated to be downward towards zero.40 So, while our reported point estimates for the AR roots are biased, the underestimated degree of persistence is nevertheless high enough to provide meaningful insight to the nature of the “puzzle” at hand.41

Table 5:

Persistence in the Real Exchange Rates 1 Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar

article image
Note: * indicates significance at the 5 percent level.

The AR root estimates in this table are downward biased (towards zero); see text for discussion.

ln(Real Exchange Rate)t = α + β*t + εt, where εt, follows an AR(1).

1n(Real Exchange Rate)t = α + β*t + γ*ln(Real Commodity Price)t + εt, where εt follows an AR(1).

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.

Having established the PPP puzzle in our specific currencies, we then control for the effects of commodity prices—removing exchange rate variations due to commodity price shocks—to see if the persistence lessens significantly. As evident from Table 5, even after controlling for commodity price shocks and instrumenting for potential endogeneity, exchange rate residuals still exhibit a generally similar degree of persistence.42 As the implied half-lives from these coefficients are far longer than one can justify if the main source of the remaining shocks is monetary, it is no surprise that, as mentioned in footnote 36, we saw little empirical support for commodity price augmented Dornbusch-type equations.

B. Other Shocks: The Balassa-Samuelson Relative Productivity Differences

As the commodity price-exchange rate connection appears more a “Down Under” phenomenon, here we analyze the Australia and New Zealand real exchange rate further by identifying and controlling for an additional source of real shocks. As discussed in Section V, the Balassa-Samuelson model suggests that country differences in traded and non-tradable sector productivity shocks may affect real exchange rate movements through their impact on relative wages. Figure 7 plots Australian and New Zealand real exchange rates with the ratios of the home country traded versus non-traded sector productivity to that of the United States.43 In contrast to the real interest rate and output differentials series presented in Figure 1A and 3A, we see much more obvious visual correlations between relative productivity differences and the real exchange rates. Indeed, results in Table 6 below show coefficient estimates roughly consistent with predictions of the Balassa-Samuelson framework presented in Section V. However, the productivity measures appear to be a less robust explanatory variable than commodity prices. If the Newey-West procedure is replaced by the parametric AR(1) specification, relative productivity no longer shows up as significant, while commodity prices remain resilient. More importantly, we note that the AR root coefficient estimates in the “commodity price cum relative productivity-augmented equations” remain high as before.44 Hence, we find the PPP puzzle to be like the Russian dolls, in that after controlling for two promising real shocks—peeling away two layers of the original PPP puzzle—we are still faced with the identical, despite smaller, PPP puzzle.

Fig. 7a:
Fig. 7a:

Australian-US Real Exchange Rate and Traded vs. Non-Traded Relative Productivity Differential

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Fig. 7b:
Fig. 7b:

NZL-US Real Exchange Rate and Traded vs. Non-Traded Relative Productivity Differential

Citation: IMF Working Papers 2002, 027; 10.5089/9781451844535.001.A001

Table 6:

Productivity Differentials and Real Exchange Rates 1 Dependent Variable: Log of Real Exchange Rate, vs. U.S. Dollar ln(Real Exchange Rate)t = α + β*t + γ1*ln(Real Commodity Price)t + γ2* Differential of ln(Tradable/Non-Tradable Productivity) vs. the U.S.)t + εt

article image
Note: * indicates significance at the 5 percent level.

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.

VII. Conclusion

In a literature largely populated by negative findings and empirical puzzles, this paper identifies a source of exogenous shocks and explores its contribution to time series exchange rate behavior, and more broadly, with standard exchange rate models. The world prices of commodity exports, measured in real U.S. dollars, do appear to have a strong and 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 free 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.

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 that rely heavily on primary commodity production. The experience of Australia, Canada, and New Zealand are of particular relevance as many of these developing countries liberate capital markets and move towards floating exchange rate systems. While this paper mainly covers the empirical links, understanding exchange rate responses to world commodity price shocks can provide important information for a broad range of policy issues, including especially the conduct of monetary policy and inflation control.

Commodity Currencies and Empirical Exchange Rate Puzzles
Author: Mr. Kenneth Rogoff and Mr. Yu-chin Chen
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    US - Australian Real Exchange Rate, Real interest Differential, Real Output Differential, 1984q1 to 2001q2

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    US -Australian Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

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    Non-Dollar Basket - Australian Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

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    UK - Australian Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

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    US - Canadian Real Exchange Rate, Real Interest Differential, Real Output Differential, 1973q1 to 2001q2

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    US - Canadian Real Exchange Rate, Real Commodity Price 1973q1 to 2001q2

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    Non-Dollar Basket - Canadian Real Exchange Rate, Real Commodity Price, 1973q1 to 2001q2

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    UK - Canadian Real Exchange Rate, Real Commodity Price, 1973q1 to 2001q2

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    US - New Zealand Real Exchange Rate, Real Interest Differential, Real Output Differential, 1986q1 to 2001q2

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    US - New Zealand Real Exchange Rate, Real Commodity Price, 1986q1 to 2001q2

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    Non-Dollar Basket - New Zealand Real Exchange Rate, Real Commodity Price, 198Sq1 to 2001q2

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    UK - New Zealand Real Exchange Rate, Real Commodity Price, 1986q1 to 2001q2

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    Detrended US - Australia Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

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    Detrended Non-Dollar Basket - Australian Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

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    Detrended UK - Australia Real Exchange Rate, Real Commodity Price, 1984q1 to 2001q2

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    Detrended US - Canadian Real Exchange Rate, Real Commodity Price, 1973q1 to 2001q2

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    Detrended Non-Dollar Basket - Canadian Real Exchange Rate, Real Commodity Price, 1973q1 to 2001q2

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    Detrended UK - Canadian Real Exchange Rate, Real Commodity Price, 1973q1 to 2001q2

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    Detrended US - New Zealand Real Exchange Rate, Real Commodity Price, 1986q1 to 2001q2

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    Detrended Non-Dollar Basket - NZL Real Exchange Rate, Real Commodity Price, 1986q1 to 2001q2

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    Detrended UK - New Zealand Real Exchange Rate, Real Commodity Price, 1986q1 to 2001q2

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    Australian-US Real Exchange Rate and Traded vs. Non-Traded Relative Productivity Differential

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    NZL-US Real Exchange Rate and Traded vs. Non-Traded Relative Productivity Differential