Blaise Gnimassoun

Valérie Mignon
email: valerie.mignon@u-paris10.fr.

How macroeconomic imbalances interact? Evidence from a panel VAR analysis 

Keywords: JEL Classification: F32, F31, C33 global imbalances, current account, output gap, exchange-rate misalignments, panel VAR

This paper aims at investigating the interactions between three key macroeconomic imbalances, namely current-account discrepancies (external imbalances), output gaps (internal imbalances), and exchange-rate misalignments. To this end, we rely on the estimation of a panel VAR model for a sample of 22 industrialized countries over the 1980-2011 period. Our findings show that macroeconomic imbalances strongly interact through a causal relationship. We evidence that if current-account disequilibria threaten the stability of the global economy, their origin can be found in internal imbalances and exchange-rate misalignments: positive output-gap shocks as well as currency overvaluation deepen current-account deficits. In addition, while variations in external imbalances mainly result from exchange-rate misalignments in the euro area, they are mostly explained by output gaps for non-eurozone members.

Introduction

The 2000 decade was marked by various key economic phenomena, among which the huge current-account deficits in the U.S. and some European countries, the public debt crisis and economic recession in the euro zone, persistence of exchange-rate misalignments leading to massive trade deficits in some developed countries and surpluses in several emerging Asia economies, etc. Focusing specifically on current accounts, Figure 1 evidences that the 2008 financial and economic crisis was preceded by a dramatic increase in global imbalances, 1 whose level remains still high in 2012 despite the adjustments that have been made since 2009.

Within this context of widespread imbalances, recent literature in international macroeconomics has focused on external disequilibria by addressing on the one side, the issue of current-account sustainability [START_REF] Edwards | Is the US current account deficit sustainable? And if not, how costly is adjustment likely to be?[END_REF][START_REF] Aizenman | Globalization and the sustainability of large current account imbalances: Size matters[END_REF][START_REF] Christopoulos | Current-account sustainability in the US: what do we really know about it[END_REF][START_REF] Chen | Current account deficits and sustainability: Evidence from the OECD countries[END_REF][START_REF] Schoder | Are the current account imbalances between emu countries sustainable? Evidence from parametric and non-parametric tests[END_REF] 2 and on the other side, the question of current-account adjustment or reversal [START_REF] Freund | Current account adjustment in industrial countries[END_REF][START_REF] Freund | Current Account Deficits in Industrial Countries: The Bigger They Are, The Harder They Fall? NBER Chapters[END_REF][START_REF] Clarida | Are there thresholds of current account adjustment in the G7?[END_REF]Debelle and Galati, 2007;[START_REF] Algieri | Patterns of current account adjustment-Insights from past experience[END_REF][START_REF] Lane | External adjustment and the global crisis[END_REF][START_REF] Gnimassoun | Current-Account Adjustments and Exchange-Rate Misalignments[END_REF] DEU+JNP: Germany and Japan; CHN+EMA: China and Emerging Asia (Hong Kong SAR, Indonesia, Korea, Malaysia, Philippines, Singapore, Taiwan Province of China and Thailand); OCADC 4 : Bulgaria, Croatia, Czech Republic, Estonia, Greece, Hungary, Ireland, Latvia, Lithuania, Poland, Portugal, Romania, Slovak Republic, Slovenia , Spain, Turkey and United Kingdom; OIL: oil exporters; ROW: rest of the world; US: United States. This growing interest in the literature for the study of current-account imbalances naturally stems from the threat they pose to the stability of the global economy, but also from the substantial economic costs often associated with their reversal. 5 Indeed, as shown by [START_REF] Freund | Current account adjustment in industrial countries[END_REF] and [START_REF] Obstfeld | The Unsustainable U.S. Current Account Position Revisited[END_REF] among others, a reversal of the current-account deficit implies a loss of economic growth and a significant exchange-rate depreciation. In other words, there would be a potential causal relationship running from the adjustment of currentaccount deficits to economic growth and exchange rates. Specifically, considering a dataset including 25 adjustment episodes from 1980 to 1997, [START_REF] Freund | Current account adjustment in industrial countries[END_REF] shows that the current-2 For earlier literature on current-account sustainability, see for example [START_REF] Milesi-Ferretti | Current account sustainability[END_REF], [START_REF] Roubini | Current Account Sustainability in Transition Economies[END_REF][START_REF] Roubini | Current Account Sustainability in Transition Economies[END_REF][START_REF] Mann | Perspectives on the US current account deficit and sustainability[END_REF]. 3 See also [START_REF] Corden | Those Current Account Imbalances: A Sceptical View1[END_REF], [START_REF] Gruber | Explaining the global pattern of current account imbalances[END_REF], and [START_REF] Aizenman | Globalization and the sustainability of large current account imbalances: Size matters[END_REF] for other interesting aspects relating to the analysis of current-account imbalances. 4 Other Current Account Deficit Countries. 5 [START_REF] Bracke | A Framework for Assessing Global Imbalances[END_REF] provide a quick overview of large current-account imbalances since 1970 and their consequences. account reversals usually start when the deficit reaches 5% of GDP, leading to a significant decline in output growth and a real depreciation of the currency around 10 to 20%. Studying the particular case of U.S. deficit, [START_REF] Obstfeld | The Unsustainable U.S. Current Account Position Revisited[END_REF] evidence that a reversal of the U.S. current account would result in a significant depreciation of the real effective exchange rate, leading to damaging consequences for economic growth.

However, several other studies argue that currency misalignments are partly the cause of current-account imbalances. Specifically, according to [START_REF] Jeong | Exchange rate misalignments at world and European levels: a FEER approach[END_REF], world currentaccount imbalances reflect, to some extent, exchange-rate misalignments. [START_REF] Gnimassoun | Current-Account Adjustments and Exchange-Rate Misalignments[END_REF] show that currency misalignments play an important role in the currentaccount adjustment, and evidence that overvaluations tend to increase persistence of currentaccount imbalances especially in the euro area. In addition, some authors claim that the current-account deficits observed recently in some countries are partly the result of intense economic activity or overly optimistic prospects in terms of economic growth. Indeed, independently of the convergence process and its potentially negative impact on current account highlighted by [START_REF] Blanchard | Current account deficits in the euro area: the end of the Feldstein-Horioka puzzle?[END_REF], [START_REF] Lane | Current Account Imbalances in Europe[END_REF] show that optimistic growth expectations can also generate current-account deficits, suggesting a causal relationship from exchange rates or economic growth to current accounts. Finally, investigating the exchange rate-growth nexus, [START_REF] Razin | Real exchange rate misalignments and growth[END_REF], [START_REF] Rodrik | The real exchange rate and economic growth[END_REF] and [START_REF] Béreau | Currency misalignments and growth: a new look using nonlinear panel data methods[END_REF] among others evidence a causal relationship from currency misalignments to economic growth without addressing the issue of reverse causality. 6While it is undeniable that current account, exchange rate and economic growth are economically linked, neither economic theory nor empirical studies clearly establish a causal relationship between these key macroeconomic variables. However, because of their interdependence, it is quite plausible that imbalances linked to one of these variables lead to imbalances related to the other variables and vice versa. In a context where external imbalances have increased significantly, it is a key issue to determine if their origin comes from internal disequilibria and / or exchange-rate misalignments. More generally, it is highly relevant to analyze the interactions between these three imbalances that we henceforth designate by macroeconomic imbalances. 7 To the best of our knowledge, there is no empirical study that examines the transmission mechanisms between these key macroeconomic imbalances.

This paper aims at filling this gap by studying the interactions between external imbalances, internal disequilibria and exchange-rate misalignments. To this end, we rely on the estimation of a panel vector autoregression (PVAR) model on a sample of 22 industrialized countries over the 1980-2011 period. We pay particular attention to the persistence of shocks, as well as the potential influence of monetary union or exchange-rate regime by distinguishing between euro area member countries and non-member economies. To shed light on the direction of the relationship between disequilibria, we also perform a panel causality analysis.

Our paper contributes to the literature on global imbalances in several ways. It provides an indepth analysis of the impact of exchange rates and economic activity on current accounts. Beyond simple variations that may result from the evolution of exchange rates and economic activity, our study assesses the impact of overvaluation and economic overheating shocks on current-account imbalances. The advantage of the PVAR approach is that it imposes no a priori constraint on the relationships between the macroeconomic imbalances, and is thus particularly suitable for our purpose given the likely endogenous interactions across those disequilibria. In addition, our causality analysis allows us to go further than previous studies, by identifying the direction of the link between the three considered macroeconomic imbalances. On the whole, our paper sheds light regarding the interactions between macroeconomic disequilibria, which is a key issue in the current context where one of the major concerns is the inversion of global imbalances.

The rest of the paper is organized as follows. Section 2 details our empirical methodology. Data and estimation results are presented in Section 3, together with a robustness analysis. Section 4 concludes the paper.

Methodology

To provide a full description of the interactions between macroeconomic imbalances, we rely on two complementary approaches. We first estimate a panel VAR model to analyze the transmission mechanisms between disequilibria. The VAR specification being not sufficient to perform an economic policy analysis since it does not provide enough information about the causal impact of shocks [START_REF] Moneta | Causal Inference by Independent Component Analysis: Theory and Applications[END_REF], we then perform a causality analysis.

Panel VAR approach

Combining the traditional VAR approach [START_REF] Sims | Macroeconomics and Reality[END_REF] with panel data econometrics, the PVAR model is particularly suitable to address a number of recent issues, including the analysis of global imbalances and their interactions.8 Indeed, impulse-response functions (IRFs) and variance decomposition (VDCs) deduced from the PVAR estimation are very useful in analyzing how macroeconomic imbalances interact.

The reduced form of a PVAR model is defined as follows:

, , , (1)
where ( 1, … , ) denotes the country, and ( 1, … , ) the time. , is the vector of endogenous stationary variables, represents the matrix polynomial in the lag operator L, denotes the vector of country-fixed effects and , is a vector of errors. The vector , is composed by our three macroeconomic imbalances, namely the output gap (ogap), currentaccount gap (CA_gap), and exchange-rate misalignment (mis):

, , , _ , , , ′ (2)
From a methodological viewpoint, implementing the VAR procedure on panel data requires imposing the same underlying structure for each cross-sectional unit (country); a constraint that may be violated in practice (see [START_REF] Love | Financial development and dynamic investment behavior: Evidence from panel VAR[END_REF]. The country-fixed effects introduced in Equation ( 1) are a way to overcome the restriction on the parameters to the extent that they capture individual heterogeneity. It is however well known that the fixedeffects estimator in autoregressive panel data models is inconsistent, fixed effects being correlated with the regressors due to lags of the dependent variable [START_REF] Nickell | Biases in dynamic models with fixed effects[END_REF]. To overcome this issue, we consider the generalized method of moments (GMM). More precisely, to remove the fixed effects, we use the forward mean-differencing procedure-also known as the Helmert procedure-following [START_REF] Love | Financial development and dynamic investment behavior: Evidence from panel VAR[END_REF] among others. In this approach, all variables are transformed into deviations from forward means, and each observation is weighted to standardize the variance. This transformation preserves orthogonality between transformed variables and lagged regressors, allowing us to use the lagged regressors as instruments and estimate the coefficients by the GMM procedure.

Once the coefficients have been estimated, we compute the IFRs and VDCs using the Cholesky decomposition. Neither economic theory nor empirical studies allow us to unambiguously choose the order to retain for the variables in the Cholesky decomposition. As an illustration, the real effective exchange rate can be viewed as the most endogenous variable given that it is determined by internal fundamentals associated with economic growth (productivity) and external fundamentals associated with the current-account position (net foreign assets). On the other hand, the real effective exchange rate is also frequently considered as an explanatory variable in the growth literature or in current-account models (Salai-i-Martin, 1997;Arghyrou and Chortareas, 2008 among others). We thus retain the order of the variables as presented in Equation ( 2), and test the robustness of our results to changes in this ordering.

Causality analysis

To specify the causal direction of the transmission mechanism between imbalances, we rely on the panel non-causality test developed by [START_REF] Dumitrescu | Testing for Granger non-causality in heterogeneous panels[END_REF]. This is a simple extension of the [START_REF] Granger | Investigating causal relations by econometric models and crossspectral methods[END_REF] test to heterogeneous panel data models. By preserving the heterogeneity of cross-sectional units, it allows us to test the direction of the relationship between macroeconomic imbalances without imposing the same dynamic model for all the countries of the sample. The starting point consists in the following heterogeneous autoregressive model:

9 , ∑ , ∑ , , (3)
where and are two stationary variables, observed on periods for countries. The individual effects are assumed to be fixed and the lag-order is supposed to be common. 10 denote the autoregressive parameters, and are the regression coefficients' slopes; both parameters differing across countries. By definition, causes if and only if the past values of the variable observed on the country improve the forecasts of the variable for this country only. The test is based on the null hypothesis of homogeneous non-causality ( ), i.e., there is no causal relationship from to for all the countries of the panel ( , … , 0, ∀ 1, … , . Under the alternative hypothesis, there exists a causal relationship from to for at least one country of the sample. The test statistic is given by the cross-sectional average of individual Wald statistics defined for the Granger noncausality hypothesis for each country ( ), and converges to a chi-squared distribution with degrees of freedom. Two standardized statistics have been defined by the authors: the first one is based on the exact asymptotic moments of the individual Wald statistics ( ), and the second one on approximated moments for finite T samples (

). 11

3 Data and empirical results

Data and preliminary tests

We rely on a panel of 22 OECD countries, half of which belonging to the euro area. 12 Data are annual and cover the period from 1980 to 2011. Internal imbalances are proxied by the output gaps calculated by the IMF. External, current-account imbalances are measured by the current-account gap, defined as the difference between the observed current account and its estimated equilibrium value. Similarly, exchange-rate misalignments are defined as the difference between the observed real effective exchange rate and its estimated equilibrium level. 13 All data used and their sources are given in Table A.1 in the Appendix. We perform panel unit root tests to ensure that our variables have suitable properties. Results presented in Table A.2 in the Appendix show that the three variables measuring macroeconomic imbalances are stationary. Those findings are not surprising since they indicate that imbalances are stabilizing, although strong persistence can sometimes be observed, requiring painful corrective policies.

11 Despite its advantages, it should be noticed that this test does not take into account the possibility of a causal link between cross-sectional units. However, [START_REF] Dumitrescu | Testing for Granger non-causality in heterogeneous panels[END_REF] show on the basis of Monte Carlo experiments that the standardized panel statistics have very good small sample properties, even in the presence of cross-sectional dependence. 12 Our sample includes (i) 11 eurozone members, namely Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal and Spain; and (ii) 11 non-eurozone countries: Australia, Canada, Denmark, Iceland, Japan, New Zealand, Norway, Sweden, Switzerland, United Kingdom, and the United States. 13 Equilibrium values for both the current account and the real effective exchange rate are derived from the estimation of models including usual fundamentals [START_REF] Gnimassoun | Current-Account Adjustments and Exchange-Rate Misalignments[END_REF]. Specifically, regarding the current account, the following determinants have been retained: relative fiscal balance, lagged net foreign asset position, relative level of PPP-adjusted GDP per capita, relative GDP growth rate, aging rate, old-age dependency ratio, population growth rate, M2 to GDP ratio, degree of openness, terms of trade, and oil balance.

Turning to the equilibrium exchange-rate model, we have expressed the real effective exchange rate as a function of the net foreign asset position (in percentage of GDP) and a proxy for relative productivity.

Panel VAR results

We focus on the impulse response functions (IRFs) derived from the estimation of Equation ( 1), 14 and also briefly comment the variance decomposition. Figure 2 displays the IRFs for the whole panel, together with the 5% standard-error bands generated through Monte Carlo simulations.

As shown, a positive shock on output gap leads to (i) a significant and negative response of current-account gap, and (ii) a significantly positive response of exchange-rate misalignments.

In other words, an economic overheating generates a huge current-account deficit together with a currency overvaluation. This finding could be explained by a demand effect or price effect that implies a deterioration of the trade balance. Indeed, when the production factors are limited to meet domestic demand, excess demand is offset by an increase in imports. Strains on production factors result in inflationary pressures and exchange-rate overvaluation that negatively affect the trade balance. A 15% economic overheating shock results in an instantaneous current-account deficit of about 4%. This deficit is maximal after one year, reaching 7% before the beginning of adjustment towards equilibrium. This output-gap shock also generates a relatively low and gradual overvaluation, being maximal around 1% after two years before the start of adjustment towards equilibrium. Regarding the current account, a shock on the current-account gap significantly affects neither exchange-rate misalignments nor output gap. Finally, turning to the last imbalance, our findings evidence that misalignment shocks significantly impact current-account disequilibria. More specifically, a 5% overvaluation gradually accentuates the current-account deficit that reaches 35% before starting the reversion towards equilibrium. Exchange-rate overvaluation has however no significant effect on output gap. These findings are consistent with the idea that overvalued currencies are associated with unsustainably large current-account deficits, balance of payments crises, and stop-and-go macroeconomic cycles (see [START_REF] Rodrik | The real exchange rate and economic growth[END_REF]. All these results are robust to changes in the variables' order retained in the Cholesky decomposition.15 Given that our panel of countries includes eurozone members as well as other countries, we now investigate whether belonging to a monetary union has an influence on our previous findings. To this end, we split our panel in two sub-samples: a panel including 11 euro area members, and a panel encompassing the other 11 countries. As evidenced by Figure 3 which reports IRFs for eurozone members, interactions between macroeconomic imbalances within the euro area are similar to those obtained for the whole panel. Indeed, an economic overheating leads to currency overvaluation and important current-account deficit, and a currency-overvaluation shock tends to deepen current-account deficit. However, imbalances' magnitude and persistence in the euro area differ from those of the whole panel. Indeed, for an equivalent output-gap shock, the response of the current-account gap is less important in the euro area, while overvaluation is larger. As for the whole panel, adjustment towards equilibrium begins after one year for the current-account gap, and after two years for misalignments. Finally, for a relatively lower overvaluation shock, current-account imbalances are larger and more persistent within the eurozone. Indeed, an overvaluation shock of about 3.2% results in a massive and persistent current-account deficit stabilizing at around 40%.

Figure 3. Impulse-response functions for euro area members

Note: Impulse-responses are represented by solid lines. Standard-error bands (dashed lines) are generated through Monte-Carlo simulations with 1000 repetitions.

Turning to non-eurozone members (Figure 4), macroeconomic imbalances interact in the same way as in the two previous cases, with the exception of the output-gap shock which does not lead to a significant currency overvaluation. However, for a similar output-gap shock, current-account imbalances are larger than in eurozone. By cons, for a similar misalignment shock, current-account deficits are less important than in the euro area. Persistence of currentaccount imbalances is also weaker and adjustment towards equilibrium occurs more rapidly, the reversion beginning after two years. To sum up, our IRF analysis shows that macroeconomic imbalances interact with each other. More specifically, an economic overheating shock (positive output-gap shock) deepens current-account deficits for both eurozone members and non-members, with a greater impact for the latter. However, currency overvaluation that results from this shock is significant only for the euro area. Finally, an overvaluation shock contributes to feed current-account imbalances for both eurozone members and non-members, with a more persistent impact for the former.

To complete our findings, we perform variance-decomposition analysis for assessing more precisely the percentage of variation in a variable explained by another variable. Results presented in Table 1 indicate that a change in output gap is mainly explained by itself. This explains why the output gap does not significantly react to both current-account gap and misalignment shocks. Indeed, current-account imbalances explain only 2.5% of the variation in output gap for eurozone members and 5.7% for non-members. Turning to external imbalances, output gap and misalignments respectively contribute for 8.3% and 17.2% in explaining current-account disequilibria in the eurozone, while these percentages amount to response of ogap to mis shock year year year 21% and 5.8% for non-members. Our findings thus show that variations in current-account imbalances mainly result from exchange-rate misalignments in the euro area, and from output gap for non-eurozone members. Changes in currency misalignments mostly come from themselves, being however explained for about 7.5% by the output gap for the eurozone. Our results are consistent with previous studies evidencing that expansionary fiscal policies, particularly in the economic convergence context, can lead to economic overheating which increases current-account deficits [START_REF] Blanchard | Current account deficits in the euro area: the end of the Feldstein-Horioka puzzle?[END_REF]. Beyond the convergence phenomenon, Lane and Pels (2012) also show that excessive current-account deficits are partly explained by overly optimistic prospects of economic growth. The importance of exchange-rate misalignments in explaining global imbalances, especially in the euro area, is consistent with the findings of [START_REF] Gnimassoun | Current-Account Adjustments and Exchange-Rate Misalignments[END_REF]. The latter indeed show that low overvaluations can lead to strong persistence in current-account imbalances in the euro area, while it is not the case for non-eurozone members. This is partly explained by the fact that the increase in current-account deficit due to a loss of price competitiveness cannot be corrected by any nominal exchange rate adjustment in a monetary union except by resorting to devaluation, which may be costly economically. Thus, improving competitiveness must be carried through other channels, such as a decline in wages or a rise in working hours that are unpopular and instability-generating measures.

Panel causality test results

As previously mentioned, knowing the causal direction between macroeconomic imbalances is obviously useful for decision-making in economic policy. We therefore perform causality tests, whose results are reported in Table 2. 16 These findings appear to be quite consistent with our previous conclusions. Indeed, whatever the test statistic and regardless of the number of lags retained in the model, the homogeneous non causality (HNC) hypothesis from misalignments to current-account imbalances is strongly rejected at conventional levels. However, the HNC null hypothesis from current-account imbalances to misalignments cannot be rejected with the standardized statistic ( ) and for a number of lags equal to 1. The HNC hypothesis from output gap to current-account imbalances is strongly rejected, this result being robust to both the lag order and the statistic test. The reverse causality hypothesis cannot be rejected for 1 and with . Regarding misalignments and the output gap, the HNC hypothesis from output gap to misalignments is generally rejected, while it is significantly rejected only for the statistic when considering the misalignment to output gap direction.

On the whole, our findings emphasize the existence of a causal relationship between macroeconomic imbalances. In particular, there is a strong and robust causal link from exchange-rate misalignments to current-account imbalances, at least for some countries in the sample. Furthermore, a causal relationship from output gap to current-account imbalances seems to be clearly established, as well as from output gap to misalignments. The latter result is very appealing regarding the literature that tends to focus on a causal link from exchangerate misalignments to economic activity, often showing a negative impact of currency overvaluation on GDP growth [START_REF] Razin | Real exchange rate misalignments and growth[END_REF][START_REF] Rodrik | The real exchange rate and economic growth[END_REF][START_REF] Berg | The Real Exchange Rate and Growth Revisited: The Washington Consensus Strikes Back? IMF Working Paper[END_REF]among others). Whereas these findings are not challenged by ours, we show that the reverse relationship is quite robust: economic overheating leads to an exchange-rate overvaluation, especially in the euro area. Such results have not been strongly highlighted in previous studies, mainly because of the a priori choice of model specification in which misalignments are often considered as an explanatory variable. All these results confirm the IRF analysis which notably revealed that current-account deficits are growing widely in response to economic overheating or overvaluation shocks. These findings are highly relevant for economic policy to the extent that they show that a reduction in misalignments and output gaps could play a key role in the perspective of reducing global imbalances.

Table 2. Causality between output gap, misalignments and current-account imbalances

Robustness analysis

Alternative measures of macroeconomic imbalances

To check the robustness of our results, we perform again the IRF analysis using alternative measures of macroeconomic imbalances. Specifically, instead of being based on fundamentals as before, we measure exchange-rate misalignments as the deviation of the actual real exchange rate from its Hodrick-Prescott detrended value as in [START_REF] Goldfajn | The aftermath of appreciations[END_REF] and [START_REF] Béreau | Currency misalignments and growth: a new look using nonlinear panel data methods[END_REF], among others. The output gap is constructed in the same way as being the deviation of the actual real GDP from its Hodrick-Prescott filtered value (see e.g., De [START_REF] De Masi | IMF estimates of potential output: theory and practice[END_REF][START_REF] Isard | Exchange Rate Assessment -Extensions of the Macroeconomic Balance Approach[END_REF]. Similarly, external imbalances are also calculated using the Hodrick-Prescott filtering method. If these alternative measures of macroeconomic imbalances have the disadvantage of having no economic foundations, they present the interest to be homogeneous. The IRFs derived from using these new proxies are reported in Figures A.1 to A.3 in the Appendix.

These results show that our previous findings are globally robust to the choice of the measure retained for macroeconomic imbalances. Indeed, as before, current-account deficits are growing massively in response to a positive output-gap shock for the whole panel as well as for the two sub-panels. This shock also leads to an exchange-rate overvaluation, which is more pronounced in the euro area. Moreover, current-account deficits are amplified in response to a positive currency misalignment shock, the impact being more persistent in the euro zone as previously.

Interactions between the observed macroeconomic variables

Whatever the approach retained-being based on economic fundamentals or statistical method-macroeconomic imbalances are determined after estimating an "equilibrium level" for the different variables. To account for potential estimation bias and as a robustness check, we complement our analysis by investigating interactions between changes in the observed macroeconomic variables (namely current account, economic growth and real effective exchange rate) for the same samples. Given that these changes concern the variables themselves and not the corresponding imbalances, we do not expect to obtain exactly the same results as before. However, given that disequilibria result from the difference between the observed variables and their equilibrium level, we may expect that imbalances and observed variables globally react in the same way without considering the magnitude of shocks and the respective responses to shocks. As an example, if the current-account gap reacts negatively to an overvaluation shock, one may attempt that a real exchange-rate appreciation should have a negative effect on the observed current account. The IRFs resulting from the interactions between current account, economic growth and real effective exchange rates are displayed in Figures A.4 to A.6 in the Appendix.

These results support our previous findings. Indeed, a positive shock on the real effective exchange rate (a real appreciation) leads to a current-account deficit for all the considered panels. Similarly, a positive shock on economic growth negatively affects the current account regardless of the sample, and leads to an exchange-rate appreciation in the euro area. Moreover, economic growth positively responds to a positive shock on current account for all samples. Finally, it is worth noting that responses to shocks are generally more persistent in case of imbalances than for the macroeconomic variables themselves. The impact of macroeconomic imbalances would thus be more painful, because it is more difficult to absorb than the effect of simple changes in macroeconomic variables, which is a relevant and expected result.

Finally and for the sake of completeness, note that we have conducted an analysis mixing observed variables and corresponding imbalances.17 Our results show that (i) a shock on economic growth or on the exchange rate produces current-account imbalances, and (ii) economic overheating leads to an exchange-rate appreciation and a deterioration of the current-account balance, in line with our previous results.

Conclusion

The explosion of global imbalances that preceded the 2008 global crisis and the issue of their adjustment have remarkably mobilized the attention of the international macroeconomic literature in recent years. This extensive literature was mainly devoted to the analysis of external imbalances in developed countries given the challenge they represent for global economy stability. In this context, the aim of this paper is to investigate the interactions between the three key macroeconomic imbalances (external imbalances, internal imbalances and exchange-rate imbalances). To this end, we estimate a panel VAR model on a sample of 22 industrialized countries over the period from 1980 to 2011.

We find evidence that macroeconomic imbalances strongly interact through a causal relationship. Specifically, current-account imbalances respond positively and significantly to an output-gap shock. Such pressure on the economy also generates an exchange-rate overvaluation in the euro area. Accordingly, although current-account deficits are often more pronounced for "small" countries because they tend to reduce savings and increase investment, developed economies are not immune against deep current-account deficits. Such deficits occur when these countries tend to produce beyond their level of potential output, in response e.g. of strong demand. Moreover, a currency overvaluation shock deepens the current-account deficit, with a more pronounced persistence for euro area members. Our findings are consistent with [START_REF] Friedman | The case for flexible exchange rates[END_REF] and the recent study by [START_REF] Ghosh | Is the exchange rate regime really irrelevant for external adjustment?[END_REF] showing that external imbalances are harder to absorb for countries belonging to a monetary union or with a fixed exchange-rate regime. Turning to the direction of the relationship between disequilibria, we evidence that there is causality running from the output gap to current-account imbalances and exchange-rate misalignments, and also establish a causal link from currency misalignments to external disequilibria.

On the whole, contributing to the debate on global imbalances, our paper evidences that if external imbalances threaten the stability of the global economy, their origin can be found in internal imbalances and currency misalignments. Consequently, policies aiming at reducing global imbalances should focus on the absorption of internal imbalances-output gaps-and plummeting exchange-rate misalignments.

  3

Figure 1 .

 1 Figure 1. Global imbalances (current account, billions of U.S. dollars)

Figure 2 .

 2 Figure 2. Impulse-response functions for the whole sample

Figure 4 .

 4 Figure 4. Impulse-response functions for non-eurozone countries

Figure

  Figure A.1. IRFs for the whole sample (H-P filter measure of imbalances)

Table 1 . Variance-decomposition results

 1

		Ogap	Ca_gap	Mis
			All sample
	Ogap	99.97	0.01	0.02
	CA_gap	14.75	77.24	8.00
	mis	3.32	0.02	96.65
			Eurozone members
	Ogap	96.69	2.57	0.74
	CA_gap	8.29	74.55	17.16
	mis	7.46	0.06	92.48
			Non-eurozone members
	Ogap	94.22	5.70	0.09
	CA_gap	21.05	73.12	5.82
	mis	1.82	0.71	97.48

Note: This table reports the percentage of variation in the variable in row explained by the variable in column. The figures reported are averages of 10, 20 and 30 years.

  X to Y" means that we test the null hypothesis of homogenous non causality (HNC) from X to Y. The letter "a" indicates rejection of null hypothesis at the 5% significance level.

						Statistic tests
	Lag order
		mis to CAgap		Ogap to CAgap		Ogap to mis
	1	2.34	4.45a	3.67a	2.57	5.20a	4.33a	2.21	4.02a	3.29a
	2	3.29	6.04a	2.23a	4.86	13.43a	5.37a	3.06	4.97a	1.78
	3	5.16	12.41a	2.96a	6.32	19.09a	4.79a	6.19	18.31a	4.58a
		CAgap to mis		CAgap to Ogap		mis to Ogap
	1	1.522	1.73	1.29	1.39	1.28	0.90	1.60	2.00a	1.53
	2	2.603	2.83a	0.87	2.51	2.37a	0.67	2.75	3.50a	1.15
	3	4.202	6.91a	1.46	4.55	8.92a	2.01a	3.87	4.98a	0.93
	Notes: "

These studies generally show that overvaluations are harmful to growth while undervaluations are growthenhancing.

 7 External imbalances or current-account imbalances are represented by the difference between the observed current account and the equilibrium level given by its fundamentals. Similarly, exchange-rate imbalances are known as exchange-rate misalignments and are defined as the deviation of the observed exchange rate to its equilibrium value. Internal imbalances refer to output gaps, generally measured as the difference between the observed GDP and its potential level.

See Canova and Ciccarelli (2013) for a survey on PVAR models and their interests.

This test is briefly presented in this paper. For more details, the reader can refer to[START_REF] Dumitrescu | Testing for Granger non-causality in heterogeneous panels[END_REF].

We consider several values for this parameter to test the robustness of our findings.

To save space, the detailed results of these estimates are not reported here, but are available upon request from the authors. Two lags have been retained for the estimation, as suggested by usual information criteria.

Complete results are available upon request to the authors.

The three test statistics have been computed for various lags ranging from 1 to 3 to assess the sensitivity of our results to the choice of common lag order.

To save space, the corresponding IRFs are not reported here, but are available upon request to the authors.

Appendix

The tests are based on the unit root null hypothesis. 2 lags are used for variables in levels, and 1 lag for variables in first differences as well as for variables measuring imbalances.

CADF is the Cross-sectionally Augmented Dickey-Fuller test of [START_REF] Pesaran | A simple panel unit root test in the presence of cross-section dependence[END_REF]. This test was performed for all variables in order to take into account crosssectional dependencies, except for the variables "Mis" and "CA_gap" whose calculation allows controlling for this phenomenon. For these two variables, we performed the IPS test proposed by [START_REF] Im | Testing for unit roots in heterogeneous panels[END_REF].


Virginie Coudert
email: virginie.coudert@banque-france.fr

Cécile Couharde
email: cecile.couharde@u-paris10.fr.

Valérie Mignon 

On the impact of oil price volatility on the real exchange rateterms of trade nexus: Revisiting commodity currencies 

Keywords: JEL Classification: C23, F31, Q43 commodity currencies, oil price, non-linearity

The aim of this paper is to study the relationship between terms of trade and real exchange rates of commodity-producing countries on both the short and the long run. We pay particular attention to the dominant role played by oil among commodities by investigating the potential non-linear effect exerted by the situation on the oil market on the real exchange rate -terms of trade nexus. To this end, we rely on the panel smooth transition regression methodology to estimate the adjustment process of the real effective exchange rate to its equilibrium value depending on the volatility on the oil market. Considering a panel of 52 commodity exporters and 17 oil exporters over the 1980-2012 period, our findings show that while exchange rates are mainly driven by fundamentals in the low-volatility regime, they are mostly sensitive to changes in terms of trade when oil price variations exceed a certain threshold. The commodity-currency property is thus at play in the short run only for important variations in the oil price.

Introduction

Commodity-producing countries are reliant on world commodity prices regarding their exports, income and inflation rates. Their currencies are also known to be affected by commodity prices, in such a way that they are dubbed "commodity currencies" on the forex market, a denomination that gathers together the Australian dollar, the New Zealand dollar, the Canadian dollar as well as a number of currencies issued by emerging commodity exporters. Indeed, their real exchange rates tend to respond to the commodity terms of trade, defined as the ratio of the country's commodity export price to the import price. Two types of theoretical effects are at stake depending on the horizon. First, in the long run, a rise (fall) in terms of trade brings about more (lower) income and wealth in the exporting countries, which causes the real exchange rate to appreciate (depreciate). This long-run effect has been extensively documented in the economic literature dealing with the influence of fundamentals on equilibrium real exchange rates [START_REF] Edwards | Real and monetary determinants of real exchange rate behavior: Theory and evidence from developing countries[END_REF][START_REF] Isard | Equilibrium Exchange Rates: Assessment Methodologies[END_REF][START_REF] Ricci | Real Exchange Rates and Fundamentals: A Cross-Country Perspective[END_REF]. Second, even if the real effect is felt only in the long term, market participants anticipate this movement and bid up the currency, as soon as commodity prices begin to rise. Consequently, commodity currencies have been shown to closely follow the fluctuations of commodity prices [START_REF] Chen | Commodity Currencies[END_REF][START_REF] Clements | Commodity currencies and currency commodities[END_REF].

In this paper, we aim at better capturing the relation between terms of trade and the real exchange rates of commodity-producing countries on both the short and the long run by paying particular attention to non-linearities. Indeed, the forex markets are subject to nonlinear responses to fundamentals, as they are often disrupted in times of financial strains. In those periods, as risk aversion rises, long positions taken on risky currencies through carry trades are abruptly unwound, and exchange rates' movements are disrupted [START_REF] Clarida | Currency Carry Trade Regimes: Beyond the Fama Regression[END_REF]. Consequently, it is very likely that the real exchanges rates of commodity producers also respond in a non-linear way to terms of trade, depending on risk aversion and uncertainty on the global economy. More precisely, we argue that commodity prices spill over into the forex markets to a larger extent in periods of uncertainty, i.e., when volatility is high.

We therefore state the hypothesis that the real exchange rates of commodity-producing countries are more tightly linked to their terms of trade in times of high volatility on commodity markets. In other words, we name "commodity-currency property" the tendency for a currency to co-move with commodity prices, and we check for this feature being exacerbated in periods of high volatility. If our hypothesis holds, the relationship between real exchange rates and commodity terms of trade should be reformulated to account for these non-linearities. We therefore test for this hypothesis in the framework of a non-linear model.

In this sense, our study can be viewed as an extension of the literature on commodity currencies (see e.g., [START_REF] Cashin | Commodity Currencies and the Real Exchange Rate[END_REF] which analyzes the link between exchanges rates and commodity prices without accounting for non-linearities caused by market volatility.

Commodity markets strongly interact with one another for a number of reasons; among them the exchange-traded funds buying futures on indexes of commodities contribute to enhance the co-movements. In this respect, the oil market has a key role by its dominating size and its preponderant weight in commodity indexes. We thus retain the oil price volatility as a gauge of strains on all commodity markets, and search for non-linearities in exchange rates' response to terms of trade depending on the volatility of oil price. Volatility spillovers from oil to commodity markets may have amplifying effects on the reaction of commodity currencies to prices, as crude oil price changes are transmitted to other commodity prices [START_REF] Baffes | Oil spills on other commodities[END_REF]. While research has been extensive on the interdependencies between oil and commodity markets, no study has been devoted to the link between real exchange rates and those interactions. This is however a key issue: if oil price volatility is transmitted to other commodity prices, it can also aggravate pressures on commodity currency markets. Thus, commodity currencies may turn more sensitive to commodity prices in times of high oil price volatility. To the best of our knowledge, our contribution is the first to tackle this issue and also to investigate the impact of commodity terms of trade on currencies within a non-linear framework.

To this end, we consider a panel made of two groups of countries-17 oil exporters and 52 commodity exporters-over the 1980-2012 period. Our empirical approach involves two steps. First, we estimate a long-run, cointegrating relationship between the real effective exchange rate and economic fundamentals, including the commodity-terms of trade. This estimation amounts to finding an equilibrium value of the real effective exchange rate, in line with the behavioral equilibrium exchange rate (BEER) approach introduced by Clark andMacDonald (1998, 2000). Second, we estimate the short-run adjustment process to this equilibrium value through a panel smooth transition regression (PSTR) which is able to account for non-linearities. To provide a full analysis and deal with potential heterogeneity across the types of commodities, we also split the commodity producers by main exported products: energy and metals, food, beverages and raw materials in order to compare the behavior of their exchange rates.

The rest of the paper is organized as follows. After a brief review of the related literature, Section 2 presents some stylized facts. Section 3 describes the methodology, and Section 4 deals with the construction of the dataset. Section 5 discusses the estimation results. Section 6 concludes.

Main literature results and stylized facts

As we aim at analyzing the link between real exchange rates and commodity terms of trade, we give a first insight by looking at main literature results as well as pinpointing some stylized facts, evidencing the key role of oil among other commodity markets.

Brief literature survey on real exchange rates, commodity and oil prices

The relationship between real exchange rates and commodity prices goes through the terms of trade, that are mainly driven by commodity prices in commodity-exporting countries. From a theoretical perspective, the influence of terms of trade on the real exchange rate was first investigated during the 1980s in the framework of two-sector models that analyzed the potential harmful impact of a natural resource sector boom on the economy, known as the "Dutch disease". The real exchange rate is defined either internally as the relative price between the two sectors, or externally by the relative price of the consumption basket between the home country and abroad. In both cases, it appreciates when the price of the non-tradable goods increases relatively to that of the tradables, due to the law of one price on tradables. In this framework, a rise in the exported commodity price triggers an appreciation of the real exchange rate through both substitution and income effects [START_REF] Neary | Determinants of the Equilibrium Real Exchange Rate[END_REF]. Indeed it brings about a reduction in the supply of non-traded goods, through a substitution effect, increasing their price and therefore pushing up the real exchange rate. It raises as well the demand for those non-traded goods, through an income effect, contributing also to swelling their relative prices. These effects directly result from two key assumptions: (i) resources are drawn towards the commodity sector and (ii) non-traded goods are normal goods, whose demand increases with income. Consequently, the effects are attenuated by the release of these assumptions, especially if the commodity sector has production links with the rest of the economy, and thus encourages production of non-traded goods.

More recently, other studies have focused on the long-run relationship between the commodity price and the real exchange rate, going beyond demand-side considerations by extending the flexible-price Balassa-Samuelson model [START_REF] Chen | Commodity Currencies[END_REF][START_REF] Cashin | Commodity Currencies and the Real Exchange Rate[END_REF]. This long-run relationship only holds to a substitution effect under the assumption that wage movements diffuse across sectors. Indeed, an increase in the international commodity price is likely to set off wage hikes in the commodity sector; as wages equalize across sectors, pay rises push up the price of the non-traded goods and therefore also the domestic consumption price relatively to the foreign one and the real exchange rate. As only the substitution effect is involved, the elasticity of the real exchange rate to the commodity price is smaller in these models than in the former ones derived from the Dutch disease effect [START_REF] Tokarick | Commodities currencies and the real exchange rate[END_REF]. This elasticity is given by the share of non-tradable goods in the consumption basket [START_REF] Cashin | Commodity Currencies and the Real Exchange Rate[END_REF], and can be larger if the non-traded goods production is more labor intensive than the export goods sector [START_REF] Chen | Commodity Currencies[END_REF].

The potential role of commodity prices in driving real exchange rate movements has also received much attention in the empirical literature. [START_REF] Cashin | Commodity Currencies and the Real Exchange Rate[END_REF] find a significant longrun relationship between the real commodity price and the real exchange rates for one-third of 58 commodity-dependent countries, over the 1980-2002 period. [START_REF] Chen | Commodity Currencies[END_REF] also evidence a cointegration relationship between these two variables for three OECD economies (Australia, Canada, and New Zealand) where primary commodities constitute a significant share of their exports. More recently, [START_REF] Bodart | Real exchanges rates in commodity producing countries: A reappraisal[END_REF] conclude to a significant long-run impact of the price of a given commodity on the real exchange rate, if this commodity is predominant in the considered country's exports, its share being greater than 20 percent.

Other empirical studies focus on oil currencies and find that a positive oil price shock is likely to generate an appreciation over the long run. [START_REF] Koranchelian | The equilibrium real exchange rate in a commodity exporting country: Algeria's experience[END_REF] and [START_REF] Zalduendo | Determinants of Venezuela's equilibrium real exchange rate[END_REF] show that oil prices play a significant role in determining the equilibrium real effective exchange rate of Algeria and Venezuela. Similarly, estimating equilibrium real exchange rates over a panel of nine OPEC countries, [START_REF] Korhonen | Equilibrium exchange rates in oil-dependent countries[END_REF] confirm the statistically significant effect of the real price of oil on exchange rates.

Evidence from the literature also highlights the role played by exchange-rate regimes in the face of terms-of-trade shocks. [START_REF] Coudert | Does Euro or Dollar Pegging Impact the Real Exchange Rate? The Case of Oil and Commodity Currencies[END_REF] find that the real exchange rates of pegged commodity currencies depend on the behavior of their anchor. In particular, USD-pegged currencies had a tendency to depreciate with the dollar in the late 2000s, while those pegged to the euro had been pushed upwards. [START_REF] Aizenman | Adjustment patterns to commodity terms of trade shocks: The role of exchange rate and international reserves policies[END_REF] emphasize the role played by international reserves and managed exchange-rate flexibility in buffering and stabilizing the real exchange rate in the presence of large commodity terms of trade. By testing this hypothesis empirically for a set of Latin American countries, they find evidence that those economies actively countered appreciation pressures due to commodity terms of trade shocks in the 1970-2007 period, by accumulating forex reserves. [START_REF] Buetzer | Global exchange rate configurations: do oil shocks matter?[END_REF] confirm and extend these results to oil-exporting countries. Moreover, those authors show that the potential role of oil price changes in driving real exchange rates depends on the nature of the oil shock. Following the decomposition of oil shocks developed by [START_REF] Kilian | Not all oil shocks are alike: disentangling demand and supply shocks in the crude oil market[END_REF], they find that oil demand shocks are more prone to exert significant appreciation pressures in oilexporting economies than oil supply and global demand shocks.

In addition to the influence of the commodity prices on real exchange rates, [START_REF] Clements | Commodity currencies and currency commodities[END_REF] explore the two-way spillovers between the two variables. They suggest that the world commodity prices may also respond to exchange rate movements in commodity currencies.

This may happen if a country has a dominant position on the market of a given commodity in such a way that its market power puts it in a position of a price-maker. In this case, all its economic fundamentals, including its exchange rate, may influence the market price.

Although this dominant position is rather unusual for a single country, the same kind of results holds if several countries are in a dominant position on one commodity market, while their currencies head for the same direction. Then the appreciation (depreciation) of their real exchange rates is liable to increase (decrease) the world price of this commodity.

Finally, as oil prices have been found to be a major source of real disturbances [START_REF] Zhou | The response of real exchange rates to various economic shocks[END_REF], a number of articles have paid close attention to the relationship between real oil prices and real exchange rates (see, for example, [START_REF] Chen | Oil prices and real exchange rates[END_REF]. While emphasizing the particular role played by oil, the existing literature in this area mainly focuses on industrialized countries. Commodity exporters have then received little attention. However, oil price fluctuations can be a key factor to consider in explaining the behavior of their real exchange rates, given the linkages between oil and commodity markets.

The special case of oil

The dominant role of oil among commodity markets stems from its price impacting numerous sectors of an economy 1 and also other commodity prices as well [START_REF] Holtham | Modeling commodity prices in a world macroeconomic model[END_REF][START_REF] Gilbert | The impact of exchange rates and developing country debt on commodity prices[END_REF] 1 See e.g., [START_REF] Jones | The macroeconomic impacts of oil price shocks: A review of literature and issues[END_REF], [START_REF] Brown | Energy Prices and Aggregate Economic Activity: An Interpretative Survey[END_REF], [START_REF] Jones | Oil price shocks and the macroeconomy: What has been learned since 1996?[END_REF] and [START_REF] Hamilton | Oil and the macroeconomy[END_REF].

1989; [START_REF] Borensztein | The macroeconomic determinants of commodity prices[END_REF][START_REF] Baffes | Oil spills on other commodities[END_REF]. As recalled by [START_REF] Baffes | Oil spills on other commodities[END_REF] among others, the pass-through of oil price variations to commodity prices can be understood from both demand and supply sides. Considering the demand side, three main factors are at play. First, an oil price increase generates a rise in the disposable income of oil exporters, leading to a surge in the demand for other commodities, obviously especially those that are characterized by a high demand and high income elasticity. Second, given their potential substitutability property, a rise in the oil price affects the price of other energy commodities, such as coal, gas and electricity. Third, due to inflationary pressures associated with an oil price increase, the demand for precious metals may rise thanks to their safe-haven role, hence leading to an increase in their price. Turning to the supply side, oil is used as an input for the production of many other commodities, as well as for transportation. Thus, an augmentation in its price obviously leads to an increase in the production cost, impacting the price of those other commodities. For all those reasons, oil price variations may impact prices of other commodities and thus play a key role in the relationship between real exchange rates and commodity terms of trade.

As a simple illustration, consider the New Zealand dollar, which is usually viewed as a casein-point for commodity currency [START_REF] Chen | Commodity Currencies[END_REF][START_REF] Cashin | Commodity Currencies and the Real Exchange Rate[END_REF][START_REF] Makin | Commodity Prices and the Macroeconomy: An Extended Dependent Economy Approach[END_REF]. Indeed, the average correlation is as high as 81.56% during periods of high volatility on the oil market, whereas it turns negative, falling to -32.09% in phases of low oil price volatility.2

These stylized facts seem to support our hypothesis that the link between the real exchange rate and terms of trade depends on the situation on the oil market.

Methodology

The PSTR specification

To investigate this potential non-linear effect exerted by the situation on the oil market on the real exchange rate-terms of trade relationship, we rely on the PSTR methodology proposed by [START_REF] González | Panel Smooth Transition Regression models[END_REF]. According to this specification, the observations are divided in-saytwo regimes, with estimated coefficients that vary depending on the considered regime. The change in the estimated value of coefficients is smooth and gradual, since PSTR models are regime-switching processes in which the transition from one state to the other is smooth rather

than discrete. Let   N i T t x s y t i t i t i ,..., 1 ; ,..., 1 ; , , , , ,  
be a balanced panel with t denoting time and i the individual (i.e., the country), y i,t being the dependent variable, s i,t the transition variable, and

x i,t a vector of k exogenous variables. The PSTR model with two regimes is given by:

  t i t i t i t i i t i c s F x x y , , , ' 1 , ' 0 , , ;           (1)
where  i denotes the country-fixed effects and  i,t is an independent and identically distributed (i.i.d.) error term. The transition function F is normalized and bounded between 0 and 1, and is given by [START_REF] González | Panel Smooth Transition Regression models[END_REF]: . The two most common cases in practice correspond to m = 1 (logistic) and m = 2 (logistic quadratic). In the case of a logistic function, the dynamics is asymmetric and the two regimes are associated with small and large values of the transition variable relative to the threshold. In the case of a logistic quadratic function, the dynamics is symmetric across the two regimes, but the intermediate regime follows a different pattern compared to that in the extremes.

    1 1 , , exp 1 , ;                        m j j t i t i c s c s F   (
We follow the three-step methodology proposed by [START_REF] González | Panel Smooth Transition Regression models[END_REF] to apply PSTR models. 3 The aim of the first, identification step is twofold: (1) testing for homogeneity against the PSTR alternative; and (2) selecting (i) between the logistic and logistic quadratic specification for the transition function, and (ii) the transition variable. In the second, estimation step, non-linear least squares are used to obtain the parameter estimates, once the data have been demeaned [START_REF] Hansen | Threshold effects in non-dynamic panels: estimation, testing, and inference[END_REF][START_REF] González | Panel Smooth Transition Regression models[END_REF]. In the third, evaluation step, various misspecification tests are applied to check the validity of the estimated PSTR model and determine the number of regimes.

The exchange-rate model

We thus use a PSTR model to study whether the real exchange rate -terms of trade relationship differs depending on oil price volatility. To this end, we account for both the long-term and short-term dynamics by considering the following PSTR specification:

    t i t t i t i t i t i i t i c LOIL F x z x z LREER , , ' 1 1 , 1 , ' 0 1 , 0 , , ;                     (3) with:   t i i t i t i x b a LREER z , ' , ,    ( 4
)
3 For details regarding the methodology, the reader is referred to the original contributions by [START_REF] Hansen | Threshold effects in non-dynamic panels: estimation, testing, and inference[END_REF] and [START_REF] González | Panel Smooth Transition Regression models[END_REF].

LREER i,t is the logarithm of the real effective exchange rate of country i at time t, t LOIL  is the absolute value of the oil price variation-i.e., a proxy of the oil price volatility4 -that acts as the transition variable, and x i,t is a vector of fundamentals which are expected to influence the long-run real effective exchange rate. Among these fundamentals, we consider those which have long been evidenced in the literature: the Balassa-Samuelson effect [START_REF] Balassa | The Purchasing-Power Parity Doctrine: A Reappraisal[END_REF], the country's net foreign asset position [START_REF] Gagnon | Net Foreign Assets and Equilibrium Exchange Rates: Panel Evidence[END_REF] and its terms of trade (De Gregorio and Wolf, 1994) (see Section 4). i a ˆ and ' b respectively denote the estimated longrun fixed effects and fundamentals' coefficients from the cointegrating relationship between the real effective exchange rate and its determinants; z i,t standing for the misalignments, i.e., the difference between the observed real effective exchange rate and its estimated long-run value.

In this model, the link between the real effective exchange rate and its determinants varies according to the value taken by the transition function. Indeed, let us define the sum of coefficients as

  c LOIL F t l l l , ; 1 0         , with k l 0 , 01 0 0 ,..., ,      and k l 1 , 11 1 1 ,..., ,     
, k being the number of explanatory variables in the x i,t vector. Then, when F(.) = 0-i.e., in the first regime-the estimated coefficients are given by l l 0    , and when F(.) = 1-i.e., in the second regime-they are equal to

l l l 1 0     
. Between those two extremes,  l takes a continuum of values depending on the realization of the transition variable.

Data

Sample of countries

We consider yearly data from 1980 to 2012 for a panel of 69 commodity-exporting countries.

The list of countries is given in the Appendix, together with the main type of commodities exported by each one. Among this panel, 17 are oil-exporting countries, 12 belonging to OPEC (Algeria, Angola, Ecuador 5 , Indonesia, Iran, Kuwait, Libya, Nigeria, Qatar, Saudi Arabia Republic, United Arab Emirates, Venezuela), 2 being other Gulf countries (Bahrain and Oman), and 3 other leading oil exporters, namely Mexico, Norway and the Syrian Arab Republic. The 52 other commodity-exporting countries are the same as in [START_REF] Cashin | Commodity Currencies and the Real Exchange Rate[END_REF] except five countries that mainly export oil and have been included in the panel of oil exporters (Ecuador, Indonesia, Mexico, Norway and Syrian Arab Republic). Nicaragua and Zimbabwe have also been discarded because of lack of available data.

The real effective exchange rates

As bilateral trade data are not available for all the considered countries, we cannot define genuine real effective exchange rates (REER). To circumvent this issue, we construct a proxy of the REERs, as an exchange rate against a world basket of currencies.

More specifically, we start from the usual formula for a REER:

    it it M i j j jt jt ij it p s p s w LREER        $ , 1 $ (5)
where w ij denote the weights put on currency j for calculating country i's REER, $ jt s (resp. $ it s ) is currency j (resp. i)'s bilateral exchange rate against USD (number of units of national currency per USD), and p j (resp. p i ) is country j (resp. i)'s consumer price index (CPI). All these variables are set to 100 in a basis year and taken in logarithms. M is the number of partner countries that should include the largest sample of countries, be them advanced or emerging. Note that an increase in the REER indicates a real appreciation of the currency.

Here, instead of defining the weights w ij according to country i's trade partners as in the usual formula (5), we define them as country j's share in the world gross domestic product (GDP) in USD. Therefore, these weights are the same for all countries i:

    M k k j j ij GDP GDP w w 1 / (6)
This amounts to defining an exchange rate against a world basket of currencies. This REER stands for the value of currencies relatively to a world sample of countries, whether they are trade partners or not.

The shares in the world GDP are calculated on average over the 1980-2012 period, using the GDP in USD, from IMF's WEO database. The sample of countries includes all economies whose GDP exceeds 0.05% of the world GDP on average on the period. Central and Eastern Europe countries as well as those belonging to the Commonwealth of independent states are excluded, because either they did not exist at the beginning of the period, or their price and exchange rates were not relevant. Overall, we retain 69 countries in the weighting scheme, standing for more than 90% of the world GDP. Bilateral exchange rates and price series are extracted from IMF's WEO database.

The long-run explanatory variables

To account for the long-run relationship between the real exchange rate and its determinants, we follow the behavioural equilibrium exchange rate (BEER) approach introduced by [START_REF] Macdonald | What Determines Real Exchange Rates? The Long and Short of It[END_REF][START_REF] Macdonald | Concepts to calculate equilibrium exchange rates: an overview[END_REF], [START_REF] Clark | Exchange rates and economic fundamentals: a methodological comparison of BEERs and FEERs[END_REF] and adopted by the IMF [START_REF] Isard | Equilibrium Exchange Rates: Assessment Methodologies[END_REF]. In this framework, the real effective exchange rate is expressed as a function of three fundamental variables standing for the Balassa-Samuelson effect, the country's net foreign asset position and its terms of trade. Hence, the long-run relationship is given by:

t i t i t i t i i t i u LTOT b NFA b LBS b a LREER , , 3 , 2 , 1 ,      (7)
where LBS i,t is the Balassa-Samuelson effect (expressed in logarithms), NFA i,t denotes the net foreign asset position (in percentage of GDP), LTOT i,t stands for terms of trade (in logarithms), and u i,t is an i.i.d. error term. Let us now specify those three explanatory variables.

The Balassa-Samuelon effect is proxied by the country's GDP per capita measured in purchasing power parity (PPP) that is extracted from the WEO database and taken relatively to the partners; the weights applied to calculate the relative PPP GDP per capita are the same w ij as for the real effective exchange rates. Net foreign assets are taken from the database constructed by [START_REF] Lane | The External Wealth of Nations Mark II: Revised and Extended Estimates of External Assets and Liabilities, 1970-2004[END_REF] that is available on the internet. They are divided by GDP in USD, extracted from IMF's WEO. We have updated the data after 2007 by cumulating the current accounts in USD to the previous NFA position. We have also done this for the few missing data in the sample (for example for Suriname).

To better capture the exogenous component of terms of trade shocks and avoid potential endogeneity problem, commodity terms of trade are calculated in the same way as in [START_REF] Cashin | Commodity Currencies and the Real Exchange Rate[END_REF]. For the 52 commodity-producing countries, terms of trade are a weighted average price of the three main commodities exported by the country deflated by the unit value of industrial countries' manufactured exports; they are therefore expressed as:

MANUF IND h h t h i t i t pex p share TOT    3 1 , (8)
where h i share denotes the share of commodity h among the three main commodity exports of country i, h t p is the price of commodity h in the world market,

MANUF IND t pex
is the unit value of manufactured exports of industrialised countries, extracted from the WEO. The weights of each commodity in the countries' exports are taken from [START_REF] Cashin | Commodity Currencies and the Real Exchange Rate[END_REF], and commodity prices are extracted from IFS database.

For the 17 oil-exporting countries, terms of trade are set equal to the crude oil price divided by the same deflator

Estimation results

Estimating the long-run relationship

As a preliminary step, we estimate the cointegrating relationship (7) 6 on our panel data.

Ordinary least squares (OLS) estimates being biased and dependent on nuisance parameters, we rely on the Dynamic OLS (DOLS) method introduced by [START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF] and [START_REF] Mark | Cointegration vector estimation by panel Dynamic OLS and long-run money demand[END_REF] in the context of panel cointegration. 7 Roughly speaking, the DOLS procedure consists in augmenting the cointegrating relationship with lead and lagged differences of the regressors to control for the endogenous feedback effect. Using this procedure, we get the following results for the estimation of the cointegrating relationship:

8 t i t i t i i est t i LTOT NFA LBS a LREER , ) 17 . 6 ( , ) 88 . 2 ( , ) 92 . 2 ( , 2027 . 0 0637 . 0 2085 . 0 ˆ    (10)
where est t i LREER , stands for the value of LREER given by the estimation of Equation ( 7).

6 Various panel unit root and cointegration tests have been applied, showing that our fourth series (LREER, LBS, NFA, TOT) can be considered as unit root processes and are cointegrated. Complete results are available upon request to the authors. 7 Other procedures exist, such as the Fully-Modified OLS (FM-OLS) method proposed by [START_REF] Phillips | Statistical inference in instrumental variables regression with I(1) processes[END_REF]. Compared to the FM-OLS estimator, the DOLS one has the same asymptotic distribution, but presents smaller size distortions (see the simulations made by [START_REF] Kao | On the estimation and inference of a cointegrated regression in panel data[END_REF]. 8 t-statistics associated with the estimated coefficients are given between parentheses.

The estimated coefficients on three fundamental variables are significant at conventional levels and have the expected sign. A rise in the relative productivity, the NFA position as well as in the terms of trade leads to an exchange-rate appreciation. Terms of trade appear to be an important determinant of the real exchange rate, consistent with [START_REF] Cashin | Commodity Currencies and the Real Exchange Rate[END_REF] findings.

Other things being equal, a 10% increase in terms of trade leads to a real exchange-rate appreciation of around 2%.

We then calculate the currency misalignments as the gap between the observed real exchange rate and the estimated one, as stated in Equation ( 4):

est t i t i t i LREER LREER z , , ,   (11)

Linearity tests

The next step is to test for the null hypothesis of linearity in Equation (3) using the [START_REF] González | Panel Smooth Transition Regression models[END_REF] test. The transition variable is oil price volatility that we calculate as the absolute values of oil price variation (in logarithm). In other words, we test if the exchange-rate response to the explanatory variables is different whether facing low or high price volatility on the oil market.

The results of the Lagrange multiplier and Fisher-type tests are displayed in Column (1) of Table 1 for our whole sample. The null hypothesis is that of linearity, it is tested against the alternative of a PSTR specification with two regimes. As expected, the null of linearity is rejected in favour of the PSTR alternative, and the significance level is far beyond the usual 5%. This result supports our hypothesis that the explanatory variables impact the exchangerate dynamics differently, depending on the situation-in terms of oil price variation-on the oil market.

Short-run estimations

We now proceed to the estimation of our non-linear PSTR specification. Results are reported in Table 2 for the whole sample of countries. The value of the threshold parameter c is estimated at 0.1860. This defines two regimes: a regime in which oil price variations (in absolute value) are lower than 18.6% (low-volatility regime) and a regime characterized by important volatility on the oil market, with oil price variations higher than 18.6% (in absolute value). As expected, results show that the impact of the explanatory variables differs according to the situation on the oil market, confirming the conclusions of the linearity tests. Some key findings can be highlighted from the estimated coefficients presented in Table 2.

First, concerning the response of the REER to the misalignments, the exchange rates behave quite differently under the two regimes: when oil price volatility is low, the exchange rate tends to return to its fundamental value (given by the cointegrating relationship) as only the misalignment variable is significant with the expected negative sign. On the other hand, in the high-volatility regime, the real effective exchange rate does not exhibit mean reversion, the misalignment series being no longer significant. Second, the Balassa-Samuelson effect is not a determinant of the exchange rate in the short run, as its coefficient is significant in neither regimes; it is only a long-term effect, attested in the cointegrating relationship. Third, the net foreign position influences the exchange-rate changes in the high-volatility regime; as expected, its impact has the same positive sign as in the long-run relation, an improvement in the foreign position resulting in an exchange-rate appreciation.

Fourth, the variations in the terms of trade also become a significant driver of exchange-rate variations (at the 10% significance level) only in the high-volatility regime. This is a very interesting finding supporting our hypothesis that the commodity-currency link is at play in the short run only when oil price volatility is high. On the whole, results in Table 2 are in line with our hypothesis of different behaviour of commodity currencies according to market volatility. More precisely, they show that the exchange rate is essentially driven by fundamentals in the low-volatility regime, whereas it turns mainly sensitive to variations in terms of trade once oil price volatility exceeds a given threshold.

Estimations by types of commodities

We now aim at checking if this overall finding may mask some heterogeneity across countries according the types of commodities they export. To investigate this issue, we subdivide our panel in four groups depending on the nature of the main commodity exported by each country: energy and metals, food, beverages, and raw materials.

We first perform the estimation of the long-term relationship for those subgroups of countries and present the estimated cointegration coefficients in Table 3. The findings confirm that terms of trade are a significant determinant of the real exchange rate for all groups of commodities. On the other hand, the results of both the other variables are mixed, being significant or not depending on the considered panel. We then turn to the PSTR estimation, and display the results for our four subgroups of countries in Table 4. Regarding first the value of c ˆ, while the estimated threshold values are quite similar for "beverages" and "raw materials" groups, they strongly differ across "energy and metals" and "food" panels. Food producers are much more likely to tip over into highvolatility regime, as their estimated threshold c ˆ is much smaller (0.0887) than the energy and metals producers (0.4516). This makes them more vulnerable to oil price volatility. A closer look at the estimated coefficients presented in Table 4 gives an insight into the response of the real exchange rates to the fundamental variables. First, as for the whole panel of countries, the misalignment variable is negatively significant only in the first regime. This confirms our previous result that the exchange rate tends to revert to its fundamental value only in times of low oil price volatility. Second, the Balassa-Samuelson effect appears significant in the low-volatility regime for energy, metals and food exporters, though it is still not significant in the short run for beverages exporters, and wrongly signed in the case of raw materials producers. Third, changes in the net foreign position exert a significant impact in both regimes, except for the "energy and metals" panel in the high-volatility state and for beverages' exporters in the low-volatility regime.

Fourth, turning to our main variable of interest, our results show that changes in terms of trade are significant in the high-volatility regime for the "energy and metals" group and, to a lesser extent, for the "food" exporters. This finding indicates that the commodity-currency property depends on the type of commodity considered and is especially strong for oil-exporting countries in case of important fluctuations on the oil market. These results are consistent with the conclusions obtained by [START_REF] Baffes | Oil spills on other commodities[END_REF] mentioning the links between prices of various commodities. Indeed, this author shows that oil price changes are heavily passed-through to the prices of other commodities, such as precious metals, energy products and, to a lesser extent, food products. Nevertheless, he does not evidence a clear effect for beverages and raw materials groups, a result that we retrieve here as terms of trade are not significant for these two panels of commodities in the above specification.

Conclusion

This paper studies the link between terms of trade and real exchange rates of commodityproducing economies on both the short and the long run. We pay particular attention to the key role played by oil among commodity markets and investigate its potential non-linear effects on the terms of trade -real exchange rates nexus. More specifically, we consider the oil price volatility as a gauge of strains on commodity markets, and account for non-linearities of exchange rates' responses to terms of trade depending on the situation-calm of volatileon the oil market.

Our findings show that the exchange rate tends to revert to its equilibrium value in the lowvolatility regime, while such mean-reverting process is not observed in the case of important variations on the oil market. Specifically, in the high-volatility regime, changes in the terms of trade become a significant driver of exchange-rate variations. Splitting our countries by main exported commodities, we also find that the exchange rate reverts to its long-term level only when oil price variations do not exceed a certain threshold. Moreover, changes in terms of trade are significant to explain the dynamics of the real exchange rate in the high-volatility state, especially for the group of "energy and metals" as well as food exporters. On the whole, our results evidence that the commodity-currency property is at play in the short run only in periods of high oil price volatility, and depends on the type of commodity exported.

Figure 1

 1 Figure 1 reports the evolution of the real effective exchange rate and commodity terms of trade of New Zealand over the 1980-2012 period, while Figure 2 displays the oil price volatility over the same period. As those figures clearly show, movements in the terms of trade have closely followed changes in the real effective exchange rate, especially during episodes of high volatility on the oil market. This overall pattern is corroborated by calculating the correlations between changes in the real exchange rate and terms of trade.

Figure 1 .

 1 Figure 1. Real effective exchange rate and terms of trade for New Zealand

  slope parameter, and c j , j = 1, …, m, are the threshold parameters satisfying

Table 1 .

 1 Results of linearity tests.

		Whole	Energy and	Food	Beverages	Raw materials
			metals
		(1)	(2)	(3)	(4)	(5)
	LM	64.939 (0)	22.126 (0.005)	14.706 (0)	73.059 (0)	34.566 (0)
	F	16.034 (0)	2.722 (0.006)	3.643 (0)	20.947 (0)	8.903 (0)
	Note: LM and F are the Lagrange multiplier and F tests for linearity. P-values are given in parentheses.

Table 2 .

 2 Estimation of the PSTR model, whole sample.

		Regime 1		Regime 2
		Low oil price volatility		High oil price volatility
	Misalignment Balassa effect Net foreign assets NFA i,t z i,t-1 LBS i,t Terms of trade LTOT i,t ˆ c ˆ	-0.1265*** 0.0578 -0.0074 -0.0269	3666 0.1860	0.0264 0.1203 0.1445*** 0.0724*
	Note: * (resp. **, ***): significant at the 10% (resp. 5%, 1%) level.

Table 3 .

 3 Estimation of the cointegrating relationship, subgroups of countries according to the main exported commodity.

		Balassa-Samuelson effect	Net asset position	Terms of trade
		LBS i,t	NFA i,t	LTOT i,t
	Energy and metals	0.3804 *** (2.92)	0.0205 (0.62)	0.1223 *** (2.90)
	Food	-0.2940 ** (-2.29)	0.0051 (0.08)	0.1794 ** (2.30)
	Beverages	-0.1745 (-1.05)	0.0263 (0.64)	0.6507 *** (6.73)
	Raw materials	0.1077 (0.89)	0.3212 *** (5.56)	0.3226 *** (3.05)
	Whole panel	0.2085 *** (2.92)	0.0637 *** (2.88)	0.2027 *** (6.17)

Note: t-statistics are given in parentheses. ** (resp. ***): significant at the 5% (resp. 1%) level.

Table 4 .

 4 Estimation of the PSTR model, subgroups of countries according to the main exported commodity.

		Energy and metals	Food		Beverages	Raw materials
		Regime 1 Regime 2 Regime 1	Regime	Regime 1 Regime 2 Regime 1 Regime 2
				2
	z i,t-1 LBS i,t NFA i,t LTOT i,t ˆ	-0.1237*** 0.2735*** 0.0959*** 0.0185 5742 0.2243*** 0.2109 -0.3393 0.0243	-0.1241*** 0.7933** 0.6512*** -0.0666 3354 -0.5745** -0.0127 -0.5207 0.1602*	-0.2307*** -0.5793 -0.0089 -0.0724 7550 0.1721*** 0.4767 0.4737 0.0607	-0.0730* -0.3185*** 0.3327*** -0.0719 276.1 0.2923*** -0.0891 -0.5132 0.0804
	c ˆ	0.4516	0.0887	0.2464	0.2108
	* (resp. **, ***): significant at the 10% (resp. 5%, 1%) level; for the name of variables see Table 2.

See below for the definition of low-and high-volatility regimes.

Note that other volatility proxies could also be used, such as the squared returns of oil prices (see e.g.[START_REF] Giles | Some properties of absolute returns as a proxy for volatility[END_REF].

To be precise, note that Ecuador joined OPEC in 1973, suspended its membership in 1992 and resumed it in 2007.

 This research has been supported by the French Energy Council (Conseil Français de l'Energie), Paris,