Bulletin of Monetary Economics and Banking, Vol. 21, No. 1 (2018), pp. 57 - 80

p-ISSN : 1410 8046, e-ISSN: 2460 9196

MACRO DETERMINANTS OF THE REAL EXCHANGE RATE

IN A SMALL OPEN SMALL ISLAND ECONOMY:

EVIDENCE FROM MAURITIUS VIA BMA

Bernard Njindan Iyke1

1Centre for Financial Econometrics, Deakin Business School, Victoria, Australia.

E-mail: bnjindan@deakin.edu.au

ABSTRACT

We assess the robust macro determinants of the real exchange rate in Mauritius under model uncertainty by utilizing Bayesian Model Averaging (BMA). We introduce a broader range of potential macro determinants of the real exchange rate in Mauritius. Then we tackle the issue of model uncertainty when identifying these macro determinants of the real exchange rate by exploring the impact of different priors on the model size, and different priors on model coefficients on the posterior estimates. We identify the real money supply, and the real productivity to be the robust macro determinants of the real exchange rate in Mauritius. Their coefficient signs are also theoretically consistent. The real money supply impact on the real exchange rate negatively, whereas the real productivity impact on it positively. Our results remain robust to different priors on the model size, and to different priors on model coefficients.

Keywords: Model uncertainty; Bayesian Model Averaging (BMA); Macro determinants, Real exchange rate; Mauritius.

JEL Classification: C11; C15; F31.

https://doi.org/10.21098/bemp.v21i1.922

I. INTRODUCTION

This paper explores the macro determinants of the real exchange rate in Mauritius for the period 1976-2012. Various studies, today, have focused on identifying the fundamental drivers of the real exchange rate.2 This is understandable because the real exchange rate, which, to a very large extent, dictates trade flows and international competitiveness, may lose its value if it determinants are not known (see Kia, 2013). On this premise, understanding the macroeconomic determinants of the real exchange rate is, therefore, very important for monetary policymakers, since the influence of the real exchange rate on the real economy can only be sufficiently assessed if the sources of shocks that drive it are known (see Detken et al., 2002).

In the literature, the issue that resurfaces frequently is the approach used to estimate the links between the real exchange rate and its macro determinants. For example, under the Purchasing Power Parity (PPP) approach, the long-run real exchange rate is assumed to be stationary so that any deviation from this rate reflects misalignment. Thus, the determinants of the real exchange rate are the shocks that drive it from the equilibrium rate. This notion has, however, been heavily criticized due to the slow mean-reverting property of the real exchange rate (see MacDonald and Ricci, 2003). The Behavioural Equilibrium Exchange Rate (BEER) approach as introduced by Clark and MacDonald (1999) contends, instead, that the real exchange rate and its determinants should be viewed as I(1) processes. This means that cointegration analysis can be utilized to assess the influence of the determinants on the real exchange rate (see Elbadawi and Soto, 1994; Edwards, 1994; Cardenas, 1997; Montiel, 1997; Loayza and Lopez, 1997; Aron et al., 2000; MacDonald and Ricci, 2003; Iman and Minoiu, 2011). Some researchers prefer to setup and simulate a dynamic general equilibrium macroeconomic model using parametric calibration and data suitable for a given country (see Clark et al., 1994; Williamson, 1994; Stein et al., 1995). Other researchers utilize single equation models and partial equilibrium models to examine the movement of the real exchange rate in the long-run (see Driver and Wren-Lewis, 1997; Ghei and Pritchett, 1999).

The current paper brings some new contributions into the literature. First, when compared to the existing studies, the paper utilizes a much broader range of potential macro determinants (i.e. 21 potential macro determinants) of the real exchange rate for a small open economy, Mauritius. To the best of our knowledge, this is the first paper to do so. Second, the paper tackles the issue of model uncertainty when identifying these macro determinants of the real exchange rate. The paper does this by exploring the impact of different priors on the model size, and different priors on model coefficients on the posterior estimates. When the BMA approach is utilized this way, the paper avoids unintended consequences of eliciting inappropriate priors, and dealing sufficiently with multicollinearity issues.

2A survey of earlier papers can be found in MacDonald (1995), Rogoff (1996), and

Hinkle and Montiel (1999). For a very recent survey, see Lee et al. (2008).

The remaining sections of this paper are structured as follows. Section II briefly explores the exchange rate history of Mauritius. Section III presents a simple model of the real exchange rate. Section IV presents the model specification and the prior structures of the BMA approach. Section V presents the empirical results. Section VI concludes the paper.

II.A BRIEF HISTORY OF THE EXCHANGE RATE POLICY OF MAURITIUS

Mauritius has practiced fairly mixed exchange rate regimes from independence to date. Prior to independence in 1968, the country shifted from a currency board system to a pegged system in November 1967. The Mauritian currency, the rupee, was pegged to the British pound (see IMF, 2008; Imam and Minoiu, 2011). Under this pegged system, the country employed a dual exchange market. All capital account transactions were separated from current account transactions. To this end, all capital transfers attracted a stamp duty of 15% under the pegged system

(see Imam and Minoiu, 2011).

In June 1972, Mauritius created a central exchange rate with Special Drawing Rights (SDRs), following the weakening of the British pound in 1971. However, the second exchange rate for capital transfers remained in place. The rupee was officially pegged to the SDR in January 1976 around a bandwidth of 2%. This was the case in theory but the rate was actually a crawling band around the US dollar

(see Imam and Minoiu, 2011). Between 1976 and 1978, the rupee was considered overvalued. Thus, the Bank of Mauritius undertook devaluation exercises in 1979 and 1981. That apart, the stamp duty was increased from 36% to 45% for capital transfers in July 1981 (see IMF, 2008).

In June 1982, the Bank of Mauritius again intervened in the foreign market by delinking the rupee from the SDR. The rupee was then pegged to a trade- weighted basket of currencies of the country’s major trade partners under an IMF liberalization initiative. In spite of these changes, the exchange rate remained pegged de facto to the US dollar with a bandwidth of 5% (see Broda, 2002; Reinhard and Rogoff, 2004). There was a limit specified on the sale of foreign currency for travelling purposes as a form of capital control. The monetary authorities maintained a multiple currency from this period till the mid-1990s. As part of the multiple currency policy, a tax of 15% was charged on some capital remittances.

This tax remained in operation till 1992 when all forms of exchange rate restrictions were eliminated. The de facto crawling bandwidth was reduced from 5% to 2% in 1992. Foreign currency transactions were fully liberalized in July 1994. The country adopted a managed float exchange rate regime from this period onwards.

The Bank of Mauritius occasionally intervenes in the foreign exchange market to minimize exchange rate volatilities.

III.A SIMPLE THEORETICAL MODEL OF THE REAL EXCHANGE RATE

Although various authors have successfully formulated formal models of the real exchange rate, which incorporates its determinants (see, e.g., Mundell, 1961; McKinnon, 1963; Ostry, 1988; Khan and Ostry, 1991; Faruqee, 1995; Frankel, 1995;

Montiel, 1999; Kia, 2013), this paper draws on the model formulated by Edwards

(1993) largely due to its empirical appeal. This is a simple model of the real exchange rate in which there is simultaneous equilibrium of the current account balance and the tradable good market (see Drine and Rault, 2015).

The basic building blocks of the model entail the following. Suppose there is a small open economy with three sectors, which produces three goods. The sectors are export, import, non-tradable. These sectors produce, respectively, exports (X), imports (M), and non-tradables (N). Suppose that the economy is populated by consumers of the imports and the non-tradables. The economy practices a floating exchange rate regime, so that its floating nominal exchange rate in all transactions is denoted E.

In addition to the above assumptions, suppose that PX, PM, and PN are the prices of exports, imports, and non-tradables, respectively. By taking the world price of exports as the numeraire (i.e. PX*=1), it holds that the domestic price of exports will be PX=EPX*=E. This relation holds directly from the absolute form of the Purchasing Power Parity (PPP) hypothesis. Denote the world price of imports as PM*. It is straightforward to define the domestic relative prices of exports (eX) and imports (eX) to non-tradables as E/PN and PM/PN, respectively. Thus, the relative price of imports to non-tradables can be formulated as (see Drine and Rault, 2015)

(3.1)

Suppose the economy imposes tariffs on imports. Then the price of imports will be

(3.2)

Let the total output (Q) in this small open economy be given by the following equation

Similarly, let private consumption (C) in the economy be defined by the following

where CM and CN denote, respectively, consumption on imports and non- tradables.

A few more equations will close the model. In the spirit of Cassel (1918), define the real exchange rate (e) for this economy as the relative price of tradables to non- tradables. That is

Now, suppose that capital in this economy is perfectly mobile, and denote net foreign assets of the economy by A. Suppose also that this economy invests its net foreign assets at the international real interest rate r*. Then, the economy’s

Current Account (CA) in any given year will be the sum of its net interest earnings on A and its trade surplus (i.e. X-M). This is given by the following expression (see Drine and Rault, 2015)

(3.6)

In addition, define a change in the foreign currency reserves (R) in the economy as

(3.7)

where KI denotes net capital inflows. Assume that in the short and the intermediate period the economy may lose or gain foreign currency reserves. Then it follows that the current account of this economy is sustainable if the current account deficit plus the net capital inflows in the long-run sum up to zero. This holds that the official reserves of the economy do not change. Thus, the economy is in an external equilibrium if the sum of the current account balance and the capital account balance equal to zero. This can be expressed as follows (see Edwards, 1993)

(3.8)

(3.9)

where GN is public spending on non-tradables. Thereby, the equilibrium real exchange rate is the rate, which ensures, simultaneously, external and internal equilibrium. Thus, using Eqs. (3.8) and (3.9), we can formulate the equilibrium real exchange rate (e*) as a function of η, r*, PM*, A, KI, and GN (see Drine and Rault, 2015). That is.

To reiterate, the equilibrium real exchange rate depends on the trade policy (i.e. trade openness), foreign interest rate, terms of trade3, foreign capital flows4, and public spending5. In principle, these are the most often identified determinants of the real exchange rate in the long-run (see Elbadawi and Soto, 1994; Cardenas, 1997; Loayza and Lopez, 1997; Montiel, 1999; Aron et al., 2000; MacDonald and Ricci, 2003; Iman and Minoiu, 2011; Drine and Rault, 2015).

Other variables such as the world commodity prices (see Cashin et al., 2002; Chen and Rogoff, 2002; MacDonald, 2002; MacDonald and Ricci, 2003), real money supply (see Kia, 2013), real productivity (see Detken et al., 2002; Kia, 2013; Drine

3See Montiel (1997), Goldfajn and Valdes (1999), and Imam and Minoiu (2011).

4See Lane and Milesti-Ferretti (2000), MacDonald and Ricci (2003), Imam and Minoiu

(2011).

5See De Gregorio et al. (1994), Montiel (1997), MacDonald and Ricci (2003), and Imam and Minoiu (2011).

and Rault, 2015), and foreign direct investment (see Drine and Rault, 2015) have also been identified in the literature as macroeconomic determinants of the real exchange rate. These variables are utilized in our paper.

On the empirical front, different approaches have been utilized to estimate the functional relationship in Eq. (3.10). Each approach has its advantages and drawbacks. We utilized the Bayesian Model Averaging (BMA) to estimate this function. We discuss this approach in the next section.

IV. MODEL SPECIFICATION AND PRIOR STRUCTURES

We analyze the core macro determinants of the real exchange in Mauritius using BMA. This approach is very useful in the sense that it addresses model uncertainty in a canonical regression specification (see Hoeting et al., 1999). To make this point clear, let us assume that our model is a linear regression of the following form

(4.1)

where y is the dependent variable (i.e. the real exchange rate), αγ and βγ denote the intercept and the coefficient terms, respectively, Xγ is a matrix of explanatory variables (i.e. the macro determinants of the real exchange rate), ε is an IID error term whose variance is σ2.

The question of interest is which variables should enter into the matrix Xγ, among a host of potential explanatory variables? Answering this is important because there is a universe of explanatory variables X that may explain the variation in y. In principle, the choice of Xγ∈{X} to be included in the model must be based on their relative importance. In the canonical linear regression problem, a single model contains all the explanatory variables, rendering the approach inefficient or even infeasible with a limited number of observations (see Chipman et al., 2001).

The BMA approach emends this model uncertainty problem by estimating models for all possible combinations of {X} and constructing a weighted average over all of them (see Feldkircher and Zeugner, 2015). Supposing that X contains K potential variables, the BMA approach entails that we estimate 2K models, which is represented by the model candidate space M={M1,M2,…,M2K}. Bayes theorem provides the useful guide for obtaining model weights, which are estimated from the posterior model probabilities. Using the Bayes theorem, we have that

(4.2)

where p(y|X) is the integrated likelihood which is constant over all models and it is thus simply a multiplicative term. Hence, the Posterior Model Probability (PMP) is proportional to the integrated likelihood p(y|Mγ,X), which reflects the probability of the data given model Mγ.

The term p(y|Mγ,X)p(Mγ), the product of the marginal likelihood of model Mγ and the prior model probability p(Mγ), shows how the researcher believes model Mγ is probable prior to observing the data. p(y|X) and p(y|Mγ,X) are different in the

sense that integration is done over the model space p(y|X) but for a given model over the parameter space p(y|Mγ,X). We can infer the Posterior Model Probabilities (PMPs) and the model weighted posterior distribution for any statistic θ (e.g., the estimator of the coefficient βγ), by renormalization Eq. (4.2) such that

(4.3)

Eq. (4.3) is very crucial because all relevant posterior computations are based on it. For example, we can compute the posterior moments of the coefficient vector βγ, which is a weighted average over all models. In a similar fashion, we can also compute the Posterior Inclusion Probabilities (PIPs), which can be used to evaluate the importance of each explanatory variable (i.e. the macro determinants) in the model. This is computed as the sum of probabilities for all models in which the covariate is included (see Feldkircher and Zeugner, 2015).

In practice, the elicitation of the model prior p(Mγ) reflects the prior believes of the researcher. A wide range of model priors exists in the literature. As argued by Crespo Cuaresma et al., (2014), majority of the studies have utilized diffuse priors, thereby assigning equal probability to all possible models. This translates to imposing a mean prior model size of K/2. Contrary to these studies, other studies have assigned more prior weight to relatively pragmatic models by assuming Bernoulli distributions with fixed parameter π on the inclusion probability for each variable and using the expected model size, πK, to elicit the prior (see Sala-i- Martin et al., 2004). Nevertheless, the recent literature has advanced the elicitation of Binomial-Beta prior distribution. Ley and Steel (2009) argued in favour of this prior, using the original ideas presented in Brown et al. (1998). Essentially, this prior elicitation strategy imposes a Beta hyperprior distribution on π, which happens to be the parameter of the Bernoulli distribution for the inclusion of each explanatory variable in the model. Ley and Steel (2009) argued that this prior elicitation strategy is powerful because it admits very different prior structures on the model size (see Crespo Cuaresma et al., 2014). We utilize the Binomial-Beta prior and compare it performance against other competing priors.

In the BMA literature, the reliability of the regression coefficients depends heavily on the prior structure imposed by the researcher. Practically all Bayesian linear models build on the Zellner’s g prior structure (1986). The value of the Zellner’s g prior corresponds to the degree of prior uncertainty (see Feldkircher and Zeugner, 2015). Majority of the studies in the literature have favoured the imposition of a fixed g prior. For example, Fernández et al. (2001) have argued for a comparatively large g prior to minimize prior impact on the results, stay close to the OLS coefficients, and represent the absolute lack of prior knowledge. In contrast, Ciccone and Jarociński (2010) have shown that a large g can be non- robust to noise innovations, thereby exposing the model to over-fitting problems. Eicher et al. (2011) favoured the choice of intermediate fixed values for the g priors, whereas Liang et al. (2008) argued for default specifications (see Feldkircher and Zeugner, 2015).

posterior distributions of interest over the model space using the birth/death MC3 sampler. In the second, we evaluate the robustness of these macro determinants to alternative elicitation of flexible Zellner’s g priors. Here, we compare the PIPs of g=UIP to competing flexible g priors such as g=RIC7, g=BRIC8, and g=EBL9. Finally, we recognize that under this setting, the inclusion of several macro determinants can pose multicollinearity problems. Hence, we controlled for multicollinearity in the macro determinants using three competing model priors namely: the tessellation prior (see George, 2010), the weak heredity prior (see Chipman, 1996), and the general dilution prior (see Chipman, 1996). In the tessellation prior case, we utilize the MC3 tessellation sampler proposed in George (2010). We maintain the flexible hyperprior g=UIP for these competing model priors and compare their PIPs with the benchmark model.

5.1. Macro Determinants of the Real Exchange Rate

Table 2 shows the results stemming from our benchmark specification of the model prior structure, and the results based on alternative specifications of the flexible Zellner’s g prior on the regression coefficients. Each of the columns in Table 2 reports, respectively, the Posterior Inclusion Probabilities (PIPs) of each macro determinant of the real exchange rate, the Posterior Mean (PM), and the Posterior Standard Deviation (PSD) of the posterior distribution for the associated parameter. These results are based on 6,000,000 draws of the MC3 sampler, 3,000,000 burn-in iterations, and a Binomial-Beta prior for the model size expected to be K/2 explanatory variables. As a rule of thumb, the importance of the macro determinants in the model can be interpreted in terms of their PIPs as follows: 50-75% PIP is weak, 75-95% PIP is substantial, 95-99% PIP is strong, and 99%+ PIP is decisive (see Kass and Raftery, 1995; Eicher et al., 2009; Crespo Cuaresma et al., 2014). Hence, an explanatory variable whose PIP is greater than the threshold of 0.5 is adjudged as robust (see Crespo Cuaresma et al., 2014).

The second column in Table 2 reports the results for the benchmark model, which is based on 21 macro determinants of the real exchange rate (see Data Appendix for details). The real money supply and the real productivity, as proxy by LNRMS and LNRGDP, respectively, are identified as the robust macro determinants of the real exchange rate in Mauritius. The coefficients of these robust macro determinants have the expected signs (see Figure 4). The real money supply impact on the real exchange rate negatively, which is consistent with the theory. Higher real money supply stimulates increases in the domestic price level,

7 RIC denotes the risk inflation criterion proposed by Foster and George (1994), whereby the hyperprior on g is set to K2 . K denotes the total number of covariates in the model.

8BRIC denotes the benchmark risk inflation prior proposed by Fernández et al. (2001), whereby the hyperprior on g is set to max(N,K2). N is the total number of observations.

9EBL denotes the local empirical Bayes prior advocated by George and Foster (2000), and Hansen and Yu (2001), whereby the hyperprior on g is set to gγ = argmaxg p(y|Mγ ,X,g). Here, the information contained in the data (y,X) is used to elicit g via maximum likelihood.

which in turn lowers the real exchange rate in the long-run (see Kia, 2013). The real productivity, in contrast, impact on the real exchange rate positively. Increasing real productivity enhances the earning capacity of the labour force. This is translated into higher real demand for money, which lowers domestic price level, thereby leading to higher real exchange rate (see Kia, 2013). However, whereas the posterior standard deviation is relatively small for the real money supply, it has been high for the real productivity. Therefore, the real money supply appears to be the more reliable macro determinant of the real exchange rate in Mauritius than the real productivity.

Figure 1 displays the marginal posterior densities for the coefficients of the robust macro determinants of the real exchange rate based on 5000 models (i.e. coefficients with the largest PIPs). The upper panel of Figure 1 shows the posterior distribution of the coefficient of the real money supply. This distribution is very concentrated around the posterior mean of -0.477 with a PIP of 99.95%. Similarly, the lower panel of Figure 1 shows the posterior distribution of the coefficient of the real productivity. This distribution is also very concentrated around the posterior mean of 0.748 with a PIP of 97%. These marginal posterior densities clearly show that the real money supply and the real productivity explain the real exchange rate in Mauritius.

5.2.Robustness of the Results to Alternative Elicitation of Zellner’s g Priors

As argued earlier (see Section 4), the choice of the prior structure on the regression coefficients can have massive influence on the posterior estimates. This issue has generated considerable discussion in the BMA literature (see Liang et al., 2008; Ciccone and Jarociński, 2010; Eicher et al., 2011; Feldkircher, 2012). Recent studies have argued for the use of hyper-g prior structure to avoid unintended posterior consequences (see Liang et al., 2008; Feldkircher, 2012). In this section, we evaluate the robustness of these macro determinants to alternative elicitation of hyper-g priors. Specifically, we compare the PIPs of g=UIP to competing hyper-g priors such as g=RIC, g=BRIC, and g=EBL. The third, fourth, and fifth columns of Table 2 report the PIPs, PMs, and PSDs of these different elicitation of Zellner’s g prior. The posterior estimates of these different hyper-g priors are remarkably similar to the benchmark specification (i.e. g=UIP) in column two of Table 2. A better way to appreciate the similarity is by looking at Figure 2, which shows the Posterior Inclusion Probabilities (PIPs) and the standardized coefficients based on the four different flexible Zellner’s g prior structures. The upper panel plots the PIPs, whereas the lower panel plots the standardized coefficients. By carefully observing Figure 2, we can see that the earlier results remain robust to different flexible Zellner’s g prior structures (albeit, the PIPs based on the g=EBL diverged minimally). Therefore, the real money supply and the real productivity remain the robust macro determinants of the real exchange rate in Mauritius.

5.3.Controlling for Multicollinearity in the Macro Determinants

In this section, we tackle a critical issue, which can render the results inefficient – multicollinearity. We have estimated a model, which contains several explanatory

variables. In theory, these variables are related. This means that we cannot ignore a potential multicollinearity problem among the variables. Some authors have devoted much attention to dealing with this problem in the Bayesian literature (see Chipman, 1996; George, 2010). To assess the robustness of the macro determinants to multicollinearity, we employ three priors on the model size, namely: (i) the weak heredity prior (see Chipman, 1996); (ii) the general dilution prior (see Chipman, 1996); and (iii) the tessellation prior (see George, 2010). In the case of the tessellation prior, we utilize the MCMC tessellation sampler proposed in George (2010). We maintain the flexible hyperprior g=UIP for these competing model priors and compare their PIPs with the benchmark model. In all cases, the estimated results are based on 6,000,000 draws and 3,000,000 burn-in iterations. These results are reported in Table 3. Clearly, the estimated results for the robust macro determinants are very similar, except in the case of the weak heredity prior where the posterior coefficients are slightly overestimated. The evidence is even clearer if we carefully observe Figure 3, which displays the Posterior Inclusion Probabilities (PIPs) and the standardized coefficients based on the four different specifications of model prior structure for the model size. The upper panel shows the PIPs, whereas the lower panel shows the standardized coefficients. That the posterior results based on the weak heredity prior diverged from the rest is to be expected because this prior deal better with multicollinearity introduced by interaction terms (see Chipman, 1996). In essence, our results appear unaffected by different elicitation of priors on the model size. Therefore, the real money supply and the real productivity remain the robust macro determinants of the real exchange rate in Mauritius.

VI. CONCLUDING REMARKS

This paper examines the robust macro determinants of the real exchange rate in Mauritius under model uncertainty by utilizing the BMA approach. The paper brings some new contributions into the literature. First, it utilizes a broader range of potential macro determinants of the real exchange rate in Mauritius. Second, it tackles the issue of model uncertainty when identifying these macro determinants of the real exchange rate. The paper does this by exploring the impact of different priors on the model size, and different priors on model coefficients on the posterior estimates. When the BMA approach is utilized this way, the paper avoids unintended consequences of eliciting inappropriate priors, and dealing sufficiently with multicollinearity issues.

The paper finds the real money supply, and the real productivity to be the robust macro determinants of the real exchange rate in Mauritius. These two robust macro determinants yield coefficient signs that are theoretically consistent. The real money supply impact on the real exchange rate negatively, whereas the real productivity impact on the real exchange rate positively. On the one hand, higher real money supply stimulates increases in the domestic price level, which in turn lowers the real exchange rate in the long run. On the other, increasing real productivity enhances the earning capacity of the labour force. This is translated into higher real demand for money, which lowers domestic price level, thereby leading to higher real exchange rate.

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Data Appendix

Table 1. The definition and source of each of the variables we used. They are of two categories. The first category includes variables that are frequently identified as the determinants of the real exchange rate. The second includes variables that may also influence the real exchange rate.

Figure 2. Posterior inclusion probabilities and standardized coefficients based on four different flexible Zellner’s g prior structures. UIP=uniform information prior, RIC=risk information criterion, BRIC=the benchmark prior suggested by Fernández et al. (2001), and EBL=local empirical Bayes prior.

Figure 3. Posterior inclusion probabilities and standardized coefficients based

on four different model prior structures. UIP=uniform information prior,

TESS=tessellation prior, WHP=weak heredity prior,

and GDilut=general dilution prior.

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