Gold price and exchange rates: A panel smooth transition regression model for the G7 countries

North American Journal of Economics and Finance 49 (2019) 27–46

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Gold price and exchange rates: A panel smooth transition regression model for the G7 countries

T

⁎,1

Nikolaos Giannellis, Minoas Koukouritakis Department of Economics, University of Crete, 74100 Rethymno, Greece

ARTICLE INFO

ABSTRACT

Keywords: G7 External balance model Panel cointegration Misalignment rate Panel smooth transition regression model

In this paper we investigate whether the price of gold is affected by internal and external macroeconomic performance, which is mainly reflected in exchange rate movements. Based on the G7 countries and using annual data for the period 1980–2016, we test the impact of the effective exchange rate and the interest rate on the price of gold. Departing from previous studies, we propose that the observed exchange rate should be taken into account in accordance with the equilibrium value of the currency and the implied misalignment. Τhe equilibrium real effective exchange rate is estimated using recent panel cointegration techniques, which are strengthened with the theoretical assumptions of an external balance model. Next, we estimate a two-regime Panel Smooth Transition Regression model with a monotonic transition function to capture the nonlinear dependency between the gold price and the macroeconomic variables. Our results show that investors tend to invest in gold as the misalignment rate of the real effective exchange rate increases. Furthermore, when the interest rate increase is rather high, investors are less willing to sell gold for higher return assets. Overall, our evidence confirms that gold serves as a hedge only when financial risk is high.

JEL Classification: E42 F31 F41

1. Introduction Gold is one the most valuable metals with many applications in daily life. First of all, its shiny view makes gold quite attractive as jewellery. It is also used in industry, in electronics and computers manufacture, in medicine, in aerospace, and of course, it is used as a financial asset. Traditionally, gold was used as a hedging tool against inflation. Moreover, there is evidence in the literature that gold serves as a hedge against financial risk.2 Previous studies have reported no evidence of correlation between gold and other financial assets, such as stocks and bonds (see, inter alia, Summers, Johnson, & Soenen, 2010). This implies that investors can use gold to diversify their portfolios. Similarly, there is evidence that gold serves as a hedge against currency risk. Most of the empirical studies in the related literature find negative relationship between gold price and fundamental currencies, such as the US dollar, the Japanese yen etc. (see, Capie, Mills, & Wood, 2005; Joy, 2011; Reboredo, 2013). Serving as a financial asset, gold is sensitive to developments in money markets. For example, an increase in the interest rate causes a decrease in demand for gold because investors realise that the opportunity cost of holding gold increases.

Corresponding author at: Department of Economics, University of Crete, University Campus, Rethymno 74100, Greece. E-mail address: [email protected] (M. Koukouritakis). 1 This work was supported by the Special Account for Research Funds (ELKE – Project KA10118) of the University of Crete. The authors would like to thank the editor of the journal and two anonymous referees for their constructive comments that improved the quality and the exposition of the paper. Of course, all the remaining errors are our own. 2 Regarding the economics of gold, see O’Connor, Lucey, Batten, and Baur (2015) for an extensive literature review. ⁎

https://doi.org/10.1016/j.najef.2019.03.018 Received 7 November 2018; Received in revised form 9 March 2019; Accepted 25 March 2019 Available online 27 March 2019 1062-9408/ © 2019 Elsevier Inc. All rights reserved.

North American Journal of Economics and Finance 49 (2019) 27–46

N. Giannellis and M. Koukouritakis

Like any other asset, the price of gold is shown to be volatile. Focusing on the financial features of gold, we can easily understand that the price of gold is sensitive to worldwide economic conditions. For example, in periods of financial distress, investors tend to invest in gold because they are anxious about financial risk. Similarly, the negative relationship between the price of gold and the exchange rate implies that investors prefer to invest in gold rather than in a depreciating currency. Equivalently, this implies that demand for gold declines as currencies appreciate. It seems that there is a negative, but straightforward, relationship between gold price and effective exchange rates. However, this does not mean that gold price can be easily predicted since the exchange rates are highly unstable. Certainly, investors’ behaviour is affected when exchange rates are unstable or/and highly misaligned. Investors worry about financial stability and may not invest in an appreciating currency if they believe that the appreciating trend is not consistent with equilibrium. In other words, investors avoid investing in highly misaligned currencies even if they currently appreciate. Thus, when examining the relationship between the effective exchange rate and the price of gold, the analysis should not be limited to the trend of the currency, but instead its equilibrium process and the level of currency misalignment should be also taken into account. The above implies that investors may change their behaviour in front of different states (i.e., different values of the effective exchange rate or/and the misalignment rate). As a consequence, the estimated impact of the effective exchange rate on gold price may change beyond a critical point. In other words, we expect the presence of nonlinear dynamics in the relationship between the gold price and its regressors. The driving force behind the nonlinear behaviour of investors is their response against risk. As risk follows an increasing trend around a critical point, investors change gradually their investment decisions. For instance, we expect that investors become gradually less willing to exchange gold with higher return asset as financial risk increases around and over a critical level. Motivated by the aforementioned dynamic and nonlinear behaviour of investors, this paper revisits the relationship between the gold price and several fundamental financial variables. Based on the G7 countries, namely Canada, France, Germany, Italy, Japan, the UK and the USA, and employing annual data for the period 1980–2016, we primarily test the impact of the real effective exchange rate and the interest rate on the price of gold. Employing alternative definitions of the relationship between gold price and macroeconomic fundamentals, we also test the impact of the nominal effective exchange rate, the inflation rate as well as real output and money supply. This paper contributes to the related literature in a number of ways: Firstly, besides the baseline model, we estimate an alternative model in which the observed effective exchange rate is replaced by the estimated equilibrium effective exchange rate and the corresponding misalignment rate. In line with the evidence from previous studies, we argue that investment in the appreciating currency will be beneficial to investors only if the appreciating trend of the currency is consistent with equilibrium. Otherwise, the exchange rate is expected to be unstable in the future (see, Giannellis & Papadopoulos, 2011). Equivalently, this means that investors will be willing to invest in the appreciating currency only if the exchange rate is not significantly misaligned. Thus, there is an indication that the observed exchange rate may not alone determine the relationship between the value of the currency and the gold price. What is proposed is that the observed exchange rate should be taken into account in accordance with its equilibrium value and the implied misalignment rate. Secondly, departing form the existing studies in this literature, we employ a Panel Smooth Transition Regression (PSTR) model in order to explore the possibility that the impact of the independent variables on the gold price may be nonlinear. As the linearity hypothesis is rejected and the parameters of the PSTR model are identified (as it is reported in Section 5 of this paper), we estimate a two-regime PSTR model with a monotonic transition function. The results show that the impact of the equilibrium exchange rate on the gold price changes as the magnitude of the misalignment rate (threshold variable) changes. Thirdly, by utilising the nonlinear characteristics of the PSTR model we distinguish two effects, which may drive the relationship between the gold price and the equilibrium exchange rate. The first one is the substitution effect: investors may substitute gold investment with currency investment when the value of the currency follows an increasing trend. The second one is a positive income effect: an increase in the real value of the currency (reflecting positive macroeconomic performance) may lead to higher investment not only in currency but also in gold. To preview our results, there is evidence that for low misalignment rates, the income effect (i.e., the positive relationship) is shown to be more important, but as the misalignment rate moves close to the upper regime, the substitution effect prevails. The rest of the paper is organised as follows. The next section presents the theoretical background, while Section 3 shows the econometric methodology. Section 4 describes the data and Section 5 reports the principal empirical findings. Section 6 includes a robustness check of the results by re-estimating augmented PSTR models (i.e., extended with more control variables). Finally, Section 7 concludes. 2. Theoretical considerations 2.1. Baseline model Based on the relative theoretical and empirical literature, it is shown that the gold price is associated with a number of macroeconomic and financial variables, such as the exchange rate, the interest rate and the inflation rate.3 In this study, we mainly 3 As reported in the literature, gold price is also affected by more macroeconomic variables. For instance, Murach (2019) shows that real income (GDP) and money supply can also determine the gold price. In addition, Baur and McDermott (2016) show that gold is also affected by a number of expectations and uncertainty variables, such as inflation expectations, consumer sentiments, economic policy uncertainty and macroeconomic uncertainty.

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N. Giannellis and M. Koukouritakis

investigate the conjecture that the price of gold is affected by internal and external macroeconomic performance, which is reflected in exchange rate movements. We capture the overall macroeconomic performance with the real effective exchange rate (REER), which allows us to consider both the effects of the nominal exchange rate and the inflation rate. Even though we focus on the REER in our analysis, we also test the impact of the nominal interest rate (i ) on the gold price. Thus, our starting model is the following: (1a)

PG = f (REER, i ), 4

where PG is the gold price. Equivalently, Eq. (1a) can be modified in the following way: (1b)

PG = f (NEER, , i),

Since gold is basically traded in US dollars, most of the empirical studies examine the relationship between the gold price and the US dollar. When examining the demand-side of gold, most researchers find a negative relationship between the gold price and the US dollar. Namely, a decrease in the value of the US dollar makes gold cheaper for worldwide buyers and thus, the demand for gold increases (Sari, Hammoudeh, & Soutas, 2010; Tully & Lucey, 2007). However, this does not mean that the US dollar dominates the relationship between the gold and the exchange rate. For instance, Sjaastad and Scacciavillani (1996) confirm the negative relationship between the gold price and an extended set of currencies. Moreover, a negative relationship is also reported when considering gold as a hedge asset. According to this view, investors prefer gold when foreign exchange markets are unstable (Capie et al., 2005; Joy, 2011; Reboredo, 2013). On the other hand, a positive relationship between the gold price and the inflation rate is also reported in the literature. From a theoretical point of view, Fortune (1987) explains that as inflation is expected to increase, rational investors substitute fixed return assets with gold. Levin, Montagloni, and Wright (2006) provide an alternative explanation. They state that the positive relationship between the gold price and the inflation rate is due to supply-side reasons. Extraction costs are higher when inflation is high and thus, gold price increases to cover the increased cost. Overall, there is strong empirical evidence in the literature in favour of this positive relationship (see, inter alia, Beckmann & Czudaj, 2013; Batten, Ciner, & Lucey, 2014). Regarding the interest rate, it is considered as the opportunity cost of holding gold. This means that if the interest rate increases, investors exchange gold with other assets (with higher expected return). Namely, a negative relationship between the gold price and the interest rate may exist. However, the empirical evidence in the literature is mixed. Fortune (1987) finds a negative relationship, but Lawrence (2003) and Tully and Lucey (2007) find no relationship between the gold price and the interest rate. Baur (2011) argues that a positive relationship exists for short-term interest rates, while it turns into a negative one for long-term interest rates. Since we use long-term interest rates in this study, we expect that the sign of the interest rate will be negative. 2.2. Alternative model The function of gold as a hedge asset implies that the gold price increases due to the substitution effect. Investors substitute other assets with gold in periods of financial distress. Moreover, the negative relationship between the nominal exchange rate and the gold price implies that as a currency depreciates, investors prefer to invest in gold rather than in the depreciating currency. To invert the case, this also implies that the demand for gold declines as a currency appreciates. However, this statement does not enclose the whole story. What is missing is that investment in the appreciating currency will be beneficial to investors only if the appreciating trend of the currency is consistent with equilibrium. Otherwise, the exchange rate is expected to be unstable in the future (Giannellis & Papadopoulos, 2011). Equivalently, this means that investors will be willing to invest in the appreciating currency only if the exchange rate is not significantly misaligned. As a consequence, there is an indication that the observed exchange rate may not alone determine the relationship between the value of the currency and the gold price. What is implied is that the observed exchange rate should be taken into account in accordance with the equilibrium value of the currency and the implied misalignment. Thus, we propose the estimation of the following alternative model, in which the observed REER is substituted by the equilibrium REER (EqREER)5: (2)

PG = f (EqREER, i).

Since we are interested in the linkage between the macroeconomic performance and the gold price, the alternative model described in Eq. (2) seems to be more appropriate in capturing the above relationship. Considering gold as an asset, we can now distinguish two effects, which may drive the relationship between the gold price and the effective exchange rate. The first one is the aforementioned substitution effect: investors may substitute gold investment with currency investment when the value of the currency follows an increasing trend. In this case, the sign of the equilibrium effective exchange rate is expected to be negative. The second one is a positive income effect: when the real value of the currency increases (reflecting positive macroeconomic performance), this may lead to higher investment not only in currency but also in gold. In this case, the sign of the equilibrium effective exchange rate is expected to be positive. Finally, as in the standard model, the sign of the interest rate is expected to be negative. When it comes to the theoretical background of the equilibrium effective exchange rate, the latter can be considered as the exchange rate at which external balance is achieved. Based on the balance of payments approach, we follow Giannellis and Koukouritakis (2018), who extended the balance of payments exchange rate equation introduced by MacDonald (2000) and estimate 4 5

In an alternative form of Eq. (1a), the nominal interest rate can be replaced by the real interest rate. Alternatively, the nominal interest rate could be replaced by the real interest rate. 29

North American Journal of Economics and Finance 49 (2019) 27–46

N. Giannellis and M. Koukouritakis

the REER by the following equation6:

REERt =

0

+ +

1NFAt

+ +/

2 (yt

yt ) +

+

3 (rt

rt ).

(3)

2.3. Nonlinear behaviour Although the expected signs of the above regressors are well defined, we doubt whether the estimated parameters remain constant over time and across different states. Namely, investors may change their behaviour in front of different values of the effective exchange rate or the interest rate. For example, given the expected negative sign of the interest rate, investors may be less (more) willing to invest in bonds (gold) if the interest rate exceeds a critical level. This means that the estimated impact of the effective exchange rate (or the interest rate) on gold price may change beyond a critical point. As a consequence, we expect the presence of nonlinear dynamics in the relationship between the gold price and its regressors. Similarly, in the alternative model, the estimated coefficient of the equilibrium real effective exchange rate is expected to change values as the misalignment rate varies. We expect that the income effect (positive sign) should prevail when the misalignment rate is low, while the substitution effect (negative sign) will be stronger when the real value of the currency is highly misaligned. The former reflects the increased confidence on macroeconomic performance and stability, while the latter reflects investor’s anxiety about future stability even though the value of the currency is currently increasing. As in the standard model, this implies that investors behave differently in front of different misalignment rates. Thus, we expect the presence of nonlinearities in the alternative model too. The theoretical assumption behind the aforementioned nonlinear relationships is that the estimated parameters take different values in different states (regimes), while the transition process between the extreme regimes is assumed to be smooth rather than discrete.7 In theory, what can explain the nonlinear behaviour of investors is their attitude against the increasing risk. As risk follows an increasing trend around a critical point, investors change gradually their investment decisions. This could imply that investors may be less willing to exchange gold with higher return assets even though they used to sell gold for relatively lower return assets. Although this result seems quite paradox in a linear framework, it is well explained by estimating a nonlinear model. The change in their behaviour is smooth and occurs around a critical point of the interest rate or the misalignment rate. 3. Econometric methodology 3.1. Panel smooth transition regression (PSTR) model In order to explore the possibility that the impact of the (equilibrium) exchange rate on the gold price may be nonlinear, we estimate a PSTR model8, which has been originally proposed by Gonzales, Terasvirta, van Dijk, and Yang (2005). This model can be seen as a generalisation of the Panel Threshold Regression (PTR) model, originally presented by Hansen (1999). As in the PTR model, regression coefficients can take different values in different regimes (or states). However, the key characteristic of the PSTR model is that the regression coefficients change smoothly when moving from one regime to another. According to Gonzales et al. (2005), the PSTR model has a dual application. It can be seen as a linear heterogeneous panel model or/and as a nonlinear homogeneous panel. Based on our baseline model, as presented by Eq. (1a), the basic PSTR model with two regimes can be shown as follows:

PGj, t = µj +

t

+

01 REERj, t

+

02 i j, t

+(

11 REERj, t

+

12 i j, t ) g (qj, t ;

, c ) + u j, t ,

(4)

for j = 1, ....N and t = 1, ...T , where N and T are the cross-sectional and time dimensions of the panel, respectively. µj stands for fixed individual effects, t denotes time effects and uj, t represents the residuals. Gold price (PG ) is the dependent variable, while regressors (REER and i) are assumed to be exogenous.9 For the alternative model (Eq. (2)), REER in Eq. (4) is replaced by its equilibrium value (EqREER). Namely, the alternative PSTR model is written as follows10:

PGj, t = µj +

t

+

01 EqREERj, t

+

02 i j, t

+(

11 EqREERj, t

+

12 i j, t ) g (qj, t ;

, c ) + uj, t ,

(5)

6 The signs below the δ parameters express the expected signs of the estimated parameters according to theory. The theoretically expected signs, the solution of the balance of payments exchange rate equation and the derivation of Eq. (3) are presented in the Appendix section. 7 As investors are heterogeneous, it is not likely that all respond in the same way and at the same time. Moreover, investors adjust gradually their decisions. These reasons imply a smooth transition process. 8 The PSTR model requires that all variables (endogenous and exogenous) should be covariance stationary (i.e., I(0)). In this empirical study, and in order to avoid the problem of spurious regression, we have tested that the variables included in all PSTR models under estimation are I(0). These tests are not reported here, but they are available upon request. 9 We also rely on Eq. (1b), which is the equivalent expression of Eq. (1a). Moreover, to ensure that Eq. (4) does not suffer of the omitted variable bias, we account for more variables that may explain the gold price, such as GDP and money supply. By adding these variables into Eq. (1b), we derive the augmented version of our baseline model. The latter is estimated as a robustness check to confirm that the estimated parameters of Eq. (4) are robust after the inclusion of more control variables (see, Subsection 6.1). 10 Likewise, we test the robustness of the estimated coefficients of Eq. (5) by including more control variables, such as GDP and money supply. The augmented version of Eq. (5) is estimated in sub subsection 6.2.

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The transition function g (qj, t ; , c ) is a continuous and bounded function of the threshold variable (qj, t ), which can be written in the logistic or the exponential specification form. The logistic specification form is a monotonic transition function, while the exponential form represents a symmetric U-shaped smooth transition process. The exponential transition function implies that investors respond symmetrically in front of low and high values of the threshold variable. Depending on the threshold variable, this would imply that investors have identical response when interest rates (or effective exchange rates) are too high or too low. What differentiates their behaviour depends on whether the interest rate (or the effective exchange rate) is close to or away from the location parameter c. On the other hand, the logistic transition function implies a monotonic smooth transition process around the threshold variable. When a single transition function is considered, the model entails two extreme regimes, which are associated with low and high values of the threshold variable (i.e., lower/higher than the location parameter c). Since we expect that gold investors make different decisions in front of low and high values of interest rates (or effective exchange rates), we believe that the logistic transition function is more suitable in our study.11 Thus, we utilize the following logistic transition function: m g (qj, t ; , c ) = [1 + exp( (qj, t c ))] 1with > 0 and c1 < c2 < . ..... < cm . is the slope parameter and indicates the smoothn=1 ness of the transition, while c = (c1, c2, ...cm) is a vector of location parameters. Form = 1, the PSTR model becomes a two-regime model with a monotonic transition of regressor coefficients as the threshold variable increases. The two regimes correspond to low and high values of the threshold variable, while the critical point is located in c1. When , the PSTR model is identical to Hansen’s two-regime PTR model and the transition function switches between zero and one. For m = 2 and , the PSTR model becomes a three-regime model with identical outer regimes. The minimum value of the transition function is (c1 + c2)/2 , while the 0 , the transition function is constant maximum value of one can be reached in low and high values of the transition variable. If and the PSTR model becomes a linear panel model. The impact of the regressors on the dependent variable can be captured by the estimated coefficients 01, 02, 11, 12 . As mentioned by Fouquau, Hurlin, and Rabaud (2008), the estimated parameters have a direct interpretation only when the threshold variable tends towards the extreme regimes. For example, in Eq. (4), the estimated parameters 01 and 02 represent the REER and interest rate coefficients, respectively, only when the transition function tends towards zero. On the other hand, when the transition function tends towards unity, the REER coefficient is given by the sum of the parameters 01 and 11, while the interest rate coefficient is given by the sum of the parameters 02 and 12 . When the transition function ranges between the bounds (i.e., zero and one), the interpretation of the above parameters is not that straightforward. For example, the REER coefficient is considered as the weighted average of the parameters 01 and 11. Similarly, the interest rate coefficient corresponds to the weighted average of the parameters 02 and 12 . However, the value of the weighted average of the parameters depends on the properties of the transition function. Since these properties are not constant, the interpretation of the values of the REER and interest rate coefficients is not clear-cut. Although we cannot interpret these values as elasticities, we can interpret the sign of the parameters, which shows the changing impact of the regressors as the threshold variable increases. 3.2. Tests for panel unit root, cross-sectional dependence and cointegration Before estimating the model described in Eq. (3), we test each series for unit roots. Initially, we implemented the test proposed by Levin, Lin, and Chu (2002) for common unit roots, and the test proposed by Im, Pesaran, and Shin (2003) for individual unit roots. Both tests test the null hypothesis of a unit root and they assume cross-sectional independence. However, when cross-sectional dependence exists the results of the above tests are no longer accurate due to inference distortions. For this reason, we also applied the Pesaran (2007) and the Palm, Smeekes, and Urbain (2011) panel unit root tests that assume cross-sectional dependence. Again, the null hypothesis for both tests is the unit root hypothesis. Next, we investigate the possible existence of a long-run relationship among the variables of the G7 countries, by implementing a proper cointegration test. In order to choose the appropriate cointegration technique, we need to test for cross-sectional dependence. To do so, we implemented four tests: the Breusch and Pagan (1980) LM test, the Pesaran (2004) scaled LM test, the Pesaran (2004) CD test and the Baltagi, Feng, and Kao (2012) bias-corrected scaled LM test. As also shown in Section 5.2, all four tests reject the null hypothesis of cross-sectional independence. Thus, cross-sectional dependence should be taken into account in our analysis. To account for cross-sectional dependence in the context of cointegration, we implemented the Westerlund and Edgerton (2007) panel cointegration test, which modifies the residual-based LM test of McCoskey and Kao (1998). In brief, the McCoskey and Kao test assumes the following data generating process for a series x i, t :

x i, t = ai + zi/, t bi +

(6)

i, t ,

where regressors z i, t are pure random walk processes and the error term i, t is decomposed into ei, t (stationary component) and t vi, t = j = 1 i, j , where i, j is an i.i.d. process with zero mean and var( i, j ) = i2 . The null hypothesis of cointegration is H0 : i2 = 0 for all

i against the alternative of no cointegration that is H1: pothesis is tested using the following LM test statistic:

2 i

> 0 for some i . With cross-sectional independence the cointegration hy-

11 However, the exponential transition function is appropriate in other studies. For example, Beckmann et al. (2013) studies the adjustment process towards Purchasing Power Parity (PPP) equilibrium. He relies on an exponential transition function since the adjustment of PPP deviations above and below equilibrium is symmetric. Similarly, in Beckmann and Czudaj (2015), the adjustment of deviations of stock returns above and below the threshold is symmetric. As a result, this kind of nonlinearity is captured by the exponential transition function.

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LM =

1 NT 2

N

T i

2

Si2, t ,

(7)

i=1 t=1

where Si2, t is the partial sum process of i, t , and i2 is the estimated long-run variance of ei, t conditional on z i, t . Also, it holds that N (LM E (LM ))Ñ(0, var(LM )) . To deal with cross-sectional dependence, Westerlund and Edgerton (2007) suggest bootstrapping. This requires the computation of the empirical distribution. Assuming an AR ( ) representation for the residuals and using ei, t and z i/, t (stationary by definition), they define the vector w = (ei, t , z i/, t ) / . Thus, the infinite autoregressive representation is: i, j wi, t j

=

i, t

(8)

j=0

where i, t is a stationary process. By approximating Eq. (8) with an AR (p) model, a sieve bootstrap scheme is obtained and new bootstrap values for x i, t and z i, t are produced. By replicating the whole process N times and computing each time the LM test, the bootstrap distribution is obtained. Once there is evidence of a valid cointegration relationship, the long run relationship between the variables of interest needs to be estimated. Since OLS estimators are biased as they depend on nuisance parameters, we implement the Fully-Modified OLS (FMOLS) approach in the context of panel cointegration (Kao & Chiang, 2000; Pedroni, 2000; Phillips & Moon, 1999).12 To choose between pooled or grouped mean estimation, we test for slope homogeneity using two tests. The first test is the modified Hausman test (Pesaran, Smith, & Im, 1996). Under the null hypothesis of slope homogeneity, the respective statistic is distributed as (2k) . The second test is the Δ test (Pesaran & Yamagata, 2008) and examines the cross section dispersion of individual slopes weighted by their relative precision. Its size and power properties are better than those of the Hausman test, while under the null hypothesis of slope homogeneity, both and -adjusted statistics are distributed normally. 4. Data description In our analysis, we use annual data for the gold price (PG ), the nominal effective exchange rate (NEER), the real effective exchange rate (REER), the net foreign asset position as a percentage of the GDP (NFA), the GDP differential ( y y ), the nominal interest rate (i ), the real interest rate differential (r r ) as well as the money supply for the G7 countries, namely Canada, France, Germany, Italy, Japan, the UK and the USA. The time span covers the period from 1980 to 2016. Annual average gold price data refer to gold fixing price 3:00 PM. (London time) in London Bullion Market. They are expressed in USD per troy ounce and have been obtained by the Federal Reserve Bank of St. Louis. Gold price data have been transformed into natural logarithms. NEER and REER data for all G7 countries have been obtained from the Bank for International Settlements (BIS). NEER series are calculated as weighted averages of bilateral exchange rates (based on the narrow index of 27 countries13), while they are adjusted by relative consumer prices to derive REER series. The weighting pattern reflects the bilateral trade between countries.14 As in gold price, NEER and REER data have been transformed into natural logarithms and by construction, an increase in the nominal (real) effective exchange rate implies the nominal (real) appreciation of the home currency. Data for the NFA positions up to 2011 have been obtained from the updated and extended version of the dataset constructed by Lane and Milesi-Ferretti (2007).15 The rest of the series has been filled by cumulating the current account (in USD) and valuation effects to the previous net foreign asset position. To express net foreign asset position as a share of GDP, we divide NFA by GDP in USD. GDP differential for each of the G7 countries is constructed as the difference between home and foreign real GDP. We use real GDP per capita in USD (at constant 2010 prices), which has been obtained from the World Development Indicators of the World Bank. For each of the G7 countries, foreign real GDP is constructed as a weighted average of its trade partners’ real GDP. We have used the same index of countries and weighting patterns as the one used in the construction of REER. As in gold price and REER data, GDP differentials are expressed in natural logarithms. Regarding nominal interest rates, we obtain 10-year government bond yields from the Eurostat for all countries except Canada. For Canada, these data have been obtained from the Statistics Canada. Real interest rate differential stands for the difference between home and foreign real interest rates. Initially, we calculate each country’s inflation rate from the corresponding GDP deflator, which has been obtained from the World Development Indicators of the World Bank. By subtracting each country’s inflation rate from the respective 10-year government bond yield, we get the real interest rates for the G7 countries. Unlike the case of foreign real GDP, 12 The FMOLS is a nonparametric approach that corrects for bias and endogeneity. An alternative (parametric) approach is the Dynamic OLS (DOLS). The FMOLS is superior to DOLS since the former sets fewer restrictions and tends to be more robust. Pedroni (2000) argues that the FMOLS estimator is robust even for small panels. Additionally, it should be preferred when the panel contains more than one regressor. 13 We did not use REER and NEER data based on the broad index of 61 countries because these data are available since 1994. The narrow index consists of Australia, Austria, Belgium, Canada, Chinese Taipei (Taiwan), Denmark, Euro area, Finland, France, Germany, Greece, Hong Kong, Ireland, Italy, Japan, Korea, Mexico, The Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, the UK and the USA. 14 We used bilateral trade data that are reported in the BIS. As BIS mentions, the trade weights are derived from manufacturing trade flows (SITCrev.3 classification 5 to 8) and obtained from the UN Commodity Trade Statistics Database (UN Comtrade), OECD International Trade by Commodity Statistics and the Directorate General of Budget, Accounting and Statistics of Taiwan. 15 http://www.philiplane.org/EWN.html.

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each county’s foreign real interest rate cannot be calculated as a weighted average of its trade partners’ real interest rates. The reason is that capital flows are not dictated by the degree of trade flows between countries. In contrast, investors compare expected yields and risk and invest in countries even if there are minimal trade flows with the home country. Thus, as foreign real interest rate we use the average (with equal weights) of the real interest rates of the G7 countries.16 Finally, for money supply we used M3 (in domestic currency) for Canada, France, Germany, Japan and the USA, while for Italy and the UK where data for M3 were not available, we used M2 and M4, respectively. Data for Canada (until 2006), France (until 1998), Germany (until 1998), Italy (until 1998), Japan and the UK have been obtained from the International Financial Statistics (IFS) of the International Monetary Fund (IMF). Data for Canada (since 2007) and the USA have been obtained from the Federal Reserve Bank of St. Louis. Data for France, Germany and Italy since 1999 have been obtained from the Bank of France, Bundesbank and the Bank of Italy, respectively.17 5. Empirical findings 5.1. Baseline model The estimation procedure starts with the specification of the PSTR model,18 as shown in Eq. (4). We should first select the threshold variable, then test the linearity hypothesis and finally define the number of regimes. The threshold variable can be exogenously determined if there is a theoretical model that describes clearly the transition process and the variable that determines the classification of the regimes. If there is not such a theoretical indication, we consider all variables as possible threshold variables and choose this variable with the strongest rejection of the linearity hypothesis. Although there is a theoretical background behind our baseline model, we have no clear exogenous indication about the mechanism of the transition process. Hence, we need to test the linearity hypothesis for the REER and the interest rate (i ) and then choose the threshold variable. The null hypothesis of a linear process is H0 : = 0 or equivalently, H0 : 0k = 1k , where k = 1, 2. Due to the presence of nuisance parameters under the null hypothesis, the transition function in Eq. (4) is replaced by its first-order Taylor expansion. The LMF test statistics are shown in Table 1. Under both candidate variables, the linearity hypothesis is strongly rejected. However, the strongest evidence is reported when the interest rate (i ) is used as a threshold variable. This implies that there is an endogenous indication that the interest rate determines the transition process of this PSTR model. Namely, the way the gold price is affected by its regressors changes as the interest rate switches between low and high values. Since the threshold variable has been defined, we need to determine the number of the transition functions or, in other words, the number of thresholds. To do so, we follow a sequential procedure. At a first stage, we test the null hypothesis of linearity (no threshold) against the alternative that there is one threshold. As shown in Table 2, the null hypothesis is strongly rejected. Next, we test the null hypothesis of one threshold against the alternative of two thresholds. The results in Table 2 report that the null hypothesis cannot be rejected. This result implies that the baseline model is a two-regime PSTR model with a monotonic transition function. As the model has been fully specified, we estimate the parameters of the model by nonlinear least squares. As shown in Table 2, the slope parameter ( ), which shows the smoothness of the transition process, is equal to 2.924, while the location parameter (c ) is equal to 4.089. These values imply that the transition from the bottom regime (low nominal interest rate) to the upper regime (high nominal interest rate) is quite smooth and the change in the interest rate is located around the value of 4.089. Fig. 1 presents the estimated transition function. It shows the smooth transition between the two extreme regimes (lower/upper) as the interest rate increases. It is also evident that the larger share of the observations belongs to the upper regime (i.e., high interest rates), in which the transition function takes the value of 1. Much more informative is Fig. 2, which plots the estimated transition function over time (for each of the countries of the sample). In all countries, the upper regime (high interest rates) is observed until the middle of 1990s, while the lower regime (low interest rates) is chronically located at the end of the estimated period. A fluctuation between the two extreme regimes in the meantime is observed. What is really interesting is that the transition function follows an upward trend towards the upper regime in periods of financial distress. This is evident during the global financial crisis of 2007–2008 and during the recent Eurozone’s sovereign debt crisis (see, for example the case of Italy). Regarding the estimated parameters 01, 02, 11, 12 , the REER variable is shown to be statistically significant only when the transition is taken into account. The parameter 01 is found to be negative but not statistically different from zero, while the para-

meter 11 is negative and statistically significant. This finding would imply that the impact of the REER variable on the gold price decreases as the interest rate moves from the bottom to the upper regime. Nonetheless, the overall impact of the REER variable

16 We use equal weights because (a) the G7 countries are advanced economies that move closely with each other, and (b) the relative economic size of each of them does not necessarily determine the amount of capital inflows and outflows. 17 For France, Germany and Italy, IFS data are expressed in French francs (FF), German marks (DM) and Italian liras (IL), respectively, while data from the central banks of these countries are expressed in euros. Thus, and in order to avoid this problem, we transformed the latter data into FF, DM and IL using the fixed euro conversion rates of these three countries. 18 In general, the STR model has higher power as the number of observations increases. In this study, we could use more observations by employing higher frequency data (i.e., quarterly). However, the use of the NFA, which is available only in annual frequency, restricts our choices. Although the use of annual data in a times series STR model implies a small number observations, the number of total observations in a panel (PSTR model) is large enough due to cross sections. In addition, Gonzales et al. (2005) have used annual data from 1973 to 1987 in their empirical exercise.

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Table 1 PSTR (Baseline model): choosing the threshold variable. Null hypothesis

Threshold

LMF statistic

Linearity

REER i

7.867* (0.00) 47.658* (0.00)

Notes: Numbers in parentheses are p-values. * denotes rejection of the linearity hypothesis at the 5% level of significance. Table 2 PSTR estimation: Baseline model. Estimated slope parameters of transition functions Parameter 01 Parameter Parameter Parameter

11

−0.232 (−0.88)

−0.295** (−11.70) −0.081* (−1.80)

02

0.096** (2.29)

12

Specification of the model Threshold variable Number of Regimes Location parameter (c ) Slope Parameter ( )

Interest rate (i ) 2 regimes (1 threshold) 4.089 2.924

Linearity tests (LMF statistics) Linear model against one threshold One threshold against two thresholds

47.658** [0.00] 1.269 [0.28]

Notes: Numbers in parentheses are t-statistics, which have been calculated based on standard errors corrected for heteroscedasticity. Numbers in brackets are p-values. 3. **(*) denotes rejection of the null hypothesis at the 5% (10%) level of significance. The number of regimes (thresholds) is determined by the procedure shown in the linearity tests.

cannot be defined because of the insignificant parameter 01.19 On the other hand, the results in Table 2 indicate that the sign of the interest rate (parameter 02 ) is found to be negative and statistically different from zero. Namely, as the interest rate increases, investors exchange gold with higher return assets and the price of gold declines. This finding confirms that the interest rate acts as the opportunity cost of holding gold and it is totally consistent with theory. Furthermore, our finding coincides with previous evidence in the literature, at least when long term interest rates are considered (see, Baur, 2011). Nonetheless, it is really interesting to test how this impact is affected when the threshold variable ranges between the extreme regimes. The sign of the parameter 12 is found to be positive and statistically significant. Although we cannot interpret this value as elasticity, we can at least interpret its sign. Having in mind the aforementioned negative relation between the interest rate and the gold price, the positive sign of the 12 parameter implies that the overall negative influence of the interest rate on the gold price is getting less strong as the threshold variable (i.e., the interest rate) switches from the bottom to the upper regime. This means that when the interest rate is already high, investors are less willing to exchange gold with other assets even though the interest rate increases. In other words, investors are less sensitive to interest rate changes when the interest rate is high. Although the opportunity cost of holding gold rises, any further increase in the already high interest rate is associated with higher risk. Thus, investors hold gold to avoid this extra risk. This empirical evidence confirms the theoretical considerations, as shown in Section 2.3, regarding the nonlinear behaviour of investors and the driving force behind the transition process. 5.2. Alternative model Based on the theoretical considerations shown above, as well as on the inconclusive evidence regarding the effect of the REER on the gold price, we turn into the estimation of our alternative model. The main theoretical argument is that the observed exchange rate may not alone determine the relationship between the exchange rate and the price of gold. Instead, we argue that investors are influenced not only by the actual trend of the exchange rate but also by its equilibrium value. Consequently, we argue that the degree of exchange rate misalignment determines the relationship between the exchange rate and the gold price and controls the transition process of the PSTR model. Under this theoretical framework, the estimation of the alternative model entails a two-stage procedure. Firstly, we estimate the equilibrium exchange rate and the implied misalignment rate and at the second stage we test whether the above estimated series affect the price of gold. 19 Although this estimated sign is consistent with theory and in line with previous evidence in the literature (see, inter alia, Sjaastad & Scacciavillani, 1996; Capie et al., 2005; Reboredo, 2013), we cannot rely on it as it is found to be statistically insignificant.

34

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Fig. 1. Baseline models: transition function and threshold variable.

5.2.1. Estimates of equilibrium real effective exchange rates Regarding the order of integration of the variables under consideration, all unit root tests (both these that assume cross-sectional independence and these that take cross-sectional dependence into account) indicate that all variables are I (1) , as the unit root hypothesis cannot be rejected for any variable at the 5 per cent level of significance.20 Before proceeding with cointegration, we need to test for cross-sectional dependence among the variables of our model. As shown in Table 3, all four tests reject the null hypothesis of cross-sectional independence. Following the above evidence, we proceed with the cointegration analysis under cross-sectional dependence. Table 4 presents the results of the Westerlund and Edgerton (2007) panel cointegration test and provide both asymptotic and bootstrap p-values. As shown, the evidence suggests the existence of a long-run (cointegrating) relationship among the variables under consideration.21 20 21

For saving space, the unit root test results are not reported here but are available under request. Notice that when both intercept and trend are included, the asymptotic p-value indicates rejection of the cointegration. However, the inference 35

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Fig. 2. Baseline models: transition function for each of the G7 countries over time.

Then, we derive a robust FMOLS estimator for Eq. (3) and we get the equilibrium REER as follows:

REERi, t =

0, i

+

1 NFAi, t

+

2 (yi, t

yi, t ) +

3 (ri, t

ri, t ),

(9)

(footnote continued) based on bootstrap p-values, which account for cross-sectional dependence, implies that the cointegration hypothesis cannot be rejected no matter what deterministic components are included. 36

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Table 3 Cross-sectional dependence tests. Breusch and Pagan (1980) LM test Pesaran (2004) scaled LM test Pesaran (2004) CD test Baltagi et al. (2012) bias-corrected scaled LM test

100.07* (0.00) 12.20* (0.00) −2.02* (0.04) 12.10* (0.00)

Notes: Numbers in parentheses are p-values. * denotes rejection of the null hypothesis of independence at the 5% level of significance. Table 4 Westerlund and Edgerton (2007) panel cointegration test. Intercept

Intercept and trend

0.406 (0.34) [0.98]

1.823 (0.03) [0.50]

Notes: The Westerlund and Edgerton test tests the null hypothesis of cointegration against the alternative of no cointegration. Numbers in parentheses are asymptotic p-values. Numbers in brackets are bootstrapped p-values (using 10,000 replications). Table 5 FMOLS estimation results, tests for deterministics and slope homogeneity tests. FMOLS estimation results NFA y y r r

0.054 (0.00) 0.486 (0.00) 0.128 (0.02)

Slope homogeneity tests Pesaran et al. (1996) modified Hausman test Pesaran and Yamagata (2008)

test

3.389 (0.33) −1.890 (0.97)

-adjusted test

−2.028 (0.98)

Tests for deterministics F test (R: constant, UNR: linear trend) F test (R: linear trend, UNR: quadratic trend)

26.392* (0.00) 1.634 (0.21)

Pesaran and Yamagata (2008)

Notes: R is for restricted model and UNR is for unrestricted model. Numbers in parentheses are p-values. * denotes statistical significance at the 5% level of significance.

where REERi, t is the estimated equilibrium REER for country i, 0, i stands for the estimated fixed effects for country i, while 1, 2 and 3 are the parameter estimates of the fundamentals. The pooled panel estimator has been chosen, as the null hypothesis of slope homogeneity cannot be rejected. Also, a constant and a linear trend have been included into the deterministic part of the model, based on several F-test statistics. The above results are reported in the bottom section of Table 5. Finally, two dummy variables are also included in the deterministic part of the model. The first one captures the effects of the 1990–1993 period during which several important events took place, such as the German unification, the ratification of the Treaty for the European Union and the ERM crisis. The second one captures the turmoil of the global financial crisis between 2007 and 2010. The FMOLS estimation results are reported in the upper section of Table 5. As shown, all three variables are statistically significant at the 5 per cent level of significance. Thus, all three variables should be taken into account when estimating the equilibrium REER. Also, all three variables have a strong positive effect on the REER of the G7 countries. Regarding the NFA position and the real interest rate differential, these positive effects are theoretically expected. However, the positive effect of the GDP differential on the REER contradicts the standard balance of payments theory, which suggests that a higher home GDP (in relation to the foreign one) is expected to depreciate the home currency. Although our result seems to be a bit paradox, it can be sufficiently explained by fact that advanced economies have greater access to capital. Easier access to capital along with knowledge accumulation allows advanced economies to develop new and high quality products, stimulating their exports. This fact militates in favour of the positive relation between the REER and the GDP differential.22

22

The empirical evidence of Giannellis and Koukouritakis (2018) also suggests a positive relation between the REER and the GDP differential. 37

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France Germany Italy

15% 10% 5% 0% -5% -10% -15% 1980

1984

1988

1992

1996

2000

2004

2008

2012

2016

Fig. 3. Misalignment rates for the Eurozone countries. 25% UK USA

20% 15% 10% 5% 0% -5% -10% 1980

1984

1988

1992

1996

2000

2004

2008

2012

2016

Fig. 4. Misalignment rates for the UK and the USA. 20%

Canada Japan

15% 10% 5% 0% -5% -10% -15% 1980

1984

1988

1992

1996

2000

2004

2008

2012

2016

Fig. 5. Misalignment rates for Canada and Japan.

Once the equilibrium REER for each sample country is calculated, we construct the misalignment rate as the percentage difference between the estimated equilibrium REER and the actual REER. Positive misalignment rates correspond to currency overvaluation, while negative rates stand for currency undervaluation. The misalignment rates for the G7 countries are reported in Figs. 3–5. As shown in these figures, the misalignment rates for France, Germany and the USA are very close to zero for the whole sample period. This means that for these three countries, the actual REER is very close to its equilibrium value. For Italy and the UK, our results indicate high misalignment rates at the early 1990s, probably due to the ERM crisis. For the former country, there is also a high negative misalignment rate between 2010 and 2012, when the sovereign debt crisis in the Eurozone took place. Regarding Canada and Japan, our evidence suggests high misalignment rates during the years of the recent financial crisis. For the latter country, there is also a high positive misalignment rate in the 1990s, which can be probably attributed to the prolonged recession that the Japanese economy suffered during this decade after the collapse of the fabled economic bubble of the 1980s. 5.2.2. Alternative PSTR model Having estimated the equilibrium exchange rate and the implied misalignment rate, we turn to the estimation of the alternative PSTR model, which can be written as follows:

PGj, t = µj +

t

+

01 EqREERj, t

+

02 i j, t

+(

11 EqREERj, t

+

12 i j, t ) g (qj, t ;

38

, c ) + uj, t ,

(10)

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Table 6 PSTR estimation: Alternative model. Estimated slope parameters of transition functions Parameter 01 Parameter Parameter Parameter

11

0.615* (2.43)

−0.099* (−1.97)

−0.116* (−10.75)

02

0.119* (5.14)

12

Specification of the model Threshold variable Number of Regimes Location parameter (c ) Slope Parameter ( )

Misalignment rate 2 regimes (1 threshold) 4.325 0.610

Linearity tests (LMF statistics) Linear model against one threshold One threshold against two thresholds

6.862* [0.00] 0.597 [0.55]

Notes: Numbers in parentheses are t-statistics, which have been calculated based on standard errors corrected for heteroscedasticity. Numbers in brackets are p-values. 3. * denotes rejection of the null hypothesis at the 5% level of significance. The number of regimes (thresholds) is determined by the procedure shown in the linearity tests.

where EqREER stands for the estimated equilibrium real effective exchange rate. Based on the theoretical arguments that presented in Section 2.2, there is a theoretical indication that the transition process may be driven by the exchange rate misalignment rate. Low misalignment rates imply that exchange rates follow an equilibrium process in consistency with overall macroeconomic stability. In contrast, high misalignment rates may cause future instability. Thus, we exogenously set the estimated misalignment rate as the threshold variable of the alternative PSTR model. The rest of the estimation procedure is the same as in Section 5.1. We test the linearity hypothesis and through a sequential approach we define the number of the thresholds (i.e., the type of the transition function). The results are reported in Table 6 and show that the null hypothesis of a linear process is strongly rejected. Next, the null hypothesis of only one threshold against the alternative of two thresholds cannot be rejected. Thus, the results show that there is a nonlinear two-regime process with a monotonic transition function. The slope parameter ( ) is equal to 0.61, which implies that the transition is much smoother compared to the baseline model. Next, the estimated location parameter (c ) shows that the regime change is located around the value 4.325 of the misalignment rate. The estimated transition function of Eq. (5) is presented in Fig. 6. As in the baseline model, the positive slope of the transition function shows the transition from the low to the upper regime as the misalignment rate increases. But, in contrast to the baseline model, a small share of the observations belongs to the extreme regimes (i.e., low and high misalignment rates). Most of the observations are located between the two extreme regimes indicating moderate misalignment rates (as also presented by Figs. 3–5). This is confirmed by the plot of the estimated transition function over time (for all countries of the sample) that is shown in Fig. 7. The vast majority of the observations lie between the two extreme regimes. Few observations belong to the low regime (i.e., low misalignment rate with zero transition function) and very few belong to the upper regime (i.e., high misalignment rate with unit transition function). Likewise, the transition from the lower regime to the upper regime coincides with periods of financial distress. Instructive examples are the cases of Italy and the UK, in which a switch from the low to upper regime is observed during the ERM crisis. Table 6 also presents the estimated parameters 01, 02, 11, 12 , which are all found to be statistically different from zero. Recall that we cannot consider these values as elasticities, but we can derive useful implications based on their sign. Starting from the impact of the equilibrium REER on the price of gold, the parameter 01 is found to be positive, while the estimated sign of the parameter 11 is negative. The positive sign denotes that as the equilibrium REER increases, or equivalently the currency appreciates, the gold price increases as well. This outcome implies that the income effect drives the relationship between the exchange rate and the price of gold. In other words, the appreciating trend of the exchange rate, which is consistent with equilibrium, reflects good macroeconomic performance and confidence on economy. Under these circumstances, investment in gold and in other assets increases. However, the negative sign of the parameter 11 implies that this positive impact on the gold price declines as the threshold variable switches between the extreme regimes. To put it differently, as the misalignment rate increases and moves from the low misalignment regime to the high misalignment regime, anxiety about future stability increases and the income effect is weakened. As the misalignment rate moves close to the upper regime (i.e., the transition function is close to one), the substitution effect prevails. Thus, there is evidence that the gold serves as a hedge only when the exchange rate misalignment is significantly high. Our findings are along the lines of the theoretical assumptions shown in subsections 2.2 and 2.3. Finally, the signs of the estimated parameters 02 and 12 are the same as in the baseline model. No matter the choice of the threshold variable, the relationship between the interest rate and the gold remains the same as reported in the previous model. Namely, as the interest rate increases, the opportunity cost of holding gold increases and investors exchange gold with other assets. But, when the transition function tends towards the upper regime, investors express less willingness to sell gold for higher return assets. Although the threshold variable is different, the driving force behind the transition process is quite similar. As the exchange

39

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Fig. 6. Alternative models: transition function and threshold variable.

rate misalignment increases, investors worry about future financial instability and invest in gold to offset the increased risk. Likewise, this indicates that gold serves a hedge only when financial risk is high.23 6. Robustness check To enhance the robustness of the estimated coefficients in Eqs. (4) and (5), we utilize alternative theoretical specifications as well as more control variables, in order to establish that there is no omitted variable bias in the estimated coefficients. Hence, we estimate augmented PSTR models to check the robustness of the original ones. 23 Under both models, financial risk is considered either as significantly high (extreme) interest rates or as significantly high (extreme) misalignment rates of the exchange rates.

40

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Fig. 7. Alternative models: transition function for each of the G7 countries over time.

6.1. Augmented PSTR of the baseline model Starting from the baseline model, we use Eq. (1b), which is the equivalent expression of Eq. (1a), in which the nominal effective exchange rate and the inflation rate are separately taken into account (along with the nominal interest rate). Furthermore, as suggested in the literature (Murach, 2019), we extend our model by considering more variables, such as the real GDP per capita (GDP) and the money supply (M). Hence, the robustness of Eq. (4) is checked by estimating the following augmented baseline (PSTR) model:

41

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Table 7 PSTR (Augmented baseline model): Choosing the threshold variable. Null hypothesis

Threshold

LMF statistic

Linearity

NEER i Inflation GDP per capita Money Supply

1.427 (0.22) 21.777* (0.00) 7.331* (0.00) 21.423* (0.00) 8.570* (0.00)

Notes: Numbers in parentheses are p-values. * denotes rejection of the linearity hypothesis at the 5% level of significance. Table 8 PSTR estimation: Augmented baseline model. Estimated slope parameters of transition functions Parameter 01 Parameter Parameter Parameter Parameter Parameter Parameter Parameter Parameter Parameter

1.013** (2.11)

−1.022* (−1.77)

11

0.097** (2.07)

02

−0.051 (−1.05)

12

−0.182** (−3.88)

03

0.171** (3.80)

13

−2.311** (−5.39)

04

0.258 (1.06)

14

0.691** (4.44)

05

0.042** (2.15)

15

Specification of the model Threshold variable Number of Regimes Location parameter (c ) Slope Parameter ( )

Interest rate (i ) 2 regimes (1 threshold) 3.970 3.424

Linearity tests (LMF statistics) Linear model against one threshold One threshold against two thresholds

21.777** [0.00] 1.289 [0.27]

Notes: Numbers in parentheses are t-statistics, which have been calculated based on standard errors corrected for heteroscedasticity. Numbers in brackets are p-values. 3. **(*) denotes rejection of the null hypothesis at the 5% (10%) level of significance. The number of regimes (thresholds) is determined by the procedure shown in the linearity tests.

PGj, t = µj + +

t

+

01 NEERj, t

15 Mj, t ) g (qj, t ;

+

02 j, t

+

03 i j, t

+

04 GDPj, t

+

05 Mj, t

, c ) + uj , t ,

+(

11 NEERj, t

+

12 j, t

+

13 i j, t

+

14 GDPj, t

(11)

As the properties of Eq. (11) are not different from those of Eq. (4), we follow the same estimation procedure. Firstly, we endogenously identify the threshold variable and then we test for the number of the regimes. The results are reported in Tables 7 And 8. As shown in table 7, the nominal interest rate is the threshold variable because it is associated with the stronger rejection of the linearity hypothesis. This, of course, implies that the nonlinear PSTR model should be estimated. Identically to the baseline model, the results in Table 8 imply that its augmented version is also a two-regime PSTR model. Also, the estimated values of the slope and location parameters (i.e., = 3.424 and c = 3.970 , respectively) are close to those reported in the original version of the baseline model of Eq. (4). This similarity is also evident in Figs. 1 and 2. Fig. 1 shows that the estimated transition function of the baseline model of Eq. (4) is almost identical to the estimated transition function of the augmented baseline model of Eq. (11). Furthermore, the plots of the estimated transition functions over time, which are illustrated in Fig. 2, confirm that the two transition processes are almost identical. Regarding the estimated parameters, those of the interest rate are statistically significant and have the same sign with those of Eq. (4), namely 03 < 0 and 13 > 0 . Identical evidence with this of Eq. (4) has also been found in the case of the effective exchange rate. As 01 is statistically insignificant, the evidence regarding the effective exchange rate remains inconclusive. On the other hand, the additional variables provide new evidence. The inflation rate is statistically significant and positively signed only in the linear part, while the corresponding parameter in the transition function (i.e., 13 ) is statistically insignificant. The positive sign of 03 implies that gold price increases as the inflation rate rises. This finding is consistent with theory and previous evidence in the literature (see, for instance, Beckmann & Czudaj, 2013). Similarly for GDP, only the parameter in the linear part (i.e., 04 ) is statistically significant. Its negative sign implies that more competitive investment choices exist when the economy grows. As a result, the demand for gold decreases and gold price declines. This evidence is in line with the view that investment in gold is higher in periods of economic 42

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Table 9 PSTR estimation: Augmented alternative model. Estimated slope parameters of transition functions Parameter 01 Parameter Parameter Parameter Parameter Parameter Parameter Parameter

0.474** (2.01)

−0.996* (−1.89)

11

−0.041** (−2.00)

02

0.119** (5.01)

12

−2.275** (−5.82)

03

0.569** (2.46)

13

1.101** (7.73)

04

−0.128** (−4.11)

14

Specification of the model Threshold variable Number of Regimes Location parameter (c ) Slope Parameter ( )

Misalignment rate 2 regimes (1 threshold) 3.497 0.430

Linearity tests (LMF statistics) Linear model against one threshold One threshold against two thresholds

7.456** [0.00] 0.261 [0.90]

Notes: Numbers in parentheses are t-statistics, which have been calculated based on standard errors corrected for heteroscedasticity. Numbers in brackets are p-values. 3. **(*) denotes rejection of the null hypothesis at the 5% (10%) level of significance. The number of regimes (thresholds) is determined by the procedure shown in the linearity tests.

recession and turmoil, since it serves as a hedge or save heaven (see, Baur & McDermott, 2010; Beckmann & Czudaj, 2013). Finally, both parameters of money supply are statistically significant and positively signed. The positive sign in the linear part (i.e., 05 > 0 ) shows that gold price increases in periods of monetary expansions. This result is consistent with theory as monetary expansions are associated with higher inflation and lower interest rates. In other words, the substitution effect prevails and investors prefer gold.24 This effect is shown to be stronger as the transition function moves from the lower to the upper regime (i.e., 15 > 0 ). Namely, the impact of monetary expansion on gold price is stronger when interest rates are high. This possibly implies that when the economy is in recession, monetary expansion is required to stabilize it. Alternatively, if economic recession is not the case but interest rates are already high, an expansionary monetary policy could imply that the monetary policy is loose. Both of the above possible scenarios explain the preference of investors on gold. In summary, the results from the augmented version of the baseline model of Eq. (11) are similar to those of the original baseline model of Eq. (4), implying robustness of our results. The estimated signs of the interest rate coefficients are identical to the original model, while the implications from the effective exchange rate remain inconclusive. Furthermore, the additional variables provide quite important evidence. 6.2. Augmented PSTR of the alternative model The augmented version of the alternative PSTR model is the following

PGj, t = µj +

t

+

01 EqREERj, t

+

02 i j, t

+

03 GDPj, t

+

04 Mj, t

+(

11 EqREERj, t

+

12 i j, t

+

13 GDPj, t

+

14 Mj, t ) g (qj, t ;

, c ) + u j, t , (12)

As before, we include two more control variables (GDP and M) in Eq. (5). However, we keep relying on the same theoretical assumptions. As in Eq. (5), we exogenously set the misalignment rate as the threshold variable. Next, we test the linearity hypothesis and once it is rejected we define the number of the regimes. As shown in Table 9, linearity is strongly rejected, while the null hypothesis that there is only one threshold (i.e., two regimes) cannot be rejected. Thus, the augmented alternative model is a tworegime PSTR model with monotonic transition function. The estimated slope and location parameters are = 0.430 and c = 3.497 , respectively, and are close to the ones of the original version of Eq. (5). Moreover, as shown in Figs. 6 and 7, the two transition functions follow the same pattern. Moving to the significance and signs of the estimated parameters, the results for the equilibrium real effective exchange rate and the nominal interest rate remain the same with those of Eq. (5). No matter the inclusion of more control variables, the implications derived from the estimation of Eq. (5) remain unchanged, implying robustness of our results. Regarding GDP, both estimated parameters are statistically significant. The parameter in the linear part is negative ( 03 < 0 ), while the one in the transition function is positive ( 13 > 0 ). As in the augmented baseline model above, the negative sign in the linear part implies that demand for gold decreases because investors choose among an extended set of assets when the economy grows. However, the positive sign in the 24

This evidence is also in line with Murach (2019), who reports a positive long run relationship between real gold price and excess liquidity. 43

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transition function shows that this negative relationship between gold price and output weakens when the misalignment rate is high (i.e., tends towards the upper regime). In other words, investors are anxious when the misalignment rate increases and invest in safer choices, such as gold. Regarding money supply, the positive parameter 04 in the linear part of the model is consistent with the

analysis of the augmented baseline model of Eq. (11). However, the negative parameter in the transition function ( 14 ) implies that investors are less willing to invest even in gold when the misalignment rate is high. The impact of monetary expansion remains positive but, it becomes less strong as the transition function tends towards the upper regime (i.e., high misalignment rates). A possible explanation for this result is that investors withhold the extra money supply and thus, total investment spending decreases.25 In summary, the above findings imply robustness of the alternative model. Furthermore, the results from the estimation of the augmented PSTR model of Eq. (12) provide important findings concerning the additional variables.

7. Conclusions In this paper we investigated the conjecture that the price of gold is affected by the internal and external macroeconomic performance of the G7 countries, namely Canada, France, Germany, Italy, Japan, the UK and the USA. This overall macroeconomic performance is mainly proxied by the REER, which embodies the critical issue of competitiveness. However, the use of the REER may not tell the whole story. As a currency depreciates, investors prefer to invest in gold rather than in the depreciating currency. However, as a currency appreciates, investors will prefer this currency instead of gold only if this appreciating trend is consistent with equilibrium. Thus, the equilibrium values of the REERs and their implied misalignment rates have been taken into account, along with the nominal interest rates. In addition, more control variables, such as real output and money supply, have been employed to ensure robustness and enrich the discussion. For estimating the equilibrium REER, we used panel cointegration techniques that have been strengthened with the theoretical assumptions of an external balance model. We also incorporated some dummy variables for capturing the effects of several important events took place during the sample period. For exploring the possibility that the impact of the equilibrium REER on the gold price may be nonlinear, we estimated a Panel Smooth Transition Regression model. Our evidence suggests that the impact of the exchange rate on the price of gold changes as the magnitude of the misalignment rate (threshold variable) changes. For low misalignment rates, the income effect is shown to be more important, but as the misalignment rate moves close to the upper regime (i.e., the transition function is close to one), the substitution effect prevails. The income effect reflects good macroeconomic performance and confidence which arise from stable and not highly misaligned currencies. As a consequence, investment in gold and in other assets increases. On the other hand, the substitution effect implies that investors avoid investing in highly misaligned currencies. In such a case, they substitute currency investment with gold investment. Regarding the relationship between the interest rate and gold, our evidence shows that when the interest rate increases normally, investors exchange gold with other assets due to the higher opportunity cost of holding gold.26 In contrast, when the interest rate increase is rather high (i.e., the transition function tends towards the upper regime), investors are less willing to sell gold for higher return assets. Investors worry about future financial instability and invest in gold to offset the increased risk. Similar implications have been reported by a number of scholars in the literature (see, inter alia, Baur & Lucey, 2010; Beckmann & Czudaj, 2013; Beckmann, Berger, & Czudaj, 2015). The above findings provide a clear-cut answer to the main question this paper aims to answer. What should matter for investors is not just the appreciating trend of exchange rates, but whether this trend is consistent with equilibrium. If the latter is the case, economic stability is enhanced and investment in gold and other financial assets increases. Overall, there is evidence that gold serves as a hedge only in periods of economic turmoil, which, however, may be harmful for several economies. This implies that domestic authorities (i.e., central banks and governments) should implement suitable monetary and fiscal policies in order to prevent high misalignment rates for their currencies, especially in periods of economic and financial instability. Appendix The balance of payments (BP) is described by the following expressions:

BPt = CAt + KAt ,

(A1)

CAt = (Xt

Mt ) + rt NFAt ,

(A2)

NXt = (Xt

Mt ) =

KAt = (rt

rt + Et [REERt + k ]

1 REERt

2 yt

+

3 yt

(A3)

,

(A4)

REERt ),

where CAt is the current account, KAt is the capital account, Xt and Mt represent exports and imports, respectively, rtNFAt stands for net interest payments on net foreign assets, NXt represents net exports, yt ( yt ) is the home (foreign) income and rt (rt ) is the home 25 This could be the case of the combination of high misalignment rates and very low interest rates. Obviously, this mechanism is not applicable to the augmented baseline model, in which the upper regime coincides with high interest rates. 26 This result is consistent with theory and previous evidence in the literature (see, for example, Baur, Beckmann, & Czudaj, 2019).

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North American Journal of Economics and Finance 49 (2019) 27–46

N. Giannellis and M. Koukouritakis

(foreign) real interest rate. In order to get the real exchange rate which is consistent with balance of payments equilibrium, we substitute (A2)–(A4) into (A1):

REERt =

1 1+

Assuming that

2

REERt =

1

2

rt NFAt

=

3

1 +

1

yt +

+

3 1

+

yt +

1

(rt

+

rt ) +

1

+

Et [REERt + k ].

(A5)

= , Eq. (A5) can be written as follows:

rt NFAt

1

(yt

+

yt ) +

1

+

(rt

rt ) +

1

+

Et [REERt + k].

(A6)

The next step is to extend the balance of payments exchange rate equation by formulating the future value of the REER. For the next period (t + 1), the expected value of the REER is:

Et [REERt + 1] =

1

1 +

Et [rt + 1 NFAt + 1

(yt + 1

yt + 1 )] +

1

+

Et [(rt + 1

rt + 1)] +

1

+

Et [REERt + 2].

(A7)

After k periods, the REER becomes:

If k

k 1

1 1+

REERt =

k

1 1+

REERt =

1

i=0

, then lim

(

Et [rt + i NFAt + i

+

) E [REER

t+k]

t

k 1

(yt + i

yt + i )] + i=0

k

1+

k 1

i

1

+

1

k

Et [(rt + i

+

rt + i )] +

1

+

Et [REERt + k ]. (A8)

= 0 . Thus, the REER can be written as: k 1

i

i=0

k

Et [rt + i NFAt + i

(yt + i

yt + i )] + i=0

k 1

+

Et [(rt + i

rt + i )].

(A9)

Eq. (A9) shows that the REER is forward-looking and depends on current and future values of real income differential, real interest rate differential and net foreign asset position. Assuming that current fundamentals, which are assumed to follow a random walk process, are a good forecast of future fundamentals, the equilibrium REER equation is presented by Eq. (A10), which is the one provided in Eq. (3):

REERt =

0

+

1 NFAt

+

2 (yt

yt ) +

3 (rt

(A10)

rt ).

An increase in the net foreign asset position is expected to appreciate the REER due to higher net interest receipts. Regarding the real income differential, its impact on REER is not straightforward. As noted above, traditional theory implies a decrease of net exports when home income increases, but recent studies have reported evidence that this is not always the case. According to this view, high-income countries can exploit new capabilities (i.e., greater access to capital) so that to develop high quality products and increase their exports. The latter may cause real appreciation of the REER. Thus, we can consider the impact of income differential on the real exchange rate as ambiguous. Finally, a higher home real interest rate yield is expected to increase capital inflows at home and thus to cause home currency appreciation. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.najef.2019.03.018.

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