Nonlinear causality between oil and precious metals

Resources Policy 46 (2015) 202–211

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Resources Policy journal homepage: www.elsevier.com/locate/resourpol

Nonlinear causality between oil and precious metals Melike E. Bildirici a,n, Ceren Turkmen b a b

Yıldız Technical University, Department of Economics, Barbaros Bulvarı, 34349 Beşiktaş, Istanbul, Turkey Sakarya University, Geyve Vocational School, Banking and Insurance Department, 54700, Geyve, Sakarya, Turkey

art ic l e i nf o

a b s t r a c t

Article history: Received 31 October 2014 Received in revised form 25 March 2015 Accepted 1 September 2015 Available online 20 October 2015

This work aims to analyze the cointegration and causality relationship among oil and precious metals of gold, silver and copper by using nonlinear ARDL and two popular nonlinear causality tests; Hiemstra and Jones (1994), and Kyrtsou and Labys (2006) test for the period from 1973:1 through 2012:11 monthly. According to the asymmetric Kyrtsou and Labys test (2006) results, an interesting finding emerges; precious metal prices returns respond nonlinearly to shocks to changes in crude oil prices only at earlier lags. Symmetric case results imply that there is evidence for bidirectional causality between pairs of oil and gold price and oil and silver price. Moreover a unidirectional relationship emerge for oil and copper prices for the asymmetric positive case and no causality for other cases. According to Hiemstra and Jones causality test, bi-directional causality between gold and oil and copper and oil and a unidirectional Granger causality running from oil price to silver price have emerged. In this way, asymmetric Kyrtsou and Labys (2006) results and Hiemstra and Jones (1994) results are different. Although the tests do not provide consistent results for the considered commodities, it can be concluded that, our models grasped the nonlinear nature in the price discovery process, hence partially captured the nonlinearity between oil and gold markets and their important role in macroeconomy. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Oil and gold price volatility Non-linear ARDL Non-linear Granger causality Mackey Glass Model

1. Introduction Oil and precious metals like gold, silver and copper are strategic commodities which volatility of their price has received much attention. Crude oil is maybe the most strategic commodity, probably is an indicator for all price trends and vital for production processes. On the other hand, the price movements in gold and crude oil have an impact on changing the price trends of the whole commodity markets. In this way, investigating their relationship over price discovery helps to provide some information for both forecasting the crude oil price, the gold price and the potential effects on commodity markets. The volatility and influence of oil and gold price has become increasingly crucial for world economic development. The volatility of the precious metal prices depends on the rise-and-fall of the oil and gold price and sudden increase of oil price causes economic slowdown and increases of other commodity prices. Moreover, increase of oil price can be thought as a tax levied from oil exporting countries to oil consumers. Additionally, gold has been an important precious metal for many centuries, and it plays a role as a means of store of value n

Corresponding author. Fax: þ90 2122366423. E-mail addresses: [email protected] (M.E. Bildirici), [email protected] (C. Turkmen). http://dx.doi.org/10.1016/j.resourpol.2015.09.002 0301-4207/& 2015 Elsevier Ltd. All rights reserved.

especially in periods of political and economic instability. There is an evident advantage and outstanding position of gold. The role of the gold market in the large commodity market has received increasing attention by both academic world and real sector. As it will be mentioned in detail at subsequent sections, gold remains as a safe haven especially considering the remarkable fluctuations in oil price, such as first and second oil price crisis and 2006 oil price shock. During I. and II. oil crisis, gold prices have increased significantly, followed a relatively flat pattern till 2005 and began to rise afterwards1. It should be noted that, oil prices has also faced with price increases at that period. This work aims to analyze the cointegration and causality relationship between oil and precious metals by using nonlinear ARDL (NARDL) and two causality tests, namely; Hiemstra and Jones test (1994), and Kyrtsou and Labys (2006) test by Mackey Glass model. The main reason beneath using two different 1 The main difference between 2006–2007 oil price shock and earlier oil price shocks lies in the cause of the shocks. While the previous shocks are caused by physical supply limitation, the 2006–2007 crisis was caused by strong demand due to “Global Modernation Era”. In 1970s energy crisis, the major industrialized countries faced with oil shortages caused by interruptions in oil exports from Middle East due to political reasons such as the oil embargo against Israeli military or the Iranian revolution. Although the causes were different, the economic results were similar, such as decreases in consumption spending and demand in automobile and related industries.

M.E. Bildirici, C. Turkmen / Resources Policy 46 (2015) 202–211

nonlinear causality tests, as it will be brought up in subsequent sections, is for a cross check for the results. This study primarily focuses on the use of nonlinear models; the main reasons for this can be stated as follows. Due to the effects of economic circumstances, energy commodities and most of precious metals exhibit a nonlinear behavior over time, like an economic or financial variable. Hence, their interaction among them is also nonlinear. The theoretical and empirical roots of this nonlinear behavior may rely upon the fragibility of macroeconomic variables may possibly be caused by economic crises (e.g., 1970s crisis, OPEC decisions, ERM Crisis, 1994 Russian Crisis the 1997–1998 Asian Crisis, the 2008–2010 global financial crisis), wars and other geopolitical extreme events effective in supplier or demander nations (e.g. first and second oil price shock and 2006 oil price shock, the Arab Spring, increasing ISID terrorism), oligopolistic behavior in refinery and redistribution, production lags, and the structure of market competition. All the aforementioned factors may generate structural breaks, cause unexpected and asymmetric responses in the behavior of economic agents, hence distorting the “linear” world. Under these circumstances, the prices of the strategic economic commodities, namely oil and precious metals, are expected to exhibit a more complex behavior than a simple and stable relationship. According to the linear ARDL model and the traditional Granger causality testing procedure; series are assumed to be linear. As stated in Anoruo (2011), one of the shortcomings of the linear causality tests is that they are unable to detect non-linear relationships whether it exists. As mentioned above, macroeconomic data in the real world follow a pattern with breaks and in addition to this, oil and gold prices follow a nonlinear pattern. Combining this structure with the additional reasons mentioned above, we will use nonlinear models; ARDL and non-linear causality tests. The second part of the work is comprised of literature, the relationship among variables is given in the third part. Fourth section is devoted to the data and econometric methodology. While econometric discussion is the fifth section of the paper, the last part is the conclusion.

2. Literature Baur and Tran (2012) and Escribano and Granger (1998) analyze the long run relationship between gold and silver prices. Baur and Tran (2012) analyzed a sample period from 1970 to 2010 and examine the existence and stability of a long run relationship by following Escribano and Granger (1998). Escribano and Granger (1998), by using monthly data from 1971 to 1990, found cointegration has occurred during some periods and especially during the bubble and post bubble periods. In addition to that, Baur and Tran (2012) studied the role of bubbles and financial crises for the relationship between gold and silver. Morales and Andreosso-O’Callaghan (2011) found that gold dominates precious metals for volatility spillover. Sensoy (2013) investigated the dynamic relationship among four precious metals, namely; gold, silver, platinum, palladium, between 1999 and 2013. According to his findings, gold shows a unidirectional shift contagion effect on other precious metals, in addition to this; silver has a unidirectional shift contagion effect on platinum and palladium. Cochran et al. (2012) found that, following the 2008 crisis, the volatility of gold platinum and silver returns have increased. Their finding is inconsistent with the study by Vivian and Wohar (2012) who did not find any exceptional volatility increase during the crisis. Cashin et al. (1999), Hammoudeh and Yuan (2008), Lescaraoux (2009) Soytas et al. (2009), Sari et al. (2010), Narayan et al. (2010),

203

Zhang and Wei (2010), Šimáková (2011), Wo and Hui (2012), Hsiao et al., (2013) and Naifar and Dohaiman (2013) are other studies that examine the relationship among gold and oil. Cashin et al. (1999), by using the data of seven commodities among 04.1960 and 11.1985, found a significant correlation between oil and gold. Hammoudeh and Yuan (2008), by examining the volatility behavior of three metals: gold, silver and copper; found that oil shocks had calming effects on precious metals excluding copper. Lescaroux (2009), investigating the correlations among crude oil and precious metals, states, most studies report that they tended to move together. Sari et al. (2010) particularly concentrates on the impact of oil price shocks over gold, silver, platinum and palladium by using the data of U.S. over 01.1999-10.2007. He found a weak asymmetric relationship among gold and oil prices. On contrary to this result, Soytas et al. (2009) investigated the long run and short run impacts of gold and silver prices on oil price. The linear causality approach of Toda-Yamamoto is applied to the data between 05.2003- 03.2007 but no causal relationship can be found. Narayan et al. (2010) examine gold and oil spot and future markets, concluding that; gold is a hedge against inflation and oil market can be used to predict gold market bi-directionally. Zhang and Wei (2010) investigated the causality between crude oil and gold market over the period January 2000 and March 2008. They found out a consistent trend between crude oil and gold price. Oil price linearly Granger causes the volatility of gold price but changes in gold price do not linearly cause oil price volatility. Šimáková (2011) focuses on the relationship between oil and gold prices. The existence of long run relationship between variables is shown by using Granger causality test, Johansen cointegration test and VECM. Wo and Hui (2012) examine the nonlinear dynamic relationship among USD/yen, gold futures, VIX, crude oil and several stock indexes. According to their findings, the role of gold is determined according to crude oil price. From this aspect; as the price of crude oil is low, gold exhibits the hedging function; when price of oil is high, gold is both a hedge and safe haven for developing countries. Hsiao et al., (2013) investigated the correlation among oil prices, gold prices and exchange rates over the period between 09.2007 and 12.2011. They conclude that the variables are considerably independent. Naifar and Dohaiman (2013) tested the nonlinear structure of oil prices by using several econometric methods and stressed the explanatory power of linear models. They compare and contrast linear models with regime switching models over the criteria of linear models' stationary distributions versus regime switching models' combinations of parametric distributions whose probabilities depend on unobserved state variables. Shortly, most of the studies explaining the link between gold and oil prices use inflation channel. As oil price rises, it leads to an overall increase in prices. The overall uncertainty at financial markets leads economic agents to buy gold as a hedging instrument. Hence, this explains the safe haven motivation.

3. Co-movement of oil and precious metals Volatility of oil and gold prices are important due to both their impact on each other and other metals. Oil prices, as stated in the introduction, fluctuate depending on many variables. Fluctuations in oil prices affect precious metals. In this context, gold can be ascribed a special place in precious metals. Gold is one of the most important precious metals that contain all the roles as a store of value and means of exchange. With these characteristics, gold is seen as a safe haven, especially in times of

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Fig. 1. Price changes of gold in the world (per ounce).

crisis. Although gold exhibits daily or weekly price volatility, the longterm price trend is important in reinforcing its safe-haven property. Fig. 1 shows the change of daily gold prices per ounce; as seen in the figure, gold remains as a safe haven in the long term, though short-term price fluctuations exist. During I. and II. oil crisis, gold prices have increased significantly, followed a relatively flat pattern till 2005 and began to rise afterwards. It should be noted that, oil prices has also faced with price increases at that period. The increase in gold demand should also be taken into account due to the fact that gold is both a consumer good and luxury good. The consumer good property should be taken into account while examining the price movements. Moreover, the effects of the presence of electronic gold transfers and availability of gold accounts in the banks should be considered In Fig. 2, yearly gold demand is shown according to its components. The blue line indicates demand for gold as jewelry, red line indicates gold demand for investment purposes and lastly, the gray line depicts gold EFT. According to the figure, stable demand trend is seen between 2004 and 2008, but after the 2008 crisis, increase in the demand for gold led to price increases. According to the gold report in 2013, total demand in 2013 has fallen 15 percent in terms of tones, and 28 percent in terms of U.S. Dollars. The relationship between oil prices (right axis) and gold prices (left axis) is shown in Fig. 3. Fig. 4 has been drawn in the same manner as Fig. 3; showing the price relationships between copper, silver and oil. According to Fig. 5, the differentiation among the relationship between copper and gold is observed. Following the crisis after the 2008 crisis; while gold prices rose rapidly, a similar movement in copper prices is unprecedented.

4. Data and econometric methodology 4.1. Data All of the data set used in this study was obtained from the World Bank World Development Indicators for the period from 1973:1 through 2012:11 monthly for price of oil, gold, silver and copper. Oil price is measured as op ¼log(OPt/OPt  1) and other variables were calculated as x ¼log(Xt/ Xt  1).

Gold price is expressed in US Dollar per troy ounce for 99.5% fine gold at London afternoon fixing average of Daily rates. Price data on oil is equally weighted average spot price of Brent, Dubai and West Texas Intermediate, expressed in US Dollar per barrel. Copper price is expressed in US Dollars per meter and trades at London Metal Exchange- (Grade A, minimum 99.9935% purity, cathodes and wire bar shapes, settlement price). Silver price is expressed in US cents per troy ounce and sourced from Handy and Herman (99.9% grade refined, New York) 4.2. Methodology Nonlinear ARDL models, Hiemstra and Jones (1994), and Kyrtsou and Labys (2006) causality tests are used in this study. In order to emphasize the nonlinear nature of the data, BDS test is used. 4.2.1. BDS test The most popular test for detecting nonlinearity is the Brock et al. (1987) (BDS) Test, which is designed for testing the null hypothesis of independent and identical distribution (iid) in order to detect nonlinearity and non-random chaotic dynamics. BDS test can be used to detect the remaining dependence and the presence of omitted nonlinear structure when it is applied to the residuals from a fitted linear time series model. One advantage of the BDS test is that it is a statistic which requires no distributional assumption on the data to be tested. Moreover, Brock et al., (1991) and Barnett et al., (1997) determined that the BDS test is powerful against a wide range of linear and nonlinear alternatives. It is possible to write down the procedures of the BDS Test (see Bildirici and Turkmen (2014) and Zivot and Wang(2003)) as follows: Given a time series xt for t¼ 1,2,3,…,Z and consider its m history as xtm = (xt , xt − 1, ... xt − m + 1) The correlation integral at dimension m can be estimated as follows: 1 Cm, ∈ = Z (Z − 1) ∑m ≤ s ≺ z ≤ Z ∑ I (xtm,xsm; ∈ ) where, Zm ¼Z  m þ1 m

m

and I(.) is the indicator function which is equal to one if xt − i − xs − i ≺ ∈ for I ¼0,1,….,m  1 and zero otherwise. It is estimated the joint probability as follows:

Pr ( xt − xs ≺ ∈ , xt − 1 − xs − 1 ≺ ∈ , .... , xt − m + 1 − xs − m + 1 ≺ ∈ )

Fig. 2. Yearly gold demand (in terms of tones).

M.E. Bildirici, C. Turkmen / Resources Policy 46 (2015) 202–211

205

Fig. 3. Price changes of gold and crude oil.

The BDS test statistic can be stated as:

BDSm, ∈ =

Z

m Cm, ∈ − C1, ∈

sm, ∈

where sm,ϵ is the standart deviation of

C1,m∈.

Under fairly moderate conditions the test converges Z C m, ∈ − in distribution to N(0,1). 4.2.2. Nonlinear ARDL Following Pesaran et al. (2001), Shin et al. (2009), Nimmo et al. (2010,2013), Karantininis et al. (2011), Katrakilidis and Trachanas (2012), Bildirici (2013) and Bildirici and Turkmen (2014) consider nonlinear ARDL model. Nonlinear ARDL model is essentially an asymmetric extension of the linear ARDL approach to modelling long-run levels relationships developed by Peseran et.al. (2001). It is possible to write ARDL model as follows: m−1

Δyt = c + δyt − 1 + βxt − 1 +

∑

m

Bi Δyt − i +

i=1

∑ γi Δxt − i + εt i=0

(1)

In this paper, it is considered the following nonlinear cointerpreting regression yt = γ +xt+ + γ −xt− + ut , where γ + and γ −are the associated long run parameters and xt is a kx1 vector of regressors decomposed as

xt = x 0 + xt+ + xt−

(2)

where, xt+ and xt−are partial sums of positive and negative changes in xt t

x+ =

x− =

t

∑ Δxi+ = ∑ i=1

i=1

t

t

∑ Δxi− = ∑ i=1

max (Δxi , 0)

(3)

min (Δxi , 0)

(4)

i=1

After inserting these into the ARDL model, nonlinear error correction model between variables becomes as follows: m−1

Δyt = c +

∑ i=1

m

Bi Δyt − i +

∑ (φi+Δxt+− i + φi−Δxt+− i) + δyt − 1 i=0

+ β +xt+− 1 + β −xt−− 1 + εt

(5)

Where, Δ and εt are the first difference operator and the white

noise term and where φ+ = − δγ + and φ− = − δγ − The analysis in this study is finalized in in three steps. (1) The long run relation between the levels of variables, yt , xt+, xt− is explored by means of a modified F tests. δ = β + = β − joint null is tested (2) Long run symmetry (β = β + = β −) and short run symmetry m m ( φi+ = φi−or ∑i = 0 φi+ = ∑i = 0 φi− ) can be tested by using standard Wald tests. The null hypothesis of no cointegration among the variables ( H0: δ = β + = β − = 0) which imply no long-run relationship, can be tested by the bounds test of Pesaran et al. (2001). (3) Lastly, the standard asymmetric cumulative dynamic multiplier κy κy ρ ρ effects, which are defined as; zρ+ = ∑i = 0 κxt ++i and zρ− = ∑i = 0 κxt +−i t t i¼ 0,1,2,… can be used by using the asymmetric ARDL model. If ρ → ∞ then, zρ+ = γ + and zρ− = γ −. The asymmetric long run coefficients are measured as γ + = −β + /δ and γ − = −β −/δ The NARDL model accounts for the asymmetric short-run dynamics through the distributed lag part and the asymmetric longrun dynamics via a single common cointegrating vector. The NARDL model provides greater flexibility in relaxing the assumption of same order integration of time-series data; it allows for combinations of I(1) and I(0) variables. Besides its estimation simplicity, In addition to that, distinguishing between the absence of cointegration, linear cointegration and nonlinear cointegration is possible. Lastly, it performs better in testing for cointegration in small samples. As stated in Pesaran and Shin (1998) the ARDL model is known to correct perfectly for the endogeneity of I(1) regressors On the other hand, if the decomposed series are not I(1) then the degree to which any endogeneity is corrected will depend on the degree of persistence 4.2.3. Nonlinear Granger causality tests With the help of the standard linear Granger causality test Granger (1969), any possible linear relationship between two stationary variables is investigated. The existence of univariate Granger causality in that manner implies that a time series of Xt Granger causes a time series Yt whether the past of Xt helps to forecast the future of Yt after controlling for the past of Yt.

Fig. 4. Price changes of silver, copper and crude oil.

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Fig. 5. Price changes of copper, gold and silver.

On the other hand, if bivariate Granger causality is investigated, which involves estimating the kth order VAR Model, the variable considered Granger causes the other whether the joint significance of the parameters associated with the lagged values of the variable considered are given. Hence, if both sets of parameters are jointly significant, then there is evidence for causality. Since economic and financial series may exhibit nonlinear pattern due to high volatility and crises, standard linear Granger causality test may be inappropriate. In addition that, according to Varsakelis and Kyrtsou (2008) any evidence for causality relationship does not reveal information about the direction of the shocks and the absence of any symmetric causality relation does not exclude the existence of causality when nonlinearity and signs of causal effects are taken into consideration. Due to the fragility of our price series which are concerned in our models, we adopt the nonlinear and asymmetric causality test developed by Hiemstra and Jones test (1994), modified Baek and Brock (1992) and Kyrtsou and Labys (2006). There are two reasons beneath using two different nonlinear causality tests. First of all, Hiemstra and Jones (1994) test, modified Baek and Brock (1992) reveal information about the positive and negative nature of the shocks. In addition to this, while Hiemstra– Jones nonparametric test is free of distribution assumptions, Kyrtsou–Labys parametric test enables the detection of any possible asymmetry in the response of a variable to another. The other reason is a cross validation of the results.

the test; Suppose X stands for the residual series when the crude oil price change acts as the dependent variable and respectively Y implies the residual series when the precious metal price change is the dependent variable.

Xtm = ( Xt , Xt + 1, ....... Xt + m − 1), m = 1, 2, ... , t = 1, 2, ... XtLx − Lx

= ( Xt − Lx , Xt − Lx + 1, ....... Xt − 1), Lx = 1, 2, ... , t = Lx + 1, Lx + 2, ...

YtLy − Ly

= ( Yt − Ly, Yt − Ly + 1, ....... Yt − 1), Ly = 1, 2, ... , t = Ly + 1, Ly + 2, ...

Ly Ly Lx if Pr (‖Xtm − Xsm ‖≺e, ‖XtLx − Lx − Xs − Lx ‖≺e , ‖Yt − Ly − Ys − Ly ‖≺e ) Lx = Pr (‖Xtm − Xsm ‖≺e ‖XtLx − Lx − Xs − Lx ‖≺e )

it means; oil price changes does not nonlinearly Granger cause a change in precious metal prices. Also suppose if,

(

C1(m + Lx, Ly, e ) = Pr ‖Xtm−+LxLx − X sm−+LxLx ‖≺e , ‖YtLy − Y sLy− Ly ‖≺e − Ly

(

C 2 (Lx, Ly, e ) = Pr ‖XtLx − XsLx− Lx ‖≺e , ‖YtLy − Y sLy− Ly ‖≺e − Lx − Ly

(

C3 (m + Lx, e ) = Pr ‖Xtm−+LxLx − X sm−+LxLx ‖≺e

(

C4 (Lx, e ) = Pr ‖XtLx − XsLx− Lx ‖≺e − Lx

4.2.3.1. Hiemstra–Jones test. Due to the aforementioned nature of the linear causality tests, Baek and Brock (1992), concluded that nonlinear alternatives to traditional parametric linear Granger causality test is more powerful especially for the cases where nonlinearities can emerge such as market microstructure, noise traders, etc. Hence, inspite of imposing directly a linear functional form, various non-parametric techniques gained popularity in the literature. Baek and Brock (1992) method is a nonparametric method used for detecting nonlinear causal relations. The method depends on the assumption that the variables are mutually i.i.d. But the i.i.d assumption eliminates the time dependence of variables and also it does not consider the nature and range of the dependence. From this aspect, Hiemstra and Jones test (1994), modified Baek and Brock (1992) approach by reducing series' mutually and individually iid property, hence allowing short term dependence. In other words, Hiemstra and Jones (1994) test tries to determine the existence of nonlinear dynamic relations among variables by testing. As an alternative, Diks and Panchenko (2006) developed a new test statistic that takes the possible linear and nonlinear effects of cointegration into account “If the series are cointegrated, then causality testing should be based on a Vector Error Correction model (VECM) rather than an unrestricted VAR model” (Engle and Granger, 1987). When cointegration is not modelled, it leads to detecting linear and nonlinear causality between variables. In other words, efficiency hypothesis will suffer damage due to absence of cointegration relationships (Dwyer and Wallace, 1992). By adopting Hiemstra and Jones (1994) method for conducting

(6)

Then,

C1(m + Lx, Ly, e ) C2 (Lx, Ly, e )

=

)

)

)

)

(7)

C3(m + Lx, e ) C 4 (Lx, e )

The joint probability is expressed below in Eq. (8).

C1(m + Lx, Ly , e , n) 2 ∑ ∑ I Xtm−+LxLx , X sm−+LxLx , e = n (n − 1) t≺s

(

(

)

)

Ly • YtLy − Ly, Ys − Ly, e C2 (Lx, Ly , e , n)

=

2 n (n − 1)

(

•

YtLy − Ly,

∑ ∑ I ( XtLx− Lx , XsLx− Lx , e) t≺s

YsLy− Ly,

)

e C3 (m + Lx, e , n)

2 = n (n − 1)

∑ ∑ I ( Xtm−+LxLx , X sm−+LxLx , e)C4 (Lx, e, n)

2 = n (n − 1)

∑ ∑ I ( XtLx− Lx , XsLx− Lx , e)

t≺s

t≺s

(8)

Where t , s = max (L x, L y ) + 1, ............... T − m + 1, n

= t − max (L x, L y ) − m + 1 And function I (X , Y , e ) takes value is 1 when the maximum norm vector X and Y proves within the given parameter e and 0 otherwise.

M.E. Bildirici, C. Turkmen / Resources Policy 46 (2015) 202–211 a ⎡ C1( m + L x, L y, e) C3 ( m + L x, e) ⎤ ⎥ = n⎢ ⎢⎣ C2 ( L x, L y, e) C4 ( L x, e) ⎥⎦

W=

(

∼ N 0, σY2 ( m, L x, L y, e)

)

(9)

If W follows the asymptotical normal distribution as stated in Eq. (9), then we may say the change of precious metal prices does not nonlinearly granger cause the change of oil prices only if m , L x, L y ≥ 1, e≻0 and stationary and dependent residual series Y and X is given. Let CS be the difference between the two ratios in, i.e., CS ¼(C1/C2)  (C3/C4). The null of no causality is not rejected when CS is relatively close to zero. Under the assumption that {Xt} and {Yt} are strictly stationary, the asymptotic distribution of CS can be standardized as TVAL = n × CS/ σ 2  N (0,1). According to Baek and Brock (1992), the removal of linear predictive power from a linear VAR model results ina kind of nonlinear predictive power defined as any remaining incremental predictive power of one residual series for another. 4.2.3.2. Kyrtsou-Labys (2006) Test. Kyrtsou-Labys (2006) Test with Mackey–Glass model (M–G hereafter) is an extension of nonlinear Granger causality test. Statistically significant M–G terms suggests a nonlinear feedback as the generating mechanism of the interdependences between X and Y. The nonlinear causality test based on M–G model tries to find out any significant nonlinear effect caused by past samples of variable Y over variable X. Operationally, the test is similar to the linear Granger causality test, except that the models fitted to the series are M–G processes. Varsakelis and Kyrtsou (2008) and Kyrtsou and Labys (2006) created the M–G model. The model in these studies can be explained as follows; Xt = a11 Yt = a21

Xt − τ1 1 + Xtc−1τ1 Xt − τ1

1 + Xtc−1τ1

− δ11Xt − 1 + a12 − δ 21Xt − 1 + a22

Yt − τ2 1 + Ytc−2τ2 Yt − τ2 1 + Ytc−2τ2

− δ12 Yt − 1 + εt − δ 22 Yt − 1 + ut

(10)

Where ut , εt ∼ N (0, 1) , t = τ , ..... , N , τ = max (τ1, τ 2), X0 , .... X τ − 1, Y0, .... Yτ − 1 and αij, and δij are the parameters to be estimated, τi are integer delays, and ci are constants. Kyrtsou-Labys test is carried in two steps; first the unconstrained model of the given series is estimated by using OLS. In the second step, a second M–G model under the constraint of “α12 ¼0” is estimated in order to test for causality. Kyrtsou-Labys test statistic, which follows an F distribution, can be derived from the SSRs of the constrained and the unconstrained model, such (S − S ) / n that; SF = S /c (N −u n restr ∼ Fnrestr , N − nfree − 12 − 1) u

free

If the test statistic is greater than a specified value, then we reject the null hypothesis that Y causes X. The test requires prior selection of the best delays (τ1 and τ2) on the basis of likelihood ratio tests and the Schwarz criterion. In addition to testing symmetric effects in the way explained above, if one is interested in investigating the causal relationships in an asymmetric manner, in other words whether those relationships hold between the identified pair when conditioning for positive or negative returns, should set conditions on the causing series being nonnegative or nonpositive. Briefly, to test whether nonnegative returns in the series Y cause the series X, an observation (Xi,Yi) is included for regression only if Y(t  τ2) Z 0. In the second step constrained model will be estimated by the same restriction mentioned above, by this way

2

Assuming; nfree is the number of free parameters in our M–G model and nrestr-1 is the number of parameters set to zero when estimating the constrained model. Further information can be found in Varsakelis and Kyrtsou (2008).

207

Kyrtsou-Labys test statistic can be calculated. In investigating whether positive returns in X cause Y, the procedure is then repeated, with the order of the series reversed and again with the subset of observations that correspond to non-positive returns (Varsakelis and Kyrtsou, 2008). From this aspect, sign conditioning is chosen due to its practical advantages. Additionally, the nonpositivity, or nonnegativity subset is not the only possible way of conditioning, other events such as start/end of the week, price movement thresholds can also be used. As stated in Varsakelis and Kyrtsou (2008) detection of Kyrtsou-Labys causality relationship gives information on the significance of a positive or negative shock. From this aspect, it is a way to “sharpen” the usual version of causality testing in which the series being tested are considered in their entirety.

5. Econometric results In order to test for cointegration and causality relationship between oil and precious metal prices, the econometric procedure implemented is as follows. The empirical analysis includes Unit Root Test, BDS test, nonlinear ARDL and nonlinear Granger causality tests. 5.1. The results of unit root tests and BDS test The method is applied on the following empirical model; ln xt = f (ln op+ , ln op−), where ln op+ and ln op−are the partial sums of the positive and negative changes of oil price. ARDL method, can be used irrespective of the regressors' order of integration but it must be ensured governmens that variables are not I(2). The unit root tests are used to determine whether the variables are I(0) or I(1). First, the order of integration of the long-run relationships among the variables is defined using ADF and ERS unit root tests. According to the results stated in Table 1 below, ADF and ERS unit root tests conclude that the OP, GP, SP and CP variables for countries are stationary in the first differences. As stated in Pesaran and Shin (1998) the ARDL model is known to correct perfectly for the endogeneity of I(1) regressors On the other hand, if the decomposed series are not I(1) then the degree to which any endogeneity is corrected will depend on the degree of persistence. 5.2. BDS Results Table 2 indicates all the test statistics are greater than the critical values significantly. Thus, the null hypothesis of i.i.d. is rejected at 5% significance level. The results strongly suggest that the series are non-linearly dependent at all dimensions. 5.3. ARDL and NARDL results We

tested

the

existence

of

cointegration

via

using

Table 1 Unit root test results. ADF

OP GP SP CP

ERS

Level

First Diff

Level

First Diff

 0.00003  0.048 0.00108 0.0052

 19.533  26.992  8.765  5.876

24.82774 7.848038 5.451738 7.24785

2.282510 0.393326 1.729767 0.139870

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Table 2 BDS test results.

Table 3b NARDL estimation resulta.

BDS test statistic Embedding dimension (m)

OP GP SP CP

2

3

4

5

6

50.05233 43.49161 44.90098 52.82386

53.22617 46.20860 47.23889 55.15439

57.21670 49.73710 50.12260 58.01877

63.17123 54.97142 54.40723 62.36797

71.38874 62.16631 60.23954 68.38484

Table 3a Bounds test results. Dependent variable

GP SP CP Outcome

F statistic Linear

Nonlinear

1.981 2.001 1.856 No-cointegration

5.1308 5.18 4.788 Cointegration

n

unrestricted error correction model. Δln yt = co + ∑i = 1 Ai Δln yt − 1

m + ∑i = 0 Bi Δln

opt − 1 + C1 ln yt − 1 + C2 ln opt − 1 + et (yt is a representative for GP, SP and CP). The lag structure of the model is chosen based on the Schwartz Information Criterion as suggested by Paseran et.al (2001). As it is seen in the Table 3a, there is evidence in favor of the non-rejection of the null hypothesis of no cointegration. This result may be due to the nunlinear structure of the variables. Conditionally, the results of the nonlinear ARDL model should be investigated. First of all, we tested the following model; m−1

Δ ln xt = c0 +

∑ i=1

m

βi Δyt − i +

∑ (φi+Δopt+− i + φi−Δopt−− i ) + δyt − 1 İ=0

+ β +opt+− 1 + β −opt−− 1 + εt Table 3a shows that the results obtained determine statistically significant evidence in favor of the existence of a long run cointegrating relationship. From the bounds test, since the F statistics, exceed the critical upper bound, we come to the conclusion that the three variables; GP, SP and CP, investigate in the long run nonlinearly. Table 3b exhibits the results of the short and long-run symmetry tests for pairs of oil price and precious metal prices. The existence of any long and/or short run asymmetric relationship can be detected by Wald test. Wald test for short-run symmetry and the Wald test for long-run symmetry are shown as WSR and WLR. According to the results, the Wald tests are able to reject the null hypothesis of no long run/short run asymmetric correlation between price changes. We first concentrated on short run dynamics of the models. The null hypothesis of symmetry against the alternative of asymmetry in short run impacts was analyzed with the Wald test. The results suggest the rejection of the null hypothesis of a weak form symmetric adjustment (WSR). L op+ and L op− in Table 3b indicate that there is a mechanism to correct the disequilibrium between oil prices and prices of precious metals. The coefficients of asymmetric long-run multipliers ( L op+ , L op−) are both statistically and economically significant, exhibiting the speed of adjustment to the equilibrium after a shock. When the long run coefficients of the L op+ and L op− are

lnx ln op þ ln op  Δlnxt − 1

Δlnopt+− 1

Model 1 Dependent variable: GP

Model 2 Dependent variable: SP

Model 3 Dependent variable: CP

0.846680(2.148) 1.0278(11.53) 0.4791(1.9298) -0.17998(2.11)nn 0.102(2.133)nn

0.805817(1.895) 1.07173(2.724) 0.53514(2.339) -0.1001(2.11)nn 0.045(1.911)nnn

0.81175(2.48) 3.2388(2.924) 4.51876(1.936) -0.09945(2.11)nn -0.1001(3.21)n

-0.019(0.036)

0.0413(1.769)nnn

-0.332(1.89)nnn Δlnop− t−1 + Lop − Lop

1.214

1.33

3.99

0.5659

0.6641

-5.5667

R2 WLR WSR

0.736412 16.11 20.45

0.674386 58.68 4.684

0.806116 11.780 6.059

a L op+ and L op− denote the long-run coeffcients associated with positive and negative changes of oil price. WLS refers to the Wald test of long-run symmetry (i.e. L op+ ¼ L op− ) while WKS denotes the Wald test of the additive short run symmetry condition. It is given t value in parenthesis short-run coefficients are accepted at a significance level of n 1% nn 5% and nnn 10%

investigated for Models 1 and 2, coefficient signs are seen to be determined as positive. For model 1, the estimated long run coefficients L op+ and L op− are determined as 1.214 and 0.5659. A %1 increase in the oil price causes a 1.214 rise in gold price and %1 decrease causes 0.5659 decline in gold price. Our results showed the asymmetric effect for positive change. The long run relationship among gold and oil reveal that prices are stickier upwards that support the validity of an asymmetric comovement. The evidence of any possible long run relationship between oil and gold can be explained from several aspects. First of all, as a primary production input, high crude oil price increases inflation. On the other hand, gold has an excellent nature to resist inflation and maintain its value, hence becoming an effective tool against inflation. So the increase of oil price ends up with a surge of gold demand and ending up with an increase in its price. Secondly the main oil exporting countries invest their profits into gold in order to maintain commodity value, which also increase the gold price parallel to oil price increases. Lastly, gold and crude oil as the representatives of the large commodity markets, are influenced by the same eco-political events. In Model 2, the long run coefficients of Lop are 1.33 and 0.6641. Positive change in the oil price of 1%, results in an increase of 1.33% in silver price. The size of the negative long run coefficient is small, implying a sticky negative change. Regarding the Model 3, the signs of the long run coefficients L op+ and L op− are expected to be positive, any opposite case is out of expectation. From this aspect, for model 3, since the sign of negative long run pass-through coefficient is negative, it is left behind for our analysis. Moreover, although L op+coefficient is econometrically significant, if its magnitude is considered, we can see that it is comparably high, showing a 3.99% increase against a 1% increase in oil price. This high magnitude of long run relationship between oil and copper can be explained by international trade. Copper is a metal that is subject to international trade. Industrial use of copper is higher than silver and gold and due to its dry bulker property, a 1% increase in oil prices leads to a 3.99% copper price increase. This result is contradicts with the findings of the study by Franses and Kofman (1991), investigating the relationships between copper, lead, zinc, nickel and aluminum. They conclude that there is a cointegrating relationship with the copper price, immediately reacting to disequilibrium errors, hence being less

M.E. Bildirici, C. Turkmen / Resources Policy 46 (2015) 202–211

exogeneous than other metals. In addition to that Cerda (2007) identifies the most important effect over the price of copper during the period between 1994 and 2003 is the demand from large economic blocks. To sum up, first noticeable observation is changes in oil price are passed through gold and silver in the long run and the effects are much more pronounced when the oil price increases. It is worth noting that the behavior of the oil price changes is asymmetric; meaning that economic agents are more willing to increase the prices of precious metals in the case of a increments in oil prices, but they are less sensitive to decreases in oil prices. This finding supports the validity of imperfect market structure. The asymmetric short-run coefficients of precious metal prices are smaller than 1% and are accepted at a significance level of *1%, **5% and ***10%. As for the short run, our results provide evidence for the presence of asymmetry. From table 3 we observe that a negative change in oil price ( Λopt−− 1 ) is not significant in model 2, between oil price and silver price. However it is significant in the case of gold and copper, indicating an immediate decline of 0.3% and 0.04% in gold and copper prices. When the opposite case of a positive change in oil price is considered ( Λopt+− 1 ), the coefficient for silver price turns out to be significant. On the other hand the coefficient for copper price becomes negatively signed. Although the short run elasticity coefficients of copper price are statistically significant, it is economically meaningless. Due to the fact that copper is only used in production instead of being used as a means of exchange or store of value, this result is not surprising. By the same way, silver is exhibiting only the property of being a luxury good; any condition resulting in a gold price decrease is also effective on silver prices. Regarding the responses of the gold prices to the oil prices, we uncover a co-movement relationship in the short-run. On contrary to long run pass-through coefficients, the effects of changes in the gold prices are much more pronounced in the case of a fall than when the prices go up. Sarı et al., (2007) found that oil and silver were shortly related in developed countries and they also displayed the inner relationship mechanism of oil and precious metals. Ciner (2001) state that, the long-term relationship between gold and silver in Tokyo Commodity Exchange is absent in 1990's. On contrary to these results, Zhu et.al (2015) state that, international oil price is an important factor for precious metal prices volatility in long and short term. Zhang and Wei (2010) state that the relation coefficient of prices of gold and oil was 0.9295, in addition to that these economic commodities exhibit a long-term equilibrium relationship. In the study by Sari et.al (2010), a weak long-term equilibrium relationship among precious metal prices, oil prices and exchange rate was found. Comparing these results with our findings, our findings indicate that the impact of oil price increases over metal commodity price changes is larger than that the impact caused by oil price decreases. Shortly, the changes in oil price are passed through to gold in the long run for positive and negative changes in oil price. The long run relationship among gold and oil reveal that prices are stickier upwards that support

209

the validity of an asymmetric co-movement. 5.4. Causality results The non-linear ARDL method does not indicate the direction of causality, but there is a long-run relationship among oil price and other variables. The main reason beneath using two different nonlinear causality tests of; Kyrtsou- Labys test with Mackey– Glass model and Hiemstra–Jones test, is due to attempting a crossvalidation. 5.4.1. Results from the Hiemstra–Jones test Table 4 presents the results from the Hiemstra–Jones test, based on the residuals of a VAR model. According to non-linear ARDL results, at least a single directional causality relationship must exist. Table 4 presents the empirical results from Hiemstra–Jones's nonlinear causality test for lag lengths of one to six lags. We determined bi-directional causality between gold and oil price.We find significant unidirectional Granger causality running from oil price to silver price. An interesting result, it was determined among oil and copper, for the pair of op and cp, the null hypothesis of no causality is strongly rejected at first two lags, in both ways. This result, implying a bidirectional relationship, is out of our expectations in such a manner that any price movement from cp to op should not have any meaning characterized “strongly”. One possible explanation may be the non-parametric structure of the model. 5.4.2. Results from the Kyrtsou–Labys tests At Table 5, the symmetric and asymmetric results from nonlinear Granger causality test are shown. As stated in Diebolt and Kyrtsou (2006), when nonlinear causality is identified, there is a strong possibility that a small variation in one variable can lead to an abnormal behavior of the others. We first carry out the symmetric version of the nonlinear Granger causality test, and report the results at the first row. The results of the symmetric case implies that there is evidence for bidirectional presence of synchronicity for causality between oil price (op) and gold price (gp) and oil price (op) and silver price (sp). By contrast, in the third case of oil and copper; there was no evidence of nonlinear Granger causality both for the symmetric and asymmetric cases, in other words, our findings show no causality in both directions for the variables (op and cp) at the conventional levels of confidence. Considering the results of different causality tests, divergent conclusions over the relationship between op and cp has emerged. Although Kyrtsou–Labys test results determine a unidirectional relationship for the asymmetric positive case, no causality has emerged for symmetric and negative case. There is a significant bidirectional causality between op and gp in positive and negative changes. In addition to that, when op and sp pair is considered, we examine a unidirectional causality running from positive changes in oil price to changes in silver price. Generally speaking, the fact that negative changes in silver prices

Table 4 Hiemstra–Jones causality test results. Laga

Δop-Δ gp

Δgp-Δop

Δop-Δ sp

Δsp-Δop

Δop-Δ cp

Δcp-Δop

1 2 3 4 5 6

5.15020 0.8418 1.08615 1.81746 0.92465 1.05642

2.29140 3.7682 0.7618 2.01746 1.007642 1.117642

8.12135 2.1752 0.1946 3.0012 1.00782 0.7146

0.9156 0.0576 1.0364 1.0561 0.0017 0.1816

11.4256 4.1862 0.0056 2.01156 0.8715

3.1856 3.05276 1.1752 7.01872 0.04657

a

We consider the null hypothesis that A does not cause B.

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Table 5 Kyrtsou–Labys causality test resultsa, Symmetric case F-statistic

b

Asymmetric (P) case F-statistic

Asymmetric (N) case F-statistic

Δop-Δgp 3.245*

4.84*

3.956*

Δgp-Δop 3.23*

4.21*

1.001

Δop-Δsp 3.789*

3.184*

0.891

Δsp-Δop 3.643*

0.21

0.16

Δop-Δcp 0.1789

0.184

0.22

Δcp-Δop 0.1643

0.21

0.16

a We consider the null hypothesis that A does not cause B. An asterisk indicates significance. b Asymmetric (P) and Asymmetric (N) indicate asymmetric case for positive and negative changes in the causing variables, respectively.

do not lead oil price changes implies that the information contained in negative precious metal price shocks cannot significantly improve the ability to predict the oil price changes. Considering the results of different causality tests, divergent conclusions over the relationship between op and cp has emerged. Although Kyrtsou–Labys test results determine a unidirectional relationship for the symmetric case, no causality has emerged for positive and negative case. Our results reinforce the related literature in showing that oil prices and gold prices interact in a nonlinear manner. This finding implies that, economic actors can take the price movements in these two markets into account in order to promote stability and economic growth. This empirical evidence appears to be parallel to the results of Narayan et al. (2010) and Lescaroux (2009). When gold and oil spot price relationship is considered, it is seen that they are affecting each other bi-directionally. Additionally, some unidirectional nonlinear causal linkages occur in the Kyrtsou–Labys case. The Hiemstra and Jones results imply that causality can vary from one direction to the other at any point in time, hence implying a changing pattern time. By the way, it can be safely concluded that, both gold and oil markets play an important role in price discovery process in this respect. Our models partially captured the nonlinearity between oil and gold markets and oil and silver markets statistically significant at lower-order moments, but this is not supported in the case of copper and oil price relationship.

6. Conclusions The market dynamics of oil and precious metal prices have gained attention in recent years. In this article, we investigated the relationship between the oil and three precious metal price, namely gold, silver and copper by NARDL model in order to capture the asymmetric responses of their prices to negative and positive changes in the oil price and both over the short- and the long-run. Using monthly data for the period 1973-2012, we find that the oil prices have long-run asymmetric effects on precious metal prices. Changes in oil price are passed through to gold in the long run for positive and negative changes in oil price. The long run relationship among gold and oil reveal that prices are stickier upwards that support the validity of an asymmetric co-movement. Another noticeable observation is changes in oil price are passed through silver in the long run and the effects are much more pronounced when the oil price increases. For the case of copper,

Lop−is insignificant and positive long run pass-through coefficient is higher than gold and silver, which can be explained by international trade. The short run elasticity coefficients of copper prices are statistically insignificant and have signs opposing to other metals. Due to the fact that copper is only used in production and trade instead of being used as a means of exchange or store of value, this result is not surprising. Kyrtsou–Labys and Hiemstra–Jones causality tests are used together in order to attempt a cross-validation. With the use of the M-G model, we concretized non-linearity and hence arrived at results that can help researchers to understand the relationship among oil and precious metal prices. The results of two nonlinear causality tests show divergence at some time. The main reason of these differences can be explained by the ways in which the tests are constructed. From this aspect, while Hiemstra–Jones nonparametric test is free of distribution assumptions, the Kyrtsou–Labys parametric test enables capturing any possible asymmetry in the response of a variable to another. According to the asymmetric Kyrtsou and Labys test (2006) results, an interesting finding emerges; precious metal prices returns respond nonlinearly to shocks to changes in crude oil prices only at earlier lags. According to Hiemstra and Jones causality test, bi-directional causality between gold and oil and copper and oil and a unidirectional causality running from oil price to silver price have emerged. In this way, asymmetric Kyrtsou and Labys (2006) results and nonlinear Granger causality results are different. Although both tests do not provide the same results, the main argument can be the linear causality tests' inability to provide correct assessment of the true relationships between variables analysed with underlying nonlinear nature and may suggest misleading policy actions. Moreover, it can be concluded that, our models grasped the nonlinear nature in the price discovery process, hence partially captured the nonlinearity between oil and gold markets and their important role in macroeconomy. As stated above, crude oil is maybe the most strategic commodity, probably is an indicator for all price trends and vital for production processes. Specially, gold is used in various sectors and is viewed as the most influential metal due to its functions; such as storage of value, reserve for money, safe haven property as an anti-inflation shelter and financial investment instrument. From this aspect, oil and precious metals are considered as leading indicators of inflation. In other words, the pro-cyclical characters of precious metals provide important information as to where finance and macro economy are heading. Similarly, silver is also used in various sectors in production processes. Further, it can serve as a hedging instrument in investment portfolios. Accordingly, we can conclude that, due to the devastating effects of the recent financial crisis, portfolios are reallocated. Besides money, precious metals gained importance for serving as an alternative investment instrument. The price movements in gold and crude oil can have an impact on changing the price trends of the whole commodity markets. In this way, investigating their relationship over price discovery helps to provide some information for both forecasting the crude oil price, the gold price and the potential effects on commodity markets. The results from this study have important policy implications. First of all, especially negative oil shocks will be persistent in gold and silver and positive oil shocks will be persistent in gold prices. The persistency property in both gold and silver is important for monetary policy especially with respect to inflation targeting. Therefore, strong policy measures need to be adopted to ensure that gold price returns to its original trend.

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