Cointegration and Causality among Dollar,Oil,Gold and Sensex across Global Financial Crisis

Abstract

Over the globe, the various financial markets are becoming integrated and the linkages among variables Gold prices, Crude Oil prices, US Dollar rate and Stock market (GODS) invite a special attention of various financial analysts and investors. For an import-dependent country like India, the interplay among these variables is vital. Thus in this study, we investigate the cointegration and causality relationship among gold, crude oil, us dollar and stock market (Sensex) across the global financial crisis of 2008. We use Johansen's cointegration technique, Vector Error Correction Model (VECM), Vector Auto Regression (VAR), VEC Granger Causality/Block Exogeneity Wald Test and Granger Causality, and Variance Decomposition to study cointegration and strength & direction of causality for three sub-periods. Johansen's cointegration test results indicate that there is long-run equilibrium relationship among the variables in the pre-crisis and the crisis periods but not in post-crisis period. VECM results report that none of four models of the variables show long-run causality in the pre-crisis period at 5% level of significance. During the crisis period, both crude oil and Sensex models show long run causality. However, in some cases short-run causality is indicated in results. Granger causality test results show that there is one-way causality from USD and Sensex to crude oil, and from gold and Sensex to USD. Thus, we conclude that the relationship among GODS is dynamic and has been affected by global financial crisis of 2008.

Keywords

Cointegration Causality Crude Oil Gold Dollar Stock Market

Introduction

Gold and crude oil are the two most important commodities that are demanded and traded internationally. Crude oil is the most important source of energy worldwide accounting for about one-third of world’s energy. India is the world’s second largest consumer and importer of gold. Since the time of gold standards, gold has been used as a part of reserves by governments. Even after the subside of Bretton Woods system and beginning of flexible exchange rate system, gold is still used as reserves, but the proportion, in general, has reduced (Jain & Ghosh, 2013). It has been majorly replaced by US dollar (USD). Also, USD comes across as the global currency, and hence most of the trades done internationally are in the dollar. Gold and crude oil prices are quoted in USD. Thus, the fluctuations in USD are transmitted to an economy through the international trade and hence to the stock market through the expectations of increase or decrease in profits of corporate. On the other hand, a shock to gold or crude oil prices may affect the exchange rate.

Over the globe, the various financial markets are becoming integrated, and the linkages among variables gold prices, crude oil prices, USD rate and stock indices (GODS) invite a special attention of various financial analysts and investors. For an import-dependent country like India, economic theory suggests that increase in crude oil price results in inflation, depreciation of home currency (Indian rupee) and fall in the stock market. To manage inflation risk, investors start purchasing gold that in turn results in a rise in gold prices. Since a significant part of gold demand is met through imports, this further influences exchange rate and vice versa. The available literature presents different findings on the relationship among these variables. A hike in oil price influences stock market returns (Jones & Kaul, 1996). Crude oil bears a positive long-run connection with the stock market indices fluctuations (Sahu, Bandopadhyay, & Mondal, 2014). Lizardo and Mollick (2010) suggest a positive relation between crude oil prices and home currency of Organization of the Petroleum Exporting Countries (OPEC). Moreover, the relationship between crude oil and USD has varied dynamically from positive to negative since 1973 (Samanta & Zudeh, 2012). In many cases, we do not find literature’s resonance with economic theory. Moreover, the economic theory fails to suggest answers to many related questions. For instance, whether a change in USD exchange rate causes changes in gold and crude oil prices or it is vice versa? Is it the stock market that leads gold or vice versa? Moreover, none of the studies in literature examines the relationship among these variables across the global financial crisis of 2008. Looking at the importance of these variables for different stakeholders namely MNCs, export–import houses, investment houses, government and so on, and failure of economic theory to expound the relationship among GODS, we are motivated to investigate the linkage and causality relationship among GODS across the global financial crisis of 2008.

Literature Review and Objectives of the Research

Levin, and Wright (2006) explore the relationship between price of gold and US price level and find that with the 1 per cent hike in general price level, there is 1 per cent increase in price of gold. They explain the positive relationship between gold with US inflation and negative relationship between gold and USD trade-weighted exchange rate and gold lease rate. Chen and Chen (2007) report that real oil price is the most critical factor that affects the real exchange rate. However, Han, Xu, and Wang (2008) analyse the relationship between Australian dollar rate, USD and gold price using interval method and ILS approach. They report a short- and long-run relationship between exchange rate and the gold price.

Narayan, Narayan, and Prasad (2008) examine the links between volatilities of crude oil price and Fiji USD rate using the generalized autoregressive conditional heteroskedasticity (GARCH) model. They find that an increase in oil price leads Fijian dollar to appreciate against USD. However, long-term equilibrium between crude oil and gold price and unidirectional linear causality between Sensex, oil and gold are reported by Zhang and Wei (2010) using cointegration and Granger causality approach. Lizardo and Mollick (2010) examine the role of oil price shocks in the determination of USD values. They conclude that with an increase in real oil prices, there is a substantial depreciation of USD against the currencies of the net oil exporter. The oil exporters currencies depreciate relative to the USD when the real oil price shoots up.

Using Johansen’s multivariate cointegration test and vector error correction model (VECM), Srivastava (2010) infers that the Indian stock market is more propelled by domestic macroeconomic factors and not by global factors in the long run. Basher, Haug, and Sadorsky (2011) report a negative response by oil prices to unexpected increase in oil supply and a positive response to unexpected rise in demand using the structural vector autoregression (VAR) model and the Dickey-Fuller generalized least squares (DF-GLS) test. In the effort to investigate the relationship between gold price, stock return, exchange rate and oil price, Sujit and Kumar (2011) report the fluctuations in gold prices and its dependence on any other variables. Also, the results reveal a weak long-term relationship between the selected variables. Samanta and Zadeh (2012) using Vector Autoregression Moving-Average (VARMA), Granger causality and Johansen cointegration suggest the possibility of existence of co-movements among oil, gold, dollar and stock price.

Jain and Ghosh (2013) explore linkage and lead–lag relationship among oil price, precious metals, Indian rupee–USD rate using ARDL bound test and Toda–Yamamoto version of Granger causality. They find that some relationship exists between the oil and precious metals. They also report long-run dependence of Indian rupee–USD rate and gold on the other variables. Narang and Singh (2012) study the causal relationship between gold and Sensex using Johansen cointegration. They suggest that there is no causality between gold price and Sensex. However, Ewing and Malik (2013) examine the volatility of gold and oil futures using univariate and bivariate GARCH model. They report the substantial evidence of transmissions of volatility between gold and crude oil. Sindhu (2013) reports an inverse relationship between gold and USD, and interdependence between gold prices and inflation rate using trend analysis, regression analysis and ANOVA.

Wang (2013) using Granger causality, GARCH and T- GARCH models reports that there exists a high correlation between gold and crude oil, but not in their returns. He concludes that volatility of crude oil return affects the volatility of gold price returns. Similar results were reported by Subhashini and Poornima (2014). However, Sahu et al. (2014) find a long-run causality movement from Indian stock market to oil price and a long-run equilibrium relationship between the two markets. But the vice versa is not found. They report that there is no short-run causality, and Indian stock markets and oil prices are strongly exogenous.

Azar (2015) examine the relation among US stocks, gold and oil with the USD rate. Their results indicate that the USD denomination as the prime reason for 1 per cent fall in the price of stocks, gold and oil due to a 1 per cent appreciation of the USD. They also report a positive correlation between intrinsic US stock returns with the USD before September 2002 and a negative correlation afterwards. Nirmala and Deepthy (2015) report valuations in USD for gold and crude oil as the reason for the positive correlation between both the commodities. Ingalhalli, Poornima, and Reddy (2016) investigate the causal relationship between oil, gold, forex and stock markets by using Granger causality test. They report the presence of only one-way causal relation among these variables. Further, they suggest that oil prices facilitate development and estimation of forex rate and gold prices, whereas variations in Sensex Granger-cause oil prices.

Tomar and Singh (2016) find bidirectional causality for exchange rate–stock market and gold prices–crude oil. They also report a unidirectional causality between gold and exchange rate. However, Singh and Sharma (2017) report contrasting results. They infer that there is no cointegration between gold and crude oil prices while gold prices lead the crude oil prices. Arfaoui and Rejeb (2017) examine the interdependencies between oil, gold, USD and stock, and instantaneous direct and indirect linkages among them. Their results reveal significant connections among all the markets and a negative relation between oil and stock prices. The oil price is positively influenced by gold and USD. They further report that USD is negatively impacted by stock market and significantly by oil and gold prices.

From the literature review, we observe that there are a number of studies on the relationship between two and three of these variables but there are a few studies on the relationship among gold prices, crude oil prices, USD rate and the stock market. Further, there is a dearth of such a study in the Indian context. The importance of such a study is evident from the economic theory. This study is novel attempt to analyse the cointegration and causality relationship among all the four variables in India across the recent global financial crisis. The objectives of this study are as follows:

To analyse cointegration relationship among gold prices, crude oil prices, INR/USD rate and BSE Sensex.

To investigate causality among these select variables.

To examine the dynamics of the relationship among the variables across the global financial crisis of 2008.

Research Design

Data

The data set comprising 2,779 data points is divided into three sub-periods namely pre-crisis, during the crisis and post-crisis periods from June 2005 to December 2016. The number of observations in the pre-crisis period (6 June 2005 to 29 August 2008), during crisis period (1 September 2008 to 31 December 2010) and post-crisis period (3 January 2011 to 30 December 2016) has 781, 561 and 1,437 number of observations, respectively. A study by Chhatwal and Puri (2013) has been taken as reference for dividing the whole period into three sub-periods. The required secondary data on daily closing spot prices of gold and crude oil are collected from the websites of Multi Commodity Exchange (MCX), India; US dollar (INR/USD) from the website of Reserve Bank of India (RBI) and Sensex (30 stocks index of Bombay Stock Exchange (BSE) that is taken a proxy for the market) from the website of BSE of India. For data analysis, software like EViews 8.0 and MS Excel are used. Only those observations are included in data set for which values on all the four variables are available. We have used natural logarithmic (ln) and continuously compounded returns series.

Methodology

This section deals with all the research techniques and tools that we have employed in this study. Before conducting cointegration and causality analysis, we first perform preliminary analysis using descriptive statistics and unit root test like augmented Dickey–Fuller (ADF) for the three sub-periods. To study the cointegration among the variables, we apply Johansen cointegration technique. To analyse strength and direction of causality among GODS, we employ VECM, VAR model, Granger causality, VEC Granger causality/Wald tests and variance decomposition test.

Johansen’s Cointegration Test

Johansen’s cointegration technique has been most widely used cointegration technique (Lizardo & Mollick, 2010; Narang & Singh, 2012; Samanta & Zadeh, 2011; Srivastava, 2010). If two or more non-stationary series combine to form a stationary series, the given series are said to be cointegrated. The kth order VAR model used to conduct Johansen’s test is given below in Equation (1).

Δ Y_{t} = μ + Π Y_{t ​ - ​ 1} + \sum_{i = 1}^{k - 1} Γ_{i} ​ Δ Y_{t ​ - ​ 1 ​} + ε_{t}

(1)

There are two likelihood ratios to test for cointegration under Johansen’s approach. These statistics are trace, λ_trace and max eigenvalue, λ_max. In case of any conflict in results of λ_trace and λ_max statistics, we should prefer trace statistics (Johansen & Juselius, 1990).

Before applying Johansen’s cointegration test, ADF test is employed to check unit root properties of the given series.

Vector Error Correction Model and Vector Autoregression

The cointegrated variables bear long-run equilibrium relationship. However, they may suffer disequilibrium in short run. The VECM is employed to find any such disequilibrium and the speed of correction or adjustment to put the variables back on long-run equilibrium trajectory. Both long- and short-run causality can be studied using VECM. If β is found to be negative and significant, then we can say that there is long-term causality between the variables. However, the short-run coefficients a_i and b_i measure short-term causality. The VECM can be represented by Equation (2).

Δ Y_{t} = α + β E C T_{t - 1} + \sum_{i = 1}^{k} α_{i} ​ Δ Y_{t - i} + \sum_{t = 1}^{k} b_{i} Δ X_{t - i} + ε_{t}

(2)

where error correction term (ECT) stands for error correction term. It represents the speed of correction or adjustment towards long-run equilibrium. If there is no cointegration among the given variables, then we run VAR model instead of the VECM model. A bivariate VAR model with k lags of both the variables can be represented as shown in Equations (3) and (4).

Y_{t} = β_{10} + \sum_{i = 1}^{k} β_{1 i} ​ ​ Y_{t - i} + \sum_{i = 1}^{k} α_{1 i} ​ X_{t - i} + ε_{1 t}

(3)

X_{t} = β_{20} + \sum_{i = 1}^{k} β_{2 i} ​ ​ X_{t - i} + \sum_{i = 1}^{k} α_{2 i} ​ Y_{t - i} + ε_{2 t}

(4)

where ε_jt is a white noise disturbance term with E(ε_jt) = 0 and E(ε_1t, ε_2t) = 0 (Brooks, 2008, p. 290).

Granger Causality and Wald Tests

The Granger causality test gives the direction of causality. This test studies the lead–lag relationship between two variables. There are two ways in which we can employ the Granger causality test. In case the given series are not cointegrated, we apply the Granger test (Granger, 1969) to study the short-run relationship. A bivariate kth order VAR to conduct the Granger causality test has been shown in Equations (5) and (6). However, in this study, we have four variables, and hence, there will be a set of 12 VAR equations or 12 null hypotheses to be tested. For the sake of convenience, we have shown only two VAR equations.

Y_{t} = α_{0} + \sum_{i = 1}^{k} α_{i} ​ Y_{t - i} + \sum_{j = 1}^{k} β_{j} ​ X_{t - j} + ε_{t}

(5)

X_{t} = γ_{0} + \sum_{i = 1}^{k} γ_{i} X_{t - i} + \sum_{j = 1}^{k} δ_{j} ​ Y_{t - j ​} + ε'_{t}

(6)

For Equation (5), if the null hypothesis is rejected, we conclude that X_t Granger-causes Y_t. In other words, there is a lead–lag relationship between the two variables. Similarly, the null hypothesis of no causality can be tested for other equations. However, this test is not applicable in case the given series are cointegrated. In such a case, the Engle and Granger (1987) error correction—VEC Granger causality/Wald test should be used to analyse the short-run causality. The null hypothesis of no short-run causality is rejected if the p-value of χ² is less than the level of significance.

Forecast Error Variance Decomposition

Causality test does not explain whether two variables have positive or negative relationship. So one may be misled from the results of causality test alone (Yang et al., 2005). Such information is given by forecast error variance decomposition. According to Sims (1980), this test may give insight into the strength and direction of causal relationship between economics variables. Forecast error variance decomposition reveals the VAR system dynamics by showing percentage variation (return) in dependent variable due to their own shock as well as shocks to other variables.

Empirical Findings

Descriptive Statistics and Correlation Analysis

The preliminary analysis of the data using descriptive statistics is shown in Table 1. From Table 1, it is depicted that average daily return of crude oil varies from widely + 0.099 per cent in the pre-crisis period to −0.040 per cent in the crisis period and further to −0.008 per cent in the post-crisis period.

Table 1.

Summary Statistics for Pre-, Post- and during the Crisis Period

	LC	LD	LG	LS	RLC	RLD	RLG	RLS
	Pre-crisis
Mean	8.072	3.761	9.120	9.443	0.098	0.001	0.085	0.098
Maximum	8.748	3.849	9.517	9.946	7.145	1.422	3.861	6.667
Minimum	7.722	3.670	8.702	8.818	−6.391	−1.622	−7.575	−7.695
Std. Dev.	0.235	0.054	0.196	0.280	1.962	0.346	1.245	1.745
Skewness	1.201	−0.325	−0.225	−0.397	0.020	0.157	−0.711	−0.316
Kurtosis	3.633	1.735	2.686	2.320	3.223	5.406	6.288	5.054
Jarque–Bera	200.9	65.813	9.846	35.578	1.676	191.40	417.11	150.16
Probability	0.000	0.000	0.007	0.000	0.432	0.000	0.000	0.000
Observations	781	781	781	781	780	780	780	780
	During Crisis
Mean	8.089	3.852	9.680	9.603	−0.040	0.002	0.097	0.062
Maximum	8.528	3.952	9.941	9.949	17.48	2.490	10.44	15.999
Minimum	7.435	3.784	9.327	9.007	−15.28	−3.001	−4.969	−11.604
Std. Dev.	0.212	0.0374	0.150	0.262	3.046	0.639	1.246	2.120
Skewness	−1.148	0.307	−0.275	−0.856	0.442	−0.135	0.823	0.447
Kurtosis	3.985	2.414	2.315	2.400	8.229	5.188	13.56	11.10
Jarque–Bera	146.10	16.865	18.078	76.949	656.33	113.46	2665.5	1550.64
Probability	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Observations	561	561	561	561	560	560	560	560
	Post-crisis
Mean	8.368	4.061	10.22	9.990	−0.007	0.029216	0.020696	0.018
Maximum	8.926	4.230	10.402	10.298	12.232	4.019982	4.396022	3.703
Minimum	7.486	3.783	9.886	9.627	−10.613	−2.679298	−8.657650	−6.996
Std. Dev.	0.297	0.129	0.105	0.193	2.336	0.517942	0.940896	1.049
Skewness	−0.525	−0.697	−1.230	0.016	0.326	0.498054	−0.636406	−0.216
Kurtosis	2.345	2.366	4.350	1.473	6.117	8.963017	12.24234	5.041
Jarque–Bera	91.870	140.6	471.68	139.56	607.3	2186.896	5207.946	260.5
Probability	0.000	0.000	0.000	0.000	0.000	0.000000	0.000000	0.000
Observations	1437	1437	1437	1437	1436	1436	1436	1436

Source: The authors.

Notes: LG, LC, LD and LS stand for in series of gold, crude oil, dollar and Sensex, respectively, while RLG, RLC, RLD and RLS stand for their respective return series.

This variation in return is further supported by similar variations in standard deviation across the three sub-periods. Similarly, the volatility (standard deviation) of USD, gold and Sensex rises during the crisis and falls after the crisis. The returns for all the variables throughout all sub-periods are leptokurtic. The nature of skewness varies positively and negatively for all variables except crude oil for all sub-periods. Skewness and kurtosis values show that returns are not normally distributed. This is further confirmed by Jarque–Bera probability. The null hypothesis of normal distribution is rejected.

Table 2 shows the correlation among the four variables across the three sub-periods. The stock market and rupee–dollar returns bear a consistent negative correlation while gold and crude oil returns exhibit a consistent positive correlation across the three sub-periods. However, in all other cases, there is change in the sign of correlation over the given sub-periods. Like correlation between crude oil and stock market returns changes from −0.02 in the pre-crisis to +0.29 in the post-crisis period. This is because the economy recovers after the crisis and hence the demand for crude oil increases. The improved corporate performance further leads to a rise in stock market. Similarly, for other variables the correlation sign changes from positive to negative across the sub-periods which are not explained by theory.

Table 2.

Correlation Matrix

	Pre-crisis				Crisis				Post-crisis
	RLD	RLS	RLC	RLG	RLD	RLS	RLC	RLG	RLD	RLS	RLC	RLG
RLD	1				1				1
RLS	−0.25	1.00			−0.38	1.00			−0.38	1.00
RLC	0.13	−0.02	1.00		−0.14	0.29	1.00		−0.14	0.29	1.00
RLG	−0.02	0.05	0.33	1.00	0.07	−0.08	0.16	1.00	0.07	−0.08	0.16	1.00

Source: The authors.

Results of Johansen’s Cointegration Test

Using the ADF test, all the log series (LG, LC, LD, and LS) are found to be non-stationary on levels in intercept, trend and intercept and none forms in pre- and post-crisis period (see Table 3). However during the crisis, unlike intercept and none forms, the null hypothesis of a unit root can be rejected for LG, LC and LD series, that is, ADF is inconclusive. In such cases, we follow theoretical arguments to build models based on cointegration methods (Engle & Granger, 1987; Hall, 1986). So based on the literature review and our findings in the pre- and post-crisis period, we assume that LG, LC and LD series are non-stationary on levels. Thus, the return series are stationary on level across the three sub-periods.

Table 3.

ADF Test Results Log and Return Series in Levels

Variable	Pre-crisis			During Crisis			Post-crisis
Variable	Intercept	Trend and Intercept	None	Intercept	Trend and Intercept	None	Intercept	Trend and Intercept	None
LG	−1.61 (0.48)	−2.12 (0.54)	1.89 (0.99)	−1.263 (0.65)	−3.67 (0.03)	1.84 (0.98)	−2.81 (0.058)	−2.48 (0.34)	0.80(0.89)
RLG	−27.28 (0.000)	−27.27 (0.000)	−27.17 (0.000)	−18.48 (0.000)	−18.47 (0.000)	−18.29 (0.000)	−38.13 (0.000)	−38.16 (0.000)	−38.12 (0.000)
LC	−0.59 (0.87)	−1.49 (0.84)	1.39 (0.96)	−2.19 (0.21)	−3.41 (0.05)	−0.37 (0.55)	−1.25 (0.65)	−1.86 (0.67)	−0.19 (0.62)
RLC	−28.58 (0.000)	−28.58 (0.000)	−28.53 (0.000)	−25.96 (0.000)	−26.04 (0.000)	−25.98 (0.000)	−43.15 (0.000)	−43.14 (0.000)	−43.16 (0.000)
LD	−0.88 (0.80)	−0.68 (0.97)	0.03 (0.69)	−2.16 (0.22)	−4.31 (0.003)	0.068 (0.70)	−1.62 (0.47)	−2.19 (0.49)	2.08 (0.99)
RLD	−26.69 (0.000)	−26.68 (0.000)	−26.70 (0.000)	−23.86 (0.000)	−23.92 (0.000)	−23.89 (0.000)	−37.31 (0.000)	−37.32 (0.000)	−37.21 (0.000)
LS	−2.23 (0.20)	−1.55 (0.81)	1.51 (0.97)	−0.55 (0.88)	−2.86 (0.18)	0.65 (0.86)	−0.90 (0.79)	−3.08 (0.11)	0.58 (0.84)
RLS	−26.12 (0.000)	−26.19 (0.000)	−26.06 (0.000)	−17.96 (0.000)	−18.01 (0.000)	−17.96 (0.000)	−34.70 (0.000)	−34.70 (0.000)	−34.71 (0.000)

Source:The authors.

Notes: T-values and p-values (figures in parenthesis) have been presented. MacKinnon critical values at 5% level of significance are −2.865030, −3.415588 and −1.941230 for intercept, trend and intercept, and none form, respectively. (LG, LC, LD and LS stand for in series of gold, crude oil, dollar and Sensex, respectively, while RLG, RLC, RLD and RLS stand for their respective return series.)

The results of unit root test indicate that Johansen’s cointegrated test can be conducted for all the variables. Here, optimal lag length is decided by using Akaike information criterion (AIC). According to AIC, an optimal number of lags in before crisis and during crisis periods are 2 and 5, respectively. From the results shown in Table 4, it is evident that the four variables are cointegrated with one cointegrating relation in the pre-crisis period. During the crisis, there is a conflict between the results of the trace and maximum Eigen tests. The former test suggests one cointegrating relation while the latter test suggests that there are two cointegrating relations at 5 per cent level of significance. In such a situation of conflict, we should prefer trace statistics (Johansen & Juselius, 1990). Therefore, we can say that the select variable series have one cointegrating equation during the crisis period. However, we cannot reject the null hypothesis of r = 0 in the post-crisis period. Thus, we conclude that there is a long-run equilibrium between gold, crude oil, dollar and Sensex before and during the crisis period but not in after crisis period. This provides evidence that the relationship between these variables is dynamic in nature. Our findings for the pre-crisis period and the crisis period are similar to results reported by Sujit and Kumar (2011) and Samanta and Zadeh (2011) for the select period of their studies.

Table 4.

Johansen’s Cointegration Results

Period	Null Hypothesis	Eigenvalue	Trace Test		Max Eigenvalue Test
Period	Null Hypothesis	Eigenvalue	Statistics	P-Value	Statistics	P-value
Pre-crisis	r = 0 (none)	0.037577	52.69486 (47.85613)	0.0164*	29.79812 (27.58434)	0.0256*
	r ≤ 1 (at most 1)	0.014401	22.89675 (29.79707)	0.2512	11.28564 (21.131620)	0.6188
	r ≤ 2 (at most 2)	0.009624	11.61111 (15.49471)	0.1766	7.523692 (14.26460)	0.4292
	r ≤ 3 (at most 3)	0.005240	4.087416 (3.841466)	0.0432*	4.087416 (3.841466)	0.0432*
During crisis	r = 0 (none)	0.066506	65.81756 (47.85613)	0.0005*	38.19542 (27.58434)	0.0015*
	r ≤ 1 (at most 1)	0.038320	27.62213 (29.79707)	0.0873	21.68552 (21.131620)	0.0418*
	r ≤ 2 (at most 2)	0.007724	5.936610 (15.49471)	0.7030	4.303719 (14.26460)	0.8260
	r ≤ 3 (at most 3)	0.002938	1.632891 (3.841466)	0.2013	1.632891 (3.841466)	0.2013
Post-crisis	r = 0 (none)	0.010886	38.56129 (47.85613)	0.2781	15.69553 (27.58434)	0.6915
	r ≤ 1 (at most 1)	0.008713	22.86576 (29.79707)	0.2527	12.54958 (21.131620)	0.4944
	r ≤ 2 (at most 2)	0.005996	10.31618 (15.49471)	0.2572	8.623773 (14.26460)	0.3188
	r ≤ 3 (at most 3)	0.001180	1.692405 (3.841466)	0.1933	1.692405 (3.841466)	0.1933

Source:The authors

Note: Figures in parenthesis represent p-values.

Results of VECM and VAR

Since the variables bear a cointegrating relationship in the pre-crisis period and the crisis period, we can employ the VECM model. For the post-crisis period of no cointegration, VAR model has been applied. For long-run causality to exist, ECT should be negative and significant. The results of VECM indicate the absence of long-run causality in the models of the four variables in the pre-crisis period at 5 per cent level of significance (see Table 5). However, oil and stock market models are found to exhibit long-run causality in the crisis period at 5 per cent level of significance, that is, the variables have a long-run causality effect on crude oil prices and Sensex value. It means that there is error correction mechanism existing in crude oil and Sensex markets that allows for correction of disequilibrium caused in the previous period.

However, in some cases, short-run causality is indicated in results. For instance, USD is consistently influenced by its own lags and the lags of gold and stock market across the three sub-periods. However, the stock market, gold and crude oil show dynamic behaviour across the sub-periods. There is short-run causality from crude oil and stock market to gold in the pre-crisis period and from USD and crude oil to gold during the crisis period. Crude oil shows most dynamic behaviour among all. There is no causality from other variables to crude oil in pre-crisis period, whereas causality runs from gold, stock market and crude oil’s own lags during the crisis period. There is consistency in the causality from gold, USD and stock market to USD in pre-crisis and during crisis periods. However, in case of the stock market, the causality runs from gold only in the pre-crisis while from gold, USD and stock market during the crisis period.

Table 5.

Results of VECM for before and during the Crisis Period

	Pre-crisis				During Crisis
	LG	LC	LD	LS	LG	LC	LD	LS
ECT	0.015 (0.00)	−0.007 (0.26)	0.002 (0.03)	0.000 (0.87)	0.001 (0.08)	−0.005* (0.00)	0.000 (0.02)	−0.007* (0.00)
LG(−1)	−0.015 (0.68)	0.107 (0.07)	0.051* (0.00)	−0.150* (0.00)	−0.034 (0.43)	0.069 (0.51)	−0.026 (0.20)	0.173* (0.02)
LG(−2)	0.021 (0.57)	0.055 (0.36)	0.005 (0.63)	0.022 (0.67)	−0.103 (0.2)	0.043 (0.68)	−0.070* (0.00)	0.157* (0.03)
LG(−3)					0.063 (0.15)	0.277* (0.01)	0.007 (0.72)	0.092 (0.20)
LG(−4)					0.082 (0.06)	0.001 (0.98)	0.047* (0.02)	0.052 (0.47)
LG(−5)					0.025 (0.56)	−0.239* (0.02)	0.056* (0.01)	−0.144* (0.05)
LC(−1)	0.067* (0.00)	−0.058 (0.13)	−0.005 (0.39)	−0.028 (0.4009)	−0.005 (0.77)	−0.134* (0.00)	0.013 (0.13)	−0.048 (0.12)
LC(−2)	−0.030 (0.21)	−0.024 (0.53)	−0.009 (0.15)	−0.052 (0.13)	0.049* (0.01)	−0.020 (0.65)	0.003 (0.66)	−0.026 (0.41)
LC(−3)					−0.030 (0.11)	0.033 (0.46)	0.012 (0.16)	−0.015 (0.62)
LC(−4)					−0.023 (0.22)	0.053 (0.24)	−0.003 (0.69)	−0.022 (0.47)
LC(−5)					−0.029 (0.11)	−0.004 (0.92)	−0.010 (0.26)	0.046 (0.13)
LD(−1)	0.007 (0.96)	0.355 (0.10)	−0.004 (0.91)	−0.047 (0.80)	−0.035 (0.71)	−0.190 (0.42)	−0.156* (0.00)	−0.414* (0.01)
LD(−2)	0.086 (0.52)	0.290 (0.17)	−0.095* (0.01)	−0.000 (0.99)	0.115 (0.24)	0.018 (0.94)	−0.047 (0.31)	−0.389* (0.01)
LD(−3)					0.008 (0.92)	0.324 (0.17)	0.024 (0.59)	−0.478* (0.00)
LD(−4)					0.218* (0.02)	−0.113 (0.63)	−0.027 (0.56)	−0.110 (0.49)
LD(−5)					−0.062 (0.49)	0.074 (0.74)	−0.059 (0.17)	−0.013 (0.93)
LS(−1)	0.061* (0.023)	0.048 (0.26)	−0.032* (0.00)	0.060 (0.11)	−0.021 (0.47)	0.139 (0.05)	−0.113* (0.00)	0.031 (0.53)
LS(−2)	−0.007 (0.98)	0.044 (0.30)	−0.013 (0.07)	0.023 (0.54)	−0.009 (0.76)	−0.076 (0.30)	−0.006 (0.65)	−0.200* (0.00)
LS(−3)					−0.002 (0.94)	0.155* (0.03)	−0.031* (0.03)	−0.077 (0.13)
LS(−4)					0.025 (0.40)	−0.012 (0.86)	−0.044* (0.00)	−0.089 (0.07)
LS(−5)					0.044 (0.14)	−0.093 (0.20)	−0.011 (0.42)	−0.046 (0.35)

Source: The authors.

Note: Coefficient values and p-values (figures in parenthesis) have been presented. * represents significance of coefficients.

For the post-crisis period, the two series are not found to be cointegrated. So we run VAR. From Table 6, it is evident that crude oil is affected by its own lags (2) as well the two lags of USD and Sensex each while gold is affected by two lags of USD and first lag of its own. Similarly, dollar is influenced by the two lags of each gold, Sensex and its own lags, while Sensex is affected by its own lags only. Thus, we infer that stock market’s dependence shifts from lags of gold in pre-crisis to lags of stock market in post-crisis period. Similarly, gold is commonly affected by the lags of crude oil in pre-crisis and the crisis periods, while it is influenced by USD in the post-crisis period. Crude oil shows most dynamic behaviour among all. There is no causality from other variables to crude oil in the pre-crisis period, whereas causality runs from gold, stock market, and crude oil’s own lags during the crisis period.

Table 6.

Results of VAR for the Post-crisis Period

	Dependent Variable
	LC		LG		LD		LS
	Coefficient	Probability	Coefficient	Probability	Coefficient	Probability	Coefficient	Probability
LC(−1)	0.882	0.00*	−0.003	0.79	0.006	0.31	0.020	0.08
LC(−2)	0.110	0.00*	0.002	0.87	−0.006	0.30	−0.019	0.10
LG(−1)	0.002	0.97	0.983	0.00*	0.070	0.00*	−0.058	0.05
LG(−2)	0.004	0.95	0.009	0.75	−0.067	0.00*	0.055	0.06
LD(−1)	0.997	0.00*	−0.105	0.04*	0.939	0.00*	−0.034	0.55
LD(−2)	−0.994	0.00*	0.110	0.03*	0.056	0.04*	0.047	0.41
LS(−1)	0.358	0.00*	−0.029	0.26	−0.103	0.00*	1.061	0.00*
LS(−2)	−0.369	0.00*	0.024	0.35	0.105	0.00*	−0.068	0.01*

Source: The authors.

Note: * Represents significant results.

Results of Granger Causality and Wald Test Results

The given series are cointegrated in before and during the crisis period, whereas no cointegration is present after the crisis period. So we apply the VEC Granger causality/Wald test for the pre-crisis and during the crisis periods while Granger test (Granger, 1969) is applied for the post- crisis period. Table 7 depicts the results of VEC Granger causality/block exogeneity Wald test for the pre-crisis and during the crisis periods for the short-run causality. The consistent short-run causality relationship is reported for Sensex and USD returns (RLD). Each of these two variables is influenced by other variables. However, gold and crude oil show dynamic causality across the pre-crisis and during the crisis. Crude oil in pre-crisis and gold during the crisis period are influenced by themselves. The results are consistent with the results of VECM. In Table 8, the Granger test results show unidirectional causality from USD and stock market to the oil and from gold and stock market to USD. The results are similar to the results of VAR. Thus, we can say that our results are robust.

Table 7.

VEC Granger Causality/Block Exogeneity Wald Test Results

Model	Dependent Variable (Differenced Series)	Independent Variable (Differenced Series)	Pre-crisis		During Crisis
Model	Dependent Variable (Differenced Series)	Independent Variable (Differenced Series)	χ² value	Prob.	χ² value	Prob.
1	LC	LG, LD and LS	9.4576	0.1494	30.1009	0.0116*
2	LG	LC, LD and LS	15.7129	0.0154*	24.4235	0.0582
3	LD	LG, LC and LS	44.6973	0.0000*	99.3100	0.0000*
4	LS	LG, LD and LC	15.0600	0.0198*	35.5670	0.0020*

Source: The authors

Note: * Represents significant results at 5% level of significance.

Table 8.

Granger Causality Test Results

Null Hypothesis	Post-crisis
Null Hypothesis	F-statistic	Prob.
RLG does not Granger-cause RLC	2.65997	0.0703
RLC does not Granger-cause RLG	2.37484	0.0934
RLD does not Granger-cause RLC	21.3328	0.0000*
RLC does not Granger-cause RLD	1.54329	0.2140
RLS does not Granger-cause RLC	6.73060	0.0012*
RLC does not Granger-cause RLS	2.23780	0.1071
RLG does not Granger-cause RLD	18.1637	0.0000*
RLD does not Granger-cause RLG	1.91651	0.1475
RLS does not Granger-cause RLD	35.7226	0.0000*
RLD does not Granger-cause RLS	0.59848	0.5498
RLS does not Granger-cause RLG	0.18809	0.8286
RLG does not Granger-cause RLS	1.85688	0.1565

Source: The authors.

Note: * Represents significant results.

From the above analysis, we infer that the association among GODS is dynamic across the global financial crisis of 2008. These variables show cointegration relationship only in pre-crisis and crisis periods only. Also, the only consistent relationship is the dependence of USD on gold and dollar across these sub-periods.

Results of Variance Decomposition Test

Table 9 shows the variance decomposition of returns on crude oil, gold, USD and Sensex for first and tenth day in future. The results show that crude oil returns are mainly affected by its own shocks across the three sub-periods. On the contrary, a shock to USD returns accounts for 5.5 per cent, 13.8 per cent and 10 per cent of variation in Sensex returns during the pre-crisis, the crisis and the post-crisis periods, respectively. During the crisis, crude oil accounts for 8.5 per cent of the variation in Sensex return. However, crude oil return’s shocks show diminishing effect from 12.3 per cent to 2.6 per cent on gold returns across the sub-periods. In case of USD, Sensex returns’ shocks are responsible for 13 per cent variation in USD returns. These results are in line with the results of VECM and Granger causality.

Table 9.

Variance Decomposition Test Results

Day	Pre-crisis				During Crisis				Post-crisis
Day	RLC	RLD	RLG	RLS	RLC	RLD	RLG	RLS	RLC	RLD	RLG	RLS
Variance Decomposition of RLC
1	100.0	0.00	0.00	0.00	100	0.00	0.00	0.00	100	0.00	0.00	0.00
10	98.92	0.29	0.56	0.21	94.4	1.01	2.16	2.32	99.3	0.32	0.27	0.09
Variance Decomposition of RLD
1	1.85	98.14	0.00	0.00	1.24	98.7	0.00	0.00	0.50	99.5	0.00	0.00
10	1.94	93.02	2.76	2.27	1.85	81.1	3.90	13.0	0.84	94.1	2.53	2.47
Variance Decomposition of RLG
1	11.23	0.22	88.54	0.00	3.48	0.23	96.28	0.00	0.15	1.48	98.36	0.00
10	12.30	0.37	86.20	1.12	5.12	1.63	92.74	0.50	2.63	1.50	91.73	4.13
Variance Decomposition of RLS
1	0.02	5.63	0.20	94.1	8.50	13.1	1.08	77.2	1.92	0.77	9.97	87.3
10	0.97	5.54	1.15	92.3	8.39	13.8	3.76	73.9	2.28	1.15	10.03	86.5

Source: The authors.

Research Implications

The research implications of the results of this study are important to the various participants of select markets (GODS) in India and similar economies. The results are not only useful to government and different policymakers but also to MNCs, export–import houses, investment houses, traders and so on. Retail investors, investment houses and fund managers who make diverse investments in stock market, yellow metal and black gold can be benefitted from the results of this study. This study can also be used by manufacturing concerns as crude oil is one of the main determinants of cost of operations and hence influences product prices. Given the criticality of imports of crude oil and gold for India, and use of gold and dollar as reserves, the results are helpful to the central bank, export–import houses and policymakers.

Concluding Remarks

Over the globe, the various financial markets are becoming integrated and the linkages among variables gold prices, crude oil prices, USD rate and stock market (GODS) invite a special attention of various financial analysts and investors. For an import-dependent country like India, the interplay among these variables is imperative. So in this study, we investigate the cointegration and causality relationship among GODS across the crisis period. Correlation analysis shows that the stock market and rupee–dollar returns bear a consistent negative correlation, while gold and crude oil returns exhibit a consistent positive correlation across the three sub-periods. The stock market and rupee–dollar returns bear a consistent negative correlation while gold and crude oil returns exhibit a consistent positive correlation across the three sub-periods. Like correlation between the oil and Sensex returns changes from −0.02 in pre-crisis to +0.29 in post-crisis period. This is because the economy recovers after the crisis and hence the demand for crude oil increases. The improved corporate performance further leads to a rise in stock market. Similarly, the correlation sign changes from positive to negative across the sub-periods which are not explained by theory.

The results of Johansen’s cointegration technique provide evidence of cointegration relationship among GODS in the pre-crisis and the crisis periods. However, no cointegration relationship is found in the post-crisis period. This indicates a significant change in the relationship among GODS. There may be some external forces like the turbulence in world economic scenario as after-effects of the crisis that disturbed long-run equilibrium dynamics among these variables. The results of VECM indicate the absence of long-run causality in the models of the four variables in the pre-crisis period at 5 per cent level of significance. However, oil and stock market models are found to exhibit long-run causality in the crisis period. In some cases, the results show the presence of short-run causality. USD is consistently influenced by its own lags and the lags of gold and stock market across the three sub-periods. However, the stock market, gold and crude oil show dynamic behaviour across the sub-periods.

The results of Wald test for the pre-crisis and the crisis periods, and the Granger causality test for the post-crisis support above results of VECM and VAR. The consistent short-run causality relationship is reported for Sensex and USD returns (RLD) in Wald test results. Each of these two variables is influenced by other variables. However, gold and crude oil show dynamic causality across the pre-crisis and during the crisis. Crude oil in pre-crisis and gold during the crisis period are influenced by themselves. Granger test results show unidirectional causality from USD and stock market to the oil and from gold and stock market to USD. The results of variance decomposition test not only support VECM and Granger causality results but also give more insight on the strength and direction of causal relationship among GODS across the global financial crisis. Thus, we can say that our results are robust. Finally, we conclude that the cointegration and causality relationship among Sensex, gold, crude oil and USD are dynamic and the global financial crisis of 2008 has affected this relationship. Further, research can be extended to find (a) the contribution of each variable in determining the other variables and (b) some other factors which affect the relationship among GODS.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

References

Arfaoui

& Rejeb

A. B.

(2017). Oil, gold, US dollar and stock market interdependencies: A global analytical insight. European Journal of Management and Business Economics, 26(3), 278–293.

Azar

S. A.

(2015). The relation of the US dollar with oil prices, gold prices, and the US stock market. Research in World Economy, 6(1), 159–171.

Basher

S. A.

Haug

A. A.

& Sadorsky

(2012). Oil prices, exchange rates, and emerging stock markets. Energy Economics, 34(1), 227–240.

Chen

& Chen

(2007). Oil prices and real exchange rates. Energy Economics, 29(3), 390–404.

Chhatwal

& Puri

(2013). Relationship between Indian spot and future crude oil prices: A phasewise empirical analysis. Asia-Pacific Journal of Management Research and Innovation, 9(3), 305–313.

Engle

R. F.

& Granger

C. W. J.

(1987). Co-integration and error correction: representation, estimation, and testing. Econometrica, 55(2), 251–276.

Ewing

B. T.

& Malik

(2013). Volatility transmission between gold and oil futures under structural breaks. International Review of Economics & Finance, 25(C), 113–121.

Hall

S. G.

(1986). An application of the Granger and Engle two-step estimation procedure to United Kingdom aggregate wage data. Oxford Bulletin of Economics and Statistics, 48(3), 229–239.

Han

& Wang

(2008). Australian dollars exchange rate and gold prices: An interval method analysis. Paper presented at the 7th International Symposium on Operations Research and Its, Applications (ISORA’08), October 31–November 3. Lijiang, China.

10.

Granger

C. W.

(1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica: Journal of the Econometric Society, 424–438.

11.

Ingalhalli

Poornima

B. G.

& Reddy

Y. V.

(2017). A study on dynamic relationship between oil, gold, forex and stock markets in Indian context. Paradigm, 20(1), 83–91.

12.

Jain

& Ghosh

(2013). Dynamics of global oil prices, exchange rate and precious metal prices in India. Resources Policy, 38(1), 88–93.

13.

Johansen

& Juselius

(1990). Maximum likelihood estimation and inference on cointegration with applications to demand for money. Oxford Bulletin of Economics and Statistics, 52(2), 169–210.

14.

Jones

& Kaul

(1996). Oil and the stock markets. Journal of Finance, 51(2), 463–491.

15.

Levin

E. J.

& Wright

R. E.

(2006). Short-run and long-run determinants of the price of gold (Research Study No. 32). Glasgow: World Gold Council.

16.

Lizardo

R. A.

& Mollick

A. V.

(2010). Oil price fluctuations and US dollar exchange rates. Energy Economics, 32(2), 399–408.

17.

Narang

S. P.

& Singh

R. P.

(2012). Causal relationship between gold price and Sensex: A study in Indian context. Vivekananda Journal of Research, 1(1), 33–37.

18.

Narayan

P. K.

Narayan

Prasad

(2008). Understanding the oil price-exchange rate nexus for the Fiji Islands. Energy Economics, 30(5), 2686–2696.

19.

Nirmala

& Deepthy

(2015). An analysis of the relationship between gold and crude oil prices. International Journal of Applied Research, 1(13), 156–159.

20.

Sahu

N. T.

Bandopadhyay

& Mondal

(2014). An empirical study on the dynamic relationship between oil prices and Indian stock market. Managerial Finance, 40(2), 200–215.

21.

Samanta

S. K.

& Zadeh

A. H.

(2012). Co-movements of oil, gold, the US dollar, and stocks. Modern Economy, 3(1), 111.

22.

Sims

C. A.

(1980). Macroeconomics and reality. Econometrica, 48(1), 1–48.

23.

Sindhu

(2013). A study on impact of select factors on the price of gold. Journal of Business and Management, 8(4), 84–93.

24.

Singh

N. P.

& Sharma

(2017). Linkage between gold and crude oil spot markets in India: A cointegration and causality analysis. International Journal of Engineering Technology, Management and Applied Sciences, 5(6), 216–223.

25.

Srivastava

(2010). Relevance of macroeconomic factors for the Indian stock market. Decision, 37(3), 69.

26.

Subhashini

& Poornima

(2014). An empirical investigation of the causal relationship between gold price, exchange rate and crude oil. International Journal of Management Research and Reviews, 4(10), 981.

27.

Sujit

K. S.

& Kumar

B. R.

(2011). Study on dynamic relationship among gold price, oil price, exchange rate and stock market returns. International Journal of Applied Business and Economic Research, 9(2), 145–165.

28.

Tomar

R. S.

& Singh

(2016). Causal relationship between stock market indices, gold prices, crude oil prices, and exchange rates. International Journal of Economic Research, 13(1), 53–65.

29.

Wang

(2013). An empirical study in the relationship between crude oil and gold futures. Halifax, NS: Saint Mary’s University.

30.

Yang

Balyeat

R. B.

& Leatham

D. J.

(2005). Futures trading activity and commodity cash price volatility. Journal of Business Finance & Accounting, 32(1–2), 297–323.

31.

Zhang

Y. J.

& Wei

Y. M.

(2010). The crude oil market and the gold market: Evidence for cointegration, causality and price discovery. Resources Policy, 35(3), 168–177.