Gold Price and Effect on Stock Exchange

Gold Price Volatility and Stock Market Returns in India P K Mishra Faculty in Economics, Siksha O Anusandhan University, Orissa, India E-mail: [email  protected] com J R Das Faculty in Management, Siksha O Anusandhan University, Orissa, India E-mail: j. [email  protected] co. in S K Mishra Faculty in Economics, TITE, Orissa, India E-mail: [email  protected] co. in Abstract The study of the capital market of a country in terms of a wide range of macroeconomic and financial variables has been the subject matter of many researches since last few decades. Recently one such variable, that is, gold price volatility has attracted the attention of many researchers, academicians and analysts. Thus, this paper is an attempt to analyse the causality relation that may run between domestic gold prices and stock market returns in India. The study by taking into consideration the domestic gold prices and stock market returns based on BSE 100 index, investigates the Granger causality in the Vector Error Correction Model for the period January 1991 to December 2009. The analysis provides the evidence of feedback causality between the variables. It infers that the Gold prices Granger-causes stock market returns and stock market returns also Granger-causes the gold prices in India during the sample period. Thus, both the variables contain some significant information for the prediction of one in terms of another. Keywords: Gold Price, Stock Market Return, BSE 100 Index, India, Volatility, Causality JEL Classification Codes: C22, C32, E44 1. Introduction The study of the capital market of a country in terms of a wide range of macro-economic and financial variables has been the subject matter of many researches since last few decades. Empirical studies reveal that once financial deregulation takes place, the stock markets of a country become more sensitive to both domestic and external factors. And, one such factor is the price of gold. From 1900 to 1971, with the global systems of gold standard and USD standard, gold price was regulated. But, since 1972, gold has been disconnected from the USD. Particularly in 1976 when the International Monetary Fund (IMF) passed Jamaica Agreement, did gold begin to evolve from currency to ordinary merchandise and since then gold price as been determined by market supply and demand. And, in India, the government started the process of globalization and liberalization since 1991 which allowed prices to be determined by the market forces. Gold Price Volatility and Stock Market Returns in India 48 Since then, the government has been taking a number of steps to reform the gold sector and ensure that India benefits from the demand-influence that it has on the gold business internatio nally. The liberalisation of the gold sector has been made in stages; first allowing a number of banks to import gold – braking the monopoly of the State Trading Corporations; then considerably reducing the import duty – destroying a lucrative parallel smuggling channel and now, allowing traders, manufacturers as well as investors to trade in gold futures in India itself. Figure 1: Annual Price Movement of Gold in Indian Market Prior to the introduction of liberalization and globalization policies, gold prices in India showed an increasing trend (Fig. 1). In the post liberalization period, the average annual prices of gold also showed an increasing trend from the year 1991 to 1996. But, it showed a decreasing trend in 1997 and 1998 and again showed an increasing trend in the year 2000. From 2000 to 2009, gold prices are continuously increasing. The domestic gold price in India is continuously increasing due to its heavy demand in the country. There are several reasons gold has high demand in India. The first reason is security; gold offers full security as long as it is retained by central banks. There is no credit risk attached to gold. Secondly, gold is able to maintain its liquidity even at times of crisis situations like high global inflation or political turbulence. The third reason for holding gold is to build a diversified portfolio. Gold also has taken the role of an asset of last resort. World Economic History shows that countries have repeatedly used gold as security against loans when they have had difficulties with their Balance of Payments and have felt the need to borrow on the international capital markets. The domestic gold prices in India are associated strongly with the import parity prices which are determined by the global spot prices, Dollar-Rupee rate and local taxes and levies. Any change in the global prices gets transmitted very quickly and gets reflected in domestic prices, particularly for countries like India who are price takers in gold with a major part of the demand met by imports. The twin factors, namely, (i) increase in global spot gold prices (as the commodity becomes dearer to those looking for safe haven during times of economic crisis, and (ii) appreciation of USD against INR, led to sharp rise in gold prices in India in the recent past. Moreover, the total annual supply of gold across the globe has also decreased from 4037 tons in 2002 to 3380 tons in 2008. India is a large buyer of gold at about 700-800 tons per annum. It also recycles about 200 tons of gold out of old jewellery. A large chunk of Indian imports is used for jewellery exports. Since the gold prices in India are influenced by international factors, its volatility is very important. Volatility involves short term – monthly, weekly or even hourly fluctuations in gold prices as measured by their absolute percentage changes during a particular period. If we look at the rolling 49 P K Mishra, J R Das and S K Mishra standard deviation of monthly gold prices since 2000, the prices are more volatile after July 2007 which is almost the same time when the slow down started in USA as a result of the sub-prime crisis (Fig. 2). Figure 2: Standard Deviation of Gold Price in India A look at the historic data brings out that when the stock market crashes or when the dollar weakens, gold continues to be a safe haven investment because gold prices rise in such circumstances (Gaur and Bansal, 2010). It is no surprise that many investors, big and small have chosen to hedge their investments through gold at the time of crises. Figure 3: Movement of Gold Price and BSE 100 Index 20000 16000 12000 8000 4000 0 92 94 96 98 00 02 04 06 08 BSE100 GOLDPRICE Gold prices have been on an uptick since 2000, while the stock market declined from 2000 to 2003 and then again in 2008 (Fig. 3). In 2008 when the market was suffering from bearish phase worldwide, gold prices spiked as panic spread across global markets. So far since March 2009 in India signs of recovery in the stock markets have emerged. At the same time gold continues to forge ahead, Gold Price Volatility and Stock Market Returns in India 50 lbeit at a slower pace. In 2008, the two assets prices – equity and gold, were moving in opposite directions, displaying the ability of the yellow metal to protect one's portfolios at the time of a dip. In fact, during each of the two prolonged bear phases (lasting at least a year) over the past decade, gold has provided an effective hedge. However, in India stocks do not seem to be perceived as an alternative to gold. The reason for holding gold is, to a large extent, guided by the individual sentiments. The gold investing habits of Indians strongly ingrained in the Indian Social Psyche. In India gold has been held by individuals for years and have passed hands of many generations. In addition, the equity culture in India is not as developed as in some other parts of the world. Gold has not yet lost its prime importance as a hedge against loss of wealth in times of crises. It is with this backdrop, this paper proceeds to investigate the direction of causality between domestic gold prices and stock market returns in India. The rest of the paper is organized as follows: Section II explains the data and methodology, Section III makes the analysis, and Section IV concludes. . Data and Methodology This paper aims at investigating the dynamic relationship between gold prices and stock market returns in India for the period 1991 to 2009. This study is mainly based on secondary data that have been collected from the database on Indian economy maintained by Reserve Bank of India. The study analyses the monthly data on domestic gold prices and stock market returns in India for the aforesaid period. Wherever data were missing, the averages of the data of the previous month and next month have been taken. The monthly stock market returns ( Rt ) based on BSE 100 Index have been calculated by the ? I ? Rt = log ? t ? ? I t ? 1 ? where I and I are the logarithmic difference change in the BSE 100 Index, i. e. , t t ? 1 closing value of monthly BSE 100 Index at time ‘t’ and‘t-1’ respectively. At the outset, the Karl Pearson’s correlation coefficient between the aforesaid time series has been calculated and its significance has been tested by the t-test. The correlation coefficient has been calculated by using the formula: N ? XY – (? X)(? Y) r= N ? X 2 – (? X)2 N ? Y 2 – (? Y)2 And, the significance of this correlation coefficient has been tested by the t-test using the tr n? 2 under the null hypothesis H 0 : ? = 0 against the alternative hypothesis of statistic t n ? 2 = 1? r2 H1 : ? ? 0 with n-2 degrees of freedom. If the calculated value of t exceeds the critical value of t, then the null hypothesis will be rejected; otherwise accepted. Then the Granger causality between the variables has been investigated in the Vector Error Correction framework. And, as the essential steps of Granger Causality test, the stationarity and cointegration between variables have been found out. The Augmented Dickey-Fuller unit root test has been used to examine the stationarity of the time series of the study and to find the order of integration between them. The ADF unit root test has been performed by estimating the regression: ? Yt = ? 0 + ? 1Yt ? 1 + ? ? j? Yt ? j + ? t j=1 p The ADF unit root test is based on the null hypothesis H 0 : Yt is not I(0) . If the calculated ADF statistic is less than the critical value, then the null hypothesis is rejected; otherwise accepted. If the 51 P K Mishra, J R Das and S K Mishra variable is stationary at level, the variable is said to be integrated of order zero, I(0). If the variable is non-stationary at level, the ADF test can be utilised and the first difference of the variable can be used for testing a unit root. In this case, the variable is said to be co-integrated of order one, I(1). In the second step, the Johansen’s cointegration test has been applied to check whether the long run equilibrium relation exists between the variables. The Johansen approach to cointegration test is based on two test statistics, viz. , the trace test statistic, and the maximum eigenvalue test statistic. i = r +1 The trace test statistic can be specified as: where ? i is the i th largest eigenvalue of matrix ? and T is the number of observations. In the trace test, the null hypothesis is that the number of distinct cointegrating vector(s) is less than or equal to the number of cointegration relations ( r ). The maximum eigenvalue test examines the null hypothesis of exactly r cointegrating relations against the alternative of r + 1 cointegrating relations with the test statistic: ? max = ? T log(1 ? ?r +1 ), where ? trace = ? T ? log(1 ? ?i ), k ?r +1 is the (r + 1)th largest squared eigenvalue. In the trace test, the null hypothesis of r = 0 is tested against the alternative of r + 1 cointegrating vectors. At the end, the Granger Causality test has been used to determine whether one time series is useful in forecasting another thereby finding out the direction of relationship between the variables of the study. In the Granger Causality test, the vector of endogenous variables is divided in two sub-vectors, Y1t and, Y2t with dimensions K1 and, K 2 respectively, so that K = K1 + K 2 . The sub-vector Y1t is said to be Granger-causal for Y2t if it contains useful information for predicting the latter set of variables. For testing this property, the levels VAR following form without exogenous variables of the model is considered. A 0 Yt = A1Yt ? 1 + †¦Ã¢â‚¬ ¦ + A p +1Yt ? p ? 1 + B0 X t + †¦Ã¢â‚¬ ¦ + Bq X t ? q + C*D*t + u t If that model contains p + 1 lags of the endogenous variables as in the above model, the test is based on a model with p + 2 lags of the endogenous variables, ? Y1t ? p + 2 ? ?11,i ? 12,i ? ? Y1,t ? i ? ? u1t ? ? ? Y ? + CD t + ? ? ? Y ? = ? ? 2t ? i =1 ? 21,i ? 22,i ? ? 2,t ? i ? ? u 2t ? as proposed by Dolado and Lutkepohl (1996). The null hypothesis that Y1t is not Granger-causal for Y2t is tested by checking the null hypothesis ? 21,i = 0, i = 1, 2,†¦. , p + 1 A Wald test statistic, divided by the number of restrictions pK1K 2 , is used in conjunction with an F(pK1K 2 , KT ? n * ) distribution for testing the restrictions. Here n * is the total number of parameters in the system (Lutkepohl, 1991), including the parameters of the deterministic term. Of course, the role of Y1t and Y2t can be reversed to test Granger-causality from Y2t to Y1t . 3. Empirical Analysis It is clear from the Fig. 3 that the direction of movements of gold prices and BSE 100 Indices in India is same. The value of Pearson’s correlation coefficient (r) between these two time series over the period 1991 to 2009 is 0. 873. To test whether this value of ‘r’ shows a significant relationship between two time series, student’s t-test has been used. The null hypothesis of the test is r = 0 against the alternative of r ? 0. Since the t-statistic at 226 degrees of freedom is 26. 9 and the critical value of t at 5% level of significance is less than it, the null hypothesis is rejected. So, it can be said that the correlation between gold prices and BSE 100 indices is statistically significant. Gold Price Volatility and Stock Market Returns in India 52 Thus, it seems that gold prices and stock market returns based on BSE 100 Index are significantly correlated. And, computation reveals that the value of ‘r’ is 0. 0143 between them which is not statistically significant for the t-statistic of 0. 217 at 226 degrees of freedom. So it can be said that although gold prices and BSE 100 Indices are significantly correlated, the correlation between gold prices and stock market returns based on BSE 100 Index is not significant. But much interesting results have been obtained from the Granger Causality test. The Granger causality test presumes that the given time series are stationary. The Augmented Dickey-Fuller unit root test has been used for this purpose. And, the results of such test are reported in Table 1. Table 1: Results of Augmented Dickey-Fuller Unit Root Test ADF Statistic -14. 61 Critical Values At 1%: -3. 459 At 5%: -2. 874 At 10%: -2. 573 At 1%: -3. 459 At 5%: -2. 874 At 10%: -2. 573 Decision Reject Null hypothesis of no unit root Variables in their First Differences Gold Prices Stock Market Returns -12. 01 Reject Null hypothesis of no unit root It is clear from the Table 1 that the hull hypothesis of no unit roots for both the time series are rejected at their first differences since the ADF est statistic values are less than the critical values at 10%, 5% and 1% levels of significances. Thus, the variables are stationary and integrated of same order, i. e. , I(1). In the next step, the cointegration between the stationary variables has been tested by the Johansen’s Trace and Maximum Eigenvalue tests. The results of these tests are shown in Table 2. The Trace test indicates the existence of two cointegrating equatio ns at 5% level of significance. And, the maximum eigenvalue test makes the confirmation of this result. Thus, the two variables of the study have long-run or equilibrium relationship between them. Table 2: Results of Johansen’s Cointegration Test Sample: January 1991 to December 2009 Included observations: 225 after adjustments Trend assumption: Linear deterministic trend Series: Gold Prices and Stock Market Returns Lags interval (in first differences): 1 to 2 Unrestricted Cointegration Rank Test (Trace) Trace 0. 05 Eigenvalue Statistic Critical Value 0. 264883 83. 69901 15. 49471 0. 062248 14. 46069 3. 841466 Hypothesized No. of CE(s) None * At most 1 * Prob. ** 0. 0000 0. 0001 Trace test indicates 2 cointegrating eqn(s) at the 0. 05 level * denotes rejection of the hypothesis at the 0. 5 level ** MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized Max-Eigen 0. 05 No. of CE(s) Eigenvalue Statistic Critical Value None * 0. 264883 69. 23832 14. 26460 At most 1 * 0. 062248 14. 46069 3. 841466 Max-eigenvalue test indicates 2 cointegrating eqn(s) at the 0. 05 level * denotes rejection of the hypothesis at the 0. 05 level ** MacKinnon-Haug-Michelis (1999) p-values Prob. ** 0. 0000 0. 0001 53 Table 3: Results of Granger Causality Test P K Mishra, J R Das and S K Mishra Null Hypothesis Gold Prices do not Granger Cause Stock Market Returns Stock Market Returns do not Granger Cause Gold Prices F-Statistic (73, 12) 11. 678 32. 997 Probability 0. 000 0. 000 Decision Reject Reject Now, the Granger causality test can be performed to determine the direction of causation between these two variables in the Vector Error Correction Model. The results of the Granger causality test are reported in Table 3. It is inferred that the null hypothesis of â€Å"Gold Prices do not Granger Cause Stock Market Returns† and â€Å"Stock Market Returns do not Granger Cause Gold Prices† are here clearly rejected. Thus, both the variables contain some significant information such that they cause each other. But it is very interesting to note that these two variables are insignificantly correlated, i. e. , a very low degree of correlation holds between them. During the period of global financial crisis, stock markets crashed but gold price continues to increase in the country. This could be explained as follows. The extent of holding of gold in India is widespread but stocks are not held by all, though retail participation in the Stock Markets might have gone up in the last few years. Indians consider gold the safe haven investment as a financial asset and as jewellery. World Gold Council Report says that India stands today as the world’s largest single market for gold consumption. Traditionally, gold has been more attractive than bank deposits, stocks and bonds. In developing countries, people have often trusted gold as a better investment. In many countries including India, gold remains an integral part of social and religious customs, besides being the basic form of savings. But recently many innovative financial products have been lunched relating to gold. In March 2003, the first Gold Exchange Traded Fund, i. e. , Gold Bullion Securities was launched on the Australian Stock Exchange. Now, gold exchange traded funds are being traded like shares on the major stock exchanges including London, New York and Sydney. In India the first gold ETF was launched in March 2007 by Benchmark Mutual Fund. And, the UTI gold ETF has emerged as the best performer since May 2009. The number of new accounts created by Gold ETFs in India surged 57% between March and September 2009. The overall AUM in Gold ETFs at the end of December 2009 was Rs 1,352 crore, up from Rs 717 crore in April 09. It shows that Indian investors are gradually moving into gold ETFs for investment instead of physical form. Recently derivatives such as gold forwards, futures and options have become very popular and have been traded on various exchanges around the world and over-the-counter directly in the private market. In the USA, gold futures are primarily traded on the New York Commodities Exchange. In India, the National Commodity and Derivatives Exchange introduced 100 gram gold futures in November 2006. The volume of Gold futures traded in this exchange during January to August 2007 was 4,479,114 which have been increased to 9,038,795 in January to August 2008. It is thus inferred that Indians have started considering gold more than jewellery and as good as investments on bonds and equities. Perhaps, this explains the co-movement of gold prices and stock prices in the aftermath of global financial crisis. Gold Price Volatility and Stock Market Returns in India 54 4. Conclusion This paper examines the gold price volatility and the causality between domestic gold prices and stock market returns in India for the period 1991 to 2009. The study uses monthly data on the defined time series. The required data have been collected from the database of Reserve Bank of India. The Augmented Dickey-Fuller test says that the time series of the study are stationary and all integrated of order one. The Johansen’s cointegration test reveals that there exists long run equilibrium relation between gold prices and stock market returns in India. Then application of Granger causality test in the vector error correction model suggests the evidence of feedback causality running between the gold prices and BSE 100 Index based stock returns in India. Thus, each variable contains some ignificant information so that one can be used to predict the other. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] Abken A. Peter (1980), â€Å"The Economics of Gold Price Movements†, Federal Reserve Bank of Richmond, Economic Review, March /April. pp 3-13. Aggarwal R. and Soenen, L. A. (1988), â€Å"The Nature and Efficiency of the Gold Market†, The Journal of Portfolio Management, Vol. 14, pp. 18-21. Agarwal, Sanjeev (2004), â€Å"Bullion Markets†, BSE Review of Markets, pp. 46-48. Aggrarwal, R. , Inclan, C. , & Leal, R. (1999). â€Å"Volatility in Emerging Stock Markets†. Journal of Financial and Quantitative Analysis, Vol. 34, 33-55. Asuncion, J. (2007). â€Å"India's Capital Markets: Unlocking the Door to Future Growth†. Germany: Deutsche Bank Research. Baillie, R. T. , & DeGennaro, R. P. (1990). â€Å"Stock Returns and Volatility†. Journal of Financial and Quantitative Analysis, Vol. 25, 203-214. Bhattacharya, Himadri, (2004), â€Å"Deregulation of Gold in India – A Case Study in Deregulation of a Gold Market†, Research Study No 27, World Gold Council, pp. 1-28 Blose, Laurence E. (1996), â€Å"Gold Price Risk and the Returns on Gold Mutual Funds†, Journal of Economics and Business, Vol. 48, pp. 499-513. Brodsky, David A. and Gray P. Sampson (1980), â€Å"The Value of Gold as a Reserve Asset†, World Development, Volume 8, Issue 3, March 1980, Pages 175-192. Cai, J. , Cheung, Y. and Wong, M (2001), â€Å"What Moves the Gold Market? †, The Journal of Futures Markets, Vol. 21, No. 3, 257-278, O John Wiley & Sons, Inc. Campbell, J. Y. , Lo, A. W. , & MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Second Edition, Princeton: Princeton University Press. Chua, J. , and Woodward, R. (1982), â€Å"Gold as an Inflation Hedge: A Comparative Study of Six Major Industrial Countries†, Journal of Business Finance and Accounting, Vol. , pp. 191-197. Citanna, A. , & Schmedders, K. (2005). â€Å"Excess Price Volatility and Financial Innovation†. Economic Theory, Vol. 26, 559-587. Dickey, D. A. , & Fuller, W. A. (1981). â€Å"Likelihood Ratio Statistics for Auto-Regressive Time Series with a Unit Root†. Econometrica, Vol. 49, 1057-1072. Dolado, J. J. a nd Lutkepohl, H. (1996), â€Å"Making Wald Tests Work for Cointegrated VAR Systems†, Econometric Reviews, Vol. 15, pp. 369-386. Dun’s Review (1980), â€Å"Bring Back the Gold Standard†, Vol. 115, No. 2, pp. 58-67. Engle, R. , & Granger, C. W. (1987). â€Å"Cointegration and Error Correction: Representation, Estimation and Testing†. Econometrica, Vol. 55, pp. 251-276. Ensers, Walter (1995), Applied Econometrics Time Series, John Wiley and Sons, Singapore. Gaur, A. and Bansal, M. (2010), â€Å"A Comparative Study of Gold Price Movements in Indian and Global Markets†, Indian Journal of Finance, Vol. 4, No. 2, pp. 32-37. Ghosh, Dipak, Levin, E. J. , Macmillan, Peter and Wright, R. E. (2002), â€Å"Gold as an Inflation Hedge†, Discussion Paper Series No. 0021, Department of Economics, University of St. Andrews. 55 [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] P K Mishra, J R Das and S K Mishra Granger, C. W. (1986). Developments in the Study of Cointegrated Economic Variables†. Oxford Bulletin of Economics and statistics, Vol. 48, 213-228. Granger, C. W. (1969). â€Å"Investigating Causal Relation by Econometric Models and Cross Spectral Methods†. Econometrica, Vol. 37, pp. 424-438. Granger, C. W. (1974). â€Å"Spurious Regressions in Econometrics†. Journal of Economet rics, Vol. 2, pp. 111-120. Granger, C. W. , & Morgenstern, O. (1963). â€Å"Spectral Analysis of New York stock Market Prices†. Kyklos, Vol. 16, 1-27. Greene, William H. (2003), Econometric analysis, 5th ed. , Pearson Education Publishers, New Delhi. Gujarati, D. N. & Sangeetha. (2007). Basic Econometrics. New Delhi: TMH Publishing Company Ltd. Johansen, S. (1995). Likelihood-Inference in Cointegrated Vector Autoregressive Models. Oxford: Oxford University Press. Johnson, H. Clark (1994), â€Å"The Gold Standard, France and the Coming of the Depression: 1919-1932†, Yale University. Kendall, M. (1953). â€Å"The Analysis of Economic Time Series†. Journal of the Royal Statistically Society, Series A, Vol. 86, 11-25. Kim, Youngje (2002), Gold Analysis, web. syr. edu/~ykim30/file/gold. pdf Lutkepohl, H. (1991), Introduction to Multiple Time Series Analysis, Springer Verlag, Berlin. MacKinnon, James G. , Alfred A. Haug, and Leo Michelis (1999), â€Å"Numerical Distribution Functions of Likelihood Ratio Tests For Cointegration,† Journal of Applied Econometrics, 14, 563-577. Poitras, G. and Neil Alan (1996), â€Å"A Study of Gold Futures Price Spreads†, Columbia University. Poon, S. H. , & Granger, C. W. (2003). â€Å"Forecasting Volatility in Financial Markets: A Review†. Journal of Economic Literature, Vol. XLI, 478-539. RBI (1997), â€Å"Gold in India†, Reserve Bank of India Bulletin. Rueff, J. and Hirsch, F. (1965), â€Å"The Role and the Rule of Gold- An Argument†, Princeton Paper No. 7, June. Salent, S. , and Henderson, D. , (1978), â€Å"Market Anticipation of Government Policies and the Price of Gold†, Journal of Political Economy, Vol. 86, pp. 227. 249 Schill, M. J. (2006). â€Å"New Perspectives on Investing in Emerging Markets†. The Research Foundation of CFA Institute, Emerging Markets (May) . Shah, A. ( 1999). â€Å"Institutional Change on india's Capital Markets†. Economic and Political Weekly, Vol. XXXIV (3-4), pp. 183-194. Sjaastad, L, and Scacciavillani, F. , (1996), â€Å"The Price of Gold and the Exchange Rate†, Journal of International Money and Finance. Vol. 15, pp. 79-897 Shiller, R. J. (1998). Market Volatility. Cambridge, MA: MIT Press. Subramaniam, S. (1989). â€Å"The Impact of Political and Economic Events on Stock Behaviour†. Doctoral Dissertation, IIM, Ahmedabad . Taylor, S. (1986). Modelling Financial Time Series. New York: John Wiley and Sons. Toda, H. Y. , & Philips, C. B. (1993). â€Å"Vector Autoregression and Causality†. Econometrica, Vol. 61, No. 6, 1367-1393. Tschoegl, A. E. (1980), â€Å"Efficiency in the Gold Market†, Journal of banking and Finance, Vol. 4, No. 4, pp. 371-379. [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45]