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A Refereed Monthly International Journal of Management

Revisit to the Determinants of Gold Price in India using Multiple Linear Regression Model

Author

Author

*Dr. Khujan Singh Haryana School of Business (Guru Jambheshwar University of Science & Technology), Hisar-125001, Haryana, India. Mobile No.: +919466174057 E mail: kh_hsb@yahoo.co.in

**Anil Kumar (Research Scholar) Haryana School of Business (Guru Jambheshwar University of Science & Technology), Hisar-125001, Haryana, India. Mobile No.: +918059071440 E mail: anilkumar8869@yahoo.com

ABSTRACT

This study has been conducted to determine macroeconomic variables that decide the gold prices in India for which the Multiple Linear Regression Model is applied. The gold prices have been taken as dependent variables and crude oil prices, repo rate, inflation rate, exchange rate of US dollar in rupees, BSE closing prices, silver prices and foreign exchange reserves of India have been taken as independent variables. Monthly data of all these macroeconomic factors and gold prices have been collected from their respective websites for the period April, 2003 to December, 2016. The empirical results found that BSE closing prices and repo rates are inversely correlated with gold prices, while crude oil prices, inflation rate, silver prices, exchange rate of US dollar in rupees and Foreign exchange reserves have significant positive correlation with gold prices. The results of the study are significant for policy makers as well as investors.

Keywords: Gold price, exchange rate, inflation rate, crude oil prices, BSE closing prices and multiple regression model.

JEL: M21

Introduction

Historically, Gold had been medium of exchange but after Second World War its role as unit of account has decreased. But today it has number of uses most importantly in the form of jewellery, financial asset and industrial uses. In urban India gold is demanded more in the form of coins and bars but in rural India gold jewellery is more preferred. According to World Gold Council report (India office) income growth derives the gold demand in the long run that is holding all other macroeconomic factors constant, a rate of change in gold demand is equal to the rise in level of income in India. But in the short run gold demand is increasing because of exchange traded products as increasing gold prices have inflation hedge characteristics. Therefore gold is used to minimize the risk caused by inflation during financial market turmoil and also the market uncertainties play significant role in new high rallies in gold prices. According Razin and Rosefielde (2011) monetary policy and fiscal policy have an impact on India’s economic growth where as inflation rate, interest rates and stock market fluctuation plays vital role for gold demand. India is fastest growing economy in the year 2016 and as a result of increase in GDP (gross domestic product) the disposable income also increases which derive the demand for gold. International gold prices also witnessed upward movement in recent years except the year 2013 to 2015. The impact of international gold price trend is also seen in Indian domestic gold market. Hence gold price movements in India got attention of researchers, investors and other segments of the society.

The present study has been divided in seven sections. After introduction the second section focuses on review of literature. Third and fourth section defines the problem of statement and hypothesis. Section five of the study deals with research methodology, section six explains the empirical results and discussion and in last section conclusion has been explained.

Review of Literature

Vuyyuri, S., & Mani, G. S. (2005) concluded silver the close substitute of gold has significant impact on gold price changes rather than stocks which are supposed be an alternative to gold investment. The study was conducted for the period 1978 to 2000 by applying multiple regression analysis.

Simakova, J. (2011) found significant positive correlation between gold prices and crude oil prices during the period January 1970 to December 2010 by using Granger causality test, Johansen cointegration test and Vector Error Correction model for quantitative analysis.

Bapna, I.,Sood, V., Kumar, N. T., & Singh, H. S. (2012) examined the relationship between macroeconomic variables and gold price for the period 2002 to 2011by applying regression analysis and Granger causality test. It was found that exchange rate, fiscal deficit, forex reserve, inflation rate have significant impact on gold prices. Growth rate, GDP, BSE Sensex and NSE Index does not have significant impact on gold prices. The study also reveals that gold is hedge against inflation.

Choong, P. S., Piong, C. K., & Wong, W. X. (2012) identified the determinants of gold price by collecting quarterly data from 1971 to 2011. The study found significant positive relationship between CPI inflation rate, silver price, Brent crude oil price and gold price where as the USA dollar trade weighted index and gold price significantly negatively correlated and data analyzed by using simple regression and multiple linear regression model.

Mishra, R. N., & Mohan, G.J. (2012) applied VAR (vector auto regression) model for period 1991 to 2011 and found that domestic gold price and international gold price are closely interrelated. The US $ exchange rate and equity prices also affects the international gold prices in long-run and short-run and investors uses gold hedge against inflation in long-term.

Patel, S. (2012) examined whether macroeconomic variables interest rate, exchange rate, index of industrial production, gold price, silver price and oil price had any significant impact on stock market during the period from January 1991 to December 2011 by applying Granger Causality test and Vector Error Correction Model (VECM). The study found that commodity prices like gold, silver and oil prices are significant determinants of stock markets.

Deepika, M. G., Nambiar, G. & Rajkumar, M. (2012) applied multiple regression analysis model and found variation in gold price significantly explained by world stock prices, US $ exchange rate index, and Inflation rate during period from 1980 to 2012. The study found a significant negative correlation between world stock prices and gold.

Baber, P., Baber, R., & Thomas, G. (2013) identified significant positive correlation between inflation rate, gold prices and exchange rate of US dollar by applying trend analysis and correlation analysis during the period from 2002 to 2012, though gold prices and interest rates are inversely correlated during same period of study.

Tufail, S., & Batool, S. (2013) by applying random walk theory found gold is significant determinant of inflation and considered hedge against unexpected inflation in Pakistan from January 1968 to December 2008.

Sindhu, D. (2013) examined the relationship between gold price and different macroeconomic variables by using trend analysis, correlation analysis and regression analysis. The inverse relationship was found between gold prices, US dollar exchange rate and repo rate. The crude oil prices and inflation rate were positively correlated with gold prices during the sample period from November 2006 to December 2011.

Ibrahim, S. N., Kamaruddin, N. I., & Hasan, R. (2014) applied multiple linear regression model and identified that gold price, inflation rate and exchange rate were significantly negatively correlated while crude oil price and gold price were significantly positively correlated for the period 2003 to 2012.

Bishnoi, R. (2014) applied multivariate regression analysis and found gold prices, US dollar exchange rate index and Crude oil prices had significant positive correlation but inflation rate, interest rates in the US and gold prices had significant negative relationship during the period from 1994 to 2013.

Table: 1. Relationship of gold price with macroeconomic variables according to the reviewed studies

Study year/period	Positive relationship	Negative relationship
Vuyyuri & Mani (2005) from 1978 to 2000	Inflation rate, exchange rate of US $ in rupees and silver prices	Interest rate
Simakova (2011) during 1970 to 2010	Crude oil price
Bapna et. al. (2012) from 2002 to 2011	Exchange rate, fiscal deficit, forex reserve, growth rate of NSE Index and interest rate	GDP, inflation and BSE Sensex
Choong et. al. (2012) from 1971 to 2011	Crude oil prices, silver prices and inflation rate	US $ trade weighted index
Mishra & Mohan (2012) from 1991 to 2011	Us stock price and US$ exchange rate(2003 to 2011)	Us stock price, world price index and US$ exchange rate(1991 to 2003)
Patel (2012) from 1991 to 2011	Exchange rate, crude oil price and stock price
Deepika et. al. (2012) from 1980 to 2012	US $ exchange rate index, inflation rate	World stock price index
Baber et. al. (2013) from 2002 to 2012	Inflation rate and US$ exchange rate	Interest rate
Tufail & Batool (2013) from 1968 to 2008	Inflation rate
Sindhu (2013) from 2006 to 2011	Inflation rate and crude oil price	Repo rate and exchange rate of US $ in rupees
Ibrahim et. al. (2014) from 2003 to 2012	Crude oil price	Inflation rate and exchange rate of US $
Bishnoi (2014) from 1994 to 2013	US $ exchange rate in rupees and crude oil price	Inflation rate, interest rate in USA and real GDP of USA

Statement of the problem and Objective of the study

After reviewing the number of studies it has been found that some studies are based on only two or three macroeconomic variables and some studies carried out by including more macroeconomic variables for given period of study. It is further found that inflation rate and US dollar exchange rate have negative as well as positive relationship with gold price in different study periods, that may be because of methodological and exchange rate regime changes. Whereas crude oil price always depicts significant positive relationship in all the study periods. Therefore to confirm the relationship once again in this highly integrated World economy in Indian rupee denomination all the major macro economic variables have been considered from 2003 to 2016. The objective of this study is to identify the determinants of gold price in India using multiple linear regression model.

Research Hypothesis

To achieve the objective following hypothesis has been formulated:

H 01 : There is no significant impact of macroeconomic variables on gold prices.

H 02 : The residuals are not auto correlated.

H 03 : The variance of residuals is homoskedastic.

H 04 : The residuals follow normal distribution.

Research Methodology

To test the above hypothesis following methodology has been used. This is an empirical research study based on secondary data for the sample period from April 2003 to December 2016. The monthly average data of BSE closing price collected from Yahoo finance website, inflation rate, repo rate, US dollar exchange rate and foreign exchange reserves data collected from Reserve Bank of India website. Monthly selling price of gold has been collected from World Gold Council website denominated in rupees and crude oil prices data is collected from OPEC (Organization of the Petroleum Exporting Countries) website. Monthly silver prices data collected from LMBA (London Bullion Market Association). Breusch-Godfrey serial correlation L-M test is applied to check the presence of autocorrelation in time series data. Heteroscedasticity of time series data is tested by using Breusch-Pegan-Godfrey test. Normality of given time series data is tested via Jarque-Bera statistics.

Multiple linear regression is a statistical tool used to establish the relationship between two or more independent variables and a dependent variable by fitting a linear equation to observed data. The proposed multiple regression for this study is as follows:

= + + + + + + + + (1)

Where, 1, 2………….n (number of observations)

y = gold Prices (dependent variable)

= constant, = error term, = BSE closing prices, = Inflation rate, = Repo rate

= Silver Prices, = Crude oil prices, = Exchange rate of US dollar in rupees

= foreign exchange reserves

6. Empirical results and discussion

Table 2 depicts the result of multiple regression analysis with different statistical values. The coefficient value of t-statistic is (-0.6394) and its corresponding p value is (0.0000) less than 0.05 which is significant, therefore null hypothesis ( H 01 ) has been rejected. The alternative hypothesis has been accepted that there is significant impact of macroeconomic variables on gold prices. The R- squared value is (0.8825) which is quite high as desirable for best fit statistical model. From the value of R- squared it can be stated that approximately 88 percent change in gold prices (dependent variable) is explained jointly by the independent macroeconomic variables. The rest approximately 12 percent variations in gold prices can be explained by residuals or other variables besides the used independent macroeconomic variables in this study. From table 2, it can be concluded that the independent variables individually significant to explain the change in dependent variable. The coefficient value of BSE closing prices is (-0.7359) and its corresponding p value is (0.0153), the coefficient value of repo rate is (-0.6826) and its corresponding p value is (0.0020) which is less than 0.05 in both cases.

Table: 2. Regression result

Variable	Coefficient	Std. Error	t- Statistic	Prob.
Constant	-0.6394	0.0574	-11.1394	0.0000*
BSE Closing Price	-0.7359	0.1369	-5.3754	0.0153*
Inflation rate	0.7455	0.2216	3.3641	0.0000*
Repo rate	-0.6826	0.1121	-6.0893	0.0020*
Silver price	0.6641	0.1185	5.6042	0.0000*
Crude oil price	0.7153	0.0965	7.4124	0.0026*
Exchange rate	0.8799	0.0642	13.7056	0.0000*
Forex reserve	0.5504	0.0713	7.7194	0.0000*
R-squared	0.8825		Meandepend. var	517.012
Adj. R-squared	0.7114		S.D. dependent var	261.217
S.E of regression	8.0137		Akaike info criter.	5.2619
Sum sq. resid.	188.09		Schwarz criterion	5.4736
Log likelihood	-352.272		Hannan-Quinn crit.	4.3471
F-statistic	235.687		Durbin-Watson stat	2.0037
Prob(F-statistic)	0.0000*

(Source: Authors own, * = level of confidence at 5%)

Therefore BSE closing prices and repo rate both have significant inverse relationship with gold prices. Inflation rate, silver prices, crude oil prices, exchange rate of US dollar in rupees and foreign exchange reserves have significant positive correlation with gold prices because their respective p values (0.0000, 0.0000, 0.0026, 0.0000 and 0.0000) which are less than 0.05. All the independent variables jointly influence the gold prices at large because the f-statistic value is (235.687) and its corresponding p value is (0.0000) significant. Therefore the model of this study is best fit model which meet the assumption of maximum change in dependent variable is individually and jointly explained by the macroeconomic independent variables.

Table 3 shows correlation between the independent macroeconomic variables. Correlation matrix shows the strength and direction between the two independent macroeconomic variables. Multicollinearity can be tested by correlation matrix.

Table: 3. Correlation matrix

	BSE closing Price	Inflation rate	Repo rate	Silver price	Crude oil price	Exchange rate	Forex reserve
BSE closing price	1.0000	0.3804	0.3315	0.5425	0.4315	0.5581	0.4251
Inflation rate	0.3804	1.0000	0.4337	0.5559	0.5851	0.6347	0.3092
Repo rate	0.3315	0.4337	1.0000	0.3943	0.4995	0.5649	0.6971
Silver price	0.5425	0.5559	0.3943	1.0000	0.3112	0.5002	0.5364
Crude oil price	0.4315	0.5851	0.4995	0.3112	1.0000	0.4110	0.3799
Exchange rate	0.5581	0.6347	0.5649	0.5002	0.4110	1.0000	0.5244
Forex reserve	0.4251	0.3092	0.6971	0.5364	0.3799	0.5244	1.0000

Source Authors own)

Table 3 displays that multicollinearity is not present between the independent macroeconomic variables. The results of correlation matrix also suggest the relationship between two or more independent macroeconomic variables is absolute and not spurious. Therefore the change in the gold prices is significantly explained by the macroeconomic variables used in this study.

Table 4 depicts the result of the autocorrelation of residuals obtained by applying Breusch-Godfrey Serial Correlation LM Test. The observed R squared value is (8.5763) and its corresponding p value is (0.0000) which is significant because it is less than the level of confidence value of 5 percent.

Table: 4. Autocorrelation test result

Breusch-Godfrey Serial Correlation LM Test
F-statistic	11.4192	Prob. F(2, 149)	0.0000
Obs R-squared	8.5763	Prob. Chi Sq.(2)	0.0000
Variable	Coefficient	Std. Error	t- Statistic	Prob.
Constant	-12.8496	3.0961	-4.1503	0.0148
BSE closing price	-0.0125	0.0814	-0.1535	0.4838
Inflation rate	0.2115	0.0107	19.7678	0.5669
Repo rate	-0.7705	0.1317	-5.8504	0.0192
Silver price	0.3249	0.0239	13.5564	0.6164
Crude oil price	0.2121	0.0844	2.513	0.0073
Exchange rate	0.0773	0.2841	0.2721	0.9751
Forex reserve	0.1607	0.0327	4.9143	0.0035
RESID(-1)	0.7105	0.0803	8.848	0.0000
RESID(-2)	0.2847	0.0811	3.5104	0.0607
R-squared	0.70777		Mean dep. var	5171.01
Adj. R-squared	0.58635		S.D. dep. var	2611.21
S.E of regression	11.8965		Akaike info criter.	7.2629
Sum sq. resid	1291.893		Schwarz criterion	6.4736
Log likelihood	-1520.272		Hannan-Quinn crit.	4.34751
F-statistic	9.7583		Durbin-Watson stat	2.7927
Prob(F-statistic)	0.6693

(Source: Authors own)

The null hypothesis ( H 02 ) has been rejected. Hence the residuals is serially correlated which is not desirable. To overcome the problem of autocorrelation the data has been tested at first lag of dependent variable.

Table 5 displays the result of the autocorrelation of residuals after one lag obtained by applying Breusch-Godfrey Serial Correlation LM Test. The value of observed R squared is (9.6421) and its corresponding p value is (0.4767) not significant because it is greater than 0.05 p value.

Table: 5. Autocorrelation test result after one lag

Breusch-Godfrey Serial Correlation LM Test
F-statistic	4.7792	Prob. F(2, 147)	0.5418
Obs R-squared	9.6421	Prob. Chi Sq.(2)	0.4767
Variable	Coefficient	Std. Error	t- Statistic	Prob.
Constant	-21.7616	2.4528	-8.8721	0.1583
BSE closing price	-0.0851	0.0212	-4.0141	0.1372
Inflation rate	0.9035	0.2129	4.2437	0.0562
Repo rate	-0.841	0.1314	-6.4003	0.0594
Silver price	0.3594	0.0523	6.8718	0.0004
Crude oil price	0.6782	0.0599	11.3222	0.0773
Exchange rate	0.0984	0.0247	3.9838	0.0698
Forex reserve	0.0821	0.0126	6.5198	0.0537
Lag Gold price	0.0469	0.0075	6.2533	0.0437
RESID(-1)	0.0715	0.0114	6.2719	0.0000
RESID(-2)	0.0778	0.0098	7.9387	0.0607
R-squared	0.65432		Mean dep. var	2398.05
Adj. R-squared	0.54396		S.D. dep. var	1501.17
S.E of regression	9.9956		Akaike info criter.	4.2854
Sum sq. resid	296.593		Schwarz criterion	4.4485
Log likelihood	-192.873		Hannan-Quinn crit.	3.9986
F-statistic	2.9162		Durbin-Watson stat	2.0018
Prob(F-statistic)	0.9715

(Source: Authors own)

The null hypothesis ( H 02 ) has been accepted. Therefore residuals are not auto correlated or not serially correlated. This is desirable and fulfilled the assumption of good fit multiple linear regression model.

Table 6 shows the result of Breusch-Pagan-Godfrey heteroskedasticity test of residuals. The value of observed R squared is (10.3058) its corresponding p value is (0.0000) significant because it is less than 0.05. Hence null hypothesis ( H 03 ) rejected.

Table: 6. Result of Heteroskedasticity test

Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic	7.5704	Prob. F(7, 151)	0.0000
Obs R-squared	10.3058	Prob. Chi-Square(7)	0.0000
Variable	Coefficient	Std. Error	t- Statistic	Prob.
Constant	-44.8357	7.9482	-5.6409	0.1854
BSE closing price	-0.2661	0.0253	-10.5177	0.0024
Inflation rate	0.4617	0.0742	6.2223	0.0057
Repo rate	0.2528	0.0213	11.8685	0.0894
Silver price	0.1352	0.0176	7.6818	0.0000
Crude oil price	0.0338	0.0031	10.9032	0.0686
Exchange rate	0.1572	0.0207	7.5942	0.1031
Forex reserve	0.0913	0.0132	6.9166	0.1318
R-squared	0.2653		Mean dep. Var.	1181.48
Adjusted R-squared	0.2156		S.D. dep. Var.	2670.95
S.E of regression	10.6912		Akaike info criter.	6.8658
Sum squared resid	182.273		Schwarz criterion	6.0709
Log likelihood	-291.829		Hannan-Quinn crit.	7.9527
F-statistic	7.5704		Durbin-Watson stat	3.0736
Prob(F-statistic)	0.0000

(Source: Authors own)

Therefore variance of residuals is not homoskedastic which is not desirable in multiple regression model. Heteroskedasticity of the residuals has been removed by taking log of dependent and independent variables.

Table 7 shows the result of Breusch-Pagan-Godfrey Heteroskedasticity test of residuals after log transformation of given dependent and independent variables of the study.

Table: 7. Result of Heteroskedasticity test after log transformation

Heteroskedasticity Test: Breusch-Pagan-Godfrey
F-statistic	4.5828	Prob. F(7, 151)	0.0729
Obs R-squared	6.3058	Prob. Chi-Square(7)	0.0995
Variable	Coefficient	Std. Error	t- Statistic	Prob.
Constant	-41.2081	5.5496	-7.4254	0.0439
Log(BSE closing price)	0.0701	0.0116	6.0431	0.0132
Log(Inflation rate)	0.1913	0.0131	14.6031	0.0006
Log(Repo rate)	0.2898	0.0185	15.6648	0.0173
Log(Silver price)	0.1996	0.0135	14.7851	0.0000
Log(Crude oil price)	0.2375	0.0168	14.1368	0.0596
Log(Exchange rate)	0.1763	0.0201	8.7711	0.0839
Log(Forex reserve)	0.2489	0.0451	5.5188	0.0008
R-squared	0.3586		Mean dep. Var.	1223.68
Adjusted R-squared	0.3211		S.D. dep. Var.	1590.65
S.E of regression	8.9945		Akaike info criter.	7.5619
Sum squared resid	216.148		Schwarz criterion	6.1715
Log likelihood	-91.9882		Hannan-Quinn crit.	4.8435
F-statistic	4.5828		Durbin-Watson stat	2.0094
Prob(F-statistic)	0.0729

(Source: Authors own)

The value of observed R squared is (6.3058) its corresponding p value is (0.0995) not significant because it is greater than 0.05 and null hypothesis ( H 03 ) has been accepted. Hence, variance of the residuals is homoskedastic which is desirable for good fit model.

Table 8 depicts the results of the normality of time series data given under the study period of different variables. The value of Jarque-Bera is (0.4206) and its corresponding p value is (0.8103) is not significant because it is greater than 0.05.

Table: 8. Normality test statistics

Mean	-3.50E+194
Median	-0.0030
Maximum	0.1434
Minimum	-0.1637
Std. Deviation	0.0607
Skewness	0.1059
Kurtosis	2.8636
Jarque - Bera	0.4206
Probability	0.8103

(Source: Authors own)

The null hypothesis ( H04 ) is accepted which means the residuals follow the normal distribution. For best fit model the residuals must be normally distributed. Therefore normality assumption of multiple linear regression model has been fulfilled.

Figure: 1. Normality test graph

(Source: Authors own)

Figure 1 shows the graph of residuals. From the graph it can be stated that the residuals follow the normal distribution. If we draw a line touching the centre point of all the histograms it reveals the normal bell shape.

Gold prices and BSE closing prices have significant inverse relationship between them means movement in gold prices and BSE closing prices in opposite direction alike to the study of Deepika, M. G., Nambiar, G. & Rajkumar, M. (2012). When there is jitteriness in stock market investors deploys their funds in gold. Repo rates and gold prices also have significant negative correlation between them similar to the study of Jaiswal, B., & Manoj, S. (2015). Repo rates categorically related to interest rates rendered by the banks. Repo rate is controlled by Reserve Bank of India to control the liquidity in market. Increase in repo rate decreases the level of funds in circulation less amount of money in hands of the investors and exert pressure on gold prices to move downwards. Inflation rate and gold prices show significant positive relationship between them similar to study of Bapna, I.,Sood, V., Kumar, N. T., & Singh, H. S. (2012). High level of inflation in the economy leads to rally in gold prices. Because investors do not want to lose the real value of money and start investing in safe assets like gold. Gold is considered hedge against inflation in long run as found in the study of Mishra, R. N., & Mohan, G.J. (2012). Crude oil prices and gold prices significantly positively correlated with each other similar to findings of Simakova, J. (2011), Ibrahim, S. N., Kamaruddin, N. I., & Hasan, R. (2014) and Sindhu, D. (2013). Crude oil is international commodity and volatility in crude oil prices indicates disturbances in global economy. Whenever there is crisis in economy, investors rush to invest in gold and this tendency increase the gold prices. Silver prices show significant positive correlation with gold prices underpinned by the study of Choong, P. S., Piong, C. K., & Wong, W. X. (2012). Rally in gold prices leads to increase in silver prices because silver is close substitute of gold. Exchange rate of US dollar in rupees and gold prices significantly positively correlated with each other similar to the findings of Mishra, R. N., & Mohan, G.J. (2012) and Tully, E., & Lucey, B. M. (2007). Increase in dollar prices increase the gold prices. Foreign exchange reserves have significant positive correlation with gold prices. Increase in the level of foreign exchange reserves increase the prices of gold.

Conclusion

Study reveals that macroeconomic factors like BSE closing prices and repo rate significantly inversely related to gold prices. If BSE closing prices and repo rate moves in upward direction but the gold prices moves in downward direction and vice versa. Macroeconomic variables such as silver prices, crude oil prices exchange rate of US dollar in rupees and foreign exchange reserves significantly positively correlated with gold prices means the movement in these macroeconomic variables follow the same trend as in gold prices and vice versa. Investors should have close watch on the macroeconomic conditions of the nation. If the uncertainty exists in the market one must prefer the investment in gold.

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Websites:

• rbi.org.in
• yahoofinance.co.in
• gold.org
• opec.org
• lbma.org.uk