Magoosh GRE

The Determinants of the High Prices of Gold

| March 18, 2015

1. Introduction
Investors become overly optimistic about investing in precious metals such as gold and platinum when price levels become high or when the economy is suffering from uncertainties. In recent years, interest rates have fallen drastically. In addition, the world is still struggling to revive from the recent global financial crisis, which has created a very high level of macroeconomic uncertainty across many countries. This has led to an increase in the attention accorded to gold and other precious metals as investment vehicles. This is because investors consider commodity markets as safe havens during periods of macroeconomic uncertainty.

Gold is one of the most important commodities. The demand for gold is very high because of its multiple uses. The uses of gold can be divided into two categories. Firstly, gold is demanded as a physical asset where it is transformed into jewellery, coins and electronics; secondly, gold is demanded for investment purposes where it is used for hedging and speculative reasons (Lampinen, 2007). Many countries across the world have used gold as a monetary exchange vehicle. Gold has played an important role in the development of money. During the gold standard, gold-convertible paper instruments were issued and used as money. During this era, the total value of issued money was represented in a store of gold reserves. Gold was therefore the main store of value during the gold standard. Following the abandonment of the gold standard gold continues to be used as a monetary exchange vehicle as many countries continue to issue gold coins.

The price of gold has maintained an upward trend for a very long time. For example, in April 2001, gold stood at a price of $260 per ounce. By December 2005, the price had risen to more than $500 per ounce and by mid-January 2006, gold was selling at $548 per ounce (Levin and Wright, 2006; Lampinen, 2007). As at May 2006 the price of gold had risen to $752 and by 2007, gold settled at a price of $650 per ounce (Lampinen, 2007; Oxford Economics, 2011).
The period from 2007 to 2011 witnessed one the most dramatic increases in the price of gold. The price of gold has witnessed significant increases in price during this period. Between January 2008 and November 2011 the price of gold almost doubled from $889.60 per ounce in January 2008 to $1,738.98 per ounce in November 2011.

The significant increase in the price of gold over recent years is a cause for concern and requires fresh evidence on the determinants of gold. Whereas there are few papers on this topic, most of the papers were written some years back. There is very limited research in recent times that incorporates changes that have taken place in the business and financial environment. This study therefore aims at contributing to existing literature by providing fresh evidence on the factors that determine the price of gold, taking into consideration recent developments in the business and economic environment. The paper begins by providing an economic framework on how the demand and supply of gold is determined; the paper then provides a theoretical framework on the factors that determine the price of gold and later on provides empirical evidence on these factors. All these are done in section 2 below. Section 3 follows with an econometric framework for studying the relationship between the price of gold and its fundamentals; section 4 provides the empirical results and findings; and section 5 provides conclusions and recommendations.

1. Theoretical Framework and Literature Review
2.1 Theoretical Framework
2.1.1 Demand and Supply of Gold
2.1.1.1 Demand for Gold
The price of gold has both long and short-run determinants. There are two categories of factors that determine the price of gold in the short run. The first category known as use demand for gold consists of gold as an input to the production of jewellery, medals, electrical components and other important products (Christian, 2006). The use demand for gold has a negative relationship with its price. This means that as price increases, the use demand decreases and vice versa.

The second category of demand for gold is the demand for investment purposes. The demand for gold as an investment vehicle is determined mainly by changes in macroeconomic conditions such as exchange rate changes, changes in inflation, and panic. Aggarwal and Lucey (2007) summarises the demand for gold as arising from consumers in the form of dental fillings, jewellery production and other activities. In addition, gold is demanded in industry because of its classification as one of the most dental metal and its ability to conduct heat and electricity (Aggarwal and Lucey, 2007). Finally, gold is demanded by central banks, speculators and investors as a store of value and as an investment.

2.1.1.2 Supply of Gold

The short-run supply of gold is determined by a number of factors. In recent years, Central banks have become increasingly willing to lease gold (World Gold Council, 2010). This indicates that gold producers offer gold to their customers from two main sources: (i) gold leased from central banks; and (ii) gold extracted directly from gold mines.

There is long time lag between the change in the price of gold and the supply response of gold extracted from gold mines because it takes time for new gold mines to be discovered and for mining to actually take place. Consequently, the long-term price elasticity of supply of gold is positive while the short-term supply of gold is inelastic. Central banks usually store gold as one of the assets that back the currency that is in circulation. During a short-term surge in the demand for gold, Central banks can lease some of their stock of gold to meet short-term supply shortages. After a given amount of time, when enough gold has been extracted, part of can be used to repay the gold that was leased from the Central Bank. It is important to understand the supply of extracted gold and the quantity of gold which is available in the market is affected by the quantity of gold that was leased in the previous period. Central Banks lease gold at a physical interest rate. The physical interest rate is the amount of extra gold that must be paid to Central Banks as interest on the gold that was leased. The higher is the amount of gold leased and the physical interest rate in the previous period, the higher is the lower is the amount of gold that is supplied to the market in the current period.

A positive relationship therefore exists between the total supply of gold from extraction and the lagged gold price. However, the relationship between the quantity of extracted gold supplied to the market and the amount of leased gold in the previous period is negative. Moreover the relationship between extracted gold supplied to the market and the physical interest rate is negative. This is because, the higher the physical interest rate, the more gold is required to pay the Central Bank and the lower is the quantity that can be retained in the market. Likewise, the higher the quantity of gold that is to be repaid, the higher is the quantity that must be repaid to the Central Bank and the lower is the quantity of extracted gold that can be retained in the market.

One of the objectives of Central banks for holding gold in their vaults is to benefit from a convenience yield. The convenience yield is the amount of benefits that are expected to accrue to the Central Bank as a result of its investment in gold over a given period of time. For example, the higher the amount of gold held by the Central Bank, the higher is its ability to print currency without increasing inflation. The amount of gold leased is determined by adjusting the gold reserves to the point where the physical interest rate received from leasing gold is equal to the convenience yield on gold forgone to other central banks holding gold plus the default risk.

The supply of gold is therefore sensitive to a number of factors including the default risk premium, the convenience yield, and the physical interest rate. The total quantity of gold supplied in the short-run will for example decline if there is a decrease in the physical interest followed by an increase in the convenience yield plus default risk premium that occurs as a result of a political or financial turmoil. The short-run supply of gold also depends on the amount of gold that was leased in the previous period that is expected to be repaid in the current period. In summary, the total quantity of gold supplied in the short-run is a function of the lagged price of gold, the gold lease rental rate, the convenience yield, default risk premium, and the quantity of gold leased in previous period.

2.1.2 Determinants of the Price of Gold
Gold has witnessed a number of changes with respect to how it is being used over time. In the medieval times, gold was regarded as both a store of value and as a currency. Gold was formally traded as an over-the-counter security in London since the 17th century. In the 19th century, it became the foundation of the fixed exchange rate regime also known as the gold standard which operated across the world during this period. In the 20th Century, the Bretton Woods System (BWS) (the IMF and World Bank) regarded gold as the pillar behind the fixed exchange rate regime. The price of gold was allowed to float freely in the early 1970s following the breakdown of the BWS.

The distinguishing factor between gold and other commodities is that it has been regarded as a store of value, an asset which could protect your wealth against inflation. Unlike other precious metals or commodities, gold is a unique commodity in that its properties are stable over time, which have promoted its use as a long-run store of value and thus a hedge against inflation. This property can be seen from the fact that gold that is mined today can still be exchanged for gold that was mined some centuries ago.
The foregoing suggests that gold is a very important commodity. However, because its supply has remained relatively fixed over the last 100 years, it is difficult to fully exploit its benefits given that it may not be available when highly needed (World Gold Council, 2010; Levin and Wright, 2006). This means that even if an investor is interested in hedging against inflation, the investor may not be able to have access to gold. Gold’s annual production represents only a small proportion of the quantity of gold that is already outstanding (Oxford Economics, 2011). Supply is further limited because of limitations in its annual production. Suppliers therefore find it extremely difficult to respond to changes in price. By contrast, in other commodity markets, it is possible for production to adjust to changes in prices over the medium-term.

Another factor that distinguishes gold from other commodities is the fact that it is used less frequently for industrial purposes. Compared to metals such as silver, platinum, aluminium, etc, gold is used mainly as an investment and not as an input into production (World Gold Council, 2010). Approximately 10 percent of gold is used in industries while the remaining 90 percent is used for jewellery (World Gold Council, 2010). Given that gold has limited industrial use, it has only a very weak relationship with business cycles (World Gold Council, 2010). As a result, the correlation between the gold price and other financial or microeconomic variables is often not significantly different from zero (Lawrence, 2003).

While gold differs from other commodities in that it is used mainly as an investment asset, gold also differs significantly from other investment assets. While other financial assets such as bonds and stocks deliver a return (e.g., coupon interest and dividends), gold does not provide its investors with a return (Oxford Economics, 2011). But the default risk of gold is zero which gives it a distinct advantage over other financial assets such as stocks and bonds.

Gold is often regarded as a long-run hedge against inflation. This is because; its long-run purchasing power has remained approximately the same over time (Dupois et al., 2006). Gold has been subjected to a variety of institutional settings such as the gold standard and the BWS. However, these settings seem to have had a very limited impact on its long-run purchasing power (Jastram, 2009; Levin and Wright, 2006). Expressed in terms of 2010 dollars, the price of gold in the 1830s was approximately US$450 per troy ounce (Oxford Economics, 2011). However, approximately 150 years later, as at 2005, the price was still about $450 per troy ounce. Although it is a long-term hedge against inflation, the price of gold does not move in perfect lockstep with the general price level (Oxford Economics, 2011). Rather, over long horizons, there is no apparent relationship between the gold price and the general price level (Oxford Economics, 2011).

Dupois et al. (2006) observes that the use of gold as an inflation hedge has evolved over time. Historically, gold has served well as a good leading indicator of inflation. For example, the sharp increase in the general price level during the period 1973 to 1979 was preceded by a sharp rise in the price of gold. Specifically, using the price of gold, it was possible to understand a year in advance that there was an imminent outbreak of inflation. The power of gold as a good leading indicator of inflation can also be seen in the 1980s when the decline in the price of gold preceded a decline in inflation. The correlation coefficient between the price of gold and the general price level was approximately 0.93 over the five year period 1981 to 1986 (Dupois et al., 2006). This goes a long way to show that over the period 1973 to 1986, gold was a good leading indicator of inflation and thus a good hedge against inflation. However, recent evidence shows that in the 1990s, gold lost its place as a leading indicator of inflation and thus an inflation hedge. Dupois et al. (2006) also observes that the price of gold exhibits and inverse relationship with the U.S dollar. The inverse relationship between the price of gold and the U.S dollar is not surprising given that a report by the World Gold Council (2006) shows that the U.S dollar also exhibits an inverse relationship with a variety of the prices of other raw materials. Despite the inverse relationship of the price of other raw materials with the U.S dollar, Dupois et al. (2006) notes that the inverse relationship is strongest for gold than for other raw materials. The relationship between the price of gold and the U.S dollar can be attributed to the changes in demand and supply for a currency when its value changes. When the value of the U.S dollar appreciates as investors shift their portfolios from gold to holding the U.S dollar. Consequently, the supply of gold and other raw materials increases, thereby leading to an increase in their prices. The reverse is true for a decline in the value of the U.S dollar.

The recent rise in the price of gold has been attributed to the rising prices of other commodities. Dupois et al. (2006) note that the price of gold has moved with the prices of other commodities. Demand for commodities especially from Asian countries has witnessed a dramatic increase since 2002. In response, commodity prices have risen sharply. Despite its unique intrinsic characteristics, gold has limited industrial use which means that the rise in the demand for gold has not been as high as those of other commodities.

Gold however, has an advantage over other commodities in that it is a liquid asset. Low inflation in Asian countries has resulted in high savings levels, and these savings have to be recycled into other types of assets. Gold with its liquidity and its inflationary hedge characteristics is an attractive asset for these savings (Dupois et al., 2006). This explains why its price has witnessed a dramatic increase lately (Dupois et al., 2006). Gold is not regarded as a raw material. Rather, gold is considered as an investment. Gold has therefore attracted the attention of many investors in recent years and as such its price has increased.
2.1 Empirical Evidence
Given the importance of gold as a precious metal over so many centuries, particularly its role as a store of value in times of economic and political uncertainties, gold has attracted the attention of many researchers.
The literature on gold has focused mainly on the relationship between the price of gold and other variables. One group of researchers focus on the long-run relationship between the gold price and the price of crude oil. For example, Nakarum and Small (2007) observe that the daily price of gold and the daily price of crude oil exhibit random walks. Moreover, using first differences, the study observes that both the price of gold and the price of crude oil are normally distributed and behave as time-varying random variables (Nakarum and Small, 2007). Zang and Wei (2010) base their study on the fact that commodity markets are dominated mainly by gold and crude oil, which means that understanding the long-run relationship between gold and crude oil is of particular importance. Of course, while it may not necessarily be true that commodity markets are dominated mainly by these two commodities, crude oil in particular represents one of the most widely used commodities across the globe due to its high demand across almost all industries. Zang and Wei (2010) show that the price of gold and the price of crude oil had a correlation coefficient of 0.9295 over the period January 2000 to January 2008. In addition, using cointegration techniques, a long-run relationship is observed between the price of gold and the price of crude oil. The long-run relationship indicates that at least one cointegration vector exists between the time series price of gold and the time series price of crude oil which means that one of the two variables depends on the other. Using granger causality, they observe that the changes in the price of crude oil linearly cause the volatility of the price of gold but not the other way round which means that the price of gold is a function of the price of crude oil over long horizons.
Shaffiee and Topal (2010) conduct an analysis on the role changes in inflation and fluctuations in the price of crude oil in determined gold’s price. A forecasting model is also presented which is based on long-term reversal, jumps/dips and diffusion. The evidence suggests that crude oil and the price of gold had a very strong linear relationship over the last four decades. On the contrary, the price of gold and inflation appear to have a very weak linear negative relationship over the past four decades (Shaffiee and Topal, 2010). Unit root tests are later employed to determine the stationary of the price of gold over the long-run. The results show that the time-series of the price of gold is non-stationary over long horizons. Based on this, Shaffiee and Topal (2010) employ a trend stationary model which is assumed to be superior over other models as a result of its ability to take into account jump and dip components into its parameters. The trend stationary model assumes that time-series prices of commodities tend to follow three different types of movements including long-run reversal to equilibrium price; diffusion and jump/dip diffusion. Validating the model with historical gold prices, it was then employed to forecast the price of gold over the next 10 years. The evidence suggests based on the assumption that the current jump in the price of gold initiated in 2006 will continue in a similar manner as that initiated in 1978, the price of gold will remain at abnormally high levels up to the end of the year 2014. Following from 2014 onwards right up to 2018, the price of gold will gradually revert to its long-run equilibrium value.

Some studies focus on the relationship between the price of gold and the impact of exchange rates and interest rates. For example, Sjaastad and Scacciavillani (1996); and Sjaastad, (2008) observe that fluctuations in the euro had a strong impact on the price of gold in the 1980s while Tully and Lucey (2007) observe that U.S dollar fluctuations were the major influences on the price of gold during the 1990s. Gunes et al. (2011) examine world gold prices over the 10-year period 2000 to 2010 to determine the factors that affect the price of gold. In particular the study focuses on determining the impact of interest rates, the Euro/US dollar exchange rate. The evidence suggests that there is a long-run relationship between ‘interest rates and exchange rates’ and the price of gold.

Kearney and Lombra (2009) observe a positive relationship between the price of gold and platinum over the period 1985 to 2006. However, it is also observed that the correlation between the price of gold and the price of platinum over the period 1996 to 2001 was negative (Kearney and Lombra, 2009). Given this puzzle, the study aims at determining whether the shift in the relationship is due to an increase in the forward sales by gold producers, which resulted in the decline in gold prices during the 1990s as observed in Kearney and Lombra (2008). The study provides evidence that falling gold prices can be attributed to large net increases in the forward sales of gold by producers in other to hedge against price declines while rising gold prices can be attributed to declining forward sales or unhedging by producers (Kearney and Lombra, 2009).
As suggested by the evidence in Kearney and Lombra (2008; 2009), the use of forward contracts by gold producers to hedge against future price declines resulted in thdecline in the price of gold during the period 1996 to 2001 thereby distorting the long-run equilibrium relationship that existed between the price of gold and the price of platinum. In order to negotiate a forward contract, several parties are involved. These include intermediaries known as bullion banks who arrange a forward contract with a gold mining company that plans to deliver gold on a specified future date. When the bullion bank arranges the forward contract, it subsequently borrows gold from the central bank and sells it immediately in the gold spot market thereby increasing the supply of gold. The increase in the supply of a commodity results in a decrease in the price of the commodity. This explains why the price of gold declined over the period 1996 to 2001.
Other studies have focused on gold spot and futures and forward markets. In a study examining the flow of information in the U.S and Japanese gold, silver and platinum futures markets, Xu and Fung (2005) make use of a bivariate asymmetric generalised autoregressive conditional heteroskedastic (GARCH) model. Based on this model, the observe a strong volatility spillover across the two markets. The study however, observes that the impact of the U.S spillover is stronger than the impact of the Japanese Spillover (Xu and Fung, 2005).

The 1990s witnessed an increased in the market preference for gold forward and spot-deferred contracts over other types of derivative products (Cross, 2000). The difference between spot-deferred forward contracts and conventional forward contracts is that deferred forward contracts enable producers to defer the delivery of the underlying asset indefinitely. As the delivery date approaches while the price of gold is still below the spot-deferred price, the producer finds it profitable to close out the contract. However, if the delivery date approaches while the spot price is above the spot-deferred contract price, the producer will find it unprofitable to close out the contract. Rather, more gold will be sold spot while deferring the previously arranged forward contract. That is the forward contract is rolled over. Spot-deferred contracts therefore increased in popularity during the 1990s, thereby enabling gold producers to profit from continuously rolling over their previously arranged forward contracts irrespective of the movement in the spot price of gold. In addition, given that leased gold remains in the market, the initial impact in the spot market on the price of gold of arranging the short sale is not reversed. Consequently, the supply of gold appears to be increasing permanently thereby leading to a decline in its price. The second half of the 1990s short selling of gold by producers increased by 79 percent as compared to the first half of the 1990s. Given that the net increase in the amount of gold sold in the forward market was usually matched by an increase in the amount of gold leased sold into the market, an increase in short positions combined with the ability to spot-defer resulted in a substantial increase in the market supply of gold well above the normal trading or production volume and delivery into the market. These factors resulted in the decline in the price of gold during the period 1996 to 2001.

The literature on the gold price as well as its determinants has focused mainly on demand side factors with very limited research on supply side factors. This study therefore aims at contributing to the literature by examining recent evidence on the factors that determine the price of gold with a particular emphasis on the supply side factors.

3 Research Methodology and Data Description
3.1 Econometric Model
The analysis will involve three steps. In the first step, unit root tests will be conducted on each of the variables included in the study to determine whether it is stationary or not. The variables will include the monthly price of gold covering the period January 2002 to November 2011; the monthly crude oil price over the same period, the monthly U.S and U.K 3-Month Treasury bill yields over the same period; the monthly series of the Euro/USD exchange rate, USD/GBP exchange rate and Euro/GBP exchange rate; and the monthly series of the U.S consumer price index (CPI) over the same period. The second part of the analysis will involve testing for cointegration. This will be conducted to determine whether there is a long-run relationship between the price of gold and each of the variables included in the analysis. Once this is completed, a vector error correction model (VECM) will be employed to determine granger causality between the price of gold and each of the variables included in the study. The Vector error correction model will enable one to determine which variable in granger-causing the other. Finally, the study will employ regression analysis to determine the strength and magnitude of the relationship between gold prices and each of the variables included in the study.

3.1.1 Unit Root Tests
In order to determine the long-run relationship between gold prices and other variables, this study begins by conducting unit root tests on the time series of the different variables included in the study. The study employs three different unit root tests in order to ensure that the results are robust. These include the Philip Peron (PP) unit root test, The Augmented Dicky-Fuller (ADF) unit root test and the Kwiathowski-Phiplips-Schmidt-Schin (KPSS) unit root test (Meng and Ahmad, 2011). Both the ADF and PP tests test the null hypothesis that the time series has no unit root. In other words, that the time series is stationary. On the contrary, the KPSS test tests the null hypothesis that there is no unit root in the time series indicating that it is stationary.

The Philip Peron Unit Root Test
The Phillips-Perron Unit Root test was developed by Phillips and Perron (1988). This test has become one of the most commonly used tests in financial time series analysis. In other to conduct the PP test, the following regression equation is estimated:
(1)
Where , the error term is assumed to be I(0) and can either be heteroskedastic or homoskedastic. Heteroskedasticty means the variance of the error term varies over time while homoskedasticity means the variance of the error term is constant over time. When conducting the PP test, any serial correlations and heteroskedasticity in the error term are automatically corrected for in the regression by directly modifying the test statistics and . The modified statistics are given by:

(2)

(3)
Where and represent consistent estimates of the variance parameters given by:
(4)
(5)
In other words, a consistent estimate of is given by the sample variance of the least squares residual while the consistent estimate of is given by the Newy-West long-run variance estimate of .
The PP test is similar to the ADF test in that under the null hypothesis that , both the ADF and statistics and the PP and statistics have the same asymptotic distributions as well as the same normalised bias statistics.
The PP test is advantageous over the ADF test in that the PP test is robust to general forms of heteroskedasticity in the error term . In addition, when conducting the PP test, it is not necessary for a lag length to be specified in the regression as the case would be if one was using the ADF test.

The ADF Unit Root Test
The ADF test differs from the PP test in the manner in which it deals with serial correlation and heteroskedasticity in the error term. While the PP test ignores any serial correlation in the test regression, the ADF test relies on the incorporation of a lagged variable in the regression to take account of serial correlation in the error term.
In the ADF test, it is necessary to include both intercept and trend parameters. This is because, while a time-series may not be stationary, it may be stationary when a trend or intercept coefficient is included.

The ADF regression equation with trend and intercept parameters can be stated as follows (Ajayi and Monguoue, 1996):
(6)

3.1.2 Cointegration Tests
Unit root tests are used to determine whether the time-series is stationary. In the case of a stationary time-series, one cannot conclude whether the series exhibits a long-run relationship with another time-series. However, when a time-series is not stationary in its own right, then it is likely that it is exhibiting a long-run relationship with another variable. In order to determine whether a non-stationary time series exhibits a long-run relationship with another non-stationary time-series variable, one needs to employ a cointegration test. This paper employs one of the most commonly used cointegration tests known as the Johansen (1991, 1995) cointegration test. The Johansen cointegration test employs a vector autoregression (VAR) model, which can be stated as follows: (Hjalmarsson and Österholm, 2007)
represents a vector of an nx1 vector of variables which are said to be integrated of order (1). is an nx1 vector of innovations. The VAR model can be re-stated as:

(7)
Where

and
The model assumes that is a coefficient matrix of reduced rank r where r is less than the number rows n in the matrix. This means that there are nxr matrices and each with rank r such that and is stationary.
r serves as a measure of the total number of cointegrating vectors.

The elements of are known as adjustment parameters in the vector error correction model and each column of is a cointegrating vector (Hjalmarsson and Österholm, 2007).

It can be shown that for a given r, the maximum likelihood estimator of is a measure of the combinations of that gives the largest r canonical correlations of with after correcting for lagged differences and deterministic trends when present. In order to determine the number of number of cointegrating vectors, two likelihood test ratios can be employed to test the canonical correlations as well as the reduced rank of the matrix. The two statistics are the trace test and the maximum eigenvalue. These trace statistic is calculated using the following formula:
While the maximum eigenvalue statistic is computed from the following expression:

T measures the sample size; and is a measure of the ith largest canonical correlation. The trace statistic enables one to test the null hypothesis that r cointegrating relationships or vectors are present against the alternative hypothesis that n cointegrtating relationships are present. On its part the maximum eigenvalue enables one to test whether the null hypothesis that there are r cointegrating relationships is true against the alternative hypothesis there exist r+1 cointegrating vectors (Hjalmarsson and Österholm, 2007).
3.1.3 Vector Error Correction Model

In order to study determine the granger-causality between gold and each of the variables included in the study, we need to specify a VECM which corrects for errors in the model. The model can be derived by reparametising the regression model which links two variables X and Y. Assuming that gold price is represented by Y and that any other variable determining the price of gold is represented by X, the relationship between the price of gold, Y and the variable, X can be stated as follows:
(8)
Taking logs on both sides, we get:
(9)
From above, the dynamic relationship between the gold price and any variable X can be written as:
(10)
Lagged variables are included to enable one to analyse dynamic patterns in the time series. In order for the long-run dynamic equilibrium relationship to stay constant, all factors that may cause distortions in the relationship must be equivalent to zero. This means that movements in and the error term, must be equivalent to zero. Since is assumed to be constant and , we can write , . Substituting, we get:

If we assume that the above is consistent with the dynamic relationship stated earlier, it means that:

From above,

Let

Therefore,
,
Substituting for and , we get

Therefore,
(11)
Equation (11) is interpreted as the vector error correction model because it relates changes in the price of gold to changes in other variables as well as the difference between the price of gold and the other variable in the previous preceding period.
3.1.4 Regression Analysis
We also study the relationship between gold prices and other variables using ordinary least squares regression. We employ four main variables the price of oil, Inflation, interest rates, and exchange rates. Given that inflation, interest rates and exchange rates vary across countries, we employ interest rates, inflation and exchange rates across two countries including the U.S.A and the U.K. The exchange rate used in the analysis is the U.S dollar/Great British Pound Exchange rate. The model for the study the relationship between gold prices and these variables is given by:
(12)
Where represents the change in the price of gold at time, t;
represents changes in the inflation rate of country i at time t;
is the change in the foreign exchange rate of country i at time t;
is the change in the interest rate at time t;
is the change in the crude oil price at time t;
is the intercept of the regression line;
, , and represent the slope coefficients of the regression line which measure the sensitivities of the gold price to changes in inflation, exchange rates, interest rates, and the crude oil price, respectively.
In order to draw conclusions on whether these factors have an impact on the price of gold, we test the null hypothesis that each of the above coefficients is equal to zero. That is
H0: , , and = 0 against the alternative hypothesis:
Ha: , , and ≠0.

Testing for structural Break
The time series employed in this study cover a period of 10 years. It is possible that the factors that affect the price of gold may have changed over the period. Particularly, the global financial crisis and other macroeconomic shocks may have had an effect on the determinants of the price of gold. Consequently, the analysis will be done over two separate time horizons: January 2002 to July 2007 and August 2007 to November 2011. The period August 2007 to November 2011 reflects the period covering the global financial crisis. While it may be argued that the crisis was over by 2010, many economies are yet to fully recover from the crisis and as such the period of the crisis is extended to November 2011. The period January 2002 to July 2007 reflects a period of macroeconomic stability.

To test for structural breaks, we estimate the linear regression for each time period and then conduct the Chow test to determine whether the parameters are stable (that is whether they were the same for the two sub-periods). For each of the two time periods, the regression equations can be restated as follows:

(13)
(14)
The subscripts 1 and 2 represent the time periods January 2002 to July 2007 and August 2007 to November 2011, respectively.

The null hypothesis of the Chow test is stated as follows:
H0: , , , , and
The hypothesis can be tested using the Chow test statistic, which is estimated using the following expression:
(15)

Where k represents the number of coefficients in the regression; N1 and N2 represent the sample sizes of the sub-periods January 2002 to July 2007 and August 2007 to November 2011, respectively; Sc is the sum of squared residual for the entire sample period; and S1 and S2 represent the sum of squared residuals for the sub-periods January 2002 to July 2007 and August 2007 to November 2011, respectively.
The Chow test statistic follows the F-distribution with N1+N2¬-2k degrees of freedom.

3.2 Data Description

The data included in this study includes, the monthly price of gold over the period January 2002 to November 2011. The price of gold is extracted from the Bank of England statistical database. The data also includes the consumer price index for the U.S. This is extracted from the website of the U.S Bureau of labour statistics. The consumer price index is also observed for the period January 2002 to November 2011. To proxy for the effect of interest rates, the yields on the U.S and U.K 3-Month Treasury bill is used. Data for the yield on the U.K 3-Month Treasury Bill is extracted from the Bank of England statistical database while that for the U.S is extracted from the statistical database of the Federal Reserve Bank of New York. The study also tests the impact of exchange rates. Three different exchange rates are included in the analysis: the USD/GBP exchange rate; the Euro/USD exchange rate; and the Euro/GBP exchange rate. Exchange rate data is extracted from the statistical database of the Bank of England. Finally, the study analyses the relationship between gold and the price of crude oil. The crude oil price is extracted from the International Financial Statistics Database (IFS) that is maintained by the International Monetary Fund (IMF).

4 Empirical Results and Findings
Figure 1: Movement in the Monthly Price of Gold

Figure 1 above illustrates the time series movement in the monthly price of gold over the period January 2002 to December 2011. It can be observed that the price of gold has maintained an upward trend throughout the period under investigation. The figure shows that the price of gold has not been stationary. It appears to exhibit an upward sloping time series trend with a very small tendency to revert to its mean value. The price of gold moved from $281.65 in January 2002 to $1,738.98 in November 2011. This represents an increase of 517.42 per cent.
As earlier mentioned, it has been suggested that gold prices tend to move in line with price levels. Figure 2 below illustrates the movement in the U.S consumer price index over the same period.
It can be observed from figure 2 that the movement in the U.S CPI has almost mirrored that of the movement in the price of gold over the period under study. This suggests that the price of gold might have moved in response to changes in price levels as suggested by the literature.

Figure 2: Movement in the U.S Consumer Price Index

The literature has also suggested that gold moves in response to changes in the prices of other commodities. This study looks at how the crude oil price might have affected the price of gold. Figure 3 illustrates the movement in the crude oil price over the same period.

Figure 3: Movement in the Crude Oil Price

It can be observed that the oil price has also maintained an upward trend throughout the period under investigation. However, there was a shock in oil market during the period January 2008 to around June 2009 when oil prices dropped from approximately $190 per barrel in January 2008 to approximately $49 per barrel in June 2009. The reason for this decline might have been as a result of the global financial crisis. Apart from this period, the crude oil price has maintained an overall upward trend consistent with the movement in the price of gold.

This study also looks at how exchange rates affect the price of gold. To this effect, the study looks at three exchange rates: U.S dollar/Euro, Euro/Pound and U.S/Pound exchange rates. Figure 4 below illustrates the behaviour of the exchange rate series over the period January 2002 to December 2011.
Figure 4: Behaviour of Exchange Rates

It can be observed from figure 4 that the Euro/Dollar and Euro/Pound exchange rates maintained a gradual downward time series trend between January 2002 and April 2009. Since April 2009, both exchange rates have been somewhat constant. On the contrary, the U.S Dollar/Pound exchange rate has maintained an upward trend between January 2002 and August 2008. It declined sharply from $1.8889/£ in August 2008 to $1.4715/£ in April 2009. Since April 2009, the exchange rate has not witnessed any significant change. The foregoing suggests that the movement in the price of gold does not depend significantly on changes in exchange rates. Gold appears to have exhibited a weak positive relationship with the U.S/Pound Exchange rate over the period January 2002 to April 2009. Since 2009, the relationship appears to have broken down. Likewise, gold appears to have had a weak negative relationship with the Euro/Pound and Euro /Dollar Exchange rate, which broke down in April 2009.

This study also considers the behaviour of interest rates over the period January 2002 to December 2011 to determine whether they had an impact on the price of gold. Figure 5 shows the behaviour of the yields on the U.S and U.K Treasury bills over this period.

Figure 5: Movement in the Yields on the U.S and U.K 3-month Treasury Bills

Figure 5 shows the movement in the yields on the U.S and U.K 3-Month Treasury Bills. It can be observed that yields of both instruments have witnessed three different time series behaviours: an upward slope, a downward slope and a zero slope throughout the period under investigation. During the period January 2002 to January 2004, the yield on the U.S 3-Month Treasury bill was downward sloping. During the period January 2004 and January 2007, the U.S 3-Month Treasury Yield Curve was upward sloping. The 3-Month Treasury bill yield was at its peak in January with an average yield of approximately 5.0 percent. Between January 2007 and January 2009 the yield on the U.S 3-Month Treasury bill declined drastically to almost 0 percent. Since then the U.S 3-month Treasury Bill Yield has remained flat. The U.K 3-Month Treasury Yield Curve has witnessed the same behaviour over the period under investigation. The movement in interest rates appear to have no impact on the movement in the price of gold.

Have analysed the time series movement of the different variables of interest and their potential relationships with the price of gold, the study will now conduct unit root tests on the variables to determine whether they are stationary and cointegration tests to see if there are long-run equilibrium relationships between each variable and the price of gold.

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It can be observed from table 1 above that the null hypothesis that the time series contain a unit root can be rejected only for the Euro/US dollar exchange rate series. The hypothesis cannot be rejected for the rest of the time-series. This indicates that the gold price, U.S CPI, the crude oil price, The U.S 3-Month Treasury bill yield, the U.K 3-Month Treasury bill yield, the Euro/Pound Exchange rate and the U.S Dollar/Pound Exchange rate time series are non-stationary.

To check for the robustness of the ADF test results, we also run a PP test on all the time series and compare the results to those obtained earlier using the ADF test. The PP test results are presented in table 2 below. It can be observed from table 2 that the results using the PP test corroborate those using the ADF test. Consistent with the ADF results, the PP test results suggest that only one of the time-series (the Euro/U.S dollar exchange rate series) is stationary. The rest of the time-series variables are non-stationary.

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Table 3 above illustrates the Johansen (1991, 1995) test for cointegration. It can be observed that all the variables have at least two cointegrating vectors with the price of gold. The only variable that does not have a cointegrating vector is the exchange rate between the US dollar and the pound. Cointergation is not tested for the Euro/U.S dollar exchange rate because unit root test results suggest that the exchange rate time series is stationary.

The criteria for determining the number of cointegrating vectors is to compare the trace statistic to the 5% critical value for each rank. If the critical value is greater than the trace statistic, then the null hypothesis that there is at least a cointegrating vector equal to the rank is rejected. Otherwise, the hypothesis that there exist at least a cointegrating vector equal to that rank is not rejected and the test for the existence of a higher number of cointegrating vectors is conducted. The maximum number of cointergating vectors is 2. As can be observed from above, the trace statistic for each of the variables is greater than the 5 percent critical values for the existence of 0 and 1 cointegrating vectors. This means that the hypothesis of the existence of at least 1 cointegrating vector cannot be rejected for all the variables. It therefore means that there are at least 2 cointegrating vectors for each of the series. The only series that has no cointegrating vector is the U.S dollar/pound exchange rate.

The presence of the cointegrating vectors is an indication that there gold prices exhibit a long-run equilibrium relationship with each of the variables included in the study. The relationship between gold and the consumer price index is consistent with the theory that gold is often regarded as a hedge against inflation. When inflation is high, investors will prefer to maintain their wealth in terms of gold so as to avoid protect its value against the decline in real purchasing power. As inflation rises, the demand for gold increases thereby leading to an increase in its price. On the contrary, a decline in inflation results to a decline in the demand for gold as investors become more confident about the economy. More investors will prefer to maintain their wealth in other assets such as equity, real estate and bonds.

The long-run equilibrium relationship between the price of gold and the price of crude oil is also understandable. Crude oil is also a commodity that can be used as a store of value and therefore a hedge against inflation. It is therefore possible that during periods of rising inflation some investors may decide to move their wealth into crude oil. This leads to an increase in its demand and thus its price. When inflation eventually falls, the price of crude oil also falls following a fall in demand. The long-run equilibrium relation between the price of gold and the exchange rate between the Euro and the pound can be as a result of the fact that investors tend to switch between holding gold and these currencies as the exchange rate changes. It is likely that when the euro appreciates, the desire to hold gold increases as confidence in the euro declines. An appreciation in euro is likely to have the opposite impact.

The remainder of the paper will now focus on testing the linear relationship between the price of gold and each of the variables included in the study.

4Table 4 above illustrates the correlation matrix of changes in the different variables. It can be observed that the correlation between changes in the price of gold and most of the variables included in the study is negative. Moreover, the correlation coefficients are very small suggesting that there is only a weak linear relationship between changes in the price of gold and movements in these variables. The relationship is negative for the yields on the U.S and U.K 3-month Treasury bills. It is also negative for the exchange rates between the Euro and the US dollar as well as for the Euro and the Great British Pound. The relationship is however, positive for the exchange rate between the U.S dollar and the Great British pound, the U.S consumer price index and the crude oil price. While correlation provides insights on the linear relationship between two variables, it does not indicate which of the two variables is causing the other. In order to determine the direction of causality, we employ linear regression analysis.
Table 5 illustrates the results obtained by running the regression between changes in the price of gold and changes in each of the variables included in the model for the entire sample period January 2002 to November 2011. The variables have varying impacts on the price of gold. While some have a negative impact, others have a positive impact. Interest rates as measured by the yields on U.S and U.K 3-month Treasury bills have a negative impact. The magnitude of the impact of interest rates is different for the two yields. Looking at the p-values, it can be observed that the impact of the U.S Treasury bill is significant at the 10 per cent level of significance. This means that the null hypothesis that the coefficient for this variable is zero can be rejected with 90 per cent confidence that a Type I error has not been committed. 5
The impact of exchange rates on the price of gold is mixed. Out of the three exchange rates employed, two have positive impacts on the price of gold while one exhibits a negative impact. Specifically, the Euro/US Dollar exchange rate has a negative impact on the price of gold while the Euro/Great British Pound and the U.S Dollar/Great British Pound Exchange rates exhibit positive effects on its price. Given the weak relationship of exchange rates as observed from the p-values of their respective coefficients, it is not possible to conclude that exchange rates determine the price of gold.

As expected, the relationship between the price of gold and changes in the consumer price index is positive. Moreover, this relationship is significant at the 10 percent level of significance. The relationship between the price of gold and the consumer price index corroborates evidence provided in earlier studies that gold is a long-term hedge against inflation. Finally, changes in the price of gold also show a positive relationship with changes in the price of crude oil. This is also consistent with earlier findings that crude oil has a positive impact on the price of gold. A possible explanation for this relationship could be the fact that the price of crude oil itself is determined by inflation. In other words, crude oil is an alternative to gold as a long-run hedge against inflation. As inflation rises, the price of crude oil, alongside that of gold rises.

As mentioned in the research methods section, the regression coefficients may be unstable owing to changes in the economy. We now test for the stability of the coefficients using the Chow test discussed in section 3. To do this, we re-estimate the coefficients for the sub-periods ‘January 2002 to July 2007’ and ‘August 2007 to November 2011’. Tables 6 and 7 each illustrate the respective regression outputs for these two time periods.

Differences can be observed between the results obtained using the sub-periods and those obtained using the entire sample period. Moreover, differences are also prominent in the results obtained using the two sample periods. For example, the coefficient for the yield on the U.S 3-month Treasury bill is positive for the sub-period January 2002 to July 2007 but negative for the entire sample period. In addition, there are also differences in the signs of the coefficients of the exchange rate variables. While the Euro/USD exchange rate coefficient exhibited a negative relationship for sample period, the relationship was positive for the sub-period January 2002 to July 2007.3_001

There are also differences in the magnitude or strength of the relationship between gold and the variables over the different periods. During the sub-period January 2002 to July 2007, none of the factors appeared to be significant as can be observed from the high p-values of the individual coefficients. However, during the sub-period August 2007 to November 2011, a significant relationship can be observed between the U.S CPI and the price of gold. In addition, a significant negative relationship can be observed between the U.K 3-month Treasury bill yield and the price of gold. The differences can be attributed to differences in macroeconomic conditions over the two sub-periods. During the period August 2007 to around December 2009, the world suffered from the global financial crisis.4_001

Over the last 2 years, many Western European countries, as well as the United States have been through debt crises. Euro-Zone countries in particular (e.g., Greece, Italy, Spain, etc) have witnessed widespread defaults on their sovereign debts. These crises have forced many investors to shift their investments into gold. In particular, declining interest rates in the U.K have forced investors to shift their portfolios away from bonds to gold thereby driving up the price of gold. In addition, rising inflation in the U.S, as well as declining interest rates have made bonds and other investments less attractive. The importance of gold as an alternative investment has increased drastically owing to these developments, which explain why its price has been so high during the last 3 years.
To confirm whether the differences in the coefficients between the two sub-periods are significant we now apply the Chow test.
N1 = 66
N2 = 52
S1 = .088154201
S2 = .072330445
Sc =.175338152
k = 8
Therefore

The critical value is 2.30. Since the t-statistic is less than the critical value we reject the null hypothesis that the coefficients were equal for the two sub-periods.

5. Conclusions and Recommendations

The main objective of this paper was to investigate the reason why gold prices have been so high recently. In order to achieve this objective, the paper conducted an analysis of the factors that are likely to affect gold prices based on a review of empirical literature. The main factors suggested in the literature include inflation (price levels), the economic climate, oil prices, etc. In line with the literature, this paper employed unit root tests to determine whether gold prices along with a number of other variables were time-series stationary over the period 2002 to 2011. Unit root test results show that the only stationary series was the euro/U.S dollar exchange rate series. The rest of the time series including the time-series price of gold, the price of crude oil, the U.S CPI, the U.S and U.K 3-month Treasury bill yield, the Euro/GBP exchange rate, the USD/GBP exchange rate were all non-stationary.
Non-stationarity in the above time-series variables led us to conduct cointegration tests to determine whether there is a long-run equilibrium relationship between each of these variables and the price of gold.

Using the Johansen (1991, 1995) cointegration technique, the results show that except for the U.S.D/GDP exchange rate, each of the variables had at least 2 cointegrating vectors with the price of gold. This shows that gold has a long-run equilibrium relationship with the U.K and U.S 3-month Treasury bill yield, the U.S consumer price index, the price of crude oil and the Euro/GBP exchange rate. From this evidence one can conclude that the major factors that determine the price of gold include interest rates, crude oil, inflation and exchange rates.

The study also sought to understand the sign and magnitude of the relationship between the price of gold and each of the variables under investigation. To do this, a multiple regression model that treats gold as a function of the above variables was estimated for the entire time period. The results show that there are two major factors that affected the price of gold over the period 2002 to 2011. These include the yield on the U.K Treasury bill and the U.S CPI. The yield on the U.K 3-month Treasury bill has a negative impact on the price of gold while the CPI has a positive impact. The conclusion that can be drawn from this is that a decrease in interest rates leads to an increase in the price of gold while an increase in inflation results to an increase in the price of gold. This is clearly the case. U.K interest rates have mainly fallen over the period under analysis. On the contrary, U.S inflation has been on the rise which corroborates the evidence and conclusions presented in this study.

Taking into account structural changes, the study also tested for structural breaks by splitting the data into two separate time-periods: a pre-crisis period running from January 2002 to July 2007; and a crisis period running from August 2007 to November 2011. The results for the pre-crisis period show that none of the variables significantly affected the price of gold. However, during the crisis period, the variables identified earlier, that is, the yield on the U.K Treasury Bill and the U.S CPI are the major factors that determine the price of gold. This leads us to the conclusion that the price of gold has been significantly high over the period 2007 to 2011 because of rising inflation as well as falling interest rates. Rising inflation has forced investors to look for a safe haven and this safe haven has been gold because its value does not change over time. In addition, falling interest rates in the U.K have forced investors to diversify their portfolios away from U.K bonds into gold. These developments have led to an increase in the demand for gold thereby pushing up its price to record high levels.

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