Magoosh GRE

Employing an Econometric model, examine the Rise of Gold

| March 14, 2015

1. Introduction
Precious metals, such as gold and platinum, have often been considered attractive assets for portfolio investment, especially during times of rising inflation and global economic and political instability. Of the two, gold has received special emphasis given its role during the Gold Standard and its comparative value which rose to a local peak at $676 per ounce in 1980 during the Volcker disinflation.
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 purposes (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).
It can be observed that the price of gold more than doubled between April 2001 and Mid-2007. Despite this impressive increase in the price of gold, at least from an investor’s point of view, Levin and Wright (2006) note that the price of gold preceded an all-time monthly average peak of $647 in September 1980. This means that gold had risen to very high levels in the past before sinking in value to its 2001 low level.
Fluctuations in the price of gold are both interesting and critical from both financial and economic perspectives (Levin and Wright, 2006). Gold investments have historically been attributed to fears of political risk, inflation and other forms of economic uncertainty. Levin and Wright (2006) argue that rising gold prices over the period 2001 to 2006 could not be attributed to fears of inflation. Rather, the authors note that during this period, the United States and Eurozone member countries maintained significantly high levels of current account and trade deficits, which might have incited investors to switch towards gold as a safe haven rather than maintaining their wealth in euro or dollar-denominated assets. For example, over the period 2002 to 2005, the U.S witnessed a cumulative trade deficit in excess of $1.8 trillion with the current account deficit hitting $2trillion in 2005. In 2005, the U.S current account deficit was 6.4 percent of GDP (Levin and Wright, 2006). In the euro area, Euro Zone member countries as at 2006 were yet to agree a European Constitution that could provide a formal ownership of the euro. This resulted in severe damage to the credibility of the currency. Over the period 2001 to 2005, France and Germany failed to comply with the growth and stability pact, which precludes member countries from allowing their government budget deficits to exceed 3 percent of GDP. As such, U.S and Euro-Zone current account and trade deficits may be held liable for the rise in the price of gold between April 2001 and mid January 2006 as investors sought a more credible means of storing wealth. Compared to holding Euro- or U.S dollar-denominated assets, gold is regarded as a more credible store of value because its supply cannot be manipulated by using the minting presses as is the case with the supply of euro- and dollar-denominated bank notes.
The rise in the price of gold has also been attributed to the global financial crisis as well as to the recent debt crisis in the Euro-Zone. The globe has been suffering from severe financial and economic volatility following the onset of the global financial crisis in mid-2007. During this period, the world has witnessed one of the deepest recessions since the 1930s as well as significant declines in the value of both traditional and innovative financial instruments (Oxford Economics, 2011). Despite the decline in the value of financial instruments, gold has maintained a strong positive performance with its price almost doubling since mid-2007. The strong performance of gold can therefore be attributed to negative perceptions on the part of investors over the value of other financial instruments as a safe haven. Consequently most investors have been transforming their wealth into gold so as to avoid any declines in value. In a nutshell, gold is regarded as an effective hedge against economic and financial uncertainty in general and inflation in particular. A very limited number of studies have examined the relationship between the movement in the price of gold and fundamentals. This paper aims at examining the factors that have contributed to the rise in the price of gold by employing an econometric model. 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.

2. Theoretical Framework and Literature Review
2.1 Theoretical Framework
2.1.1 Demand and Supply of Gold Demand for Gold
In the short run, the demand for gold is determined by two categories of factors. The first category is referred to as the use demand of There are two components to the short-run demand for gold. The first category consists of the “use” demand for jewellery, medals, electrical components etc. The “use” demand for gold is a negative function of the price of gold. The demand for jewellery is also affected by price volatility but the impact of this variable may be too short-term to affect this analysis. The second category is the “asset” demand for gold as an investment. This demand is based on a number of factors including dollar exchange rate expectations, inflationary expectations, “fear”, the returns on other assets and the lack of correlation with other assets. There has been considerable debate surrounding the assertion that gold reduces portfolio volatility because the types of events that cause stock prices to Supply of Gold

Assuming that gold’s price in the short-run depends on demand and supply it is right to say that gold’s will fluctuate over time in response to fluctuations in the factors that determine the demand and supply of gold. For example, if the demand and supply of gold depends on short-term interest rates or the general price level, it means that gold’s price will fluctuate in response to changes in short-term interest rates and the general price level.

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 (O’Callaghan, 1991). 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. As a result, the relationship between the gold price change and the supply of extracted gold in any time period is positive. In other words the higher the price of gold, the higher is the quantity of extracted gold supplied. Central banks usually store gold as one of the assets that back the currency that is in circulation. During a short-term supply of gold, Central banks can lease a certain quantity of gold to meet short-term supply shortages. After a certain period of time, when enough gold has been extracted, part of it is used to repay the gold that was leased from the Central Bank. It is important to understand the relationship between the supply of extracted the gold and the quantity of gold that is used in repaying gold that was used in the previous period. Central banks lease gold at a physical interest rate. This physical interest rate is the amount of extra gold that must be offered to central banks as interest for the gold that was lease. The higher the physical interest rate in the previous period, the lower is the amount of extracted gold that is supplied in the current period.

A positive relationship therefore exists between the total supply of gold from extraction and the lagged gold price. In addition, the relationship between the quantity supplied of extracted gold and the amount of leased gold in the previous period is negative. Finally, the quantity supplied of extracted gold and the physical interest rate is also negative.

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. The amount of gold to lease out 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 forgone to other central banks holding gold plus default risk. The equilibrium quantity is determined as the quantity for which the convenience yield plus default risk premium is equivalent to the lease rental rate for gold.

A decline in the physical interest rate accompanied by an increase in the default risk premium plus convenience yield owing to political or financial instability leads to a decline in the quantity of gold that Central banks are willing to lease, thereby leading to a decline in the total quantity of gold supplied in the short-run. The quantity of gold supplied in the short run is also a function of the repayment of gold leased in previous 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
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, gold was 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 institutions (the IMF and World Bank) regarded gold as the pillar behind the exchange rate mechanism (ERM). The price of gold was allowed to float freely in the early 1970s following the breakdown of the ERM.
The distinguishing factor between gold and other commodities is that it has been regarded as a store of value and thus a proof against inflation. Unlike other precious metals or commodities, gold does not depreciate as time passes. As a result it has the unique properties as a very long-term store of value. 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.
Over the last 100 years, gold has maintained a relatively fixed supply. Annual production is only a small proportion of the total inventory of outstanding gold. Moreover, production capacity is limited which makes it difficult for suppliers to respond to fluctuations in the price of gold. On the contrary, in other commodity markets, it is possible for production to adjust to changes in prices over the short- and medium-term.
Another distinguishing factor between gold and other commodities is the fact that it is use 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 to production. Approximately 10 percent of gold is used in industries while the remaining 90 percent is used for jewellery production and for investment purposes. 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 gold and other financial or microeconomic variables is often negative (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). Moreover, the default risk of gold is zero which makes it preferable as a long-term investment over other financial assets such as stocks, bonds, and their derivatives.

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. Gold has been subjected to a variety of institutional settings such as the gold standard, the ERM, the floating rate mechanism, and as an investment vehicle. 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, the price was approximately the same in 2005 suggesting that gold can be used as a long-term hedge against inflation. The reality of gold’s description as a long-run hedge against inflation is paradoxical in that the price of gold does not move in perfect lockstep with the general price level (Oxford Economics, 2011). Rather, long periods can be observed where gold moves without any apparent relationship with trends in the general price level (Oxford Economics, 2011).
Dupois et al. (2006) observes that the power 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 general price levels that began in the 1980s. 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 recent rise in the price of gold has been attributed to rising prices of other commodities. Dupois et al. (2006) note that the price of gold has tried maintain parity 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 enthusiasm for gold has not been as high as those of other commodities. As a result, the value of gold has often depreciated in response to increases in the prices of other commodities such as oil and other precious metals.
Gold however, has an advantage over other commodities in that it has excess liquidity. In the absence of inflation pressure on consumer prices, Asian countries have increased their savings levels, which have increased their liquidity. This liquidity has to be recycled in other types of assets. Gold appears to be the most liquid asset that investors can use to save their excess wealth. This explains why its price has witnessed a dramatic increase lately. Gold is not regarded as a raw material. Rather, gold is considered as an investment. It provides investors with substantially high returns compared to the returns of other traditional investments. Gold has therefore attracted the attention of many investors in recent years and as such its price has increased in response to this increased attention.

2.2 Empirical Evidence
Given the increasing 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 in recent years. Most studies focus on understanding the long-run relationship between the price of gold and the prices of other commodities while others focus on understanding the relationship between the price of gold and macroeconomic variables such as interest rates, inflation and exchange rates. Gunes et al. (Undated) employ 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, Eurodollar parity, and oil prices on the price of gold. Ordinary least squares regression is used to find the relationship between gold price changes and fluctuations in each of the variables stated above. Cointegration tests are used to determine whether there are long-run relationships between the price of gold and each of the variables while the Augmented Dicky-Fuller unit root tests are employed to determine whether the time-series are stationary. The evidence suggests that there is a long-run equilibrium relationship between the price of gold and the following variables: interest rates; and Eurodollar parity. The results also show that there is no Granger Causality for gold price-interest rate and interest rate-gold prices, as well as for gold price-eurodollar parity and Eurodollar parity-gold price.

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. They empirically analyse the long-run equilibrium relationship between gold and crude oil using cointegration techniques. The study provides evidence of consistent trends between the price od gold and the price of crude oil. The prices of the two commodities exhibit a positive correction coefficient of 0.9295 over the period January 2000 to January 2008. In addition, the study observes that there is a long-run equilibrium between the gold market and the price of crude oil. 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. In addition, the study observes no significant mnon-linear granger causality between the two markets which indicates that there is a fairly direct interactive mechanism between the two markets. The permanent transitory (PT) model and the information share (IS) model are used to determine the common effective price between the two markets. Based on the latter analysis, the evidence suggests that the price of crude oil appears to be larger than the price of gold in both the PT and IS cases. This means that the crude oil has a had a greater impact on global economic growth in recent years which explains why crude oil has attracted so much attention in recent years.
Xu and Fung (2005) employ a bivariate asymmetric GARCH model to examine the information flow across the U.S and Japanese gold, silver and platinum futures markets. Their study provides evidence that there is a strong volatility spillover across the two markets. However, the role of the U.S market appears to be stronger than that of the Japanese market (Xu and Fung, 2005). Some studies observe a strong influence of exchange rates on the price of gold. During the 1980s, gold prices were strongly affected by the euro while during the 1990s, gold prices were mostly affected by the U.S dollar (Sjaastad and Scacciavillani, 1996; Sjaastad, 2008). Tully and Lucey (2007) employ an APGARCH model to analyse how the gold spots futures market is affected by shocks of the macroeconomy. They study provides evidence that the U.S dollar was a major macroeconomic variable that contributed to the volatility in the price of gold. 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).
Shaffiee and Topal (2010) study the role of oil price and inflation in determining the price of gold. They study also presents a model for forecasting the price of gold which is based on long-term reversal, jumps/dips, and diffusion. A very strong linear relationship is observed between the price of crude oil and the price of gold over the last four decades while a weak linear negative relationship is observed for the price of gold and inflation over the same period (Shaffiee and Topal, 2010). Using unit root tests, Shaffiee and Topal (2010) show that the price of gold is non-stationary over long horizons. Given then non-stationary behaviour over long horizons, a new model for modelling the price of gold which assumes a trend stationary process in operation is proposed. The new model is assumed to be superior over other models in that it incorporates jump and dip components into its parameters (Shaffiee and Topal, 2010). The model is based on the assumption that historical prices of commodities exhibit three types of behaviour including: long-run reversal to their mean values; 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. 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.
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 thereby leading to a break down in the long-run equilibrium relationship between gold and platinum.

3. Econometric Model
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:
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:


Where and represent consistent estimates of the variance parameters given by:
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 often assumed that there is a trend and intercept coefficient in the time series. The ADF regression can be stated as follows (Ajayi and Monguoue, 1996):

The unit root test results are necessary to determine whether to apply the Johansen (1991, 1995) cointegration test. This model can be stated in terms of a vector autoregression (VAR_ of order p as follows (Hjalmarsson and Österholm, 2007):
Where is a vector of n rows and 1 column of variables that are integrated of the same order (in this case order 1) I(1); is an nx1 vector of innovations. This VAR can be re-written as:

Assuming that is a coefficient matrix of reduced rank r<n, then it means that nxr matrices and each with rank r exist such that and is stationary. r is a measure of the 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).

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:
Where represents the change in the price of gold at time, t;
represents the change 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 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 and interest rates 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:
, , and ≠0.

4. Empirical Results and Findings

5. Conclusions and Recommendations

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