Literature Review



Determinants of the US/UK Bilateral Exchange Rate:

A Regression Model Analysis

Chris Webb

ECO 328A

December 10, 2007

ABSTRACT

This paper examines the different factors that affect the US/UK bilateral exchange rate. Using quarterly data from 1975 through 2007, this model seeks to investigate the validity of the three main theories relating to exchange rate determination: Relative Purchasing Power Parity (PPP), the Monetary Approach, and the Asset Market Approach. The result from this study is that the US/UK exchange rate can not be modeled, disputing the three traditional exchange rate theories. The model suggests that the US/UK exchange rate actually follows a random walk model. This paper also concludes that the 9/11 terrorist attacks on the US positively impacted the value of the pound in relation to the dollar.

Table of Contents

Introduction........................................................................................................................... Page 4

Literature Review.................................................................................................................. Page 6

Model Specification............................................................................................................... Page 10

Data………………………………………………………………………………………… Page 16

Empirical Results…………………………………………………………………………... Page 18

Conclusion..........................................................................................…............................... Page 22

Appendix............................................................................................................................... Page 24

References.............................................................................................................................. Page 29

Data Sources……………………………………………………………………………….. Page 30

Introduction

In today’s world of globalization and international trade and finance, exchange rates play an important role in influencing economic and financial decision making. Fluctuating exchange rates impact international purchasing decisions for companies, profitability opportunities for investors, and international trade policies for governments throughout the world. Thus, due to the significance of this variable, economists have been attempting to develop a model for exchange rates ever since floating exchange rates were first introduced. However, existing studies have reported mixed results regarding the ability to model exchange rates for various currencies throughout the world.

This paper continues this field of study by attempting to model the US/UK bilateral exchange rate since it was first floated back in 1971. In attempting to model this variable, specific independent variables are included in order to test the validity and legitimacy of the three main theories pertaining to exchange rate determination—Relative Purchasing Power Parity, the Monetary Approach, and the Asset Market Approach. This paper also examines the impact that the 9/11 terrorist attacks had on the US/UK exchange rate. The hypotheses that are being tested are that each of the three exchange rate theories hold and that the 2001 terrorist attacks had a negative impact on the value of the dollar (positive impact on the value of the pound).

The data for this study are all government issued statistics. The US data are published predominantly on the Federal Reserve Bank’s (St. Louis branch) website and . The UK data are published predominantly on the Bank of England’s website and .uk. The dependent variable is the US/UK bilateral exchange rate, using quarterly observations from 1971 through 2007.

The results of this study reject the null hypotheses that each of the three exchange rate theories hold. The results provide evidence that the US/UK exchange rate actually follows a random walk model and thus can not be modeled or predicted. This study also provides evidence that the 9/11 terrorist attacks on the US did impact the US/UK exchange rate. The event decreased the relative value of the dollar (increased the relative value of the pound) due to investors moving their capital to the currencies of more stable countries such as the UK. This in turn increased the demand for the pound and consequently its price.

Literature Review

The topic of exchange rate determination has been hotly debated and critiqued ever since the introduction of floating exchange rates in 1971. Upon initial review of the existing literature surrounding the topic, it soon became clear that economists are yet to find a universally agreeable model that accurately describes the determinants of exchange rates. Fisher, Tanna, Turner, Wallis and Whitley (1990) summarized this outlook in stating that “The success in deriving an acceptable model belies the popular belief that it is an impossible task” (p. 1232). In their analysis of the historical tracking performance of the main UK macroeconomic models, they “[found] that no model has a particularly good static simulation record with respect to the exchange rate” (Fisher et al., 1990 p.1230). This conclusion is also applicable to international studies, as Isard (1978) concluded that “empirical modeling of exchange rates over the past decade has been largely a failure” (p.1). However, I am still able to sift through the vast amount of research and literature covering the topic of exchange rate economics and extract plenty of useful information.

Van Bergen (2004) states that numerous factors determine exchange rates and that they “are all related to the trading relationship between two countries.” He outlines six main factors, whose relative importance is subject to much debate, that are the principle determinants of the exchange rate between two countries. These factors are differentials in inflation, differentials in interest rates, current-account deficits, public debt, terms of trade, and political stability and economic performance. He concludes that because exchange rates are determined by numerous complex factors, “even the most experienced economists are often left flummoxed by the topic” (Van Bergen, 2004). This explains why so much of the literature out there contradicts and disputes one another.

The three main theories that I want to test are outlined in the International Economics textbook by Dominick Salvatore. These are the absolute purchasing power parity (PPP) theory, the monetary approach, and the asset market approach. The PPP theory stipulates that exchange rates are affected by differentials in price levels across nations, the monetary approach stipulates that exchange rates are affected by differentials in money supply and income across nations, and the asset market approach stipulates that exchange rates are affected by differentials in interest rates across nations. I therefore aim to include variables relating to each of these factors in order to test each of these three theories (Salvatore, 2001, p.507-538).

Creedy, Lye and Martin (1996) constructed a non-linear model of the real US/UK exchange rate over the period of 1973-1990. They were hoping to show that a non-linear model was superior to a linear model in estimating exchange rates. In their model they used the real US/UK bilateral exchange rate as their dependent variable. The independent variables that they used were the domestic and foreign real money supply, domestic and foreign real income, and domestic and foreign interest rates. They noted that they made the assumption of flexible prices which is why they used the real exchange rate instead of electing to use the nominal exchange rate and including some measure of price level as an independent variable. The real income variables that they used were the industrial production indexes of the US and the UK. For the US money supply they used M1 whereas for the UK money supply they used M0 as these are equivalent measures of the money stock. Similarly, they used the Federal Funds rate for the US interest rate and the London Interbank Offer for the UK interest rate as these are also equivalent measures. Creedy et al. (1996) commented that “the set of market fundamentals could be expanded to include other variables” but they limited it to these in order to replicate and compare against the previously constructed linear model (p.674).

After running the data in their non-linear model, the results obtained were excellent. All the signs of the parameter estimates had the right sign according to monetarist theory, and the adjusted R-squared was equal to 73.6%. Creedy et al. (1996) were able to show that in this instance the non-linear model was superior in terms of goodness of fit and explaining the non-linearities in the data. They concluded that this is the best method to estimate exchange rate models and that this could be the reason that past models have perhaps falsely rejected economic theories such as the purchasing power parity in the long-run model.

Ahking and Miller (1987) conducted a study examining the bilateral exchange rates of seven countries using monthly data from 1973 to 1984. In their model the dependent variable was the log of the bilateral spot exchange rate. Their independent variables included: the differential of the log of the domestic and foreign nominal money supply (defined as M1); the differential of the log of the domestic and foreign real income level (defined as industrial production index); the differential of the log of the domestic and foreign interest rate (defined as the short-term interest rate); the differential of the log of the domestic and foreign expected inflation rate (using a long-term interest rate as a proxy for expected inflation); the differential of the log of the domestic and foreign price level (defined as the consumer price index); and the differential of the cumulative domestic and foreign trade balance (obtained by summing the trade balance for each country).

In concluding their paper, Ahking and Miller (1987) stated that “if a structural model is correctly specified, then the actual time-series behavior of the [dependent] variable is the same as that implied by the time-series behavior of the [independent] variables” (p.501). Thus, by comparing the actual and implied time-series properties of the independent variables, we are provided with useful insight into the validity of any structural economic model. They conclude that (with the exception of Canada), the six monthly bilateral exchange rates are modeled as random walks—random paths in which each step depends on the past in a complicated manner. So for consistency, the time-series behavior of the independent variables must also be random walks. However, all independent variables “are, with few exceptions, not random walks. Thus, existing exchange rate models appear to be misspecified” (Ahking & Miller, 1987, p.501). They therefore conclude that various exchange rate models that already exist, fail to perform better than a random walk model. They are essentially saying that many exchange rate models constructed in this manner are fundamentally flawed. This is in line with the conclusion of numerous other studies into this topic, disputing the economic theories behind exchange rate determination. I therefore am eager to go on with this project to further investigate this highly disputed field of study.

One of the factors that Van Bergen (2004) described as a determinant of exchange rates is political stability and economic performance. He stated that investors will seek out countries with strong political performance and, conversely, avoid countries with weak or poor political and economic performance. Economic turmoil in a country will cause a loss in confidence in a currency and “a movement of capital to the currencies of more stable countries,” consequently affecting the exchange rate (Van Bergen, 2004).

Model Specification

The main purpose of this study is to investigate the main determinants that affect the US/UK exchange rate. My dependent variable for this study is therefore the US/UK nominal exchange rate, as a quarterly average since March 1971, when the US first floated its exchange rate (Creedy et al., 1996, p.674). This variable will be defined as the value of one British pound in US dollars.

Numerous factors determine exchange rates, and all of them are related to the trading relationship between two countries. Bearing in mind that the relative importance of each of these factors is subject to much debate, there are three main theories that should be considered (Bergen, 2004). In this study I plan on testing all of these three theories and so will include the appropriate independent variables for each:

The Relative Purchasing-Power Parity (PPP) Theory: this approach to the exchange rate is a very influential way of thinking about the topic. This theory is a more refined version of the absolute purchasing power parity (PPP) theory, which has been proved not to hold. The absolute PPP theory postulates that “the equilibrium exchange rate between two currencies is equal to the ratio of the price levels in the two nations” (Salvatore, 2001, p.508). This is essentially saying that, according to the law of one price, a given commodity should have the same price in both countries when expressed in a common currency. Thus, the “exchange rate is equal to the price level in the home nation divided by the price level in the foreign nation” (Salvatore, 509, p.508). However, due to the fact that this theory does not take into account non-traded commodities and that it fails to take into account transportation costs or other obstructions to the free flow of international trade, the absolute PPP theory can be very misleading.

The more refined relative PPP theory “postulates that the change in the exchange rate over a period of time should be proportional to the relative change in the price levels in the two nations over the same period” (Salvatore, 2001, p.509). This can be expressed as follows:

% ∆E = % ∆P - % ∆Pf

Where E = Exchange rate (value of foreign currency—pound sterling), P = Price of domestic (US) goods, and Pf = Price of foreign (UK) goods. The implication from this theory is that a high rate of US inflation depreciates the dollar and (relatively speaking) appreciates the pound. This in turn will increase demand for the pound and subsequently its value. Thus, if I was to include a variable for the percentage change in CPI (inflation rate) for the US, I would predict that the coefficient will have a positive sign. Conversely, I would predict that the coefficient on the percentage change in CPI (inflation rate) for the UK will have a negative sign. This is because a high rate of inflation in the UK will depreciate the pound and (relatively speaking) appreciate the dollar, thus decreasing the demand for the pound and subsequently its value.

Monetary Approach: this theory states that the relative money supply of a nation has a direct impact on the nation’s exchange rate. The rationale is as follows:

MV = PY

Where M = Money Supply, V = Velocity, P = Price Level, and Y = Real GDP

Thus,

P = (MV / Y) and PUK = (MUKVUK / YUK)

Where PUK = UK Price Level, MUK = UK Money Supply VUK = UK Velocity, and YUK = UK Real GDP. By substituting these formulas into the equation derived from the relative PPP theory:

E = P/ PUK

Where E = Exchange Rate (value of the pound), we are left with:

E = (MV YUK) / (MUKVUK Y)

By taking the natural log of this equation we have:

lnE = lnM + lnV + lnYUK – lnMUK – lnVUK - lnY

↓

∆lnE = ∆lnM + ∆lnV + ∆lnYUK – ∆lnMUK – ∆lnVUK - ∆lnY

This equation can be thought of as being approximately equal to the following equation:

%∆E = %∆M + %∆V + %∆YUK – %∆MUK – %∆VUK - %∆Y

The implication from this formula is that countries with relatively high growth in money supply will lead to depreciation in the value of the domestic currency. Thus, relatively high growth in US money supply will depreciate the value of the dollar and appreciate the value of the pound. This in turn will increase the relative value of the pound and consequently increase the US/UK exchange rate. The opposite can be said about relatively high growth in UK money supply.

A further implication of this equation is that countries with relatively high economic growth will lead to appreciation in the value of the domestic currency. Thus, relatively high growth in US Real GDP will appreciate the value of the dollar and depreciate the value of the pound. This in turn will decrease the relative value of the pound and consequently decrease the US/UK exchange rate. The rationale is that a strong US economy will increase the demand for the dollar and consequently the price for the dollar. As the dollar appreciates, the pound (relatively speaking) depreciates and accordingly decreases the value of the pound (the US/UK exchange rate). Again, the opposite can be said about relatively high growth in UK Real GDP.

I will make the assumption that velocity (the turnover rate of money) is held constant in testing this theory. I will therefore include the variables of percentage change in US and UK money supply, and percentage change in US and UK Real GDP.

From the above formula I predict that the coefficient on the percentage change in US money supply will be positive. Conversely, the coefficient on the percentage change in UK money supply should have a negative sign. I further predict that the coefficient on the percentage change in US Real GDP will be negative, and the coefficient on the percentage change in UK Real GDP will be positive.

Asset Market Approach: this theory adopts the stance of viewing currency as an asset. With this in mind, people are faced with the option of investing their money either domestically or internationally in stocks, bonds, or in cash (the money market account). Accordingly, people’s decision as to where they spend their money is largely determined by interest rates. If interest rates in the US increase today, relative to the percentage change in UK interest rates, the demand for US assets increases as they receive a higher rate of return. Consequently, demand for the dollar increases and the value of the US dollar will increase (value of the pound decreases). Conversely, if the relative interest rate in the UK increases, investors will look to invest their money in the UK and thus demand for the pound sterling will increase and consequently so will the value of the pound (value of the US dollar will decrease). I will therefore include the variables of interest rates in the US and the UK in my model.

For the independent variable, US interest rate, I predict a negative relationship. This is because according to this theory, the higher the relative US interest rates, the higher the demand for US dollars (lower relative demand for British pound), and thus the lower the value of the pound—exchange rate decreases. Conversely, I predict a positive relationship between the UK interest rate and the exchange rate due to the increased demand for the pound relative to the dollar.

Along with testing these three popular exchange rate theories, I will also include a dummy variable with the intent of investigating another belief regarding exchange rate determination. In his summary of the topic, Van Bergen (2004) describes political stability and economic performance as an influential determinant of exchange rates. He states that investors will seek out countries with strong political performance and, conversely, avoid countries with weak or poor political and economic performance. Economic turmoil in a country will cause a loss in confidence in a currency and “a movement of capital to the currencies of more stable countries,” consequently affecting the exchange rate (Van Bergen, 2004). Therefore, I also plan to include a dummy variable signifying the occurrence of the September 11 terrorist attacks on the US. This event caused a drastic loss of confidence in US financial markets as people were unsure about the stability of the markets and the threat of future attacks. After the attacks occurred on 9/11/2001, investors shied away from US financial markets and thus the demand for the US dollar decreased and demand for the British pound increased relatively. As a result the value of the pound increased and I therefore predict a positive relationship between this dummy variable and the exchange rate.

As previously stated, I will be constructing a time-series regression model in order to test the different theories surrounding exchange rate determination. The mathematical representation of my hypothesized model is as follows:

Dlog(Et)= β0 + β1(TA) + β2Dlog(MSUSt) + β3 Dlog(MSUKt)+ β4 Dlog(RGDPUSt) + β5Dlog(RGDPUKt) + β6D(iUS t) + β7D(iUKt) + Єt

t: 1….n quarterly observations

Dlog(E): Percentage change in US/UK bilateral exchange rate, US dollars to one British pound

TA: September 11 terrorist attacks (dummy; 0 = before, 1 = after)

Dlog(MSUS): Percentage change in US money supply

Dlog(MSUK): Percentage change in UK money supply

Dlog(RGDPUS): Percentage change in US Real Gross Domestic Product (GDP)

Dlog(RGDPUK): Percentage change in UK Real Gross Domestic Product (GDP)

D(iUS): Change in US interest rate—Federal Funds Rate

D(iUK): Change in UK interest rate—Official Bank Rate

I will be testing the statistical significance of each of these variables in order to investigate the validity of the three main exchange rate theories: Relative PPP, the Monetary Approach, and the Asset Market Approach. I am also investigating what effect, if any, the 9/11 terrorist attacks had on the US/UK exchange rate. Based on my predictions on the hypothesized signs, I will be conducting the following hypothesis tests:

Ho: β1≤0; β2≤0; β3≥0; β4≥0; β5≤0; β6≥0; β7≤0

Ha: β1>0; β2>0; β3 0

The d-stat from the regression output is 1.521245. With N = 129 and K = 7, the dl = 1.53 and the du = 1.83. Because the d-stat < dl, we can reject the null hypothesis and conclude that there is slight evidence of positive auto correlation. However, because this value is so close to dl, it is unlikely that auto correlation is significantly impacting the results of my regression, but I will still use the Newey-West correction of the standard errors to help make the hypothesis testing more legitimate. Table 5 shows the regression after the Newey-West adjustment has been made to the model. As can be seen from the model, the significance of each independent variable is not impacted in a significant way. The only noticeable difference is that the TA variable is now significant at a higher confidence level (98%, one-sided).

Although my model is time-series, I also check for heteroskedasticity by performing the White test (table 6). The hypothesis test is as follows:

Ho: Homogeneity

Ha: Heteroskedasticity

By observing the N*R-squared value of 47.38937 and comparing this to the critical value from the Chi-squared table of 37.6 (99% confidence interval), I can reject the null hypothesis and conclude that there is actually some evidence of heteroskedasticity. I had not predicted this to be a potential issue, but this heteroskedasticity may be a result of the overall insignificance of my model. Either way, I use the White correction in order to compensate for this apparent heteroskedasticity (table 7). Again, after correcting the standard errors, the significance of each independent variable is not significantly impacted except for the TA variable, which is now significant at a 99% confidence level (one-sided).

It is also highly possible that my model is being affected by a simultaneity bias. The variables for Real GDP in both the US and the UK are endogenous and on the right hand side of my model. It is highly probable that they are both affected by the interest rate in their respective countries and even the US/UK exchange rate itself. Furthermore, the Federal Funds Rate is not completely exogenous due to the fact that the Federal Reserve simply sets a target rate and the actual interest rate is impacted by various other factors. As a result of this, my model may violate Classical Assumption III, as one or more of the explanatory variables may be correlated with the error term. This in turn will produce biased estimates of the coefficients, or simultaneity bias. This may explain why my model exhibits such insignificant results.

In order to test the asset market approach by itself, I run a regression including just the variables denoting interest rates in the US and the UK. The theory postulates that demand for a currency (and consequently the price of a currency) is affected by the relative interest rates in two countries. By isolating these two variables I was hoping to observe significant results, but as can be seen from table 8, the regression results are equally as disappointing. Neither USFFR nor UKBR are significant and the overall model is not remotely significant at a reasonable confidence level.

|Variable |Coefficient |Prob. |

|C |-0.153350 |0.7111 |

|D(USFFR) |0.019739 |0.9624 |

|D(UKBR) |-0.249854 |0.5446 |

D(USFFR) = 0.019739—A 1 percentage point increase in US Federal Funds Rate will cause a 0.019739 percentage point increase in the US/UK exchange rate, all else held constant. However, this is not significant at a reasonable confidence level.

D(UKBR) = -0.249854—A 1 percentage point increase in UK Official Bank Rate will cause a 0.249854 percentage point decrease in the US/UK exchange rate, all else held constant. However, this is not significant at a reasonable confidence level.

Conclusion

The insignificance of all but one of the independent variables (and the model as the whole) shows that my model does a terrible job at explaining the variance in the US/UK exchange rate. This regression analysis provides empirical evidence to dispute the three main theories pertaining to exchange rate determination. It can be concluded that the relative PPP theory, the Asset Market Approach, and the Monetary Approach are insufficient explanations for fluctuations in the US/UK exchange rate over the past 32 years. Instead, it would appear as though the US/UK bilateral exchange rate follows a random walk.

This conclusion is in line with the increasingly popular efficient market hypothesis. This theory stipulates that exchange rates should follow a random walk due to the fact that in an efficient market, all unexploited profit opportunities will be eliminated. For example, if people were able to predict that a currency would appreciate, they would immediately buy the currency in order to make a profit. As a result, the price of the currency (the exchange rate) would be bid up, thus reducing the expected return and eliminating the profit opportunity. This process would only stop when the predictable change in the exchange rate dropped to near zero so that the optimal forecast of the return no longer differed from the equilibrium return. The efficient market hypothesis therefore implies that “future changes in exchange rates should... be unpredictable; in other words, exchange rates should follow random walks” (Mishkin, 2007, p.165).

One notable result from this study is the significance of the September 11, 2001 terrorist attacks on the US/UK exchange rate. The positive, significant (one-sided) coefficient on this dummy variable shows that the US/UK exchange rate (value of the pound) increased after the event occurred. As predicted, the economic and financial turmoil and panic that followed this event scared investors away from the US financial markets as they looked to invest their money in safer markets such as the UK. This relative increased demand for UK investments increased the demand for the pound which in turn increased the value of the pound.

Although this study provides empirical evidence supporting the theory that the US/UK exchange rate follows a random walk model, it is certainly not conclusive evidence. Further work and studies need to be completed in an attempt to account for the possible simultaneity bias that may be biasing my coefficients. It may also be worth conducting a similar study using different datasets for the independent variables. Different variables may be used to represent national income, money supply, and interest rates as this may more accurately model the US/UK exchange rate. Furthermore, before completely disregarding the three popular exchange rate determination theories, further regression analyses should be conducted investigating bilateral exchange rates for other currencies.

Appendix

Table 1: Summary Statistics (a)

|Sample: 1975:1 2007:2 |

| |E |USMS |UKMS |USRGDP |UKRGDP |USFFR |UKBR |

| Mean | 1.709805 | 841.1838 | 21347.92 | 7461.417 | 210587.6 | 6.514026 | 8.746846 |

| Median | 1.653517 | 841.2000 | 18378.00 | 7125.500 | 203127.0 | 5.698333 | 8.600000 |

| Maximum | 2.392033 | 1381.500 | 47013.00 | 11520.10 | 310787.0 | 17.78000 | 17.00000 |

| Minimum | 1.115167 | 275.1000 | 5962.000 | 4237.600 | 143379.0 | 0.996667 | 3.530000 |

| Std. Dev. | 0.246334 | 357.8784 | 11394.80 | 2127.862 | 48855.87 | 3.500892 | 3.603618 |

| Skewness | 0.736229 |-0.137033 | 0.718332 | 0.304927 | 0.419568 | 1.014202 | 0.375005 |

| Kurtosis | 3.634798 | 1.626489 | 2.413147 | 1.857003 | 1.965478 | 4.267117 | 1.984872 |

| | | | | | | | |

| Jarque-Bera | 13.92680 | 10.62558 | 13.04548 | 9.091132 | 9.611247 | 30.98339 | 8.628744 |

| Probability | 0.000946 | 0.004928 | 0.001470 | 0.010614 | 0.008184 | 0.000000 | 0.013375 |

| | | | | | | | |

| Sum | 222.2747 | 109353.9 | 2775230. | 969984.2 | 27376386 | 846.8233 | 1137.090 |

| Sum Sq. Dev. | 7.827794 | 16521925 | 1.67E+10 | 5.84E+08 | 3.08E+11 | 1581.056 | 1675.202 |

Table 2: Summary Statistics (b)

|Sample: 1975:1 2007:2 |

| |DLOG(E)*100 |DLOG(USMS)*100 |DLOG(UKMS)*100 |DLOG(USRGDP)*100 |DLOG(UKRGDP)*100 |D(USFFR) |D(UKBR) |

| Mean |-0.144098 | 1.247438 | 1.600789 | 0.775268 | 0.585941 |-0.008165 |-0.037674 |

| Median | 0.163622 | 1.272811 | 1.474631 | 0.742213 | 0.663854 | 0.006667 | 0.000000 |

| Maximum | 11.86097 | 4.258826 | 4.065453 | 3.865686 | 4.185788 | 6.016667 | 2.940000 |

| Minimum |-18.77254 |-1.810915 |-0.476637 |-2.039308 |-2.393355 |-3.990000 |-3.840000 |

| Std. Dev. | 4.658636 | 1.298797 | 0.834670 | 0.753502 | 0.788060 | 0.997983 | 1.015386 |

| Skewness |-0.599221 | 0.166024 | 0.683658 |-0.168920 |-0.287638 | 0.668949 | 0.074427 |

| Kurtosis | 4.681231 | 2.645426 | 3.578837 | 6.268103 | 7.579562 | 15.27227 | 5.041083 |

| | | | | | | | |

| Jarque-Bera | 22.91256 | 1.268384 | 11.84976 | 58.02117 | 114.5054 | 819.1425 | 22.51145 |

| Probability | 0.000011 | 0.530364 | 0.002672 | 0.000000 | 0.000000 | 0.000000 | 0.000013 |

| | | | | | | | |

| Sum |-18.58869 | 160.9196 | 206.5018 | 100.0096 | 75.58642 |-1.053333 |-4.860000 |

| Sum Sq. Dev. | 2777.970 | 215.9200 | 89.17422 | 72.67395 | 79.49289 | 127.4841 | 131.9691 |

Table 3: Regression Results

|Dependent Variable: DLOG(E)*100 |

|Method: Least Squares |

|Date: 12/02/07 Time: 14:11 |

|Sample(adjusted): 1975:2 2007:2 |

|Included observations: 129 after adjusting endpoints |

|Variable |Coefficient |Std. Error |t-Statistic |Prob. |

|C |0.459448 |1.117421 |0.411168 |0.6817 |

|DLOG(USMS)*100 |0.018657 |0.334432 |0.055788 |0.9556 |

|DLOG(UKMS)*100 |-0.317426 |0.520571 |-0.609765 |0.5432 |

|DLOG(USRGDP)*100 |-0.408020 |0.615940 |-0.662434 |0.5090 |

|DLOG(UKRGDP)*100 |-0.224291 |0.545050 |-0.411505 |0.6814 |

|D(USFFR) |0.138520 |0.457445 |0.302812 |0.7626 |

|D(UKBR) |-0.207929 |0.431616 |-0.481745 |0.6309 |

|TA |1.807994 |1.108680 |1.630762 |0.1055 |

|R-squared |0.037746 | Mean dependent var |-0.144098 |

|Adjusted R-squared |-0.017921 | S.D. dependent var |4.658636 |

|S.E. of regression |4.700195 | Akaike info criterion |5.993094 |

|Sum squared resid |2673.112 | Schwarz criterion |6.170447 |

|Log likelihood |-378.5546 | F-statistic |0.678065 |

|Durbin-Watson stat |1.521245 | Prob(F-statistic) |0.690317 |

Table 4: Correlation Coefficients

| |DLOG(USMS)*100 |DLOG(UKMS)*100 |DLOG(USRGDP)*100 |DLOG(UKRGDP)*100 |D(USFFR) |D(UKBR) |TA |

|DLOG(USMS)*100 | 1.000000 | 0.005559 | 0.063278 |-0.043396 |-0.093984 |-0.196233 |-0.189550 |

|DLOG(UKMS)*100 | 0.005559 | 1.000000 | 0.166718 | 0.071020 | 0.153442 | 0.209969 |-0.077551 |

|DLOG(USRGDP)*100 | 0.063278 | 0.166718 | 1.000000 | 0.195311 | 0.358499 |-0.012302 |-0.064299 |

|DLOG(UKRGDP)*100 |-0.043396 | 0.071020 | 0.195311 | 1.000000 |-0.010816 | 0.098635 | 0.042524 |

|D(USFFR) |-0.093984 | 0.153442 | 0.358499 |-0.010816 | 1.000000 | 0.122696 | 0.039546 |

|D(UKBR) |-0.196233 | 0.209969 |-0.012302 | 0.098635 | 0.122696 | 1.000000 | 0.024359 |

|TA |-0.189550 |-0.077551 |-0.064299 | 0.042524 | 0.039546 | 0.024359 | 1.000000 |

Table 5: Newey-West Corrections

|Dependent Variable: DLOG(E)*100 |

|Method: Least Squares |

|Date: 12/02/07 Time: 19:39 |

|Sample(adjusted): 1975:2 2007:2 |

|Included observations: 129 after adjusting endpoints |

|Newey-West HAC Standard Errors & Covariance (lag truncation=4) |

|Variable |Coefficient |Std. Error |t-Statistic |Prob. |

|C |0.459448 |1.251065 |0.367245 |0.7141 |

|DLOG(USMS)*100 |0.018657 |0.341753 |0.054593 |0.9566 |

|DLOG(UKMS)*100 |-0.317426 |0.679062 |-0.467448 |0.6410 |

|DLOG(USRGDP)*100 |-0.408020 |0.581482 |-0.701690 |0.4842 |

|DLOG(UKRGDP)*100 |-0.224291 |0.496993 |-0.451297 |0.6526 |

|D(USFFR) |0.138520 |0.448546 |0.308819 |0.7580 |

|D(UKBR) |-0.207929 |0.647691 |-0.321030 |0.7487 |

|TA |1.807994 |0.840845 |2.150210 |0.0335 |

|R-squared |0.037746 | Mean dependent var |-0.144098 |

|Adjusted R-squared |-0.017921 | S.D. dependent var |4.658636 |

|S.E. of regression |4.700195 | Akaike info criterion |5.993094 |

|Sum squared resid |2673.112 | Schwarz criterion |6.170447 |

|Log likelihood |-378.5546 | F-statistic |0.678065 |

|Durbin-Watson stat |1.521245 | Prob(F-statistic) |0.690317 |

Table 6: White Heteroskedasticity Test

|White Heteroskedasticity Test: |

|F-statistic |1.608025 | Probability |0.038430 |

|Obs*R-squared |47.38937 | Probability |0.063285 |

| | | | | |

|Test Equation: |

|Dependent Variable: RESID^2 |

|Method: Least Squares |

|Date: 12/02/07 Time: 19:16 |

|Sample: 1975:3 2007:2 |

|Included observations: 128 |

|Variable |Coefficient |Std. Error |t-Statistic |Prob. |

|C |21.92179 |23.64159 |0.927255 |0.3562 |

|DLOG(USMS)*100 |-15.58913 |12.36381 |-1.260868 |0.2105 |

|(DLOG(USMS)*100)^2 |2.843458 |2.205662 |1.289163 |0.2005 |

|(DLOG(USMS)*100)*(DLOG(UKMS)*100) |10.33924 |5.802411 |1.781886 |0.0780 |

|(DLOG(USMS)*100)*(DLOG(USRGDP)*100) |0.678609 |6.122707 |0.110835 |0.9120 |

|(DLOG(USMS)*100)*(DLOG(UKRGDP)*100) |0.514714 |7.163771 |0.071850 |0.9429 |

|(DLOG(USMS)*100)*(D(USFFR)) |17.12689 |6.831022 |2.507222 |0.0139 |

|(DLOG(USMS)*100)*(D(UKBR)) |-23.00875 |5.453419 |-4.219142 |0.0001 |

|(DLOG(USMS)*100)*TA |-8.789509 |15.30683 |-0.574221 |0.5672 |

|DLOG(UKMS)*100 |-4.021443 |19.05738 |-0.211018 |0.8333 |

|(DLOG(UKMS)*100)^2 |-4.830197 |5.080222 |-0.950785 |0.3442 |

|(DLOG(UKMS)*100)*(DLOG(USRGDP)*100) |4.487079 |8.950172 |0.501340 |0.6173 |

|(DLOG(UKMS)*100)*(DLOG(UKRGDP)*100) |3.744914 |8.422540 |0.444630 |0.6576 |

|(DLOG(UKMS)*100)*(D(USFFR)) |5.119511 |9.548550 |0.536156 |0.5931 |

|(DLOG(UKMS)*100)*(D(UKBR)) |9.745309 |7.022137 |1.387798 |0.1685 |

|(DLOG(UKMS)*100)*TA |-3.224638 |22.82729 |-0.141262 |0.8880 |

|DLOG(USRGDP)*100 |18.76282 |18.12658 |1.035100 |0.3033 |

|(DLOG(USRGDP)*100)^2 |-14.73379 |6.554292 |-2.247961 |0.0269 |

|(DLOG(USRGDP)*100)*(DLOG(UKRGDP)*100) |9.510345 |9.388556 |1.012972 |0.3137 |

|(DLOG(USRGDP)*100)*(D(USFFR)) |-12.00673 |10.96516 |-1.094989 |0.2763 |

|(DLOG(USRGDP)*100)*(D(UKBR)) |7.442230 |6.358979 |1.170350 |0.2449 |

|(DLOG(USRGDP)*100)*TA |0.916578 |33.83139 |0.027093 |0.9784 |

|DLOG(UKRGDP)*100 |-20.32976 |19.41054 |-1.047357 |0.2976 |

|(DLOG(UKRGDP)*100)^2 |0.635180 |3.588633 |0.176998 |0.8599 |

|(DLOG(UKRGDP)*100)*(D(USFFR)) |8.884866 |10.89227 |0.815704 |0.4168 |

|(DLOG(UKRGDP)*100)*(D(UKBR)) |-4.798358 |6.521879 |-0.735732 |0.4637 |

|(DLOG(UKRGDP)*100)*TA |3.208810 |53.60429 |0.059861 |0.9524 |

|D(USFFR) |-34.88009 |20.80921 |-1.676185 |0.0971 |

|(D(USFFR))^2 |1.612149 |3.714190 |0.434051 |0.6653 |

|(D(USFFR))*(D(UKBR)) |-7.492907 |5.044080 |-1.485485 |0.1408 |

|(D(USFFR))*TA |-1.699542 |36.13576 |-0.047032 |0.9626 |

|D(UKBR) |13.86627 |18.68372 |0.742158 |0.4599 |

|(D(UKBR))^2 |4.149289 |3.144630 |1.319484 |0.1902 |

|(D(UKBR))*TA |-25.03270 |55.35534 |-0.452218 |0.6522 |

|TA |5.768233 |48.26340 |0.119516 |0.9051 |

|R-squared |0.370229 | Mean dependent var |19.27660 |

|Adjusted R-squared |0.139991 | S.D. dependent var |46.80215 |

|S.E. of regression |43.40276 | Akaike info criterion |10.60637 |

|Sum squared resid |175193.4 | Schwarz criterion |11.38622 |

|Log likelihood |-643.8075 | F-statistic |1.608025 |

|Durbin-Watson stat |2.016910 | Prob(F-statistic) |0.038430 |

Table 7: White Correction

|Dependent Variable: DLOG(E)*100 |

|Method: Least Squares |

|Date: 12/02/07 Time: 19:44 |

|Sample(adjusted): 1975:2 2007:2 |

|Included observations: 129 after adjusting endpoints |

|White Heteroskedasticity-Consistent Standard Errors & Covariance |

|Variable |Coefficient |Std. Error |t-Statistic |Prob. |

|C |0.459448 |1.074456 |0.427610 |0.6697 |

|DLOG(USMS)*100 |0.018657 |0.350391 |0.053247 |0.9576 |

|DLOG(UKMS)*100 |-0.317426 |0.546155 |-0.581201 |0.5622 |

|DLOG(USRGDP)*100 |-0.408020 |0.607711 |-0.671405 |0.5032 |

|DLOG(UKRGDP)*100 |-0.224291 |0.602917 |-0.372010 |0.7105 |

|D(USFFR) |0.138520 |0.375208 |0.369181 |0.7126 |

|D(UKBR) |-0.207929 |0.551539 |-0.376997 |0.7068 |

|TA |1.807994 |0.730241 |2.475887 |0.0147 |

|R-squared |0.037746 | Mean dependent var |-0.144098 |

|Adjusted R-squared |-0.017921 | S.D. dependent var |4.658636 |

|S.E. of regression |4.700195 | Akaike info criterion |5.993094 |

|Sum squared resid |2673.112 | Schwarz criterion |6.170447 |

|Log likelihood |-378.5546 | F-statistic |0.678065 |

|Durbin-Watson stat |1.521245 | Prob(F-statistic) |0.690317 |

Table 8: Asset Market Approach

|Dependent Variable: DLOG(E)*100 |

|Method: Least Squares |

|Date: 12/02/07 Time: 14:17 |

|Sample(adjusted): 1975:2 2007:2 |

|Included observations: 129 after adjusting endpoints |

|Variable |Coefficient |Std. Error |t-Statistic |Prob. |

|C |-0.153350 |0.413096 |-0.371222 |0.7111 |

|D(USFFR) |0.019739 |0.418416 |0.047177 |0.9624 |

|D(UKBR) |-0.249854 |0.411244 |-0.607556 |0.5446 |

|R-squared |0.002927 | Mean dependent var |-0.144098 |

|Adjusted R-squared |-0.012900 | S.D. dependent var |4.658636 |

|S.E. of regression |4.688587 | Akaike info criterion |5.951121 |

|Sum squared resid |2769.839 | Schwarz criterion |6.017628 |

|Log likelihood |-380.8473 | F-statistic |0.184942 |

|Durbin-Watson stat |1.495255 | Prob(F-statistic) |0.831378 |

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