group a report

Group Assignment

Questions 1 and 2

Name: Lee Rock. Jazmen Boone, Bas Süß, Henry Doku

Student Number: 20038860, 20070746, 20069935, 20044757

Department: Department of Graduate Business

Course: MSc in Global Financial Information Systems

Module: Econometrics

Presented To: Dr Tom Egan

Assignment 1 of 1

Signature:______________________________ Date:__________________________________

Signature:______________________________ Date:__________________________________

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We firmly declare that this is assignment was completed by our own accord and to the best of my abilities in accordance with the plagiarism regulations and in line with the standards of academia set out by Waterford Institute of Technology.

Table of Contents1.0 Introduction.....................................................................................................................................1

1.1 Definition of Terms......................................................................................................................1

2.0 Question 1.......................................................................................................................................2

2.1 Part A...........................................................................................................................................2

2.1.1 USA Descriptive Statistics Analysis........................................................................................5

2.1.2 Netherlands Descriptive Statistics Analysis...........................................................................6

2.2 Part B...........................................................................................................................................7

2.2.1 Consumption........................................................................................................................7

2.2.2 Investment............................................................................................................................8

2.2.3 Government Spending..........................................................................................................8

2.2.4 Net Exports...........................................................................................................................8

2.3 Part C...........................................................................................................................................8

2.3.1 USA OLS Regressions............................................................................................................8

2.3.2 USA Multiple Regression.....................................................................................................13

2.3.3 Netherlands OLS Regressions.............................................................................................15

2.3.4 Netherlands Multiple Regression........................................................................................20

2.4 Part D.........................................................................................................................................22

2.4.1 Autocorrelation Testing for USA.........................................................................................22

2.4.2 Autocorrelation Testing Netherlands..................................................................................24

2.4.3 Normal Distribution for the USA Multiple Regression Model Residuals.............................26

2.4.4 Normal Distribution for the Netherlands Multiple Regression Model Residuals................27

2.5 Part E.........................................................................................................................................29

2.5.1 Specification Error of the US model....................................................................................29

2.6 Part F.........................................................................................................................................30

2.6.1 Adding the Dummy Variable...............................................................................................30

2.6.2 Interaction Effect................................................................................................................31

2.7 Part G.........................................................................................................................................32

2.7.1 Lag of Government Spending for the USA..........................................................................32

2.7.2 Lag of Government Spending for the Netherlands.............................................................34

2.8 Part H.........................................................................................................................................36

2.8.1 Forecasting GDP for the USA..............................................................................................36

2.8.2 Forecasting GDP for the Netherlands.................................................................................39

3.0 Question 2.....................................................................................................................................42

Equation 1 Open Economy GDP Theoretical Function...........................................................................7Equation 2 Standard Format for USA FDI OLS Regression Output.........................................................9Equation 3 Standard Format for USA Government Expenditure OLS Regression Output....................10Equation 4 Standard Format for USA Household Consumption OLS Regression Output.....................12Equation 5 Standard Format for USA Net Exports OLS Regression Output.........................................13Equation 6 Standard Format for USA Multiple Regression Output......................................................15Equation 7 Standard Format for Netherlands FDI OLS Regression Output..........................................16Equation 8 Standard Format for Netherlands Government Expenditure OLS Regression Output.......17Equation 9 Standard Format for Netherlands Household Consumption OLS Regression Output........18Equation 10 Standard Format for Netherlands Net Exports OLS Regression Output..........................20Equation 11 Standard Format for Netherlands Multiple Regression Output.......................................22Equation 12 Jarque Bera Equation for the USA Multiple Regression Model.......................................27Equation 13 Jarque Bera Equation for the Netherlands Multiple Regression Model..........................29Equation 14 Ramsey Reset Equation for USA......................................................................................30Equation 15 Standard Format for USA Two Period Distributive Lag of Government Spending Regression on GDP (Current US$)........................................................................................................34Equation 16 Standard Format for Netherlands Two Period Distributive Lag of Government Spending Regression on GDP (Current US$)........................................................................................................35

Figure 1 Bar Chart of USA GDP (Current US$)........................................................................................3Figure 2 Bar Chart of Netherland GDP (Current US$)............................................................................3Figure 3 Boxplot of USA GDP (Current US$)..........................................................................................4Figure 4 Boxplot of Netherlands GDP (Current US$).............................................................................4Figure 5 Overall Residual Plot for the USA Model...............................................................................23Figure 6 Overall Residual Plot for the Netherlands Model..................................................................24Figure 7 Histogram of USA Multiple Regression Residuals..................................................................26Figure 8 Histogram of the Netherlands Multiple Regression Residuals...............................................28Figure 9 Line Graph of US GDP (Current US$) from 1970-2013...........................................................37Figure 10 Line Graph of the Natural Log US GDP (Current US$) from 1970-2013...............................37Figure 11 Line Graph of the Change in US GDP (Current US$) from 1970-2013..................................38Figure 12 Line Graph of the change in the Natural Log of US GDP (Current US$) from 1970-2013.....38Figure 13 Line Graph of the Netherlands GDP (Current US$) from 1970-2013...................................40Figure 14 Line Graph of the Natural Log of the Netherlands GDP (Current US$) from 1970-2013......40Figure 15 Line Graph of the Change in the Netherlands GDP (Current US$) from 1970-2013.............41Figure 16 Line Graph of the Change in the Natural Log of the Netherlands GDP (Current US$) from 1970-2013...........................................................................................................................................41

Table 1 Descriptive Statistics of the USA and Netherlands GDP (Current US$).....................................2

Table 2 Normal Distribution for USA GDP (Current US$).......................................................................5Table 3 Normal Distribution for Netherlands GDP (Current US$)..........................................................5Table 4 Correlation Matrix for the USA Multiple Regression Model....................................................14Table 5 Collinearity Diagnostics for the USA Multiple Regression Model............................................15Table 6 Correlation Matrix for the Netherlands Multiple Regression Model.......................................21Table 7 Collinearity Diagnostics for the Netherland Multiple Regression Model................................22Table 8 Model Summary for the USA Multiple Regression Model.......................................................23Table 9 Model Summary for the Netherlands Multiple Regression Model..........................................24Table 10 USA Multiple Regression Residual Descriptive Statistics.......................................................26Table 11 Netherlands Multiple Regression Residual Descriptive Statistics..........................................28Table 12 Coefficients and Significance Values for the USA Government Spending Lag Model............33Table 13 Collinearity Diagnostics for the USA Government Spending Lag Model...............................33Table 14 Coefficients and Significance Values for the Netherlands Government Spending Lag Model.............................................................................................................................................................35Table 15 Collinearity Diagnostics for the Netherlands Government Spending Lag Model..................35Table 16 Autocorrelation Functions for USA GDP (Current US$).........................................................36Table 17 Autocorrelation Functions for Netherlands GDP (Current US$)............................................39Table 18 Cumulative Abnormal Returns for Individual Companies.....................................................45Table 19 Cumulative Abnormal Returns for Portfolio..........................................................................46

1.0 IntroductionThe following assignment has been completed Lee Rock, Jazmen Boone, Henry Doku, and

Bas Süß, consisting of two questions. The first question is regarding a regression analysis of

two chosen countries (United States of America and the Netherlands) to analyse, compare

and interpret these results. The second question is an event study based on analysing merger

and acquisition data for the year 2011. Data used for question one has been sourced from the

World Bank’s database and the lecturer has provided data for question two internally.

Appendix B contains the power point presentation concerning question 1 that the group

delivered on the 1st of December 2015.

1.1 Definition of TermsUS or USA: United States of America

NETH or Neth: Netherlands

STD Dev: Standard Deviation

GDP: Gross Domestic Product at Current Prices Denominated in US dollars

Max: Maximum

Min: Minimum

FDI: Foreign Direct Investment

Y or y: Dependent Variable

X or x: Independent Variable

Dum: Dummy Variable

GDP: Gross domestic product at current US dollars

C: Consumption (Household final consumption expenditure, etc. at current US dollars)

I: Investment (Foreign direct investment, net inflows, balance of payments at current US dollars)

G: Government Expenditure (General government final consumption expenditure at current US dollars)

1

NX: Net Exports (Exports less imports at current US dollars)

X: Exports (Exports of goods and services at current US dollars)

M: Imports (Imports of goods and services at current US dollars)

2.0 Question 1

2.1 Part A USA GDP (current US$) NETH GDP (current US$)

Mean 7.38E+12 Mean 3.79E+11Standard Error 7.41E+11 Standard Error 4.1E+10Median 6.36E+12 Median 3.35E+11Mode #N/A Mode #N/AStandard Deviation 4.91E+12 Standard Deviation 2.72E+11Sample Variance 2.41E+25 Sample Variance 7.41E+22Kurtosis -1.12598 Kurtosis -0.7363Skewness 0.43018 Skewness 0.686606Range 1.57E+13 Range 8.94E+11Minimum 1.08E+12 Minimum 3.75E+10Maximum 1.68E+13 Maximum 9.31E+11Sum 3.25E+14 Sum 1.67E+13Count 44 Count 44Largest(1) 1.68E+13 Largest(1) 9.31E+11Smallest(1) 1.08E+12 Smallest(1) 3.75E+10Confidence Level (95.0%) 1.49E+12 Confidence Level (95.0%) 8.28E+10Table 1 Descriptive Statistics of the USA and Netherlands GDP (Current US$)

2

Figure 1 Bar Chart of USA GDP (Current US$)

Figure 2 Bar Chart of Netherland GDP (Current US$)

3

Figure 3 Boxplot of USA GDP (Current US$)

Figure 4 Boxplot of Netherlands GDP (Current US$)

4

Normal Distribution for US GDPDeviations 1 Deviation 2 Deviations 3 DeviationsTails Tail 1 Tail 2 Tail 1 Tail 2 Tail 1 Tail 2Max/Min 1.23E+13 -2.5E+12 1.72E+13 -2.5E+12 2.21E+13 -7.4E+12Count 35 44 44Sample 45 45 45STD Dev 78% 98% 98%Table 2 Normal Distribution for USA GDP (Current US$)

Normal Distribution of Netherland GDPDeviations 1 Deviation 2 Deviations 3 DeviationsTails Tail 1 Tail 2 Tail 1 Tail 2 Tail 1 Tail 2Max/Min 6.51E+11 -1.1E+11 9.23E+11 -1.7E+11 1.2E+12 -4.4E+11Count 35 43 44Sample 45 45 45STD Dev 78% 96% 98%Table 3 Normal Distribution for Netherlands GDP (Current US$)

2.1.1 USA Descriptive Statistics Analysis The mean is the standard arithmetic average of all the variables added up and divided by the

amount, in this case the mean GDP at current prices in US dollars for the USA between1970-

2013 is 7.3775E+12.

The median is the middle number in a given data set when arranged in chronological order;

the median for this particular data set is 6.35668E+12.

The mode is the most common number to appear in the dataset, the mode cannot be

calculated in this case as no GDP-Value at current prices in US dollars has replicated itself

between 1970 -2013.

The mean and median are not equal with a difference of 1.02083E+12 which suggests

skewness in the normal distribution of the data. The skewness figure of 0.430179959

suggests a significant skewness to the right due to the value being positive. This is consistent

with the boxplot diagram as it can be seen the upper whisker is longer than the bottom

whisker indicating skewness to the right. The boxplot also identifies the median which

appears to be lower than the centre of the box. This indicates that more of the data is on the

upper side of the median rather than below it which may further indicate skewness to the

right. The boxplot does not show any outliers "o" or extreme outliers "*". The histogram

further backs up this significant skewness with 9 bars to the right of the highest bar compared

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to one on the left. No bars appear to pass the normal distribution line when it collapses

suggesting there are no outliers in the data.

For a dataset to fit a normal distribution 68% of the data occurs within one standard deviation

from the mean, a standard deviation is a measure of the average variance of data from the

mean itself. Also, 95% of the data should be within 2 standard deviations and practically

100% should rest within 3 standard deviations.

As can be seen from the table the USA GDP at current prices in US dollars, 78% occurs

within one deviation, 98% within two and 98% within three suggesting the data is normally

distributed but skewed to the right in lieu of previous arguments made.

The heavy significant skewness to the right suggests that the USA GDP at current prices in

US dollars generally increases year on year without any large sigma or unusual events that

cause an abnormal increase or decrease in the variable.

2.1.2 Netherlands Descriptive Statistics AnalysisThe mean is the standard arithmetic average of all the variables added up and divided by the

amount, in this case the mean GDP at current prices in US dollars for the Netherland

between1970-2013 is 3.78828E+11.

The median is the middle number in a given data set when arranged in chronological order;

the median for this particular data set is 3.34864E+11.

The mode is the most common number to appear in the dataset, the mode cannot be

calculated in this case as no GDP-Value at current prices in US dollars has replicated itself

twice between 1970 -2013.

The mean and median are not equal with a difference of 43964145552, which suggests

skewness in the normal distribution of the data. The skewness figure of 0.686605536

suggests a heavy skewness to the right due to the value being positive and quite close to 1.

This is consistent with the boxplot diagram as it can be seen the upper whisker is longer than

the bottom whisker indicating skewness to the right. The boxplot also identifies the median

which appears to be centred in the box indicating an even spread of data both above and

below the median. The boxplot does not show any outliers "o" or extreme outliers "*". This

histogram further back up this heavy skewness with 8 bars to the right of the highest bar

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compared to one on the left. No bars appear to pass the normal distribution line when it

collapses suggesting there are no outliers in the data.

For a dataset to fit a normal distribution 68% of the data occurs within one standard deviation

from the mean, a standard deviation is a measure of the average variance of data from the

mean itself. 95% should be within 2 standard deviations and practically 100% should rest

within 3 standard deviations.

As can be seen from the table the Netherlands GDP at current prices in US dollars, 78%

occurs within one deviation, 96% within two and 98% within three suggesting the data is

normally distributed but skewed to the right in lieu of previous arguments made.

The heavy skewness to the right suggests that the Netherlands GDP at current prices in US

dollars generally increases year on year without any large sigma or unusual events that cause

an abnormal increase or decrease in the variable.

2.2 Part BAll of the variables selected for the model have be denominated in US dollars to allow for

greater consistency during interpretation between the two datasets. The chosen variables have

been selected at current prices for the year 2014. Current prices can be defined as “prices of

the current reporting period” (OECD.com). Again this will allow for greater consistency

during interpretation between the two datasets.

GDP at current prices denominated in US dollars (GDP) has been chosen for the Y variable.

This GDP type was chosen for the reasons outlined above and GDP has been identified as the

mandatory variable in answering question 1.

Standard economic theory presents the GDP Equation as:

GDP=C+ I+G+NX(X−M )

Equation 1 Open Economy GDP Theoretical Function

We decided to test this theory by regressing GDP (Y) on consumption (X1), investment (X2),

government spending (X3) and net exports i.e. exports less imports (X4). As the equation

suggests we expect all variables will have a positive slope against GDP.

2.2.1 ConsumptionHousehold final consumption expenditure i.e. consumption (C) covers all purchase made by

resident households (home and abroad) to meet their everyday needs such as food, clothing,

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housing service (rents), energy, transport, durables goods, health, leisure and miscellaneous.

It also includes a number of imputed expenditures, for example agricultural products

produced for own-consumption.

2.2.2 InvestmentForeign direct investment, net inflows i.e. investment (I) has been used as a proxy for

investment as we were unable to source a more accurate investment variable for general

investment. FDI net inflows are inward direct investment made investors who do not reside in

the respective economy.

2.2.3 Government Spending General government final consumption expenditure i.e. government spending (G) includes all

government consumption, investment, and transfer payments. The acquisition by

governments of goods and services are used to directly satisfy the collective needs of the

respective population.

2.2.4 Net Exports Net exports (NX) have been derived by taking imports of goods and services from exports of

goods and services.

2.3 Part C

2.3.1 USA OLS RegressionsFull regression results for part C regarding the USA can be found in appendix A.

2.3.1.1 FDI The sample size of the regression is acceptable to make generalizations about the population

because it is greater than 30 (specifically 44 observations). Along with a good sample size,

the simple linear regression model had a high r-squared of 0.747 or 74.7% telling us that FDI

explains 74.7% of the variation in GDP. The adjusted r-square (which considers sample size)

is extremely close to the r square with a value of 0.741, which shows that this model is so far

useful. More importantly, the r-squared value is statistically significant, using the p-value

approach, as it has a p-value of 3.94E-14. This p-value surpasses the 1% standard so we can

conclude that the overall regression model is statistically significant at the 1% level.

After regressing GDP (y) on FDI (x), FDI's slope coefficient was 38.74517. This is

interpreted as GDP (US$) is expected to increase by 38.74517 for each dollar rise of FDI.

8

We assessed FDI's significance level through the three statistical tests where it passed all

three evaluations: p-value, confidence interval, and t-test. The slope coefficient is statistically

significant with a p-value of 3.94E-14, so the model is very significant at a 99% level of

confidence (1% level of significance). The confidence intervals of the slope coefficient

further justifies significance of the variable, FDI, because zero is not in the range; thus, the

regression output shows that we can be 95% confident that the unknown population slope lies

between 31.73295 and 45.75738. Since zero is not in the confidence interval, we can

therefore be 95% confident that the real population slope is not zero and that there is a

positive relationship between the variables GDP and FDI. Lastly with a critical value of 1.98

with a 5% assumed level of confidence (two tailed), the regression output creates a t-stat of

11.15067 for the slope coefficient of FDI. The t stat of 11.15067 is greater than the critical

value 1.98 (11.15067 > 1.98), so there is a 5% level of significance as we are 95% confident

to pass the t-test. This adds more support that the slope coefficient is statistically significant

overall.

Equation 2 Standard Format for USA FDI OLS Regression Output

2.3.1.2 Government ExpenditureThe sample size of the regression is acceptable to make generalizations about the population


the simple linear regression model had a very high r-squared of 0.990 or 99.0% telling us that

government consumption expenditure explains 99.0% of the variation in GDP. The high r-

squared tells us that it is a good model because it is close to an ideal value of 100%. The

adjusted r-square (which considers sample size) is extremely close to the r square with a

value of 0.990 demonstrating that this model is so far useful. More importantly, the r-squared

value is statistically significant, using the p-value approach, as the model’s p-value is 1.75E-

44. This p-value surpasses the 1% standard so we can conclude that the overall regression

model is statistically significant at the 1% level. Although the r-square is significantly high

for this model, it is important to note that the presence of outliers may have reduced the r-

9

square value (-2.69 and -2.62 is outside of the +/- 2.5 outlier rule). There is an option to

regress the output of the model without the outliers (observation 43 and 44) to see its impact

on the overall regression model and its r-square value to help make the regression a better

one.

After regressing GDP (y) on government consumption expenditure (x), government

consumption expenditure's slope coefficient was 6.403442. This is interpreted as GDP (US$)

is expected to increase by 6.403442 for each dollar rise of government consumption

expenditure.

We assessed government consumption expenditure's significance level through the three

statistical tests where it passed all three evaluations: p-value, confidence interval, and t-test.

The slope coefficient is statistically significant with a p-value of 1.75E-44, so the model is

very significant at a 99% level of confidence (1% level of significance). The confidence

intervals of the slope coefficient further justifies significance of the variable, government

consumption expenditure, because zero is not in the range; thus, the regression output shows

that we can be 95% confident that the unknown population slope lies between 6.212212 and

6.594671. Since zero is not in the confidence interval, we can therefore be 95% confident that

the real population slope is not zero and that there is a positive relationship between the

variables GDP and government consumption expenditure. Lastly with a critical value of 1.98


67.57683 for the slope coefficient of government consumption expenditure. The t stat of

67.57683 is greater than the critical value 1.98 (67.57683 > 1.98), so there is a 5% level of

significance or a 95% confidence level to pass the t-test. This adds more support that the

slope coefficient is statistically significant overall.

Equation 3 Standard Format for USA Government Expenditure OLS Regression Output

10

2.3.1.3 Household Consumption The sample size of the regression is acceptable to make generalizations about the population



household consumption expenditure explains 99.9% of the variation in GDP. The high r-


adjusted r-square (which considers sample size) is extremely close to the r-square with a

value of 0.999, which shows that this model is so far useful. More importantly, the r-squared

value is statistically significant, using the p-value approach, as its p-value is 2.13E-68. This

p-value surpasses the 1% standard so we can conclude that the overall regression model is

statistically significant at the 1% level.

After regressing GDP (y) on net exports (x), house consumption expenditure's slope

coefficient was 1.443829. This is interpreted as GDP (US$) is expected to increase by

1.443829 for each dollar rise of house consumption expenditure.

We assessed house consumption expenditure's significance level through the three statistical

tests where it passed all three evaluations: p-value, confidence interval, and t-test. The slope

coefficient is statistically significant with a p-value of 2.49E-30, so the model is very

significant at a 99% level of confidence (1% level of significance). The confidence intervals

of the slope coefficient further justifies significance of the variable, house consumption

expenditure, because zero is not in the range; thus, the regression output shows that we can be

95% confident that the unknown population slope lies between 1.432256 and 1.455403. Since

zero is not in the confidence interval, we can therefore be 95% confident that the real

population slope is not zero and that there is a positive relationship between the variables

GDP and house consumption expenditure. Lastly with a critical value of 1.98 with a 5%

assumed level of confidence (two tailed), the regression output creates a t-stat of 251.763 for

the slope coefficient of household consumption expenditure. The t-stat of`251.763 is greater

than the critical value 1.98 (251.763 > 1.98), so there is a 5% level of significance or a 95%

confidence level of passing the t-test. This adds more support that the slope coefficient is

statistically significant overall.

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Equation 4 Standard Format for USA Household Consumption OLS Regression Output

2.3.1.4 Net exportsThe sample size of the regression is acceptable to make generalizations about the population



net exports explains 82.3% of the variation in GDP. The adjusted r-square (which considers

sample size) is extremely close to the r-square with a value of 0.818 showing that this model

is so far useful. More importantly, the r-squared value is statistically significant, using the p-

value approach, which its p-value of 2.13E-17. This p-value surpasses the 1% standard so we

can conclude that the overall regression model is statistically significant at the 1% level.

After regressing GDP (y) on net exports (x), net export's slope coefficient was -17.7806. This

is interpreted as GDP (US$) is expected to decrease by 17.7806 for each dollar rise of net

exports.

We assessed net export's significance level through the three statistical tests where it passed

all three evaluations: p-value, confidence interval, and t-test. The slope coefficient is

statistically significant with a p-value of 2.13E-17, so the model is very significant at a 99%

level of confidence (1% level of significance). The confidence intervals of the slope

coefficient further justifies significance of the variable, net exports, because zero is not in the

range; thus, the regression output shows that we can be 95% confident that the unknown

population slope lies between -20.3472 and -15.2139. Since zero is not in the confidence

interval, we can therefore be 95% confident that the real population slope is not zero and that

there is a negative relationship between the variables GDP and net exports. Lastly with a

critical value of 1.98 with a 5% assumed level of confidence (two tailed), the regression

output creates a t-stat of -13.9806 for the slope coefficient of net exports. The t-stat of -

13.9806 (absolute value) is greater than the critical value 1.98 (13.9806 > 1.98), so there is a

5% level of significance or a 95% confidence level of passing the t-test. This adds more

support that the slope coefficient is statistically significant overall.

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Equation 5 Standard Format for USA Net Exports OLS Regression Output

2.3.2 USA Multiple RegressionWith a sample size of 44 observations in this multiple regression, it is acceptable to make

generalizations about the population because it is greater than 30. Along with a good sample

size, the model has a high r-squared of 0.9995 or 99.95% telling us that the independent

variables (FDI, Government Consumption Expenditure, House Consumption Expenditure and

Net Exports) explain 99.95% of the variation in GDP. The adjusted r-square (which considers

sample size) is extremely close to the r-square with a value of 0.99945 illustrating that this

model is so far useful. More importantly, the r-squared value is statistically significant, using

the p-value approach, which its p-value of 8.8397E-64. This p-value surpasses the 1%

standard so we can conclude that the overall regression model is statistically significant at a

99% confidence interval. It is important to note that the presence of the one outlier in the

standard residuals column may have reduced the r-square value (-2.55891 is outside of the +/-

2.5 outlier rule). There is an option to regress the output of the model without the outlier

(observation 44) to see its impact on the overall regression model and its r-square value to

help make the regression a better one. Despite one outlier, this multiple regression model is

good and useful thus far.

It is common in a multiple regression equation output to not be too concerned with the

intercept term as shown in the standard format, but interpreting the slope coefficients,

deciding if they are relevant (which all are theoretically relevant) and if they are statistically

significant is very important when determining the goodness of the regression model. An

example in interpreting the regression slope coefficients for FDI would be: GDP (US$) is

expected to increase by 38.74517 for each dollar rise of FDI ceteris paribus (keeping all other

independent variables constant). This interpretation goes for the other three independent

variables as well.

Testing if the slope coefficients are statistically significant through the three tests (p-value, t-

test, and confidence intervals) help determine if this model is useful and good. Government

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consumption expenditure, house consumption expenditure, and net exports are the only three

independent variables of the four that pass the hypothesis testing for the regression model.

FDI had a p-value exceeding 0.05 (specifically 0.637), had the presence of zero in the

confidence intervals (-0.5339888, 0.86206896) and has a t value (0.475342) that is lower than

the critical value (two sided) of 1.98. It also important to note that the government spending

variable for the USA had a negative sign when modern theory indicates that government

spending should have a positive correlation with GDP which may indicate the variable is not

relevant to the model, however the variable remains statistically significant.

The correlation matrix revealed very high correlations among the independent variables

ranging from 0.84 to 0.996, which indicates the presence of multicollinearity.

Multicollinearity may be caused by the presence of outliers, an irrelevant variable, an omitted

relevant variable or using data that basically measures the same thing.

Detail USA GDP

(current US$)

USA Foreign direct

investment, net inflows (BoP,

current US$)

USA General

government final

consumption

expenditure

(current US$)

USA Househol

d final consump

tion expenditu

re, etc. (current

US$)

USA Net

Exports

(Current

US$)

USA GDP (current US$) 1USA Foreign direct investment, net inflows (BoP, current US$)

0.864582

1

USA General government final consumption expenditure (current US$)

0.995433

0.846306 1

USA Household final consumption expenditure, etc. (current US$)

0.999669

0.863119 0.996601 1

USA Net Exports (Current US$) -0.9072

6

-0.83613 -0.90267 -0.91009 1

Table 4 Correlation Matrix for the USA Multiple Regression Model

Analysing the condition index and VIF for the US model, there is some discrepancy in the

results. For multicollinearity to be present the condition index must be greater than 20 and the

VIF must be greater than 10. The condition index of US net exports is 71.129 but the VIF is

less than 10 for the corresponding variable. Likewise the VIF for US consumption and US

government spending is greater than the 10 threshold but the condition index is less than 20

as can be seen in the table below. Thus we rule out the presence of multicollinearity.

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Detail VIF Condition Index

(Constant) 1.000

USFDI 4.630 3.302

USCON 167.942 6.783

USGOV 191.660 9.614

USEXP 6.181 71.129

Table 5 Collinearity Diagnostics for the USA Multiple Regression Model

Equation 6 Standard Format for USA Multiple Regression Output

Due to the possible presence of multicollinearity and presence of autocorrelation (examined

in part D) along with the government spending variable not sloping in the direction of

modern theory it can be concluded that this model of the USA is not very useful.

2.3.3 Netherlands OLS RegressionsFull regression results for part C regarding the Netherlands can be found in appendix B.

2.3.3.1 FDIThe sample size of the regression is acceptable to make generalizations about the population


the simple linear regression model has a very low r-squared of 0.469 or 46.9% telling us that

FDI explains 46.9% of the variation in GDP. The adjusted r-square (which considers sample

size) is extremely close to the r-square with a value of 0.456, which is a good thing. More

importantly, the r-squared value is statistically significant, using the p-value approach, as its p

-value is 2.94E-07. This p-value surpasses the 1% standard so we can conclude that the

overall regression model is statistically significant at the 1% level.

After regressing GDP (y) on foreign direct investment (x), FDI's slope coefficient was

1.228757. This is interpreted as GDP (in US$) is expected to increase by 1.228757 for each

dollar rise of FDI.

15

We assessed FDI's significance level through the three statistical tests where it passed all

three evaluations: p-value, confidence interval, and t-test. The slope coefficient is statistically

significant with a p-value of 2.94E-07, so the model is very significant at a 99% level of

confidence (1% level of significance). The confidence intervals of the slope coefficient

further justifies significance of the variable, FDI, because zero is not in the range; thus, the

regression output shows that we can be 95% confident that the unknown population slope lies

between 0.821652 and 1.635862. Since zero is not in the confidence interval, we can

therefore be 95% confident that the real population slope is not zero and that there is a

positive relationship between the variables GDP and FDI. Lastly with a critical value of 1.98


6.091136 for the slope coefficient of FDI. The t stat of 6.091136 is greater than the critical

value 1.98 (6.091136 > 1.98), so there is a 5% level of significance or a 95% confidence

passing the t-test. This adds more support that the slope coefficient is statistically significant

overall.

Equation 7 Standard Format for Netherlands FDI OLS Regression Output

2.3.3.2 Government ExpenditureThe sample size of the regression is acceptable to make generalizations about the population



government consumption expenditure explains 98.6% of the variation in GDP. The high r-


adjusted r square (which considers sample size) is extremely close to the r square with a value

of 0.985 as this is a good thing. More importantly, the r squared value is statistically

significant, using the p-value approach, which its p-value of1.22E-40. This p-value surpasses

the 1% standard so we can conclude that the overall regression model is statistically

significant at the 1% level.

16

After regressing GDP (y) on government consumption expenditure (x), government

consumption expenditure's slope coefficient was 3.881761. This is interpreted as GDP (US$)

is expected to increase by 3.881761 for each dollar rise in government consumption

expenditure.

We assessed government consumption expenditure's significance level through the three




intervals of the slope coefficient further justifies significance of the variable, government





variables GDP and government consumption expenditure. Lastly with a critical value of 1.98


54.60619 for the slope coefficient of government consumption expenditure. The t-stat of


significance with 95% confidence level to pass the t-test. This adds more support that the


Equation 8 Standard Format for Netherlands Government Expenditure OLS Regression Output

2.3.3.3 ConsumptionThe sample size of the regression is acceptable to make generalizations about the population



household consumption expenditure explains 99.5% of the variation in GDP. The high r-



17

value of 0.995 exemplifying that this model is so far useful. More importantly, the r-squared

value is statistically significant, using the p-value approach, which its p-value of 3.4E-51.

This p-value surpasses the 1% standard so we can conclude that the overall regression model

is statistically significant at the 1% level.

After regressing GDP (y) on household consumption expenditure (x), household consumption

expenditure’s slope coefficient was 2.21298. This is interpreted as GDP (US$) is expected to

increase by 2.21298 for each dollar rise of household consumption expenditure.

We assessed household consumption expenditure’s significance level through the three




intervals of the slope coefficient further justifies significance of the variable, household





variables GDP and household consumption expenditure. Lastly with a critical value of 1.98


97.85771 for the slope coefficient of household consumption expenditure. The t-stat of


significance along with a 95% confidence level of passing the t test. This adds more support

that the slope coefficient is statistically significant overall.

Equation 9 Standard Format for Netherlands Household Consumption OLS Regression Output

2.3.3.4 Net ExportsThe sample size of the regression is acceptable to make generalizations about the population


18


net exports explains 95.7% of the variation in GDP. The high r-squared tells us that it is a

good model because it is close to an ideal value of 100%. The adjusted r-square (which

considers sample size) is extremely close to the r-square with a value of 0.955 showing that

this is a good thing for the model. More importantly, the r-squared value is statistically

significant, using the p-value approach, where the p-value of the model is 2.49E-30. This p-

value surpasses the 1% standard so we can conclude that the overall regression model is

statistically significant at the 1% level. Although the r-square is significantly high for this

model, it is important to note that the presence of the outlier may have reduced the r-square

value (-3.00 is outside of the +/- 2.5 outlier rule). There is an option to regress the output of

the model without the outlier (observation 44) to see its impact on the overall regression

model and its r-square value to help make the regression a better one.

After regressing GDP (y) on net exports (x), net export's slope coefficient was 10.27151. This

is interpreted as GDP (US$) is expected to increase by 10.27151 for each dollar rise of net

exports.

We assessed net export's significance level through the three statistical tests where it passed

all three evaluations: p-value, confidence interval, and t-test. The slope coefficient is

statistically significant with a p-value of 2.49E-30, so the model is very significant at a 99%

level of confidence (1% level of significance). The confidence intervals of the slope

coefficient further justifies significance of the variable, net exports, because zero is not in the

range; thus, the regression output shows that we can be 95% confident that the unknown

population slope lies between 9.593672 and 10.94936. Since zero is not in the confidence

interval, we can therefore be 95% confident that the real population slope is not zero and that

there is a positive relationship between the variables GDP and net exports. Lastly with a

critical value of 1.98 with a 5% assumed level of confidence (two tailed), the regression

output creates a t-stat of 30.5805 for the slope coefficient of net exports. The t-stat of 30.5805

is greater than the critical value 1.98 (30.5805 > 1.98), so there is a 5% level of significance

of passing the t-test. This adds more support that the slope coefficient is statistically

significant overall.

19

Equation 10 Standard Format for Netherlands Net Exports OLS Regression Output

2.3.4 Netherlands Multiple RegressionWith a sample size of 44 observations in this multiple regression, it is acceptable to make

generalizations about the population because it is greater than 30. Along with a good sample

size, the multiple linear regression model had a high r-squared of 0.9996 or 99.96% telling us

that the independent variables (FDI, Government Consumption Expenditure, House

Consumption Expenditure and Net Exports) explain 99.96% of the variation in GDP. The


value of 0.99959 displaying how this model is so far useful. More importantly, the r-squared

value is statistically significant, using the p-value approach, since its p-value is 3.15E-66.

This p-value surpasses the 1% standard so we can conclude that the overall regression model

is statistically significant at the 99% confidence interval. It is important to note that the

presence of the two outliers may have reduced the r square value (-2.81251 and 3.848636 are

outside of the +/- 2.5 outlier rule). There is an option to regress the output of the model

without the outlier (observation 1 and 44) to see its impact on the overall regression model

and its r square value to help make the regression a better one. Despite outliers, this multiple

regression model is good and useful thus far.

It is common in a multiple regression equation output to not be too concerned with the

intercept term as shown in the standard format, but interpreting the slope coefficients,

deciding if they are relevant (which all are theoretically relevant) and if they are statistically

significant is very important when determining the goodness of the regression model. An

example in interpreting the regression slope coefficients for household consumption would

be: GDP (US$) is expected to increase by 2.21298 for each dollar rise of household

consumption expenditure ceteris paribus (keeping all other independent variables constant).

This interpretation goes for the other three independent variables as well.

Testing if the slope coefficients are statistically significant through the three tests (p-value, t-

test, and confidence intervals) help determine if this model is useful and good. All of the

20

independent variables, FDI, government consumption expenditure, house consumption

expenditure, and net exports pass the hypothesis testing for the regression model. Despite the

presence of the two outliers, this model is still very good or useful thus far due to the an

overall statistically significant regression model, high r-square, good sample size, high

adjusted r-square, and all independent variables that are statistically significant.

However, the correlation matrix revealed very high correlations among some of the

independent variables such as government spending and household consumption ranging

from 0.84 to 0.996, which indicates the presence of multicollinearity. Multicollinearity may

be caused by the presence of outliers, an irrelevant variable, an omitted relevant variable or

using data that basically measures the same thing.

Detail NETH GDP (current

US$)

NETH Foreign direct

investment, net inflows

(BoP, current US$)

NETH General government

final consumption expenditure

(current US$)

NETH Household

final consumption expenditure, etc. (current

US$)

NETH Net Exports (Current

US$)

NETH GDP (current US$)

1

NETH Foreign direct investment, net inflows (BoP, current US$)

0.684865 1

NETH General government final consumption expenditure (current US$)

0.993031 0.695656 1

NETH Household final consumption expenditure, etc. (current US$)

0.997814 0.661969 0.984356 1

NETH Net Exports (Current US$)

0.978273 0.753447 0.983997 0.966786 1

Table 6 Correlation Matrix for the Netherlands Multiple Regression Model

Analysing the condition index and VIF for the US model, there is some discrepancy in the

results. For multicollinearity to be present the condition index must be greater than 20 and the

VIF must be greater than 10. The condition index for consumption and net exports are greater

than 20 and the VIF for the corresponding variables are greater than 10. We can conclude that

house consumption expenditure and net exports for the Netherlands data set has

multicollinearity present. Government expenditure has a VIF of 68.526 with which are

21

greater than 10 but a condition index of 4.644 which is less than the 20 threshold. The

presence of multicollinearity cannot be ruled out as can be seen from the table below.

Detail VIF Condition Index

(Constant) 1.000NETHFDI 2.817 2.620

NETHGOV 68.526 4.644

NETHCON 33.230 21.178

NETHEXP 44.560 33.918Table 7 Collinearity Diagnostics for the Netherland Multiple Regression Model

Equation 11 Standard Format for Netherlands Multiple Regression Output

With the presence of multicollinearity and autocorrelation (examined in part D) in the

Netherlands model, we can conclude that the model is not very useful as not all of the noise

in the error term is random and may be affected by an omitted or irrelevant variable in the

model.

2.4 Part D

2.4.1 Autocorrelation Testing for USAThe overall residual plot for the USA appears largely homoscedastic excluding the outliers;

however, the residuals appear to form a pattern of peaks and troughs throughout the time

period. This indicates that GDP will increase for a number of years and decrease for a

number of years, which underestimates true variance making the statistical slope tests

irrelevant. A miss-specified model may cause these conclusions where such models occur

from omitted variables, irrelevant variables, or outliers. The pattern can be seen from the

graph below and the data will be further tested using the Durban Watson test.

22

1960 1970 1980 1990 2000 2010 2020

-350000000000

-300000000000

-250000000000

-200000000000

-150000000000

-100000000000

-50000000000

0

50000000000

100000000000

150000000000

Overall Residual Plot for the USA Model

Time (years)

Resid

uals

Figure 5 Overall Residual Plot for the USA Model

Model Summaryb

Mode

l

R R

Square

Adjusted R

Square

Std. Error of

the Estimate

Durbin-

Watson

1 1.000a .999 .999 11862001770

3.45859

.348

a. Predictors: (Constant), netexport, FDI, govexpenditure, householdconsump

b. Dependent Variable: GDPTable 8 Model Summary for the USA Multiple Regression Model

The D-W (= 0.348) is below 2 which indicates positive serial correlation but this needs to be

compared to critical values (which can be obtained from D-W tables) before one can decide

whether we can accept or reject the null hypothesis of no serial correlation in the data.

The hypothesis test for autocorrelation is as follows:

Step 1: H 0 : No autocorrelation in the regression model.

H a : There is autocorrelation in the regression model.

Step 2: Critical Value from Durbin Watson tables.

From the extract of D-W critical values, we generate two values dL and dU which represent

upper and lower limits for the D-W statistic – for the data in the autocorrelation sheet with n

= 45 (closest to n = 44, our sample size) and k = 4 (four X variables), we get dL = 1.156 and

dU = 1.528.

23

Step 3: Calculate the Durbin-Watson statistic from SPSS – this is 0.348.

Step 4: Conclusion: We can reject H 0with 1% significance (these are 1% tables). In this case,

the Durbin-Watson statistic, 0.348, is less than the dL, 1.159, and therefore, we can conclude

that there is positive autocorrelation in this data. Thus we reject the null hypothesis and

accept the alternative hypothesis.

2.4.2 Autocorrelation Testing NetherlandsThe overall residual plot for the Netherlands appears homoscedastic; however, the residuals

appear to form a pattern of peaks and troughs throughout the time period. This indicates that

GDP will increase for a number of years and decrease for a number of years, which

underestimates true variance making the statistical slope tests irrelevant. A miss-specified

model may cause these conclusions where such models occur from omitted variables,

irrelevant variables, or outliers. The pattern can be seen from the graph below and the data

will be further tested using the Durban Watson test.

1960 1970 1980 1990 2000 2010 2020

-20000000000

-15000000000

-10000000000

-5000000000

0

5000000000

10000000000

15000000000

20000000000

25000000000

Overall Residual Plot for the Netherlands Model

Time (years)

Resid

uals

Figure 6 Overall Residual Plot for the Netherlands Model

Model Summaryb

Mode

l

R R

Square

Adjusted R

Square

Std. Error of

the Estimate

Durbin-

Watson

1 1.000a 1.000 1.000 5492329398.

62595

.896

a. Predictors: (Constant), householdconsump, netexport, govexpenditure, FDI

b. Dependent Variable: GDPTable 9 Model Summary for the Netherlands Multiple Regression Model

24

The D-W (0.896) is below 2 which indicates positive serial correlation but this needs to be

compared to critical values (which can be obtained from D-W tables) before one can decide

whether we can accept or reject the null hypothesis of no serial correlation in the data.

The hypothesis test for autocorrelation is as follows:

Step 1: H 0 : No autocorrelation in the regression model.

H a : There is autocorrelation in the regression model.

Step 2: Critical Value from Durbin Watson tables.

From the extract of D-W critical values, we generate two values dL and dU which represent

upper and lower limits for the D-W statistic – for the data in the autocorrelation sheet with n

= 45 (closest to n = 44, our sample size) and k = 4 (four X variables), we get dL = 1.156 and

dU = 1.528.

Step 3: Calculate the Durbin-Watson statistic from SPSS – this is 0.896.

Step 4: Conclusion: We can reject H 0 with 1% significance (these are 1% tables). In this

case, the Durbin-Watson statistic, 0.896, is less than the dL, 1.159, and therefore, we can

conclude that there is positive autocorrelation in this data. Thus we reject the null hypothesis

and accept the alternative hypothesis.

25

2.4.3 Normal Distribution for the USA Multiple Regression Model ResidualsLooking at the normal distribution of the USA residuals we can see that the shape of the

distribution is not symmetrical a fat tail to the right. However, the histogram appears to show

a heavy skewness to the left with all of the bars to the left of the highest bar.

Figure 7 Histogram of USA Multiple Regression Residuals

The negative skewness of -.0781 as seen in the table below further signifies skewness to the

left.

USA Residuals Descriptive Statistics

Mean -0.000965465Standard Error 16569744409Median 24395340639Mode #N/AStandard Deviation 1.09911E+11Sample Variance 1.20805E+22Kurtosis -0.420720907Skewness -0.781885131Range 4.0583E+11Minimum -2.81252E+11Maximum 1.24577E+11Sum -0.042480469Count 44Largest(1) 1.24577E+11Smallest(1) -2.81252E+11Confidence Level(95.0%) 33416074292Table 10 USA Multiple Regression Residual Descriptive Statistics

26

The Jarque Bera test is a statistical analysis to identify whether or not the residuals of a given

data set are normally distributed. It is a hypothesis test with the following null and alternative

hypothesis:

H 0 : Skewness is zero and kurtosis is 3.

H a : Skewness is not zero and kurtosis is not 3.

The critical value (chi value) was determined by the "=Chiinv(0.05,2)" function in excel

which equates to 5.991. The formula to derive the Jarque Bera statistic (JB) can be seen

below were "n" equals the sample size, "k" equals kurtosis and "s" equals skewness.

JB=n ( s2

6+

(k−3 )2

24 )JB=44(−0.7812

6+ (−0.421−3 )2

24 ) JB=¿ 25.93

Equation 12 Jarque Bera Equation for the USA Multiple Regression Model

The JB statistic of 25.93 is greater than the critical value of 9.497 which means we must

reject the null hypothesis and accept the alternative hypothesis. Combining the analysis of the

Jarque Bera test as well as the analysis of the histogram and skewness we can determine that

the residuals for the USA multiple regression model are not normally distributed and do not

have a kurtosis of 3.

2.4.4 Normal Distribution for the Netherlands Multiple Regression Model ResidualsAs can be seen on the histogram below, the residuals for the Netherlands multiple regression

model appear to be skewed to the left with 4 boxes on the left of the highest box on the chart

compared to one box on the right which is deemed to be an outlier as it occurs where the bell

curve flattens out.

27

Figure 8 Histogram of the Netherlands Multiple Regression Residuals

The skewness figure of 0.594 contradicts this analysis as data, which is skewed to the left,

tends to have a negative skewness figure, though this contradiction may be caused by the

outlier as seen on the histogram.

Netherlands Residual Descriptive Statistics

Mean -3.5546E-06Standard Error 794443405.1Median 1089217220Mode #N/AStandard Deviation 5269741384Sample Variance 2.77702E+19Kurtosis 5.028523526Skewness 0.594789731Range 35102516448Minimum -14821202345Maximum 20281314103Sum -0.000156403Count 44Largest(1) 20281314103Smallest(1) -14821202345Confidence Level (95.0%) 1602147818Table 11 Netherlands Multiple Regression Residual Descriptive Statistics

28

The Jarque Bera test is a statistical analysis to identify whether or not the residuals of a given

data set are normally distributed. It is a hypothesis test with the following null and alternative

hypothesis:

H 0 : Skewness is zero and kurtosis is 3

H a : Skewness is not zero and kurtosis is not 3

The critical value (chi value) was determined by the "=Chiinv(0.05,2)" function in excel

which equates to 5.991. The formula to derive the Jarque Bera statistic (JB) can be seen

below were "n" equals the sample size, "k" equals kurtosis and "s" equals skewness.

JB=n ( s2

6+

(k−3 )2

24 )JB=44( 0.5942

6+

(5.028−3 )2

24 ) JB=¿ 10.138

Equation 13 Jarque Bera Equation for the Netherlands Multiple Regression Model

The Jarque Bera statistic of 10.138 is greater than the critical value of 9.497 which means we

must reject the null hypothesis and accept the alternative hypothesis. Combining the analysis

of the Jarque Bera test as well as the analysis histogram and skewness we can determine that

the residuals for the Netherlands multiple regression model are not normally distributed and

do not have a kurtosis of 3.

2.5 Part E

2.5.1 Specification Error of the US model As a part a classical linear regression model, assumption ten verifies if the model is correctly

specified or not. This ensures that all drivers of the dependent variable are relevant and

included to visualize their impact on the dependent variable. The Ramsey RESET test

determines whether or not there is a specification error by measuring if non-linear

combinations of the fitted values explain the dependent variable. If the combinations do not

explain the dependent variable properly, then the model is most likely miss-specified. Below

gives the procedure of the Ramsey RESET test:

29

Step 1: H 0 : The correct specification is linear.

H a : The correct specification is non-linear.

Step 2: Get a Critical Value from F tables – this will be based on the degrees of freedom in

an unrestricted regression model. 2.49 (at 5% significance level, v_1=7 and v_2=36).

Step 3: Get an F statistic - Compare the fit of the two equations using an F test.

F=(SSRM−SSRU ) /MSSRU /(n−k−1)U

F=(519460765112148000000000.00−35229096389330200000000.00 )/3

35229096389330200000000.00 /(44−7−1)

F=164.9426361

Equation 14 Ramsey Reset Equation for USA

Step 4: Conclusion – reject H 0 if the F statistic exceeds the critical value.

As the F statistic is greater than the critical value, we will reject the null hypothesis and

accept the alternative hypothesis meaning that that the true specification of the model is non-

linear (with 5% level of significance). Since we are 95% confident that the USA model is

miss-specified, the rejection shows that our model has non-linear combinations of the

independent variables that have power in explaining the dependent variable, GDP. Possible

reasons for miss-specification in our model could be an inclusion of an irrelevant variable,

exclusion of a relevant variable (it’s omitted), or miss-specification of the functional form

such as an inappropriate linear relationship.

2.6 Part F

2.6.1 Adding the Dummy VariableA multiple regression was run pooling both the US and Netherlands datasets together. This

regression was run twice, one with the dummy variable and one without the dummy variable.

The slope of the dummy variable is "2.4E+11" where it can be interpreted in two ways since

the US = 1 and the Netherlands = 0. If the dummy variable is equal to zero then we can

expect GDP to be 3.2E+11 in the Netherlands or if the dummy variable is equalled to one

30

then we can expect GDP to be 3.2E+11 - 2.4E+11 = 82116505677 (intercept plus the slope

multiplied by 1) in the United States.

As for the statistical significance of the dummy variable:

H 0 : A country has no effect on the growth rate in GDP (B=0)

H a : A country has an effect on the growth rate in GDP (B=1)

The dummy variable difference surpasses all three statistical significant tests of p-value, t-

test, and confidence interval. The slope coefficient is statistically significant with a p-value of

9.37E-11, so the model is significant at a 99% level of confidence (1% level of significance).

When the dummy variable is included, foreign direct investment becomes statistically

significant passing the p-value test at a 99% confidence interval. However government

spending remains statistically insignificant. There are two outliers present in the dummy

variable model at observation 1 and 2. Both these observations have a standard residual

greater than the nominal value of 2.5.

The confidence intervals of the slope coefficient further justifies significance of the dummy

variable because zero is not in the range; thus, the regression output shows that we can be

95% confident that the unknown population slope lies between -3.0204E+11 and -1.7E+11.

Lastly with a critical value of 1.98 with a 5% assumed level of confidence (two tailed), the

regression output creates a t-stat of -7.4282 for the dummy variable's slope coefficient. The t-

stat of -7.4282 (absolute value) is greater than the critical value 1.98 (7.4282 > 1.98), so there

is a 5% level of significance or a 95% confidence level of passing the t test. Thus we can

reject the null hypothesis accept the alternative hypothesis. This adds more support that the


2.6.2 Interaction EffectWe are looking to test the hypothesis that household consumption has a different impact on

GDP in the United States as opposed to the Netherlands. We multiplied the dummy variable

by consumption and performed a multiple linear regression with all of the other variables

present in the model. The model has a high-adjusted r-square of 0.999 but also has a high

standard error of 8.19E+10. All of the variables in this model are statistically significant with

the exception of foreign direct investment as its p-value of 0.272 is greater than the

significance level of 0.05. The significance F is also less than 0.05 indicating that the overall

model is statistically significant.

31

H 0 :Consumption has the same effect in both countries.

H a :Consumption has a differing effect in both countries.

With all other independent variables being held constant and subbing a 1 into the model to

simulate the USA we find that GDP is 3.53021E+11. However, when we sub in 0 into the

model to simulate the Netherlands we find that GDP is negative at -2.2618E+10. This

indicates that household consumption expenditure has a positive effect on GDP in the USA

with all other variables being held constant and a negative effect in the Netherlands, which

does not make theoretical sense, as consumption cannot be negative.

With these results in mind we can reject the null hypothesis that consumption has the same

effect in both countries and accept the alternative hypothesis and assumption that

consumption has a differing effect in both countries.

2.7 Part G

2.7.1 Lag of Government Spending for the USASome variables may not have an immediate effect on Y and thus take time before their impact

is realised. For example when the government spends money on infrastructure the impact on

GDP may not occur until a number of years after the event. As a result distributed lags are

used on variables whose output has a time delay on Y. The more periods you lag the more

degrees of freedom you give up which can hinder the goodness of the model during the

significance hypothesis tests.

Government expenditure (General government final consumption expenditure (current US$))

was chosen to test the effect of lagging a variable. Government expenditure (GE) was lagged

for two periods 1972-2013 with 42 observations as opposed to 1970-2013 with 44

observations.

The slope of government expenditure is 16.738, which indicate when all other variables are

held constant GDP will increase in the US by 16.738 for every one-unit increase in

government spending.

When government spending is lagged by a period of one, the slope drastically changes to -

20.743 indicating when all other variables are held constant government spending has a

negative effect on GDP by 20.743 for the US when increased by a unit of one.

32

When government spending is lagged for a second period the slope reverts to 10.465. Thus

when all other variables are held constant the second lag of government spending will

increase GDP by 10.465 in the US for every one-unit increase in government spending.

The independent variables in this model are statistically significant at a 95% confidence

interval as the p-value for the independent variables are all less than the significance level of

0.05 (5%) as can be seen in the table below under the p-value heading. Thus we can reject the

null hypothesis that the slopes are statistically insignificant and not representative of the

sample size and do not reject the alternative hypothesis that the slopes are statistically

significant and relevant of the sample size.

Coefficients Standard Error t Stat P-valueIntercept 1.57E+09 1.43E+11 0.010972 0.991303GE 16.73863 3.354576 4.98979 1.37E-05Lag of GE X1 -20.743 6.754004 -3.07122 0.003927Lag of Ge X2 10.46563 3.86703 2.706373 0.010131Table 12 Coefficients and Significance Values for the USA Government Spending Lag Model

Multicollinearity is also present between the lag variables, which are another downside of

distributive lags. The VIF for the lagged independent variables are greater than 10 and the

condition index for these variables are greater than 20 as seen in the table below. Thus we can

conclude that multicollinearity is present for the two period distributive lag for the

Netherland’s government spending which can be seen from the table below. The unlagged

government consumption expenditure variable (USAGE) has a VIF greater than 10 at

1181.612 and a conflicting condition index which is less than 20 at 4.033. As a result we

cannot rule out the possibility of multicollinearity with regards to unlagged government

spending variable, which can be seen from the table below.

Detail Condition Index VIF

(Constant) 1.000

USAGE 4.033 1181.612

USAGELAG1 66.689 4464.390

USAGELAG2 294.452 1401.786

Table 13 Collinearity Diagnostics for the USA Government Spending Lag Model

33

Equation 15 Standard Format for USA Two Period Distributive Lag of Government Spending Regression on GDP (Current US$)

2.7.2 Lag of Government Spending for the NetherlandsSome variables may not have an immediate effect on Y and thus take time before their impact

is realised. For example when the government spends money on infrastructure the impact on

GDP may not occur until a number of years after the event. As a result distributed lags are

used on variables whose output has a time delay on Y. The more periods you lag the more

degrees of freedom you give up which can hinder the goodness of the model during the

significance hypothesis tests.

Government expenditure (General government final consumption expenditure (current US$))

was chosen to test the effect of lagging a variable. Government expenditure (GE) was lagged

for two periods from 1972-2013 with 42 observations as opposed to 1970-2013 with 44

observations.

The slope of government expenditure is 4.923 which indicate when all other variables are

held constant GDP will increase in the Netherlands by 4.923 for every one-unit increase in

government spending.

When government spending is lagged by a period of one, the slope drastically changes to -

0.729 indicating when all other variables are held constant government spending will

decrease GDP in the Netherlands by 0.729 for every one-unit in government spending.

When government spending is lagged for a second period the slope increases slightly to -

0.394; thus when all other variables are held constant the second lag of government spending

will decrease GDP by 0.394 in the Netherlands for every one unit increase in government

spending.

Government spending is statistically significant as its p-value is less than the significance

level of 0.05 (5%) meaning we can reject the null hypothesis that the slope is statistically

insignificant and not representative of the population size and accept the alternative

hypothesis that the slope is statistically significant and representative of the population size.

34

The lag variables failed the significance tests as their p-value was greater than the

significance level of 0.05 (5%) as can be seen on the table below under the p-value section.

Thus we must not reject the null hypothesis as aforementioned before and reject the

alternative hypothesis.

Coefficients Standard Error t Stat P-valueIntercept 3.61E+10 8.22E+09 4.39445 8.62E-05

GE 4.923062 0.560679 8.780533 1.11E-10Lag of GE X1 -0.72973 0.916904 -0.79586 0.431058Lag of GE X2 -0.3941 0.579334 -0.68027 0.500458

Table 14 Coefficients and Significance Values for the Netherlands Government Spending Lag Model

Multicollinearity is also present between the lag variables, which are another downside of

distributive lags. The VIF for the lagged independent variables are greater than 10 and the

condition index for these variables are greater than 20 as seen in the table below. Thus we can

conclude that multicollinearity is present for the two period distributive lag for the

Netherland’s government spending which can be seen from the table below. In summation,

the failing of the significance tests by the lag variables and the presence of multicollinearity

indicate that lagging government expenditure for a period of 1 or 2 is not effective to the

model.

Detail Condition Index VIF

(Constant) 1.000

NethGE 3.552 61.210

NethGELAG1 20.443 153.173

NethGELAG2 48.385 57.515

Table 15 Collinearity Diagnostics for the Netherlands Government Spending Lag Model

Equation 16 Standard Format for Netherlands Two Period Distributive Lag of Government Spending Regression on GDP (Current US$)

35

2.8 Part H

2.8.1 Forecasting GDP for the USATime series collects random variables over time in attempt to forecast future values of the

random variables based on its past and present values. However, such models assume the data

is stationary, meaning there is not variance over the time or the mean is constant, as well as

no presence of autocorrelation in the data. By looking at the graphs without the change of

GDP to the left, there is stationary and constant over time. The bottom two graphs with the

change of GDP do not show a constant, stationary line implying. It is clear that there are

collinearity issues by looking at the autocorrelation functions table, which is common with

distributed lag models. The table exemplifies that GDP is highly correlated over time as

shown in the first two graphs with their clear trends, but the difference/change of time does

not have this problem as there is not much pattern in the bottom two time series graph.

Autocorrelation Functions

Lag Length Y Log Y Y log Y

1 0.999328 0.999736 0.57924 0.6846492 0.998009 0.99933 0.25287 0.5599753 0.99659 0.998943 0.066808 0.5313414 0.995435 0.99857 0.036035 0.5006415 0.994656 0.998353 0.26192 0.571386 0.994514 0.998251 0.471831 0.548999

Table 16 Autocorrelation Functions for USA GDP (Current US$)

For example, the correlation between y and y lagged by one period is 0.999328 whereas the

between change of GDP and log of GDP change lagged by one period is only 0.57924. We

can see the difference below in the graphs how using the change of GDP and the change in

the natural log of GDP removes the autocorrelation by transforming stationary data in

nonstationary data.

36

1960 1970 1980 1990 2000 2010 20200.00E+00

2.00E+12

4.00E+12

6.00E+12

8.00E+12

1.00E+13

1.20E+13

1.40E+13

1.60E+13

1.80E+13

Line Graph of US GDP 1970-2013

Time (Years)

GD

P (C

urre

nt U

S$)

Figure 9 Line Graph of US GDP (Current US$) from 1970-2013

1960 1970 1980 1990 2000 2010 202026

26.5

27

27.5

28

28.5

29

29.5

30

30.5

31

Line Graph of US Ln(GDP) 1970-2013

Time (Years)

Nat

ural

Log

GD

P (C

urre

nt U

S$)

Figure 10 Line Graph of the Natural Log US GDP (Current US$) from 1970-2013

37

1960 1970 1980 1990 2000 2010 2020

-4.00E+11

-2.00E+11

0.00E+00

2.00E+11

4.00E+11

6.00E+11

8.00E+11

1.00E+12

Line Graph of US (GDP) 1970-2013

Time (Years)

Chan

ge in

GD

P (C

urre

nt U

S$)

Figure 11 Line Graph of the Change in US GDP (Current US$) from 1970-2013

1960 1970 1980 1990 2000 2010 2020

-4.00E-02

-2.00E-02

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

Line Graph of US Ln (Y) 1970-2013

Time (Years)

Chan

ge in

Nat

ural

log

of G

DP

(Cur

rent

US$

)

Figure 12 Line Graph of the change in the Natural Log of US GDP (Current US$) from 1970-2013

38

2.8.2 Forecasting GDP for the NetherlandsTime series collects random variables over time in attempt to forecast future values of the

random variables based on its past and present values. However, such models assume the data

is stationary, meaning there is not variance over the time or the mean is constant, as well as

no presence of autocorrelation in the data. By looking at the graphs without the change of

GDP to the left, there is stationary and constant over time. The bottom two graphs with the

change of GDP do not show a constant, stationary line implying. But the It is clear that there

are collinearity issues by looking at the autocorrelation functions table, which is common

with distributed lag models. The table exemplifies that GDP is highly correlated over time as

shown in the first two graphs with their clear trends, but the difference/change of time does

not have this problem as there is not much pattern in the bottom two time series graph.

Autocorrelation Functions

Lag Length Y Log Y Y log Y

1 0.98925 0.992835 0.155338 0.3879432 0.973977 0.979641 -0.15339 0.0477573 0.962269 0.965112 0.175418 0.0314994 0.944479 0.950051 0.11437 0.1169095 0.924037 0.93285 -0.15299 -0.177856 0.916906 0.919247 -0.39885 -0.25205

Table 17 Autocorrelation Functions for Netherlands GDP (Current US$)

For example, the correlation between y and y lagged by one period is 0.98925 whereas the

between change of GDP and log of GDP change lagged by one period is only 0.155338. We

can see the difference below in the graphs how using the change of GDP and the change in

the natural log of GDP removes the autocorrelation by transforming stationary data into non

stationary data.

39

1960 1970 1980 1990 2000 2010 20200

100000000000

200000000000

300000000000

400000000000

500000000000

600000000000

700000000000

800000000000

900000000000

1000000000000

Line Graph of Netherlands GDP (Y) Over Time

Time (Years)

GD

P (C

urre

nt U

S$)

Figure 13 Line Graph of the Netherlands GDP (Current US$) from 1970-2013

1960 1970 1980 1990 2000 2010 202022

23

24

25

26

27

28

Line Graph of Netherlands Ln(GDP) Over Time

Time (Years)

Nat

ural

Log

of G

DP

(Cur

rent

US$

)

Figure 14 Line Graph of the Natural Log of the Netherlands GDP (Current US$) from 1970-2013

40

1960 1970 1980 1990 2000 2010 2020

-100000000000

-50000000000

0

50000000000

100000000000

150000000000

Line Graph of Netherlands (GDP) 1970-2013

Time (Years)

Chan

ge in

GDP

(cur

rent

US$

)

Figure 15 Line Graph of the Change in the Netherlands GDP (Current US$) from 1970-2013

1960 1970 1980 1990 2000 2010 2020

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Line Graph of Netherlands Ln (GDP) 1970-2013

Years (Time)

Chan

ge in

Nat

ural

Log

of G

DP (C

urre

nt U

S$)

Figure 16 Line Graph of the Change in the Natural Log of the Netherlands GDP (Current US$) from 1970-2013

41

3.0 Question 2For our group, we were assigned the year 2011 for the Merger Deal Negotiations of Question

Two of this Group Assignment. We conducted an analysis for the following mergers: EP

Global Opportunities Trust, Carrillion PLC, Sinclair Pharma PLC, Pearson PLC, Qatar,

Smiths News PLC, Greene King PLC, Infrastructure India PLC, Premier Oil PLC, and

Quindell Portfolio PLC. The time period of data we utilized in the year 2011, we used 125

days before and 25 days after as estimation. First, we calculated the abnormal return (AR)

and Cumulative abnormal return (CAR) for each of our ten mergers. To find the AR, we

subtracted the stock price from its previous day stock price to get the stock return; to find the

market return, known as the expected return, we subtracted the stock exchange shares from

its previous day share amount where the abnormal return is the difference between the stock

return and the market return. As for the CAR, there are two ways to discover the CAR: one

by the regression (CAR Part (ii)) and the other manually through market return (CAR Part i).

First, we regressed Y (Stock Return) on X (Market Return) to obtain the predicted Y and

residual values of each merger for the previous 125 days to 25 days before the announcement.

Starting 25 days before up to 25 days after the market marks the time period needed to

calculate both sets of CAR outside of the regression results. To predict the results, the predict

y was calculated as multiplying the slope and intercept with that day’s abnormal return rate

and the residuals were calculated as the difference between that same day’s stock price with

the predicted residuals. For CAR Part (i), we added the abnormal return of that day and the

next days. For instance, for Day 1 would equal that day’s sum and for Day 2 it would be the

sum of Day 1 and Day 2 and so forth. The same concept was applied for CAR Part (ii),

except the data derived from the residuals of the regression model. The table below analyses

the results of each merger based on their individual graphs. It is important to note that dips or

spikes refer to overreaction to stock news and gradual changes refer to a delayed response to

the stock news. Results can be seen in the table below.

Merger Strengths GraphEP The model displays a downward trend the

event window. Initially it made a positive abnormal return rate, but will drift off in the future (bad news). There is no immediate reaction on the announcement date suggesting an inefficient market, as there is a delayed reaction to proposed bad news.

42

Carrillion The model displays a downward trend event window. There are some spikes and consistency in the middle but still drifts downward eventually (bad news). The delayed reaction to the proposed bad news suggests an inefficient market, as there was no immediate reaction to bad news followed by a normal trend.

Sinclair The model displays a downward trend event window. There is a spike in the end for CAR (i), but drifts back down (bad news). The market would appear to be inefficient in this example due to the lack of reaction to the news announcement followed by a downward trend in cumulative abnormal returns.

Pearson The model displays an upward trend during the event window. Initially it is consistent in its positive abnormal return rate, but will shift up in the future. It is important note that there is a sharp dip in the rate before shooting back upwards (good news). In the Pearson announcement there was an immediate reaction to the announcement but there were a couple of over reactions post announcement which suggests market inefficiency

Qatar The model displays a consistent trend during the event window. Initially it held a consistent abnormal return rate, but dipped rapidly before remaining consistent at its new abnormal return rate in the future (no news – sudden dip means overreaction to bad news). The over-reaction 10 days prior to the announcement day suggests an inefficient market and no reaction on the announcement date. It would also be an indicator of insider trading as a sharp move in cumulative abnormal returns before a major merger announcement is a little suspicious.

43

Smiths The model displays a consistent downward trend during the event window. There are some dips and spikes along the way in the abnormal return rate, and it will drift off in the future (no news). The delayed over-reaction indicated by a price spike 9 days after the announcement suggests inefficiency in the market.

Greene The model displays a constant trend during the event window. Eventually it is expected to drift off by CAR Part (ii), but CAP Part (i) expects the continuation of its constant rate (no news except end predicts overreaction to news). The fact that there was no immediate reaction on the announcement date followed by a delayed downward over-reaction from the CAR (ii) suggests inefficiency in the market.

Infrastructure

The model displays a downward trend during the event window on the CAR Part (ii) results. Initially it was consistency through its abnormal return rate. There is some erratic behaviour of peaks and dips in the future in both trends (no news with some overreactions and delayed responses). The cumulative abnormal returns exhibit an almost immediate downward reaction on the announcement date. The fact that the trend starts a little before the announcement date may indicate some insider trading. The CAR (i) becomes a little bit volatile having a couple of over-reactions ins opposite trends and the CAR (ii) line continues a rather steep decent which indicates an inefficient market.

Premier The model displays an upward trend during the event window and is expected to have a positive abnormal return rate (good news). Premier exhibits an immediate negative reaction on the announcement date but then begins to rebound in the upward direction, especially from the CAR (ii) line. The fact that the cumulative abnormal returns trend upward as opposed to remaining constant after the news announcement suggests an inefficient market.

44

Quindell The model displays a constant trend during the event window in the abnormal return rate. There is a steady decline in the CAR Part (ii), but levels out eventually (no news). Quindell does not exhibit and immediate reaction to the news announcement and cumulative abnormal returns appears to continue relatively consistent after the announcement suggesting an inefficient market.

Table 18 Cumulative Abnormal Returns for Individual Companies

The table below identifies overall market return and overall market model for each merger.

For the Overall Using Market Return, we gathered each merger’s entire abnormal return rate

into separate columns to calculate the average abnormal rate, the t-score and CAR as one

overall average of all the mergers for the market that particular day. In doing so, we took

each mergers abnormal rate for that day and averaged it to obtain the average abnormal rate.

For the t-score, we divided the current day’s average abnormal rate by the standard deviation

of the entire mergers daily abnormal rate. To calculate the CAR, we summed the current

day’s average abnormal rate with the previous day’s average abnormal rate and graphed the

CAR’s results. For the Overall Using Market Model, we followed the same steps except the

data of each merger derived from the residual regression results. Table 19 will summarize,

analyse and conclude the cumulative average abnormal returns for both the market return and

market model.

Overall the cumulative abnormal returns from the ten mergers analysed appear to provide

evidence for an inefficient market in the FTSE All Share from but CAR (i) and CAR (ii)

testing. The studied merges in general tended to have delayed over reactions to the news

announcements both before and after the announcement date and did not continue a relatively

stable sideward trend after the announcement rather a more volatile period existed during the

post 25 days of announcement which in general suggests an inefficient market.

Event Window Conclusions GraphOverall Using

Market ReturnThis model displays the

cumulative average abnormal rate of the market return. The trend displayed indicates that there is not much reaction to the stock

news. In other words, there was not much news revealed within this market of all the mergers.

45

Overall Using Market Model

This model displays the cumulative average abnormal rate of the market model (regression residuals). The trend displayed indicates that there is a lot of reaction to the stock news. In other words, there was a lot of overreaction to the bad news

revealed within this market of all the mergers. Towards the end of the trend, it levels out implying there wasn’t much news in the

market.Table 19 Cumulative Abnormal Returns for Portfolio

Appendix A will give a full size view of each of the graphs for the event studies.

46

Appendix-A Event Study Graphs

-30 -20 -10 0 10 20 30

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

CUMULATIVE ABNORMAL RETURNS FOR EP

CAR Part (i)CAR Part (ii)

DAYS

CAR

-30 -20 -10 0 10 20 30

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

CUMULATIVE ABNORMAL RETURNS FOR CARRILLION


DAYS

CAR

-30 -20 -10 0 10 20 30

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

CUMULATIVE ABNORMAL RETURNS FOR SINCLAIR


DAYS

CAR

-30 -20 -10 0 10 20 30

-0.04

-0.02

0

0.02

0.04

0.06

0.08

CUMULATIVE ABNORMAL RETURNS FOR PEARSON


DAYS

CAR

-30 -20 -10 0 10 20 30

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

CUMULATIVE ABNORMAL RETURNS FOR QATAR


DAYS

CAR

-30 -20 -10 0 10 20 30

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

CUMULATIVE ABNORMAL RETURNS FOR SMITHS


DAYS

CAR

-30 -20 -10 0 10 20 30

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

CUMULATIVE ABNORMAL RETURNS FOR GREENE


DAYS

CAR

-30 -20 -10 0 10 20 30

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

CUMULATIVE ABNORMAL RETURNS FOR INFRA


DAYS

CAR

-30 -20 -10 0 10 20 30

-0.05

0

0.05

0.1

0.15

0.2

CUMULATIVE ABNORMAL RETURNS FOR PREMIER


DAYS

CAR

-30 -20 -10 0 10 20 30

-2

-1.5

-1

-0.5

0

0.5

1

CUMULATIVE ABNORMAL RETURNS FOR QUINDELL


DAYS

CAR

-20

-18

-16

-14

-12

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24

0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

OVERALL (i) CUMULATIVE ABNORMAL RETURNS

CAR

DAYS

CA

R

-20

-18

-16

-14

-12

-10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 24

-0.25

-0.2

-0.15

-0.1

-0.05

0

OVERALL (ii) CUMALITIVE ABNORMAL RETURNS

CAR

DAYS

CA

R

Appendix – B Power Point Presentation of Question 1 Delivered 01/12/2015

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Econometrics Group A’s Assessment Project

JazmenBoone (20070746)Henry Doku(20044757)Lee Rock (20038860)Bas Süβ(20069935)

Question 1

Introduction

United States Netherlands

Regression analysis for two countries:

Part A: USA

The distribution of the dependent variable, GDP:

• Histogram• Descriptive Statistics• Boxplot

Descriptive Statistics

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Part A: USA

Histogram Boxplot

Part A: USA

Part A: Netherlands

The distribution of the dependent variable, GDP:• Histogram• Descriptive Statistics• Boxplot

Descriptive Statistics

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Part A: NetherlandsHistogram Boxplot

Part A: Netherlands

Part B: Independent Variables Standard Economic Theory: ൌ�� ሺ ൌ� ሻ

C: Household Consumption Expenditure

I: Foreign Direct Investment

G: Government Consumption Expenditure

NX: Net Exports

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Part B: Independent Variables Our expectations of our independent variables on GDP:

Household Consumption Expenditure

Government Consumption Expenditure

Foreign Direct Investment

Net Exports

POSITIVE

POSITIVE

POSITIVE

POSITIVE

• High observations • High R squared & Adjusted R

Squared• Model is Statistical Significant • Outliers – 2• Slopes follow expectations?• Multicollinearity?

Part C: Regression on GDP

USA

Part C: Regression on GDPUSA

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Part C: Regression on GDPNetherlands

• High observations • High R squared & Adjusted R

Squared• Model is Statistical

Significant • Outliers – 2• Slopes follow expectations?• Multicollinearity?

Part C: Regression on GDPNetherlands

Part D – AutocorrelationUSA

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Part D – AutocorrelationUSA

Part D – AutocorrelationNetherlands

Part D – AutocorrelationNetherlands

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Part D – Normality of ResidualsUSA

Part D – Normality of ResidualsUSA

JarqueBeraTest

Part D – Normality of ResidualsNetherlands

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Part D – Normality of ResidualsNetherlands

JarqueBeraTest

Part E – Specification USA

Ramsey RESET Test

Part F – Addition of Dummy Variable

if the dummy variable is equalled to one then we can expect GDP to be

3.2E+11 -2.4E+11 = 82116505677

If the dummy variable is equal to zero then we can expect GDP to be

3.2E+11

USA = 1 NETHERLANDS = 0

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Part F – Addition of Dummy Variable

Outliers? 2

Statistical Significance? P-Value = 9.37E-11 Confidence Interval = (-

3.0204E+11, -1.7E+11) T-stat = 7.4282 (7.4282 >

1.98)

Reject or Accept Null?

Part F – Interaction Effect

Purpose of Interaction Effect?

Variable Chosen?

R Square? Model Statistically

Significant? Independent Variables

Statistically Significant?Household

Consumption Expenditure

Part F – Interaction Effect

Reject or Accept the Null?

Results?1 = USA we find that GDP is 3.53021E+11

0 = Netherlands we find that GDP is negative at -2.2618E+10

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Part G – Lag VariablesUSA

Government Consumption Expenditure lagged for 2 periods


Results


Presence of Multicollinearity?

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Part G – Lag VariablesNetherlands

Results?

Part G – Lag VariablesNetherlands

Standard Format of Lagged Regression Model


Presence of Multicollinearity?

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• Purpose of Time Series?• CollinearityIssues?

Part H – Time SeriesUSA

Part H – Time Series USA

Part H – Time SeriesNetherlands

CollinearityIssues?

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Part H – Time Series Netherlands

Thank You Questions?

group a report

Documents