# Effects of FDI, Interest rates and Government Expenditure on GDP

ECONOMIC ANALYSIS

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Tableof Contents

Introduction 2

Data Description 2

Graphical plots of the Variables 2

Regression Analysis 2

Relation between the dependent and the independent variables 3

Hypothesis tests 4

Redundant variables test 4

Omitted Variable test 5

Ramsey’s test 6

Durbin-Watson d Test 6

Breusch-Godfrey (BG) test or The LM test 7

Application of Analysis 7

References 8

Introduction

Economic analysis features a category in the branch of economics thatrelates theory to practices using various factors or elements thatare considered to have an impact in the performance of the economicvariables in question. Econometrics has played a major part incontributing to the economic models that assist economists andanalysts of different fields of studies to develop and device moresuperior models that can project dependable and reliable analysisresults. This paper is aimed at providing an insight of how theFederal Direct Investment (FDI), interest rates and GovernmentExpenditure affect the Gross Domestic Product of United States ofAmerica. Eviews version 8 software was used to analyze this data.

Data Description

Data was acquired from the Food and Agriculture Organization for boththe Federal Direct Investment and Government Expenditure. The dataranged from 1991 to 2013 for FDI while Government Expenditure rangedfrom 2001 to 2014 (FAO, 2017). Gross Domestic Product and Interestrates data were acquired from the US-government Spending website inquarterly record which was averaged to have an annual figure(Chantrill, 2017). These data ranged between 1991 Q1 and 2014 Q4.

Graphical Plots ofVariables

Understanding the distribution of the Variables in analysis isimportant before delving into the regression process especiallydealing with time series data. This will assist in the development ofa model in a process known as the stochastic process (Box, Jenkins,Reinsel, & Ljung, 2016).

Categoricalplot of the raw data

*Source: Eviews Analysis, 2017*

This clearly is an indication of non stationarity in the data thus wehave to apply either unit root test or other mechanism to make ourdata stationary. Using the logs of the variables may provide somestationarity too thus we can easily transform the data and use themin log form. Log transformation helps to stabilize the variancesacross time in time series data.

Regression Analysis

The regression equation to this analysis can be estimated as shownbelow. The results of this analysis are assumed to be working under*ceteris paribus *conditions.

LOG(US_GDP)= C(1) + C(2)*LOG(GOVTEX) + C(3)*LOG(US_FDI) + C(4)*LOG(US_INTRST)

Analysisregression to fit the above estimated equation were fitted asfollows,

LOG(US_GDP)= 4.02504758315 + 0.357070975123*LOG(GOVTEX) +0.00351172884367*LOG(US_FDI) + 0.0118221741081*LOG(US_INTRST)

Thisis acquired from the estimated output below

*Source: Eviews Analysis, 2017*

According to the results above, only two variables appear to behighly significant based on the P values and the t-statistics. FDIand Interest rate variables are highly insignificant and this couldbe attributed to the data manipulation since all data was acquiredfrom the internet. The R-squared value is very high which impliesthat 90.28% of the variation in log(US_GDP) can be explained by theother variables in the model. This does not necessarily imply a goodfit for the model. For these reason further more tests are alwaysapplied to verify fitness of the model as shall be discussed.

Relation Between TheDependent and The Independent Variables

In the above fitted regression equation, conclusion can be made thateach of the independent variables has a positive effect on thedependent variable but at a different rate. This is depicted by thecoefficient values of each of the independent variable in theequation. Holding all factors constant, the log(US_GDP) is expectedto have a value of 4.025 at 5% level of significance.

Government Expenditure is expected to have a positive 0.357 % effecton the GDP holding all other factors constant. This simply means thata one unit increase in the government spending will increase the GDPby 0.357% at 5% level of significance.

Federal Direct Investment and Interest rates were highlyinsignificant even at 10% level of significance. This as mentionedearlier can be as a result of inconsistency in the data acquiredhence there is need for more accurate and reliable data for betteroutput performance of the regression analysis.

Examining the residuals of this regression provides us with moreinsight on which tests to undertake using this data. The residuals ofthis regression have long periods of positive followed by negativevalues which indicates a strong visual evidence of serialcorrelation.

Actual, Fitted and Residual Graph

*Source: Eviews Analysis, 2017*

Hypothesis TestsRedundant VariablesTest

Redundant variable test is used to determine statistical significanceof a subset of included variables in a model equation.

*Source: Eviews Analysis, 2017*

*H*_{0}:LOG(US_FDI)= LOG(US_INTRST)=0

Test statistics of the redundant variables are indicated by theF-Statistics (1.3643) and the Log likelihood ratio (3.4424). Thedecision rule dictates that we reject null hypothesis if computedF-Statistics>Tabulated critical values (F_{(2,9)}=4.2565).We therefore accept the null hypothesis since 1.3643<4.2565 at 5%level of significance.

Conclusionon the test

Thereis no enough evidence in the data used to dispute the claim thatLOG(US_FDI)= LOG(US_INTRST)=0

Omitted Variable Test

This test enables one to add new variables to an equation andevaluate for the significant contribution of the new variables in theregression.

*Source: Eviews Analysis, 2017*

*H*_{0}:LOG(US_FDI)^2 and LOG(US_INTRST)^2 ≠ jointly significant.

Omittedtest statistics are F statistics (3.2057) and the log likelihoodratio (8.4526).

Decision rule: Reject null hypothesis if computed F-Statistics>Critical value (F_{(2,7)}=4.7374). We therefore acceptthe null hypothesis since 3.2057<4.7374 at 5% level ofsignificance and conclude that there is no enough evidence in thedata to dispute that the two series additional series do not belongto the equation.

Ramsey’s Test

This is a regression specification error test also commonly known asthe RESET test.

*H*_{0}:LOG(US_FDI)^2= LOG(US_INTRST)^2=0

Teststatistics results are T-statistics (2.4059), F statistics (5.7885)and Log likelihood ratio (7.0771) which are all significant accordingto the probability values.

The decision rule states that we reject null hypothesis if computedvalues exceed the critical values. For F statistics critical valuesare (F_{(1,8)}=5.3177), T statistics T_{0.05(8)}=2.306and Log likehood ratio is 7.0771. The F-statistics accepts the nullhypothess while on the contrary, with the T-statistics rejects it.Thus we base our decision on the Loglikelihood which is a smallfigure hence the data does not fit the model well.

*Source: Eviews Analysis, 2017*

Durbin-Watson d Test

This is a test for first-order serial correlation. It measures thelinear association between adjacent residuals from the regressionmodel. Using the eviews version 7 onwards the test is integrated inother serial correlation test the is presented in the lower teststatistics of the Langrange Mutiplier tests or the BG.

*H*_{0}:No serial correlation

Teststatistics results as shown in the BG first-order test results below.Durbin Watson stats= 1.6816.

As a rule of thumb, with 50 or more observations and only a fewindependent variables, a DW statistics below 1.5 is a strongindication of positive first order serial correlation (Montgomery,Peck, & Vining, 2012). Absence of serial correlation always givesa DW statistics of 2 and any measure below that indicates presence ofpostive correlation (Wisniewsk, 2016). We can therefore reject thenull hypothesis since 1.6816<2 at 5% level of significance andconclude that the data residuals exhibit a positive serialcorrelation.

Breusch-Godfrey (BG)Test or The LM Test

This test is also used to determine the presence of serialcorrelation in the residuals.

*H*_{0}:No serial correlation

Teststatistics results are F-Statistics (10.1264), and LM test statistics(7.2625)

The decision rule is also based on the comparisson betweeen thecomputed F-statistic and the tabulated F-statistics. We reject thenull hypothesis if computed exceeds the critical valuesF_{(1,8)}=5.3177. We can therefore reject the null hypothesissince 10.1264>5.3177 and conclude presence of serial correlationin the data used which is also a confirmation of the Durbin-Watsontest above.

*Source: Eviews Analysis, 2017*

Application ofAnalysis

Econometrics and economic analysis has been assimilated in almost allthe sectors globally and thereby nearly all analysts have toincorporate these skills in their work if they are to present aprofessional and relevant work in their career.

As a student, econometric modelling and analysis will assist in thedevelopment of a high quality standard research paper that is aimedat achieving and delivering the best in the society bothacademically, career wise and even in the simplified basic economicactivities since the key player in any economic is the basic unit(household). The above mentioned statistical analysis will also helpin performing analysis of data collected. They will specify,linearize, stabilize and detect any presence of correlation in thedata.

References

Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M.(2016). *Time Series Analysis: Forecasting and Control.* NewJersey: John Wiley & Sons. Inc.

Chantrill, C. (2017, February 26). *Government spending details*.Retrieved from US government Spending:http://www.usgovernmentdebt.us/year2014_0.

FAO. (2017, February 26). *FAOSTAT*. Retrieved from Food andAgricultural Organization of the United Nations:http://www.fao.org/faostat/en/#data/PE

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012).*Introduction to Linear Regression Analysis.* New Jersey: JohnWiley & Sons. Inc.

Wisniewsk, J. W. (2016). *Microeconometrics in Business Management.*West Sussex, United Kingdom: John Wiley & Sons, Ltd.