Multiple Regression Model for US GDP - Coursework Example

Multiple Regression Model for US GDP Introduction Statistical analyses have become an important part of contemporaryworld. Statistical analyses provide an understanding of various aspects. Based on specific raw data, statistical analyses can be used to make an understanding out of such data or information. There are various statistical tools, methods, and techniques that can be used on raw data in order to make sense of given raw data. Amongst the many tools and techniques is the regression analysis. Regression is a statistical tool or technique that estimates or identifies the relationship amongst specific variables. There are various forms of regression depending on the number of variables involved. A simple regression estimates relationship between two variables whereas multiple regression models are used in estimating relationships amongst more than two variables. The following is a discussion on how multiple regression models can be used to estimate the relationship between GDP, consumer, government spending, and wars. 2. Literature Research Economic analysis continues to form an essential part in the growth, development, and prosperity of various economies. Through economic analyses, nations or economies are able to obtain adequate information in respect to various economic variables. Such economic variables become very useful and significant in assisting economies to develop accurate, effective, and efficient economic policies (McEachern, 2011). One of the ways through which economic analyses have been carried out is through understanding of correlation. Indisputably, there are economic variables that are correlated. Correlations amongst economic variables provide an overview and deeper understanding to various economies and nations in coming up with effective, efficient, and attainable economic principles. There are different economic relationships that an economy can use in order to develop effective, efficient, and attainable economic principles. One such relationship is that which exist amongst the Gross Domestic Product (GDP), consumption, government spending, and war conditions. Gross Domestic Product (GDP) refers to the market value of all the final goods and services that an economy produces within a given fiscal year (McEachern, 2011). In most cases, the Gross Domestic Product (GDP) per capital is used in measuring and judging the standard of living and performance of a given economy. For instance, when an economy has a higher Gross Domestic Product (GDP) then it would be concluded that there is a high standard of living. On the other hand, lower standards of living are associated with low values of Gross Domestic Product (GDP). There is a relationship between the Gross Domestic Product (GDP) and the national accounts of every economy; hence making the subject a macroeconomic variable (McEachern, 2011). Consequently, a deeper understanding of the factors associated with Gross Domestic Product (GDP) will definitely assist an organization in developing accurate macroeconomic principles. Given the various ways through which Gross Domestic Product (GDP) is measured in every economy, various factors can be deduced to be affecting the macroeconomic variable. Gross Domestic Product (GDP) is determined through production, income, and expenditure approaches (McEachern, 2011). Amongst these three approaches, majority of the global economies employ the product approach in order to determine the Gross Domestic Product (GDP). The product approach defines the Gross Domestic Product (GDP) as the sum of all the inputs that are employed by every individual throughout the economy in order to produce goods and services (McEachern, 2011). As a result, GDP is the sum of the consumption, investment, net exports, and government spending as represented by the following formula. Various studies have indicated that there is a positive correlation between the GDP and the consumption, investments, net exports, and government spending. A positive correlation means that as the consumption increases so does the GPD (Madrick, 2008). On the other perspective, an increase in investment, government spending, and net exports will definitely cause an increase in the GDP. Nonetheless, besides the aforementioned factors, there are external factor that would affect the GDP through its components (Higgs, 2006). For instance, political instability caused by wars may affect the GDP through its components. Other external factors include natural calamities such as droughts, hurricanes, floods, lightning, and storms. These factors may affect the components of the GDP hence affecting the overall GDP. During wars, the government spends a lot in purchasing military equipments for protection. As a result, the GDP is likely to increase on the basis of the government spending. Wars create a political instability within a given economy (Blattman & Miguel, 2009). With such political instability, investments are unlikely and citizens are likely to buy huge amount of goods or products in order to hold for the purposes of sustainability. However, it is important to note that in most cases when war erupts, many citizens lose their personal property hence the need to work hard and acquire the same (Madrick, 2008). It has been established that wars within economies tend to cause serious economic problems thus affecting the components of the GDP. In order to establish the relationship between GDP, consumption, government spending and wars with respect to multiple regression model. In this multiple regression model, the dependent variable is GDP, which is determined by the independent variables of consumption, government spending, and wars (a dummy variable; 0 for no war and 1 for warring conditions). Table 1: US Data on the GDP and its Components US GDP (Billions of $) Year GDP (Y) Consumption (C) Investment (I) Net Exports (X-M) Govt Spending (G) 1972 1,237.9 770.2 207.6 -3.4 263.4 1973 1,382.3 852.0 244.5 4.1 281.7 1974 1,499.5 932.9 249.4 -0.8 317.9 1975 1,637.7 1,033.8 230.2 16.0 357.7 1976 1,824.6 1,151.3 292.0 -1.6 383.0 1977 2,030.1 1,277.8 361.3 -23.1 414.1 1978 2,293.8 1,427.6 438.0 -25.4 453.6 1979 2,562.2 1,591.2 492.9 -22.5 500.7 1980 2,788.1 1,755.8 479.3 -13.1 566.1 1981 3,126.8 1,939.5 572.4 -12.5 627.5 1982 3,253.2 2,075.5 517.2 -20.0 680.4 1983 3,534.6 2,288.6 564.3 -51.7 733.4 1984 3,930.9 2,501.1 735.6 -102.7 796.9 1985 4,217.5 2,717.6 736.2 -115.2 878.9 1986 4,460.1 2,896.7 746.5 -132.5 949.3 1987 4,736.4 3,097.0 785.0 -145.0 999.4 1988 5,100.4 3,350.1 821.6 -110.1 1,038.9 1989 5,482.1 3,594.5 874.9 -87.9 1,100.6 1990 5,800.5 3,835.5 861.0 -77.6 1,181.7 1991 5,992.1 3,980.1 802.9 -27.0 1,236.1 1992 6,342.3 4,236.9 864.8 -32.8 1,273.5 1993 6,667.4 4,483.6 953.3 -64.4 1,294.8 1994 7,085.2 4,750.8 1,097.3 -92.7 1,329.8 1995 7,414.7 4,987.3 1,144.0 -90.7 1,374.0 1996 7,838.5 5,273.6 1,240.2 -96.3 1,421.0 1997 8,332.4 5,570.6 1,388.7 -101.4 1,474.4 1998 8,793.5 5,918.5 1,510.8 -161.8 1,526.1 1999 9,353.5 6,342.8 1,641.5 -262.1 1,631.3 2000 9,951.5 6,830.4 1,772.2 -382.1 1,731.0 2001 10,286.2 7,148.8 1,661.9 -371.0 1,846.4 2002 10,642.3 7,439.2 1,647.0 -427.2 1,983.3 2003 11,142.2 7,804.1 1,729.7 -504.1 2,112.6 2004 11,853.3 8,270.6 1,968.6 -618.7 2,232.8 2005 12,623.0 8,803.5 2,172.3 -722.7 2,369.9 2006 13,377.2 9,301.0 2,327.1 -769.3 2,518.4 2007 14,028.7 9,772.3 2,295.2 -713.1 2,674.2 2008 14,291.5 10,035.5 2,087.6 -709.7 2,878.1 2009 13,973.7 9,845.9 1,549.3 -388.7 2,967.2 2010 14,498.9 10,215.7 1,737.3 -511.6 3,057.5 2011 15,075.7 10,729.0 1,854.9 -568.1 3,059.8 2012 15,681.5 11,120.9 2,058.6 -560.8 3,062.9 3. Discuss your primary independent variable. The independent variables in this research are consumption, government expenditure, and war. Each of the independent variable under analysis in this research is important. However, there is a primary independent variable that is considered to be of utmost importance especially in as far as the GDP of the United States of America is concerned (Madrick, 2008). The most important variable in this analysis is war given that it is an external factor from the components of GDP (Higgs, 2006). The components of GDP are consumption, government spending, investment, and net exports (Imai & Weinstein, 2000). Therefore, war affects the GDP but from an external point of view. War affects the GDP on the basis of its components. It is for the reasons that war affects the GDP through its components that make it an important independent variable and of significant interest. Imai and Weinstein (2000) have indicated that wars especially civil wars have negative impact on economic growth. In respect to domestic investment, an economy is described as one that is growing given an increase in the capital stock. Change within the capital stock arises from investments and depreciations (Blattman & Miguel, 2009). However, civil and other forms of war affect the capital stock through reducing the existing capital stock. During wars, an economy’s infrastructural investments such as residential buildings, ports, factories, roads, and communication investments amongst others are usually targeted and destroyed hence reducing the capital stock (Madrick, 2008). In this perspective, civil war would be increasing the rate of depreciation whilst causing a barrier to investment. For an economic growth the depreciation rate should be lower than the investment (Blattman & Miguel, 2009). Therefore, wars will on this basis cause a decrease in economic growth as seen within the Gross Domestic Product. On a different perspective, wars cause a reduction within the domestic investments. Indisputably, it can be argued that war causes negative impact on the domestic economy through reduction of gross domestic investment (Blattman & Miguel, 2009). Domestic investment in this case refers to both public and private investments. Based on the formula of the GDP, it is evident that investment as a component is negatively affected by wars (Imai & Weinstein, 2000). Consequently, there is enough evidence to confirm that wars affect GDP through negatively affecting the domestic investments (Imai & Weinstein, 2000). It is also important to note that wars negatively affect the domestic economy through negative impact on private domestic investment, which also forms part of the GDP. For the purposes of sustainable economic growth there is need for stable macroeconomic frameworks. Wars therefore are likely to cause unstable economic growth due to the fact that wars cause political instability (Madrick, 2008). Political economy models are good ways of describing how wars negatively affect the gross domestic product through its components. In the event that an economy experiences war, the political environment would be unfavorable thus preventing the government to carry out its mandate and activities towards sustainable economic growth and prosperity (Higgs, 2006). Therefore, governments that experience political instability always end up having increased or high deficits (Imai & Weinstein, 2000). Such deficits are likely to influence the gross domestic product through its components such as consumption, government spending, and investments. Nevertheless, there are circumstances where wars may affect the GDP in a positive way through increasing its components. For instance, in the event of wars, the government spending towards purchase of military equipment will increase thereby increasing the GDP (Madrick, 2008). In this perspective, it is clear that even though wars largely affect GDP negatively, there are cases where existence of wars may cause an increase in GDP. From the above theoretical review, it is evident that war as a factor affecting gross domestic product through its components is inevitable (Blattman & Miguel, 2009). As a result, war is an external factor that affects GDP. This makes it interesting to analyze and study the impact of war on GDP. It is therefore difficult to establish whether there correlation between GDP and wars is negative or positive. It is on the basis of the fact that it is difficult to understand whether the correlation between the GDP and wars is negative or positive that prompts into conducting multiple regressions. Hence, a multiple regression model will be used in order to ascertain whether the relationship between GDP and wars is negative or positive besides identifying the strength of such a relationship. This forms the basis of the analysis or discussion provided below. 4. General Form of Your Model GDP is composed of consumption, investment, government spending, and net exports as internal factors or components. However, there are external factors that affect the GDP of an economy such as USA. In this analysis, the external factor taken into consideration is war. Therefore, the general form of the model in respect to inclusion of the three independent variables of consumption, government spending, and wars will be as follows: Y = a + bX1 + cX2 + dX3 + e Y = the dependent variable, in this case GDP X1 = Consumption independent variable, controlling for X2, X3 X2 = Government spending independent variable 2, controlling for X1, X3 X3 =War independent variable 3, controlling for X1, X2 e = random error a, b, c, and d are constants 5. Definition of Variables The variables are GDP represented by Y, consumption that is represented by X1, (measured in billions of dollars) government spending represented by X2 (measured in billions of dollars), and war represented by X3. The dependent variable entirely depends on the independent variables, that is, the change in GDP relies significantly on the consumption, government spending, and war, which happens to be an external component in the determination of the GDP. In this basis, it is expected that consumption and government spending are likely to have positive correlation with the dependent variable whereas it is expected that the dummy independent variable is likely to affect the GDP negatively. From the general formula of GDP, consumption and government spending has positive correlation with the GDP since their increase will enhance an increase in GDP. The war independent variable will have the reverse role. The following is a scatter diagram between the dependent variable Y and the two independent variables, X1 and X2 represented by C and G respectively. The third independent variable is still to be estimated hence not represented in the scatter diagram. Figure 1: Scatter Diagram for the GDP, Consumption, and Government Spending The scatter diagram above is obtained from the following data: Table 2: Used Data in Developing Scatter Diagram Year GDP (Y) Consumption (C) Government Spending (G) 1972 1,237.9 770.2 263.4 1973 1,382.3 852.0 281.7 1974 1,499.5 932.9 317.9 1975 1,637.7 1,033.8 357.7 1976 1,824.6 1,151.3 383.0 1977 2,030.1 1,277.8 414.1 1978 2,293.8 1,427.6 453.6 1979 2,562.2 1,591.2 500.7 1980 2,788.1 1,755.8 566.1 1981 3,126.8 1,939.5 627.5 1982 3,253.2 2,075.5 680.4 1983 3,534.6 2,288.6 733.4 1984 3,930.9 2,501.1 796.9 1985 4,217.5 2,717.6 878.9 1986 4,460.1 2,896.7 949.3 1987 4,736.4 3,097.0 999.4 1988 5,100.4 3,350.1 1,038.9 1989 5,482.1 3,594.5 1,100.6 1990 5,800.5 3,835.5 1,181.7 1991 5,992.1 3,980.1 1,236.1 1992 6,342.3 4,236.9 1,273.5 1993 6,667.4 4,483.6 1,294.8 1994 7,085.2 4,750.8 1,329.8 1995 7,414.7 4,987.3 1,374.0 1996 7,838.5 5,273.6 1,421.0 1997 8,332.4 5,570.6 1,474.4 1998 8,793.5 5,918.5 1,526.1 1999 9,353.5 6,342.8 1,631.3 2000 9,951.5 6,830.4 1,731.0 2001 10,286.2 7,148.8 1,846.4 2002 10,642.3 7,439.2 1,983.3 2003 11,142.2 7,804.1 2,112.6 2004 11,853.3 8,270.6 2,232.8 2005 12,623.0 8,803.5 2,369.9 2006 13,377.2 9,301.0 2,518.4 2007 14,028.7 9,772.3 2,674.2 2008 14,291.5 10,035.5 2,878.1 2009 13,973.7 9,845.9 2,967.2 2010 14,498.9 10,215.7 3,057.5 2011 15,075.7 10,729.0 3,059.8 2012 15,681.5 11,120.9 3,062.9 6. Data Description The above table (Table 2) represents the data that will be used in conducting the multiple regression analysis. Besides the above table, Table 3 provides the war timeline in the United States of America. The data was obtained from 1972 to 2012, which represents approximately 40 years. Whereas Table 2 was obtained from National Income and Products Accounts Tables (http://www.bea.gov/iTable/iTable.cfm?reqid=9&step=1&acrdn=2#reqid=9&step=3&isuri=1&910=X&911=0&903=5&904=1972&905=1000&906=A), Table 3 is obtained from The American History Timeline (http://americanhistory.about.com/library/timelines/bltimelineuswars.htm). Table 4 is a combination of Table 2 and Table 3 in order to find the accurate data to be used in estimating the impact of war on the GDP through a multiple regression model. It is important to note YES indicates a year when there was war while a NO indicates when there was no war. (War is a dummy variable). Table 3: American War Timeline Period War Participants 1960-1975 Vietnam War United States and South Vietnam vs. North Vietnam 1961 Bay of Pigs Invasion United States vs. Cuba 1983 Grenada United States Intervention 1989 US Invasion of Panama United States vs. Panama 1990-1991 Persian Gulf War United States and Coalition Forces vs. Iraq 1995-1996 Intervention in Bosnia and Herzegovina United States as part of NATO acted peacekeepers in former Yugoslavia 2001 Invasion of Afghanistan United States and Coalition Forces vs. the Taliban regime in Afghanistan to fight terrorism. 2003 Invasion of Iraq United States and Coalition Forces vs. Iraq Besides, it should be noted that there are no limitations in respect to the data. Since a multiple regression model will be used on the basis of Excel functions for the purposes of calculations, the raw data presented in Table 4 will be used. Table 4: All Dependent and all the Independent Variables The following table represents the raw data for estimating relationship of GDP and war in US. Year GDP (Y) Consumption (X1) Government Spending (X2) War (X3 = YES or NO) 1972 1,237.9 770.2 263.4 YES 1973 1,382.3 852.0 281.7 YES 1974 1,499.5 932.9 317.9 YES 1975 1,637.7 1,033.8 357.7 NO 1976 1,824.6 1,151.3 383.0 NO 1977 2,030.1 1,277.8 414.1 NO 1978 2,293.8 1,427.6 453.6 NO 1979 2,562.2 1,591.2 500.7 NO 1980 2,788.1 1,755.8 566.1 NO 1981 3,126.8 1,939.5 627.5 NO 1982 3,253.2 2,075.5 680.4 NO 1983 3,534.6 2,288.6 733.4 YES 1984 3,930.9 2,501.1 796.9 NO 1985 4,217.5 2,717.6 878.9 NO 1986 4,460.1 2,896.7 949.3 NO 1987 4,736.4 3,097.0 999.4 NO 1988 5,100.4 3,350.1 1,038.9 NO 1989 5,482.1 3,594.5 1,100.6 YES 1990 5,800.5 3,835.5 1,181.7 YES 1991 5,992.1 3,980.1 1,236.1 YES 1992 6,342.3 4,236.9 1,273.5 NO 1993 6,667.4 4,483.6 1,294.8 NO 1994 7,085.2 4,750.8 1,329.8 NO 1995 7,414.7 4,987.3 1,374.0 YES 1996 7,838.5 5,273.6 1,421.0 YES 1997 8,332.4 5,570.6 1,474.4 NO 1998 8,793.5 5,918.5 1,526.1 NO 1999 9,353.5 6,342.8 1,631.3 NO 2000 9,951.5 6,830.4 1,731.0 NO 2001 10,286.2 7,148.8 1,846.4 YES 2002 10,642.3 7,439.2 1,983.3 NO 2003 11,142.2 7,804.1 2,112.6 YES 2004 11,853.3 8,270.6 2,232.8 NO 2005 12,623.0 8,803.5 2,369.9 NO 2006 13,377.2 9,301.0 2,518.4 NO 2007 14,028.7 9,772.3 2,674.2 NO 2008 14,291.5 10,035.5 2,878.1 NO 2009 13,973.7 9,845.9 2,967.2 NO 2010 14,498.9 10,215.7 3,057.5 NO 2011 15,075.7 10,729.0 3,059.8 NO 2012 15,681.5 11,120.9 3,062.9 NO 7. Presentation and Interpretation of Results An estimation of the multiple regression model (Obtained through Excel) is provided below:   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 426.0348 38.26675 11.13329 2.27E-13 348.499 503.5706 348.499 503.5706 X1 1.49709 0.051526 29.05514 4.48E-27 1.392689 1.601492 1.392689 1.601492 X2 -0.39792 0.19168 -2.07594 0.044903 -0.7863 -0.00953 -0.7863 -0.00953 X3 -93.552 44.27816 -2.11282 0.041424 -183.268 -3.83591 -183.268 -3.83591 Given that Y = a + bX1 + cX2 + dX3 + e, The multiple regression model obtained through the Excel indicates that the coefficient of X1 is positive whereas the coefficients of X2 and X3 are negatives. This means that there is a positive correlation between the GDP and the consumption whereas there is a negative correlation between the GDP and the government spending as well as the war situation within the economy. Therefore, the predicted equation will be as follows: Y = 426.0348 + 1.4971X1 – 0.3979X2 – 93.552X3 Figure 2: Regression Output 8. Identify and interpret the adjusted R2. Table 5: Summary Output of the Multiple Regression Model SUMMARY OUTPUT Regression Statistics Multiple R 0.999741798 R Square 0.999483663 Adjusted R Square 0.999441798 Standard Error 106.7573859 Observations 41 The adjusted R2 = 0.9994 What does the value of the adjusted R2 reveal about your model? If the adjusted R2 is low, how has the choice of independent variables created this result? 9. Identify and Interpret the F-test The null hypothesis is that there is a negative correlation between GDP and war conditions. From the F-test and the p-value approach, the null hypothesis is accepted. This means that at a significant level of 5%, it is true that the correlation between GDP and war. Table 6: ANOVA Table ANOVA   df SS MS F Significance F Regression 3 8.16E+08 2.72E+08 23873.87 7.65E-61 Residual 37 421694.2 11397.14 Total 40 8.17E+08         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 426.0348 38.26675 11.13329 2.27E-13 348.499 503.5706 348.499 503.5706 X1 1.49709 0.051526 29.05514 4.48E-27 1.392689 1.601492 1.392689 1.601492 X2 -0.39792 0.19168 -2.07594 0.044903 -0.7863 -0.00953 -0.7863 -0.00953 X3 -93.552 44.27816 -2.11282 0.041424 -183.268 -3.83591 -183.268 -3.83591 10. Identify and interpret the t-tests for each of the coefficients at a .05 level of significance (one separate paragraph for each variable, in numerical order) The first variable, X1 has a positive sign indicating a positive relationship with the dependent variable. Theoretically, consumption and GDP are positively correlated. Therefore, the sign of the coefficient of the variable is as expected. From the coefficients, 1.49709 it means that the GDP is one and half times the consumption. From the p-value approach, the null hypothesis for the t-test accepted that for this independent variable, there is a positive correlation with the dependent variable, GDP. The second variable, X2 has a negative sign indicating a negative relationship with the dependent variable. Theoretically, government spending and GDP are positively correlated. However, the sign indicates the otherwise. From the coefficients, -0.39792 it means that the GDP is -0.4 times the government spending. From the p-value approach, the null hypothesis based on the t-test is rejected that for this independent variable, there is a negative correlation with the dependent variable, GDP. The third variable, X1 has a negative sign indicating a positive relationship with the dependent variable. Theoretically, war and GDP are negatively correlated. Therefore, the sign of the coefficient of the variable is as expected. From the coefficients, -93.552 it means that the GDP is -93.552 times the consumption. From the p-value approach, the null hypothesis for the t-test accepted that for this independent variable, there is a negative correlation with the dependent variable, GDP. References Blattman, C., & Miguel, E. (2009). Civil war (No. w14801). National Bureau of Economic Research. Higgs, R. (2006). Depression, War, and Cold War: Studies in Political Economy. Oxford University Press. New York Imai, K. & Weinstein, J. (2000). “Measuring the economic impact of civil war.” CID Working Paper No. 51. Retrieved on March 6, 2013 from http://imai.princeton.edu/research/files/cid.pdf Madrick, J. (2008). Is War Good for the Economy? Retrieved on March 6, 2013 from http://www.huffingtonpost.com/jeff-madrick/is-war-good-for-the-econo_b_84886.html McEachern, W. A. (2011). Economics: A contemporary introduction. Mason, OH: Southern-Western Cengage Publishers. Read More