Data Analysis by eViews 8 - Example

Data analysis by eViews 8 [Student Name] [Course Title] [Instructor Name] [Date] The abstract The theories that guard this particular thinking are supported by several notable studies that impose on the collaborative effect of investment and consumption on the GDP. The project was to show the relevance and effectiveness of the Cobb-Douglas function of production in analysing GDP. Data was obtained from secondary sources and was tested using EViews. Acknowledgements Several individuals were of great help for the development of this study. Their contributions added significantly to the quality of the work. I would like to extent my humble gratitude Many people have contributed to the development of this research work and I would like to express my sincere and humble gratitude to them all. To start with, I must thank and acknowledge ------------- and ----------- for their advice and support. Without their help, I would not have achieved this feat. Furthermore, I am very grateful to all those who helped me shape this work. I convey my heartfelt thanks to them now. In completing this study, I’d also like to take a moment to thank my family. They have made a significant contribution by helping me in several ways. It is wonderful to have them with me. Above all, I thank the Almighty for giving me the wisdom, knowledge, and strength to complete this research and submit this thesis in its present form. Table of contents The abstract 2 Acknowledgements 3 The introduction 5 The Literature Review 5 Methodology, 7 Data 8 Results and discussion 9 Trends of GDP, Consumption and Investment in Australia 9 Descriptive statistics 9 Unit root test 10 The VAR model 13 Impulse response function 15 Conclusions 15 References 16 Appendices 17 Appendix 1: Trends of GDP, Consumption and Investment in Australia 17 APPENDIX 2: Descriptive statistics 18 Appendix 3: ln(consumption) 18 Appendix 4: log(gdp) 20 Appendix 5 : log(investment) 21 Appendix 6: Vector Autoregression Estimates 22 Appendix 7: Impulse response function 24 The introduction The climbing trends in the investment, GDP and consumption that these areas need to be focused primarily in the national fiscal and monetary policy because these areas have further opportunities for employment. However, it is unlikely that the investment trend may seriously hinder the consumers to buy the products due to economic barriers and the multiplication of costs. The Literature Review Gross Domestic Product (G.D.P) is the market value of all final goods and services that are produced within a country in a particular year. G.D.P consists of total consumption, investment, government spending and net exports within a country in a particular year (Boyes & Melvin, 2010). G.D.P is categorized as either real or nominal. Nominal GDP is a measure of a country's total output in terms of the prevailing currency value, for U.S, this is measured in U.S dollars. Nominal or unadjusted GDP focuses on changes occurring in both prices and quantities of products. Nominal GDP is determined through prevailing prices as no adjustments are made on the value of the output to reflect inflation or deflation in an economy. When either the quantity or price of goods and services in a country increases, nominal G.D.P also increases. The reverse happens when prices and quantities drop (Boyes & Melvin, 2010). Real GDP is, according to the Bureau of Economic Analysis, the output of goods and services produced by both labor and property within the United States in a particular year (BEA, 2011).Real or adjusted G.D.P. reflects an adjustment where the value goods and services produced in a country reveal price level changes due to inflation or deflation. In Real GDP, final output value is based on prices set in a particular base year. The base year in U.S is in most cases, 2005. Real GDP reflects the exact changes in quantity produced, not changes in prices (Tucker, 2010). For instance, the US GDP was recorded to be $ 2,790 billion in 1980 but in 2008, the GDP was about $14, 265 billion, reflecting a 411 per cent increase. If the GDP reported is real GDP, it implies that there has been a 411 per cent increase in quantity of output because the price evaluation is based on a fixed year, say 1980. However, if the above GDP is recorded as nominal, it is hard to detect whether the 411 per cent change is as a result of change in price or quantity of output because price has not been set to a specific year (Boyes & Melvin, 2010). Real GDP helps economists to verify the exact quantity of final goods and services produced in an economy when price effects have been eliminated (Tucker, 2010). Real GDP is essential in ascertaining the exact value of output produced within the United States. Nominal GDP on the other hand helps economists to determine the total output as is currently produced in a country without considering any changes. Nominal GDP helps economists and citizens to understand the current prevailing overall output and capability at prevailing price levels. Personal consumption expenditures, non-residential fixed investment, net exports of goods and services, and federal government consumption expenditures and gross investment are key components in measuring both real and nominal GDP. The price index records average price levels in an economy, showing how prices have changed on average, and contributes towards measurement of real and nominal GDP (BEA, 2011). Both price and production changes are included in measuring real and nominal GDP. Methodology, Vector Autoregressive Model This is mainly used for forecasting systems of interrelated time series and for analyzing the dynamic impact of random fluctuations on given factors. A combination of simultaneous equation models and univariate time series models form the vector autoregressive model are treated as a function of lagged values of all the endogenous variables in the system. That is to say, current values depend on previous values of all variables and error terms. Variables in a VAR model are taken as endogenous and no restrictions are imposed. Least square method is used for each equation with assumption of all of the components being stationary. EViews was used to analyse the data as it has inbuilt functions to handle Vector Autoregressive Model. The function can be stated as: P = bLαKβ The function can be broken down to individual functions as (i) P = (bLα) (ii) P = (K β) Finding the log of (i) above: (iii) Α log bK Assuming the value of P to be Y (linear function): P = Y The derivative of the function is: (i) ΔYt = δYt-1 + Ut This becomes a retrogression equation without constant and trend (ii) ΔYt = α + δYt-1 + Ut Adding constant to the equation (i) (iii) ΔYt = α + βT + δYt-1 + Ut Adding trend to the equation (ii) The reason for adding trend and constant is to obtain a panel data. The equation is of time series hence has a trend. The hypothesis becomes: H0: δ = 0 H0: δ ≠ 0 The assessment imperative therefore becomes: If t* is greater than ADF critical value; do not reject null hypothesis as unit root exists. If t* is less than ADF critical value; reject null hypothesis as unit root is not present. The retrogressive equation ΔYt = α + βT + δYt-1 + Ut is submitted to ADF and Wald tests using EViews program. The variables are substituted with K, L and GDP for investment and consumption respectively. Data The research on this function was based on data from one country between 1980Q1 and 2012Q4. For each period of the year, there are corresponding GDP, consumption, and investment as shown appendix 8. Results and discussion Trends of GDP, Consumption and Investment in Australia The graphs in Appendix 1, shows an increasing trend from Q4 1960 to Q4 2012 for all the three variables that is consumption, GDP and investment. Consumption trend appears to be smooth as compared to investment and GDP. There are peaks and downs on the graphs for investment and GPD. However, the investment graph has many twists than GPD. The fluctuations can also be noted which are in Q4 of 1989-1990 then 2000-2001 and years on as investment appears to increase significantly in the fourth quarter of each year except the fourth quarters of year 2008-2009. The trend where there is an increasing positive gap between consumption and investment is worrying as the future GDP always depends on investment. From this research viewpoint, the change in GDP value is critical. We see the evidence of sharp increase in GDP, declining in 2007-09 followed by a substantial increase into the present. That this decline had a triggering effect on foreclosures is evident. Descriptive statistics This summary includes the upper and lower extremes of the data set. It also includes the median and the Skewness, Kurtosis and Jarque-Bera. Sometimes the upper and lower are treated as outliers and are ignored from the data set. This summary is in Table of appendix 2. From the table it shows that consumption varied between 2.4 and 207.9 with a mean of 59.50802 and standard deviation of 59.08934. The distribution shows a strong skew because of the increased 0.914 in the recent years. The results showed that the consumption has kurtosis of 2.6796, which implies that there is a distinct peak near the mean in the histogram. The ‘goodness of fit’ test that is Jarque-Bera of 30.46940 indicates that data is not normally distributed. For GDP, it could be inferred that mean of 105.3623, median of 67.3 with stand deviation of106.3026 does not support the normal distribution of data. This distributional coefficients reveals a more pertinent non-normality in the context of the data that have larger positivity in skewness of 1.016816 and excessive kurtosis of 2.966419. The Jarque-Bera test of 36.54159 shows that data is not normally distributed. The findings suggests that GPD data sets meet the not criteria of lornormally distributed. On the other hand, investment has mean of 27.97547, median of 18.55 with standard deviation of 29.06990. The upper and lower extremes of the data set are 106.9 and 1.3 respectively. The skewness of the data is 1.1715 and excessive kurtosis of 3.332581. This shows that the data is not normally distributed. To confirm this, Jarque-Bera test was carried out and a value of 49.46866. this means Investment data does not have lognormality and is almost lognormal. Log of Consumption, GDP and investment suggest that the standard deviations are close to the mean value of the variables. The reason for using log is that it improves the findings of the statistical testing. The standard deviations are 1.421313, 1.413463 and 1.359253 on either side of the mean. Furthermore, by observing the values of the variables collected over a period of 40 years it could be concluded that the data is not normally distributed, as majority of the values does not lie within two standard deviations of the mean value. Unit root test For ln(consumption) Looking at the table in appendix 3, Augmented Dickey-Fuller test statistic t-Statistic test is -0.174229, which is greater than critical values of t-statistics at 1%, 5%, and 10%. The test critical values are -4.002786 for 1%, -3.431576 for 5% and -3.139475 for 10%. The test statistic is less negative than the critical t-statistics and hence the null hypothesis of a unit root in the first differences is rejected. This is confirmed by p- values which is 0.9932. Using the variables (LNCONS (-1), D (LNCONS (-1)), D (LNCONS (-2)) and D (LNCONS (-3))) separately, the null hypothesis that the coefficients are =0 i.e. they have no effect whatsoever on the dependent variable is not borne out by the results as the P-value in the case of LNCONS(-1), is significantly higher than the threshold value of 1%, 5% and 10%. This indicates that these factors significantly influence LNCONS.this is confirmed by their t-values where all of them are greater than -0.174229. The regression equation delivered is Yt= 0.180620 D(LNCONS(-1)) - 0.000580 LNCONS(-1) + 0.223049 D(LNCONS(-2)) + 0.270691 D(LNCONS(-3)) + 0.010188 C The result of the traditional F-Test is a significantly high 21.86 helps reject the null hypothesis that none of the variables, LNCONS (-1), D (LNCONS (-1)), D (LNCONS (-2)) and D (LNCONS (-3)) has power to explain the variations in the variable. Deploying the F-test (p-value) delivers a similar result, in that because of the significant difference (5% > 0.00000%) between the 5% hypothesis and the probable F-statistic the model has significant power to explain the changes in LNCONS. In addition, the R-Square value of 34.979% shows that there exists a good fit between the independent and the dependent variables. From the analysis above and table observation the test statistic exceeds the critical value, even at the 1% level, so that the null hypothesis of a stationary series is strongly rejected, thus confirming the result of the unit root test previously conducted on the same series. For log(gdp) The table in appendix 4 shows that Augmented Dickey-Fuller test statistic t-Statistic test is 0.565198, that is greater than critical values of 1%, 5%, and 10%. The calculated t-statistic is less than the critical t-statistics and hence the null hypothesis of a unit root in the first differences is rejected. Looking at variables LNGDP(-1) and D(LNGDP(-1)) ) separately, the null hypothesis that the coefficients are =0 i.e. they have no effect whatsoever on the dependent variable is not borne out by the results as the P-value in the case of LNGDP(-1), is significantly higher than the threshold value of 1%, 5% and 10%. This indicates that these factors significantly influence D(LNGDP). This is confirmed by their t-values where all of them are greater than 0.565198. The regression equation delivered is Yt= 0.364457 D(LNGDP(-1)) + 0.014188C The result of the traditional F-Test of 17.47985 is a significantly high thus it helps reject the null hypothesis that none of the variables has power to explain the variations in the variable. Deploying the p-value delivers a similar result, in that because of the significant difference (5% > 0.00000%) between the 5% hypothesis and the probable F-statistic the model has significant power to explain the changes in LNGDP. In addition, the R-Square value of 20.2908% shows that there exists a good fit between the independent and the dependent variables. From the analysis above and table observation the test statistic exceeds the critical value, even at the 1% level, so that the null hypothesis of a stationary series is strongly rejected, thus confirming the result of the unit root test previously conducted on the same series. For log(investment) The table appendix 5 depicts that Augmented Dickey-Fuller test statistic t-Statistic test is greater than critical values. The test critical values are -4.002569for 1%, -3.431471 for 5% and -3.139414 for 10% as opposed to -1.167770. The test statistic is less negative than the critical t-statistics and hence the null hypothesis of a unit root in the first differences is rejected. The Augmented Dickey-Fuller Test Equation question formed by the coefficients of the table is Yt= 0.048268 D(LNINVEST(-1)) + 0.234636D(LNINVEST(-2)) - 0.012369LNINVEST(-1)+ 0.022360C Using the variables separately, the null hypothesis that the coefficients are =0 i.e. they have no effect whatsoever on the dependent variable is not borne out by the results as the P-value in the case of D(LNINVEST(-1)), is significantly higher than the threshold value of 1%, 5% and 10%. This indicates that these factors significantly influence LNCONS.this is confirmed by their t-values where all of them are greater than -1.167770 From the analysis above and table observation the test statistic exceeds the critical value, even at the 1% level, so that the null hypothesis of a stationary series is strongly rejected, thus confirming the result of the unit root test previously conducted on the same series. The VAR model From appendix 6, the negative value of coefficient is perhaps opposite to the expectations one could have regarding the relationship between variables. The relationship between LNGDP and other depend variables of model have positive coefficients as well a positive t-statistics except LNGDP (-2), LNINVEST (-2) and LNCONS (-3) which have negative t-statistics. Moreover, it could also be suggested that individuals tend to plan their next period’s spending on the basis of their previous period’ income. Therefore, the regression model implemented has predicted a positive relationship. The results show only modest evidence of lead–lag interactions between the series. Since we have estimated a tri-variate VAR, three panels are displayed, with one for each dependent variable in the system. There is causality from the consumption to the GPD and from the consumption to the investment that is significant at the 5% and 1% levels respectively, but no causality in the opposite direction in the case of the GDP to consumption and no causality between the GDP–investment and the investment–GDP in either direction. It is worth also noting that the term ‘Granger causality’ is something of a misnomer since a finding of ‘causality’ does not mean that movements in one variable physically cause movements in another. The conventional VAR model assumes p as being equal to1 that matches with the predictable returns in being relative to variation in returns. Specifications involve the normal deviation [p = 0.5], which has also been relatively important statistically. The analysis revealed from the perspective of the log Likelihood Estimation that there are different kinds of such statistics. The results clearly indicated that the volatility processes are much persistent in establishing the superiority of the normal deviation models over the variation models. A consequence of such estimations relates to a time series and time phase that forecasts in advance about the volatility. In conducting tests for robustness, the unreported results reveal that there is considerable variation amongst the use of LNGDP, LNCON and LNINVEST value weighed return and the equal weighed return. The issue becomes quite risky when reliance is placed on the frequency related to the use of data. It is possible to conceive that the volatility that is ascertained by using the statistics will be extra accurate. Although in some respects such results point at the success of ascertaining simple volatility estimation from high frequency statistics, they still appear to be more complex than the volatility estimation obtained from VaR model. Impulse response function The impulse functions appendix 7 indicate that the response of LNCONS to LNGDP, LNGDP to LNGDP and LNINVEST to LNGDP is on upward trend while the response of LNCONS to LNINVEST, LNGDP to LNINVEST and LNINVEST to LNINVEST is on the downward trend. The impulse functions above indicate that the response of LNCONS to LNCONS, LNGDP to LNCONS and LNINVEST to LNCONS is show similar reason upward trend Conclusions The purpose of the project was to test the relevance of the production function with modern trends. There results show similar trend for all the variables growth that is investment, GDP also depends on investment. There is unit root that proves the function relevant to the current production trends. The main limitation of study was that data used was obtained from secondary sources. References Boyes, W, Melvin, M. (2010). Economics, Ed. 8. Florence, KY: Cengage Learning. Bureau of Economic Analysis (2014, October 02). National Income and Product Accounts. Retrieved on December 8, 2011 from http://www.bea.gov/newsreleases/national/gdp/gdpnewsrelease.htm National Economic Accounts (2011, November 22). Current-dollar and "real" GDP. Retrieved on December 8, 2011 from http://www.bea.gov/national/index.htm#gdp Tucker, I. (2010). Macroeconomics for Today, Ed.7. Florence, KY: Cengage Learning. Appendices Appendix 1: Trends of GDP, Consumption and Investment in Australia APPENDIX 2: Descriptive statistics CONSUMPTION GDP INVESTMENT LNCONS LNGDP LNINVEST  Mean  59.50802  105.3623  27.97547  3.337586  3.911759  2.611953  Median  38.55000  67.30000  18.55000  3.651814  4.209106  2.920466  Maximum  207.9000  374.6000  106.9000  5.337057  5.925859  4.671894  Minimum  2.400000  4.100000  1.300000  0.875469  1.410987  0.262364  Std. Dev.  59.08934  106.3026  29.06990  1.421313  1.413463  1.359253  Skewness  0.914701  1.016816  1.171496 -0.339902 -0.338725 -0.271285  Kurtosis  2.679600  2.966419  3.332581  1.726503  1.766298  1.788117  Jarque-Bera  30.46940  36.54159  49.46866  18.40803  17.49847  15.57353  Probability  0.000000  0.000000  0.000000  0.000101  0.000159  0.000415  Sum  12615.70  22336.80  5930.800  707.5682  829.2928  553.7339  Sum Sq. Dev.  736717.1  2384353.  178307.5  426.2474  421.5523  389.8372  Observations  212  212  212  212  212  212 Appendix 3: ln(consumption) Null Hypothesis: LNCONS has a unit root Exogenous: Constant, Linear Trend Lag Length: 3 (Automatic - based on SIC, maxlag=14) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -0.174229  0.9932 Test critical values: 1% level -4.002786 5% level -3.431576 10% level -3.139475 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNCONS) Method: Least Squares Date: 09/28/14 Time: 21:53 Sample (adjusted): 1961Q1 2012Q4 Included observations: 208 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   LNCONS(-1) -0.000580 0.003329 -0.174229 0.8619 D(LNCONS(-1)) 0.180620 0.067009 2.695461 0.0076 D(LNCONS(-2)) 0.223049 0.065321 3.414653 0.0008 D(LNCONS(-3)) 0.270691 0.065987 4.102197 0.0001 C 0.010188 0.003572 2.852441 0.0048 @TREND("1960Q1") -1.24E-05 7.87E-05 -0.157567 0.8750 R-squared 0.349785     Mean dependent var 0.021254 Adjusted R-squared 0.333691     S.D. dependent var 0.012638 S.E. of regression 0.010316     Akaike info criterion -6.281765 Sum squared resid 0.021498     Schwarz criterion -6.185490 Log likelihood 659.3035     Hannan-Quinn criter. -6.242836 F-statistic 21.73334     Durbin-Watson stat 2.079958 Prob(F-statistic) 0.000000 Appendix 4: log(gdp) Null Hypothesis: LNGDP has a unit root Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic - based on SIC, maxlag=14) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic  0.565198  0.9994 Test critical values: 1% level -4.002354 5% level -3.431368 10% level -3.139353 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNGDP) Method: Least Squares Date: 09/28/14 Time: 21:54 Sample (adjusted): 1960Q3 2012Q4 Included observations: 210 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   LNGDP(-1) 0.002349 0.004155 0.565198 0.5726 D(LNGDP(-1)) 0.364457 0.065082 5.599938 0.0000 C 0.014188 0.006426 2.207764 0.0284 @TREND("1960Q1") -9.33E-05 9.66E-05 -0.965719 0.3353 R-squared 0.202908     Mean dependent var 0.021273 Adjusted R-squared 0.191300     S.D. dependent var 0.014121 S.E. of regression 0.012699     Akaike info criterion -5.875777 Sum squared resid 0.033219     Schwarz criterion -5.812023 Log likelihood 620.9566     Hannan-Quinn criter. -5.850004 F-statistic 17.47985     Durbin-Watson stat 2.077838 Prob(F-statistic) 0.000000 Appendix 5 : log(investment) Null Hypothesis: LNINVEST has a unit root Exogenous: Constant, Linear Trend Lag Length: 2 (Automatic - based on SIC, maxlag=14) t-Statistic   Prob.* Augmented Dickey-Fuller test statistic -1.167770  0.9136 Test critical values: 1% level -4.002569 5% level -3.431471 10% level -3.139414 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNINVEST) Method: Least Squares Date: 09/28/14 Time: 21:54 Sample (adjusted): 1960Q4 2012Q4 Included observations: 209 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   LNINVEST(-1) -0.012369 0.010592 -1.167770 0.2443 D(LNINVEST(-1)) 0.048268 0.068213 0.707609 0.4800 D(LNINVEST(-2)) 0.234636 0.068179 3.441486 0.0007 C 0.022360 0.005222 4.282265 0.0000 @TREND("1960Q1") 0.000236 0.000236 1.001493 0.3178 R-squared 0.069423     Mean dependent var 0.021098 Adjusted R-squared 0.051176     S.D. dependent var 0.028512 S.E. of regression 0.027773     Akaike info criterion -4.305876 Sum squared resid 0.157353     Schwarz criterion -4.225916 Log likelihood 454.9640     Hannan-Quinn criter. -4.273548 F-statistic 3.804691     Durbin-Watson stat 1.988403 Prob(F-statistic) 0.005251 Appendix 6: Vector Autoregression Estimates  Vector Autoregression Estimates  Date: 09/28/14 Time: 21:55  Sample (adjusted): 1960Q4 2012Q4  Included observations: 209 after adjustments  Standard errors in ( ) & t-statistics in [ ] LNGDP LNINVEST LNCONS LNGDP(-1)  1.126035  0.412982  0.321086  (0.08654)  (0.19418)  (0.07182) [ 13.0119] [ 2.12677] [ 4.47080] LNGDP(-2) -0.201511 -0.634341 -0.189537  (0.11703)  (0.26261)  (0.09713) [-1.72182] [-2.41554] [-1.95146] LNGDP(-3)  0.079556  0.311617  0.058985  (0.08765)  (0.19668)  (0.07274) [ 0.90764] [ 1.58439] [ 0.81089] LNINVEST(-1)  0.103049  0.952299 -0.010915  (0.03346)  (0.07508)  (0.02777) [ 3.07965] [ 12.6833] [-0.39305] LNINVEST(-2) -0.063395  0.211905 -0.011071  (0.04393)  (0.09857)  (0.03646) [-1.44312] [ 2.14977] [-0.30366] LNINVEST(-3) -0.040615 -0.231710 -0.018698  (0.03452)  (0.07745)  (0.02865) [-1.17668] [-2.99172] [-0.65274] LNCONS(-1)  0.152341 -0.051281  0.950350  (0.09639)  (0.21630)  (0.08000) [ 1.58039] [-0.23708] [ 11.8797] LNCONS(-2)  0.136244  0.375750  0.127638  (0.12575)  (0.28216)  (0.10436) [ 1.08347] [ 1.33168] [ 1.22308] LNCONS(-3) -0.292915 -0.350626 -0.230066  (0.08306)  (0.18638)  (0.06893) [-3.52647] [-1.88124] [-3.33754] C  0.008785 -0.080777 -0.119982  (0.03675)  (0.08247)  (0.03050) [ 0.23903] [-0.97953] [-3.93387]  R-squared  0.999928  0.999608  0.999951  Adj. R-squared  0.999925  0.999590  0.999949  Sum sq. resids  0.029049  0.146263  0.020007  S.E. equation  0.012082  0.027111  0.010027  F-statistic  306811.8  56371.47  450888.1  Log likelihood  631.5164  462.6014  670.4853  Akaike AIC -5.947526 -4.331114 -6.320433  Schwarz SC -5.787605 -4.171194 -6.160513  Mean dependent  3.947089  2.645679  3.372732  S.D. dependent  1.392138  1.339198  1.400554  Determinant resid covariance (dof adj.)  7.05E-12  Determinant resid covariance  6.09E-12  Log likelihood  1808.994  Akaike information criterion -17.02387  Schwarz criterion -16.54411 Appendix 7: Impulse response function Read More