Econometrics - Cross Section and Experimental Data Analysis - Essay Example

ECONOMETRICS PART Question a) From table the correlation coefficient between health status and years of education is 0.33. When the correlation coefficient in absolute values is between 0.1 and 0.5, there is a weak correlation between the variables and when the values are between 0.5 and 0.9 there is a strong correlation. In this case, there is a weak positive correlation between the two variables. Since the coefficient is positive, there is a positive linear relationship between health status and years of education. When years in education increase, there is an improvement in health status of the individual. Question 1 (b) i. Number of doctor visits and gender The results of the regression are demonstrated in table 2. The coefficient of male is 0.011. This indicates that the number of doctor visits increases if the individual is male by 0.011. The value is not statistically significant at 10, 5 and 1 percent level of significance since the probability is greater than the critical values in each of the alpha value. ii. Mean number of private medical expenditure and gender The regression results are illustrated in the table 3 in the appendix. The male coefficient is 14.89. This coefficient is positive which indicates that males spend 14.89 more on private medical services than the females. The value is statistically significant at the 1 percent level of significance since the probability value is very low. This means that there statistical significance that the level of private expenditure on medical services is highly influenced by gender. Question 1 (c) The coefficient of number of visits to the doctor in the past years is -0.562. This has been indicated in table 4 below. The coefficient is negative which indicates that there are an inverse relation between the number of visits to the doctor in the past years and health status. When the endogenous variable increases by one unit, the health status will decline by 0.562 units. The coefficient is statistically significant at 1 per cent level of significance indicating that the number of visits to the doctor in the past years is a good indicator of changes in health status. A casual interpretation exists when there is a cause and effect reaction on the regression results (Wayne A. Woodward, 2011). This means that there is a two way impact of the variables. In this case, no casual interpretation exists. This is because the number of doctor visits in the past affects the present health status negatively and on the other hand, health status in the present cannot affect the number of doctor visits in the past. Question 2 (a) The regression equation employed in this case is; The results are as demonstrated in table 5. Age: The coefficient of age is -0.897 which indicates that there is a negative relation between age and health status. As an individual advances in age, the health status declines. Male: The coefficient of the male is -3.987. This means that when an individual is male, the health status will decline by 3.987. Therefore, females have a better health status compared to their counterparts the males. Education: the coefficient of education is 2.487. There exists a positive relationship between years spent in acquiring education and health status. When an individual spent more years in acquiring education, their health status will improve since they have more knowledge on health and hence they can effectively take care of their health status. Hence the regression equation becomes; Question 2 (b) i. Health status when education is increased from 8 years to 11 years. Health status will improve due to an increase in education level. When individuals acquire more knowledge and education, they can be in a position to take care of their health and hence an improvement of health. This is also the case when education increases from 12 years to 15 years. Question 3 (a) In this question the regression model employed is given by; After conducting the regression the following results were obtained which are demonstrated in table 5. The marginal effect measures the impact of the independent variable on the dependent variable (Agung, 2011). It measures the probability that the dependent variable will change as a result of a change in the endogenous variable. The formula for calculating marginal effect is given by; Since we cannot interpret the coefficient of, alone as measuring the change in health with respect to age,, needs to be considered also. Therefore, the need to calculate the turning point of age. This can be calculated with the following formula (SHARP, 2010); In the case of age, the turning point will be; Question 3 (b) So as to develop a model that varies across gender, I will include the gender variable “male” into the above regression equation. The equation then becomes; From the results in table 7 it is evident that the parameters vary across gender. This is attributed by the fact that the coefficient of the male is -3.939. The value is also statistically significant at one percent significance level. When an individual is male, there will be a decline in the health status of 3.939 from that of the female health status. This shows that males are less healthy than the females. Question 3 (c) So as to determine the effect of gender on income, a regression on gender and income will be conducted and the results are tabulated in table 8 in appendix. From the results it is evident that income significantly differs across genders. Males receive 554.33 more income than females. Question 4 (a) The regression equation to be used in this model is; After conducting the regression analysis, the following results were obtained which are demonstrated in table 8 in the appendix. The coefficient of log income is 21.04. It indicates that a 100 percent change in income causes a 21.041 increases or improvement in health status. The coefficient of log income is statistically significant at the 1 percent level of significance. Question 4 (b) After extending the model by adding an additional control for blue-collar work status, the regression model becomes; The regression model after conducting a regression analysis will become as illustrated in table 9; An individual who is employed in a blue-collar job is 5.34 less healthier than an individual who is employed in the white collar market. Therefore, when an individual moves from blue collar market in white collar market, their health status improves by 5.34 units. Question 4 (c) In this case a regression will be conducted on the blue collar worker against gender of the individual. The results obtained are indicated in table 10 in the appendix where the coefficient of the male is -0.07. This value indicates males are less likely to work in blue collar jobs than the females. Question 4 (d) So as to determine whether the effect of being a blue collar worker differs with the gender of the individual, a regression is conducted of blue collar worker against gender. The results obtained are indicated in the table 11 in the appendix. The coefficient of male is -0.067 which is statistically significant at the one percent level of significance. This value indicates that males have a lower probability of being a blue collar employer than the females by 0.067. This value will indeed influence the health status of the male worker. Question 5 (a) After conducting the regression the results obtained are indicated in table 12 in the appendix. The specification test conducted in this case was white’s test of heteroskedasticity. The results indicate that the observed r-squared is greater that the critical value at 5 per cent level of significance and hence there is no heteroskedasticity in this model. Question 5 (b) After running the regression analysis the results in table 13 in the appendix were obtained. The specification test conducted in this case is the Breusch Godfrey serial correlation LM test. The test indicates that the probability value of the observed R squared is higher than the critical test statistic at 5 per cent significance level. Since the probability value is high, there is no presence of serial correlation in the residuals. Question 5 (c) The heteroskedasticity test to be employed in this case is the White test (Uma Joshi, 2002). The results obtained are indicated in table 14 in the appendix. The probability value of the observed R-squared is greater than the critical test statistic at 5 percent significance level. Hence we reject the null hypothesis that there is no heteroskedasticity in this model. Question 5 (d) There is a casual interpretation of the variable log income. This is because; the 100 percent change in log income only causes a 19.9 unit change in the health status. On the other hand, when health status changes, they will have an impact on the individual’s income and as a result of the log income. Hence, a causal relationship exists between health status and log income. Question 5 (e) So as to determine whether lotwins are a good instrument for measuring the income of the individual, a regression of income against lotwins will be conducted. From the regression results demonstrated in table 15in the appendix the coefficient of lotwins is 1 which indicates that when lotwins increase by 1 unit, the income of the individual will also increase by one unit. The coefficient is statistically significant at the 1 percent level of significance. Therefore it is a good instrument of explaining changes in the individual’s income. Question 5 (f) Like the above case, so as to determine the how parinc affects the income of an individual, a regression of income on parinc is conducted. The results are as indicated in table 16 below. The coefficient of parinc is -0.0005 which indicates that the income earned by parents in the previous year is inversely related to income today. The value is not statistically significant since the probability value is very large. PART 2 Question one (a) From the figure 1 in the appendix, the log GDP of UK has been considerably higher over the estimated period. This has been attributed by the fact that economic growth has increased since the 1979 because of the policies set in place by Margaret Thatcher concerning privation of the public sector. However, it declined considerably in the 2000s due to the economic crisis experienced. Just like GDP, consumption also increased considerably in the 1980s and 1990s since the economy was growing and people had sufficient income for consumption. It also declined in the early 2000s due to the economic crisis experienced. This is demonstrated in the figure 2 in the appendix. Question one (b) According to (Sørensen, 1973), the Dickey Fuller unit root test in this question will be based on the following regression firms; With constant; With constant and trend; The hypothesis to be tested in this case is The decision rule will be; If calculate t-static > ADF critical value; do not reject the null hypothesis which means that the unit root exists. If calculated t-statistic < ADF critical value; reject the null hypothesis, that is, unit root does not exist. It is important to determine the lag length for the implementation of the ADF test. This is because; If is too large then the significance of the test will suffer. If is too small then the remaining serial correlation in the errors will bias the test (Wayne A. Woodward, 2011). In this case, so as to determine the optimal lag length, the following procedure was followed; An upper bound for is set. An estimated ADF test regression is then conducted with If the absolute value of the t-static for testing the significance of the last lagged difference is greater than 1.6 then set and performs the unit root test. Otherwise, reduce the lag length by one and repeat the process. When an augmented Dickey Fuller unit root test is conducted on the log consumption without including linear trend and constant the results obtained are indicated in table 17 in the appendix. There is no chosen critical value since the computed absolute t-statistics is larger than the absolute critical value. When an augmented Dickey Fuller unit root for log consumption with including linear trend and constant is conducted the results obtained are demonstrated in table 18. The critical value chosen in this case is at 1%, 5% and 10%. This is because; the calculated absolute t-static is less that the critical absolute t-statistics at this level of significance. Estimating the critical values of the ADF test statistics for the log gross domestic product makes the calculated absolute test static statistically significant at 1, 5 and 10 per cent critical values. This is because the calculated value is less than the tabulated critical values. This can be effectively demonstrated in the results in table 20 where no intercept and constant was included. When the ADF test is conducted with inclusion of trend and intercept as demonstrated in the table 19, there is no a chosen critical value since the resulting ADF test statistic is greater than that of all the critical values. In all the cases where an intercept and a constant were included, the calculated ADF test statistic is less than the critical values in all levels of significance. Therefore, unit root does not exist. When neither intercept nor trend is included in the model, the ADF test statistic is greater than the critical test statistic which indicates that unit root does exist in the model. Question one (c) From figure 3, the graph of first difference log of consumption is approximately constant over time. This indicates that the model is stationary over time. When a constant and a trend are included in the model and considering first difference, the resulting test statistic is greater than the critical t-static. This is illustrated in table 22. Therefore, the model is not significant. This indicates that the inclusion of the first difference of the variable makes unit root to exist. When neither intercept nor trend is included in the model, the chosen test statistic is 1, 5 and 10 percent critical values as illustrated in table 21. This is because the ADF test statistic is smaller than the stated critical values. Hence unit root does not exist. Just like the case of the log consumption, the graph of the log of GDP is also approximately constant over time which indicates that the model is stationary. When testing for the unit root with first difference and a constant and intercept is included in the model, the overall model becomes statistically significant at 1% alpha value. This is demonstrated in table 24. This is because the calculated t-statistic is less than the critical t-statistic at this alpha value. Therefore, unit root does not exist in this case. On the other hand, when neither a constant or trend is included, the results obtained are statistically significant at the 1 and 5 percent level of significance. Hence, at this critical value, unit root does not exist. This is demonstrated in table 23 below. Just like the above case the lag length was selected using the Ng and Perron method. The most appropriate model that should be employed is the one where no intercept and trend are included since the models do not exhibit unit root. Question one (d) From the above results it is evident that the unit root does not exist when intercept and trend are not included in the model whether the first difference is obtained or not. This means that the original data is statistically significant and hence should be employed in economic analysis. Question two (a) The stationary transformation of the log consumption and log GDP are as demonstrated in figure 3 and 4. Obtaining first difference makes the models to be stationary. Question two (b) The ACF and PACF graph of the log of consumption is indicated in table 25 below. The characteristic ACF and PACF patterns exhibit beginning spikes that are negative in sign. The ACF spikes gradually taper off in the correlogram. The gradual decay is not exponential since it seems to drop, level off, then drop, level off and so on. This pattern continues until the ACF spikes drop below significance. In addition, since the partial autocorrelation (PACF) function is significantly negative at time lag one and close to zero thereafter, the pattern of autocorrelation can be captured by an autoregressive of order one, that is, AR (1). Similarly, this is also the case for the sample autocorrelation function and the partial autocorrelation function of the log of gross domestic product. The PAC is also negative at time lag one and alternates in all other lag lengths. Therefore, just like in the case of the log consumption, the pattern of autocorrelation can be captured by an auto regression of order one. Question two (c) In this case, the AR (1) model is estimated as suggested in the ACF and PACF models above. So as to estimate the AR (1) and MA (1) models, a regression analysis is conducted. After estimation of the parsimonious model of the log of consumption, the regression results are given in table 27 below. The probability value of the MA model is less than the critical value of 5 percent significance level and therefore, statistically significant. After conducting the regression, diagnostic tests have been conducted to check the independence of the random shock terms. The results obtained are in table 28. The Ljung Box Q statistic for the testing Is 16.908 with a probability value of 0.596. The independence of random shocks is certainly not rejected even at 21 lags. Hence, an assumption is made that the random shock term is white noise under an AR (1) model. Therefore, AR (1) model is appropriate for the quarterly changes in log of consumption. As in the above case, the regression results obtained are illustrated in table 21 of the first difference of log GDP. The probability values of AR (1) and MA (1) are less than that of 5 percent alpha value. Hence, statistically significant. When diagnostic tests are conducted, the results are demonstrated in table 30. From the results it is evident that the shock term is not rejected even at 21 lags and hence,the random shock is white noise under AR (1) model. Question 3 (a) The regression results of the log of GDP on the log of consumption is given in Table 31. A 100 percent change in consumption causes a 100*0.49 change in GDP. That is, it causes a 49 percent increase in GDP. So as to test for the Engle-Granger co-integration approach, I first run a simple regression of the variable and then save the residuals (SHARP, 2010). The results of the regression are as indicated above. After that, I tested co-integration by checking stationarity of the saved residuals. The results obtained are indicated in table 31. From the results obtained, the calculated test statistic is larger than the critical test statistic at all levels of significance. This indicates that the Augmented Dicker Fuller test employed here rejects the null hypothesis of non stationary at all levels of significance. Hence, there is co-integration of all the alpha values included. The results, therefore, indicate that we reject the hypothesis that there is no co-integration between log of consumption and log of GDP. After the inclusion of the intercept and trend, the findings obtained are also indicated in table 31. The calculated ADF test statistic is still larger than the critical test statistics.. Hence the inclusion of trend and intercept has no impact on the co-integration between consumption and GDP. In this case there is no appropriate Engle Granger ADF test statistic since in both cases the results have indicated that there is co-integration between consumption and GDP. Question three (b) After conducting a regression analysis of log consumption on log GDP, the results demonstrated in table 32 in the appendix were obtained. The coefficient of dlogrgdp is 1.105 which indicates that a 100 percent increase in consumption causes a 110.5 percent change in GDP. After conducting a co-integration test of the two variables, the results obtained are indicated in the table 32. The ADF test statistic calculated is greater than the test statistic at all the critical value. Therefore, there is co-integration between consumption and GDP at all significance levels. Just like the above case, after the inclusion of the intercept and trend, the findings obtained are indicated in the table. The ADF test statistic is greater than the critical test statistic at all included alpha values. Hence there exists co-integration between the two variables. Just like in other case, there is no chosen critical value since the ADF test statistic are greater than the critical test statistics and hence there exists co-integration between the variables. Question 3 (c) The two models have high R-squared. This means that the variables included in each model are good predictors of the dependent variable. Therefore the variables are good indicators and hence they should be considered in economic analysis. Question 4 (a) The model in the appendix, table 33, of the error correction model, seems to be correct as the coefficient at error correction term is negative and statistically significant. The number of lags included in this model is 3 time lags that make the error term statistically significant and negative. Question 4 (b) In the case of the log GDP, the regression model in table 27 seems to be correct as the coefficient at error correction term is negative and statistically significant. The number of lag length included in this model is 4 time lags that male the error term statistically significant and negative. Question 5 A Granger causality test is a test for variables for example, X and Y which evaluates whether the past values of X are important in predicting the values of Y. The basic assumption in this analysis is that the past values of Y have been modeled. In this case, the null hypothesis is that the past values of X are not essential in predicting the values of Y. After performing the Granger causality test on the log consumption and the log GDP, the results demonstrated in the table 35 was obtained. The Granger causality test is very sensitive to the number of lags included in the regression. The optimal number of lags for this case is two. This indicates that this is the amount of lag length that is required to minimize the overall serial correlation in the errors. The F test is employed to determine whether the past value of log of GDP is jointly equal to zero. From the results obtained, we cannot reject the hypothesis that log of consumption does not Granger cause log of GDP. On the other hand, we do reject the hypothesis that log of GDP does not Granger cause log of consumption. Question 6 I would suggest the autoregressive model. This will be essential in this case since GDP and consumption often involve large amounts of data and information. Works Cited Agung, I. G. N., 2011. Cross Section and Experimental Data Analysis Using EViews. New York: John Wiley & Sons. SHARP, G. D., 2010. LAG LENGTH SELECTION FOR VECTOR ERROR CORRECTION MODELS. Rhodes: RHODES UNIVERSITY PRESS. Sørensen, A. B., 1973. Causal Analysis of Cross-sectional and Over-time Data: With Special Reference to the Study of the Occupational Achievement Process. Wisconsin: University of Wisconsin. Uma Joshi, A. P. A. M., 2002. Media Research: Cross-sectional Analysis. New Delhi: Authors Press. Wayne A. Woodward, H. L. G. A. C. E., 2011. Applied Time Series Analysis. Florida: CRC Press. APPENDIX Table 1: Correlation between health and years of education Health Education Health 1.00 0.33 Education 0.33 1.00 Table 2: regression of number of doctor visits and gender Dependent Variable: DOCVIS Method: Least Squares Date: 04/29/13 Time: 17:38 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. MALE 0.011388 0.020793 0.547696 0.5839 C 4.488385 0.013799 325.2704 0.0000 R-squared 0.000030 Mean dependent var 4.493400 Adjusted R-squared -0.000070 S.D. dependent var 1.032213 S.E. of regression 1.032249 Akaike info criterion 2.901556 Sum squared resid 10653.24 Schwarz criterion 2.902998 Log likelihood -14505.78 F-statistic 0.299971 Durbin-Watson stat 1.990647 Prob(F-statistic) 0.583913 Table 3: regression on mean private medical expenditure and gender Dependent Variable: PRIV Method: Least Squares Date: 04/29/13 Time: 17:46 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. MALE 14.89332 3.256137 4.573921 0.0000 C 185.0874 2.160859 85.65456 0.0000 R-squared 0.002088 Mean dependent var 191.6464 Adjusted R-squared 0.001988 S.D. dependent var 161.8070 S.E. of regression 161.6461 Akaike info criterion 13.00890 Sum squared resid 2.61E+08 Schwarz criterion 13.01034 Log likelihood -65042.48 F-statistic 20.92076 Durbin-Watson stat 2.022463 Prob(F-statistic) 0.000005 Table 4 Dependent Variable: HEALTH Method: Least Squares Date: 04/27/13 Time: 12:23 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. LNINCOME 25.328 1.078 23.5 0.000 AGE 9.245 1.619 5.711 0.000 AGESQUARED -0.117 0.023 -4.998 0.000 FEMALE 3.547 0.165 21.45 0.000 DOCVIS -0.562 0.077 -7.28 0.000 C -237.55 28.13 -8.44 0.000 R-squared 0.157 Mean dependent var 46.77 Adjusted R-squared 0.157 S.D. dependent var 8.62 S.E. of regression 7.972 Akaike info criterion 6.99 Sum squared resid 635087.3 Schwarz criterion 6.99 Log likelihood -34945.27 F-statistic 373.64 Durbin-Watson stat 2.01 Prob(F-statistic) 0.000 Table 5 Dependent Variable: HEALTH Method: Least Squares Date: 04/27/13 Time: 11:56 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. AGE -0.897 0.111 -8.045 0.000 MALE -3.987 0.166 -24.06 0.000 EDUC 2.487 0.094 26.47 0.000 C 55.824 3.088 18.08 0.000 R-squared 0.16 Mean dependent var 46.77 Adjusted R-squared 0.16 S.D. dependent var 8.68 S.E. of regression 7.95 Akaike info criterion 6.98 Sum squared resid 631601.2 Schwarz criterion 6.99 Log likelihood -34917.75 F-statistic 644.69 Durbin-Watson stat 2.01 Prob(F-statistic) 0.000 Table 6 Dependent Variable: HEALTH Method: Least Squares Date: 04/27/13 Time: 13:12 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. AGE 8.132 1.635 4.97 0.000 AGESQUARED -0.133 0.024 -5.616 0.000 INC 0.001 2.93E-05 18.06 0.000 EDUC 1.965 0.096 20.518 0.000 C -102.20 28.26 -3.616 0.000 R-squared 0.144 Mean dependent var 46.769 Adjusted R-squared 0.144 S.D. dependent var 8.683 S.E. of regression 8.035 Akaike info criterion 7.006 Sum squared resid 645279.6 Schwarz criterion 7.01 Log likelihood -35024.88 F-statistic 420.26 Durbin-Watson stat 2.012 Prob(F-statistic) 0.000 Table 7 Dependent Variable: HEALTH Method: Least Squares Date: 04/27/13 Time: 17:44 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. AGE 7.63 1.59 4.80 0.00 AGESQUARED -0.12 0.02 -5.43 0.00 INC 0.001 2.85E-05 18.28 0.00 EDUC 2.20 0.094 23.53 0.00 MALE -3.94 0.16 -24.19 0.00 C -94.95 27.48 -3.46 0.06 R-squared 0.19 Mean dependent var 46.77 Adjusted R-squared 0.19 S.D. dependent var 8.68 S.E. of regression 7.81 Akaike info criterion 6.95 Sum squared resid 609597.1 Schwarz criterion 6.95 Log likelihood -34740.45 F-statistic 472.85 Durbin-Watson stat 2.01 Prob(F-statistic) 0.000 Table 8: Income and gender Dependent Variable: INC Method: Least Squares Date: 05/01/13 Time: 23:56 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. MALE 554.3280 59.88272 9.256893 0.0000 C 14774.43 39.73975 371.7795 0.0000 R-squared 0.008498 Mean dependent var 15018.55 Adjusted R-squared 0.008399 S.D. dependent var 2985.352 S.E. of regression 2972.789 Akaike info criterion 18.83259 Sum squared resid 8.84E+10 Schwarz criterion 18.83403 Log likelihood -94160.94 F-statistic 85.69007 Durbin-Watson stat 1.992096 Prob(F-statistic) 0.000000 Table 8 Dependent Variable: HEALTH Method: Least Squares Date: 04/27/13 Time: 17:58 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. AGE -0.996 0.11 -9.003 0.00 LNINCOME 21.041 1.07 19.612 0.00 MALE -3.955 0.16 -24.317 0.00 EDUC 2.147 0.094 22.87 0.00 C -25.6 5.140 -4.980 0.00 R-squared 0.19 Mean dependent var 46.76850 Adjusted R-squared 0.19 S.D. dependent var 8.682641 S.E. of regression 7.801 Akaike info criterion 6.946790 Sum squared resid 608196.8 Schwarz criterion 6.950396 Log likelihood -34728.95 F-statistic 598.2333 Durbin-Watson stat 2.010043 Prob(F-statistic) 0.000000 Table 9 Dependent Variable: HEALTH Method: Least Squares Date: 04/27/13 Time: 18:35 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. AGE -1.162309 0.107282 -10.83412 0.0000 LNINCOME 20.26874 1.048758 19.32641 0.0000 MALE -3.335182 0.161415 -20.66220 0.0000 EDUC 1.274060 0.100000 12.74055 0.0000 BLUEC -5.338899 0.244307 -21.85322 0.0000 C -6.596472 5.096570 -1.294296 0.1956 R-squared 0.229963 Mean dependent var 46.76850 Adjusted R-squared 0.229577 S.D. dependent var 8.682641 S.E. of regression 7.621076 Akaike info criterion 6.900312 Sum squared resid 580459.6 Schwarz criterion 6.904638 Log likelihood -34495.56 F-statistic 596.9184 Durbin-Watson stat 2.012878 Prob(F-statistic) 0.000000 Table 10 Dependent Variable: BLUEC Method: Least Squares Date: 05/01/13 Time: 22:21 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. MALE -0.066971 0.009310 -7.193726 0.0000 C 0.341494 0.006178 55.27490 0.0000 R-squared 0.005149 Mean dependent var 0.312000 Adjusted R-squared 0.005050 S.D. dependent var 0.463333 S.E. of regression 0.462162 Akaike info criterion 1.294396 Sum squared resid 2135.507 Schwarz criterion 1.295838 Log likelihood -6469.979 F-statistic 51.74969 Durbin-Watson stat 2.006857 Prob(F-statistic) 0.000000 Table 11 : regression of blue collar job and gender Dependent Variable: BLUEC Method: Least Squares Date: 04/29/13 Time: 18:43 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. MALE -0.066971 0.009310 -7.193726 0.0000 C 0.341494 0.006178 55.27490 0.0000 R-squared 0.005149 Mean dependent var 0.312000 Adjusted R-squared 0.005050 S.D. dependent var 0.463333 S.E. of regression 0.462162 Akaike info criterion 1.294396 Sum squared resid 2135.507 Schwarz criterion 1.295838 Log likelihood -6469.979 F-statistic 51.74969 Durbin-Watson stat 2.006857 Prob(F-statistic) 0.000000 Table 12 Dependent Variable: HEALTH Method: Least Squares Date: 04/27/13 Time: 18:58 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. INC 0.000498 2.76E-05 18.03534 0.0000 AGE -1.149339 0.106343 -10.80784 0.0000 FEMALE 3.286777 0.160039 20.53737 0.0000 EDUC 1.377785 0.099019 13.91431 0.0000 PRIV -0.005969 0.000471 -12.66389 0.0000 BLUEC -5.455215 0.242156 -22.52773 0.0000 DOCVIS -0.574840 0.073228 -7.850009 0.0000 C 69.44243 3.063596 22.66697 0.0000 R-squared 0.243414 Mean dependent var 46.76850 Adjusted R-squared 0.242884 S.D. dependent var 8.682641 S.E. of regression 7.554974 Akaike info criterion 6.883089 Sum squared resid 570319.7 Schwarz criterion 6.888857 Log likelihood -34407.44 F-statistic 459.2426 Durbin-Watson stat 2.008262 Prob(F-statistic) 0.000000 Specification test Table 13 Dependent Variable: HEALTH Method: Least Squares Date: 04/27/13 Time: 19:03 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. LNINCOME 19.91270 1.037958 19.18449 0.0000 AGE -1.159641 0.106135 -10.92608 0.0000 FEMALE 3.297932 0.159704 20.65023 0.0000 EDUC 1.335204 0.099025 13.48357 0.0000 PRIV -0.005941 0.000470 -12.63075 0.0000 BLUEC -5.389974 0.241740 -22.29657 0.0000 DOCVIS -0.571279 0.073079 -7.817318 0.0000 C -5.378614 5.072219 -1.060407 0.2890 R-squared 0.246538 Mean dependent var 46.76850 Adjusted R-squared 0.246010 S.D. dependent var 8.682641 S.E. of regression 7.539363 Akaike info criterion 6.878952 Sum squared resid 567965.1 Schwarz criterion 6.884720 Log likelihood -34386.76 F-statistic 467.0640 Durbin-Watson stat 2.008455 Prob(F-statistic) 0.000000 Specification test Table 14: Heteroskedasticity test Table 15: Lotwins and income Dependent Variable: INC Method: Least Squares Date: 05/01/13 Time: 23:12 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. LOTWINS 1.000959 0.004591 218.0159 0.0000 C 10000.55 26.16624 382.1927 0.0000 R-squared 0.826209 Mean dependent var 15018.55 Adjusted R-squared 0.826192 S.D. dependent var 2985.352 S.E. of regression 1244.602 Akaike info criterion 17.09122 Sum squared resid 1.55E+10 Schwarz criterion 17.09266 Log likelihood -85454.10 F-statistic 47530.95 Durbin-Watson stat 2.008829 Prob(F-statistic) 0.000000 Table 16: Income and parinc Dependent Variable: INC Method: Least Squares Date: 05/01/13 Time: 23:28 Sample: 1 10000 Included observations: 10000 Variable Coefficient Std. Error t-Statistic Prob. PARINC -0.000462 0.005016 -0.092146 0.9266 C 15032.91 158.6593 94.74964 0.0000 R-squared 0.000001 Mean dependent var 15018.55 Adjusted R-squared -0.000099 S.D. dependent var 2985.352 S.E. of regression 2985.500 Akaike info criterion 18.84112 Sum squared resid 8.91E+10 Schwarz criterion 18.84256 Log likelihood -94203.61 F-statistic 0.008491 Durbin-Watson stat 1.989156 Prob(F-statistic) 0.926584 Part 2 Figure 1 Figure 2 Table 17: augmented DF unit root test for log of consumption without including linear trend and constant ADF Test Statistic 4.988933 1% Critical Value* -2.5912 5% Critical Value -1.9442 10% Critical Value -1.6178 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LOGRCONS) Method: Least Squares Date: 05/05/13 Time: 07:31 Sample(adjusted): 1986:3 2006:4 Included observations: 82 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. LOGRCONS(-1) 0.000513 0.000103 4.988933 0.0000 D(LOGRCONS(-1)) 0.267091 0.107016 2.495789 0.0146 R-squared 0.071232 Mean dependent var 0.008940 Adjusted R-squared 0.059623 S.D. dependent var 0.008199 S.E. of regression 0.007951 Akaike info criterion -6.806895 Sum squared resid 0.005058 Schwarz criterion -6.748195 Log likelihood 281.0827 F-statistic 6.135638 Durbin-Watson stat 2.008094 Prob(F-statistic) 0.015356 Table 18: augmented DF unit root test for log of consumption with including linear trend and constant ADF Test Statistic -2.398507 1% Critical Value* -4.0787 5% Critical Value -3.4673 10% Critical Value -3.1601 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LOGRCONS) Method: Least Squares Date: 05/05/13 Time: 07:33 Sample(adjusted): 1987:3 2006:4 Included observations: 78 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. LOGRCONS(-1) -0.076002 0.031687 -2.398507 0.0191 D(LOGRCONS(-1)) 0.317100 0.112193 2.826390 0.0061 D(LOGRCONS(-2)) -0.001174 0.139324 -0.008425 0.9933 D(LOGRCONS(-3)) 0.222961 0.136868 1.629023 0.1078 D(LOGRCONS(-4)) -0.102139 0.143133 -0.713591 0.4779 D(LOGRCONS(-5)) 0.253316 0.140527 1.802608 0.0758 C 0.938743 0.389694 2.408925 0.0186 @TREND(1986:1) 0.000687 0.000286 2.401451 0.0190 R-squared 0.214876 Mean dependent var 0.008804 Adjusted R-squared 0.136364 S.D. dependent var 0.008234 S.E. of regression 0.007652 Akaike info criterion -6.810763 Sum squared resid 0.004099 Schwarz criterion -6.569049 Log likelihood 273.6198 F-statistic 2.736847 Durbin-Watson stat 2.094429 Prob(F-statistic) 0.014332 Table 19: augmented DF unit root test for log of GDP without including linear trend and constant ADF Test Statistic 3.083494 1% Critical Value* -2.5915 5% Critical Value -1.9442 10% Critical Value -1.6178 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LOGRGDP) Method: Least Squares Date: 05/05/13 Time: 07:37 Sample(adjusted): 1986:4 2006:4 Included observations: 81 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. LOGRGDP(-1) 0.000250 8.09E-05 3.083494 0.0028 D(LOGRGDP(-1)) 0.354078 0.110677 3.199194 0.0020 D(LOGRGDP(-2)) 0.224559 0.111001 2.023028 0.0465 R-squared 0.246882 Mean dependent var 0.007408 Adjusted R-squared 0.227571 S.D. dependent var 0.005512 S.E. of regression 0.004844 Akaike info criterion -7.785707 Sum squared resid 0.001830 Schwarz criterion -7.697023 Log likelihood 318.3211 F-statistic 12.78471 Durbin-Watson stat 1.916955 Prob(F-statistic) 0.000016 Table 20: augmented DF unit root test for log of GDP with including linear trend and constant ADF Test Statistic -2.302546 1% Critical Value* -4.0742 5% Critical Value -3.4652 10% Critical Value -3.1589 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LOGRGDP) Method: Least Squares Date: 05/05/13 Time: 07:39 Sample(adjusted): 1986:4 2006:4 Included observations: 81 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. LOGRGDP(-1) -0.054899 0.023843 -2.302546 0.0240 D(LOGRGDP(-1)) 0.357377 0.108400 3.296827 0.0015 D(LOGRGDP(-2)) 0.274732 0.110850 2.478402 0.0154 C 0.671240 0.290148 2.313439 0.0234 @TREND(1986:1) 0.000397 0.000174 2.277673 0.0256 R-squared 0.296543 Mean dependent var 0.007408 Adjusted R-squared 0.259519 S.D. dependent var 0.005512 S.E. of regression 0.004743 Akaike info criterion -7.804539 Sum squared resid 0.001710 Schwarz criterion -7.656733 Log likelihood 321.0838 F-statistic 8.009460 Durbin-Watson stat 1.955641 Prob(F-statistic) 0.000019 Figure 3: First difference graphs of log consumption Figure 4: first difference graph of log GDP Table 21: first difference on log of consumption ADF test without including intercept and constant ADF Test Statistic -1.597897 1% Critical Value* -2.5926 5% Critical Value -1.9444 10% Critical Value -1.6179 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LOGRCONS,2) Method: Least Squares Date: 05/05/13 Time: 08:07 Sample(adjusted): 1987:3 2006:4 Included observations: 78 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. D(LOGRCONS(-1)) -0.140992 0.088236 -1.597897 0.1144 D(LOGRCONS(-1),2) -0.479162 0.127993 -3.743657 0.0004 D(LOGRCONS(-2),2) -0.436411 0.154064 -2.832654 0.0060 D(LOGRCONS(-3),2) -0.172348 0.164863 -1.045397 0.2993 D(LOGRCONS(-4),2) -0.271532 0.136811 -1.984718 0.0509 R-squared 0.352629 Mean dependent var -0.000150 Adjusted R-squared 0.317157 S.D. dependent var 0.009764 S.E. of regression 0.008069 Akaike info criterion -6.739695 Sum squared resid 0.004753 Schwarz criterion -6.588624 Log likelihood 267.8481 F-statistic 9.940955 Durbin-Watson stat 2.077479 Prob(F-statistic) 0.000002 Table 22: first difference on log of consumption with inclusion of intercept and constant ADF Test Statistic -6.810044 1% Critical Value* -4.0727 5% Critical Value -3.4645 10% Critical Value -3.1585 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LOGRCONS,2) Method: Least Squares Date: 05/05/13 Time: 08:12 Sample(adjusted): 1986:3 2006:4 Included observations: 82 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. D(LOGRCONS(-1)) -0.733446 0.107701 -6.810044 0.0000 C 0.006456 0.002077 3.108310 0.0026 @TREND(1986:1) 1.70E-06 3.73E-05 0.045613 0.9637 R-squared 0.370093 Mean dependent var -0.000107 Adjusted R-squared 0.354146 S.D. dependent var 0.009952 S.E. of regression 0.007998 Akaike info criterion -6.783287 Sum squared resid 0.005054 Schwarz criterion -6.695236 Log likelihood 281.1148 F-statistic 23.20763 Durbin-Watson stat 2.007576 Prob(F-statistic) 0.000000 Table 23: first difference of log GDP without inclusion of intercept and constant ADF Test Statistic -1.867731 1% Critical Value* -2.5915 5% Critical Value -1.9442 10% Critical Value -1.6178 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LOGRGDP,2) Method: Least Squares Date: 05/05/13 Time: 08:15 Sample(adjusted): 1986:4 2006:4 Included observations: 81 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. D(LOGRGDP(-1)) -0.120634 0.064589 -1.867731 0.0655 D(LOGRGDP(-1),2) -0.378951 0.104265 -3.634505 0.0005 R-squared 0.222914 Mean dependent var 4.19E-05 Adjusted R-squared 0.213078 S.D. dependent var 0.005747 S.E. of regression 0.005098 Akaike info criterion -7.695377 Sum squared resid 0.002054 Schwarz criterion -7.636255 Log likelihood 313.6628 F-statistic 22.66188 Durbin-Watson stat 2.004373 Prob(F-statistic) 0.000009 Table 24: first difference of log GDP with inclusion of intercept and trend ADF Test Statistic -3.642912 1% Critical Value* -4.0742 5% Critical Value -3.4652 10% Critical Value -3.1589 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LOGRGDP,2) Method: Least Squares Date: 05/05/13 Time: 08:17 Sample(adjusted): 1986:4 2006:4 Included observations: 81 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. D(LOGRGDP(-1)) -0.422318 0.115929 -3.642912 0.0005 D(LOGRGDP(-1),2) -0.224230 0.111653 -2.008278 0.0481 C 0.003168 0.001431 2.214318 0.0298 @TREND(1986:1) -9.61E-07 2.32E-05 -0.041489 0.9670 R-squared 0.307887 Mean dependent var 4.19E-05 Adjusted R-squared 0.280922 S.D. dependent var 0.005747 S.E. of regression 0.004874 Akaike info criterion -7.761796 Sum squared resid 0.001829 Schwarz criterion -7.643552 Log likelihood 318.3527 F-statistic 11.41784 Durbin-Watson stat 1.916716 Prob(F-statistic) 0.000003 Table 25: ACF and PACF functions of log of consumption Date: 05/05/13 Time: 11:12 Sample: 1986:1 2006:4 Included observations: 82 Autocorrelation Partial Correlation AC PAC Q-Stat Prob ***| . | ***| . | 1 -0.412 -0.412 14.469 0.000 .*| . | ***| . | 2 -0.104 -0.330 15.399 0.000 . |*. | .*| . | 3 0.112 -0.109 16.501 0.001 .*| . | **| . | 4 -0.171 -0.262 19.087 0.001 . |*. | .*| . | 5 0.079 -0.155 19.651 0.001 . |*. | . | . | 6 0.074 -0.043 20.143 0.003 .*| . | .*| . | 7 -0.118 -0.121 21.416 0.003 . |*. | . | . | 8 0.093 -0.028 22.228 0.005 . | . | .*| . | 9 -0.053 -0.074 22.491 0.007 . | . | . | . | 10 0.038 0.027 22.626 0.012 . | . | . | . | 11 0.027 0.037 22.698 0.019 .*| . | . | . | 12 -0.058 0.013 23.029 0.027 . | . | .*| . | 13 -0.039 -0.074 23.179 0.040 . | . | . | . | 14 0.038 -0.052 23.324 0.055 .*| . | .*| . | 15 -0.076 -0.152 23.923 0.066 . |*. | . | . | 16 0.150 0.018 26.264 0.050 . | . | . | . | 17 -0.023 0.030 26.320 0.069 .*| . | .*| . | 18 -0.105 -0.065 27.513 0.070 . | . | .*| . | 19 0.039 -0.084 27.678 0.090 . | . | . | . | 20 0.024 -0.019 27.740 0.116 . | . | . | . | 21 0.005 0.025 27.743 0.148 Table 26: ACF and PACF graphs of log GDP Date: 05/05/13 Time: 11:16 Sample: 1986:1 2006:4 Included observations: 82 Autocorrelation Partial Correlation AC PAC Q-Stat Prob ***| . | ***| . | 1 -0.428 -0.428 15.547 0.000 . | . | .*| . | 2 0.030 -0.187 15.625 0.000 . | . | . | . | 3 0.028 -0.046 15.695 0.001 .*| . | **| . | 4 -0.151 -0.190 17.705 0.001 . | . | .*| . | 5 0.028 -0.159 17.775 0.003 . | . | .*| . | 6 0.027 -0.072 17.839 0.007 . |*. | . |*. | 7 0.082 0.079 18.450 0.010 .*| . | .*| . | 8 -0.111 -0.076 19.603 0.012 . | . | .*| . | 9 -0.020 -0.147 19.641 0.020 . |*. | . | . | 10 0.082 0.002 20.281 0.027 . |*. | . |** | 11 0.091 0.217 21.082 0.033 .*| . | .*| . | 12 -0.177 -0.081 24.171 0.019 . | . | **| . | 13 0.016 -0.193 24.195 0.029 . | . | .*| . | 14 0.008 -0.071 24.202 0.043 .*| . | .*| . | 15 -0.101 -0.065 25.243 0.047 . |*. | .*| . | 16 0.076 -0.110 25.842 0.056 . |*. | . | . | 17 0.084 -0.044 26.587 0.064 . | . | . | . | 18 -0.005 0.060 26.589 0.087 .*| . | .*| . | 19 -0.118 -0.059 28.107 0.081 . | . | .*| . | 20 0.007 -0.174 28.113 0.107 . | . | .*| . | 21 0.009 -0.144 28.123 0.137 Table 27 Dependent Variable: DLOGRCONS Method: Least Squares Date: 05/05/13 Time: 12:25 Sample(adjusted): 1986:3 2006:4 Included observations: 82 after adjusting endpoints Convergence achieved after 14 iterations Backcast: 1986:2 Variable Coefficient Std. Error t-Statistic Prob. C 0.009016 0.001044 8.634944 0.0000 AR(1) -0.379200 0.281951 -1.344911 0.1825 MA(1) 0.638521 0.248826 2.566136 0.0122 R-squared 0.078190 Mean dependent var 0.008940 Adjusted R-squared 0.054853 S.D. dependent var 0.008199 S.E. of regression 0.007971 Akaike info criterion -6.790024 Sum squared resid 0.005020 Schwarz criterion -6.701973 Log likelihood 281.3910 F-statistic 3.350464 Durbin-Watson stat 1.886876 Prob(F-statistic) 0.040118 Inverted AR Roots -.38 Inverted MA Roots -.64 Table 28 Date: 05/05/13 Time: 12:27 Sample: 1986:3 2006:4 Included observations: 82 Q-statistic probabilities adjusted for 2 ARMA term(s) Autocorrelation Partial Correlation AC PAC Q-Stat Prob . | . | . | . | 1 0.050 0.050 0.2101 . |*. | . |*. | 2 0.142 0.140 1.9548 . |*. | . |*. | 3 0.131 0.120 3.4482 0.063 . | . | . | . | 4 0.040 0.012 3.5910 0.166 . |*. | . | . | 5 0.080 0.045 4.1605 0.245 . |*. | . |*. | 6 0.113 0.091 5.3176 0.256 . | . | .*| . | 7 -0.040 -0.070 5.4648 0.362 . | . | . | . | 8 0.064 0.026 5.8413 0.441 . | . | .*| . | 9 -0.048 -0.065 6.0588 0.533 . | . | . | . | 10 -0.031 -0.037 6.1526 0.630 .*| . | .*| . | 11 -0.094 -0.104 7.0132 0.636 .*| . | .*| . | 12 -0.124 -0.110 8.5294 0.577 .*| . | .*| . | 13 -0.168 -0.135 11.349 0.414 . | . | . | . | 14 -0.056 -0.010 11.667 0.473 .*| . | .*| . | 15 -0.137 -0.060 13.592 0.403 . | . | . |*. | 16 0.006 0.068 13.595 0.480 .*| . | . | . | 17 -0.100 -0.032 14.646 0.477 .*| . | .*| . | 18 -0.141 -0.097 16.773 0.400 . | . | . | . | 19 -0.027 0.019 16.854 0.464 . | . | . | . | 20 -0.012 0.040 16.871 0.532 . | . | . | . | 21 -0.018 0.027 16.908 0.596 Table 29 Dependent Variable: DLOGRGDP Method: Least Squares Date: 05/05/13 Time: 12:30 Sample(adjusted): 1986:3 2006:4 Included observations: 82 after adjusting endpoints Convergence achieved after 7 iterations Backcast: 1986:2 Variable Coefficient Std. Error t-Statistic Prob. C 0.007228 0.001359 5.320657 0.0000 AR(1) 0.762192 0.136812 5.571105 0.0000 MA(1) -0.404070 0.194978 -2.072383 0.0415 R-squared 0.239912 Mean dependent var 0.007391 Adjusted R-squared 0.220670 S.D. dependent var 0.005480 S.E. of regression 0.004838 Akaike info criterion -7.788881 Sum squared resid 0.001849 Schwarz criterion -7.700830 Log likelihood 322.3441 F-statistic 12.46769 Durbin-Watson stat 2.010532 Prob(F-statistic) 0.000020 Inverted AR Roots .76 Inverted MA Roots .40 Table 30 Date: 05/05/13 Time: 12:31 Sample: 1986:3 2006:4 Included observations: 82 Q-statistic probabilities adjusted for 2 ARMA term(s) Autocorrelation Partial Correlation AC PAC Q-Stat Prob . | . | . | . | 1 -0.016 -0.016 0.0225 . | . | . | . | 2 0.050 0.050 0.2411 . | . | . | . | 3 0.020 0.021 0.2754 0.600 .*| . | .*| . | 4 -0.125 -0.127 1.6565 0.437 . | . | . | . | 5 0.000 -0.006 1.6565 0.647 . | . | . |*. | 6 0.052 0.066 1.9011 0.754 . | . | . | . | 7 0.051 0.060 2.1421 0.829 .*| . | .*| . | 8 -0.107 -0.132 3.2068 0.782 . | . | .*| . | 9 -0.045 -0.061 3.3938 0.846 . |*. | . |*. | 10 0.073 0.106 3.9045 0.866 . | . | . |*. | 11 0.038 0.073 4.0452 0.908 **| . | **| . | 12 -0.205 -0.269 8.1986 0.609 .*| . | .*| . | 13 -0.103 -0.167 9.2607 0.598 .*| . | . | . | 14 -0.090 -0.010 10.083 0.609 .*| . | .*| . | 15 -0.135 -0.063 11.952 0.532 . | . | . | . | 16 0.045 -0.055 12.168 0.593 . |*. | . | . | 17 0.083 0.026 12.901 0.610 . | . | . | . | 18 -0.031 0.014 13.005 0.672 .*| . | .*| . | 19 -0.145 -0.144 15.298 0.574 . | . | .*| . | 20 -0.035 -0.111 15.434 0.632 . | . | . | . | 21 0.032 0.042 15.547 0.687 Table 31 Dependent Variable: DLOGRGDP Method: Least Squares Date: 05/05/13 Time: 12:50 Sample(adjusted): 1986:2 2006:4 Included observations: 83 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. DLOGRCONS 0.490303 0.050109 9.784649 0.0000 C 0.003006 0.000610 4.927298 0.0000 R-squared 0.541698 Mean dependent var 0.007440 Adjusted R-squared 0.536040 S.D. dependent var 0.005465 S.E. of regression 0.003722 Akaike info criterion -8.325167 Sum squared resid 0.001122 Schwarz criterion -8.266882 Log likelihood 347.4944 F-statistic 95.73935 Durbin-Watson stat 1.731599 Prob(F-statistic) 0.000000 The Engle Granger results without inclusion of intercept and constant ADF Test Statistic -4.529730 1% Critical Value* -2.5919 5% Critical Value -1.9443 10% Critical Value -1.6179 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESID01) Method: Least Squares Date: 05/05/13 Time: 12:54 Sample(adjusted): 1987:1 2006:4 Included observations: 80 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. RESID01(-1) -0.825221 0.182179 -4.529730 0.0000 D(RESID01(-1)) -0.043966 0.156182 -0.281507 0.7791 D(RESID01(-2)) -0.028095 0.122144 -0.230014 0.8187 R-squared 0.443148 Mean dependent var -5.81E-05 Adjusted R-squared 0.428684 S.D. dependent var 0.004898 S.E. of regression 0.003702 Akaike info criterion -8.323215 Sum squared resid 0.001055 Schwarz criterion -8.233889 Log likelihood 335.9286 F-statistic 30.63862 Durbin-Watson stat 2.016968 Prob(F-statistic) 0.000000 Inclusion of trend and intercept ADF Test Statistic -4.423141 1% Critical Value* -4.0756 5% Critical Value -3.4659 10% Critical Value -3.1593 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESID01) Method: Least Squares Date: 05/05/13 Time: 12:55 Sample(adjusted): 1987:1 2006:4 Included observations: 80 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. RESID01(-1) -0.820539 0.185510 -4.423141 0.0000 D(RESID01(-1)) -0.048357 0.159286 -0.303584 0.7623 D(RESID01(-2)) -0.029856 0.123875 -0.241015 0.8102 C -0.000343 0.000896 -0.382874 0.7029 @TREND(1986:1) 6.25E-06 1.83E-05 0.342203 0.7332 R-squared 0.444234 Mean dependent var -5.81E-05 Adjusted R-squared 0.414594 S.D. dependent var 0.004898 S.E. of regression 0.003747 Akaike info criterion -8.275169 Sum squared resid 0.001053 Schwarz criterion -8.126292 Log likelihood 336.0067 F-statistic 14.98725 Durbin-Watson stat 2.021486 Prob(F-statistic) 0.000000 Table 32 Dependent Variable: DLOGRCONS Method: Least Squares Date: 05/05/13 Time: 12:57 Sample(adjusted): 1986:2 2006:4 Included observations: 83 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. DLOGRGDP 1.104823 0.112914 9.784649 0.0000 C 0.000823 0.001040 0.791300 0.4311 R-squared 0.541698 Mean dependent var 0.009043 Adjusted R-squared 0.536040 S.D. dependent var 0.008203 S.E. of regression 0.005588 Akaike info criterion -7.512750 Sum squared resid 0.002529 Schwarz criterion -7.454465 Log likelihood 313.7791 F-statistic 95.73935 Durbin-Watson stat 2.094425 Prob(F-statistic) 0.000000 Without inclusion of intercept and constant ADF Test Statistic -6.174474 1% Critical Value* -2.5919 5% Critical Value -1.9443 10% Critical Value -1.6179 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESID02) Method: Least Squares Date: 05/05/13 Time: 12:58 Sample(adjusted): 1987:1 2006:4 Included observations: 80 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. RESID02(-1) -1.580493 0.255972 -6.174474 0.0000 D(RESID02(-1)) 0.472751 0.202510 2.334458 0.0222 D(RESID02(-2)) 0.145976 0.140786 1.036860 0.3030 R-squared 0.563977 Mean dependent var 2.07E-05 Adjusted R-squared 0.552651 S.D. dependent var 0.008161 S.E. of regression 0.005458 Akaike info criterion -7.546562 Sum squared resid 0.002294 Schwarz criterion -7.457236 Log likelihood 304.8625 F-statistic 49.79802 Durbin-Watson stat 2.018994 Prob(F-statistic) 0.000000 With inclusion of intercept and constant ADF Test Statistic -6.058242 1% Critical Value* -4.0756 5% Critical Value -3.4659 10% Critical Value -3.1593 *MacKinnon critical values for rejection of hypothesis of a unit root. Augmented Dickey-Fuller Test Equation Dependent Variable: D(RESID02) Method: Least Squares Date: 05/05/13 Time: 12:59 Sample(adjusted): 1987:1 2006:4 Included observations: 80 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. RESID02(-1) -1.609639 0.265694 -6.058242 0.0000 D(RESID02(-1)) 0.498021 0.211242 2.357579 0.0210 D(RESID02(-2)) 0.157872 0.144447 1.092940 0.2779 C -0.000288 0.001330 -0.216735 0.8290 @TREND(1986:1) 1.10E-05 2.74E-05 0.400096 0.6902 R-squared 0.565402 Mean dependent var 2.07E-05 Adjusted R-squared 0.542223 S.D. dependent var 0.008161 S.E. of regression 0.005522 Akaike info criterion -7.499837 Sum squared resid 0.002287 Schwarz criterion -7.350960 Log likelihood 304.9935 F-statistic 24.39332 Durbin-Watson stat 2.019905 Prob(F-statistic) 0.000000 Table 33 Dependent Variable: D1DLOGRCONS Method: Least Squares Date: 05/05/13 Time: 16:08 Sample(adjusted): 1986:3 2006:4 Included observations: 82 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. D1DLOGRGDP 0.996660 0.115697 8.614371 0.0000 RESID01(-1) -0.209769 0.178904 1.172523 0.2445 C 0.001554 0.000620 2.509162 0.0141 R-squared 0.496675 Mean dependent var 0.001524 Adjusted R-squared 0.483932 S.D. dependent var 0.007809 S.E. of regression 0.005610 Akaike info criterion -7.492786 Sum squared resid 0.002486 Schwarz criterion -7.404736 Log likelihood 310.2042 F-statistic 38.97807 Durbin-Watson stat 1.931310 Prob(F-statistic) 0.000000 Table 34 Table 28: The gradger casualty test Pairwise Granger Causality Tests Date: 05/05/13 Time: 16:17 Sample: 1986:1 2006:4 Lags: 2 Null Hypothesis: Obs F-Statistic Probability DLOGRGDP does not Granger Cause DLOGRCONS 81 6.79063 0.00193 DLOGRCONS does not Granger Cause DLOGRGDP 0.05858 0.94314 Read More