The Estimated Economic Model - Report Example

Stimulus - Third one Table of Contents Stimulus - Third one Table of Contents 2 Introduction 3 The Economic Model 3 Data Collection 4 Methodology 5Data Analysis 7 Linearity Test 9 Jarque-Bera Test 9 White’s Test 10 Conclusion 10 Reference 11 Appendix 12 Introduction The recent financial crash had a ruinous effect on the economic positions of a large number of developing nations around the world. Its sudden occurrence has forced the administrations of many nations globally, to postpone their efforts to accomplish a number of other projects waiting in line, and focus their full attention to this single problem. The problem needs to be attended promptly so as to avoid any difficulty arising due to the persisting effects of the shock. However, the government of a developing nation cannot act on the basis of an imaginary impact; rather it must assess the entire situation before putting a step forward. Since the government is usually afraid of a diminishing GDP growth rate, the starting point of the evaluation criteria would be to find out the exact impact that the shock will have on the GDP growth rate and what positive impact will any resource injection probably have on the same. This is the underlying idea, being employed in the present paper to evaluate whether the investment of funds would be more fruitful when subjected to heal the ravages in the financial sector, or when channeled towards a policy measure for the enhancement in the secondary school enrolment situation in the nation. The Economic Model The model that needs to be estimated in the present context, to ease down the brainwork of the government is as under – dlypci = 1 + 2lypc90i + 3lsecedi + 4govgdpi + 5openi + 6infli + 7crediti + ui …. (1) where, dlypci = Change in growth rate of per capita GDP (lypc) between 1990 and 2005, calculated as, lypc2005 – lypc1990, lseced = Growth rate of secondary education, recorded for 1990, measured as, natural log of percentage of secondary school age population enrolled in secondary schools in 1990, govgdp = The domestic government’s share in the nation’s GDP, open = The openness of the nation towards international trade; it is the ratio of gross exports and imports to GDP for the year 1990 infl = Change in the rate of inflation over the last five years, calculated as the difference between the natural logarithms of CPI for years 1990 and 1985 and credit = ratio of private credit by deposit money banks and other financial institutions to GDP in 1990 Though the basic objective is to estimate and test significance of the corresponding coefficients of some variables only, there are some additional variables included in the model as well, so as to increase the significance of the model as a whole. Data Collection Data has been sampled from 50 countries around the world, in order to find out the mean effect that each variable had on the dependent variable over the years. Note should be taken of the fact that most of the nations being incorporated in the study are still in their developing phase. Methodology Ordinary Least Square method has been used to estimate the regression model (1), after which the estimated coefficients have been subjected to hypothesis testing, with their respective hypotheses as follows – 1. H01: 2 = 3 = 4 = 5 = 6 = 7 = 0 against H11: j  0 for at least one j  (2...7), using a significance level of 0.05. 2. H02: 2 = 0 against H12: 2  0 using a significance level of 0.05. 3. H03: 3 = 0 against H13: 3 > 0 using a significance level of 0.05. 4. H04: 7 = 0 against H14: 7 > 0 using a significance level of 0.1. To test compliance with the first hypothesis, the model will be subjected to an F-test; while for the remaining three, the relevant test will be Student’s t-statistic. Irrespective of the test-statistic, decision about the rejection or acceptance of the null hypotheses will be based on the following rules – If the p-value or the level of significance of the estimated statistic falls below the standard level of significance, reject the null hypothesis and If the p-value or the level of significance of the estimated statistic exceeds the standard level of significance, do not reject the null hypothesis.1 While comparison, the displayed p-value is halved in case of a one-tailed test, unlike that in case of a two-tailed one. Diagnostic tests are the second most important step before zeroing upon a steady conclusion. These tests are supposed to establish the accordance of the estimated model with CLRM assumptions. Some such assumptions and details of the corresponding tests to ascertain their fulfillment have been listed below. Linearity Assumption – The assumption points out that the model should follow linearity or rather must be a linear function of the estimated coefficients. An universally followed way to prove this, is through plotting a scatter diagram of the predicted residuals against the fitted values of the dependent variable. Normality Assumption – This assumption establishes that the predicted residuals follow a normal distribution, i.e., have zero mean and constant variance. A highly proclaimed way to establish the same is the Jarque-Bera test for normality. Hence, the null hypothesis in this case can be designed as, H05: The predicted residuals follow a normal distribution. Homoscedasticity Assumption – This assumption further assumes that, the predicted residual terms have a constant variance that might not vary from sample to sample. An ideal test employed to confirm the same is, White’s Test. The relevant null hypothesis in this case is, H06: The predicted residuals have a constant variance. In the latter two cases, the test statistic which judges the rejection or non-rejection of the null hypotheses is chi-square (χ2). The rules being applied in this context are similar to the ones mentioned to test for the significance of the estimated coefficients. In cases when the diagnostic tests in any particular case, alienate the CLRM assumptions, the estimated model needs to be subjected to a close examination and the presence of any outlier in the data should be explored. A unanimous way of doing so is to note down those observations whose predicted residuals exceed three times the standard error of the estimated model, i.e., the square root of Mean Sum of Squares. Once noted, place a dummy variable ‘1’ corresponding to the observation(s) and ‘0’ for the remaining ones. After the dummy variables have been designed, the model needs to be estimated once again and then subjected to the same diagnostic tests to ensure that no more discrepancies remain. All the above procedure has been conducted with the help of the statistical software STATA, which not only has eased down the process, but has also ensured accuracy of the results. Data Analysis The samples being collected estimates the economic model as follows - dlypci = 1.9094 – 0.1998lypc90i + 0.2503lsecedi + 0.0100govgdpi + 0.0002openi + 0.1143infli + (2.88) (2.67) (2.59) (1.60) (0.10) (1.08) 0.2125crediti + ui (1.52) The absolute values of the estimated Student’s t-statistics have been provided in parentheses. The sample data being estimated, found that, the relevant F-statistic is equal to 1.77. the corresponding p-value of the estimated statistic at (6, 43) degrees of freedom is, 0.1289, which is greater than the given standard level of significance, i.e., 0.05. Thus, the respective null hypothesis (H01) can be considered not to be rejected at 5% level of significance. Further, enquiry of the Student’s t-statistics corresponding to the estimated coefficients of lypc90 (β2), lseced (β3) and credit (β7) reveal that, P-value of lypc90 = 0.011 < 0.05, P-value of lseced = 0.0065 (one-tailed test) < 0.05 and P-value of credit = 0.0685 (one-tailed test) > 0.01 Hence, it is obvious that, though the null hypotheses, H02 and H03 are rejected at 5% levels of significance, the null hypothesis, H04 cannot be treated in a similar manner, i.e., cannot be rejected at 1% level of significance. Despite the estimated F-statistic being an insignificant one, the model being framed cannot be ruled out as a whole. This is because, F-statistic finds out how far the explanatory variables as a whole can explain variations in the dependent variable. An insignificant statistic in that case would mean that the variables being included can only partly explain the total variation and that most of it remains unexplained. To explain this remaining part, there is need for more economically viable explanatory variables. In cases when the t-statistics of individual explanatory variables are found to be significant, an insignificant F-statistic raises a slight issue. Linearity Test The line fit plot of the residuals reveals that the predicted model follows a linear function of the estimated coefficients. Had it not been so, the residual points would not have been scattered in a linear manner, rather, they would have been spread haphazardly. Jarque-Bera Test Again, the Jarque-Bera test outcome for testing the normality assumption, finds that, estimated JB = 0.1381 and the p-value of the corresponding chi-square (χ2) statistic is, 0.9333. Clearly, p-value of χ2 = 0.9333 > 0.05 Thus, the relevant null hypothesis, H05 cannot be rejected at 5% level of significance. The implication of this test outcome is that, the estimated residuals are normally distributed, i.e., the estimated model complies with the normality assumption. White’s Test On the other hand, the White’s test to test for heteroscedasticity in the predicted error terms divulge that, estimated chi-square (χ2) statistic is 15.97, with the corresponding probability equal to 0.9547. However, 0.9547 > 0.05, implying that null hypothesis cannot be rejected at 5% level of significance. This in turn indicates that the homoscedasticity assumption core to CLRM model is undisturbed in the present case. Thus, it is quite evident from the no-rejection status of the above two null hypotheses that the estimated model neither hampers the normality assumption and nor the homoscedasticity assumption of Classical Linear Regression Model. Since none of the assumptions or suppositions is violated, the presence of any discrepancy in the observations can be ruled out as well. Conclusion The economic model being estimated tries to find out whether the resource injection would be more fruitful in case when the Finance Ministry pours it into the depressed financial sector of the economy or the equally important steps towards policy implementation to promote secondary education in the nation. The effects of the shock can devastate the financial position of the nation, while a negligence of the education sector can deteriorate the nation’s human resource quality. Given that both the aftermath effects can have equally harmful impact on the nation’s future, the Ministry chose to conduct an examination to find out which one of the two factors will contribute more towards a positive change in the national GDP. The regression analysis found that a rise in the level of secondary enrolment can have a significantly positive impact on the average growth rate of GDP, while that in the inflow of credit might not affect the dependent variable significantly, even though it is positive. Thus, the possibilities of gains are more when an infusion is made into the education sector rather than the financial sector even amidst the shock effects. Hence, it would be advised that the government inject the given sum of money in the education sector as was planned beforehand. Reference Heston, A., Summers, R. and Aten, B. (August 2009) Penn World Table Version 6.3, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania. Appendix Estimated Economic Regression Model Estimated Results of Jarque-Bera Test for Normality Estimated Results of White Test for Homoscedasticity Read More