The trend in economic growth of a country - Coursework Example

? Econometrics Number Outline Introduction The model Hypotheses testing Interpretation of the findings: Preferred model Conclusion Introduction This initial report is going to carry out the study of the economic growth of a series of countries with different characteristics. To develop this project we will analyse the dependence of economic growth in GDP-Gross Domestic Product-, international trade, years of schooling, the average of annual number of revolutions and insurrections, the average of annual number of political assassinations and finally if the country has oil production and it represents at least half of the annual exports. Throughout history there have been many studies on economic growth. Overall economic growth of a country is measured every year by the difference that has occurred in GDP over the previous year.Should we consider that a country grows only by analyzing the monetary value of the production of final goods and services during a period? In my opinion would have no sense not to consider the benefit that provides a trained workforce, or the economic stability of a country… To reinforce this idea I will investigate past developments on this theory. Mincer (1974) elaborated a study about the relationships of the individual’s earnings as variable dependent in age, experience and education. Mincer considers that the benefits of education to the people can be extrapolated to countries. Considers that an educated workforce directly affects the growth of a country. He justifies that an extra year of education in a white man who did not work on a farm contributes a extra seven per cent of profit. Adam Smith (1776) was the first person that found some link between International Trade and Economic Growth. The work of Grossman and Helpman (1991) and Rivera-Batiz and Romer (1991) has also aided to clarify why the participation of a country in an integrated world economy can stimulate its growth. Oil production and exports affect economic growth. Limiting the supply of oil to a country can cause serious economic consequences. We must highlight the oil crisis of 1973 or the current threat from Iraq to the European Union countries to limit its supply. In relation to the political unrest, the IMF warned in its 60 years that a lack of political stability could affect economic growth.Regarding the number of murders; the current Mexican central bank governor Agustin Cartens (2011) said that violence inhibited economic growth. The model To begin with, we need to find the relationship between the dependent variables and independent variable (growth). The initial econometric model of the of this study is: y = ?0+ ?1(GRDP)+ ?2(TRADEHARE)+ ?3(YEARSSCHOOL)+ ?4(ASSASINATIONS)+ ?5(REV_COUPS)+?. Some of the coefficients are expected to negative because some of the figures of variables are greater than the figures in dependant variable. From the SPSS output table below us can note that there is a negative relationship between growth and rgdp60 as well rev-coups. This means that other factors help to increase growth as they have positive coefficients’. Coefficients Unstandardized Coefficients Standardized Coefficients t Sig. Model B Std. Error Beta 1 (Constant) .490 .690 .710 .480 RGDP60 -4.693E-04 .000 -.622 -3.167 .002 TRADESHA 1.562 .758 .238 2.060 .044 YEARSSCH .575 .139 .770 4.126 .000 RECOUPS -2.158 1.110 -.256 -1.943 .057 ASSIS .354 .477 .092 .742 .461 a Dependent Variable: GROWTH The model econometric model of the of this study will be y= 0.49 -0.00047(GRDP) + 1.561696 (tradeshare)+ 0.575 (Yearsschool)+ 0.354 (assassinations) -2.1575 (rev_coups)+? Goodness-of-Fit Chi-Square df Sig. Pearson 232.676 4032 1.000 Deviance 188.381 4032 1.000 Link function: Logit. The goodness –of-fit- statistics for model is 232.6 this means that the data obtained from the random sample is greater than 5 thus it does not fit into a specific pattern. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .599 .359 .305 1.582084957 a Predictors: (Constant), ASSIS, RGDP60, TRADESHA, RECOUPS, YEARSSCH ANOVA Model Sum of Squares df Mean Square F Sig. 1 Regression 82.663 5 16.533 6.605 .000 Residual 147.677 59 2.503 Total 230.340 64 a Predictors: (Constant), ASSIS, RGDP60, TRADESHA, RECOUPS, YEARSSCH b Dependent Variable: GROWTH Regression Statistics Multiple R 0.599062 R Square 0.358876 Adjusted R Square 0.287594 Standard Error 1.582085 Observations 65 ANOVA   df SS MS F Significance F Regression 6 82.66348 13.77725 6.605171 2.33E-05 Residual 59 147.6766 2.502993 Total 65 230.3401         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.48976 0.6896 0.71021 0.480372 -0.89013 1.869646 -0.89013 1.869646 Oil 0 0 65535 #NUM! 0 0 0 0 grdp -0.00047 0.000148 -3.16673 0.002441 -0.00077 -0.00017 -0.00077 -0.00017 tradeshare 1.561696 0.757948 2.060427 0.043776 0.045046 3.078345 0.045046 3.078345 yearsschool 0.574846 0.139338 4.125554 0.000118 0.296032 0.853661 0.296032 0.853661 rev_coups -2.1575 1.110292 -1.94319 0.056769 -4.37919 0.064185 -4.37919 0.064185 assassinations 0.354078 0.477394 0.74169 0.461218 -0.60119 1.309342 -0.60119 1.309342 From the regression analysis performed, the following regression equation can be derived based on stepwise method: Growth= 0.49 -0.00047(GRDP) + 1.561696 (tradeshare)+ 0.575 (Yearsschool)+ 0.354 (assassinations) -2.1575 (rev_coups)+? The stepwise regression equation above indicates the coefficient of determination R-squared as 0.359, which suggests that the stepwise regression performed between variables, is only able to predict 35.9% of the total variations observed in the values. Due to the certain values that could be considered as outliers observed within the data. The coefficient of rev_coups is -2.1575. The negative value of coefficient is perhaps opposite to the expectations one could have regarding the relationship between GROWTH and rev_coups. Hypotheses testing Null hypothesis: There is a relationship between the independent and dependant variable Null hypothesis: There is no a relationship between the independent and dependant variable The level of significance is 5% Regression coefficients and Residual analysis: Regression Statistics Multiple R 0.599062 R Square 0.358876 Adjusted R Square 0.287594 Standard Error 1.582085 Observations 65 ANOVA   df SS MS F Significance F Regression 6 82.66348 13.77725 6.605171 2.33E-05 Residual 59 147.6766 2.502993 Total 65 230.3401         Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.48976 0.6896 0.71021 0.480372 -0.89013 1.869646 -0.89013 1.869646 Oil 0 0 65535 #NUM! 0 0 0 0 grdp -0.00047 0.000148 -3.16673 0.002441 -0.00077 -0.00017 -0.00077 -0.00017 tradeshare 1.561696 0.757948 2.060427 0.043776 0.045046 3.078345 0.045046 3.078345 yearsschool 0.574846 0.139338 4.125554 0.000118 0.296032 0.853661 0.296032 0.853661 rev_coups -2.1575 1.110292 -1.94319 0.056769 -4.37919 0.064185 -4.37919 0.064185 assassinations 0.354078 0.477394 0.74169 0.461218 -0.60119 1.309342 -0.60119 1.309342 The regression results have been obtained by carrying out Ordinary Least Squares linear regression process. The results of regression presented above show that the coefficient of the independent variable, i.e. growth is equal to 0.4898. According to the ANOVA presented in the table above, residual sum of squares that measure the deviation of predicted value from the actual value is 147.677, while regression sum square which measures the amount of explained deviation of the actual values from average is equal to 82.66. R squared on the other hand, is found to be equal to 0.36. Interpretation of the findings: From the results of the regression, the regression coefficients is found to be equal to the figures shown in the equation Growth= 0.49 -0.00047(GRDP) + 1.561696 (tradeshare)+ 0.575 (Yearsschool)+ 0.354 (assassinations) -2.1575 (rev_coups)+?. It implies that if growth increases by 1 unit, the RGDP will fall by around 0.00047, trade share will increase by 1.561696, years school will increase by 0.575, assassinations will increase by 0.354 and rev-coups decrease by 2.1575 . This regression coefficients indicates towards a close association between the variables. The ANOVA on the other hand suggests residual sum of squares is very low implying that variables trade share, rev-coups and RGDP are efficient enough in predicting the value of growth. Very high level of explained sum of squares suggests that the independent variable is efficient enough in explaining variation in the values of dependent variables around average. This finding is further reinforced by the value of R squared. Very low value of r squared, 0.36, suggests that variation in the given data of variables is capable of explaining 36 percent of total variation in growth around its average value. It implies that the regression model is a good fit in the given data. To check the above hypothesis, the regression equation to be solved will look like as follows- The error term is included in the regression equation because practically all of the variation in the dependent variable can not be explained by variables GRDP, trade share, Years school, assassinations and rev_coups. In a regression model, it is not possible to incorporate all possible factors that affect the dependent variable. The error term, is incorporated in a regression model in order to capture the effect of those factors on the dependent variables that are not included as the independent variable in the regression equation (Berk, 2003) The basic assumptions made for running the above regression are as follows: a. Mean of the disturbance or the error term would be zero, i.e. E(ui) = 0. b. Variance of the error term is constant for all i, i.e V(ui)=?i, for all i. c. ui and uj are completely independent of each other. (Stigler, 1981) In this kind of regression model, squared ryp and squared rya measure partial correlation coefficient of growth with all variables, respectively. Here, small r squared is not capable of finding out to what extent variation in growth can be explained by the independent variables. Here comes the importance of R2 which is nothing but a ratio of explained sum of square of total sum of square. This ratio is known to as coefficient of determination. It measures what proportion of total variation in the dependent variable, can be explained by the independent variables. If the value of this coefficient of determination is found to be very high then the regression model can said to be a good fit for the given set of data. (Stigler, 1981) The result of the traditional F-Test is a significantly low 0.0000233 helps reject the null hypothesis that none of the selected independent variables has power to explain the variations in the dependent variables. Deploying the F-test (p-value) delivers a similar result, in that because of the significant difference (5% > 48.0372%) between the 5% hypothesis and the probable F-statistic the model has significant power to explain the changes in foreclosure rates. In addition, the R-Square value of 36% shows that there exists a good fit between the independent and the dependent variables. Using the independent 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-values in the case of assassinations and rev_coups are significantly higher than the threshold value of 5%. This indicates that these factors significantly influence growth. On the other hand, GRDP, trade share, and Years school have little significance also borne out by the correlation analysis. Because growth are very small numbers themselves, the coefficients appear as small numbers also but the effect is important if we look at these as percent changes in growth. The ‘goodness of fit’ of the regression is evident from Chart below, which shows the plot of actual and predicted values and the residuals. Preferred model Linear regression allows a better estimation of the trends, costs and other related factors between dependent (Y) and independent variable (X) as the method allows the presentation of data through a best-fit line. The reason due to which the line is termed as best fit is that the line minimizes the Sum of the Squared Errors of prediction and therefore the line formed after minimizing the sum of squares is likely to be more correct as compared to other methods. The error (Y – Y’) shown in this regression method is the difference found between the value of the dependent variable determined through regression (Y’) and the actual value (Y). Due to this, it is comparatively easy to identify the trends between the dependent and independent variables by means of the line passing through the points representing the standard errors. Other benefits associated with the application of linear regression are that, The method enables the determination of trends by providing a single slope; The data fit to the line is not biased, if it is considered that the deviations are randomly distributed with respect to the trend; The best fit allows the minimization of errors; and There is consistency in the trends shown by the line and it is therefore possible that whenever linear regression is applied over similar values, the results will always be same. Product Moment Correlation Coefficient: This coefficient has been developed by Karl Pearson. It is measures of the association between two variables, say X and Y. the value of this coefficient lies between -1 to +1. It is also called Pearson’s r. mathematically, it is presented as follows: (Maddala, 1977) r = [1/(n-1)]?{(Xi – X*)/sx}{(Yi – Y*)/sy, where X* and sx are mean and standard deviation of X and Y* and sy are mean and standard deviation of Y. The product moment correlation coefficient is related regression analysis through the coefficient of determination which is used in order to explain how appropriately a regression model fits a given set of data on X and Y. In a regression model where Y is regressed on X, if Y^ is the predicted value of Y, then correlation between Y and Y^ can be represented as Cor(Y, Y^) = var(Y^)/(sy * sy^) = sy^/ sy. The square of this correlation is nothing but coefficient of determination, commonly known as ‘R squared’. Regression coefficient: In building a regression model, regression coefficients pay a vital role. A regression coefficient is a value that tells the rate at which the hypothesized dependent variable would change following a change in independent variable. In a regression model, a regression coefficient is generally expressed by the term ?. Mathematically, the estimated value of it corresponding to the independent variable X is given as follows: (Maddala, 1977) ?^ = [?{(xi – x*)(yi – y*)}/?(xi – x*)2 Residual Analysis: Residual analysis is very important in a regression model. Given a set of data, a regression model is built to find out to what extent the value of dependent variable can be predicted by independent variable. For a given set of data, a regression model is built in such a way that the deviation of predicted values from the actual values is minimized. A residual analysis helps in finding out to what extent this deviation has been reduced by the regression model. If the value of residual sum of square after running a regression on a data set is found to be low, then it can be said that the model is efficient enough in predicting the value of the independent variable given the value of dependent variable t ratios and the significance level of the t ratios which is captured through P values is important for finding out significance of the independent variables of the regression equation explained in part a. If the values of t ratios with degrees of freedom (n-2) lies in the confidence interval considering 95 percent confidence level, and p values of the t ratios are found to be greater than 0.05, it can be said that the independent variables fails to significantly affect demand or vice versa. Conclusion This research attempted an analysis of the trend in economic growth of a country. The aim was to understand whether a relationship exists between growth trends and factors such as GRDP, trade share, Years school, assassinations and rev_coups. Overall, the empirical model developed from a brief review of earlier literature helps explain trends in growth rates. This analysis has thrown up several areas that require further research because the findings appear contrary to one would expect intuitionally. For example, rgpd ought to lead to financial success among citizens and affect their ability to meet commitments. Reference List Berk, R. A. 2003. Regression Analysis: A Constructive Critique. London : Sage. Stigler, S. M. 1981. Gauss and Intervention of Least Squares. The Annals of statistics, 9(3):465-474. Maddala, G. S. 1977. Economietrics. New York: McGraw Hill. Read More