Economic Growth of the United Kingdom Since 1970 - Essay Example

Economic Growth of the United Kingdom, 1970-2002 I. Introduction In this investigation, we apply econometrics to national income function Y = C+ I + G + (X – M) which is a basic model in macroeconomics. Following Gujarati (2004: 175), the national income function can have a logarithmic format and, therefore, it is possible to express the function in logarithm or log Y = a+log C+logI+logG+logX+logM where a is a constant. The logarithms pertain to natural logarithms. We express Y in terms of the gross national product. Meanwhile, I or investment can either be measured as domestic investment or domestic investment (DI) and foreign direct investment (FDI). We apply econometric techniques over the period 1970 to 2002, involving 33 observations. In our notation, LGDP is natural logarithm (ln) of real Gross Domestic Product, LC is the log of consumption, LDI is the log of domestic investment, LX is the log of exports, LM is the log of imports, LG is the log of government expenditure and LFDI is the log of FDI. According to Gujarati (2004: 176-177), this model is called as the constant elasticity model that assumes a constant elasticity relationship between the independent variables and the dependent variable, logarithm of gross domestic product. The coefficients associated with the independent variables measure the elasticity of the dependent variable with respect to independent variables, or the percentage increase in the dependent variable (Gujarati 2004: 176). The methodology of this work is informed by the works of Woolridge 2004:2-6 as well as Gujarati 2004:10-12. II. Growth Models and Analysis 1. Economic Growth Model 1 We begin with economic growth model 1 in which the national income function Y=C+I+G+(X-M). In model 1, however, I = DI + FDI where DI = domestic investment and FDI = foreign direct investment. For model 1 and for the rest of model as well, we assume the existence of constant C in the regression. Otherwise, interpretation of the regression will be different without a slope (Gujarati 2004: 167-169). We need not worry on the interpretation of the constant in a regression because it need not always have an interpretation (Gujarati 2004: 167-169). Using Eviews, statistical software, we find out the empirical implementation of model 1. Model 1: LGDPt = 1 + 2LCt + 3LDIt +4LFDIt+C5LGt + 6LXt + 7LMt + ut We obtained Table 1 as the empirical implementation of model 1. Table 1. Regression via ordinary least square of model 1 Variable Coefficient Std. Error t-Statistic Prob.   C -0.984570 0.638140 -1.542875 0.1349 LC 1.006169 0.042372 23.74632 0.0000 LDI 0.182090 0.012388 14.69926 0.0000 LFDI -0.000538 0.001011 -0.531836 0.5994 LG -0.055379 0.032564 -1.700629 0.1009 LX 0.257777 0.017102 15.07332 0.0000 LM -0.343588 0.028081 -12.23571 0.0000 R-squared 0.999777     Mean dependent var 27.56267 Adjusted R-squared 0.999726     S.D. dependent var 0.216843 S.E. of regression 0.003593     Akaike info criterion -8.234063 Sum squared resid 0.000336     Schwarz criterion -7.916622 Log likelihood 142.8620     F-statistic 19425.91 Durbin-Watson stat 0.628918     Prob(F-statistic) 0.000000 Table 1 suggests that all regressor variables of the regression, except for LFDI and LG are significant at the 0.01 level. This means that for all coefficients, except LFDI and LG, we can reject the applicable null hypothesis that i =0 to accept alternative hypotheses that are consistent with economic theory. Based on the theory of the national income function in economics, we expect the signs to be as follows: 2>0, 3>0, 4>0, 5>0, 6>0, and 7 0. 2. Economic Growth Model 2 We develop model 2 by removing LFDI or the logarithm of foreign direct investment from the regression. The non-significance of LFDI indicates that LFDI is not significantly affecting LGDP or the logarithm of gross domestic product. It indicates that it is LDI or domestic investments that is significantly affecting LGDP not LFDI. Again, we used Eviews to determine the empirical implementation of model 2 below. Model 2: LGDPt = 1 + 2LCt + 3LDIt + 4LGt + 5LXt +6LMt + ut Table 2. Regression via ordinary least square of model 2 Variable Coefficient Std. Error t-Statistic Prob.   C -0.922271 0.618909 -1.490155 0.1478 LC 1.000000 0.040208 24.87054 0.0000 LDI 0.181102 0.012084 14.98690 0.0000 LG -0.051744 0.031413 -1.647229 0.1111 LX 0.255047 0.016095 15.84639 0.0000 LM -0.339901 0.026848 -12.66037 0.0000 R-squared 0.999775     Mean dependent var 27.56267 Adjusted R-squared 0.999733     S.D. dependent var 0.216843 S.E. of regression 0.003545     Akaike info criterion -8.283849 Sum squared resid 0.000339     Schwarz criterion -8.011756 Log likelihood 142.6835     F-statistic 23947.10 Durbin-Watson stat 0.634621     Prob(F-statistic) 0.000000 Similarly, we obtained Table 2 above as the empirical implementation of model 2. Based on the figures of Table 2, model 2 appears to be the better econometric model. Although the F and R2 of model 1 are as good as model 2, model 2 has a lower standard error of regression and can be described as more accurate than model 1. As in model 1, model 2 allows us to reject the null hypothesis that the coefficients are simultaneously equal to zero based on the F-statistics. It also allows us to reject the null hypothesis that R2 is equal to zero and accept that alternative hypothesis that R2 is greater than zero. Further, except for LG, the coefficients have signs consistent with the economic theory on national income. Except for LG and the constant, the coefficients are significant at the 0.01 level which would allow us to reject the null hypothesis that the value of the coefficients is zero to accept the alternative hypotheses consistent with their signs. Based on the Durbin-Watson test for autocorrelation outline in Gujarati 2004: 467-471, there is evidence that there is positive autocorrelation in model 2. Nevertheless, based on Gujarati 2004: 454, the regression remains BLU. However, the estimate are not efficient or that they will provide minimum variance. BLU means being best and linearly unbiased estimate or that they are “consistently and asymptotically distributed”. This being the case, we can rely on the regression to a certain extent especially because the standard error of the regression is small anyway. Meanwhile, following Gujarati (2004: 411-412), the Breusch-Godfrey test for autocorrelation was applied on regression model 2 and the Breusch-Godfrey test obtain a significance in the F-statistics of 0.019871. Adopting a critical alpha of 0.01 will not allow us to reject the null hypothesis of no autocorrelation of any order under the Breusch-Godfrey test. Thus, we have a good basis for claiming the reliability of regression model 2. Regression theory says that auto-correlation would make estimates still BLU but inefficient. 3. Economic Growth Model 3 Model 3 improves model 2 by decreasing further the standard error of the regression. All inferences made on the coefficients and regression for model 2 also applies to model 3. As in regression 2, the F-statistics indicate that the null hypothesis that the coefficients of the regressors are simultaneously equal to zero can be rejected to accept the alternative hypothesis that they are not equal to zero. Following this, the null hypothesis that R2 equals zero can be rejected to accept the alternative hypothesis that R2 is greater than zero. Model 3: LGDPt = 1 + 2LCt + 3LDIt + 4LXt + 5LMt +6LGt + 7LGDPt-1+ ut Table 3. Regression via ordinary least square of model 3 Variable Coefficient Std. Error t-Statistic Prob.   C -0.706029 0.670567 -1.052883 0.3025 LC 0.987796 0.051746 19.08927 0.0000 LDI 0.178674 0.012137 14.72191 0.0000 LG -0.071263 0.034925 -2.040456 0.0520 LX 0.253316 0.018048 14.03579 0.0000 LM -0.338057 0.027229 -12.41529 0.0000 LGDP(-1) 0.024906 0.037661 0.661304 0.5145 R-squared 0.999775     Mean dependent var 27.57353 Adjusted R-squared 0.999721     S.D. dependent var 0.210990 S.E. of regression 0.003525     Akaike info criterion -8.267045 Sum squared resid 0.000311     Schwarz criterion -7.946415 Log likelihood 139.2727     F-statistic 18502.78 Durbin-Watson stat 0.673530     Prob(F-statistic) 0.000000 Table 3 indicates that except for LG, the empirical implementation of model 3 leads to a regression function that has coefficients consistent with the economic theory on national income. Nevertheless, that LG is associated with negative signs need not always be contrary to theory because one perspective in economics says that government spending can lead to crowding out and can negatively affect economic growth. Although there is a 2-t rule of the thumb (Gujarati 2004: 129), the more appropriate interpretation is that we cannot reject the null hypothesis that coefficients 6 and 7 are both equal to zero. 4. Economic Growth Model 4 Table 4 next page results from the empirical implementation of model 4 that is described immediately following this paragraph. Based on the larger standard error of the regression of model 4, Table 4 indicates that models 3 and 2 appear to be the better models in terms of its ability to reduce the standard error of the regression Models 2 and 3 are therefore more accurate than model 4 depicted on Table 4. Model 4: LGDPt=1+2LCt+ 3LCt-1+ 4LDIt+ 5LDIt-1+6LGt+7LGt-1 +8X t+9X t-1+10LMt+ 11LM t-1+ut Table 4. Regression via ordinary least square of model 4 Variable Coefficient Std. Error t-Statistic Prob.   C -0.858540 0.634049 -1.354059 0.1901 LC 0.906045 0.050588 17.91019 0.0000 LC(-1) 0.141025 0.050380 2.799247 0.0107 LDI 0.170692 0.014055 12.14488 0.0000 LDI(-1) -0.002239 0.012858 -0.174138 0.8634 LG -0.066184 0.054000 -1.225626 0.2339 LG(-1) -0.014696 0.049679 -0.295827 0.7703 LX 0.260761 0.022474 11.60271 0.0000 LX(-1) -0.006634 0.022299 -0.297495 0.7690 LM -0.281856 0.029977 -9.402405 0.0000 LM(-1) -0.067385 0.029105 -2.315237 0.0308 R-squared 0.999881     Mean dependent var 27.57353 Adjusted R-squared 0.999825     S.D. dependent var 0.210990 S.E. of regression 0.002793     Akaike info criterion -8.657407 Sum squared resid 0.000164     Schwarz criterion -8.153560 Log likelihood 149.5185     F-statistic 17693.74 Durbin-Watson stat 1.309572     Prob(F-statistic) 0.000000 III. Summary and Conclusions Based on our discussion in Section II, model 2 can be chosen as the best empirical implementation of the national income model. Model 3 improves model 2 but the Breusch-Godfrey test on first order autocorrelation does not allow us to reject the null hypothesis of no first order autocorrelation on model 2, thereby removing the basis for adopting model 3 that assumes that there is first-order autocorrelation. Bibliography Gujarati, D., 2004. Basic econometrics. 4th Ed. New York & London: McGraw Hill Companies. Wooldridge, Jeffrey M., 2003. Introductory econometrics: A modern approach. 2nd edition. Cincinnati: South Western College Publishing. Read More