Model of the Gross Domestic Production - Case Study Example

Introduction: This paper focuses on the estimation of a model that states what determines the gross domestic production. The variables considered in this analysis include the GDP level, exports, foreign direct investment, domestic investment and inflation. The data used is for the period 1970 to 2002 regarding the UK economy; series include gross domestic production, exports, foreign direct investment, domestic investment and inflation which is all in log. Estimation of the models uses the Eviews statistical program. The estimated model must meet all the assumptions of OLS (ordinary least square method) method, due to the nature of the data which in this case is time series data there is a high possibility of the occurrence of autocorrelation, the existence of autocorrelation will violate the assumptions of the OLS estimation method and therefore our model will not be BLUE. The existence of autocorrelation in our estimation is determined using the Durbin Watson test and the Breusch Godfrey test to check for first order correlation. Autocorrelation however has its own remedies and one of the remedies involves time lagging variables also known as general least square method, this method involves replacement of the model with the serially correlated error term with a model with a serially independent error term. This paper focuses on the estimation of three models which are stated as follows: Model 1 LGDPt = 1 + 2LXt + 3LFDIt + 4LDIt+5INF Model 2 LGDPt = 1 + 20LXt + 21LXt–1 + 30LFDIt + 31LFDIt–1 + 40LDIt + 41LDIt–1 + 50INFt + 51INFt–1 + 5LGDPt–1 + ut Model 3 LGDPt = 1 + 20LXt + 21LXt–1 + 30LFDIt + 31LFDIt–1 +40LDIt + 41LDIt–1 + 5LGDPt–1 + ut Results: Model 1 Estimation of the model one LGDPt = 1 + 2LXt + 3LFDIt + 4LDIt+5INF involves the use of the data for the period 1970 to 2002 regarding the UK economy, estimation of the above model using Eviews had the following results: LGDPt = 11.15785+ 0.366704LXt - 0.006544LFDIt + 0.265253LDIt - 0.001313INF From the results of the correlation of determination R squared which is equal to 0.99229 we can conclude that 99.22% of variations in LGDP are explained by the independent variables, this shows a very strong relationship between the dependent and the independent variables. From the results if we hold all other factors constant and the level of LX, LFDI, LDI and INF are equal to zero then the level of LGDP will be equal to 11.158 which is also our autonomous value, we can explain the coefficient of the log of exports by stating that if we hold all other factors constant and increase the level of LX by one unit then the level of LGDP will increase by 0.366704 units, also if we hold all other factors constant and increase the level of LFDI by one unit then the level of LGDP will decrease by 0.006544 units. If we also hold all the other factors constant and increase the level of LDI by one unit then the level of LGDP will increase by 0.265253 units, finally if we hold all factors constant and increase the level of INF by one unit then the level of LGDP will decline by 0.00131. Having explained the coefficients of the estimated model we can conclude that if we increase the level of exports and domestic investment then the level of gross domestic product will increase, on the other hand an increase in the level of inflation and foreign direct investment will reduce the level of gross domestic production. Statistical significance: Our estimated coefficients may be statistically significant of statistically insignificant, for this reason there is a need to undertake hypothesis test to determine their significance in the model, a two tail T test at 95% level of test showed the following results: 95% TEST LEVEL VARIABLE coefficient null hypothesis alternative hypothesis T calculated T critical reject or accept null C B1 B1=0 B1≠0 14.3179 2.04841 REJECT INF B2 B2=0 B2≠0 -1.459259 2.04841 ACCEPT LDI B3 B3=0 B3≠0 5.183639 2.04841 REJECT LFDI B4 B4=0 B4≠0 -1.010641 2.04841 ACCEPT LX B5 B5=0 B5≠0 13.04894 2.04841 REJECT From the above test of hypothesis it is clear that at 95% test level the autonomous value, LDI coefficient and LX coefficient are statistically significant following the rejection of the null hypothesis that they are equal to zero, the rest of the coefficient which include the INF coefficient and the LFDI coefficient are not statistically significant at the 95% level of test, this follows the acceptance of the null hypothesis that they are equal to zero. Despite the two coefficients that are not statistically significant in the model we can still use the model to forecast, this is due to the strength of the model portrayed by the correlation of determination r squared which shows that 99% of variations in the dependent variables is explained by the independent variables. Hypothesis test: LGDPt = 1 + 2LXt + 3LFDIt + 4LDIt+5INF LGDPt = 11.15785+ 0.366704LXt - 0.006544LFDIt + 0.265253LDIt - 0.001313INF The export (LX) coefficient: Null hypothesis 2 = 0 Alternative hypothesis 2 > 0 The test T calculated = B2 / SB2 T calculated = 0.366704/0.028102 T calculated = 13.049036 A two tail test At 95% test level T critical from the T table taking into consideration degrees of freedom due to the 5 coefficients in the model therefore degrees of freedom for the test will be 33 – 5 = 28, therefore: T critical = 2.04841 Because our T calculated is greater than our T critical we reject the null hypothesis and accept the alternative hypothesis, therefore the coefficient of LX is statistically significant. The foreign direct investment (LFDI) coefficient: Null hypothesis 3 = 0 Alternative hypothesis 3 > 0 The test T calculated = B3 / SB3 T calculated = -0.006544/0.006475 T calculated = -1.010641 A two tail test At 95% test level T critical from the T table taking into consideration degrees of freedom due to the 5 coefficients in the model therefore degrees of freedom for the test will be 33 – 5 = 28, therefore: T critical = 2.04841 Because our T calculated is less than our T critical we accept the null hypothesis and reject the alternative hypothesis, therefore the coefficient of LFDI is not statistically significant. The domestic investment (LDI) coefficient: Null hypothesis 4 = 1 Alternative hypothesis 4 > 1 The test T calculated = B4 - 1 / SB4 T calculated = (0.265253 – 1)/ 0.051171 T calculated = -0.734747/ 0.051171 T calculated = -14.35866018 A two tail test At 95% test level T critical from the T table taking into consideration degrees of freedom due to the 5 coefficients in the model therefore degrees of freedom for the test will be 33 – 5 = 28, therefore: T critical = 2.04841 Because our T calculated is greater than our T critical we reject the null hypothesis and accept the alternative hypothesis, therefore we reject the hypothesis that 4 = 1 and accept that 4 > 1. The Inflation (INF) coefficient: Null hypothesis 5 = 0 Alternative hypothesis 5 < 0 The test T calculated = B5/ SB5 T calculated = -0.001313/ 0.000899 T calculated = -1.459259 A two tail test At 95% test level T critical from the T table taking into consideration degrees of freedom due to the 5 coefficients in the model therefore degrees of freedom for the test will be 33 – 5 = 28, therefore: T critical = 2.04841 Because our T calculated is less than our T critical we accept the null hypothesis and reject the alternative hypothesis, therefore we accept the hypothesis that 5 = 0 and accept that 5 < 0. Autocorrelation: The Durbin Watson test is a test used to determine the presence of autocorrelation, it is a problem which occurs in time series data, and the test involves the calculation of a value d which is estimated as follows: ∑ (et – et-1)2 D = _____________ ∑et2 The value of D derived from the above function usually lies between the number 0 and 4, a d value of 2 indicates that there exist no autocorrelation, if the d value is less than two then there is positive correlation, however if the value is greater than two this shows negative correlation, in our case the value of d from the Eviews estimate is 0.646833 showing that our error terms in the model are correlated. The presence of autocorrelation violates the OLS estimation assumptions, for this reason therefore the existence of autocorrelation leads to our conclusion that the estimates are not BLUE, meaning best linear unbiased estimates. Model two: This involves the estimation of the model that involves variables that are time lagged as follows: LGDPt = 1 + 20LXt + 21LXt–1 + 30LFDIt + 31LFDIt–1 + 40LDIt + 41LDIt–1 + 50INFt + 51INFt–1 + 5LGDPt–1 + ut This model includes the addition of other variables which include time lagged exports(LXt-1), foreign direct investment(LFDIt_1), time lagged domestic investment(LDIt–1) time lagged inflation (INFt–1 ) and time lagged gross domestic production (5LGDPt–1 ). When we time lag these variables we will have 32 variables and not 33 variables this is because when we lag the first year which is 1970 then the first year lagged variable is unknown so we need to start at 1971 in order to have complete data. Results of the estimated model using eveiws are as follows: LGDPt = 3.251747 + 0.068721 LXt + 0.011649 LXt–1 + 0.001123 LFDIt - 0.003232 LFDIt–1 + 0.250335 LDIt -0.156964 LDIt–1 - 0.001963 INFt + 0.000493 INFt–1 + 0.719464 LGDPt–1 From the above estimated model it is clear that if we hold all other factors constant and all independent variables are equal to zero then the level of LGDP will be 3.251747, if we hold all other factors constant and increase level of exports (LX) by one unit then the level of LGDP will increase by 0.068721, also if we hold all other factors constant and the previous level of LX increase by one unit then the level of LGDP will increase by 0.011649. the level of foreign direct investment and the previous level will also affect the level of LGDP, is we hold all factors constant and increase level of LFDI by one unit then the LGDP will increase by 0.001123 however if the previous level of LFDI increase by one unit then the level of LGDP will reduce by 0.003232, the previous level of LGDP has a positive sign in the model meaning that if we increase the previous LGDP level by one unit then the level of LGDP will increase by 0.719464 units. Autocorrelation: From our estimated value using the Durbin Watson test it is clear that the value of d = 2.026241 showing that there is still autocorrelation, this is because the value of d =2 shows no autocorrelation in our model, however our estimate exceeds this value. For this reason therefore because the estimated model violates the assumptions of OLS then the estimates are not BLUE. Model 3: This model is similar to model two but this model does not inflaude inflation or lagged inflation independent variable, the model estimated is as follows: LGDPt = 1 + 20LXt + 21LXt–1 + 30LFDIt + 31LFDIt–1 +40LDIt + 41LDIt–1 + 5LGDPt–1 + ut. After estimation the results of this model is as follows: LGDPt = 2.322694+ 0.137682LXt -0.054333LXt–1 -0.002289LFDIt -0.004492LFDIt–1 + 0.278083LDIt -0.185637LDIt–1 + 0.750794LGDPt–1 Having estimated outr model we can test for autocorrelation using the Durbin Watson test, the test give us a value of d = 1.959, if we round off this value to the nearest whole number then the value is 2 and we can conclude that this model does not show the existence of autocorrelation, for this reason therefore we can conclude that this model is BLUE because it does not violate the assumptions of OLS estimation. Conclusion: From our estimated models it is clear that the best model to use in the estimation of gross domestic production is the final model that involves time lagged variables in the absence of inflation, this is because the probability of the existence of autocorrelation in this model from the Durbin Watson test shows that this model has no correlation, for this reason therefore the final model is the best because it is BLUE. References: Bluman A. (2000) Elementary Statistics: A Step by Step Approach, McGraw Hill press, New York Patton M. (1990) Qualitative evaluation and research method, Sage publishers, Newbury Appendixes: Estimation 1: Dependent Variable: LGDP Method: Least Squares Date: 04/12/08 Time: 01:28 Sample: 1970 2002 Included observations: 33 Variable Coefficient Std. Error t-Statistic Prob.   C 11.15785 0.779293 14.31790 0.0000 INF -0.001313 0.000899 -1.459259 0.1556 LDI 0.265253 0.051171 5.183639 0.0000 LFDI -0.006544 0.006475 -1.010641 0.3208 LX 0.366704 0.028102 13.04894 0.0000 R-squared 0.992292     Mean dependent var 27.56269 Adjusted R-squared 0.991191     S.D. dependent var 0.216879 S.E. of regression 0.020355     Akaike info criterion -4.812252 Sum squared resid 0.011601     Schwarz criterion -4.585509 Log likelihood 84.40216     F-statistic 901.1990 Durbin-Watson stat 0.646833     Prob(F-statistic) 0.000000 Estimation 2: Dependent Variable: LGDP Method: Least Squares Date: 04/12/08 Time: 01:32 Sample (adjusted): 1 32 Included observations: 32 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   C 3.251747 1.328749 2.447224 0.0228 INF -0.001963 0.000666 -2.946612 0.0075 INFT_1 0.000493 0.000667 0.738533 0.4680 LDI 0.250335 0.051932 4.820457 0.0001 LDIT_1 -0.156964 0.056338 -2.786108 0.0108 LFDI 0.001123 0.003823 0.293811 0.7717 LFDIT_1 -0.003232 0.004046 -0.798710 0.4330 LGDPT_1 0.719464 0.110128 6.532978 0.0000 LX 0.068721 0.071608 0.959683 0.3476 LXT_1 0.011649 0.075604 0.154077 0.8790 R-squared 0.997893     Mean dependent var 27.57356 Adjusted R-squared 0.997031     S.D. dependent var 0.211029 S.E. of regression 0.011498     Akaike info criterion -5.842928 Sum squared resid 0.002909     Schwarz criterion -5.384885 Log likelihood 103.4868     F-statistic 1157.767 Durbin-Watson stat 2.026241     Prob(F-statistic) 0.000000 Estimation 3: Dependent Variable: LGDP Method: Least Squares Date: 04/12/08 Time: 01:35 Sample (adjusted): 1 32 Included observations: 32 after adjustments Variable Coefficient Std. Error t-Statistic Prob.   C 2.322694 1.339033 1.734605 0.0956 LDI 0.278083 0.052720 5.274759 0.0000 LDIT_1 -0.185637 0.062068 -2.990870 0.0063 LFDI -0.002289 0.004104 -0.557712 0.5822 LFDIT_1 -0.004492 0.004350 -1.032660 0.3121 LGDPT_1 0.750794 0.123053 6.101389 0.0000 LX 0.137682 0.076493 1.799921 0.0845 LXT_1 -0.054333 0.082150 -0.661392 0.5147 R-squared 0.997034     Mean dependent var 27.57356 Adjusted R-squared 0.996169     S.D. dependent var 0.211029 S.E. of regression 0.013062     Akaike info criterion -5.625897 Sum squared resid 0.004095     Schwarz criterion -5.259463 Log likelihood 98.01435     F-statistic 1152.491 Durbin-Watson stat 1.959273     Prob(F-statistic) 0.000000 Read More