Calculating Year-On-Year Growth of GDP

Calculating Year-On-Year Growth of gross domestic productIntroductionThe model which is to be developed is real gross domestic product in the UK. From some(prenominal)(prenominal) a series of real hold dears, it is straightforward to calculate year-on-year development of GDP.Selection of variablesTo model GDP, key factors identified by Easton (2004) include hollow costs, savings ratio, tax revenue issues, inflation and terms of trade. However, many of these variables argon not available for the required 40 year sequence span.The variables eventually chosen and the justification were as followsGDP the mutualist variable, measured at 1950 prices. As GDP deflator figures were not available back to 1960, the eventual starting spirit level of the analysis, the RPI inflation measure was used to commute the series into real prices.Exim this variable is the sum of imports and exports, at constant 1950 prices. As a measure of trade volumes, EXIM would be expected to increment as GDP also increases. The RPI deflator was also used for this series. Total trade was plasced into one variable was to abide by the constraint of no much than four independent variables. brawn energy consumption was calculated as production plus imports minus exports in tonnes of oil equivalent. As energy use increases, we would expect to enamor an increase in the proportion of GDP attributable to manufacturing.1Labour this variable is the total number of days lost through disputes. We would expect this variable to have a negative coefficient, since an increase in the number of days lost will lead to a reduction of GDP.Scatter diagrammes showing the relationship between the dependent variable GDP and individually of the independent variables is sown in Appendix 1. These diagrammes support each of the hypotheses outlined above.Main resultsThe regression equation produced by EViews, at one time the energy variable is excluded, is as followsGDP = -73223.22384 + 1.062678514*EXIM 0.13910 51564*LABOUR + 1.565374397*POPNThe adjusted R2 is equal to 0.978 or, 97.8% of the variation in GDP is accounted for by the variation in EXIM, LABOUR and POPN. distributively of the coefficients of the three independent variables, EXIM, LABOUR and POPN, have t-statistics sufficiently high to reject the null hypothesis that any of the coefficients is equal to zero in other words, each variable makes a significant contribution to the overall equation.To trial the overall fit of the equation, the F value of 703 allows us similarly to reject the hypothesis that the coefficients are simultaneously all equal to zero.Dependent inconsistent GDPMethod least(prenominal) SquaresDate 04/15/08 Time 0910Sample 1960 2006Included observations 47 changeableCoefficientStd. Errort-StatisticProb.C-73223.2223204.60-3.1555480.0029EXIM1.0626790.1174459.0482970.0000LABOUR-0.1391050.036951-3.7645850.0005POPN1.5653740.4435413.5292700.0010R- shape0.980046Mean dependent var32813.25Adjusted R-square0.978654S. D. dependent var10905.60S.E. of regression1593.331Akaike info criterion17.66631Sum squared residual oil1.09E+08Schwarz criterion17.82377Log likelihood-411.1582F-statistic703.9962Durbin-Watson stat0.746519Prob(F-statistic)0.000000The Akaike and Schwartz criteria are used principally to compare two or more models (a model with a lower value of either of these statistics is preferred). As we are analysing only one model here, we will not discuss these two further.Using tables provided by Gujarati (2004), the upper and lower limits for the DW test areDL = 1.383 DU = 1.666The DW statistic calculated by EViews is 0.746, which is infra DL. This results leads us to infer that there is no positive auto correlation in the model. This is an unlikely result, given that we are relations with increasing variables over time, but we shall examine the issue of autocorrelation in detail later on.MulticollinearityIdeally, there should be little or no significant correlation between the dependent va riables if two dependent variables are perfectly correlated, then one variable is redundant and the OLS equations could not be solved.The correlation of variables table below shows that EXIM and POPN have a oddly high level of correlation (the removal of the ENERGY variable early on solved two other cases of multicollinearity).It is important, however, to point out that multicollinearity does not violate any assumptions of the OLS process and Gujarati points out the multicollinearity is a consequence of the data being observed (indeed, section 10.4 of his book is entitled Multicollinearity much ado about nothing?).Correlations of VariablesGDPEXIMPOPNENERGYGDP1.000000EXIM0.984644POPN0.9609600.957558ENERGY0.8350530.8362790.914026LABOUR-0.380830-0.320518-0.259193-0.166407Analysis of ResidualsOverviewThe following graph shows the relationship between actual, fitted and remnant values. At starting line glance, the residuals appear to be reasonably well behaved the values are not incre asing over time and there several points at which the residual switches from positive to negative. A more detailed tabular variant of this graph may be found at Appendix 2.HeteroscedascicityTo examine the issue of heteroscedascicity more closely, we will employ Whites test. As we are use a model with only three independent variables, we may use the version of the test which uses the cross-terms between the independent variables.White Heteroskedasticity TestF-statistic1.174056 hazard0.339611Obs*R-squared10.44066Probability0.316002Test EquationDependent Variable RESID2Method Least SquaresDate 04/16/08 Time 0824Sample 1960 2006Included observations 47VariableCoefficientStd. Errort-StatisticProb.C-2.99E+094.06E+09-0.7357440.4665EXIM-49439.9845383.77-1.0893760.2830EXIM2-0.1754280.128496-1.3652490.1804EXIM*LABOUR-0.0492230.047215-1.0425320.3039EXIM*POPN0.9821650.8791511.1171740.2711LABOUR-18039.8318496.29-0.9753220.3357LABOUR2-0.0184230.009986-1.8448490.0731LABOUR*POPN0.3446980.3364461. 0245260.3122POPN120773.0157305.50.7677610.4475POPN2-1.2175231.523271-0.7992820.4292R-squared0.222142Mean dependent var2322644.Adjusted R-squared0.032933S.D. dependent var3306810.S.E. of regression3251902.Akaike info criterion33.01368Sum squared resid3.91E+14Schwarz criterion33.40733Log likelihood-765.8215F-statistic1.174056Durbin-Watson stat1.306019Prob(F-statistic)0.339611The 5% critical value for chi-squared with nine degrees of freedom is 16.919, whilst the computed value of Whites statistic is 10.44. We may therefore conclude that, on the basis of the White test, there is no evidence of heteroscedascicity.AutocorrelationThe existence of autocorrelation exists in the model if there exists correlation between residuals. In the context of a time series, we are particularly interested to see if successive residual values are related to prior values.To determine autocorrelation, Gujaratis rule of thumb of using between a third and a quarter of the length of the time series was used. In this particular case, a lag of 15 was selected.Date 04/16/08 Time 0805Sample 1960 2006Included observations 47AutocorrelationPartial CorrelationACPACQ-StatProb. **** . **** 10.4940.49412.2340.000. *** . ** 20.4230.23721.4090.000. *. .* . 30.155-0.17122.6690.000. . .* . 40.007-0.14522.6720.000.* . .* . 5-0.109-0.06923.3190.000** . .* . 6-0.244-0.16026.6740.000** . . . 7-0.1940.03728.8450.000** . . . 8-0.202-0.00431.2470.000** . .* . 9-0.226-0.16234.3440.000** . .* . 10-0.269-0.18638.8590.000.* . . *. 11-0.1340.12240.0130.000.* . . . 12-0.0790.04740.4280.000.* . .* . 13-0.078-0.15140.8370.000. . . . 140.0130.02940.8490.000. . . . 150.0410.01840.9700.000The results of the Q statistic indicate that the data is nonstationary in other words, the mean and standard divergence of the data do indeed vary over time. This is not a surprising result, given growth in the UKs economy and population since 1960.A further test available to test for autocorrelation is the Breusch-Godfrey t est. The results of this test on the model are detailed below.Breusch-Godfrey Serial Correlation LM TestF-statistic15.53618Probability0.000010Obs*R-squared20.26299Probability0.000040Test EquationDependent Variable RESIDMethod Least SquaresDate 04/16/08 Time 0923Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C9294.87918204.510.5105810.6124EXIM0.0472920.0921760.5130650.6107LABOUR0.0391810.0310721.2609670.2144POPN-0.1822870.348222-0.5234790.6035RESID(-1)0.7880840.1541445.1126550.0000RESID(-2)-0.1802260.160485-1.1230090.2680R-squared0.431127Mean dependent var0.000100Adjusted R-squared0.361753S.D. dependent var1540.499S.E. of regression1230.710Akaike info criterion17.18731Sum squared resid62100572Schwarz criterion17.42350Log likelihood-397.9019F-statistic6.214475Durbin-Watson stat1.734584Prob(F-statistic)0.000225We can observe from the results above that RESID(-1) has a high t value. In other words, we would reject the hypothesis of no f irst order autocorrelation. By contrast, second order autocorrelation does not appear to be present in the model.Overcoming serial correlationA method to overcome the conundrum of nonstationarity is to undertake a difference of the dependent variable (ie GDPyear1 GDPyear0) An initial attempt to improve the equation by using this differencing method produced a very sad result, as can be seen below.Dependent Variable GDPDIFFMethod Least SquaresDate 04/16/08 Time 0817Sample 1961 2006Included observations 46VariableCoefficientStd. Errort-StatisticProb.C14037.5812694.291.1058180.2753EXIM0.0842870.0526011.6023980.1167ENERGY0.0114700.0117100.9794870.3331LABOUR-0.0042510.014304-0.2972300.7678POPN-0.3009420.265082-1.1352790.2629R-squared0.207408Mean dependent var816.6959Adjusted R-squared0.130082S.D. dependent var657.1886S.E. of regression612.9557Akaike info criterion15.77678Sum squared resid15404304Schwarz criterion15.97555Log likelihood-357.8660F-statistic2.682255Durbin-Watson stat1.401 626Prob(F-statistic)0.044754ForecastingThe forecasts for the dependent variables are based on Kirby (2008) and are presented below.The calculation of EXIM for future years was based upon growth rates for exports (47% of the 2006 total) and imports (53%) separately. The two streams were added together to produce the 1950 level GDP figure, from which year-on-year increases in GDP could be calculated. The results of the forecast are shown below.The 2008 figure was felt to be particularly unrealistic, so a sensitivity test was applied to EXIM (population growth is relatively certain in the myopic term and calculating a forecast of labour days lost is a particularly difficult challenge).Instead of EXIM growing by an average of 1.7% per annum during the forecast period, its growth was constrained to 0.7%. As we can see from the GDP2 column, GDP forecast growth is significantly lower in 2008 and 2009 as a result.Critical evaluation of the econometric approach to model building and progno sticationGDP is dependent on many factors, many of which were excluded from this analysis due to the unavailability of data covering forty years. Although the main regression results appear passing significant, there are many activities which should be trialled to try to improve the approacha shorter time series with more available variables using a short time series would enable a more intuitive set of variables to be trialled. For example, labour days lost is effectively a surrogate for productivity and cost per labour hour, but this is unavailable over 40 yearstransformation of variables a logarithmic or other transformation should be trialled to encounter if some of the problems observed, such as autocorrelation, could be mitigated to any extent. The other, more relevant transformation is to undertake differencing of the data to remove autocorrelation the one attempt do in this paper was particularly unsuccessfulApproximate word count, excluding all tables, charts and append ices 1,400 Appendix 1 Scatter diagrammes of GDP against dependent variablesAppendix 2obs existentFittedResidualResidual Plot196017460.515933.81526.78 . * 196117816.116494.51321.57 . *. 196217883.816714.11169.67 . * . 196318556.718153.6403.108 . * . 196419618.019117.8500.191 . * . 196520209.719558.9650.773 . * . 196620699.120272.1426.905 . * . 196721303.120973.3329.754 . * . 196822037.122395.3-358.204 . * . 196922518.622824.6-305.982 . * . 197023272.723147.8124.912 . * . 197123729.923395.8334.070 . * . 197224806.322418.62387.67 . . * 197326134.927249.5-1114.60 . * . 197425506.228880.9-3374.64 * . . 197525944.628401.8-2457.14 * . . 197626343.730306.2-3962.47* . . 197726468.829829.1-3360.31 * . . 197828174.429922.0-1747.61 * . 197929232.727846.91385.71 . *. 198028957.229271.0-313.855 . * . 198128384.029590.8-1206.86 .* . 198228626.229526.2-899.933 . * . 198329915.330883.9-968.627 . * . 198430531.729677.7853.960 . * . 198531494.333289.4-1795.09 * . 198632748.533293.0- 544.520 . * . 198734609.234223.2385.976 . * . 198836842.234669.42172.76 . . * 198937539.835938.61601.20 . * 199037187.735988.51199.22 . *. 199136922.235080.41841.84 . .* 199237116.435793.71322.74 . *. 199338357.738051.2306.418 . * . 199439696.739790.8