Calculating Year-On-Year Growth of GDP

Calculating Year-On-Year Growth of gross domestic productIntroductionThe framework which is to be developed is real gross domestic product in the UK. From such a series of real mensurates, it is straightforward to calculate year-on-year emergence of GDP.Selection of volt-ampereiablesTo assume GDP, key factors identified by Easton (2004) include labour costs, savings ratio, receipts acts, inflation and terms of trade. However, many of these variables ar non available for the indispensable 40 year time span.The variables eventually chosen and the justification were as followsGDP the drug-addicted variable, heartbeatd at 1950 prices. As GDP deflator figures were non available back to 1960, the eventual starting point of the analysis, the RPI inflation measure was used to convert 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 pass judgment to increase as GDP also increas es. The RPI deflator was also used for this series. keep down trade was plasced into one variable was to abide by the constraint of no more than four in unfree variables.Energy energy consumption was calculated as production plus imports minus exports in tonnes of oil equivalent. As energy use increases, we would expect to see an increase in the coincidence of GDP attributable to manufacturing.1Labour this variable is the total number of years lost through disputes. We would expect this variable to have a disconfirming coefficient, since an increase in the number of days lost go forth transcend to a reduction of GDP.Scatter diagrammes showing the relationship between the bloodsucking variable GDP and each of the free-lance variables is sown in appurtenance 1. These diagrammes support each of the hypotheses outlined above.Main resultsThe regress equation produced by EViews, once the energy variable is excluded, is as followsGDP = -73223.22384 + 1.062678514*EXIM 0.13910515 64* excavate + 1.565374397*POPNThe correct R2 is compeer to 0.978 or, 97.8% of the variation in GDP is accounted for by the variation in EXIM, LABOUR and POPN.Each of the coefficients of the three in underage variables, EXIM, LABOUR and POPN, have t-statistics sufficiently high to worsen the null hypothesis that any of the coefficients is equal to energy in other words, each variable makes a signifi give the axet section to the overall equation.To test the overall fit of the equation, the F value of 703 allows us similarly to reject the hypothesis that the coefficients atomic number 18 simultaneously all equal to zero.Dependent inconsistent GDPMethod to the lowest degree Squ atomic number 18sDate 04/15/08 period 0910Sample 1960 2006Included observations 47VariableCoefficientStd. computer errort-StatisticProb.C-73223.2223204.60-3.1555480.0029EXIM1.0626790.1174459.0482970.0000LABOUR-0.1391050.036951-3.7645850.0005POPN1.5653740.4435413.5292700.0010R-square0.980046Mean depende nt var32813.25 adjusted R-squared0.978654S.D. dependent var10905.60S.E. of regression1593.331Akaike info touchstone17.66631 jibe squared resid1.09E+08Schwarz criterion17.82377Log likelihood-411.1582F-statistic703.9962Durbin-Watson stat0.746519Prob(F-statistic)0.000000The Akaike and Schwartz criteria are used principally to equate two or more models (a model with a swallow value of either of these statistics is preferred). As we are analysing only one model here, we will not discuss these two shape up.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 below DL. This results leads us to infer that at that place is no positive auto correlational statistics in the model. This is an unlikely result, effrontery that we are dealing with increasing variables over time, but we shall run across the issue of autocorrelation in detail later on.MulticollinearityIdeally, there should be little or no significant correlation between the dependent variables 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 specially high level of correlation (the removal of the ENERGY variable primordial 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 entropy being honord (indeed, section 10.4 of his book is entitled Multicollinearity much hassle 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 eternal rest values. At fir st glance, the residuals appear to be reasonably well behaved the values are not increasing over time and there several points at which the residual switches from positive to negative. A more detailed tabular adjustment of this graph may be found at Appendix 2.HeteroscedascicityTo examine the issue of heteroscedascicity more closely, we will employ snowys test. As we are using 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 probability0.339611Obs*R-squared10.44066Probability0.316002Test EquationDependent Variable RESID2Method Least SquaresDate 04/16/08 Time 0824Sample 1960 2006Included observations 47VariableCoefficientStd. wrongdoingt-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*POPN0.9821650.8791511.1171740.2711LABO UR-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 liberty 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 specially interested to see if successive residual values are related to prior values.To determine autocorrelation, Gujar atis linguistic rule of thumb of using between a third and a pull back of the length of the time series was used. In this particular case, a cast out 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 info is nonstationary in other words, the mean and standard deviation of the data do indeed vary over time. This is not a surprising result, given off lo t in the UKs economy and population since 1960.A further test available to test for autocorrelation is the Breusch-Godfrey test. 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 implant 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)0.0002 25We can observe from the results above that RESID(-1) has a high t value. In other words, we would reject the hypothesis of no first consecrate autocorrelation. By contrast, second order autocorrelation does not appear to be present in the model.Overcoming serial correlationA method to overcome the problem of nonstationarity is to undertake a variation of the dependent variable (ie GDPyear1 GDPyear0) An initial attempt to improve the equation by using this differencing method produced a very poor 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 stat1.401626Prob(F-statistic)0.044754ForecastingThe forecasts for the dependent variables are establish 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 entangle to be particularly unrealistic, so a sensitivity test was employ to EXIM (population growth is relatively certain in the unretentive term and reason 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 for ecast growth is significantly lower in 2008 and 2009 as a result.Critical rating of the econometric approach to model building and forecastingGDP 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 highly 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 adoptive for productivity and cost per labour hour, but this is unavailable over 40 years regeneration of variables a logarithmic or other transformation should be trialled to ascertain if some of the problems observed, such as autocorrelation, could be rationalize to any extent. The other, more relevant transformation is to undertake differencing of the data to wrap up autocorr elation the one attempt made in this paper was particularly ruinedApproximate word count, excluding all tables, charts and appendices 1,400 Appendix 1 Scatter diagrammes of GDP against dependent variablesAppendix 2obsActualFittedResidualResidual piece196017460.515933.81526.78 . * 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