Economics Essays

Introduction

The model which is to be developed is real GDP in the UK. From such a series of real values, it is straightforward to calculate year-on-year growth of GDP.

Selection of variables

To model GDP, key factors identified by Easton (2004) include labour costs, savings ratio, taxation issues, inflation and terms of trade. However, many of these variables are not available for the required 40 year time span.

The variables eventually chosen and the justification were as follows:

GDP: the dependent variable, measured at 1950 prices. As GDP deflator figures were not 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 expected to increase 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 more than four independent 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 proportion of GDP attributable to manufacturing.^[1]

Labour: 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 each of the independent variables is sown in Appendix 1. These diagrammes support each of the hypotheses outlined above.

Main results

The regression equation produced by EViews, once the energy variable is excluded, is as follows:

GDP = -73223.22384 + 1.062678514*EXIM – 0.1391051564*LABOUR + 1.565374397*POPN

The 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.

Each 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 test 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.

The 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 are:

D_L = 1.383 D_U = 1.666

The DW statistic calculated by EViews is 0.746, which is below DL. This results leads us to infer that there is no positive autocorrelation in the model. This is an unlikely result, given that we are dealing with increasing variables over time, but we shall examine the issue of autocorrelation in detail later on.

Multicollinearity

Ideally, 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 particularly 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 Variables

Analysis of Residuals

Overview

The following graph shows the relationship between actual, fitted and residual values. At first 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 version of this graph may be found at Appendix 2.

Heteroscedascicity

To examine the issue of heteroscedascicity more closely, we will employ White’s 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.

The 5% critical value for chi-squared with nine degrees of freedom is 16.919, whilst the computed value of White’s statistic is 10.44. We may therefore conclude that, on the basis of the White test, there is no evidence of heteroscedascicity.

Autocorrelation

The 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, Gujarati’s 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.

The results of the Q statistic indicate that the data 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 growth in the UK’s 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.

We 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 order autocorrelation. By contrast, second order autocorrelation does not appear to be present in the model.

Overcoming serial correlation

A method to overcome the problem of nonstationarity is to undertake a difference of the dependent variable (ie GDP_year1 – GDP_year0) An initial attempt to improve the equation by using this differencing method produced a very poor result, as can be seen below.

Forecasting

The 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 short 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 forecasting

GDP 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 approach:

–a 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 years;

–transformation of variables: a logarithmic or other transformation should be trialled to ascertain 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 made in this paper was particularly unsuccessful!

Approximate word count, excluding all tables, charts and appendices: 1,400 Appendix 1 – Scatter diagrammes of GDP against dependent variables

Appendix 2

obs	Actual	Fitted	Residual	Residual Plot
1960	17460.5	15933.8	1526.78	| . | * |
1961	17816.1	16494.5	1321.57	| . | *. |
1962	17883.8	16714.1	1169.67	| . | * . |
1963	18556.7	18153.6	403.108	| . |* . |
1964	19618.0	19117.8	500.191	| . | * . |
1965	20209.7	19558.9	650.773	| . | * . |
1966	20699.1	20272.1	426.905	| . |* . |
1967	21303.1	20973.3	329.754	| . |* . |
1968	22037.1	22395.3	-358.204	| . *| . |
1969	22518.6	22824.6	-305.982	| . *| . |
1970	23272.7	23147.8	124.912	| . * . |
1971	23729.9	23395.8	334.070	| . |* . |
1972	24806.3	22418.6	2387.67	| . | . * |
1973	26134.9	27249.5	-1114.60	| . * | . |
1974	25506.2	28880.9	-3374.64	| * . | . |
1975	25944.6	28401.8	-2457.14	| * . | . |
1976	26343.7	30306.2	-3962.47	|* . | . |
1977	26468.8	29829.1	-3360.31	| * . | . |
1978	28174.4	29922.0	-1747.61	| * | . |
1979	29232.7	27846.9	1385.71	| . | *. |
1980	28957.2	29271.0	-313.855	| . *| . |
1981	28384.0	29590.8	-1206.86	| .* | . |
1982	28626.2	29526.2	-899.933	| . * | . |
1983	29915.3	30883.9	-968.627	| . * | . |
1984	30531.7	29677.7	853.960	| . | * . |
1985	31494.3	33289.4	-1795.09	| * | . |
1986	32748.5	33293.0	-544.520	| . * | . |
1987	34609.2	34223.2	385.976	| . |* . |
1988	36842.2	34669.4	2172.76	| . | . * |
1989	37539.8	35938.6	1601.20	| . | * |
1990	37187.7	35988.5	1199.22	| . | *. |
1991	36922.2	35080.4	1841.84	| . | .* |
1992	37116.4	35793.7	1322.74	| . | *. |
1993	38357.7	38051.2	306.418	| . |* . |
1994	39696.7	39790.8	Share this: Facebook  Twitter  Reddit  LinkedIn  WhatsApp   Cite This Work To export a reference to this article please select a referencing stye below: APA MLA MLA-7 Harvard Vancouver Wikipedia OSCOLA Copy to Clipboard  Related Services View all  Essay Writing Service From £124 Dissertation Writing Service From £124 Assignment Writing Service From £124 DMCA / Removal Request If you are the original writer of this essay and no longer wish to have your work published on UKEssays.com then please: Request the removal of this essay Related Services Our academic writing and marking services can help you! Find out more about our Essay Writing Service  Dissertation Writing Service  Assignment Writing Service  Marking Service  Samples of our Service  Full Service Portfolio  Related Lectures Study for free with our range of university lectures! Accounting Lectures  Business Lectures  Economics Lectures  Finance Lectures  All Available Lectures  Freelance Writing Jobs Looking for a flexible role? Do you have a 2:1 degree or higher? Apply Today! Study Resources Free resources to assist you