Polishing our Co2 Model

By  Apresai Oghenemagan Kereokiye

     Kingsley Onuoha

     Yetunde Esan

     Nneka Iyabode Eze

     Abimbola Shode

MODEL SPECIFICATION

To determine the adequacy of our model we go beyond the p, t and F statistics performed above to examine the residuals, the Durbin – Watson statistics as well as the Regression Error Specification Test (RESET) test.

RESIDUAL PLOT

Figure 4 shows a plot of the residuals for our regression model.

Figure 4. Residual Plot.

The plot does not show any obvious pattern but nonetheless, we can see a little bit of systematic movement in the error terms. This indicates that our model could be mis-specified.

DURBIN – WATSON TEST

Using the square and the cube of the error terms, a Durbin – Watson test was performed with the null and alternative hypotheses as shown below;

Ho:  The model is adequately specified

Ha:  Model mis-specification exists.

Table 11 below summarizes the results of the test.

Table 11: Durbin –Watson statistics.

The critical values were obtained at T = 90 and K = 8,9,10 respectively for each model. The results show that our log - linear model is adequately specified. But it also suggests that a cubic model can possibly be a better functional form than the log-linear model.

RESET TEST

For a definitive statement about the specification of our model, we perform a Ramsey RESET test assuming a squared and a then a combination of a squared and a cubed explanatory variable.

The null and alternative hypotheses are stated below;

Ho: The model is adequately specified

Ha:  Model mis-specification exists.

Table 12 summarizes the results.

Table 12: Summary of the Ramsey RESET test.

 Based on the test we can observe that the F values of the squared and cubed models are greater than their respective critical values. As such, we can reject the null hypothesis that our model is adequately specified and make adjustments to the model.

NUTSHELL:

This is the 4th instalment in a 5-part series which seeks to employ a quantitative approach to investigating the impact of OECD and EU membership on Carbon (CO2) Emissions. In the third instalment, investigations revealed that though the model variables are overall statistically significant, there existed some mis-specifications in the model. In this installment, Abimbola has been able to establish via durbin-watson and Ramsey RESET tests that the model is adequately specified but will need slight adjustments. To view Abimbola's professional profile and for more information on this article please click here.-->