Econometric analysis of the general linear model with Gretl

Estimation and validation of an econometric model

The following analysis will address factors that influence the price of gold. The observations are obtained from the database that has Gretl, but more specifically, it is an example from Gujarati where the price of gold, PRICE, is estimated from the same consumer index, CPI, and the New York Stock Exchange, NYSE. The estimate obtained is:

PRICE = 5'81097 CPI + 1'89673 NYSE,   R-squared = 0'9455, R-corrected = 0'9413.

After such an estimate we can see the actual values of the price of gold, the estimates and the estimated residuals so that it may represent the first two together and the third.

This is followed by the contrast of normality of residuals. In this case, since the p-value is less than 0.05, the hypothesis of normality is null. Therefore, in this case there is no normality in the model, so there can be no inference in it and therefore it would not be feasible to draw legitimate conclusions from the adjustment made.

However, as an example, let’s assume that normality was obtained in the residuals and move on to interpreting the various tests on the parameters and model. With respect to the p-values associated with the individual significance contrasts, we have them both at less than 0.05, so we reject the null hypothesis that the coefficients of the independent variables are zero. That is to say, both the consumer index and the stock market affect the price of gold. Moreover, as the estimated coefficients are positive, as the independent variables increase, so do the dependent ones. These conclusions can also be reached from each coefficient’s confidence intervals since, as you can see, none of the intervals contain zero. Finally, the p-value associated with the ANOVA contrast is also lower than 0.05, so we reject the null hypothesis that all regressors are zero simultaneously. Therefore, you could argue that the model is valid because it can be confirmed that there is some kind of association, which is not due to chance, between the independent and dependent variables. Mentioning that both the coefficient of determination and that corrected are quite high, the correction made explains about 94% of the variability in the price of gold.

Note that this example shows that the conclusions drawn are valid provided that the underlying hypotheses are verified. In this case, neither the hypotheses or the-normality of residuals are verified, but even if they came true, we would have to analyze the possible existence of heteroscedasticity and autocorrelation. While not all the basic hypotheses are verified, the conclusions drawn will be put in doubt.