1. Specific to General Modelling The traditional approach to econometrics modelling was as follows: 1.Start with an equation based on economic theory. 2.Estimate the equation using an appropriate technique (OLS, IV or something else). 3. Check the equation for statistical problems using diagnostic tests for serial correlation, heteroscedasticity etc. 4. If the equation fails the tests then respecify it. 5. Continue until the equation performs satisfactorily.

2. Problems with the specific to general approach 1. If the equation is misspecified then statistical inference based on it will be unreliable. 2. Misspecification of one type may produce failure in multiple diagnostic tests. 3. There may be a number of ways to respecify an equation and it is not automatically clear which one should be used.

3. Suppose the true model is: but we estimate: OLS estimates will be biased unless cov(X i1,X i2 ) = 0. Moreover since: the errors will not have the Gauss-Markov properties and we cannot rely on inference based on OLS estimation.

4. General to Specific Modelling General to specific modelling is an alternative modelling strategy. In GS modelling we: 1. Begin with a very general model including as many lags as possible 2. Simplify the model by eliminating insignificant variables to obtain a parsimonious specification. 3. Rewrite the final specification in error correction form to make it easier to interpret.

5. Advantages of the General to Specific Strategy 1. Because the initial model is very general, it is less likely that it will be misspecified. 2. The specification search procedure allows the data to determine the shape of the distributed lag relationship. 3. Because we test for misspecification at each stage, the final model provides a balance between obtaining a well specified model and a parsimonious specification.

6. It is important to look for the most parsimonious specification which is consistent with the data because including irrelevant variables leads to inefficient estimates. Suppose the true model is: but we include an irrelevant variable X 2 in the regression. We can show that: where r 12 is the sample correlation coefficient for the two X variables.

7. General Model

8. Parsimonious Specification

9. How do we choose the best model? R 2 can be misleading because it will always increase as we add extra regressors even if they are irrelevant. The adjusted R 2 penalises insignificant regressors. This statistic is always less than the usual coefficient of determination. It may fall as insignificant regressors are added and may even be negative for very poorly fitting models.

10. Other model selection criteria The log-likelihood is based on the residual sum of squares: The log-likelihood will always increase as we add extra regressors. However, there are statistics based on the log- likelihood which penalise insignificant regressors.