Model Selection: Introduction to gretl Functions
Choosing an appropriate model is part art and part science. Omitting relevant variables that are correlated with regressors causes least squares to be biased and inconsistent. Including irrelevant variables reduces the precision of least squares. So, from a purely technical point, it is important to estimate a model that has all of the necessary relevant variables and none that are irrelevant. It is also important to use a suitable functional form. There is no set of mechanical rules that one can follow to ensure that the model is correctly specified, but there are a few things you can do to increase your chances of having a suitable model to use for decision-making.
Here are a few rules of thumb:
1. Use whatever economic theory you have to select a functional form. For instance, if you are estimating a short-run production function then economic theory suggests that marginal returns to factors of production diminish. That means you should choose a functional form that permits this (e. g., log-log).
2. If the estimated coefficients have the wrong signs or unreasonable magnitudes, then you probably want to reevaluate either the functional form or whether relevant variables are omitted.
3. You can perform joint hypothesis tests to detect the inclusion of irrelevant sets of variables. Testing is not fool-proof since there is always positive probability that type 1 or type 2 error is being committed.
4. You can use model selection rules to find sets of regressors that are ‘optimal’ in terms of an estimated bias/precision trade-off.
5. Use a RESET test to detect possible misspecification of functional form.
In this section, I will give you some gretl commands to help with the last two: model selection and RESET.
In this section we consider three model selection rules: R2, AIC, and SC. I’m not necessarily recommending that these be used, since there are plenty of statistical problems caused by using the sample to both specify, estimate, and then test hypotheses in a model, but sometimes you have little other choice. Lag selection discussed later in this book is a reasonable application for these.