# Model Specification

There are several issues of model specification explored here. First, it is possible to omit relevant independent variables from your model. A relevant independent variable is one that affects the mean of the dependent variable. When you omit a relevant variable that happens to be correlated with any of the other included regressors, least squares suffers from omitted variable bias.

The other possibility is to include irrelevant variables in the model. In this case, you include extra regressors that either don’t affect y or, if they do, they are not correlated with any of the other regressors. Including irrelevant variables in the model makes least squares less precise than it otherwise would be-this increases standard errors, reduces the power of your hypothesis tests, and increases the size of your confidence intervals.

The example used in the text uses the dataset edu-inc. gdt. The first regression

famine = ві + в2 he + p3we + в4 kl6 + в5Х*5 + вбХіб + e* (6.7)

where famine is family income, he is husband’s years of schooling, we is woman’s years of schooling, and kl6 are the number of children in the household under age 6. Several variations of this model are estimated. The first includes only he, another only he and we, and one includes the two irrelevant variables, x5 and x6. The gretl script to estimate these models and test the implied hypothesis restrictions follows. If you type this in yourself, omit the line numbers.

1 list all_x = const he we kl6 xtra_x5 xtra_x6

2 ols famine all_x

4 omit xtra_x5 xtra_x6

6 omit kl6