Unit 9 Which Model Should We Fit?

Up to now, regression has looked almost mechanical. Someone gave us an equation, we estimated it, interpreted the coefficients and checked the assumptions.

Real empirical work is different. Before a regression can be estimated, someone has to decide what the equation should be.

Two decisions have to be made, and neither is settled by the data alone.

The first is the form of the relationship. We have assumed throughout that a one-unit rise in \(x\) produces the same change in \(y\) wherever it occurs — that the tenth year of schooling is worth what the second was. Economics rarely believes this.

The second is which variables belong. Unit 8 showed that omitting a relevant variable biases the estimate. It is tempting to conclude that more controls are always safer.

They are not. Some variables belong in a regression, some are merely wasteful, and some make the estimate worse than leaving them out.

This unit takes the two decisions in turn.