8.11 Looking ahead

This unit took the assumptions and the variables as given. Both deserve questioning.

The model has assumed throughout that a one-unit rise in \(x\) has the same consequence wherever it occurs — that the tenth year of schooling is worth what the second was, and that the effect of experience never flattens. Economics rarely believes this. The next unit shows how logarithms let a linear model describe relationships that are not linear at all, and how they turn a coefficient into a percentage or an elasticity — at no cost to any of the machinery developed here.

The unit also treated the choice of controls as settled. It is not. Some variables belong in a regression, some are harmless, and some make the estimate worse than leaving them out — a possibility that surprises most readers, since the instinct is that controlling for more is always safer. Distinguishing good controls from bad ones is the second theme of the next unit, and it depends on exactly the bias formula derived here.