4.8 Working with the BLP

Why Linear?

• In some cases, we might try to estimate the CEF. More commonly, however, we work with linear predictors. Why?

• We don’t know joint density function of \(Y\). So, it is “difficult” to derive a suitable CEF.

• To estimate flexible functions requires considerably more data. Assumptions about distribution (e.g. a linear form) allow you to leverage those assumptions to learn ‘more’ from the same amount of data.

• Other times, the CEF, even if we could produce an estimate, might be so complex that it isn’t useful or would be difficult to work with.

• And, many times, linear predictors (which might seem trivially simple) actually do a very good job of producing predictions that are ‘close’ or useful.