Colin Vance asks:
A brief question about statistical significance: taking a “population first” approach to econometrics, you note on page 36 that “the regression coefficients defined in this section are not estimators; rather, they are nonstochastic features of the joint distribution of dependent and independent variables.” You later imply on page 40 that the issue of statistical inference arises when we draw samples. My question is how do we interpret standard errors in those (admittedly rare) instances when we have data on the entire population. Does this circumstance render the notion of statistical significance moot?
Good question Colin. No single answer, I’d say.
Some would say all data come from “super-populations,” that is, the data we happen to have could have come from other times, other places, or
other people, even if we seem to everyone from a particular scenario. Others take a model-based approach:some kind of stochastic process generates the data at hand; there is always more where they came from. Finally, an approach known as randomization inference recognizes that even in finite populations, counterfactuals remain hidden, and therefore we always require inference. You could spend your life pondering such things. I have to admit I try not to.