Eric Rasmusen’s Weblog

Suppose lagged Y is in a time series cross section regression like this:

y_{it} = \alpha_i + \gamma y_{i,t-1} + e_{it}

Is OLS consistent?

Yes, I think, but this is
a nice setting for thinking about what “consistency” means. If we replicated the same 10 years and 50 industries 1,000 times, with new disturbances each time, the Within Groups estimator would get better and better, I think. What is more natural is to think of going to 1,000 years and 1,000 industries, and that gets better too.

But going to 10 years and 1,000 industries does not make the bias get any smaller. This, I think, is what Nickell (1981, Econometrica) says.

And in a small sample, estimators are often biased, which we forget. When we only have 10 observations for something– the years here– the bias can be pretty serious.

Though, actually, maybe there’s not a bias, just inconsistency. This seems to be a Gauss-Markov Theorem BLUE situation. Maybe ex ante there is no way to know which direction the mistaken estimation will go, positive or negative.

This entry was posted on Saturday, January 6th, 2007 at 1:14 am and is filed under Math, Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.