st: Not a stata question but need help with basic econometrics. Bias with lagged dependent variables.

[Herberto Gomez <herbogomez@gmail.com>]

Hello,

In a basic regression with lagged dependent variables of the form

             yt = a + b yt-1 + ut

I understand why OLS estimator gives biased estimate for b. But in
many places, including in Wooldridge's Modern Econometrics, I read
that estimate of b will be downward biased. This is how his sentence
reads:

              Unfortunately, beta_1 hat is biased, and this bias can be large
              if the sample size is small or beta_1 is near 1. (For beta_1 near
              1 beta_1 hat can have severe downward bias.

I am trying to understand this bias in terms of

E(b) = b + cov(yt-1, u) / var (yt-1).

The downward bias suggests that cov(yt-1, u) should be negative. But, I do
not see why that should be.

In other places I read that estimate of b is attenuated. I do not see that
either.

Also, how does this bias relate to Nickell's bias in Panels?

I hope some kind soul takes a few minutes to explain this to me.

Best regards,

Herb
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