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

 From Robson Glasscock To statalist@hsphsun2.harvard.edu Subject Re: st: Not a stata question but need help with basic econometrics. Bias with lagged dependent variables. Date Tue, 17 Jan 2012 08:58:49 -0500

```Hi Herberto,
You can iterate backwards and see that each value of y contains a
stochastic element. Since you are using a lagged dependent variable,
which necessarily includes a stochastic element, this may be framed
within the classic "errors-in-variables" problem. The white noise
portion of yt-1 causes the attenuation bias. Wooldrige discusses
measurement error in chapter 15.

best,
Robson Glasscock

On Tue, Jan 17, 2012 at 8:15 AM, Herberto Gomez <herbogomez@gmail.com> wrote:
> 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
>
>              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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