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From |
Robson Glasscock <glasscockrc@vcu.edu> |

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 > 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 > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Not a stata question but need help with basic econometrics. Bias with lagged dependent variables.***From:*Herberto Gomez <herbogomez@gmail.com>

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