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From |
"Clive Nicholas" <clivelists@googlemail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Constant terms in AR1 error regressions |

Date |
Fri, 19 Dec 2008 21:27:58 +0000 |

Michael Hanson replied: > You've defined your "task" very narrowly as using -regress- to estimate an > AR(1) equation on residuals from (what I presume to be) a prior regression. > If you could give a more general idea of what you are trying to accomplish, > I and others on the list might be able to make better suggestions. For > example, one might give different advice if you were concerned that the > residuals were I(1) than if you were fairly confident they were stationary. This example probably best illustrates what I was originally getting at: webuse union xtset idcode year reg grade south union black if year==70 predict r70, r forval i=71(1)73 { local j = `i'-1 reg grade south union black if year==`i' predict r`i', r reg r`i' r`j' if year==`i' reg r`i' r`j' if year==`i', nocons } Notice that the coefficients on \rho and their attendant t-ratios are not always the same. Unit-root tests via -pperron- and -dfuller-, within unit, suggests my pooled time-series is stationary. > That said, Wooldridge (2006, p. 418) discusses testing for AR(1) serial > correlation with strictly exogenous regressors, and advises "this regression > may or may not contain an intercept; the t statistic for \hat{\rho} will be > slightly affected, but it is asymptotically valid either way." Later, he > notes that strictly exogenous regressors are not very common with time > series data, and that such simple tests are not robust to higher order > autocorrelation. (You did test for higher order terms before settling on an > AR(1) specification, right?) Wooldridge recommends a Breusch-Godfrey test, > but there are others: see -help regress postestimationts- (yes, that is a > "ts" at the end) for discussion of what is implemented in Stata. Because, like -union-, my dataset is pooled, I ran -corrgram- with selected units (i.e., those possessing a long enough time-series to be worth performing Q tests on) and found one AR1 process and one AR3 process; the rest had none at all. That said, a pooled regression using BSS's -xtivreg2, bw(2) small robust i() t() fe- showed my lagged dependent variable to be significant; running (mean-centered) pooled regressions using -xtpcse-, however, showed my LDV failed to reach significance. I did look carefully at -help regress postestimationts-, as it would be much easier to run any of those AC tests automatically than do it 'by hand', as I had to. However, g lagrade=l.grade quietly reg grade lagrade south union black if year==73 estat bgodfrey sample may not include multiple panels r(459); estat archlm sample may not include multiple panels r(459); estat durbinalt sample may not include multiple panels r(459); estat dwatson sample may not include multiple panels r(459); and so on. > Two final thoughts: First, if you include the intercept in a regression of > a residual series on its first lag, and the estimated intercept is > significantly different from zero, then you probably should revisit your > prior estimation: your residuals should be mean-zero by definition. Second, > if your results are very different when the intercept is excluded -- if that > one extra degree of freedom is enough to change your results -- then I would > caution you to be very skeptical of them to begin with, as you are working > with large-T asymptotics by using -reg-. Indeed, my T has a maximum of 13 in this pooled dataset, and I'm running -reg- on single cross-sections in order to obtain \rho by hand. -- Clive Nicholas [Please DO NOT mail me personally here, but at <clivenicholas@hotmail.com>. Please respond to contributions I make in a list thread here. Thanks!] "My colleagues in the social sciences talk a great deal about methodology. I prefer to call it style." -- Freeman J. Dyson. * * 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: Constant terms in AR1 error regressions***From:*"Clive Nicholas" <clivelists@googlemail.com>

**Re: st: Constant terms in AR1 error regressions***From:*Michael Hanson <mshanson@mac.com>

**Re: st: Constant terms in AR1 error regressions***From:*"Clive Nicholas" <clivelists@googlemail.com>

**Re: st: Constant terms in AR1 error regressions***From:*Michael Hanson <mshanson@mac.com>

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