Re: st: Explanatories that vary only over time in panel data

[Jeffrey Wooldridge <jmwooldridge60@gmail.com>]

Oh, an easy question. :-) It is hard to say. It depends on whether
there is lots of dependence across time, and whether there is
cross-sectional dependence. If one includes fixed effects in the cross
section and time series dimensions, this often cleans up the
dependence. But especially in the time series dimension there can be
lots of autocorrelation. So N sufficiently larger to cluster for
arbitrary serial correlation is ideal. Duflo et al. and Chris Hansen
have shown, in simulations, that N = 40, T = 10 or maybe even T = 20,
seems to work well. But this is with independence in the cross section
(after time effects have been removed) and a stable AR(1) process in
the time series.

JW

On Tue, Feb 5, 2013 at 4:59 PM, Jacobs, David
<jacobs.184@sociology.osu.edu> wrote:
> Professor JW:
>
> About how much greater does N have to be relative to T to enter dummies for periods and get plausible (consistent) results?
>
> Dave Jacobs
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jeffrey Wooldridge
> Sent: Tuesday, February 05, 2013 4:54 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Explanatories that vary only over time in panel data
>
> Agree there is nothing special that needs to be done, provided you are still able to assume observations are independent across i. One drawback is that if you insist on having P_t as an element of X_it then you cannot include a full set of time period dummies. If you are not interested in the coefficient on P_t then I would drop it and opt for a a full set of time dummies -- provided your N is sufficiently large relative to T.
>
> JW
>
> On Wed, Jan 30, 2013 at 12:17 PM, Aljar Meesters <aljar.meesters@gmail.com> wrote:
>> Estimating a panel regression model where variable(s) do not vary over
>> individuals is possible, as long as they vary over time. The same
>> holds for adding a time trend to your model. Of course, the
>> variable(s) that you want to add should not be collinear with the time
>> trend.
>> I do not completely understand what you mean with: "If we just repeat
>> the price entries for all i districts in our input data we assume that
>> Stata will think that there are in fact multiple observations. So the
>> standard errors can not be correct.".
>> You have these multiple observations per district, so, why should the
>> standard errors not be correct? Maybe what worries you is your
>> assumption that all prices are equal between all districts. I do not
>> know if such an assumption is justified. You can take the average Y
>> over districts and regress Y_t = a + b*X_t + c*t instead.
>> Best,
>>
>> Aljar
>>
>> 2013/1/30 ARDE DE <wsbbarde@gmail.com>:
>>> Dear All:
>>>
>>> Our question is about both, the theory of panel data analysis and
>>> (later on) its implementation in Stata.
>>>
>>> The model we have in mind is:
>>> Y_it = a_i + b*X_it + c*t + u_it,
>>> i.e. the standard FE/RE framework but with a linear time trend.
>>> One of our explanatory variables in X_it does not vary across
>>> individuals, it only varies across time (it is a price variable that
>>> is assumed to be the same across all districts i within the country
>>> we consider).
>>> How do we tell Stata about this?
>>> If we just repeat the price entries for all i districts in our input
>>> data we assume that Stata will think that there are in fact multiple
>>> observations. So the standard errors can not be correct.
>>> The same question applies to our linear time trend c*t. Can we just
>>> include the "year" variable repeatedly (although it does not vary
>>> across the index i)?
>>>
>>> We were not able to find an answer in Wooldridge (2001): Econometric
>>> Analysis of Cross Section and Panel Data, nor in Matyas et al. (2008):
>>> The Econometrics of Panel Data, 3rd ed.
>>>
>>> Has someone used a similar model?
>>> Any help/hints will be highly appreciated
>>>
>>> Arde
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