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Re: st: RE: RE: time trend in a panel with very SHORT time dimension


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: RE: time trend in a panel with very SHORT time dimension
Date   Fri, 13 Feb 2009 14:02:13 -0500

Jun Zhou <Jun.Zhou04@rotman.utoronto.ca>:
A minor clarification--you don't need at least two observations for
each firm, but firms with only one observation will contribute nothing
to the estimate of trend in a FE model, and will only water down the
results.  You will get slightly smaller standard errors on the trend
if you exclude firms that can only contribute one observation (and
same unbiasedness, assuming missing data is missing at random as
before, but you can actually do better or worse with respect to bias
if missingness is nonrandom).

Steven suggested that the underlying trend may be changing over time
(i.e. nonlinear change with time), or different firms may have
different trends--these questions go back to: what do you want to
estimate?  If there is some hypothetical superpopulation or DGP with a
linear trend, and you regard variation around that linear trend (by
time period or by firm or both) as error, then you will do pretty well
with your current approach, but presumably you can do slightly better
if you impose some structure on those putative errors, or much worse
if your assumptions turn out to be wrong.

On Fri, Feb 13, 2009 at 12:10 PM, Austin Nichols
<austinnichols@gmail.com> wrote:
> Jun Zhou <Jun.Zhou04@rotman.utoronto.ca>:
> Your existing estimates from
>  areg expense year, absorb(FirmID) cluster(FirmID)
> are fine for estimating a time trend.  You only need two observations
> per firm (to estimate a very short trend), so 5 is plenty, even with
> an unbalanced panel.  You can convince yourself of this using
> simulations, creating 2000 firms and 5 years per firm, dropping some
> randomly, then generating an outcome with a known trend, and
> estimating that trend.  The only issue arises when the missing data is
> not randomly distributed--firms that fail during your time window, or
> new firms, may have very different trends from the average over firms
> in existence at all time periods in the window.  But this is a
> question about what average trend you wish to estimate--a trend
> averaged over all firms during that window, or only firms in existence
> at all time periods in the window, etc.
>
...
>> -----Original Message-----
>> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jun Zhou
>> Sent: Thursday, February 12, 2009 7:31 PM
>> To: statalist@hsphsun2.harvard.edu
>> Subject: st: time trend in a panel with very SHORT time dimension
>>
>> Dear all,
>>
>> I have an unbalanced panel dataset with 5 years observations from 2000 firms.
>> I would like to test whether there is a positive time-trend in one variable (e.g. expense).
>> I tried the following two ways:
>>       xi: areg expense year, absorb(FirmID) cluster(FirmID)
>>       reg expense year, cluster(FirmID) Both methods show that the slope (i.e. the coefficient of 'year') is positive and statistically significant. Can I conclude that there is a positive time trend in variable 'expense'?
>>
>> I understand that it is improper to try to test time trend in a time series of 5 observations, but I am not sure whether 2000 firms can allow me to test the time trend although each firms have no more than 5 observations.
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