# Re: st: Re: Rsquared within using id & time dummies. xtreg returnscollineality error

 From "David M. Drukker" To statalist@hsphsun2.harvard.edu Subject Re: st: Re: Rsquared within using id & time dummies. xtreg returnscollineality error Date Sat, 26 Nov 2005 10:28:46 -0600 (CST)

```"Jorge Morgenstern" <jmorgenstern@utdt.edu> wrote that he was having trouble using
-areg- and -xtreg, fe- to estimate a model with id indicators, time indicators and
their interactions.

If I understand correctly, Jorge tried to fit a model with 300 observations and
and about 30+10+300=330 covariates.  If my understanding of what he did is correct,
the fact he tried to estimate a model with more parameters than observations would
explain any odd results obtained.

If Jorge's data does not contain any gaps and he is willing to assume that
only the intercepts and the coefficients on a time trend vary over the
individuals, the following model may be of interest to him.

y_it = x_it b + a_i + g_i t + e_it                                        (1)

where x_it   is a vector of exogenous covariates
b      is a vector of coefficients
a_i    are the N intercepts that differ for each of the N individuals
g_i    is the coefficient on the time trend for individual i
t      is a variable contains calender time
e_it   is the idiosyncratic error

While this model is more parsimonious than the one Jorge suggested, it still contains
too many parameters to estimate directly.  If we are going to use large N sample
theory, we need to remove the a_i and the g_i from the estimating equation.

As long as there are no gaps in the data, first differencing equation
equation (1) yields

D.y_it = D.x_it b +  g_i + D.e_it                                          (2)

Equation (2) is a simple fixed-effect model whose parameters can be
estimated by -xtreg, fe-.  Jorge should cluster() on the id variable to
account for the serial correlation caused by first-differencing the
variables.

-David
ddrukker@stata.com

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