# Re: st: Fixed Effects estimation with time-invariant variables

 From Darby Jack <[email protected]> To [email protected] Subject Re: st: Fixed Effects estimation with time-invariant variables Date Tue, 26 Jul 2005 11:34:37 -0400

I think something analogous to the SAS command you reference is implemented in Stata 9 as -xtmixed-

-xtmixed- fits linear mixed models. Mixed models are characterized as containing both fixed effects and random effects. The fixed effects are analogous to standard regression coefficients and are estimated directly. The random effects are not directly estimated, but summarized according to their estimated variances and covariances. Random effects may take the form of either random intercepts or random coefficients, and the grouping structure of the data may consist of multiple levels of nested groups. The error distribution of the linear mixed model is assumed to be Gaussian.

On Jul 26, 2005, at 11:12 AM, [email protected] wrote:

Joana:
The model you are trying to apply is generally known as a mixed model. It is possible to use time invariant variables and what would be the equivalent of a fixed effect model in SAS, the procedure is called Proc mixed. The terminology is not the same (random and fixed can mean different things), but it basically allows you to create an intercept for each country, and then "extract" from that intercept the explanatory power of your variables. Concerning your question about random and fixed effects, there is a theory reason and a mathematical one. The theory reason for random effects is that the relationship between the two variables it�s different for each country (basically, a different beta), while the fixed effect assumes just a change in the intercept for each country. The mathematical reason for using random effects is that the independent variables you are using are not correlated with belonging to a particular country (the country you belong to does not change the !
probability of having a particular value in one of your independent variables). This is a strong assumption (called orthogonal). If you use random effects under conditions in which the country determines, even partially, the value of your independent variables, then you will have specification bias and your results will not be thrustworthy. There is also the GLAMM procedure in STata, but I never had good luck with it (it requires too much processing power).

Hope this helps.

Martha Martinez.

Quoting Joana Quina <[email protected]>:

```Thank you Mark.  I was told that Hausman and Taylor have an
Econometrica paper where they tackle the problem of time-invariant
variables and fixed-effects. Are you familiar with this?
Regarding whether it is acceptable to use random effects, my
supervisor has a strong view that in this case it would be wrong.
Could you tell me why you say it is not obviously wrong to do so?

Thank you again,
Joana

On 26/07/05, Mark Schaffer <[email protected]> wrote:

```
Joana,

Date sent: Tue, 26 Jul 2005 13:56:55 +0100
From: Joana Quina <[email protected]>
To: [email protected]
Subject: st: Fixed Effects estimation with time- invariant

```variables

```
```Send reply to:          [email protected]

```
Fixed Effects estimation with time-invariant variables

I have a problem and I wonder whether anyone can help. I have a panel
dataset of 32 Sub-Saharan African countries and four time periods
(N=32, T=4). I am looking at the determinants of aid for these
countries. Given that they are not randomly selected countries, I am
using Fixed Effects. However, I have a few time-invariant variables
that are important but that get dropped because of using FE. Is there
any way of obtaining estimates for these time-invariant variables and
still use FE?

```No.  The fixed effects are perfectly collinear with the time-
want to use fixed effects.

```
```Also, given the data I'm using, is there any
justification for using Random Effects?

```
It's not obviously wrong to try random effects, especially as you can
use a Hausman test to check whether random effects can be accepted.
The fact that the time-invariant variables aren't included in the FE
estimation doesn't prevent you from using the test.

Hope this helps.

Cheers,
Mark

```Any comments would be much appreciated.

Thanks.
Joana

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```
```Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS  UK
44-131-451-3494 direct
44-131-451-3296 fax
http://www.sml.hw.ac.uk/cert

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```
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```
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```
```
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```

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