# Why are my constraints getting dropped?

I'm currently applying the Roy Zelner test of poolability as shown in the excellent article of Andrea Vaona, in fact I'm working with panel N=17 T=5, and my model looks like this : $$Y_{it}= a_0+B_1X_1+B_2X_2+B_3X_3+B_4X_4+e_{it}$$

My question is the following. When I'm testing for coefficient equality of the unpooled data (the last stage), many of my constraints are getting dropped. This impacts the degrees of freedom of $\chi^2$, and I would like to understand the reason? Is this because the time dimension of my panel is too small? or because the number of my constraints is too high?

Ama

• Might help if you told us what software package you're using, and what command(s) you typed. – onestop Jan 9 '11 at 19:55
• @onestop, the article in the link mentions stata, so probably stata is used. Does not matter though, since any statistical package would encounter problems in this particular case. – mpiktas Jan 9 '11 at 20:17

You have a panel data regression

$$y_{it}=x_{it}'\beta+u_{it},$$

where $x_{it}$ in your case is $(1,X_1,X_2,X_3,X_4)$. Poolability tests test whether alternative model is actually correct:

$$y_{it}=x_{it}'\beta_i+u_{it}.$$

So the null hypothesis is that $\beta_i=\beta$. To test this hypothesis we need to estimate $\hat{\beta_i}$. In your case, you need to estimate 17 $\beta_i$. Since $T=5$, your are estimating regressions with 5 parameters having 5 observations. This of course gives you a lot of problems, since the usual practice for statistical packages in this case is to drop some of the variables from the regression.

In general if $T$ is small do not test whether you can pool the data. Simply use panel data regression and check whether the resulting model is appropriate.

• @Ama, your are welcome. At this site and similar stackexchange sites, there is a standard way of thanking for the answers. You simply accept the answer. Just press the check box outline to the left of the answer. I am bringing this up only because I noticed that you haven't accepted any of the answers you asked, so maybe this something you do not know. – mpiktas Jan 12 '11 at 12:44