Two-Way Fixed Effect Model - No Estimate

[shenflow]

I use the following code to estimate a two-way fixed effect model:

proc panel data = pers_a_input_2abc outest = output.pers_a_h2ab;
	id gvkey rankyear;
	model pers_a_diff = readj_avg sum_AA sum_AB sum_AC sum_AR sum_AS sum_AT sum_AZ sum_DB sum_EE
		 				/ fixtwo;
	ods output FitStatistics = temp_fit_pers_a_h2ab;
run;
quit;

The independent variables are all continuous variables. Moreover, the variables are not perfectly mutlicollinear. When I estimate the model. The following warning appears:

NOTE: The transformed regression does not have full rank. Be aware of possible multicollinearity
and/or identification problems before using the FixTwo method results.
WARNING: Unable to scale time series group 10 for variable CSIndex. Values are all missing, or
series is nearly constant.
WARNING: Unable to scale time series group 44 for variable CSIndex. Values are all missing, or
series is nearly constant.

The WARNING message appears for around 20-30 more groups.

Moreover, no estimation for sum_AS is given, as shown below (it is in German, sorry for that).

However, as the following screenshot clearly indicates. Values for sum_AS that correspond to values of the dependent variable exist. However, the variable is only unequal zero in a total of 5 observations (out of a panel of around 1500 observations).

So my question is. What does this warning message tell me? And second, why does the procedure not give me an estimate for sum_AS?

Thanks in advance.

[PaigeMiller · Accepted solution]

Moreover, the variables are not perfectly mutlicollinear.

You don't show us how you know this. Moreover, if a linear combination of independent variables is perfectly correlated with another linear combination of independent variables, then you can get this message as well. Probably, you are stuck with being not able to estimate the effect of one of your variables.

Also, don't ignore the WARNING messages.

[shenflow]

If it were perfectly multicollinear, the model wouldnt be estimatable in the first place as far as I am concerned. Also, the second screenshot shows that the variables are not perfectly multicollinear.

I am not ignoring the warning messages. I am asking what they mean because I do not understand them. I do not use any variable that is called csindex. My dataset does not contain a variable csindex. So I am left wondering what this actually tells me.

[PaigeMiller]

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@shenflow wrote:

If it were perfectly multicollinear, the model wouldnt be estimatable in the first place as far as I am concerned.

---

If there is a linear combination that is perfectly collinear with another linear combination (which is apparently the case), you can still estimate the effects of some of the variables but not all of the variables.\

Also, the second screenshot shows that the variables are not perfectly multicollinear.

I don't agree. It shows nothing of the sort.

As I understand PROC PANEL, CS variables are created by the time series portion of your data. And you have, as the WARNING says, bad data in the sense that it is all missing or the time series is nearly constant, and this affects your ability to estimate the model of interest.

[shenflow]

If there is a linear combination that is perfectly collinear with another linear combination (which is apparently the case), you can still estimate the effects of some of the variables but not all of the variables.

Is there any source that explains this a bit more in detail? Right now, I am unable to grasp this.

As I understand PROC PANEL, CS variables are created by the time series portion of your data. And you have, as the WARNING says, bad data in the sense that it is all missing or the time series is nearly constant, and this affects your ability to estimate the model of interest.

I just figured out that the error message appears for the groups for which I only have one observation. So this seems to be the reason. However, what does this imply now? Am I still able to use the output as it is?

[PaigeMiller]

---

@shenflow wrote:

If there is a linear combination that is perfectly collinear with another linear combination (which is apparently the case), you can still estimate the effects of some of the variables but not all of the variables.

Is there any source that explains this a bit more in detail? Right now, I am unable to grasp this.

---

You can look up generalized inverses of a matrix. Typically, for regression, the X'X matrix is inverted and you get the regression coefficients. But if it can't be inverted, a generalized inverse is used and you can still estimate many of the parameters in the model, just not all of them, and because generalized inverses are not unique, your estimates are not unique either. (Actually, I think a generalized inverse is always used, which is identical to the actual inverse if X'X can be inverted, and in that case the estimates are unique.) 

I just figured out that the error message appears for the groups for which I only have one observation. So this seems to be the reason. However, what does this imply now? Am I still able to use the output as it is?

As I am not really all that familiar with PROC PANEL, I'm not sure what the answer is. But, WARNINGS are placed there by SAS for a reason, and I think you ought to consider removing those groups with a single observation.

[shenflow]

Alright, thank you for the answers.

I would appreciate any input regarding the WARNING message issue from other users.