Simultaneous equations: -cmp- versus -reg3-

[Courtney Bass]

Hi everyone,

I have implemented the following code within Stata, and the results are consistent with expectations. As can be seen below, the variable "sldummy" is being treated as endogenous, but the two dependent variables are exogenous.

reg3 (wnetreins sldummy wra_roa3 wsize wsurplus wrelsize stock lob geo cat wnetextreins i.year) (wnetextreins sldummy wra_roa3 wsize wsurplus wrelsize stock lob geo cat wnetreins i.year), endog (sldummy) exog(wnetreins wnetextreins)

The only problem with using these results is that I do have heteroskedasticity and serial correlation within the dataset. A suggestion online indicated that an advantage of -cmp- over -reg3- was that it would allow me to correct for the heteroskedasticity by using either -,robust- or -,cluster- commands. At this point, I still have not figured out a way to correct for the serial correlation using -cmp-. I have included the code (below) that I am trying to use with the -cmp- command. While the results do generate, almost all results for the first equation are missing (with the exception of the coefficients). Specifically, there are four variables (including one of the year indicators) that have have full results. The remaining variables have coefficients, but missing values for everything else. After searching online, it seems that a common suggestion is to check for collinearity. I have checked variance inflation factors, and also have run pairwise correlation tests for all of the variables, and all VIFs are below 2. There is never a correlation meeting or exceeding 50% when using the -corr- command. Thus, I'm at a loss as to why I'm not receiving full results for the first equation.

cmp (wnetreins = sldummy wra_roa3 wsize wsurplus wrelsize stock lob geo cat wnetextreins i.year) (wnetextreins = sldummy wra_roa3 wsize wsurplus wrelsize stock lob geo cat wnetreins i.year), ind ($cmp_cont $cmp_cont) cluster(cocode) difficult nonrtolerance tech(dfp)

Additionally, I do not think that my code for the -cmp- command is acknowledging that the sldummy variable is to be treated as endogenous. I have spent a lot of time reading from the -help cmp- file, but it's very complicated code. I would just like to be sure that I'm essentially running the model from my -reg3- code using the -cmp- command, with the only change being that I correct for the heteroskedasticity.

My dataset is balanced, covering 12 years with 1,074 firms each year (for a total of 12,888 firm-year observations).

To recap, I have the following questions.

1. Is there a way to correct for serial correlation when using -cmp-?
2. Why do I get missing results in the first equation from the -cmp- command?
3. Could someone please comment as to whether changes need to be made to the specific -cmp- code I am using, so that sldummy is treated as endogenous (and all other variables as assumed to be exogenous)?
4. Alternatively, is there a way to control for heteroskedasticity when using -reg3-?

Thanks so much,
Courtney

[David Roodman]

Courtney,
As specified in the reg3 equation your model can be thought of having endogenous variable, sldummy, modeled with equations whose rights sides contain only exogenous variables, and which differ from each other only in having wnetreins or wnetextreins. Is that right?

In cmp, endogenous variables must be put to the left of the equal sign. So you would have to do

cmp (sldummy = wnetreins wra_roa3 wsize wsurplus wrelsize stock lob geo cat wnetextreins i.year) (sldummy = wnetextreins wra_roa3 wsize wsurplus wrelsize stock lob geo cat wnetreins i.year), ind ($cmp_cont $cmp_cont) cluster(cocode)

But that is going to very hard to fit because that error terms in the two equations will tend to be highly correlated and so the correlation parameter will go toward the degenerate extreme of 1.0.

If you just have one endogenous variable, why don't you just do

regress sldummy wnetreins wnetextreins wra_roa3 wsize wsurplus wrelsize stock lob geo cat wnetreins i.year