PPML estimation, error regarding Variance matrix

[Garima Dhir]

Dear All,

I'm working with panel data for 13 years which includes exports at industry level (31 industries) from 11 exporter countries to 106 countries importer countries (13*31*11*106 = 469898 observations). I'm using PPML to estimate the regression equation. My regression includes year, importer, exporter and industry dummies separately. Clustering is done at exporter*importer*industry*year level. Other independent variables include GDP of importer and and exporter countries, some industry specific variables and dummy variables that capture whether the two countries are a part of jth FTA in that year

When I run this regression for my complete dataset (i.e. 469898 observations) I get my estimates but when I run the same specification for individual exporter countries - 42718 obs each (I exclude GDP of exporter) I get the following warning messages - "variance matrix is nonsymmetric or highly singular" and "The model appears to overfit some observations with total_exports_usd=0"

Is it because of the level of clustering? If yes, how do I know the most appropriate level of cluster?

Thank you.

[Joao Santos Silva]

Hi there,

I assume that you are using -ppml- with the prefix -xi- to generate the dummies. If this is right, try to first create the dummies using -xi- with the -noomit- option, and then run -ppml- with those dummies.

Best of luck,

Joao

[Garima Dhir]

Dear Joao,

Thank you so much for the help...using noomit worked. However, changing the level of clustering also generated results. Taking clusters at importer level generates results but if the cluster is made from a combination of exporter*importer*industry*year (let’s call it ‘id’) then the above mentioned error message appears.

Given this, how should I decide the level at which clusters should be formed?

Thanks,

Garima

[Joao Santos Silva]

Dear Garima,

Clustering at id level, as you defined it, does not sound like a good idea because the clusters will be too small. I am not falimiar with your problem and cannot give specific advice, but it is generally better to have larger clusters.

Best wishes,

Joao

[Garima Dhir]

Dear Joao,

Thanks a lot for your advice. It was really helpful. Cheers!

Regards
Garima

[Garima Dhir]

Dear Joao,

How do we check for endogeneity while running ppml on panle data?

Regards
Garima

[Joao Santos Silva]

Dear Garima,

This is an interesting question and it may have been better to have a new thread for it.

Anyway, PPML estimates a conditional expectation and by definition all regressors are weakly exogenous with respect to the parameters being estimated. So, the short answer is that the problem does not arise in this context and the same can be said for OLS.

Going a bit further, I would add that endogeneity is not a problem with the estimator and it depends the parameters you want to estimate. If you care about the parameters of a certain economic model and you believe that the corresponding errors are correlated with the regressors, then you have an endogeneity problem. However, the parameters of conditional expectations are defined as the parameters that make the errors orthogonal to functions of the regressors and therefore when you estimate conditional expectations the regressors are always weakly exogenous.

I realize that my explanation may raise more questions than it answers; this is subtle issue and it is generally poorly treated in textbooks and not well understood by many economists. I suggest you have a look at the 1991 book "A Course in Econometrics" by Arthur Goldberger.

Best regards,

Joao

[Garima Dhir]

Dear Joao,

Thank you for the help.

Best,
Garima