The question about endogeneity test of panel data model without instrument variables

[David Lu]

Dear all,

I used balanced panel data and have googled with the following string -test for endogeneity in panel data- gives back some Stata-related entries. But there is no specific case fits for my model which contains no instrument variables. I attached the commands and results in stata below. Based on the regression of -xtreg-, how should I start to the test of endogeneity in stata?

xtset id yr
sort id yr
xtreg ex  tfpch  logavem  c_tfpch_c_logavem avlogperavar  logperavinterest shock east_1,re vce(r)

Thanks,
David

[Alberto Camus]

Well, you should specify what kind of endogeneity you want to test. Generally, I'd suggest you perform Hausman's specification test to verify the consistency and efficiency of your estimators under FE vs RE. This allows you, to some extent, to discern whether there is correlation between your time variant variables and your time invariant random effects (see also Mundlak's specification). If, however, you are looking to test for endogeneity in your residual and time invariant variables, then you would need an instrument to do so.
To perform Hausman:

xtset id yr
xtreg ex tfpch logavem c_tfpch_c_logavem avlogperavar logperavinterest shock east_1, fe vce(r)  

estimates store fixed
xtreg ex tfpch logavem c_tfpch_c_logavem avlogperavar logperavinterest shock east_1, re vce(r)
hausman fixed ., sigmamore

[David Lu]

Well, you should specify what kind of endogeneity you want to test. Generally, I'd suggest you perform Hausman's specification test to verify the consistency and efficiency of your estimators under FE vs RE. This allows you, to some extent, to discern whether there is correlation between your time variant variables and your time invariant random effects (see also Mundlak's specification). If, however, you are looking to test for endogeneity in your residual and time invariant variables, then you would need an instrument to do so.
To perform Hausman:

xtset id yr
xtreg ex tfpch logavem c_tfpch_c_logavem avlogperavar logperavinterest shock east_1, fe vce(r)

estimates store fixed
xtreg ex tfpch logavem c_tfpch_c_logavem avlogperavar logperavinterest shock east_1, re vce(r)
hausman fixed ., sigmamore

Hi Alberto,

Thank you for your helpful reply. I did it and received an error reported by Stata.

. hausman fixed ., sigmamore
hausman cannot be used with vce(robust), vce(cluster cvar), or p-weighted data
r(198);

Also, my model contain a dummy time invariant variable -east_1- to control the region effect. So, it seems more suitable to use time invariant random effect model. But when it comes to test for endogeneity in your residual and time invariant variables, as you suggested, I would need an instrument to do so. Can you tell me the reason why it has to get an instrument into the model? Or, could you give an example or arcticle about finding such instrument variables?

Thanks again,
David

[Alberto Camus]

Apologies, you are right in that Hausman in Stata does not work with the robust option. You should try generalized Hausman (omit vce(r)) or the xtoverid command (see here).
The reason why you want an instrument available to test for that kind of endogeneity, in very simple terms, is because it gives you the opportunity to test how your residuals behave in different (restricted and unrestricted) specifications of your model. I find Wooldridge (2009), Econometric Analysis of Cross Section and Panel Data to be the best book reference for this. You can also check out these slides to get a sense of what is the maths behind it (not the best looking nor comprehensive -- very basic overview).

[David Lu]

Apologies, you are right in that Hausman in Stata does not work with the robust option. You should try generalized Hausman (omit vce(r)) or the xtoverid command (see here).
The reason why you want an instrument available to test for that kind of endogeneity, in very simple terms, is because it gives you the opportunity to test how your residuals behave in different (restricted and unrestricted) specifications of your model. I find Wooldridge (2009), Econometric Analysis of Cross Section and Panel Data to be the best book reference for this. You can also check out these slides to get a sense of what is the maths behind it (not the best looking nor comprehensive -- very basic overview).

Hi Alberto,

Thank you for your explanation about the reason behind. However, as I followed the post and run -xtoverid-, I got an error from Stata.

. xtoverid
xtoverid not compatible with xtreg model fe

As in my case, the potential endogenous variable is -logavem-, which is expected to have casusal ambiguity (Simultaneity) with the dependent variable -ex-. For that kind of endogeneity (the slides only mentioned the case of omitted variables), which set of commands can we use to if it's an endogeneous variables?


Thanks,
David