Confusion w/ model specifications and outcomes

[Tobias Maier]

Hello,

I write my thesis atm and I want to investigate the relationship between an almost constant independent variable on country-level (a special law index which hardly ever changes over times) and a firm-level dependent outcome. Additionally, I use several firm-level and country-level control variables. As I have an extensive data sample spanning over almost 40 years, I thought using panel data is the best way. However, my supervisor told me that I should also try to run a "pooled OLS White corrected".

Now, I tried running different regressions and the outcomes are very confusing to me. I get their individual meaning (interpreting the coefficients and significance), however, I am not sure which one I should follow now. Especially, I don't understand the extreme differences between the t-statistics and the SE.

Maybe anyone here knows an answer or can give me a hint Thank you very much!

Here is the code I use:

regress DepVar IndepVar Firm-levelControls Country-levelControls i.Year i.SIC2, vce(robust)
regress DepVar IndepVar Firm-levelControls Country-levelControls i.Year i.SIC2, vce(cluster Country)
xtreg DepVar IndepVar Firm-levelControls Country-levelControls i.Year i.SIC2, re vce(robust)
xtreg DepVar IndepVar Firm-levelControls Country-levelControls i.Year i.SIC2, fe vce(robust)
xtreg DepVar IndepVar Firm-levelControls Country-levelControls i.Year i.SIC2, re vce(cluster Country)

This is the outcome I get:

	OLS-robust	OLS-cluster	Panel-re-robust	Panel-fe-robust	Panel-re-cluster
	b/t/se	b/t/se	b/t/se	b/t/se	b/t/se
IndepVar	-0.020	-0.020	-0.011	0.008	-0.011
	-76.806	-4.193	-15.516	5.080	-2.802
	0.000	0.005	0.001	0.002	0.004
Firm-levelControl1	0.138	0.138	0.118	0.114	0.118
	95.319	7.730	34.310	28.624	7.333
	0.001	0.018	0.003	0.004	0.016
Firm-levelControl2	0.000	0.000	0.000	0.000	0.000
	1.820	2.737	1.479	-0.658	3.688
	0.000	0.000	0.000	0.000	0.000
Firm-levelControl3	-0.001	-0.001	-0.001	-0.001	-0.001
	-8.442	-1.197	-10.033	-9.570	-3.733
	0.000	0.001	0.000	0.000	0.000
Firm-levelControl4	-0.005	-0.005	-0.002	-0.001	-0.002
	-52.006	-5.058	-9.951	-5.870	-1.778
	0.000	0.001	0.000	0.000	0.001
Firm-levelControl5	-0.062	-0.062	-0.044	-0.041	-0.044
	-47.703	-12.482	-27.317	-23.572	-10.049
	0.001	0.005	0.002	0.002	0.004
Firm-levelControl6	-0.060	-0.060	-0.047	-0.040	-0.047
	-8.784	-1.952	-3.727	-2.755	-4.024
	0.007	0.031	0.013	0.015	0.012
Firm-levelControl7	0.004	0.004	0.004	0.005	0.004
	7.397	1.113	4.409	4.947	1.619
	0.001	0.004	0.001	0.001	0.003
Firm-levelControl8	0.011	0.011	0.010	0.009	0.010
	88.155	9.032	26.417	15.420	7.679
	0.000	0.001	0.000	0.001	0.001
Country-levelControl1	-0.006	-0.006	-0.010	0.000	-0.010
	-17.466	-0.760	-11.094	.	-1.060
	0.000	0.008	0.001	.	0.010
Country-levelControl2	-0.033	-0.033	-0.032	0.031	-0.032
	-56.210	-2.695	-17.664	3.107	-2.071
	0.001	0.012	0.002	0.010	0.016
Country-levelControl3	0.000	0.000	0.000	0.000	0.000
	-10.976	-4.427	-7.354	-3.726	-9.560
	0.000	0.000	0.000	0.000	0.000
Country-levelControl4	0.001	0.001	0.000	0.000	0.000
	11.790	0.674	-3.178	-3.551	-0.770
	0.000	0.002	0.000	0.000	0.001
Constant	0.033	0.033	0.044	-0.043	0.044
	7.560	0.959	4.848	-5.380	1.136
	0.004	0.034	0.009	0.008	0.038
Year dummies	Yes	Yes	Yes	Yes	Yes
Industry dummies	Yes	Yes	Yes	Yes	Yes
N	458158	458158	458158	458158	458158
r2_a	.140	.140		.030

[Clyde Schechter]

Well, for starters, without knowing whether you -xtset- your data at the firm or country level it's really impossible to know what these models mean.

But speaking generically, for approaching this dilemma, the output you show omits the most important statistics: the sigma_u, sigma_e and rho results from the -xtreg- models. If rho is meaningfully different from zero (or, equivalently, if sigma_u is), then using OLS with robust VCE is simply a mis-specified model and its results are wrong. If sigma_u and rho are close to zero, then OLS results will be more or less the same as those from -xtreg-. The fact that you are getting results that you consider meaningfully different from these models suggests to me that sigma_u and rho are appreciably non-zero.

In -regress-, -vce(robust)- is not adequate to correct for clustering. I should also point out that there actually is no such thing as -vce(robust)- with -xtreg, fe-. When Stata encounters -xtreg, fe vce(robust)-, because the vce(robust) is actually invalid in that context, it automatically substitutes vce(panel_var) for it, where panel_var is the panel variable specified in your -xtset- command.

As for choosing between -xtreg, fe- and -xtreg, re-, that is yet another discussion. In economics and finance it is common to rely on the Hausman test for this. Personally, I disagree with that approach and recommend instead fixating on whether you are looking to identify within- or between-panel effects.

Anyway, I have answered your questions with more questions.

[Tobias Maier]

Hi Clyde,

Thank you for your quick response! My panel is set on company-level.

The results for rho, sigma_e, and sigma_u are 0.551, 0.106, and 0.117 respectively. The correct conclusion is that the OLS does not fit my data, isn't it? But how are these statistics calculated and what do they tell me exactly?

Ok. I have read about the Hausham test. My results suggest to use random effects. However, what is fixating? As my variable of interest hardly ever changes, I focus on between panel effects I guess.

best regards

[Clyde Schechter]

rho is the intraclass correlation, calculated as (sigma_u^2)/(sigma_u^2 + sigma_e^2). sigma_u is the standard deviation of the company-level fixed effects, and sigma_e is the standard deviation of the regression residuals. With a rho of 0.551 you are far, far from the territory where OLS is a reasonable model.

If you are focusing on between-panel effects, then I would recommend using -xtreg, be- as that is what it estimates. -xtreg, fe- estimates only within panel effects, and -xtreg, re- estimates a weighted average of within- and between- panel effects and is used when it is reasonable to assume that the within- and between- panel effects are actually the same. There are also situations where people are interested in both the within- and the between- panel effects and want to get both, for which the -xthybrid- command (available from SSC) is useful.

[Tobias Maier]

Again, thank you very much! You shed light into the dark