Using Fixed effects model for cross country analysis

[Sarah Steel]

Hello all. I am doing my thesis on the effect of the institutional environment on the CSR performance of firms in China and Russia. My data consists of 110 of both Chinese and Russian firms that run through the time period of 9 years. (2012-2020). I conducted a Hausman test to choose between fixed effects or random effects and the test result revealed that I should use fixed effects. However, I am very confused about how to proceed further. I need to do a cross-country analysis and see how the effect differs between Russia and China. The dummy variable for the countries gets omitted when I run the fixed effects model therefore I am not sure how to go about it. I want to know how I can do a cross-country analysis using the fixed effects model. Is it a wise idea to split the dataset into Chinese firms and Russian firms and then run the regression analysis accordingly?
Any help is much appreciated. Thanks a lot.

[Clyde Schechter]

This is an excellent example of why you should not let statistical tests dictate the choice of an analysis.

The fixed-effects model estimates only within-panel effects. But your research question, is there a difference between Russian and Chinese firms on CSR (whatever that is--this is not a finance/economics forum, it is an interdisciplinary forum on Stata and statistics: please do not use discipline specific abbreviations or jargon here) is inherently a between-panel question. It is literally impossible to answer that question with a fixed effects model. So regardless of what Hausman says, a fixed-effects model is simply inappropriate here.

If your data set consisted of firms that operated in both Russia and China, you could do within-firm comparisons of the outcome for their Chinese and Russian operations. But if you had that kind of data, the country indicator ("dummy") would not get omitted. So you have the more typical data where each firm operates just within one country at every time. You must use random effects, OLS, or -xtreg, be- to answer this research question. Among these, I would start with random effects. If the intraclass correlation comes out very close to zero, then I might go to OLS for simplicity (the results will not be much different from those of -xtreg, re- in this situation). I'm not fond of -xtreg, be- because it completely obliterates the time dimension of the data, but if the time dimension is irrelevant, then this is a viable option, too.

[Sarah Steel]

Thank you so much for responding. That gave me a lot of clarity! You mention that I start with random effects, I just have a follow-up question on that. Does that mean I add the dummy variable (in this case the country) into the prompt? So for example xtreg de ie, country_dummy? Or how do I conduct two separate regression analyses using the random-effects model? So in my case, it would be China first and then Russia. I want to know which is the best way to go about this? Thank you so much once again.

[Clyde Schechter]

Speaking schematically, as you did not show example data, it would be along these lines:

xtset firm year
xtreg CSR i.china_vs_russia, re

Here china_vs_russia should be replaced by the actual name of your variable that distinguishes Chinese from Russian firms. You may want to also include year fixed effects (i.year) to the list of right-hand-side variables if that is appropriate substantively. There may be other covariates worth including, and perhaps some options like cluster robust variance estimation you might want to add. But the heart of it is as above.

[Sarah Steel]

Thank you very much for your answer, Clyde! I followed what you said and conducted the analysis using the code you mentioned. The country_dummy variable is created for each firm where 0 denotes Chinese firms and 1 denotes Russian firms. I conducted the analysis using the random effects method and got the coefficient result as = -9. 62 and the robust standard error is= 5.10. How do I interpret this result? Does this mean that there is a negative relationship between the Chinese firms or the Russian firms with my dependent variable?

And secondly, I got the following results for my R-squared value: Within= 0.33, Between = 0.19 and Overall = 0.26. How do I get the adjusted R-squared value from these?

Thanks a lot again!

[Clyde Schechter]

It means that the expected value of CSR for Russian firms is 9.62 less than that of the Chinese firms. You don't show the confidence intervals, but a quick approximate calculation from the standard error and coefficient tells me it's approximately -19.6 to 0.38. So your data are compatible with the difference being in the range from Russians 19.6 less than Chinese (on average) to 0.38 more.

[Jeff Wooldridge]

Sarah: Do you really want to just know the average difference between CSR between Chinese and Russian firms? If you show Stata output then we can see what other variables are in the equation. Rather than just seeing whether there's a difference in means, you can see whether firm-specific characteristics have different effects across China and Russia. This is done via interactions.

If the question is really just a difference in means, averaged across time, then you should at least cluster the standard errors to get a proper confidence interval. You can interact the dummy china_vs_russia with year dummies to see if the difference has grown or shrunk over time. Something like this:

xtreg CSR c.china_vs_russia c.china_vs_russia#i.year, re vce(cluster firmid)

[Sarah Steel]

Dear Clyde and Jeff,
Thank you both for your answers! I apologize for not attaching the output in my previous post. I am attaching the outputs as pictures now. A little background info: I am testing to see if there is a positive relationship between the independent variable (in this case the FIPscore) and the dependent variable (ESG score aka the CSR performance). The rest of the variables are the control variables. So from the Hypothesis1.jpg image, it tells me that there is a positive relationship. Although I am not sure if the values make sense.. And for my other hypothesis: I am trying to do a cross-country analysis to see if the CSR performance of the firms in Russia are higher than that of China due to the influence of the independent variable. This is the part that is very confusing to me because I am still confused about how to go about it. Could you maybe take a look at my output and let me know how I should go about it?
The first image tests for hypothesis 1 and the second image tests for hypothesis 2.
I would really appreciate it, thank you!