Selecting Appropriate Model for Firm-Level and Country-Level Variable

[Karina Harjanto]

Hi everyone,

I'm doing research where my dependent variable is sustainability reporting score (firm-level data). I have 2 groups of independent variable. First group is firm-level governance: board size, diversity, compensation, reporting experience. Second group is country-level: the 6 components of Worldwide Governance Indicators. I also use firm-level control variables: size, ROA, DTA and country-level control variable: GDP and dummy mandatory sustainability reporting. I have 840 observations (420 companies x 2 year) that comes from 5 countries. The problem is when I use fixed effect model (based on the result of Hausman test), Stata omitted the country-level variable. However, my research objectives are to examine the impact of both firm-level and country-level governance. After some research, I come across mixed model, Mundlak model, and multi-level modelling. I am unfamiliar with these models, as I usually use FE model. Are my variables suitable with those models? Please advise.


Best regards,
Karina

[Clyde Schechter]

Your problem arises because, I presume, in your data, each firm operates in only one country. Consequently any country-level variable will be constant within firm, and therefore will be colinear with the firm fixed effects. So, as you have discovered, you can't use a firm-level fixed-effects model for this analysis if the country-level effects are important.

Mixed model and multi-level modelling are, for practical purposes, the same thing. The major problem here is that you would have to represent firm as a random effect in the model. Since your data are observational, not randomized, it is likely that these firm level random effects will fail to be independent of the predictor variables--a requirement that must be met in order to assure consistent estimation in the mixed model. That requirement is usually fulfilled in randomized studies, but only seldom are we fortunate enough for it to hold with observational data.

The Mundlak model gives you the best compromise. It will give you both within-firm and between-firm estimates of the variable effects whenever possible. You can use the within-firm effects just as you would use the output of a fixed-effects analysis, and for the country-level effects (which are not estimable within-firm) you will have the between-firm effects available to use.

On the assumption that you are using the current version of Stata (19), you do not need to install any user-written ado-files to run this. You can simply use -xtreg- with the -cre- option instead of the -fe- option.

[Karina Harjanto]

Clyde Schechter thank you for your reply, it really helps me.

Indeed, each firm only exist in 1 country. Therefore for country-level variable, all firms in the same country and year have identical values. For example, every firm in Country A in 2022 has the same corruption score, which changes in 2023. However the changes in score from 2022 to 2023 is not significant. Problem also occurs because country-level control variables highly correlated with the WGI index.

One thing that confuse me, after running the data using Mundlak model in Stata 19, the within-firm effects (xit_vars) give me the result for both firm-level and country-level independent variable. However, the between-firm effect (xt_means) omit the 6 indicators of WGI (country-level variable) due to collinearity. The VIF for each of the 6 WGI indicators indeed very high (>100). Therefore, I still can't analyse the country-level effects for each indicator based on the between-firm effect.

I try the second model that combine all firm-level IVs into 1 index and all country-level IVs into 1 index using principal component analysis, and it works fine

My question:
1. Is there any alternative method to include multiple collinear country-level variables without dropping them?
2. I try to include only 1 indicator in the model, and it works. Is this methodologically acceptable to estimate separate Mundlak model for each indicator, if my objective is to examine not only the total index, but also the impact of each component?
3. Would a mixed-effects model with a country-level random intercept be a better approach in this case?
4. Is it acceptable to drop the collinear country-level controls to avoid multicollinearity?

Thank you in advance.

[Clyde Schechter]

First, the VIF, whose usefulness for any purpose is questionable, is not useful for looking at the colinearity of a batch of indicators for the same variable. But, this shouldn't even come up: if your variable is called WGI, you should not be entering separate indicator variables for each of its levels into your equation. Doing that will always result in one of them being dropped for colinearity. You should use factor variable notation (-help fvvarlist- if you are not familiar with it) instead: -xtreg ... i.WGI, cre-.

Stata will automatically omit one of them as the reference category, and the remainder of the levels will not be colinear. They very well may have a high VIF, but that is not the issue.

To respond specifically to your questions:
1. No, there is no kind of linear model that will give you estimates of the effects of a batch of colinear variables. Linear algebra makes such effects unidentifiable, which is just a technical way of saying that the effects are so strongly confounded with each other that it is impossible to separate them into individual components, even if you had an enormous sample size. And do remember that when you do run a linear model with indicators for (all but one of) the levels of a categorical variable, the results that you get are not estimates of the effects of each level: they are estimates of the effects of each level relative to the omitted reference level.
2. No. You have highly correlated variables here, and if you omit all but one you are then failing to properly adjust for the confounding effects of the others.
3. Probably not. Random effects models often work poorly with non-randomized treatment assignment because the independence of the random intercepts from the fixed effects cannot be guaranteed and is only occasionally incidentally true.
4. Well, this is normally what is done. But in your case you said that exploring these effects is one of the research goals, so, in your case, no, it would not be acceptable.

I think the way out of your dilemma is to either reconsider your research goals or reconsider how you are operationalizing this country-level variable. It doesn't really make sense to create a bunch of colinear variables and then set the impossible goal of ascertaining their separate effects. It's like setting the goal of hunting a unicorn. As unicorns do not exist, you will never succeed in hunting one, no matter what you try. So I would say that there is probably something wrong with the way you are constructing/using this country-level variable in the first place. If there isn't, then there is no way to sustain the research goal you have set.

[Karina Harjanto]

Hi Clyde Schechter, thank you for answering my questions, I very much appreciated it. After applying your suggestion, I can use the index score for country-level governance (WGI) and the model runs fine. Each of the components (based on World Bank data) is continuous variable, not categorical. The challenge is that I want to see the impact of each of the 6 components of WGI on the dependent as extra analysis, but I understand it is not possible to run all the components together due to the collinearity. Thanks again for your guidance and suggestions!