[Patrick Lang]

Thanks for the feedback again. That was just to make sure that the application of the fixed-effects estimator is valid in my case. The overall analysis is of course more sophisticated .

[Patrick Lang]

Dear Clyde Schechter Erik Ruzek,

I have two addtional questions. As I have already outlined, I have a panel data set comprised of organizations from different countries. I try to analyze the effect of an IV (organizational level) on a DV (organizational level). Variables on the country level moderate this relationship. As shown in my previous post, I use organizational and year-fixed effects to account for unobserved heterogeneity. Additionally, I know that I cannot compare different countries as I am applying a within-estimator on the organizational level.

Two questions remain. 85% of the analyzed organizations are based in the U.S., the rest are spread throughout Europe.

1. My understanding of the fixed-effect estimator is that as I am including fixed-effects on the organizational level they also account for any fixed-effects on the higher level (in this case country) - is this correct? Or do I have to include country-fixed effects besides the already implemented organizational fixed-effects?

2. Is the distribution of my sample (dominance of U.S.-based organizations) biasing my results? My first assumption was that the results should be fine due to the within-estimation. However, if I analyze only the U.S. organizations the moderating effect switches signs. If it biases my results, would you have any recommendations? Regarding the sample, there is not much I can do as the analyzed industry mostly consists of organizations based in the U.S.

Thanks again
Patrick

[Patrick Lang]

Concerning my second point - is the within-estimator still valid if I solely analyze U.S. organizations as the moderator variable would be the same for all units of observations? My understanding is that it is still valid even though some year-fixed effects will be dropped due to collinearity. Nonetheless, the differences between the regression results between the complete sample vs. the U.S. sample still strike me.

[Clyde Schechter]

With regard to your first question, the answer is yes.

Your second question cannot be answered without a clarification of what your research goal is. "Bias" is always relative to something. If I measure height in a random sample of US adults, the mean will be an unbiased estimator of the mean height of US adults. But it will be a biased estimator of the mean height of Mexican adults or US children. So you need to be clear about exactly what you are trying to estimate. If what you are trying to estimate is itself trans-national, then a US-only sample will produce biased results unless it happens to be the case that the distribution of what you are estimating happens to be the same in the US as it is globally (which is not going to be true of many things.) But if what you are trying to estimate is itself a US phenomenon, or is one of those things known not to vary across nations, then a US dominated sample is fine.

That said, with regard to what you ask in #18, if the moderator variable is actually a constant when restricted to US observations in your data, then it will be impossible to estimate any kind of effect (including moderation of other effects) with that data. Constants explain nothing.

[Patrick Lang]

Thanks Clyde Schechter .
I want to estimate an industry phenomenon. This industry consists mainly of U.S. organizations. The moderator variable is "environmental policy stringency" (country-level). This moderator changes with year and country. Thus, it is also not constant for U.S. organizations. However, as this moderator will be the same for 85% of organizations - all U.S. organizations have the same value for 2011, 2012 etc. -, I fear that this will bias the interpretability of the moderator. After what you said, I assume that my results are valid as it is just the nature of this industry that the majority of organizations are located in the U.S.. However, as already pointed out, if I analyze the U.S. organizations in isolation the moderator switches signs compared to the global sample (85% US, 15% Europe). The 15% of organizations located in Europe are distributed across 10 countries with different values for the moderator across time and country.

[Clyde Schechter]

Well, the fact that you get such different results in the US only sample and in the international sample says that the workings of this moderator are different in the US and in Europe. Under the circumstances I think we would have to say that the results from the US sample only generalize to US organizations.

[Patrick Lang]

Yes, I agree. However, isn't that somehow contradicting the properties of the fixed-effect estimator, which should account for the heterogeneity between different countries?

[Clyde Schechter]

The fixed-effects estimator accounts for time-invariant effects within countries. But it does not account for effect modification across countries. Notice, for example, that if you were to introduce this moderator into your -xtreg- command as -xtreg outcome regressors moderator, fe-, the moderator would be omitted due to its colinearity with the country fixed effects. But if you introduce this same variable as a moderator, -xtreg outcome regressors i.moderator##i.country, fe-, the interaction terms do not get omitted: they are not constant within country--in fact they explicitly vary across countries.

[Patrick Lang]

Probably I used the wrong words in #22. What I meant was that if my fixed-effects estimator (xtset organization year) accounts for the time-invariant effects within countries all the variance can solely be traced back to time-variant factors. Thus, the difference between the complete sample (organizations from the U.S. and EU) and the U.S. sample cannot be traced back to time-invariant factors - right? However, I realize that these different effects are probably due to different time-variant effects in the respective countries.

[Clyde Schechter]

Effect moderation involves a product between the moderator and some other variable in your model. If that other variable in your model is time-varying, then the interaction will be, too. If you tried to include the interaction between a time-invariant within country moderator and a variable that is also time-invariant, the interaction would be time invariant and it would be omitted due to colinearity with the fixed effects.

[Patrick Lang]

Thanks for the clarification Clyde. I think I am still not sure about one thing. If my full sample (US+EU) shows a different moderation effect compared to the European sample and I use a fixed-effect estimator (organizational and year) for both samples then I can conclude that the different sign must stem from differences in time-variant factors that seem to be different for the U.S. and EU as both within-estimators have controlled for all the time-invariant factors? Thus, I would conclude that the moderator on the country-level (environmental policy stringency) is affecting the indendepent variable (organizational level) differently due to some time-invariant factors that differ between the U.S: and EU.

[Clyde Schechter]

I can conclude that the different sign must stem from differences in time-variant factors that seem to be different for the U.S. and EU as both within-estimators have controlled for all the time-invariant factors? Thus, I would conclude that the moderator on the country-level (environmental policy stringency) is affecting the indendepent variable (organizational level) differently due to some time-invariant factors that differ between the U.S: and EU.

No, this isn't right either.
You are estimating the way your putative moderator M modifies the effect of some time-varying variable X on your outcome Y. This is done by including M##X in your model of Y. Now, because X is time varying, so is M##X even though M by itself is not. (If this were not the case, you would be unable to estimate the moderation.)

I don't think you can make any attribution of causes of the different estimates of M#X in the US model and in the EU model based on the information you have discussed here. It could be due to differences in the distribution of X, or of M, or due to some other modeled or unmodeled difference between the US and EU countries that influences the way M interacts with X. All of those are on the table. And those factors, even if they are, on their own, time-invariant, become "entangled" with X and M when you interact it with them. The interaction with X will be time varying regardless of whether these factors are time-varying or time-invariant.

[Patrick Lang]

Thanks Clyde, really appreciate your help.

[Marry Lee]

I was reading this thread and I found it very interesting. I have a question please, if you can answer me Clyde Schechter.
A following question from #27: the moderator M is time invariate for each individual over time (assuming this is a continuous variable) and X is time varying (assuming this is a dummy variable), in a fixed effects model such as

xtreg Y beta c.M##i.X, fe

Stata will give an estimation for the effect when X=1 and an estimation for the interation c.M#i.X (coefficient for M should be omitted).
My question is that I don't know how to interpret the coefficient for c.M#i.X? since M is constant.
Is it only possible to interpret such a model when we use margins with certain values of M?