Analysis of different institutional settings.

[Catalin Mos]

Dear all,

I have Y, the interest variable and the phenomena X (economic uncertainty). I analyzed the relation between these elements (regression analysis) but I want to go deeper and study the interaction between the X and Y in different institutional settings (for example EU countries and non-EU countries, common law vs code law). My question is how to deal with this, I think that just a dummy variable in regression analysis is not enough. I appreciate any suggestion.

Thank you for the support!

[Clyde Schechter]

You have phrased your question is fairly general terms, and provided no specific data. So, it sounds like the most useful thing for you to do now would be to learn about interaction models. Try the excellent Richard Williams' lucid explanation: https://www3.nd.edu/~rwilliam/stats2/l53.pdf.

[Catalin Mos]

Dear Clyde, many thanks for your guidance, it was really helpful.
I still have one question, in creating the interaction term if one variable of the interaction term is a dummy variable (0 and 1) could the model work? In my case I have the Y, X is economic uncertainty and the interaction term is economic uncertainty * EU/Non-EU Countries (1 if EU, 0 if non-EU).

Thank you again!

[Clyde Schechter]

Yes. I don't know what kind of variable your economic uncertainty measure is: it could be continuous or it could be categorical. Anyway, if continuous, the interaction term would be c.X##i.eu_country. If categorical it is i.X##i.eu_country. (In both cases, replace eu_country by the actual name of the variable indicating EU vs non-EU countries.

[Catalin Mos]

Dear Clyde,

Thank you again for support, please if you are kind and consider the following additional questions after I finalized the data and run the tests:


- I have data for 2007-2021 for 21 countries and 7498 firms, I want to study the effects of uncertainty over the financial reporting, I performed the ADF test to check if my panel is stationary or dynamic, the results show that the panel is stationary. Then consistent with the literature i used fixed effects (I performed also Hausman test).The results of regression analysis are great and I validate my hypothesis
- I want to go further and analyze the effects of different institutional settings (strong rule of law, strong financial markets efficiency, UE vs Non-UE, these are categorial variables 1 for strong and 0 for weak). Initially I considered to create an interaction term between uncertainty and institutional settings and to see if EPU has the same effects but now I think that it will be better to split the population into two cluster for each institutional setting and to analyze so. What do you think ?
- Additionally, if I go with the interaction term between uncertainty and institutional setting characteristics (listed above) how to proceed, to create the interaction term (e.g. uncertainty x rule of law) and to include this in my regression and to eliminate the uncertainty and rule of law (as standalone variables)? (please see below the regression)
Initial: Y (financial reporting) = X (uncertainty) + X1 (rule of law) + Other control variables + constant
Analysis with interaction term Y (financial reporting) = X (uncertainty) # X1 (rule of law) + Other control variables + constant

Thank you!

[Clyde Schechter]

Based on the equations you wrote at the end, you would do this:

xtreg Y i.X##i.X1 covariates, fe vce(cluster firm_id)

is the basic code. Don't try to eliminate X and X1 as standalones from the code. Let Stata decide for you. If they are constant within your firms over time, Stata will eliminate them for you. If they are not, then they should not be removed!

The regression output for 1.X#1.X1 will tell you how much rule of law modifies the effect of uncertainty on Y.

But I don't see how this fits with the longer description of your problem. Where does EPU fit in? Where does UE vs non-UE fit in? Your explanation doesn't seem to match your equation, and your explanation is not clear to me.

[Catalin Mos]

Dear Clyde,

Thank you so much for the response, I will do as you indicated.
Regarding you question, EPU is uncertainty, my interest variable, sorry for misunderstanding.

For the other institutional settings (EU vs Non EU, strong financial market and rule of law) my initial thoughts was to run a separate regression for each of these three aspects with an interaction term uncertainty # dummy variable for each of the three elements. If I include the interaction term I should keep in the regression also the standalone variables for EPU and Dummies for strong rule of law, financial market, and EU or will be better to form clusters and to run the regression separately for each cluster (1 cluster for countries with strong rule of law one cluster for countries with weak rule of law).

Thank you again!

[Clyde Schechter]

There are a few differences between using an interaction term and running separate subanalyses for each cluster.

1. The interaction term approach makes use of the entire data set and is therefore more powerful than the analyses within clusters.
2. The way I have shown in #6 will also produce somewhat different coefficient estimates. This is because in the separate cluster analyses, the coefficients of the covariates are estimated separately in each cluster, whereas in the interaction method, the covariates receive a single coefficient that applies to all of the clusters. If you prefer the separate estimation of covariate coefficients because you believe their effects may also be modified by rule of law, etc., then you can still use the interaction method, but the code is somewhat different: -xtreg Y i.X1##(i.X covariates), fe vce(firm_id)-. In doing this make sure you precede each of the covariates by an i. or c., according as whether it is a discrete or continuous variable.
3. If you do the separate cluster analyses, you will have separate estimates of the X effect for each cluster, but there will be no straightforward way to do a comparison of the effects in the different clusters. Since doing the comparison seems to be important to your research goals, this would argue strongly for using the interaction method, where the comparisons are directly shown in the interaction coefficients themselves.

[Catalin Mos]

Dear Clyde,

I want to thank you for your help and effort.
I have only one additional question regarding this.

For example i have the capital market development index (continuous variable) and I introduced this in my regression analysis (as stated above my research objective is to analyze the impact of uncertainty on financial reporting quality). Then I divided the countries (based on capital market development index) between countries with high development of capital markets and countries with low development of capital markets (a dummy variable). I introduce the interaction between uncertainty and capital market development (the dummy variable) and I also kept the capital market development index (continuous variable), the results are as expected, but is this correct from the point of view of statistical methodology?.

Thank you!

[Clyde Schechter]

It is a legitimate statistical model. But it may or may not make economic sense. By including both the dichotomous version and the continuous version in the model you are stating that the outcome mostly increases linearly with the actual value of capital market development. But at the level of capital market development that serves as the cutoff for the dichotomy, there is an abrupt jump in the outcome, after which the relationship between them continues on in the same direction it was going previously, shifted by the amount of the abrupt jump. Is that the kind of relationship you want to model?

[Catalin Mos]

Dear Clyde,

Thank you again.

I must recognize that I am a little bit confused.
I used in the first instance the continuous variable for the interaction between capital markets development and uncertainty and the results were not conclusive. The uncertainty and capital markets development (as standalone variables) becomes more significant and the interaction term is contrary with the hypothesis (that in countries with high development of capital markets the effects of uncertainty on financial reporting quality is reduced). But if I divide the countries in two categories as stated above, the results validate my hypothesis.
Initially I thought that this is due to high correlation between the interaction term and standalone variables (main effect) (the correlation was over 90%). I centered the variables for the purpose of interaction and I obtained the same results.

How to proceed in this case?

[Clyde Schechter]

I do not work in finance or economics, so I am in no position to advise you on what kinds of models are sensible to look at. You need advice from somebody in your discipline about that. I can only give you generic statistical advice.

One strong generic statistical principle is that making dichotomies out of continuous variables is usually a bad idea, often a very bad one. See https://www.fharrell.com/post/errmed/#catg for a full explanation.

Another general principle is to make sure, before you fit a model to data, you understand what that model stipulates about the relationships among the variables in the model. You should be able to sketch a graph of the general shape of the y:x relationships implied by the model. And you should then explicitly judge whether those shapes make sense in terms of the real-world content you are studying.