FE Regression: Interaction Term of continous variable with time variant dummy variable

[Fabian Noth]

Hi everyone,

I want to scrutinize the effect of works councils on the adaption of firm’s employment to sales changes. I am using a fixed effect model to limit OMVB. Works Council is a binary coded dummy variable. which is rather stable within firms but still time varying.

The panel dataset is an unbalanced panel of firms.

I estimate the follwing regression:

XTREG, FE Vce (cluster firm)

Employmemt_Change(i,t) = ß *c.sales_change(i,t) + ß * i.WorksCouncil(i,t) + ß (c.sales_change(i,t) * i.WorksCouncil(i,t)) +(controls)

My question:

Is STATA :

• (A) splitting up the sample between the values of WorksCouncils like in a normal OLS Regression?
• (B) or does the dummy only measure the case where a within firm change occured or both?

And is the same then true for the interaction term with sales?


I would be fine with case (A) as I would then measure the difference between firms with/without a works council but having controlled for fixed effects. Does STATA then also split up within firms if there occured a change?

Then, in order to only identify case (B) (within firm change) I thought of:

(1) To generate a sub sample only for firms that had a within firm change in Works Councils?
(2) Coding WorksCouncil as continous (c.) instead of a factor variable to tell STATA to not split the sample?

Your help is really much appreciated.

[Clyde Schechter]

In any fixed effects regression, the effects estimated are within-panel effects only. If a firm does not change its works-council status, then it is uninformative about the within-panel effect of change in that variable. If it does, it is. So B is correct.

No regression commands "split up" the sample in any way. I don't know what you're asking about when you mention this. So, I don't know what to say about A. Normal OLS regression doesn't split up anything either.

As for (1), there is no need to delete the firms with no change in works council status from the sample: Stata's calculations of the works counceil effect will ignore them anyway. And excluding them may introduce some selection bias on other variables in your model.

As for (2), this will accomplish nothing, assuming Works Council is an ordinary dichotomous variable. If, however, it has more than two levels, then using c.works_councils in your model makes it a different model, one in which you are implying that the effect of having, say, works_council = 3 has three times the effect on employment change compared to works_council = 0 as does having works_council = 1. I don't know what works_council status even means, I can't advise you, but you should give serious thought to whether such an assertion is plausible.

[Fabian Noth]

Hi Clyde,


thank you for the quick and precise answer.

I was not precise/wrong when I wrote splitting up the sample, I meant that the Dummy would measure the effect between firms with/without a WorksCouncil.

So to clarify again:
(B) is correct, which means that my dummy and interaction term only measures the within firm effects of a change in WorksCouncil status?

This is exactly what I wanted!
So I will not consider option (1) or (2) then


Thank you again,

Fabian

[Fabian Noth]

Dear Clyde and dear Community,


I will soon submit my thesis and came into thinking again after reading some posts here on time-invariant interactions in FE models. (Especially this one:https://www.statalist.org/forums/for...-effects-model )

Slightly different from above, I am regressing cyclical deviations in employment on a spline of positive/negative cylical sales deviation and some controls. The deviation is interacted with a dummy on WorksCouncils that is 1/0. The dummy is not time-invariant but highly persistent (The included dummy is not ommited by STATA. I include it to control for direct effects of WC unrelated to interaction):
STATA calculates a transition probability of ca.8% for WorksCouncils. My sample has about 70,000 observations with mean 11 years. Below you find the STATA Output for pseudo test data:

Hint, I also do the estimation on a linear spline with 4 bins: <-15 0 > 15 and find signficant effects on the interaction terms (reduction of strong negativ deviations and positive deviations, but an increase in moderate deviations through Works Councils) and small but sigfnicant effects for the dummy itself.

I identify (in real data) significant reductionary effect of works councils on the coefficient for negative cylical deviations. (Works Council hinder the cyclical negative deviation in employment)
As the dummy variable is highly persistent, there probably will be many establishment ID's with no change in the dummy variable. Can I then think of the interaction of sales_cyc with WorksCouncils(betrrat), like the interaction of time-invariant dummy with years (as often used in examples)?

Is the interaction term in the Fixed Effect approach than measuring both 1) the effect of a change in WorksCouncil Status (e.g. a foundation of a Works Council) within an establishemnt but also 2) the effect of the WorksCouncil when there is no change wihtin the establishment. My reasonig is that the interaction of the factor variable WorksCouncil with sales_cyc is time-variant even if WorksCouncil is time invariant for an establishment.
So, the difference shown by the interaction term then still stems from between differences in establishments? For instance, Works Councils are more frequent in large establishments and then the dummy value = 1 could falsly measure the effect of establishment size, despite of using a FE model. Intuitively, results suggest that there is no issue of establishment size as I would suppose that large establishments are more reluctant to employment deviations from the trend in both a positive and negative direction.

I hope I made my point understandable and I am grateful for a quick response

All the best,

Fabian


PS: I am doing the same for a variable for union representation, however this variable is less persistent and not as strongly correlated with firm size.

[Fabian Noth]

An Addition:

So, I am clustering at the ID/Establishment Level. Differences in Industry and firm size cannot be controlled in this Setting? The firm size in Terms of the employment Level is included in the controls, but this does not capture firm size differentials. I would Need to use a BE-Model, right?

Correction: the dummy of Works Councils does measure the Impact of WorksCouncils for the case that sales_cyc == 0, which is not necessarily of interest in the Dynamics I want to know.

Best,

Fabian

[Clyde Schechter]

So, I am clustering at the ID/Establishment Level. Differences in Industry and firm size cannot be controlled in this Setting? The firm size in Terms of the employment Level is included in the controls, but this does not capture firm size differentials. I would Need to use a BE-Model, right?

Well if firm size does not vary over time, then it cannot be explicitly modeled in an analysis of firm-level fixed effects; that would indeed require a between effects model.

[Fabian Noth]

Thank you for your answer, I will also check by interacting sizeclass with sales_cyc instead of WorksCouncil and look for signficiant similar patterns.

I have a second questions, is my string of thought from above right?

the interaction term in the Fixed Effect approach than measuring both 1) the effect of a change in WorksCouncil Status (e.g. a foundation of a Works Council) within an establishemnt but also 2) the effect of the WorksCouncil when there is no change wihtin the establishment. My reasonig is that the interaction of the factor variable WorksCouncil with sales_cyc is time-variant even if WorksCouncil is time invariant for an establishment.
So, the difference shown by the interaction term then still stems from between differences in establishments?

[Clyde Schechter]

In a fixed-effects model, all of the estimated effects are purely within panel effects. Assuming that your grouping variable, id, identifies establishments, no aspect of an establishment that is constant over time can be explicitly estimated: those effects are all "absorbed" in the fixed effect itself and cannot be separately distinguished.

Please bear in mind that I don't even know what a Works Council is; I've never even heard the term before. So I'm at a loss to interpret any of this in substantive terms It seems, however, that whatever it is, it does vary over time because the variable betrrat is not dropped in the regression. But the estimated effects of bettrat, as modified by whatever sales_cycle_pos represents, reflect only the effect of that variation within firms. If your research goals require you to examine the between-firm effects of that variable, you will need to do a -be- or -re- model to get at those.

[Fabian Noth]

Thank you for the response. I prefer within effects, so a FE model is fine.
A Works Council is part of the german industrial relation system, where workers have the right to be informed and decide over hirings and firings etc. And I want to find out how a introduction / or dismissal of this institution, changes how establishments adapt employment to sales. Hence, I want to look on the within effects of Works Councils .

[Clyde Schechter]

Thanks for the explanation.

[Fabian Noth]

Thank you again for your help. This really resolved my question. And as an information: Sales_cyc_pos is a variable that captures the percentage deviation from sales-trend. Such, that I can examine if cyclical sales deviations (due to economic up- or downswings) are translated into cyclical deviatons in employment (gesamt_cyc).And how this transmission of deviations is affected by a WorksCouncils.