Time standardization VS time fixed effects

[Peter Woodruff]

I work on a firm-level data panel (15years) and I have a serious doubt about the method considering I'm using a time standardized outcome variable and time fixed effects.

I want to do regression on a score from 0 to 100 I have for all my firm all years. But the rating differs across sector. So I have assumed I should calculate the Z-score with the annual mean and standard deviation of the sector for each observation.

Then I want to do a simple DID with firm and time fixed effects :

xtset idfirm annee
xtreg Zscore $treatment $controlvariables i.year, fe cluster(idfirm)

But according to the bad results of the regression, I was wondering if I should keep the time fixed-effect or if the time variation isn't already lost with the standardization ?

It's a rookie question but I just start. Thanks a lot!

Peter

[Carlo Lazzaro]

Peter:
- as I fail to get how the score vary among industries, I would keep the score in its original metric;
- I'm not clear with clustering standard errors at -idfirm- level, unless you suspect heteroskedasticity and/or autocorrelation in your dataset;
- you may want to consider interacting -treatment- with -time- among your predictors:

i.treatment##i.time

- if firms are nested within industries (as it should be the case); you may also consider a -mixed- appoach.

[Peter Woodruff]

Hi Carlo and thanks for your answer,

I tried to do the regression with the original metric but I think the large difference across industries mean mask the effect on the treatment. For exemple, on a score dealing with environmental issues, the mean can be high in some indsutries because they are very concerned and low in others. The framework of rating isn't universal.
I also tried to interact the treatment with a sector_id factor but even that doesn't lead to clear results as when I study the distance to the industry mean (Zscore).

So I'm still concerned to well take in account the time effect. If I use the distance to the annual sectoral mean, the time effect should be removed, right ? But, it doesn't seem reasonable to don't measure a time effect, even with the Zscore.
I'm wondering if add the lag Zscore of the firm could be a answer to that ?

Concerning the interaction between time and treatment, I didn't specify but I already look at this because there is no reason the treatment effect is the same each year.

I will try the mixed approach modelling the firms as random effects and the years as fixed: mixed Y X i.time_id || firm_id:

Thanks

Peter

[高佳]

I know this is late. But I encountered a similar situation like yours recently and would be grateful to know how you end up solving your problem and why.@Peter Woodruff