Difference in Differences

[Omar Shaher]

Hi,
I have a question about how to code the variables in the following DID equation.

Dep.Var= B1 IFRS + B2 Post + B3 Post * IFRS + Controls + e.


There are three cases that I want to present and I want to confirm if my coding is correct or not, please!

Case one:

Let’s suppose that I aim to examine the impacts of mandatory adoption of International Financial Reporting Standards (IFRS )in Country A, which mandated the adoption of the IFRS in 2005. Country A serves as the treatment group, while Country B, which follows Generally Accepted Accounting Principles (GAAP) and has no plans to adopt the IFRS, serves as the control group. The study will utilize DID model. In this model, the IFRS variable will be coded as one for firms in Country A and zero for firms in Country B. The Post variable, which is related to the fiscal period and not to individual firms, will be coded as one for all firms in both countries after 2005 and zero for all firms in both countries prior to 2005.

Does the coding is correct?

Case two:

Let’s suppose that I aim to examine the impacts of mandatory adoption of IFRS in Country A, which mandated the adoption of the IFRS in 2005. Country A serves as the treatment group while Country B, which follows its own local GAAP and plans to mandate IFRS adoption in 2007 with the option for firms to adopt IFRS prior to 2007. Firms in country B that didn’t apply IFRS voluntarily before 2007 will serve as a control group. To illustrate, IFRS variable will be coded as one for firms in Country A and zero for firms in Country B. The Post variable, which is related to the fiscal period and not to individual firms, will be coded as one for all firms in both countries after 2005 until 2006 (inclusive) and zero for all firms in both countries prior to 2005.

Does the coding is correct?

Case three:

Let’s suppose that we aim to examine the impacts of voluntary adoption of IFRS in Country A. Firms in Country A that voluntarily adopt IFRS serves as the treatment group, while firms that didn’t apply IFRS will serve as a control group. The study will utilize DID model. In this model, the IFRS variable will be coded as one for firms in Country A that adopted IFRS, and zero for firms in Country A that didn’t adopt. Post variable ???

How the Post variable will be coded??

Apologies for the long question and I truly appreciate your understanding. I am eager to receive a response. Thank you for your cooperation.

[Clyde Schechter]

Case one: I agree with your proposed coding of the variables.

Case two: I disagree. You are proposing exactly the same coding as for case one, so you are completely overlooking the possible impact of voluntary adoption in country B prior to 2007. You are also overlooking the impact in country B of mandatory adoption after 2007. This data is not amenable to simple DID analysis. You need generalized DID.
In-Treatment Variable: 0 for any firm in either country during years when they have not adopted IFRS, 1 for any firm in either country during years when they have adopted IFRS and did so voluntarily, and 2 for any firm in either country during years when they have adopted IFRS under mandate to do so. You then need to do a two-way fixed-effects regression (with firm and year fixed-effects) of Dep.Var against this In-Treatment Variable, along with your covariates (so-called "control" variables).

Case three: This would be handled the same way as case two. You have a three-level in-treatment variable, 0 for those firms in those years where they have not adopted IFRS, 1 for those firms in those years where they have adopted IFRS and did so voluntarily, and 2 for any firm in those years where they have adopted IFRS under mandate. And then you do a two-way fixed effects (with firm and year fixed effects) regression of Dep. Var against this in-treatment variable, along with your covariates.

[Omar Shaher]

Hi Clyde Schechter ,
Thanks very much for your answer. I genuinely appreciate your consideration and cooperation. Greatly appreciated.

Now, I understood the case. Do you mean I should apply the Generalized DID with two way fixed effect as below instead of the simple DID??

Dependent variable = B1 variable of interest + B2 control variable + B3 IFRS + B4 IFRS * variable of interest + B5 IFRS * control variable + e.

[Clyde Schechter]

Dependent variable = B1 variable of interest + B2 control variable + B3 IFRS + B4 IFRS * variable of interest + B5 IFRS * control variable + e.

is not a two-way fixed effects model. And for a generalized DID, the variable IFRS would not be used.

Assuming you have panel data with a firm_id variable and a year variable, another variable, IFRS which is 1 if the firm has adopted IFRS in that year, and zero otherwise, and another variable, firm_type which is 0 if the firm is a never-adopter, 1 if it is a voluntary adopter, and 2 if it is a mandatory adopter.

gen byte ifrs_effect = cond(IFRS, firm_type, 0)
xtset firm_id year
xtreg dependent_variable i.ifrs_effect i.year, fe

[Omar Shaher]

Dear Clyde Schechter
It seems I got confused now again. I am sorry.

If I am going to examine the effect of IFRS on the relationship between financial reporting quality and conservatism in country A for industrial firms for the period 2006-2018. Until this period, adoption is not mandatory. The standards were issued, let’s say, in 2006, and firms started adopting the standards voluntarily. In specific, firms that did not adopt in 2006, adopted in 2007, those that did not adopt in 2007 adopted in 2008, and so on. In very simple words, the adoption of the standards is not simultaneous, in this way I will code IFRS one for firm-year observations after the adoption of the standards, and zero for firm-year observations before the adoption of the standards. The theoretical model of the Generalized DID with two ways fixed effect will be as below:

FRQ = B1 conservatism + B2 control variable + B3 IFRS + B4 IFRS * conservatism + B5 IFRS * control variable + e.

Q1: Is this correct??

In #32:

Case three: This would be handled the same way as case two. You have a three-level in-treatment variable, 0 for those firms in those years where they have not adopted IFRS, 1 for those firms in those years where they have adopted IFRS and did so voluntarily, and 2 for any firm in those years where they have adopted IFRS under mandate. And then you do a two-way fixed effects (with firm and year fixed effects) regression of Dep. Var against this in-treatment variable, along with your covariates.

How the theoretical model will be so I can understand the full image?

I am so sorry Clyde if I have bothered you with my question, but I still can't see the big image. If you don't mind. If it's not too much trouble, would you mind answering the two questions mentioned earlier? Thank you very much in advance!

[Clyde Schechter]

in this way I will code IFRS one for firm-year observations after the adoption of the standards, and zero for firm-year observations before the adoption of the standards.
FRQ = B1 conservatism + B2 control variable + B3 IFRS + B4 IFRS * conservatism + B5 IFRS * control variable + e.

Q1: Is this correct??

With IFRS defined the way you state, you can use this variable, but it does not distinguish voluntary from mandatory adopters, and the equation you show is not a two-way fixed effects model. Isn't that distinction important?

The theoretical model would look something along these lines:
FRQ = B1*IFRS + covariates + u_i + v_t + e_it
Here u_i is a firm fixed effect and v_t is a year fixed effect.

[Omar Shaher]

With IFRS defined the way you state, you can use this variable, but it does not distinguish voluntary from mandatory adopters, and the equation you show is not a two-way fixed effects model. Isn't that distinction important?

Sure, in this instance, I am focused solely on the voluntary adopters. To create a two-way fixed effect model, should I include both the firm fixed effect and the year fixed effect? Is that correct?

But, if I am interested in examining the impact of IFRS on the relationship between FRQ and conservatism under three periods for the same country (i.e., before adoption =0, voluntary adopters = 1, mandatory adopters = 2), the following generalised DID with two way fixed effect model can be used:

FRQ = B1 conservatism + B2 control variable + B3 IFRS + B4 IFRS * conservatism + B5 IFRS * control variable + u_i + v_t + e_it.
Here u_i is a firm fixed effect and v_t is a year fixed effect.

I hope that this is correct now?

[Clyde Schechter]

o create a two-way fixed effect model, should I include both the firm fixed effect and the year fixed effect? Is that correct?

Yes, precisely so.

FRQ = B1 conservatism + B2 control variable + B3 IFRS + B4 IFRS * conservatism + B5 IFRS * control variable + u_i + v_t + e_it.
Here u_i is a firm fixed effect and v_t is a year fixed effect.

This is fine. If you don't have any reason to believe that the effects of the "control variable(s)" will differ according to IFRS, then the interaction term (B5*...) can be omitted. But if you think IFRS will also modify the "control variable" effects, then leave it exactly as you have it.

[Omar Shaher]

Dear Clyde Schechter

I wanted to express my sincere gratitude for taking the time to respond to my questions. Your insights and guidance have been invaluable to me, and I am grateful for the opportunity to learn from you.

Thank you again for your expertise and support.

[Omar Shaher]

Dear Clyde Schechter , I've read the comments again today and i think I have one last question, please.

Which of the below two modules is called the generalized DID with two way fixed effect:
1) FRQ = B1 conservatism + B2 control variable + B3 IFRS + B4 IFRS * conservatism + B5 IFRS * control variable + u_i + v_t + e_it.
Here u_i is a firm fixed effect and v_t is a year fixed effect.

2) FRQ = B1*IFRS + covariates + u_i + v_t + e_it
Here u_i is a firm fixed effect and v_t is a year fixed effect.

[Clyde Schechter]

Both of them are generalized DID with two-way fixed effects. I should point out that generalized DID always requires a two-way accounting of entity (firm, person, whatever) and time effects. In observational studies this is done as a two-way fixed effects analysis. In experimental studies, one can instead use a random effect for the entity instead, which provides more efficient estimates.

The difference between the two models you show in #10 is just whether or not you also investigate IFRS effect being modified by conservatism and covariates. Either way it's still a generalized DID model.

You might find this review of generalized DID helpful: https://www.annualreviews.org/doi/pd...-040617-013507.

[Omar Shaher]

Dear Clyde, I can't thank you enough for the answer and for the article you mentioned.

[Omar Shaher]

Dear Clyde Schechter ,

I would like to extend my sincerest apologies if my previous inquiries have been excessive and imposed upon your time. Please know that I fully understand if you prefer not to respond to this message. However, I promise that this will be my final question.

Referring to #2, for the following equation which related to case one:

Dep.Var= B1 IFRS + B2 Post + B3 Post * IFRS + Controls + e.

IF I want to examine the impact of IFRS on the relationship between De.Var and let's say conservatism. Do you think I can still use the same equation, if yes, then how the theoretical form will be? or I should go with the following generalised DID with two way fixed effect equation:

Dep.Var= B1 conservatism + B2 control variable + B3 IFRS + B4 IFRS * conservatism + B5 IFRS * control variable + u_i + v_t + e_it.
Here u_i is a firm fixed effect and v_t is a year fixed effect.

Thank you for your consideration and understanding.

[Clyde Schechter]

I would use Dep.Var= B1 conservatism + B2 control variable + B3 IFRS + B4 IFRS * conservatism + B5 IFRS * control variable + u_i + v_t + e_it..

[Omar Shaher]

Dear Clyde, Thanks so much! Greatly appreciated.