Does it make sense to use decadal dummies for quinquennial data?

[Alex Mai]

Dear Statalists,

I have a question of if it is reasonable to use decadal dummies as time fixed effects in quinquennial data (which I read from a paper). The data in question are arranged as the average of every five-year period. That paper does not use quinquennial dummies as time effects. Instead, it uses decadal dummies. So could I ask if this treatment is econometrically reasonable or appropriate? And what is the rationale behind this treatment?

If this treatment is okay, can I set decadal dummy as shown in the following sample data? period stands for quinquennial period and dummy1-7 stand for decadal dummies. So there are 14 quinquennial time points (the variable period has 14 observations) and 7 decadal dummies (e.g. period 1 and 2 constitute the first decade).

* Example generated by -dataex-. To install: ssc install dataex
clear
input float period byte(dummy1 dummy2 dummy3 dummy4 dummy5 dummy6 dummy7)
 1 1 0 0 0 0 0 0
 2 1 0 0 0 0 0 0
 3 0 1 0 0 0 0 0
 4 0 1 0 0 0 0 0
 5 0 0 1 0 0 0 0
 6 0 0 1 0 0 0 0
 7 0 0 0 1 0 0 0
 8 0 0 0 1 0 0 0
 9 0 0 0 0 1 0 0
10 0 0 0 0 1 0 0
11 0 0 0 0 0 1 0
12 0 0 0 0 0 1 0
13 0 0 0 0 0 0 1
14 0 0 0 0 0 0 1
end

Thank you very much!

[Clyde Schechter]

Concerning your creation of dummy variables, what you show would be correct, but it is not the best way to go about this. I'm assuming ultimately you want to use these variables as time fixed effects. The better way to do that would be to just create a 7-level decade variable

clear
input float period
 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
end

gen decade = ceil(period/2)

and then use factor-variable notation to have Stata create "virtual" indicator variables for the decades in your regression:

regression_command outcome_var predictors i.decade, options

Read -help fvvarlist-. There are hardly any circumstances in modern Stata where it makes sense to create a whole series of actual indicator variables any more.

Concerning your question about the econometric reasonableness of using decadal fixed effects with quinquennial data, I cannot advise you, but there are several econometricians active in the Forum and, hopefully, one of them will respond to that.

[Alex Mai]

Concerning your creation of dummy variables, what you show would be correct, but it is not the best way to go about this. I'm assuming ultimately you want to use these variables as time fixed effects. The better way to do that would be to just create a 7-level decade variable

Dear Clyde,

Thank you very much for your suggestions!

[Alex Mai]

Any suggestions of the econometric rationale or reasonableness underlying the use of decadal dummies as time fixed effects for quinquennial data would be appreciated! Thank you very much.