Dropped Time dummy - collinearity

[Mario Scintille]

Dear all,

I am running a regression where i try to test the effect of employment policy on several outcomes, including some count data for which i use the negative binomial regression. More in detail, my model is the following

xtnbreg OUTCOME_VAR EMPLOYMENT_PROTECTION CONTROLS i.time, fe

where i.time is supposed to introduce time dummies. The data is a panel data at country level.

My problem is that when i introduce in my controls a variable that is supposed to capture how employment_protection rules are defined in other countries (not in country i) stata drops the time dummy for last year in the model because of collinearity. I have no idea what this happens, do you have some advice? correlation with what also??

Thanks a lot,
Mario

[Clyde Schechter]

If you want to find out what the colinearity is all about, create a new variable to represent the time indicator ("dummy") that is dropped and regress it against the the other regressors. So if, let's say 5.time is being dropped, re-run your regression and then run

levelsof time, local(times)
foreach t of local times {
    gen time_`t' = `t'.time
}
rename time_5 TIME_5
regress TIME5 time_* EMPLOYMENT_PROTECTION CONTROLS if e(sample)

Inspecting the output of that regression will show you which of your control variables is (are) collinear with the dropped time variable. Then you will need to figure out why this colinear relationship exists. There are basically three possibilities:

1. Your data are incorrect and, by coincidence, have created this colinearity. In that case you need to correct your data.

2. This is, in fact, an expected colinear relationship. For example, if the employment protection rules defined in other countries take on one value during certain time periods and a different value in all other time periods, then one of your time dummies will necessarily be colinear with that. If this is the situation, then there is nothing wrong and you should just forget about it and move on. (If I had to make a bet, sight unseen, I would bet on this situation.)

3. There is some other colinear relationship among these variables that 5.time happens to coincidentally play a role in. In this case you can chose to omit one of the other variables so that all the time periods will be represented, if you feel that it is more important to have every time period than that other variable. No matter what you do, however, you can't have a complete set of colinear variables in the model: something has to go.

[Mario Scintille]

Dear Clyde, thank a lot for your very helpful answer. I have followed your advice and the collinearity is apparently between the time dummies, if I read correctly the Stata Output below. Any idea about what might be wrong?

 regress TIME_2011 time_* $ EMPLOYMENT_PROTECTION CONTROLS  if e(sample)

and stata tells me that

 
note: time_1990 omitted because of collinearity
note: time_2012 omitted because of collinearity

[Clyde Schechter]

Well, remember that you always lose one of the time variables due to colinearity. The question is why you are losing two. The usual situation here is what I described as point 2 in #2 above. I'm guessing one of your other variables is constant within each level of time. For example, one of your variables encodes the presence or absence of some employment protection policy, and if that policy was enacted in, say 2005, so it is 0 before then and 1 from that point on, then you will have to lose one time variable before 2005, and one in the period starting in 2005. If that's what's going on, it's not a problem and you shouldn't worry about it.

[Mario Scintille]

I might have understood the problem. I have inspectioned the data and it seems that my variable of foreign employment protection has the same value for several countries in each year. This is by construction since I compute foreign_emp_protection for each country i at time t as the following

and for many countries emp_pro is equal to zero. As such, the sum minus zero results in a value that is the same for several countries

[Clyde Schechter]

Well, having foreign_EMP_PRO be the same for several different countries wouldn't be enough to cause colinearity. If it were the same for all countries, however, that would do it.

I doubt I can provide you with any specific assistance here without seeing your data.

[Mario Scintille]

thanks a lot Clyde,

In my case, in year 1990, it is 1.2 for all countries except one where it is ZERO. This is the cause of collinearity, i think. do you consider it reasonable?

[Clyde Schechter]

Yes.

[Mario Scintille]

thanks a lot! I really appreciated your help and advice!

Have a great day,
Mario

[Valentin Longrider]

Dear Clyde Schechter ,

I just stumbled over this thread, as I am currently having a similar issue: in my case, I want to investigate the Impact of a policy reform that took place in 2007. All individuals in my sample that were observed in 2007 and later are part of the treatment group, while all individuals that were observed before 2007 are part of the control group. As a result, my treatment dummy variable takes the value 1 for all observations in 2007 and later and 0 otherwise.
Now I want to also control for year fixed effects, using dummy variables for each year. The result is what you called "expected colinear relationship" in the quote below: There are effectively two time dummies dropped - one from the control group (the first year of observation) and one from the treatment group (the last year of observation).

Now you also wrote in #2 that the omitted second dummy isn't anything to worry about.

2. This is, in fact, an expected colinear relationship. For example, if the employment protection rules defined in other countries take on one value during certain time periods and a different value in all other time periods, then one of your time dummies will necessarily be colinear with that. If this is the situation, then there is nothing wrong and you should just forget about it and move on. (If I had to make a bet, sight unseen, I would bet on this situation.)

My question now is: Were you referring to the special situation of the OP? Because as far as my situation is concerned i was wondering whether the omitted dummy variable will cause the estimator of my treatment dummy to be biased.

Thank's in advance!

Valentin