strict exogeneity assumption fixed effects

[Sandra Bloem]

Hi there,

I was wondering something. I have panel data and need to check the strict exogeneity assumption of a fixed effects model (idiosyncratic error term is uncorrelated with variable of interest).

I was wondering if there is a way to check this in Stata. Also, I'm looking at results of a study and was wondering if you could say something about this assumption from those results. Just to get a better understanding of the model and the what the assumption actually entails.


The study checks whether sport participation and/or club participation (both dummy variables) influence the test score of students in high school. T = 3.

Column 1 (4) is the base model. Column 2 (5) add some time-varying variables that could be correlated with both participation and test score. In column 3 (6) even more time-varying variables are added.

In the article they say that it's likely the strict exogeneity assumption holds, since adding the time-varying variables doesn't change the coefficients of sport participation and club participation much and remain significant. Therefore, it's likely that other time-varying variables don't matter as well, and hence there is no endogeneity.

However, I was wondering if you could really state that. Some coefficients of these time-varying variables are significant. In addition, the coefficient of club participation changes quite a lot (in my opinion) from column 1 to column 3.


Sorry for the long story. I hope everything is clear. In short, I have 2 questions:

1. Is there a way to test the strict exogeneity assumption in Stata?

2. Is it possible to say something about the strict exogeneity assumption in results like these below?


Thank you in advance (:

[Eric de Souza]

With FE and more than three time periods

Assume that this is your model:
y d2 ... dT x1 ... xK w1 ... wJ, fe vce(cluster)
where
d2 to dT are time dummies for periods 2 to T
You are sure that x1 ... xK are strictly exogenous
you assume that w1 ... wJ are strictly exogenous but are not sure and would like to test them for strict exogeneity.

Regress:

xtreg y d2 ... d(T-1) x1 ... xK w1 ... wJ F.w1 ... F.wJ, fe vce(cluster)

where d2 to d(T-1) are time dummies for periods 2 to T-1 (T is the total number of time periods)
and F.w1 ... F.wJ are the w variables lagged forward one period

Then

test F.w1 F.w2 ... F.wJ.

The null hypothesis is that F.w1 F.w2 ... F.wJ are strictly exogenous.

Example:

webuse grunfeld
* The model:
xtreg invest mvalue kstock i.time, fe vce(cluster company)

* The test (both mvalue and kstock are suspect):
xtreg invest mvalue kstock i.time F.(mvalue kstock), fe vce(cluster company)
test F.(mvalue kstock)
test F.mvalue F.kstock

The test rejects the null hypothesis.

I have not produced the output here since grunfeld.dta is publicly available.

With i.time the first period time dummy is dropped in the model regression
and both the first and last period time dummies are dropped in the test regression.

This test was proposed by Prof. Wooldridge.

[Sandra Bloem]

Eric de Souza

Wow, this makes everything very clear! Thank you so much (: