Regression specification for panel data with a dummy variable as an IV

[Ahmed Chaudhry]

Hello everyone,

I want to estimate the effect of x_1, which is a continuous variable on the Economic Complexity Index (eci). Currently, I am using unbalanced panel data for about 50 countries from the period 1965 to 2016.
To estimate the effect of x₁, I am using the following regression models:

1. Pooled OLS:

  reg eci initial_eci x1 (set of controls), vce(robust)

2. Panel LSDV (Fixed Effects) Model:

  xtreg eci x1 (set of controls) i.year, fe vce(robust)

3. Panel LSDV (Fixed Effects) Model:

  xtreg eci lag_eci x1 (set of controls) i.year, fe vce(robust)

4. Panel LSDV (Fixed Effects) Model:

  xtreg eci lag_eci x1 (set of controls) , fe vce(robust)

5. 2SLS:

  xtivreg2 eci (x1  = IV) (set of controls) i.year, fe small robust first

6. 2SLS:

  xtivreg2 eci (x1  = IV) (set of controls) , fe small robust first

Note: initial_eci is the value of eci at the beginning of the sample period.

These are the questions that I have:

Q1. The inclusion of year fixed effects makes x₁ insignificant, with almost all the year dummies being highly significant (Model 2). When I use lag_eci all year dummies become insignificant (Model 3). And then, when I exclude year dummies, x₁ again becomes significant (Model 4). Given this, can I plausibly argue that year-fixed effects are irrelevant when I control for lag_eci, and thus should not be included in the regression model? Can I use the joint significance test for year dummies to prove my point? If yes, then how can I test it in STATA?

Q2. My instrumental variable is a dummy variable that takes the value of 1 after 1988 for all countries. The 2SLS does not proceed forward when I run Model 5 with the year FE. However, omitting year FE (Model 6) does the job, and all the IV first stage and 2nd stage tests look good as well. Do you think that year FE and my instrument are colinear in this case? Is there a way I can include year FE and run the IV regression (Sorry if this question is too naive!)? Is it plausible to not include year FE in the 2SLS model?

Again, the problem here seems to be the year FE, i.e., unobserved/unchanging characteristics across time that affect the outcome.

Also, there is a possibility that I am not thinking about my model specifications in the correct way here, so irrespective of my questions, I am open to other suggestions as well.

Any suggestions would be greatly appreciated!

[Carlo Lazzaro]

Ahmed:
unless it is an assignement (and, if that were thae case, please see https://www.statalist.org/forums/help#adviceextras #4).
That said, I'm going to reply to your first question only.
As you've probably coded up a pooled OLS (which is poor first choice tool when dealing with panel data), other things being equal, I should go:

reg eci initial_eci x1 (set of controls), vce(cluster panelid)

as, under -regress-, the -robust- option takes heteroskedasticity only into account.

[Ahmed Chaudhry]

Carlo Lazzaro, I am working on a paper, not an assignment.

Let me first correct the no. of cross-section units in my sample is 42 to be exact. I was reading that using cluster robust SE for a panel < 50 is not advisable. Do you still think that I should be using cluster robust SE?
Thanks!

[Carlo Lazzaro]

Ahmed:
yes, I think so. Otherwise, with the -robust- option only, you're not telling Stata that the observations belonging to the same panel are correlated.