Fixed effect, Random Effect, Lagged Dependent Variable, Robustness Check (Econometrics, Urgent!!)

[Johnny Evans]

I am constructing an equation with

y_it = a + x_1it + x_2it + y_it-1 + error term .

In this case, would it be appropriate for me to still use fixed effect and what command should I use in order to check for the robustness

[Carlo Lazzaro]

Johnny:
welcome to this forum.
Given the very limited details that you provided, the theoretical answer is: yes, you can.
Assuming that you have a continuous regressand, see -xtreg- for static panel data regressions and -xtbabond- for dynamic ones (as you mentioned a lagged dependent variable).

[Joro Kolev]

Claims of urgency are strongly discouraged around here. It might be urgent to you, but it is not urgent to us, and your priorities in no way have precedence over our priorities.

As to your question the fixed effects model is appropriate only if you have large T. For large N small T data, your regression (called dynamic regression) will suffer of something called Nickell bias. See this source here http://fmwww.bc.edu/ec-c/s2013/823/E...n05.slides.pdf.

If you have large N, small T, look for -[XT] xtabond-, this is an appropriate estimator for dynamic models with fixed effects.

Another appropriate estimator for your equation and large N , small T is the Anderson-Hsiao estimator, that you can do with -xtivreg- as explained in this thread:
https://www.stata.com/statalist/arch.../msg00280.html

[Johnny Evans]

Dear Carlo,

Thanks for the reply.

I am researching the topic related to migration

Because the initial equation that I am using is

log(wages)_it = Education _it + Housing Prices _it + error term

But I am planning to change it with

log(wages)_it = Education _it + Housing Prices _it + log(wages)_it-1 +error term.

Under this case is fixed effect is still be suitable given my T=13 (Annual) with N= 110.
Should I change to random effect instead ?

Kind Regards,
Johnny

[Carlo Lazzaro]

Johnny:
Joro's reply is enlightening in this respect: you shoud go -xtabond-.
Going -fe- or -re- does not depend on your regression equation but on the data generating process.

[Johnny Evans]

Dear Joro,

Thanks for the reply.

May I ask how do you determine whether the data has a large or small N or T value. The N of my data is 110 and T is 13 years (measured in year).

Therefore, is it mean that using (xtreg, fe) would be inappropriate and instead (xtabond) should be used ?

Kind Regards,
Johnny

[Johnny Evans]

Dear Carlo and Joro,

Thanks for the reply.

I understand now xtabond is a better option if the data is large N small T. But I would like to know the is there any reason why xtreg is less preferably option except the Nickell bias?

Kind Regards,
Johnny

[Carlo Lazzaro]

Johnny:
1) if you have a N>T panel dataset and you're interested in static panel data regression, go -xtreg-;
2) if you have a N>T panel dataset and you're interested in dynamic panel data regression, go -xtabond- (please note that the dynamic panel data regressions are much more theoretically demanding than their static counterparts).

1) and 2) imply a continuous regressand.

[Joro Kolev]

Yes, the only reason that makes -xtreg- inappropriate in dynamic models is the Nickell bias, and the reason is serious enough. Kit Baum writes in the source I cited above:

For reasonably large values of T, the limit of (ρˆ− ρ) as N → ∞ will be approximately −(1 + ρ)/(T − 1): a sizable value, even if T = 10. With ρ = 0.5, the bias will be -0.167, or about 1/3 of the true value. The inclusion of additional regressors does not remove this bias. Indeed, if the regressors are correlated with the lagged dependent variable to some degree, their coefficients may be seriously biased as well.

There is no exact method to say what is "large" and what is "small" in econometrics, and it always depends on the context. Most econometricians (or maybe all econometricians? ) would say that T=13 is small.

In short you either have to choose the static model and omit the lagged value of log-wage on the right hand side; then you can proceed with -xtreg-.

Or if you really want to have lagged log-wage on the right hand side, do either -xtabond-, or the Anderson-Hsiao through -xtivreg-.

Dear Carlo and Joro,

Thanks for the reply.

I understand now xtabond is a better option if the data is large N small T. But I would like to know the is there any reason why xtreg is less preferably option except the Nickell bias?

Kind Regards,
Johnny

[Johnny Evans]

Dear Carlo and Joro,

I decided to take the latter option by using the command xtivreg

As my data lies from 2000 to 2011 with the IV being a dummy variable after 2005

i.e. log(wages)_it = Education _it + Housing Prices _it + log(wages)_it-1 + Dummy Variable_it + error term.

Which one I should choose between RE, FE, FD, BE for this case and why is it the case ?

Also, the command would be looks like (I did the parts on the lag wages, and let stata to understand it is a panel data)

tab dummy, generate (Dummy)
rename Dummy1 Pre_Dummy
rename Dummy2 Post_Dummy
xtivreg lnwages Education HousingPrices Lnwages_L1 (Dummy=Post_Dummy), fe/re/fd/be ?

Kind Regards,
Johnny

[Johnny Evans]

Also, how can I check the robustness error in this case ? Like what commands should I use ?

[Johnny Evans]

As in like if I am using a panel data model with instrument variable (i.e. xtivreg) with a fixed effect. Should I need to care about the robustness error ?