GMM xtabond2 with external IVs

[junlei luo]

Hello miracle makers,

I would like to use GMM and external IVs at the same time and struggling to see the difference between putting the external IVs as gmm vs as ivstyle. As a starting point, here is the 2SLS model with two external IVs meant to instrument for the endogenous L.x1, where the external IVs associated with L.x1 are L.z1a L.z1b.

ivregress 2sls y L.y L.x2 L.x3 i.year i.id (L.x1 = L.z1a L.z1b)

L.x2 may also be endogenous, but I'm not sure, so would like to just instrument it with its lags in the GMM in one of two manners:

(1)

xtabond2 y L.y L.x1 L.x2 L.x3 i.year, gmm(L.y L.x2) ivstyle(L.x3 L.z1a L.z1b i.year, equation(level)) twostep

(2)

xtabond2 y L.y L.x1 L.x2 L.x3 i.year, gmm(L.y L.x2) gmm(L.z1a L.z1b) ivstyle(L.x3 i.year, equation(level)) twostep

Three important questions I have are:
Assuming these are both possibly logical, does (2) make a more robust model with L.z1a L.z1b as GMM, thereby including their lags as the instruments for the main endogenous variable L.x1?
Does changing

gmm(L.z1a L.z1b)

to

gmm(L.z1a L.z1b, laglimit(1 1))

in (2) make it the same as (1)?
And lastly, why is equation(level) not included in the gmm area (in any of the examples and usually in discussions online) - I cannot make sense of this in the help file.

Thanks very much for your time!

[Sebastian Kripfganz]

The gmm() option without the eq() suboption creates instruments both for the first-differenced and for the level model. The following specifications of options should be equivalent:

iv(L.z1a L.z1b, eq(level) mz)
gmm(L.z1a L.z1b, lag(0 0) eq(level) collapse passthru)

Notice that an implicit assumption for such instruments is that they are uncorrelated with the unobserved unit-specific effects; which essentially amounts to a random-effects assumption.

If you specify the gmm() option without the passthru suboption, the instruments for the level model will be differenced. Assuming that those differenced instruments are uncorrelated with the unobserved unit-specific effects is a weaker (and therefore more robust) assumption than the above random-effects assumption.

The following presentation and the references therein might be of further help:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

[Sabrin Rahman]

I am struggling to choose Exogenous Variables for GMM ivstyle? My Dependent variable is Gender Equality Index and Independent Variable is FDI?.

I also wanted to check whether GMM is fine or not I have 80 countries and my T is 24. I was reading somewhere that you T must not exceed 15 and N must be more than 100. Is it true??? If true then what shall I do.
I am having difficulties to find exogenous variable for my model. My model is given below.
Gender Inequality Index = a+bFDI+ (ControlV)+U

[Dario Maimone Ansaldo Patti]

Do you want to instrument..what? Which variable you think is endogenous? Is it FDI? Or what else? You want to estimate a static panel data model from what you show us. If so and you have difficulty in finding out instruments, a solution could be to use the approach indicated in Lewbel 2012, where instruments are generated from the heteroscedastic residuals. The user written routine ivreg2h allows the option fe, for a fixed panel data with endogenous variable, where the latter is instrumented using the approach suggested above.

i hope it helps,

Dario

[Sabrin Rahman]

Sorry I think I made a mistake with the equation as I am very new to GMM. I am going to use Dynamic Panel Model. My lagged Dependent Variable is lag of GII which I am going to use in GMMSTYLE() but I am not sure what to include in the IVSTYLE(). I am not sure whether I should use lags of control variables in the ivstyle(external Instruments) command under XTABOND2.

My Control Variables are: Fertility rate, GDP growth,tradeopenness, natural resource rent, Polity IV etc.

My Main Explanatory variable is FDI Inflows

Model:
Gender Inequality Index(GII) = a+GIIt-1+bFDI+ (ControlV)+U