Using external Instruments in xtabond2 GMM (Arellano Bond FD GMM and System GMM)

[Josh Dawson]

Hello,

I have a cross country panel data set (attached). I am running Arellano Bond GMM using xytabond2. I am regressing deficit on its lag, fiscal rule strength (fr) and controls VFI and fed. The code is as follows:

tsset id year, yearly
xi: xtabond2 deficit l.deficit fr VFI fed , gmm(deficit fr VFI fed, lag(2 6)) robust noleveleq

In the code above, past lags from t-2 to t-6 of all variables are used as internal instruments. The variable of interest is fr. However, it is probably endogenous so I want to instrument for it using two political variables pol1 and pol2 that I want to use as external instruments. How can I use these variables to instrument for fr using xtabond2?


Thank you,
Josh

[Josh Dawson]

Does anyone have advice on this? Many thanks.

[Shiping Tang]

If you want to use exogenous IV as well as GMM-style lagged DV as instruments, you should use ivreg2. See the Baum et al (2007) STATA journal paper. But you better have sound logic for doing so. I have seen way too many papers doing IVs without a sound logic.

[Sebastian Kripfganz]

You can still use xtabond2. Simply add the option ivstyle(pol1 pol2), potentially with suboptions to specify in which equation the instruments should be used.

[Shiping Tang]

Thanks, Sebastian. Learned something new again.

[Dario Maimone Ansaldo Patti]

Sebastian Kripfganz Dear Sebastian, I have a similar problem in my estimation. However, your answer is not clear to me. Basically, you suggest to use ivstyle(pol1 pol2) to add external instruments (possibly with some suboptions). However, how can I be sure that pol1 and pol2 instrument exactly the variable fr and not the others as well? Or does this option mean that it adds external instruments for ALL the endogenous variables in the regression? Thanks for your explanation.

[Sebastian Kripfganz]

There is no mapping from specific instruments to specific regressors. All instrumental variables instrument all endogenous variables. This is true in general and not specific to xtabond2.

[Domenico Candido]

Since there is no mapping from specific instruments to specific regressors, how is it possible to prove (or at least justify) that adding this new external instruments are used for the specific purpose of better quantify the effect of a particular endogeneous variable? An example to be clear: if I regress gdp on lagged gdp, other control variables (some endogeneous and some exogeneous), and two variables of interests such as criminal organization index and corruption, and I want to use in the iv style command two instruments: a policy against crime and a policy for the improvment of associations between people which improves the level of "trust". This two external variables respect the requirements in order to be valid instruments (see Angrist) and of course permit an "indirect" interpretration of the coefficients of the variables of interest (the impact of the change of crime index and corruption caused by the two instruments), that is good when one is interested in the effects of a policy. Since it s impossible to map (how you say before) but it s clear that the new external instruments are "useful" (in sense of adding information) only for the variables of interest, can this latter consideration be considered sufficient to intuitively think that this is the role of this new instruments (like an artifically map) with all the good interpretation corollary? I m sorry if I am not too technical. I hope you can understand my question. Thanks in advance
best regards

[Domenico Candido]

Sebastian Kripfganz, I forgot to tag you in the previous post

[Sebastian Kripfganz]

When you have multiple endogenous variables and multiple instruments, such an "indirect interpretation" of the coefficients can become quite complicated. For the justification of your instruments, you could still use the usual argumentation that the external instruments are validly excluded, i.e. do not have a direct effect on the dependent variable, but have an indirect effect via the endogenous variables (although this indirect effect might go via one or more of the endogenous variables). Not sure if this answers your question.

[Domenico Candido]

Yes, perfectly answered. Many thanks.

[Domenico Candido]

Dear Sebastian Kripfganz,

If I want to implement a system gmm in which log gdp per capita is regressed on lagged log gdp per capita, log HumanCapital, log R&D, Demography, Corruption and Organized Crime with all regressors endogeneous except for HumanCapital (exogeneous), can the following code be considered appropriated?

xtabond2 logGDPpercapita L.logGDPpercapita logHumanCapital logR&D Demography Corruption Organized Crime, gmmstyle(L.logGDPpercapita, lag(1 2) collapse eq(diff)) gmmstyle(logR&D Demography Corruption OrganizedCrime, lag(2 3) collapse eq(diff)) gmmstyle(L.logGDPpercapita, lag(0 1) collapse eq(level)) gmmstyle(logR&D Demography Corruption OrganizedCrime, lag(1 2) collapse eq(level)) ivstyle (logHumanCapital, eq(level)) robust twostep noconst small

The objective is to use a twostep sys gmm with corrections for small sample size and robust standard errors(WIndmeijer). I use collapse and minimal laglimits to reduce the number of instruments. Sometimes I saw in examples the presence of D.nameofinstruments (i.e. D.logHumanCapital) in eq(level) both on gmmstyle and ivstyle, why exactly? Is it appropriate in my case?
Last little question: noconst eliminates the intercept (right?), is it a problem to add this command in the code?
Thanks in advance
Best regards

[Sebastian Kripfganz]

The specification looks allright. Note that in your case exogeneity of human capital requires that this variable is also uncorrelated with the unobserved country-specific effect.

The gmmstyle() option of xtabond2 by default applies a first differencing of the instruments for eq(level). Thus, explicitly specifying the D. operator is not necessary. This is not the case for the iv() option. Here, you would need to specify the D. operator if you want the instrument to be first differenced for eq(level).

When you use the system GMM estimator with instruments for eq(level), it is almost never appropriate to omit the intercept (unless all of your variables are already in deviations from their mean, which is clearly not the case here).

More on linear dynamic panel data GMM estimation in Stata:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.
• XTDPDGMM: new Stata command for GMM estimation of linear (dynamic) panel data models

[Domenico Candido]

Ok, I will add D. before logHumanCapital in ivstyle command and eliminate noconst from the code.
What can I do to reduce the number of instruments? Is it better to reduce lags in eq(diff) or eq(level)?
I know that it is insignificant but you will be thanked in my thesis, your help is very useful

[Sebastian Kripfganz]

It is common practice to just use 1 lag for the model in levels. Other than that there is not much you can do given that you are already using the collapse option.