Xtabond2 use confusion for Difference/System GMM

[Gian Zeoli]

Hello everyone,

I am writing to ask whether someone could help me with the implementation of a GMM model using xtabond2. Unfortunately, I am a bit confused about the use of the package and related code.
This is the setting: I have a dynamic panel, with the lagged version of the dependent variable being on the right side of the equation. Also, I have a set of other variables that I hypothesize should be correlated with y in their lagged version. More specifically, the model comprises the following variables:

• military casualties (which is the y)
• new_policy (which maps whether in a given year a government has issued a new war-related policy)
• weapon_purchase (which maps whether in a given year a government has increased its spending on weapons by a certain threshold)
• density (population density in given year)
• democratic (level of democracy of a country in a given year)
• year (mapping each year)

Now, I am interested in finding relationships between y and 1) the lagged version of y, 2) the lagged (t-1) version of new_policy and weapon_purchase.

Given this aim, is the following model specification correct?

xtabond2 L(0/1).military_casualties new_policy weapon_purchase density democratic i.year, gmm(military_casualties new_policy weapon_purchase, equation(diff) lag(0 1) collapse) gmm(military_casualties new_policy weapon_purchase, equation(level) lag(0 1) collapse) iv(i.year density democratic, eq(level)) iv(i.year density democratic, equation(diff)) robust

My concern is that this specification is not using the lagged version of x in the model, hence it is only studying the relationship between e.g. weapon_purchase(t) with military_casualties(t). If the above specification is not correct (namely, does not investigate the relationship I am interested in), should I modify it like:

xtabond2 L(0/1).military_casualties L.new_policy L.weapon_purchase density democratic i.year, gmm(military_casualties L.new_policy L.weapon_purchase, equation(diff) lag(0 1) collapse) gmm(military_casualties L.new_policy L.weapon_purchase, equation(level) lag(0 1) collapse) iv(i.year density democratic, eq(level)) iv(i.year density democratic, equation(diff)) robust

Unfortunately, I cannot share the data as they are confidential.

I thank in advance anyone who will help me on this. Sorry but I am new to Stata, I appreciate your understanding and cooperation.

[Sebastian Kripfganz]

Whether the effect is from the lagged variables or the contemporaneous variables is a question you need to answer yourself based on the underlying theory. You could also employ an empirical approach and include both the contemporaneous and the lagged term jointly as regressors, to see which of them is having an effect.

In any case, specifying military_casualties as an instrument with lag(0 1) is invalid for both the level and the differenced model. This is the dependent variable, which is endogenous. For the first-differenced model, the first valid instrument is at best the lag 2, and for the level model lag 1.

You also need to decide about the other variables whether they are endogenous, predetermined, or exogenous.

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.

[Gian Zeoli]

Thank you very much for your reply, Sebastian. Regarding the first part: can you confirm then that the first code snippet in my post does not consider Weapon_purchase and new_policy as lagged? If so, and then I have to modify it using lagged versions, and considering them to be endogenous, where should I put them? In the gmm instruments with a lag that is at least equal to?

thanks a million for your help again.

[Sebastian Kripfganz]

In your first code, the regressors enter without lags. Slides 11 and 31 in my presentation tell you which lags are appropriate instruments.