GMM xtabond2 command specification

[Guest]

Hello,

I am running system GMM regressions to estimate and compare the impacts of remittances, FDI and foreign aid on inequality. Moreover, I check whether the impacts differ for Latin American countries (LAC). For FDI, I perform the following command:
xtabond2 difgini gini1 Female1 Male1 capital101 LAC1 FDI1 FDI1xLAC1 ydummy1-ydummy26, gmm(gini1 FDI1 FDI1xLAC1, lag(2 15) collapse) iv(Female1 Male1 LAC1 capital101 eq(both)) iv(ydummy1-yummy26, eq(level)) small robust twostep
where Female, Male, capital and LAC are exogeous controls and I assume the lagged dependent variable and FDI inflows are endogenous.

However, I am not sure how many lags I should include in my model. I have run regressions with lag(2 2) until lag(2 15). In all cases, the SOSC and Hansen statistics are not rejected. Moreover, the difference-in Hansen test is also never rejected. Knowing this, how can I determine which lag length I should use? The FDI variable is only significant at lag 14 and 15.

Hoping someone could help me.

[Sebastian Kripfganz]

What do you mean by "SOSC"?

If your time dimension is reasoably small and your cross-sectional dimension is large, then you could just use all the valid available lags as instruments. Lag length restriction is primarily done to avoid a too-many-instruments problem. If the latter becomes a concern, restricting the lag length to about 4 or 5 is usually fine, in particular if the results are robust to alternative lag lengths. Yet, there is no general rule.

[Tim Grünebaum]

Welcome Guest,

You should always first consult the Statalist FAQ and offer your code in a code box, maybe with some sample data or results.

Concerning your problem 15 lags for your instruments seem way to much. You should consider a famous souce by Roodman (2006): How to do xtabond2, which you can easily find on the internet. He gives very practical adive. In a nutshell do not go "too far". I would say about 3 lags should do it, then you might get rid of the collapse option if the number of instruments is not to high to avoid the weak instrument problem which you probably get using very deep lags.
Furthermore look up some recent posts by Maarten Buis here on Statalist for SysGMM models to consider the correct use of the iv() option. You should always specify a diff or level option for your exogenous variables. Also using dummies in the iv() environment can couse problems because using differences of dummies as instruments can cause biased results.

[Guest]

Thank you for you reply and advice.

I'm sorry Sebastian, I abbreviated second order serial correlation with SOSC, thus I mean the second specification test of no second order serial correlation in the first-differenced error.

Tim, I have read the 'how to do xtabond2' paper by Roodman and indeed understood that the lag length should not be too long. However, I just do not know how to determine how many instruments is 'too many'. I feel like I need some explanation for the lag length I choose? For example, could I support my decision by looking at the difference-in Hansen test? I read that this test examines the validity of additional instruments. Anyway, I have to use the collapse option because otherwise the number of lags exceeds the number of countries included in my sample.

I will have a look at Maarten Buis' posts. Thank you for the tip. However, I thought I could use both level and difference equations for the exogenous variables? Should I type iv(Female1 Male1 capital101, eq(level)) iv(Female1 Male1 capital101, eq(diff)), instead of iv(Female1 Male1 capital101, eq(both))?

Again, thank you for your reply. I am looking forward to receive your answer on my follow up questions

[Sebastian Kripfganz]

I do not think it was Maarten Buis who made these statements about System GMM, but I am happy for him to take the fame (and to be corrected if my memory is incorrect).

Tim is nevertheless right with his statement that using the eq(both) suboption (or no eq() suboption at all) for the iv() option may not do what you think it does. It does not create the same instruments as when you specify them separately for eq(diff) and once for eq(level). If the latter is what you have in mind, then do not specify the eq(both) suboption.

Furthermore, once you have specified the iv() instruments for eq(level), there is in most situations no need to specify the same instrumental variables for eq(diff) because the latter are usually redundant. Also keep in mind that the instruments for eq(level) are assumed to be uncorrelated with the unobserved individual-specific effects.

More on GMM estimation of dynamic panel data models:
XTDPDGMM: new Stata command for efficient GMM estimation of linear (dynamic) panel models with nonlinear moment conditions

As you are using time-invariant variables in your model, the following article might be of interest as well:
Kripfganz, S. and C. Schwarz (2019). Estimation of linear dynamic panel data models with time-invariant regressors. Journal of Applied Econometrics 34 (4), 526-546

[Tim Grünebaum]

I am deeply sorry, Sebastian. I think the useful comments on this topic were yours and not Maarten's. I simply mixed something up because I appriciated both your comments in this forum on different topics :-)
Would you recommend either using the collapse option to include more lags or go for less lags but without collapse to balance the number of instruments? I prefer the latter to make full use of low-order lags which probably have higher predictive power than a very long lag structure. I suppose there again is no general rule.

Obviously Femke withdrew from statalist... maybe she got what she needed.

[Sebastian Kripfganz]

I often combine collapsing with a lag-order restriction but there is indeed no general rule. I would say that collapsing is probably more relevant when the cross-sectional dimension is relatively small, and the lag restriction is particularly relevant when the time-series dimension is not very small.

[Nariman Sayed]

How can I determine lag-order restriction if I cannot find theoretical reference ,pls?