dynamic GMM analysis and confounder problem

[Dao DinhNguyen]

Hi everyone,

I am conducting research using the dynamic system GMM analysis. My model specification is:
Y_i,t=F(Y_i,t-1, X_{i, t}, F_i)
Suppose: X is time-variant variable (access to improved water)
F if time-unvariant variable. (pregnancy care at time t=1)
Y: child malnutrition
t runs from 2 to 5
I aim to estimate the impacts of access to improved water and pregnancy care (initial condition of child health) on child malnutrition when growing up.

Firstly, I would estimate the dynamic panel data analysis with time-invariant regressors. I did follow the paper "Estimation of linear dynamic panel data models with time-invariant regressors" by Sebastian Kripfganz and Claudia Schwarz, published in the Journal of Applied Econometrics (2018). However, the authors assume that X and F are strictly exogenous (Assumption 2, page 528). But in my case, I suppose that X is not strictly exogenous (can be strictly endogenous or weakly endogenous).

Hence, I come back to the system-GMM model which also allows estimating the impact of time-invariant variables (xtabond2). To avoid the over-instrumentation problem, I will use the collapse option. Besides, I also use the orthogonal option to increase the sample size.

However, currently, I face a new problem that F can be a confounder because pregnancy care can affect both the probability of access to improved water after giving birth and the child malnutrition when growing up.
We usually use the different-GMM to overcome the confounding effect by eliminating time-invariant regressors. I don't know whether system-GMM can address this issue?

I hope that anyone can give me some suggestions or papers about using dynamic panel data analysis to estimate my model specification with a time-invariant confounder regressor.

I would appreciate your kind supports!

[Dao DinhNguyen]

Sebastian Kripfganz I really hope for your help!

[Sebastian Kripfganz]

A few comments:

• Assumption 2 in our paper is not restrictive at all. As stated in footnote 7, predetermined or endogenous regressors can be easily incorporated by adjusting the GMM instruments in the usual way.
• Forward-orthogonal deviations only "increase the sample size" if there are gaps in your data.
• If F_i is both a confounder for X_it and a variable of interest, you could use the two-stage procedure that we propose in Section 4 of our paper. In the first stage, you treat F_i as part of the unobserved effects. In the second stage, you estimate the effect of F_i. This can be done with my xtseqreg command. With instruments that are uncorrelated to unobserved time-invariant effects (including F_i), you obtain consistent estimates for the coefficient of X_it in the first stage. This is straightforward with a difference GMM estimator. With a system GMM estimator, you need the additional assumption that the changes in child malnutrition and the changes in access to improved water are uncorrelated to pregnancy care at time t=1. Given your setup, this would require that all of the effect of pregnancy care at time t=1 on access to improved water happens at t=1. In other words, if there is a better access to improved water at a later time period for someone with pregnancy care at t=1, then this better access must have been in place already at t=1. (There should not be any delayed response from pregnancy care on access to improved water.)
• Note that system GMM does not per se allow estimating the impact of time-invariant variables. (See footnote 1 of our paper.) It requires the possibly strong assumption that F_i is uncorrelated with any other unobserved effects such that F_i can be used as an instrument (in the level equation) for itself. The same assumption would be required in the second stage of the two-stage procedure suggested above. The advantage of the two-stage procedure is that the first stage is robust to a violation of this assumption. Alternatively, you could use excluded instruments for F_i.

[Dao DinhNguyen]

Dear Sebastian Kripfganz

Thank you so much for your valuable comments. I think I need to read your paper carefully to understand more about your method.

I have some concerns, therefore, I would like to grab your support.

1. I understand that system GMM (by xtabond2) require the strong assumption that Fi is strictly exogenous, so it can be the excluded instrument (in option iv(..)). However, in my case, F, pregnancy care, can be endogenous. For example, in developing countries, pregnancy care of women can be affected by their husband's power, which cannot be measured. Therefore, this assumption fails to hold for system GMM. But it can be relaxed by the two-stage procedure as you suggested. Hence, the two-stage procedure is more appreciate in my study case.
2. About the additional assumption in your second comment, I understand that the System GMM required the uncorrelation between F and change in Y and change in X. To test that assumption, I just to see the correlation between F and X at time t. If they are significantly correlated, meaning that at t=1, pregnancy care can increase the possibility of having improved water. Therefore, in the future, women with pregnancy care will have better access to improved water if nothing else affect. In Vietnam, I think it can happen when Vietnamese policies try to support vulnerable women to access clean water. But, do I need to test it if using the two-stage GMM?

Many thanks!

[Sebastian Kripfganz]

1. The two-stage procedure does not really relax this assumption. You still need this assumption in the second stage. It just makes the first stage robust to any violation of this assumption.

2. A simple sanity check for the system GMM assumption in the first stage might be

pwcorr D.Y D.X F, sig

If F is correlated with D.Y or D.X, then you probably should better stick to a difference GMM estimator (or estimate the model in a single stage with the exogeneity assumption for F).

[Dao DinhNguyen]

Dear Sebastian Kripfganz
Thank you so much for your kind support!
Best wishes!
Dao