Hi Ayesha,

Unfortunately I can't help you with any materials on implementing panel GMM in EVIEWS, but nonetheless here are my two cents with reference to your questions:

(1) You have a "Large-N, Small-T" dataset, and as such your asymptotics are not coming from T-> inf. Therefore, non-stationarity is not a statistical concern in your model as the coefficient distributions will still be Normal/Gaussian in the limit assuming all standard assumptions are verified.

(2) Endogeneity in your model will come from three potential cases: (i) classic omitted variable bias, (ii) reverse causality i.e, Y -> X, (iii) endogeneity from including a lagged dependent variable.

Adding a lagged dependent variable will not solve any endogeneity problems in your model, but may well introduce endogeneity (see next paragraph) and so your decision to add a lagged dependent variable in your model should depend on whether (a) you think there is persistence in the dependent variable that is important to explain in your model, or (b) your dependent variable measures an outcome and you want to control for prior levels of that outcome (e.g. studies estimating effects on exam/school results control for baseline prior student achievement).

Note, if you want to account for fixed-effects in your model (either using a dummy variables to include them or by using a within or first-difference transformation to eliminate them before estimating the model using GMM/OLS), there will be an endogeneity bias between the lagged dependent variable and the residuals as corr (Yt-1, et) !=0 - but this is only true for Small-T, which is unfortunately your case.

Therefore, you know that you may have endogeneity from either:

- Xt (reverse causality or omitted variable bias)

- Yt-1 (correlation with error in the case of eliminating/including fixed effects)

(3) Unfortunately, there is no 'true' test for endogeneity, but all your model results will be conditional on the statistical assumptions being true, so it is down to you to decide based on theory whether OVB or reverse causality may exist, and then recover your exogeneity assumptions through appropriate instrumenting. However, as explained above, there will be endogeneity (mathematically) if LDV is included and any attempt to remove or include fixed effects is undertaken (in small-T).

For any variable that you do think is endogenous (either Xt or Yt-1), using their lags (Xt-1 or Yt-2) is a reasonable approach to recover unbiasedness, if the standard IV assumptions are satisfied: i.e. the instrument has no direct effect on Yt, is exogeneous and is relevant to the variable that is being instrumented. You could also pick a maximum lag length and then use BIC or AIC to select the optimal lag structure to prevent overfitting the endogenous variables

However, there are other powerful approaches that take advantage of maximum predictive information in the IV process (e.g. system-GMM, difference-GMM). These methods list moment conditions for each time period, where each moment condition lists the full available set of historical lags of the dependent variable depending on T (I will not discuss the intricacies of system-GMM and difference-GMM here).

The two things to consider if using system or difference GMM are:

(i) stationarity of the variables you are instrumenting

(ii) the relative number of instruments to observations (for each instrumented variable).

Looking at each in turn:

(i) stationarity: difference GMM can lead to the issue of weak instruments if the data is highly persistent or non-stationary, so system-GMM is preferred here.

(ii) relative instruments to observations: system/difference GMM both use a large number of parameters [e.g. (T-1+T-2+....1)*K parameters in the DGMM case, where K = number of endogenous variables], and so can easily overfit the endogenous variable in the process as T gets bigger (T=10, N=113 will definitely be problematic), which will fail to remove all endogeneity. Two solutions to this are (a) to "collapse" the moment conditions into a single moment condition with a pre-determined lag length (BIC or AIC can be used separately to select this), or (b) to restrict the maximum lag length across all moment conditions.

(4) Using "external" instruments as you mention, is also a valid approach, provided all the IV assumptions are satisfied. The important thing to note is that it doesn't really matter how you achieve exogeneity through instrumenting, just that you do and that all your IV assumptions are satisfied (and the instruments are not weak!). Of course, choosing the procedure that minimizes efficiency loss through using more predictive exogenous instruments (without overfitting) is most ideal - this is the motivation behind GMM-IV approaches (and not needing to find an external valid instrument!)

I hope this helps, below are a few resources for assistance:

Difference GMM: https://academic.oup.com/restud/article-abstract/58/2/277/1563354?redirectedFrom=fulltext

System GMM: Article Initial Conditions and Moment Conditions in Dynamic Panel Data Model

Bias in dynamic panels with fixed effects: https://www.jstor.org/stable/1911408

Instrument selection in system and difference GMM: Article A Note on the Theme of Too Many Instruments

Hugh Dance Thank you so much for a detailed answer. I found it really helpful.

Hi Ayesha,

I’ll be short and straight:

When N=113 and T=10 (as in your case) you should use the first-differenced GMM.

1) Non-stationarity is not your problem.

GMM does not require distributional assumptions.

2) Yes, you may use a dynamic panel data model. Instrument (including your AR variable) your predetermined variables with their first and all further lagged levels, while your potentially endogenous variables with their second and all further lagged levels.

3) Follow the economic theory – you’ll find which variables are potentially endogenous. Instrument them as noted in the previous item.

4) You may use external instruments, but they are very hard to find.

Yes, you can use only internal instruments.

In e-views, there is an option “Dynamic Panel Data Model Wizard”. It may also help you….

Best wishes,

Dimitar

Thank you Dimitar Eftimoski ..very important explanation