Unit root test in dynamic data model

[Yugen Chen]

Dear Statalists,

In dynamic panel data model, difference GMM (arellano and bond, 1991) and System GMM (blundell and bond 1998) applies when the coefficient of lagged dependent variable RHS has absolute value smaller than 1. However, xtabond2 or the built-in xtabond seemingly has no such test to check this assumption.

Thus I wonder whether this test is in fact trivial in dpd?

Kind regards,
Yugen

[Sebastian Kripfganz]

It is indeed not trivial to perform this test because the estimators might perform poorly in the vicinity of an autoregressive coefficient equal to 1. Some instruments may no longer be relevant and the identification of the parameters might fail.

These GMM estimators are usually constructed for models with a short time horizon. Unit-root tests usually require a long time horizon.

In practice, what matters is less the fact that there might be a unit root but more generally the concern that the coefficients could be underidentified. The community-contributed ivreg2 command computes underidentification tests. For underidentification tests in the context of dynamic panel models, see my recent presentation at the London Stata Conference:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.

Further information on dynamic panel model estimation:

• XTDPDGMM: new Stata command for GMM estimation of linear (dynamic) panel data models

[Yugen Chen]

Hi Sebastian,

Thanks for your reply.

These GMM estimators are usually constructed for models with a short time horizon. Unit-root tests usually require a long time horizon.

By saying short horizon, do you mean the time span is smaller than the # of panels? Also if this rule of thumb comes from some specific papers, i wonder could you please tell me where I can find these references.

Kind regards,

[Sebastian Kripfganz]

The time span (T) is usually supposted to be (much) smaller than the number of panels (N), but there is no fixed threshold. If you look at the papers mentioned in your initial post, you find that the authors derive the asymptotic properties of the estimators under the assumption that T is fixed and N tends to infinity. For finite samples, the properties are usually obtained with Monte Carlo simulations but there is no real consensus about what constitutes a typical small-T, large-N data set, and it also varies a lot depending on the data-generating process.

[Yugen Chen]

I see your point.

Thanks!!!

Yugen