Based on dynamic panel data models and the generalized method of moments, if the DIF GMM or SYS GMM are not subject to serial correlation (in particular of second order) and the instruments are valid, then the estimators ensures efficiency and consistency. Subsequently, it seems that unit root tests are unnecessary, or what do you think?
Yes, although often omitted unit root tests are necessary. For DIF GMM the instruments become extremely weak once the process approaches a unit root (because levels no longer predict differences). SYS GMM is often used in this case, because it is meant for fairly (!) persistent time series processes. However, technically this only refers to persistent but stationary (!) processes. While being pointed out in the literature from the very beginning this has been recently highlighted by Moral-Benito (in JBES 2013) in a simulation study that accompanies his newly proposed estimator.
Best
Makram
They are necessary because not serial correlation is not related to the stationarity of the data. Besides, any type of testing in the presence of Unit Root is not valid anymore because you don't know the asymptotic distribution of the statistics.
Testing for stationarity properties of variables is important in order to ensure the appropriateness of the methodology of dynamic panel (Chen et al., 2014; Chang et al., 2011). It has been confirmed that the problem of non-stationarity of variables which is more prevalent in time-series also become pronounced in panel analysis when the number of cross-sectional units (N) is much greater than time-series observation (T) [see Holtz-Eakin et al., 1988; Arellano, 2003; Buck et al., 2008]. First-difference GMM only takes care of variables that are integrated of order one [I(1)]. The approach breaks down when we have variables which are integrated of order two [I(2)]. This is tenable because the first-difference GMM estimate models in first-differences.
Definitively, the unit-root tests are necessary. Otherwise, there is a risk of estimating spurious regressions.
Thanks for these great points, yet I still have clarifying question.
When using difference GMM, is it sufficient when the differenced variables are stationary ?
I am asking because in difference GMM we are using the levels as instruments and I do not get my around whether non-stationarity in levels is a problem for the estimation ?
Thanks for any hints and best
Tobi
@Clement. I appreciate your response. Pls, I would like the references of the authors you mentioned so I can cite them when justifying this position in the future.
Yes, even when using GMM estimator, we carry out unit root testing first. The purpose of unit root testing is to avoid spurious regression by ensuring a financial variable follows a random walk. .GMM uses assumptions about specific moments of the random variables instead of assumptions about the entire distribution, which makes GMM more robust than ML, at the cost of some efficiency. The assumptions are called moment conditions.
whenever you use a long period of time, it is better to show unit root test.
Yes, unit root tests are necessary before you apply the GMM either with difference moments conditions or else system moments conditions (which includes both level and difference equations). This is also applicable for static panel data models such as Random effects and Fixed effects models. Therefore, before you apply either system or else difference GMM make sure that all variables are stationery in its level form.
In case all the variables are non-stationary one may use FMOLS or else DOLS. While panel ARDL can be used irrespective of the order of integration of the variables.
A panel consisting of countries with at least twenty years must go for stationary checking. Here there is a purpose! You must go for testing long-run relationship after getting the results of Integrated Order (Either I(1) or I(0)). Merely using GMM (a dynamic estimation) or static one (Pooled OLS, FE Effect OLS, or RE OLS) after unit root tests simply does not make sense. What mandates is exploring short-run and long-run dynamics. Thanks
check this: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwju6Jr34M34AhUYKhoKHWpFDZ8QFnoECAoQAQ&url=https%3A%2F%2Fwww.researchgate.net%2Fpost%2FDoes_GMM_need_a_unit_root_test_before_running_the_model&usg=AOvVaw1tXce2rFRsN2vTJ8vG2GdP
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