Lag structure in dynamic panel estimation

[Prateek Bedi]

Hi,

I am using system GMM (specifically, xtdpdgmm) to estimate a dynamic panel model for corporate cash holdings. For the endogenous explanatory variables (to be put in the gmmiv option) including the lagged dependent variable, I would like to know the basic rules to be kept in mind while deciding the lag structure. For instance, Roodman (2009) mentions that we need to use lags 2 and longer for endogenous variables. Given that I am using forward orthogonal (fodev) treatment for all endogenous variables and 'model(level)' option for all exogenous variables,, I would like to know tentative ideal starting and ending values for lag structure of endogenous variables. For a better understanding, here is my model:

xtdpdgmm CashHoldings1 L.CashHoldings1 Size1 Leverage1 Liquidity1 Profitability4 GrowthPotential2 OperatingCashflow Dividend2 CapitalExpenditure1 CashFlowVol15years WIndianPromotersInShar AgeoftheFirm AgeWIndianPromotersIn , teffects twostep vce(cluster CompanyID) gmmiv(L.CashHoldings1, lag(1 14)coll model(fodev)) gmmiv(Leverage1 Liquidity1 GrowthPotential2 Dividend2 CapitalExpenditure1, lag(1 3) coll model(fodev)) iv( AgeWIndianPromotersIn AgeoftheFirm Size1 Profitability4  WIndianPromotersInShar CashFlowVol15years OperatingCashflow, model(level)) nofootnote

Thanks

[Prateek Bedi]

Waiting for a response!

[Prateek Bedi]

Any guidance would be highly appreciated!

[Prateek Bedi]

Eagerly waiting for a response!

[Prateek Bedi]

Waiting for a reply!

[Prateek Bedi]

Waiting for help!

[Sebastian Kripfganz]

Please have a look at the following presentation slides:

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

[Prateek Bedi]

Thanks a lot, Prof. Sebastian for your reply and this very helpful presentation. I did go through the presentation. I noticed that the lag range for lagged dependent variable usually start with 2 whereas for endogenous variables, the lag range starts with 1, 2 and even 0. In fact, at some places, the lag range for endogenous variables was also mentioned as (0 0). However, I could not figure out the reason for these different starting points for lag range of lagged dependent variables and endogenous variables (I might have missed something). I humbly request you to please provide guidance and justification with regard to specification of lag range in system GMM estimation (specially in case when fodev transformation is used for both lagged lagged dependent variables and endogenous variables).

Hope to get some brilliant help from you, as always!!

[Sebastian Kripfganz]

Could you please provide a specific example from my presentation (with slide number) where the lag structure is unclear to you.

[Prateek Bedi]

Sure. For instance, I could not understand lag specification on slide 36. In fact,it would be very helpful if you could please throw some light as to why have we included two gmm brackets each for n and w, k respectively. I ask this specifically because I generally use only one gmm bracket each for specifying the instruments for the endogenous variables. Below is the specific command I am referring to.

xtdpdgmm L(0/1).n w k, model(diff) collapse gmm(n, lag(2 4)) gmm(w k, lag(1 3)) gmm(n, lag(1 1) diff model(level)) gmm(w k, lag(0 0) diff model(level)) two vce(r)

Thanks!

[Sebastian Kripfganz]

You do not necessarily have to use separate gmm() options. You could have specified it equivalently as gmm(L.n w k, lag(1 3)). (Note that L.n enters the variable list instead of n.)

I just have used separate options to illustrate which lags can be used for the dependent variable n and which lags can be used for predetermined variables w k.

For the dependent variable, the first lag is not a valid instrument for the first-differenced model because it is correlated with the first-differenced error term. If there is no serial error correlation, all further lags starting at lag 2 are valid instruments because they are no longer correlated with the first difference of the contemporaneous error term.

A predetermined variable, by definition, can be correlated with any past error term. That is, the contemporaneous w k are not valid instruments because can be correlated with the first-differenced error term which included the error from the previous period. The first lag of the predetermined w k can be correlated with errors lagged 2 or more periods but not the contemporaneous or one-period lagged error. Thus, fhe first lag and any further lag are valid instruments (if there is no serial error correlation).

If a variable is endogenous, it is also allowed to be correlated with the contemporaneous error term. Hence, the first lag can still be correlated with the first-differenced error term which includes the first lag of the errors. Therefore, similar to the dependent variable, only lag 2 and onwards are valid instruments.

For strictly exogenous variables, any lag qualifies as a potential instrument.

[John Sgr]

Dear Sebastian,

I did not get one point in your slide p.30. You say that if T is small, the diff-GMM could be strongly biased. What's the threshold for being small? I have panel data with 12 month. How can I decide which one to use diff GMM or level GMM?

Thanks in advance.

Best regards,
John

[Sebastian Kripfganz]

There is no fixed threshold for T being small. It also depends on how persistent the dependent variable is. While 12 months is not super small, it is also not large enough to completely ignore any such worries. If you worry about identification issues with the diff-GMM estimator, before switching to the sys-GMM estimator you could also first try the Ahn-Schmidt GMM estimator with nonlinear moment conditions that can help to avoid such identification problems (see slide 58). It also might help to use the underidentification tests (slides 43-47) after the diff-GMM estimator. If the null hypothesis of underidentification is rejected, there would be less reason to worry.

[John Sgr]

Thanks a lot! It's very clear now.

[John Sgr]

If you worry about identification issues with the diff-GMM estimator, ... It also might help to use the underidentification tests (slides 43-47) after the diff-GMM estimator. If the null hypothesis of underidentification is rejected, there would be less reason to worry.

I run the underidentification tests at your presentation (slides 43-47) after using model(fodev) specification rather than model(diff). Cragg-Donald test do not reject underidentification (p=0.84) but Kleibergen-Paap test rejects both overidentification (p=0.003) and underidentification (p=0.002). On the other hand, 2-step-GMM-based (LM version) Hansen test do not reject overidentification with p=0.13.

1.Should I consider my fodev-GMM model as true model?
2. Can I consider fodev estimator as diff-GMM estimator and apply all test that are relevant for diff-GMM?