[Prateek Bedi]

Hi,

I have two doubts as mentioned below.

1. From the output of difference-in-Hansen test shown below, what can we infer? Specially with regard to the last two moment conditions where the degrees of freedom are negative.

2-step weighting matrix from full model

                  | Excluding                   | Difference                  
Moment conditions |       chi2     df         p |        chi2     df         p
------------------+-----------------------------+-----------------------------
  1, model(fodev) |     0.4063      2    0.8162 |      0.2431      1    0.6220
  2, model(fodev) |     0.0360      1    0.8496 |      0.6134      2    0.7359
  3, model(fodev) |     0.0146      1    0.9038 |      0.6348      2    0.7281
  4, model(fodev) |     0.0654      1    0.7981 |      0.5839      2    0.7468
  5, model(level) |          .     -2         . |           .      .         .
  6, model(level) |          .    -11         . |           .      .         .

2. If there are two competing models, both of which satisfy AR(2) and Sargan-Hansen tests, how do decide which one is better? What are the criteria which we can use to choose one model over the other?

Thanks and Regards

[Nishant Kathuria]

Thank you so much for the explanation It is indeed very helpful. And for #4 above, my apologies as c.x1##c.x2##c.x3##c.t gives same results with separate interaction terms.... I realize that I was missing an interaction term, so the results were different..

[Sebastian Kripfganz]

1. No, adding more lags of the dependent variable as regressors does not mean that you also need to start with higher lags (a1) for the instruments. The reason for starting with the second lag is that the first lag is correlated with the first-differenced error term. The second lag is uncorrelated with the first-differenced error term if the errors are serially uncorrelated. This does not depend on the number of lags of the dependent variable used as regressors. In fact, the more lags of the dependent variable you use as regressors, the more likely it is that the errors are indeed serially uncorrelated.
2. model(fod) has the advantage that the transformed errors are still serially uncorrelated if the untransformed errors were serially uncorrelated, while model(diff) produces first-order serial correlation in the transformed error term. As long as you make sure that your instruments are uncorrelated with the transformed error term, it should not really matter which of the two model transformations you use. However, there is one additional benefit of model(fod): If your panel data set is unbalanced with gaps, the model(diff) would lose more observations than model(fod) does. Regarding model(level), this still contains the unobserved time-invariant "fixed effects" (which are removed by the other model transformations) such that you need to take extra care to ensure that your instruments are uncorrelated with them. This can often be hard to justify. Please see my 2019 London Stata Conference presentation and the references therein for details: Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.
3. If all firms stay in the same industry throughout the entire sample, i.e. if the industry classification remains constant over time, then model(diff), model(fod), and model(mdev) all account for these effects. In fact, they account for all time-invariant effects by removing them from the transformed model. If you still obtain estimates for some industry effects, this would mean that there must be some variation over time in the industry classification or that you have combined the model(mdev) instruments with further instruments for model(level).
4. It looks like the two specifications should be the same, aren't they?

[Nishant Kathuria]

Hi Prof. Kripfganz,

I am writing to ask very basic questions that may seem too primitive to you and the audience:

1. If I use dependent var with 2 lags, for instance, xtdpdgmm L(0/2).y x1 x2 x3, model(diff) gmm(y, lag(a1 . )) gmm(x1 x2 x3, lag(a2. )) , do I need to start a1 with 3 and a2 with 1? My understanding is that if I use a1=1 or 2, then the y variable (because of L(0/2)) in the equation will be endogenous with the controls. Please let me know if I am correct.

2. How do I decide if I need to use model(diff) or model(fod) or mod(level)?

3. In a study with large # of firm-year observations, does the model(mdev) control for the industry effects automatically or do I need to add industry_effects* in the equation? When I use both the industry effects and model(mdev), very few industry effects appear and most of the industries are omitted.

4. I am using a four-way interaction, with one of the variables as time effect such that t=0 or t=1, to test difference in differences.
Can I use xtdpdgmm L(0/2).y c.x1##c.x2##c.x3##c.t, model(diff) gmm(y, lag(3 . )) gmm(c.x1##c.x2##c.x3##c.t, lag(1 . )) teffects instead of
xtdpdgmm L(0/2).y c.x1##c.x2##c.x3##c.t, model(diff) gmm(y, lag(3 . )) gmm(c.x1#c.x2#c.x3#c.t c.x1#c.x2#c.x3 c.x1#c.x2#c.t c.x2#c.x3#c.t c.x1#c.x3#c.t c.x1#c.x2 c.x2#c.x3 c.x1#c.x3 c.x1#c.t c.x2#c.t c.x3#c.t x1 x2 x3 , lag(1 . )) teffects ?

I look forward to your reply. Thank you so much for continued support

Nishant

[Rita Juliana]

Thank you Prof Kripfganz for your comment and suggestion. I will try your suggestions, really appreciate your comment.