[Sebastian Kripfganz]

No. Let's look at a simple example. Suppose, you have (untransformed) data for T=4 time periods, t=1,2,3,4. In first differences, the last available observation is for t=4. The largest lag would be to use an instrument from the observation t=1. Thus, the maximum lag order is 4-1=3 (i.e. T-1). In forward-orthogonal deviations, the last available observation is for t=3. The largest lag would still be to use an instrument from the observation t=1. Thus, the maximum lag order is 3-1=2 (i.e. T-2).

[Prateek Bedi]

Alright, Prof. Kripfganz. If we talk about the transformation of the regressors with the suboption model(), should the maximum lag order be T-2 for both first difference (i.e. model(diff)) and forward orthogonal deviations (i.e. model(fodev))? (assuming that I do not specify any transformation of the instruments in my command)

[Sebastian Kripfganz]

My previous statement was about the first-difference transformation of the instruments with the suboption difference, not the first-difference transformation of the regressors with the suboption model(difference). The question is always how many lags are in the data set relative to the last effective observation. For the first-differenced model, the last effective observation is also the last actual observation in the data. For the model with forward-orthogonal deviations, the last effective observation is the second-last actual observation.

Note that this does not constitute an advantage for the first-differenced model over forward-orthogonal deviations, because with the latter you would start already with a smaller lag. Say, if you start with lag 1 for the first-differenced model, then you would start with lag 0 for the model with forward-orthogonal deviations. Therefore, you would use the same number of lagged instruments in both cases.

[Prateek Bedi]

Prof. Kripfganz:

Thanks a lot for your prompt response. So, it seems clear that maximum lag order should be T-2 in the case of forward orthogonal deviations as well as first-differenced transformation. But, I noticed that xtdpdgmm allows the use of T-1 as the maximum lag order in case of first-differenced transformation. Could you please help me understand the reason for this?

Thanks!!!

[Sebastian Kripfganz]

Your questions are perfectly legit. In fact, my previous answer was incorrect. My sincere apology.

It is correct: For the model in forward-orthogonal deviations, the maximum lag order is only T-2 instead of T-1 because the last observation is effectively removed. Moreover, when the instruments are first differenced, the maximum lag order is as well only T-2, as you correctly expected.

[Prateek Bedi]

Prof. Sebastian:

Thanks for a quick response. I have these follow-up queries:

1. If the determination of maximum lag order is not affected by presence of lagged dependent variable in the model or by model transformation, I would like to know why does xtdpdgmm provide an error when I try to specify a maximum lag order of more than T-2 in a model which has lagged dependent variable as an explanatory variable and employs forward orthogonal deviations?

2. I agree that for the first-differenced model, there are indeed T-1 lagged instruments available at level. However, for the level model, should not there be T-2 first-differenced instruments available? This is because the first-differenced values begin from second year onwards. Now, for the level model, there are only T-2 lagged first differenced values left to be used as instruments because the contemporaneous value cannot be used as instrument and the first-differenced values begin from the second year itself (so one value is lost there as well).

Please pardon me if my queries sound silly to you..

[Sebastian Kripfganz]

1. If you have T observations in your data set, then you can have at most T-1 lags. Everything beyond that is outside of the range of the data set.
2. I think my earlier statement in that regard was misleading. Apologies. For the maximum lag order, it does not matter whether there is a lagged dependent variable in the model or whether the model is transformed. For the first-differenced model, you are still typically using instruments in levels; so the maximum lag order T-1 applies again (see point 1).
3. It is again T-1. Same argument as in point 2.

[Prateek Bedi]

Alright, Prof. Kripfganz. In light of your response, please consider the following doubts:

1. Is there any specific reason as to why maximum admissible lag order has been set at T-1 in xtdpdgmm?
2. Conceptually (not in relation to xtdpdgmm), when we use first difference transformation (using model(diff)) option, the maximum admissible lag order should be T-1 because presence of lagged dependent variable and first-difference transformation lead to the omission of the same year i.e. first year of the dataset only. Is this understanding conceptually correct?
3. Conceptually (not in relation to xtdpdgmm), when we use forward orthogonal deviations, the maximum admissible lag order should be T-2 because of presence of lagged dependent variable (which leads to omission of the first year of dataset) and loss of the last year of the dataset on account of forward orthogonal deviations. Is this understanding conceptually correct?

Thanks!

[Sebastian Kripfganz]

I double-checked the code again. The program actually determines the maximum admissible lag order for the lag() option as T-1, where T is the maximum time length across all groups. This is irrespective of whether you include a lagged dependent variable or estimate the model in first differences or forward-orthogonal deviations. The effective maximum lag order could be smaller than T-1, which you can observe from the list of instruments below the output table (without the nofootnote option).

[Prateek Bedi]

1. The presence of the lagged dependent variable reduces the sample size effectively by 1 year. Another time dummy is dropped to avoid perfect collinearity of all the time dummies with the regression constant.
2. Again, T is effectively reduced by 1 due to the lagged dependent variable. Transforming the model into first differences or forward-orthogonal deviations reduces the effective sample size by another period, hence T-2.

Dear Prof. Sebastian:

Thanks one more time for your precise and insightful response. Following are my next queries

1. With regard to the upper limit of lag range for instruments, I just noticed that when we use first difference transformation (using model(diff)) option, we can still use a maximum value of T-1 in xtdpdgmm. This is perhaps because of the fact that presence of lagged dependent variables and first-difference transformation lead to the omission of the same year i.e. first year of the dataset. However, when we use forward orthogonal transformation (using model(fodev)), we are required to restrict our upper limit of lag range to T-2 on account of presence of lagged dependent variable (which leads to omission of the first year of dataset) and loss of the last year of the dataset. Please confirm if this understanding is correct.
2. Also, I noticed that when I do not include lagged dependent variables in my model and use level transformation throughout the model, I am still not able to increase my upper limit of lag range beyond T-1. However, I should be able to use the entire set of periods as instruments in such a model. Isn't? Below is the sample model I am talking about (my dataset is :

xtdpdgmm CashHoldings1 Size1 Leverage1 Liquidity1 Profitability4, twostep vce(cluster CompanyID) gmmiv(Leverage1 Liquidity1 Profitability4, lag(1 16) collapse model(l)) iv(Size1, model(level)) nofootnote

When I run the abovementioned command, I get the following error:

lagrange () invalid -- invalid numlist has elements outside of allowed range

Thanks

[Sebastian Kripfganz]

1. The presence of the lagged dependent variable reduces the sample size effectively by 1 year. Another time dummy is dropped to avoid perfect collinearity of all the time dummies with the regression constant.
2. Again, T is effectively reduced by 1 due to the lagged dependent variable. Transforming the model into first differences or forward-orthogonal deviations reduces the effective sample size by another period, hence T-2.

[Prateek Bedi]

I have an unbalanced dataset of 1696 companies over the period 2001-2016. I am running the following model:

xtdpdgmm Cash L.Cash Size Leverage Liquidity Profitability, teffects twostep vce(cluster CompanyID) gmmiv(L.Cash, lag(0 1) model(fodev)) gmmiv(Leverage Liquidity Profitability, lag(1 6) collapse model(fodev)) iv(Size, model(level)) nofootnote

1. When I run the above-mentioned model, the year dummies start from 2003 and go up till 2016. The dummies for initial two years i.e. 2001 and 2002 do not appear in the model. I would like to understand the specific reasons for omission of the dummies for 2001 and 2002.
2. I also observe that I cannot use upper limit of lag range greater than 14 for endogenous variables (else, I receive an error). What are the specific reasons due to which the lag range is restricted to T-2?

Thanks!

[haiyan lin]

Great thanks for your advice!

[Sebastian Kripfganz]

Then the results in the first test means the absence of the second-order serial correlation in disturbances. And the results with Hansen test means that there is not problem of overidentifying restrictions. Is it right?
Which is the most appropriate test of overindetifying restrictions to show in the results, 2-step weighting matrix or 3-step weighting matrix?

Yes, your test results do not reject the model specification.
It is usually sufficient to consider the overidentification test with the 2-step weighting matrix. The two tests are asymptotically equivalent. If they differ substantially, then this would be an indication that the weighting matrix is poorly estimated. Here, they are very similar which is a good sign.

If I have two regression using sys-GMM with different lags, say lag (0 7) and lag (4 6) [the maximum lag is 7] for the predetermined variables, both specification tests [AR(2), Hansen] imply the instruments are valid. And also the instruments are strong. Which result should I take in the end? In addition, if one estimation is significant, while the other one is not, which result should I take?

If all lags are valid and strong instruments, then you could simply use all of them. Usually, larger lags tend to become weaker instruments. Thus, as long as they are valid, you should always keep the small lags.
Statistical significance of the coefficient estimates itself should not be a selection criterion here, unless the significance in one specification is a result of substantially smaller standard errors due to a more efficient estimation with better instruments.

[haiyan lin]

Dear Sebastian,

Hope you don't mind that I raise a question here. I was confusing about how to choose lags in the GMM regression.

If I have two regression using sys-GMM with different lags, say lag (0 7) and lag (4 6) [the maximum lag is 7] for the predetermined variables, both specification tests [AR(2), Hansen] imply the instruments are valid. And also the instruments are strong. Which result should I take in the end? In addition, if one estimation is significant, while the other one is not, which result should I take?

Many thanks.
Haiyan