t statistic (p-value) of lower order coefficients in models with interaction terms

[Prateek Bedi]

Hi,

In the following system GMM model based on a panel dataset of 1696 firms across 16 years, I am interested in calculating the ultimate coefficient for lagged cash holdings (CashHoldings1) and promoter.ownership (WPromoterS).

xtdpdgmm CashHoldings1 L.CashHoldings1 Size1 Leverage1 WPromoterS c.WPromoterS#c.L.CashHoldings1, gmmiv(L.CashHoldings1, lag(1 4) model(fodev)) gmmiv(Leverage1 c.WPromoterS#c.L.CashHoldings1, lag(1 7) collapse model(fodev)) iv(Size1 WPromoterS, model(level)) teffects twostep vce(cluster CompanyID) nofootnote

Below is the output of this model.

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  .00033582
Step 2         f(b) =  .06917731

Group variable: CompanyID                    Number of obs         =     21705
Time variable: Year                          Number of groups      =      1676

Moment conditions:     linear =      77      Obs per group:    min =         1
                    nonlinear =       0                        avg =  12.95048
                        total =      77                        max =        15

                                   (Std. Err. adjusted for 1,676 clusters in CompanyID)
---------------------------------------------------------------------------------------
                      |              WC-Robust
        CashHoldings1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
        CashHoldings1 |
                  L1. |    .970056   .2444395     3.97   0.000     .4909633    1.449149
                      |
                Size1 |   -.000663   .0003608    -1.84   0.066    -.0013701    .0000442
            Leverage1 |   -.029561   .0094004    -3.14   0.002    -.0479854   -.0111365
   WPromoterSharesin1 |   .0359299   .0162391     2.21   0.027     .0041019     .067758
                      |
 c.WPromoterSharesin1#|
     cL.CashHoldings1 |  -.9789452   .4334874    -2.26   0.024    -1.828565   -.1293254
                      |

Below are my questions.

1. I am aware that calculation of coefficient of promoter ownership can be calculated for a certain level of lagged cash holdings (say, 0.04) in this way: .0359299 -.9789452*(0.04) = -0.003227908. However, I would like to know a convenient and short way of calculating the t-statistic for this calculated coefficient (specially considering that this is a system GMM regression on an unbalanced panel dataset).
2. Following general practice, I plug in the mean value of lagged cash holdings (i.e. 0.04) in the above calculation. I would like to know if there is another standard practice regarding this. Is there any other alternative than the mean value?

Thanks!

[Prateek Bedi]

Waiting for a reply!

[Phil Bromiley]

Have you tried margins? xtdpdml uses sem/gsem so the margins discussion for sem/gsem will probably work. You may need to tell xtdpdml not to reformat the data after the estimation.

Sometimes folks center their variables (subtract the mean) so the main effect is the effect for the middle of the interacting variable. Personally, I'm inclined to look at the effect for some reasonable levels of the interacting variable (say -2sd, mean +2sd or -1sd mean 1sd).

[Prateek Bedi]

Thanks Phil Bromiley for your reply. I am using xtdpdgmm for my model. I came across lincom command to estimate the t-statistic of the lower order coefficients. I think it works fine. Further, I relate to your inclination of calculating the main effect of interacting variable for reasonable levels of interest. In this regard, I have a doubt. One of my interacting variables (promoter ownership) is significant at rather low or high values of the other interacting variable (cash holdings) but not at the mean/median values. So, is it rational to claim that this interacting variable (promoter ownership) is significant in my model in general?