[Sarah Magd]

Dear Prof. Sebastian Kripfganz
I have two questions about the specification of the variables:
1) Our sample includes the year 2020, and we want to control for it. Therefore, we add a dummy variable for this year. Should we specify this variable as an exogenous variable?
2) Our dataset includes dummy variables for the availability of technology in some countries in our sample, we want to interact this variable with our main variable of interest. How should we specify the dummy variables and the interaction variables? Should they be exogenous, predetermined, or endogenous variables?

Thanks a lot!

[Taka Sakamoto]

Thank you, Sebastian. I started learning system-GMM two weeks ago and am still in the process of learning it. Your advice has been tremendously helpful, and I am deeply grateful.

When I remove the lagged level of real GDP per capita, the results look this. Does it look okay?:

. xtdpdgmm gdpgrow sme inflation gfcfgrow hfcegrow tradeopen ,gmm(gdpgrow inflation  gfcfgrow hfcegrow , lag(2 
> 2) collapse model(diff)) gmm(gdpgrow inflation  gfcfgrow hfcegrow , lag(1 1) diff collapse model(level)) iv(s
> me,model(level))  one vce(cl id) small overid 

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  2.1473921

Fitting reduced model 1:
Step 1         f(b) =  1.340e-18

Fitting reduced model 2:
Step 1         f(b) =  9.209e-16

Fitting reduced model 3:
Step 1         f(b) =   2.099871

Group variable: id                           Number of obs         =       959
Time variable: year                          Number of groups      =        21

Moment conditions:     linear =      10      Obs per group:    min =        41
                    nonlinear =       0                        avg =  45.66667
                        total =      10                        max =        46

                                    (Std. err. adjusted for 21 clusters in id)
------------------------------------------------------------------------------
             |               Robust
     gdpgrow | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         sme |   3.166296   1.565061     2.02   0.057    -.0983644    6.430957
   inflation |  -.2519669   .0893019    -2.82   0.011    -.4382475   -.0656863
    gfcfgrow |   .2801333   .0899877     3.11   0.005     .0924223    .4678443
    hfcegrow |   .3007462   .3989567     0.75   0.460    -.5314629    1.132955
   tradeopen |  -.0859884   .0266657    -3.22   0.004    -.1416121   -.0303647
       _cons |   6.186441    2.29732     2.69   0.014     1.394314    10.97857
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(diff):
   L2.gdpgrow L2.inflation L2.gfcfgrow L2.hfcegrow
 2, model(level):
   L1.D.gdpgrow L1.D.inflation L1.D.gfcfgrow L1.D.hfcegrow
 3, model(level):
   sme
 4, model(level):
   _cons

Many thanks for your generous and kind help.

Taka

[Sebastian Kripfganz]

Initially, you put it in because that is what economic theory tells you. Then you conclude that you cannot obtain a reliable estimate; i.e., you cannot reject the null that there is no conditional convergence, but you can also hardly reject the null of any other meaningful value for this coefficient. Thus, in the final step you estimate the model without it to obtain more efficient estimates for the remaining coefficients.

[Taka Sakamoto]

Thank you for giving me advice on this. lrgdpopc is real GDP per capita (level), whereas gdpgrowth is annual GDP growth rate. The former is included to account for conditional convergence. So, I should remove lrgdpopc both as regressor and instrument?

[Sebastian Kripfganz]

No, I meant removing L.lrgdpopc from the model entirely (both as regressor and instruments).

[Taka Sakamoto]

You mean like this?

. xtdpdgmm gdpgrow sme inflation gfcfgrow hfcegrow tradeopen l.lrgdpopc ,gmm( inflation  gfcfgrow hfcegrow lrgd
> popc , lag(2 3) collapse model(diff)) gmm( inflation  gfcfgrow hfcegrow lrgdpopc, lag(1 2) diff collapse mode
> l(level)) iv(sme,model(level))  one vce(cl id) small overid

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  4.7191492

Fitting reduced model 1:
Step 1         f(b) =   .3986962

Fitting reduced model 2:
Step 1         f(b) =  .93970412

Fitting reduced model 3:
Step 1         f(b) =  4.5853153

Fitting no-level model:
Step 1         f(b) =  .93970412

Group variable: id                           Number of obs         =       919
Time variable: year                          Number of groups      =        21

Moment conditions:     linear =      18      Obs per group:    min =         6
                    nonlinear =       0                        avg =   43.7619
                        total =      18                        max =        46

                                    (Std. err. adjusted for 21 clusters in id)
------------------------------------------------------------------------------
             |               Robust
     gdpgrow | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         sme |   .6794376   .2367041     2.87   0.009     .1856815    1.173194
   inflation |  -.1636133    .045614    -3.59   0.002    -.2587624   -.0684641
    gfcfgrow |   .0980104   .0328853     2.98   0.007     .0294129     .166608
    hfcegrow |   .6692242   .1605369     4.17   0.000     .3343501    1.004098
   tradeopen |  -.0166245   .0134452    -1.24   0.231    -.0446707    .0114218
             |
    lrgdpopc |
         L1. |  -1.220907   1.060466    -1.15   0.263       -3.433     .991187
             |
       _cons |   14.09685   10.72928     1.31   0.204    -8.284046    36.47775
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(diff):
   L2.inflation L3.inflation L2.gfcfgrow L3.gfcfgrow L2.hfcegrow L3.hfcegrow
   L2.lrgdpopc L3.lrgdpopc
 2, model(level):
   L1.D.inflation L2.D.inflation L1.D.gfcfgrow L2.D.gfcfgrow L1.D.hfcegrow
   L2.D.hfcegrow L1.D.lrgdpopc L2.D.lrgdpopc
 3, model(level):
   sme
 4, model(level):
   _cons

[Sebastian Kripfganz]

The standard errors of the lagged dependent variable are now indeed much smaller, but this way too large for any meaningful inference. You might just conclude that you cannot reliably estimate this coefficient, and estimate a static model without lagged dependent variable instead.

[Taka Sakamoto]

Thank you for your help. Does it look better with one more lags like these?

. xtdpdgmm gdpgrow sme inflation gfcfgrow hfcegrow tradeopen l.lrgdpopc ,gmm(gdpgrow inflation  gfcfgrow hfcegr
> ow lrgdpopc , lag(2 3) collapse model(diff)) gmm(gdpgrow inflation  gfcfgrow hfcegrow lrgdpopc, lag(1 2) diff
>  collapse model(level)) iv(sme,model(level))  one vce(cl id) small overid

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  6.5119593

Fitting reduced model 1:
Step 1         f(b) =  1.7495734

Fitting reduced model 2:
Step 1         f(b) =  2.0088941

Fitting reduced model 3:
Step 1         f(b) =  6.4917358

Fitting no-level model:
Step 1         f(b) =  2.0088941

Group variable: id                           Number of obs         =       919
Time variable: year                          Number of groups      =        21

Moment conditions:     linear =      22      Obs per group:    min =         6
                    nonlinear =       0                        avg =   43.7619
                        total =      22                        max =        46

                                    (Std. err. adjusted for 21 clusters in id)
------------------------------------------------------------------------------
             |               Robust
     gdpgrow | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         sme |   .9128761   .2466531     3.70   0.001     .3983667    1.427386
   inflation |  -.1421567   .0417887    -3.40   0.003    -.2293263   -.0549871
    gfcfgrow |   .1127319   .0368393     3.06   0.006     .0358865    .1895773
    hfcegrow |   .6901123   .1433662     4.81   0.000     .3910556     .989169
   tradeopen |  -.0239375   .0116199    -2.06   0.053    -.0481762    .0003012
             |
    lrgdpopc |
         L1. |  -.8863398   .8513687    -1.04   0.310    -2.662264    .8895842
             |
       _cons |   10.84036   8.734277     1.24   0.229    -7.379021    29.05974
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(diff):
   L2.gdpgrow L3.gdpgrow L2.inflation L3.inflation L2.gfcfgrow L3.gfcfgrow
   L2.hfcegrow L3.hfcegrow L2.lrgdpopc L3.lrgdpopc
 2, model(level):
   L1.D.gdpgrow L2.D.gdpgrow L1.D.inflation L2.D.inflation L1.D.gfcfgrow
   L2.D.gfcfgrow L1.D.hfcegrow L2.D.hfcegrow L1.D.lrgdpopc L2.D.lrgdpopc
 3, model(level):
   sme
 4, model(level):
   _cons

[Sebastian Kripfganz]

By removing your instrument for sme, the coefficient of that regressor might be poorly identified. Not surprisingly, the standard errors of that coefficient estimate become huge. It (unsuccessfully) tries to borrow some identification strength from the other instruments, which then also slightly inflates the other standard errors.

The coefficient of your lagged dependent variable also appears to be poorly identified. It would probably require additional lags as instruments, which in turn would however increase the number of instruments, which can cause further trouble.

[Taka Sakamoto]

Thank you. Could you tell me what's happening in the following estimation? I enter the command:

xtdpdgmm gdpgrow sme inflation gfcfgrow hfcegrow tradeopen l.lrgdpopc ,gmm(gdpgrow inflation  gfcfgrow hfcegrow lrgdpopc , lag(2 2) collapse model(diff)) gmm(gdpgrow inflation  gfcfgrow hfcegrow lrgdpopc, lag(1 1) diff collapse model(level)) iv(sme,model(level))  one vce(cl id) small overid

I get the following results:

. xtdpdgmm gdpgrow sme inflation gfcfgrow hfcegrow tradeopen l.lrgdpopc ,gmm(gdpgrow inflation  gfcfgrow hfcegr
> ow lrgdpopc , lag(2 2) collapse model(diff)) gmm(gdpgrow inflation  gfcfgrow hfcegrow lrgdpopc, lag(1 1) diff
>  collapse model(level)) iv(sme,model(level))  one vce(cl id) small overid

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =   3.170343

Fitting reduced model 1:
Step 1         f(b) =  8.867e-16

Fitting reduced model 2:
Step 1         f(b) =  1.413e-14

Fitting reduced model 3:
Step 1         f(b) =  3.1380076

Group variable: id                           Number of obs         =       919
Time variable: year                          Number of groups      =        21

Moment conditions:     linear =      12      Obs per group:    min =         6
                    nonlinear =       0                        avg =   43.7619
                        total =      12                        max =        46

                                    (Std. err. adjusted for 21 clusters in id)
------------------------------------------------------------------------------
             |               Robust
     gdpgrow | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         sme |   1.371398    .415195     3.30   0.004     .5053168     2.23748
   inflation |  -.2012583   .0656044    -3.07   0.006    -.3381068   -.0644099
    gfcfgrow |   .1756431   .0365951     4.80   0.000     .0993071    .2519791
    hfcegrow |   .6537494   .2542447     2.57   0.018     .1234043    1.184095
   tradeopen |  -.0440692   .0166601    -2.65   0.016    -.0788215   -.0093169
             |
    lrgdpopc |
         L1. |  -.3924132   1.467164    -0.27   0.792    -3.452864    2.668037
             |
       _cons |   7.086845   15.30321     0.46   0.648     -24.8351    39.00879
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(diff):
   L2.gdpgrow L2.inflation L2.gfcfgrow L2.hfcegrow L2.lrgdpopc
 2, model(level):
   L1.D.gdpgrow L1.D.inflation L1.D.gfcfgrow L1.D.hfcegrow L1.D.lrgdpopc
 3, model(level):
   sme
 4, model(level):
   _cons

When I remove "iv(sme,model(level))" from the command I get the results:

. xtdpdgmm gdpgrow sme inflation gfcfgrow hfcegrow tradeopen l.lrgdpopc ,gmm(gdpgrow inflation  gfcfgrow hfcegr
> ow lrgdpopc , lag(2 2) collapse model(diff)) gmm(gdpgrow inflation  gfcfgrow hfcegrow lrgdpopc, lag(1 1) diff
>  collapse model(level))  one vce(cl id) small overid

Generalized method of moments estimation

Fitting full model:
Step 1         f(b) =  3.1380076

Group variable: id                           Number of obs         =       919
Time variable: year                          Number of groups      =        21

Moment conditions:     linear =      11      Obs per group:    min =         6
                    nonlinear =       0                        avg =   43.7619
                        total =      11                        max =        46

                                    (Std. err. adjusted for 21 clusters in id)
------------------------------------------------------------------------------
             |               Robust
     gdpgrow | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         sme |    -.64922   6.394653    -0.10   0.920    -13.98823    12.68979
   inflation |  -.1814501   .1103874    -1.64   0.116    -.4117143    .0488141
    gfcfgrow |    .181537   .0435933     4.16   0.000     .0906029    .2724712
    hfcegrow |   .6699812   .2849286     2.35   0.029     .0756305    1.264332
   tradeopen |  -.0526704   .0459819    -1.15   0.266    -.1485869    .0432461
             |
    lrgdpopc |
         L1. |   .1360665     2.8836     0.05   0.963    -5.879018    6.151151
             |
       _cons |    3.10732   25.29937     0.12   0.903    -49.66625    55.88089
------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(diff):
   L2.gdpgrow L2.inflation L2.gfcfgrow L2.hfcegrow L2.lrgdpopc
 2, model(level):
   L1.D.gdpgrow L1.D.inflation L1.D.gfcfgrow L1.D.hfcegrow L1.D.lrgdpopc
 3, model(level):
   _cons

"sme" is an invariant dummy variable, but the same results happen when I use a continuous version of "sme".

I am sorry I have taken time from you. And I appreciate your generous, kind help.

Many thanks.

TS

[Sebastian Kripfganz]

The variable that you specify in iv() (or gmmiv()) should not be correlated with the error term. In other words, if it is excluded from your regression specification, it should not have a direct effect on the dependent variable after controlling for any indirect effects through the included regressors. This is the standard requirement for a valid instrument.

As mentioned earlier, iv() is just a special case of gmmiv(). If the relevant instruments are already specified with gmmiv(), then there is often no need to use iv(). In some cases, e.g. for dummy variables, the iv() option is easier to use.

[Taka Sakamoto]

Sorry, I have one more question. The variable that goes in iv() cannot and should not be correlated with the dependent variable?

[Taka Sakamoto]

Thank you. What am I making happen if I do not use iv() option? I have read your 2019 slides, and see that you sometimes do not use iv() option.

Thank you for your help.

[Sebastian Kripfganz]

That's an error message you should not see. Would it be possible for you to send me your data set by e-mail, so that I can replicate the problem?

[Sarah Magd]

Thanks Prof. Sebastian Kripfganz
I have tried the following code:

xtdpdgmm L(0/1).GDP Labor Capital Financial_Development Temperature, model(diff) collapse gmm(GDP Labor Capital , lag(2 4)) gmm(Financial_Development, lag(1 2)) gmm(Temperature, lag(. .))  two vce(r) overid nl(noserial)

So I consider Temperature as a predetermined variable, and Temperature as an exogenous variable. However, when I run this code, I get this error:
xtdpdgmm_init_nl(): 3498 touse variable for model 'diff' required
<istmt>: - function returned error
r(3498);

Could you please help me figure out the problem?