[Sebastian Kripfganz]

Possible remedies for serial correlation are the inclusion of higher-order autoregressive lags of the dependent variable or distributed lag of the other variables as additional regressors.

[Sarah Magd]

Dear Prof. Sebastian Kripfganz
If the second order autocorrelation is significant, what should I do to control for this rather than adding time fixed effects?

[Sebastian Kripfganz]

No, the bias-corrected estimator implemented in xtdpdbc does not account for reverse causality. It requires all X-regressors to be strictly exogenous in that regard.

[Sarah Magd]

Thanks Prof. Sebastian Kripfganz for your answer in #594

I have one more question. You have introduced a package for Bias Corrected Estimator in Stata. If I am estimating the following model:
Y = L.Y + X1 + X2 + ai + u

If there is a reverse causality from Y to X2, resulting in an endogeneity problem. Would estimating the model with the Bias Corrected Estimator, while controlling for the individual specific effects, control for the endogeneity of X2 as well? or does it only control for that of L.Y?

[Mrisho Rajabu Mrisho]

dear Proffesor @Sebastian Kripfganz,


I am estimating the effects of Islamic banks and convectıonal banks on underground economy within the OIC natıons

I then set up dummıes of Islamic banks to be islamicoic and dummies for non ıslamic banks to be nonislamicoic

code :

[xtabond2 se L.se ATM CBBRNCH10K DEP1KSWTCHCB BORRWERZ1KCB DOMCREDPRVTSECGDP CAPTOASSETRATIO fxreal Taxes gdppercapitagrowthannualnygdppca, robust nomata iv(L2.ATM L2.CBBRNCH10K L2.DEP1KSWTCHCB L2.BORRWERZ1KCB L2.DOMCREDPRVTSECGDP L2.CAPTOASSETRATIO L2.fxreal L2.Taxes L2.gdppercapitagrowthannualnygdppca ) gmm(L.se l.islamicoıc,collapse)]

these are the results ı got are they correct

se	Coef.		St.Err.	t-value		p-value	[95% Conf		Interval]		Sig
L	.968		.033	29.11		0	.903		1.033		***
ATM	0		.001	-0.32		.748	-.002		.001
CBBRNCH10K	0		.001	0.22		.828	-.001		.001
DEP1KSWTCHCB	.001		.001	1.00		.316	-.001		.002
BORRWERZ1KCB	.002		.001	2.63		.008	.001		.004		***
DOMCREDPRVTSECGDP	0		.001	0.84		.402	-.001		.002
CAPTOASSETRATIO	-.003		.001	-2.27		.023	-.006		0		**
fxreal	.003		.001	2.12		.034	0		.006		**
Taxes	-.001		.001	-0.78		.437	-.003		.001
gdppercapitagrowth~a	-.089		.033	-2.67		.008	-.154		-.024		***
Constant	.751		1.271	0.59		.555	-1.74		3.242
Mean dependent var		34.572			SD dependent var			9.808
Number of obs		735			Chi-square			3697.568
*** p<.01, ** p<.05, * p<.1

Instruments for first differences equation

Standard

D.(L2.ATM L2.CBBRNCH10K L2.DEP1KSWTCHCB L2.BORRWERZ1KCB

L2.DOMCREDPRVTSECGDP L2.CAPTOASSETRATIO L2.fxreal L2.Taxes

L2.gdppercapitagrowthannualnygdppca)

GMM-type (missing=0, separate instruments for each period unless collapsed)

L(1/.).(L.se L.islamicoıc) collapsed

Instruments for levels equation

Standard

_cons

L2.ATM L2.CBBRNCH10K L2.DEP1KSWTCHCB L2.BORRWERZ1KCB L2.DOMCREDPRVTSECGDP

L2.CAPTOASSETRATIO L2.fxreal L2.Taxes L2.gdppercapitagrowthannualnygdppca

GMM-type (missing=0, separate instruments for each period unless collapsed)

D.(L.se L.islamicoıc) collapsed

Arellano-Bond test for AR(1) in first differences: z = -3.68 Pr > z = 0.000

Arellano-Bond test for AR(2) in first differences: z = -0.90 Pr > z = 0.366

Sargan test of overid. restrictions: chi2(30) = 40.85 Prob > chi2 = 0.089

(Not robust, but not weakened by many instruments.)

Hansen test of overid. restrictions: chi2(30) = 31.85 Prob > chi2 = 0.375

(Robust, but weakened by many instruments.)

[Sebastian Kripfganz]

1) Such time dummies can typically be treated as fully exogenous.
2) There is no general answer; it depends on whether you can justify the exogeneity of these dummy variables. It certainly seems likely that these dummy variables are correlated with the unobserved country-specific effects. It could be reasonable to assume that they are strictly exogenous with respect to the idiosyncratic error component. With regard to interaction terms, there exogeneity is typically driven by the weakest interaction component; i.e., if the main variable of interest is endogenous, then the interaction terms should normally be treated as endogenous as well.

[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.