[Sebastian Kripfganz]

xtabond2 ..., orthogonal gmmstyle(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), laglimits(1 .) collapse equation(diff))

and

xtdpdgmm ..., model(fod) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), lag(1 .) collapse)

are not equivalent. To make the two equivalent, you either need to specify laglimits(2 .) with xtabond2, or lag(0 .) with xtdpdgmm. The coefficient estimates will nevertheless still not coincide because of the bug in xtabond2 that you mentioned.

[Tegh Summy]

xtabond2 ..., orthogonal gmmstyle(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), laglimits(1 .) collapse equation(diff))

and

xtdpdgmm ..., model(fod) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), lag(1 .) collapse)

are not equivalent. To make the two equivalent, you either need to specify laglimits(2 .) with xtabond2, or lag(0 .) with xtdpdgmm. The coefficient estimates will nevertheless still not coincide because of the bug in xtabond2 that you mentioned.

I see thanks - i presume changing xtdpdgmm with (0 .) and leaving xtabond2 unchanged at (1 .) takes the first lag of endogenous variables and doesnt solve the endogeneity issue. In contrast, changing xtabond2 with (2 .) and leaving xtdpdgmm unchanged at (1 .) takes second lags of endogenous variables and hence avoids the endogeneity issue?

[Sebastian Kripfganz]

I a variable is endogenous, i.e. contemporaneously correlated with the error term, then xtdpdgmm with lag(0 .) indeed does not solve the endogeneity problem, but lag(1 .) would (assuming no serial correlation of the idiosyncratic error term). For a predetermined (e.g. a lagged dependent variable) or strictly exogenous variable, lag(0 .) would be fine.

If you assume that gini_disp is endogenous such that L.gini_disp is predetermined, you could thus use lag(0 .) in your above specifications. If L.gini_disp itself is endogenous, you need to use lag(1 .).

[Tegh Summy]

I a variable is endogenous, i.e. contemporaneously correlated with the error term, then xtdpdgmm with lag(0 .) indeed does not solve the endogeneity problem, but lag(1 .) would (assuming no serial correlation of the idiosyncratic error term). For a predetermined (e.g. a lagged dependent variable) or strictly exogenous variable, lag(0 .) would be fine.

If you assume that gini_disp is endogenous such that L.gini_disp is predetermined, you could thus use lag(0 .) in your above specifications. If L.gini_disp itself is endogenous, you need to use lag(1 .).

Ah okay thanks - in this case income is an endogenous lagged variable as is assumed in the inequality-growth literature. Is the level (0 0) still taking first levels though or for first levels should it be (1 1) for both the xtdpdgmm and xtabond2?

The test results do not reject the model specification although the Hansen test p-value is not very comfortable.

Typically, in the system-GMM literature you would only use the first lag (not the first and second) for the equation in levels, and potentially further lags for the equation in first differences, e.g.

xtabond2 gdpgr L.ineq L.lngdp L.fseced L.mseced L.pli i.t, ///
gmmstyle(L.(lngdp ineq fseced mseced pli), equation(diff) laglimits(1 2) collapse) ///
gmmstyle(L.(lngdp ineq fseced mseced pli), equation(level) laglimits(0 0) collapse) ivstyle(i.t, equation(level)) robust

That said, your specification is not necessarily problematic. It is just unconventional.

For example, from the quoted post above, it looks like each variable is assumed as endogenous yet lags are specified as (1 2). Is this because it is first differences used and hence if it were forward orthogonal deviations, then (2 3) would have to be used per our discussion?

[Tegh Summy]

I a variable is endogenous, i.e. contemporaneously correlated with the error term, then xtdpdgmm with lag(0 .) indeed does not solve the endogeneity problem, but lag(1 .) would (assuming no serial correlation of the idiosyncratic error term). For a predetermined (e.g. a lagged dependent variable) or strictly exogenous variable, lag(0 .) would be fine.

If you assume that gini_disp is endogenous such that L.gini_disp is predetermined, you could thus use lag(0 .) in your above specifications. If L.gini_disp itself is endogenous, you need to use lag(1 .).

In your 2019 presentation, it says to treat lagged dependent variables in the same way as endogenous variables regarding start time period in the command on slide 67 (t=1 for both). But here you mention the lagged dependent variable you should use t=0. I thought it was the former, not the latter?

[Sebastian Kripfganz]

Ah okay thanks - in this case income is an endogenous lagged variable as is assumed in the inequality-growth literature. Is the level (0 0) still taking first levels though or for first levels should it be (1 1) for both the xtdpdgmm and xtabond2?

Not sure what you mean by "first levels". With xtdpdgmm, what you specify is exactly what you get.

For example, from the quoted post above, it looks like each variable is assumed as endogenous yet lags are specified as (1 2). Is this because it is first differences used and hence if it were forward orthogonal deviations, then (2 3) would have to be used per our discussion?

This might be confusing here again because the variable list itself is specified with the lag operator. If those variables (before taking the lag) are endogenous, then after taking lags they are predetermined. For such predetermined variables, lag(1 2) is a valid specification for the instruments in the first-differenced model. For forward-orthogonal deviations, lag(0 1) would be valid for such predetermined variables.

In your 2019 presentation, it says to treat lagged dependent variables in the same way as endogenous variables regarding start time period in the command on slide 67 (t=1 for both). But here you mention the lagged dependent variable you should use t=0. I thought it was the former, not the latter?

Slide 67 treats the dependent variable in the same way as endogenous regressors. As a consequence, the lagged dependent variable will be treated as predetermined.

[Tegh Summy]

Not sure what you mean by "first levels". With xtdpdgmm, what you specify is exactly what you get.


This might be confusing here again because the variable list itself is specified with the lag operator. If those variables (before taking the lag) are endogenous, then after taking lags they are predetermined. For such predetermined variables, lag(1 2) is a valid specification for the instruments in the first-differenced model. For forward-orthogonal deviations, lag(0 1) would be valid for such predetermined variables.


Slide 67 treats the dependent variable in the same way as endogenous regressors. As a consequence, the lagged dependent variable will be treated as predetermined.

Okay so, if I am treating gini_disp as endogenous, and hence L.gini_disp as predetermined, and the lagged dependent variable is predetermined, then the code is different for xtabond2 and xtdpdgmm under FOD in that the lags would have to be e.g. (1 3) for xtabond2 predetermined variables, but (0 2) for the same thing but with xtdpdgmm. But under first differences, both xtabond2 and xtdpdgmm would treat predetermines variables with (1 3)? :

 
 xtabond2 growth L.gini_disp L.EFW L.ln_Income L.ln_pl_i L.fyr_sch_sec L.myr_sch_sec, orthogonal gmmstyle(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), laglimits(1 3) collapse equation(diff))  gmmstyle(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), laglimits(0 0) collapse equation(level))

 
 xtdpdgmm growth L.gini_disp L.EFW L.ln_Income L.ln_pl_i L.fyr_sch_sec L.myr_sch_sec, model(fod) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), lag(0 2) collapse) gmm(l.(gini_disp EFW ln_Income ln_pl_i fyr_sch_sec myr_sch_sec), lag(0 0) collapse diff model(level))

[Sebastian Kripfganz]

That is correct.

Leaving aside the particular Stata programs: From an econometric perspective, it is in the nature of the different transformations that (for a predetermined variable) lag 0 is the first valid lag for FOD while lag 1 is the first valid lag for first differences.

[Sinem Ates]

Dear Sebastian,

I have just developed a model specification including interaction term between two explanatory variables. The model passes all specification tests. However I am confused about the interpretation of coefficients because of interaction term and different lags. Could you please help me to interpret the coefficients of ESGSCORE (which is a measure of sustainability performane of the firm) and OverallScore (which is a measure of economic freedom of the firm's country) and interaction term.

xtdpdgmm L(0/1).TOBINSQ_w  L(0/3).( ESGSCORE ) SIZE_w ROA_w  LEV_w CAPEXSALES_w L(0/2).OverallScore c.ESGSCORE#c.OverallScore i.ICBIC, model(fod) collapse gmm( TOBINSQ_w  , lag(1 .)) gmm( ESGSCORE , lag(1 .)) gmm( SIZE_w  , lag(1 .)) gmm( LEV_w  , lag(1.)) gmm( ROA_w  , lag(1 .)) gmm( CAPEXSALES_w  , lag(1 .)) gmm( OverallScore  , lag(1 .)) gmm(ESGSCORE SIZE_w LEV_w ROA_w CAPEXSALES_w OverallScore c.ESGSCORE#c.OverallScore, lag(0 0)) iv(i.ICBIC, model(level)) teffects two vce(r) overid
 
Generalized method of moments estimation
 
Fitting full model:
Step 1         f(b) =  .01013173
Step 2         f(b) =  .10142921
 
Fitting reduced model 1:
Step 1         f(b) =  .07740627
 
Fitting reduced model 2:
Step 1         f(b) =  .09445782
 
Fitting reduced model 3:
Step 1         f(b) =  .08429092
 
Fitting reduced model 4:
Step 1         f(b) =  .08862122
 
Fitting reduced model 5:
Step 1         f(b) =  .07572473
 
Fitting reduced model 6:
Step 1         f(b) =  .08666812
 
Fitting reduced model 7:
Step 1         f(b) =   .0861233
 
Fitting reduced model 8:
Step 1         f(b) =  .08308427
 
Fitting reduced model 9:
Step 1         f(b) =  .08920645
 
Fitting reduced model 10:
Step 1         f(b) =  .08920645
 
Fitting no-level model:
Step 1         f(b) =  .08920645
 
Group variable: ID                           Number of obs         =      2147
Time variable: YEAR                          Number of groups      =       440
 
Moment conditions:     linear =      80      Obs per group:    min =         1
                    nonlinear =       0                        avg =  4.879545
                        total =      80                        max =         7
 
                                                (Std. Err. adjusted for 440 clusters in ID)
-------------------------------------------------------------------------------------------
                          |              WC-Robust
                TOBINSQ_w |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------------+----------------------------------------------------------------
                TOBINSQ_w |
                      L1. |   .6984193   .0654179    10.68   0.000     .5702027     .826636
                          |
                 ESGSCORE |
                      --. |   .1128105   .0421064     2.68   0.007     .0302835    .1953376
                      L1. |   .0004991   .0014639     0.34   0.733    -.0023702    .0033683
                      L2. |   .0005379   .0013991     0.38   0.701    -.0022043    .0032801
                      L3. |  -.0018574   .0011518    -1.61   0.107    -.0041149    .0004001
                          |
                   SIZE_w |  -.0847096   .0469912    -1.80   0.071    -.1768107    .0073915
                    ROA_w |   .0210984   .0063408     3.33   0.001     .0086706    .0335261
                    LEV_w |   .2967615   .4005586     0.74   0.459    -.4883189    1.081842
             CAPEXSALES_w |  -.0094638   .0038115    -2.48   0.013    -.0169342   -.0019934
                          |
             OverallScore |
                      --. |   .1059354   .0452059     2.34   0.019     .0173335    .1945373
                      L1. |  -.0030094   .0069359    -0.43   0.664    -.0166035    .0105848
                      L2. |  -.0535394   .0147168    -3.64   0.000    -.0823839   -.0246949
                          |
c.ESGSCORE#c.OverallScore |  -.0021031   .0007813    -2.69   0.007    -.0036344   -.0005718
                          |
                    ICBIC |
                      15  |  -.0685422    .258174    -0.27   0.791     -.574554    .4374695
                      20  |  -.1219692   .2260116    -0.54   0.589    -.5649439    .3210054
                      30  |  -.1223279   .3039111    -0.40   0.687    -.7179827    .4733269
                      35  |  -.2328229    .282328    -0.82   0.410    -.7861757    .3205298
                      40  |  -.0843717   .2157424    -0.39   0.696     -.507219    .3384757
                      45  |   .1119753    .209816     0.53   0.594    -.2992564     .523207
                      50  |  -.2074905    .261164    -0.79   0.427    -.7193624    .3043815
                      55  |   -.013833   .2326584    -0.06   0.953    -.4698351    .4421692
                      60  |  -.2676219   .2424246    -1.10   0.270    -.7427655    .2075217
                      65  |   -.293426   .2462262    -1.19   0.233    -.7760206    .1891685
                          |
                     YEAR |
                    2013  |   .0290727   .0261003     1.11   0.265    -.0220829    .0802284
                    2014  |   .1111872   .0295596     3.76   0.000     .0532516    .1691229
                    2015  |   .0811373   .0320161     2.53   0.011      .018387    .1438877
                    2016  |    .104873   .0394908     2.66   0.008     .0274724    .1822737
                    2017  |   .1532381   .0412709     3.71   0.000     .0723487    .2341276
                    2018  |    .046619   .0427592     1.09   0.276    -.0371875    .1304255
                          |
                    _cons |  -.8009295   2.118316    -0.38   0.705    -4.952753    3.350894
-------------------------------------------------------------------------------------------
Instruments corresponding to the linear moment conditions:
 1, model(fodev):
   L1.TOBINSQ_w L2.TOBINSQ_w L3.TOBINSQ_w L4.TOBINSQ_w L5.TOBINSQ_w
   L6.TOBINSQ_w L7.TOBINSQ_w L8.TOBINSQ_w
 2, model(fodev):
   L1.ESGSCORE L2.ESGSCORE L3.ESGSCORE L4.ESGSCORE L5.ESGSCORE L6.ESGSCORE
   L7.ESGSCORE L8.ESGSCORE
 3, model(fodev):
   L1.SIZE_w L2.SIZE_w L3.SIZE_w L4.SIZE_w L5.SIZE_w L6.SIZE_w L7.SIZE_w
   L8.SIZE_w
 4, model(fodev):
   L1.LEV_w L2.LEV_w L3.LEV_w L4.LEV_w L5.LEV_w L6.LEV_w L7.LEV_w L8.LEV_w
 5, model(fodev):
   L1.ROA_w L2.ROA_w L3.ROA_w L4.ROA_w L5.ROA_w L6.ROA_w L7.ROA_w L8.ROA_w
 6, model(fodev):
   L1.CAPEXSALES_w L2.CAPEXSALES_w L3.CAPEXSALES_w L4.CAPEXSALES_w
   L5.CAPEXSALES_w L6.CAPEXSALES_w L7.CAPEXSALES_w L8.CAPEXSALES_w
 7, model(fodev):
   L1.OverallScore L2.OverallScore L3.OverallScore L4.OverallScore
   L5.OverallScore L6.OverallScore L7.OverallScore L8.OverallScore
 8, model(fodev):
   ESGSCORE SIZE_w LEV_w ROA_w CAPEXSALES_w OverallScore
   c.ESGSCORE#c.OverallScore
 9, model(level):
   15bn.ICBIC 20.ICBIC 30.ICBIC 35.ICBIC 40.ICBIC 45.ICBIC 50.ICBIC 55.ICBIC
   60.ICBIC 65.ICBIC
 10, model(level):
   2013bn.YEAR 2014.YEAR 2015.YEAR 2016.YEAR 2017.YEAR 2018.YEAR
 11, model(level):
   _cons
 
. estat serial, ar(1/3)
 
Arellano-Bond test for autocorrelation of the first-differenced residuals
H0: no autocorrelation of order 1:     z =   -4.8072   Prob > |z|  =    0.0000
H0: no autocorrelation of order 2:     z =   -0.1908   Prob > |z|  =    0.8487
H0: no autocorrelation of order 3:     z =   -0.0397   Prob > |z|  =    0.9683
 
. estat overid
 
Sargan-Hansen test of the overidentifying restrictions
H0: overidentifying restrictions are valid
 
2-step moment functions, 2-step weighting matrix       chi2(50)    =   44.6289
                                                       Prob > chi2 =    0.6880
 
2-step moment functions, 3-step weighting matrix       chi2(50)    =   51.6707
                                                       Prob > chi2 =    0.4084
 
. estat overid, difference
 
Sargan-Hansen (difference) test of the overidentifying restrictions
H0: (additional) overidentifying restrictions are valid
 
2-step weighting matrix from full model
 
                  | Excluding                   | Difference                 
Moment conditions |       chi2     df         p |        chi2     df         p
------------------+-----------------------------+-----------------------------
  1, model(fodev) |    34.0588     42    0.8034 |     10.5701      8    0.2273
  2, model(fodev) |    41.5614     42    0.4901 |      3.0674      8    0.9301
  3, model(fodev) |    37.0880     42    0.6861 |      7.5408      8    0.4796
  4, model(fodev) |    38.9933     42    0.6037 |      5.6355      8    0.6880
  5, model(fodev) |    33.3189     42    0.8283 |     11.3100      8    0.1847
  6, model(fodev) |    38.1340     42    0.6414 |      6.4949      8    0.5920
  7, model(fodev) |    37.8943     42    0.6517 |      6.7346      8    0.5655
  8, model(fodev) |    36.5571     43    0.7454 |      8.0718      7    0.3263
  9, model(level) |    39.2508     44    0.6751 |      5.3780      6    0.4963
 10, model(level) |    39.2508     44    0.6751 |      5.3780      6    0.4963
     model(fodev) |          .    -13         . |           .      .         .
     model(level) |    39.2508     34    0.2462 |      5.3780     16    0.9935

[Sebastian Kripfganz]

The interpretation works in the same way as with interaction effects in any other linear regression model:
Assuming both scores are positive, the negative interaction effect means that the positive effect of either score is attenuated, more so the larger the respective other score is.

Ideally, you would want to compute marginal effects. The xtdpdgmm command does not yet support the margins command for that purpose.

[Sinem Ates]

Thank you Sebastian

[Sinem Ates]

Dear Sebastian,

Could you please check whether these two codes are equilavent? I know the coefficients will not be the same due to the bug in xtabond2, I am only interested with the equality in terms of sytanxes.

xtabond2 L(0/1).TOBINSQ_w  L(0/3).( ESGSCORE ) SIZE_w ROA_w  LEV_w CAPEXSALES_w ICBIC2 ICBIC3 ICBIC4 ICBIC5 ICBIC6 ICBIC7 ICBIC8 ICBIC9 ICBIC10 ICBIC11 YEAR5 YEAR6 YEAR7 YEAR8 YEAR9 YEAR10 , gmm(TOBINSQ_w,lag(2 .) collapse) gmm (ESGSCORE SIZE_w ROA_w  LEV_w CAPEXSALES_w, lag(1  .) collapse) iv(ICBIC2 ICBIC3 ICBIC4 ICBIC5 ICBIC6 ICBIC7 ICBIC8 ICBIC9 ICBIC10 ICBIC11 YEAR5 YEAR6 YEAR7 YEAR8 YEAR9 YEAR10, equation(leve l)) twostep robust orthogonal

xtdpdgmm L(0/1).TOBINSQ_w  L(0/3).( ESGSCORE ) SIZE_w ROA_w  LEV_w CAPEXSALES_w i.ICBIC, model(fod) collapse gmm( TOBINSQ_w  , lag(1 .)) gmm( ESGSCORE , lag(1 .)) gmm( SIZE_w  , lag(1 .)) gmm( LEV_w  , lag(1 .)) gmm( ROA_w  , lag(1 .)) gmm( CAPEXSALES_w  , lag(1 .)) gmm(ESGSCORE SIZE_w LEV_w ROA_w CAPEXSALES_w , lag(0 0)) iv(i.ICBIC, model(level)) teffects two vce(r) overid

[Sebastian Kripfganz]

As far as I can see, the two specifications look equivalent, yes.

[Tegh Summy]

The underid command is not an official Stata command. It seems that it is not yet publicly released by its author. So, I am afraid you cannot yet use it.

Is there any built-in command to test for whether instruments using the differences equation or the level equation are weak instruments for each individual independent variable? I'd like to test whether a reduced form equation with d.l.X1 on l2.X1 (first differences) or l.X1 on d.l.X1 (levels) are weak instruments. This can be done using 2sls in stata, but wondered if anything is was an update available in xtdpdgmm command wise which conducts this test already.

[Sebastian Kripfganz]

There is no such test yet available directly within the xtdpdgmm package. Sorry.