Dear All,
My model tries to estimate risk due to surge in credit demand (Ln_Loss_CC) as a function of various bank-specific and macroeconomic variables. Due to endogeneity concerns and dynamic nature of risk, I employed dynamic panel GMM estimation using -xtabond2- command. The p-value corresponding to AR(2) comes out to be 0.08. Although it doesn't rejects null hypothesis at 5% significance level, the low p-value doesn't instill much confidence either. My codes and results are as follows.
I checked for higher order serial correlation using artests(3) and the results indicated the absence of third order serial correlation between first differenced error terms (Pr > z = 0.121). The results are as as follows.
On estimating the model with third lag of dependent variable as instrument (code and Arellano-Bond AR test outcomes are attached below), however, didn't yield significant improvement in p-value (0.083) corresponding to AR(2) test.
AR test outcomes:
Although using fourth lag of dependent variable as an instrument, slightly improved theAR(2) test p-value to 0.107, I remain skeptical about using deeper lags as they serve as weak instruments. Additionally, as an alternative often suggested in this forum, I also tried including the second lag of dependent variable in the estimation model as one of the regressors. In this case, even though AR(2) test didn't reject null (p- value of 0.171), but most of the variables turned insignificant.
Under such circumstances, kindly suggest me the right and logical way to proceed. Any inputs would be warmly appreciated.
Thanks
pankaj
My model tries to estimate risk due to surge in credit demand (Ln_Loss_CC) as a function of various bank-specific and macroeconomic variables. Due to endogeneity concerns and dynamic nature of risk, I employed dynamic panel GMM estimation using -xtabond2- command. The p-value corresponding to AR(2) comes out to be 0.08. Although it doesn't rejects null hypothesis at 5% significance level, the low p-value doesn't instill much confidence either. My codes and results are as follows.
Code:
xtabond2 Ln_Loss_CC L.Ln_Loss_CC L.Pub_Dummy L.CAR_T1 L.GNPARatio L.PCR L.NIM L.CorpLoan L.Ln_ContLiab L.OpExpOpRev
> L.Ln_Assets L.ROA GDPGr GsecYld CMR, gmmstyle(Ln_Loss_CC, lag(2 2) collapse) gmmstyle(NIM CAR_T1 Ln_ContLiab OpExpOp
> Rev GNPARatio ROA, lag(2 2) collapse) ivstyle(Year4 Year5 Year13 Year14 Year15 Year16, equation(level)) ivstyle(L.Pu
> b_Dummy L.PCR L.Ln_Assets GDPGr GsecYld CMR, equation(level)) twostep robust
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: BankID Number of obs = 643
Time variable : Year Number of groups = 39
Number of instruments = 27 Obs per group: min = 14
Wald chi2(14) = 539359.21 avg = 16.49
Prob > chi2 = 0.000 max = 17
------------------------------------------------------------------------------
| Corrected
Ln_Loss_CC | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
Ln_Loss_CC |
L1. | .7705289 .103337 7.46 0.000 .5679921 .9730657
|
Pub_Dummy |
L1. | .1722594 .0984679 1.75 0.080 -.0207342 .3652529
|
CAR_T1 |
L1. | 1.419991 1.394901 1.02 0.309 -1.313965 4.153947
|
GNPARatio |
L1. | -.4934302 1.010798 -0.49 0.625 -2.474558 1.487698
|
PCR |
L1. | -.012697 .1018071 -0.12 0.901 -.2122353 .1868413
|
NIM |
L1. | .4599867 6.564143 0.07 0.944 -12.4055 13.32547
|
CorpLoan |
L1. | -4.781232 3.541441 -1.35 0.177 -11.72233 2.159864
|
Ln_ContLiab |
L1. | -.0135174 .0623081 -0.22 0.828 -.135639 .1086042
|
OpExpOpRev |
L1. | .9801034 .5533458 1.77 0.077 -.1044344 2.064641
|
Ln_Assets |
L1. | .2279908 .1539175 1.48 0.139 -.0736819 .5296635
|
ROA |
L1. | 8.120565 5.287054 1.54 0.125 -2.241872 18.483
|
GDPGr | -.2634084 .4712794 -0.56 0.576 -1.187099 .6602822
GsecYld | 5.727651 3.362606 1.70 0.089 -.8629366 12.31824
CMR | -.9495302 1.930086 -0.49 0.623 -4.73243 2.83337
_cons | .8257405 1.462094 0.56 0.572 -2.039911 3.691392
------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L2.(NIM CAR_T1 Ln_ContLiab OpExpOpRev GNPARatio ROA) collapsed
L2.Ln_Loss_CC collapsed
Instruments for levels equation
Standard
L.Pub_Dummy L.PCR L.Ln_Assets GDPGr GsecYld CMR
Year4 Year5 Year13 Year14 Year15 Year16
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL.(NIM CAR_T1 Ln_ContLiab OpExpOpRev GNPARatio ROA) collapsed
DL.Ln_Loss_CC collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.88 Pr > z = 0.004
Arellano-Bond test for AR(2) in first differences: z = 1.75 Pr > z = 0.080
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(12) = 28.93 Prob > chi2 = 0.004
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(12) = 13.08 Prob > chi2 = 0.363
(Robust, but weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(5) = 5.82 Prob > chi2 = 0.325
Difference (null H = exogenous): chi2(7) = 7.27 Prob > chi2 = 0.402
gmm(Ln_Loss_CC, collapse lag(2 2))
Hansen test excluding group: chi2(10) = 9.90 Prob > chi2 = 0.449
Difference (null H = exogenous): chi2(2) = 3.18 Prob > chi2 = 0.204
gmm(NIM CAR_T1 Ln_ContLiab OpExpOpRev GNPARatio ROA, collapse lag(2 2))
Hansen test excluding group: chi2(0) = 0.00 Prob > chi2 = .
Difference (null H = exogenous): chi2(12) = 13.08 Prob > chi2 = 0.363
iv(Year4 Year5 Year13 Year14 Year15 Year16, eq(level))
Hansen test excluding group: chi2(6) = 7.45 Prob > chi2 = 0.282
Difference (null H = exogenous): chi2(6) = 5.64 Prob > chi2 = 0.465
iv(L.Pub_Dummy L.PCR L.Ln_Assets GDPGr GsecYld CMR, eq(level))
Hansen test excluding group: chi2(6) = 8.60 Prob > chi2 = 0.198
Difference (null H = exogenous): chi2(6) = 4.49 Prob > chi2 = 0.611
Code:
Arellano-Bond test for AR(1) in first differences: z = -2.88 Pr > z = 0.004 Arellano-Bond test for AR(2) in first differences: z = 1.75 Pr > z = 0.080 Arellano-Bond test for AR(3) in first differences: z = -1.55 Pr > z = 0.121
Code:
xtabond2 Ln_Loss_CC L.Ln_Loss_CC L.Pub_Dummy L.CAR_T1 L.GNPARatio L.PCR L.NIM L.CorpLoan L.Ln_ContLiab L.OpExpOpRev > L.Ln_Assets L.ROA GDPGr GsecYld CMR, gmmstyle(Ln_Loss_CC, lag(3 3) collapse) gmmstyle(NIM CAR_T1 Ln_ContLiab OpExpOp > Rev GNPARatio ROA, lag(2 2) collapse) ivstyle(Year4 Year5 Year13 Year14 Year15 Year16, equation(level)) ivstyle(L.Pu > b_Dummy L.PCR L.Ln_Assets GDPGr GsecYld CMR, equation(level)) twostep robust
Code:
Arellano-Bond test for AR(1) in first differences: z = -2.69 Pr > z = 0.007 Arellano-Bond test for AR(2) in first differences: z = 1.73 Pr > z = 0.083
Code:
xtabond2 Ln_Loss_CC L.Ln_Loss_CC L2.Ln_Loss_CC L.Pub_Dummy L.CAR_T1 L.GNPARatio L.PCR L.NIM L.CorpLoan L.Ln_ContLiab
> L.OpExpOpRev L.Ln_Assets L.ROA GDPGr GsecYld CMR, gmmstyle(Ln_Loss_CC, lag(2 2) collapse) gmmstyle(NIM CAR_T1 Ln_Co
> ntLiab OpExpOpRev GNPARatio ROA, lag(2 2) collapse) ivstyle(Year4 Year5 Year13 Year14 Year15 Year16, equation(level)
> ) ivstyle(L.Pub_Dummy L.PCR L.Ln_Assets GDPGr GsecYld CMR, equation(level)) twostep robust
Favoring speed over space. To switch, type or click on mata: mata set matafavor space, perm.
Dynamic panel-data estimation, two-step system GMM
------------------------------------------------------------------------------
Group variable: BankID Number of obs = 604
Time variable : Year Number of groups = 39
Number of instruments = 27 Obs per group: min = 13
Wald chi2(15) = 551320.37 avg = 15.49
Prob > chi2 = 0.000 max = 16
------------------------------------------------------------------------------
| Corrected
Ln_Loss_CC | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
Ln_Loss_CC |
L1. | .7680015 .0697107 11.02 0.000 .6313712 .9046319
L2. | .0704301 .046449 1.52 0.129 -.0206082 .1614684
|
Pub_Dummy |
L1. | .1365109 .0860715 1.59 0.113 -.0321861 .305208
|
CAR_T1 |
L1. | .5344809 .9822235 0.54 0.586 -1.390642 2.459604
|
GNPARatio |
L1. | .2529465 1.022552 0.25 0.805 -1.751218 2.257111
|
PCR |
L1. | .0867373 .1030018 0.84 0.400 -.1151426 .2886172
|
NIM |
L1. | -2.060311 6.979274 -0.30 0.768 -15.73944 11.61881
|
CorpLoan |
L1. | .1713231 1.325391 0.13 0.897 -2.426395 2.769041
|
Ln_ContLiab |
L1. | -.0072898 .0602268 -0.12 0.904 -.1253323 .1107526
|
OpExpOpRev |
L1. | .9642729 .6461956 1.49 0.136 -.3022473 2.230793
|
Ln_Assets |
L1. | .1472428 .1319228 1.12 0.264 -.1113212 .4058068
|
ROA |
L1. | 13.01347 5.783117 2.25 0.024 1.678767 24.34817
|
GDPGr | .0652841 .4530557 0.14 0.885 -.8226888 .9532571
GsecYld | 4.25321 4.160357 1.02 0.307 -3.90094 12.40736
CMR | -.4878538 2.104557 -0.23 0.817 -4.612709 3.637002
_cons | -.9568033 .6629169 -1.44 0.149 -2.256097 .3424899
------------------------------------------------------------------------------
Instruments for first differences equation
GMM-type (missing=0, separate instruments for each period unless collapsed)
L2.(NIM CAR_T1 Ln_ContLiab OpExpOpRev GNPARatio ROA) collapsed
L2.Ln_Loss_CC collapsed
Instruments for levels equation
Standard
L.Pub_Dummy L.PCR L.Ln_Assets GDPGr GsecYld CMR
Year4 Year5 Year13 Year14 Year15 Year16
_cons
GMM-type (missing=0, separate instruments for each period unless collapsed)
DL.(NIM CAR_T1 Ln_ContLiab OpExpOpRev GNPARatio ROA) collapsed
DL.Ln_Loss_CC collapsed
------------------------------------------------------------------------------
Arellano-Bond test for AR(1) in first differences: z = -2.65 Pr > z = 0.008
Arellano-Bond test for AR(2) in first differences: z = 1.37 Pr > z = 0.171
------------------------------------------------------------------------------
Sargan test of overid. restrictions: chi2(11) = 28.25 Prob > chi2 = 0.003
(Not robust, but not weakened by many instruments.)
Hansen test of overid. restrictions: chi2(11) = 13.69 Prob > chi2 = 0.251
(Robust, but weakened by many instruments.)
Difference-in-Hansen tests of exogeneity of instrument subsets:
GMM instruments for levels
Hansen test excluding group: chi2(4) = 4.98 Prob > chi2 = 0.289
Difference (null H = exogenous): chi2(7) = 8.71 Prob > chi2 = 0.274
gmm(Ln_Loss_CC, collapse lag(2 2))
Hansen test excluding group: chi2(9) = 11.11 Prob > chi2 = 0.268
Difference (null H = exogenous): chi2(2) = 2.58 Prob > chi2 = 0.275
iv(Year4 Year5 Year13 Year14 Year15 Year16, eq(level))
Hansen test excluding group: chi2(5) = 5.89 Prob > chi2 = 0.317
Difference (null H = exogenous): chi2(6) = 7.80 Prob > chi2 = 0.253
iv(L.Pub_Dummy L.PCR L.Ln_Assets GDPGr GsecYld CMR, eq(level))
Hansen test excluding group: chi2(5) = 5.94 Prob > chi2 = 0.312
Difference (null H = exogenous): chi2(6) = 7.75 Prob > chi2 = 0.257
Thanks
pankaj
