Hello all,
I am running a panel data analysis with multiple firms of 5 countries for 9 years (2014-2022) to examine the interaction effect of Corporate Social Responsibility (L_CSR) on Earnings Management (ABS_DA). I conducted an endogeneity test using xtivreg2 with the industry mean of CSR performance (L.INDCSR_x) as the instrumental variable. Specifically, I used the industry mean of CSR scores as an instrumental variable to address potential endogeneity issues. The result from 2SLS is significant between CSR and ABS_DA. However, the F statistic and Cragg-Donald Wald F statistic are very high in the first stage, 15,382.46 and 27,000 in the second stage, respectively.
My questions are: 1) Have I made any misspecifications in my regression analysis? 2) How can I address the very high F statistic and Cragg-Donald Wald F statistic observed in the analysis? 3) Would these high values affect the reliability of my results?
Thank you very much for your help.
1) Here is the 2SLS code & result:
I am running a panel data analysis with multiple firms of 5 countries for 9 years (2014-2022) to examine the interaction effect of Corporate Social Responsibility (L_CSR) on Earnings Management (ABS_DA). I conducted an endogeneity test using xtivreg2 with the industry mean of CSR performance (L.INDCSR_x) as the instrumental variable. Specifically, I used the industry mean of CSR scores as an instrumental variable to address potential endogeneity issues. The result from 2SLS is significant between CSR and ABS_DA. However, the F statistic and Cragg-Donald Wald F statistic are very high in the first stage, 15,382.46 and 27,000 in the second stage, respectively.
My questions are: 1) Have I made any misspecifications in my regression analysis? 2) How can I address the very high F statistic and Cragg-Donald Wald F statistic observed in the analysis? 3) Would these high values affect the reliability of my results?
Thank you very much for your help.
1) Here is the 2SLS code & result:
Code:
xi: xtivreg2 ABS_DA (L_CSR = L.INDCSR_x) L_LEV L_SIZE L_GROWTH L_MB L_ROA L_BR L_LOSS L_GDP i.year, fe cluster(Firm_id) first
i.year _Iyear_2014-2022 (naturally coded; _Iyear_2014 omitted)
Warning - singleton groups detected. 181 observation(s) not used.
Warning - collinearities detected
Vars dropped: _Iyear_2022
FIXED EFFECTS ESTIMATION
------------------------
Number of groups = 592 Obs per group: min = 2
avg = 4.1
max = 8
Warning - collinearities detected
Vars dropped: _Iyear_2022
First-stage regressions
-----------------------
FIXED EFFECTS ESTIMATION
------------------------
Number of groups = 592 Obs per group: min = 2
avg = 4.1
max = 8
First-stage regression of L_CSR:
Statistics robust to heteroskedasticity and clustering on Firm_id
Number of obs = 2416
Number of clusters (Firm_id) = 592
------------------------------------------------------------------------------
| Robust
L_CSR | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
INDCSR_x |
L1. | -.9684834 .0078087 -124.03 0.000 -.9837984 -.9531683
|
L_LEV | -.0187826 .0131859 -1.42 0.154 -.0446437 .0070785
L_SIZE | .008681 .0041772 2.08 0.038 .0004883 .0168736
L_GROWTH | -.0086074 .002948 -2.92 0.004 -.0143894 -.0028255
L_MB | -.0005313 .0006001 -0.89 0.376 -.0017082 .0006456
L_ROA | -.0125525 .0242489 -0.52 0.605 -.0601113 .0350064
L_BR | .0336876 .0128807 2.62 0.009 .0084251 .0589502
L_LOSS | .0014308 .0026607 0.54 0.591 -.0037875 .0066492
L_GDP | -.070959 .0165907 -4.28 0.000 -.103498 -.0384199
_Iyear_2015 | -.1242973 .0062454 -19.90 0.000 -.1365463 -.1120484
_Iyear_2016 | -.068923 .0058886 -11.70 0.000 -.0804722 -.0573738
_Iyear_2017 | -.0272291 .0056558 -4.81 0.000 -.0383218 -.0161364
_Iyear_2018 | .0255326 .0045209 5.65 0.000 .0166659 .0343994
_Iyear_2019 | -.0292436 .0042435 -6.89 0.000 -.0375663 -.0209209
_Iyear_2020 | -.0074886 .0035226 -2.13 0.034 -.0143974 -.0005799
_Iyear_2021 | -.0265515 .002445 -10.86 0.000 -.0313467 -.0217562
_Iyear_2022 | 0 (omitted)
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F test of excluded instruments:
F( 1, 591) = 15382.46
Prob > F = 0.0000
Sanderson-Windmeijer multivariate F test of excluded instruments:
F( 1, 591) = 15382.46
Prob > F = 0.0000
Summary results for first-stage regressions
-------------------------------------------
(Underid) (Weak id)
Variable | F( 1, 591) P-val | SW Chi-sq( 1) P-val | SW F( 1, 591)
L_CSR | 15382.46 0.0000 | 15504.79 0.0000 | 15382.46
NB: first-stage test statistics cluster-robust
Stock-Yogo weak ID F test critical values for single endogenous regressor:
10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for i.i.d. errors only.
Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic Chi-sq(1)=146.96 P-val=0.0000
Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic 27434.85
Kleibergen-Paap Wald rk F statistic 15382.46
Stock-Yogo weak ID test critical values for K1=1 and L1=1:
10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test F(1,591)= 2.95 P-val=0.0865
Anderson-Rubin Wald test Chi-sq(1)= 2.97 P-val=0.0847
Stock-Wright LM S statistic Chi-sq(1)= 3.21 P-val=0.0733
NB: Underidentification, weak identification and weak-identification-robust
test statistics cluster-robust
Number of clusters N_clust = 592
Number of observations N = 2416
Number of regressors K = 16
Number of endogenous regressors K1 = 1
Number of instruments L = 16
Number of excluded instruments L1 = 1
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on Firm_id
Number of clusters (Firm_id) = 592 Number of obs = 2416
F( 16, 591) = 11.06
Prob > F = 0.0000
Total (centered) SS = 33.73609012 Centered R2 = 0.1716
Total (uncentered) SS = 33.73609012 Uncentered R2 = 0.1716
Residual SS = 27.94700095 Root MSE = .1238
------------------------------------------------------------------------------
| Robust
ABS_DA | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
L_CSR | -.0735145 .0424734 -1.73 0.083 -.1567609 .0097319
L_LEV | .0720565 .0608729 1.18 0.237 -.0472522 .1913651
L_SIZE | .0091343 .0195308 0.47 0.640 -.0291453 .0474138
L_GROWTH | -.0124812 .0138465 -0.90 0.367 -.0396198 .0146573
L_MB | -.0067423 .0019932 -3.38 0.001 -.0106489 -.0028357
L_ROA | .0739117 .1130375 0.65 0.513 -.1476376 .2954611
L_BR | .0885418 .0683608 1.30 0.195 -.0454428 .2225265
L_LOSS | .0140924 .0205092 0.69 0.492 -.0261049 .0542897
L_GDP | .2684111 .0780064 3.44 0.001 .1155213 .4213008
_Iyear_2015 | .1288262 .0357963 3.60 0.000 .0586667 .1989857
_Iyear_2016 | .0522632 .0290552 1.80 0.072 -.0046839 .1092102
_Iyear_2017 | .0556726 .0275315 2.02 0.043 .0017119 .1096333
_Iyear_2018 | .0343631 .0219225 1.57 0.117 -.0086042 .0773304
_Iyear_2019 | .0245027 .0170516 1.44 0.151 -.0089179 .0579233
_Iyear_2020 | .1159361 .0160905 7.21 0.000 .0843992 .147473
_Iyear_2021 | .1320435 .0150436 8.78 0.000 .1025586 .1615284
_Iyear_2022 | 0 (omitted)
------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 146.956
Chi-sq(1) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 2.7e+04
(Kleibergen-Paap rk Wald F statistic): 1.5e+04
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
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Instrumented: L_CSR
Included instruments: L_LEV L_SIZE L_GROWTH L_MB L_ROA L_BR L_LOSS L_GDP
_Iyear_2015 _Iyear_2016 _Iyear_2017 _Iyear_2018
_Iyear_2019 _Iyear_2020 _Iyear_2021
Excluded instruments: L.INDCSR_x
Dropped collinear: _Iyear_2022
------------------------------------------------------------------------------
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