Table 5 Robustness test 2 for Hypothesis...

Table 5

Robustness test 2 for Hypothesis 1: PSM

Panel A: T-test for control variables with matched samples
	ESO = 0 (N = 2,693)	ESO >0 (N = 2,693)	Diff	T-value
	(1)	(2)	(3) = (1)–(2)
dTURN_t	0.000	0.000	0.000	0.231
NCSKEW_t	−0.410	−0.389	−0.021	−0.976
DUVOL_t	−0.245	−0.230	−0.014	−1.103
VCRASH_t	2.348	2.344	0.004	0.245
SIZE_t	11.748	11.753	−0.005	−0.154
MB_t	1.665	1.712	−0.046	−0.938
LEV_t	1.091	1.057	0.034	1.072
ROE_t	−0.018	−0.019	0.000	0.055
SIGM_t A	0.056	0.056	0.000	0.358
RET_t	−0.193	−0.190	−0.002	−0.392
ADACC_t	0.066	0.066	−0.001	−0.392
HHI_t	0.173	0.170	0.003	0.857

Panel A: T-test for control variables with matched samples
	ESO = 0 (N = 2,693)	ESO >0 (N = 2,693)	Diff	T-value
	(1)	(2)	(3) = (1)–(2)
dTURN_t	0.000	0.000	0.000	0.231
NCSKEW_t	−0.410	−0.389	−0.021	−0.976
DUVOL_t	−0.245	−0.230	−0.014	−1.103
VCRASH_t	2.348	2.344	0.004	0.245
SIZE_t	11.748	11.753	−0.005	−0.154
MB_t	1.665	1.712	−0.046	−0.938
LEV_t	1.091	1.057	0.034	1.072
ROE_t	−0.018	−0.019	0.000	0.055
SIGM_t A	0.056	0.056	0.000	0.358
RET_t	−0.193	−0.190	−0.002	−0.392
ADACC_t	0.066	0.066	−0.001	−0.392
HHI_t	0.173	0.170	0.003	0.857

Panel B: Association between ESO and future stock price crash risk with PSM samples
	NCSKEW_t+1	DUVOL_t+1	VCRASH_t+1
	(1)	(2)	(3)
ESO_t	−0.047	−0.021	−0.041
ESO_t	(−2.729)***	(−2.039)**	(−3.338)***
dTURN_t	−0.371	−0.225	−0.691
dTURN_t	(−0.751)	(−0.743)	(−1.709)*
CRASH_t	−0.094	−0.114	−0.114
CRASH_t	(−5.394)***	(-6.921)***	(−6.426)***
SIZE_t	0.186	0.097	0.078
SIZE_t	(4.693)***	(4.121)***	(2.281)**
MB_t	0.024	0.019	0.025
MB_t	(1.597)	(2.045)**	(1.833)*
LEV_t	0.026	0.016	0.019
LEV_t	(0.996)	(0.977)	(1.017)
ROE_t	−0.139	−0.084	−0.159
ROE_t	(−1.935)*	(−1.938)*	(−2.546)**
SIGMA_t	0.259	−0.606	−1.308
SIGMA_t	(0.128)	(-0.475)	(−0.838)
RET_t	−0.075	−0.163	−0.186
RET_t	(−0.291)	(−1.007)	(−0.931)
ADACC_t	0.399	0.167	0.22
ADACC_t	(1.906)*	(1.284)	(1.271)
HHI_t	1.502	0.870	1.511
HHI_t	(2.862)***	(2.623)***	(3.862)***
Constant	−2.782	−1.500	1.439
	(−6.182)***	(−5.608)***	(3.737)***
Year-fixed	Yes	Yes	Yes
Firm-fixed	Yes	Yes	Yes
F-value	15.033	15.128	10.881
Adj. R²	0.075	0.073	0.050
N	5,386	5,386	5,386

Panel B: Association between ESO and future stock price crash risk with PSM samples
	NCSKEW_t+1	DUVOL_t+1	VCRASH_t+1
	(1)	(2)	(3)
ESO_t	−0.047	−0.021	−0.041
ESO_t	(−2.729)***	(−2.039)**	(−3.338)***
dTURN_t	−0.371	−0.225	−0.691
dTURN_t	(−0.751)	(−0.743)	(−1.709)*
CRASH_t	−0.094	−0.114	−0.114
CRASH_t	(−5.394)***	(-6.921)***	(−6.426)***
SIZE_t	0.186	0.097	0.078
SIZE_t	(4.693)***	(4.121)***	(2.281)**
MB_t	0.024	0.019	0.025
MB_t	(1.597)	(2.045)**	(1.833)*
LEV_t	0.026	0.016	0.019
LEV_t	(0.996)	(0.977)	(1.017)
ROE_t	−0.139	−0.084	−0.159
ROE_t	(−1.935)*	(−1.938)*	(−2.546)**
SIGMA_t	0.259	−0.606	−1.308
SIGMA_t	(0.128)	(-0.475)	(−0.838)
RET_t	−0.075	−0.163	−0.186
RET_t	(−0.291)	(−1.007)	(−0.931)
ADACC_t	0.399	0.167	0.22
ADACC_t	(1.906)*	(1.284)	(1.271)
HHI_t	1.502	0.870	1.511
HHI_t	(2.862)***	(2.623)***	(3.862)***
Constant	−2.782	−1.500	1.439
	(−6.182)***	(−5.608)***	(3.737)***
Year-fixed	Yes	Yes	Yes
Firm-fixed	Yes	Yes	Yes
F-value	15.033	15.128	10.881
Adj. R²	0.075	0.073	0.050
N	5,386	5,386	5,386

Note(s): We derive propensity scores by conducting a logit regression using all the control variables included in Equation (4) with year and industry dummies. Subsequently, we use one-to-one matching, resulting in a matched sample of 5,386 observations of 2,693 firms without ESO and 2,693 of firms with ESO. The numbers in parentheses are t-statistics based on heteroskedastic robust standard errors.*, ** and *** denote significance at the 10%, 5% and 1% levels (two-tailed), respectively. See Appendix A2 for variable definitions

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