Table 4 Difference-in-differences...

Table 4

Difference-in-differences analysis using the 2001 decimalization

Panel A: Pre-match propensity score regression and post-match diagnostic regression
Variable	Pre-match		Post-match
Variable	Coeff.	t-stat	Coeff.	t-stat
RET_t	0.723^**	8.65	0.066	0.60
MC_t−1	0.094^**	3.17	0.039	1.08
B/M_t−1	−0.015	−0.25	0.046	0.60
MOM_t−1	0.386^**	3.67	0.118	0.87
D_NS_t−1	−0.008	−0.03	−0.297	−0.85
NS_t−1	−0.579^**	−2.85	−0.032	−0.12
dA/A_t−1	−0.062	−0.37	−0.065	−0.28
D_Y/B_t−1	−0.524^**	−3.87	0.075	0.43
Y/B(+)_t−1	0.543	0.66	−0.077	−0.07
ACC_t−1	−0.367	−1.26	0.230	0.57
LIQ_HL_t−1	−1.496^**	−13.11	0.031	0.19
ACC_t−1 × LIQ_HL_t−1	−0.570	−1.45	−0.011	−0.02
Industry fixed effects	Yes		Yes
N	1,231		612
p-value of χ²	< 0.001		1.000
Pseudo R²	0.279		0.019

Panel A: Pre-match propensity score regression and post-match diagnostic regression
Variable	Pre-match		Post-match
Variable	Coeff.	t-stat	Coeff.	t-stat
RET_t	0.723^**	8.65	0.066	0.60
MC_t−1	0.094^**	3.17	0.039	1.08
B/M_t−1	−0.015	−0.25	0.046	0.60
MOM_t−1	0.386^**	3.67	0.118	0.87
D_NS_t−1	−0.008	−0.03	−0.297	−0.85
NS_t−1	−0.579^**	−2.85	−0.032	−0.12
dA/A_t−1	−0.062	−0.37	−0.065	−0.28
D_Y/B_t−1	−0.524^**	−3.87	0.075	0.43
Y/B(+)_t−1	0.543	0.66	−0.077	−0.07
ACC_t−1	−0.367	−1.26	0.230	0.57
LIQ_HL_t−1	−1.496^**	−13.11	0.031	0.19
ACC_t−1 × LIQ_HL_t−1	−0.570	−1.45	−0.011	−0.02
Industry fixed effects	Yes		Yes
N	1,231		612
p-value of χ²	< 0.001		1.000
Pseudo R²	0.279		0.019

Panel B: Statistical distributions of estimated propensity scores
	N	Mean	SD	Min	P5	P25	P50	P75	P95	Max
Treatment	306	0.487	0.200	0.022	0.154	0.354	0.477	0.609	0.860	0.967
Control	306	0.496	0.206	0.020	0.154	0.353	0.490	0.612	0.856	0.997
Difference		−0.009	−0.006	0.002	0.000	0.000	−0.013	−0.002	0.004	−0.030

Panel B: Statistical distributions of estimated propensity scores
	N	Mean	SD	Min	P5	P25	P50	P75	P95	Max
Treatment	306	0.487	0.200	0.022	0.154	0.354	0.477	0.609	0.860	0.967
Control	306	0.496	0.206	0.020	0.154	0.353	0.490	0.612	0.856	0.997
Difference		−0.009	−0.006	0.002	0.000	0.000	−0.013	−0.002	0.004	−0.030

Panel C: Differences in post-match characteristics
Variable	Control	Treatment	Difference	t-stat
RET_t	0.083	0.122	−0.039	−0.91
MC_t−1	5.927	6.137	−0.210	−1.24
B/M_t−1	−0.636	−0.616	−0.020	−0.26
MOM_t−1	−0.038	0.005	−0.042	−1.22
D_NS_t−1	0.029	0.020	0.010	0.78
NS_t−1	0.067	0.058	0.009	0.47
dA/A_t−1	0.125	0.114	0.010	0.44
D_Y/B_t−1	0.245	0.225	0.020	0.57
Y/B(+)_t−1	0.063	0.065	−0.001	−0.28
ACC_t−1	0.075	0.074	0.001	0.07
LIQ_HL_t−1	4.360	4.414	−0.054	−1.24
ACC_t−1 × LIQ_HL_t−1	−0.012	−0.009	−0.003	−0.34

Panel C: Differences in post-match characteristics
Variable	Control	Treatment	Difference	t-stat
RET_t	0.083	0.122	−0.039	−0.91
MC_t−1	5.927	6.137	−0.210	−1.24
B/M_t−1	−0.636	−0.616	−0.020	−0.26
MOM_t−1	−0.038	0.005	−0.042	−1.22
D_NS_t−1	0.029	0.020	0.010	0.78
NS_t−1	0.067	0.058	0.009	0.47
dA/A_t−1	0.125	0.114	0.010	0.44
D_Y/B_t−1	0.245	0.225	0.020	0.57
Y/B(+)_t−1	0.063	0.065	−0.001	−0.28
ACC_t−1	0.075	0.074	0.001	0.07
LIQ_HL_t−1	4.360	4.414	−0.054	−1.24
ACC_t−1 × LIQ_HL_t−1	−0.012	−0.009	−0.003	−0.34

Panel D: Difference-in-differences test
Variable	Coeff.	t-Stat
ACC_t (⁠ $β_{1}$ ⁠)	−0.671^**	−3.10
D_T × ACC_t (⁠ $β_{2}$ ⁠)	−0.113	−0.46
D_A × ACC_t (⁠ $β_{3}$ ⁠)	−1.716^**	−2.68
D_T × D_A × ACC_t (⁠ $β_{4}$ ⁠)	1.767^*	2.24
Fiscal year-end month fixed effects	Yes
Industry fixed effects	Yes
N	1,224
R²	0.120
$β_{1}$ + $β_{2}$	−0.784^**	5.17
$β_{1}$ + $β_{3}$	−2.388^**	3.95
$β_{1}$ + $β_{2}$ + $β_{3}$ + $β_{4}$	−0.734^†	1.71
$β_{3}$ + $β_{4}$	0.050	0.10

Panel D: Difference-in-differences test
Variable	Coeff.	t-Stat
ACC_t ( $β_{1}$ )	−0.671^**	−3.10
D_T × ACC_t ( $β_{2}$ )	−0.113	−0.46
D_A × ACC_t ( $β_{3}$ )	−1.716^**	−2.68
D_T × D_A × ACC_t ( $β_{4}$ )	1.767^*	2.24
Fiscal year-end month fixed effects	Yes
Industry fixed effects	Yes
N	1,224
R²	0.120
$β_{1}$ + $β_{2}$	−0.784^**	5.17
$β_{1}$ + $β_{3}$	−2.388^**	3.95
$β_{1}$ + $β_{2}$ + $β_{3}$ + $β_{4}$	−0.734^†	1.71
$β_{3}$ + $β_{4}$	0.050	0.10

Panel E: Falsification test
Variable	Coeff.	t-stat
ACC_t (⁠ $β_{1}$ ⁠)	−0.495^†	−1.94
D_T × ACC_t (⁠ $β_{2}$ ⁠)	−0.202	−0.50
D_A × ACC_t (⁠ $β_{3}$ ⁠)	0.269	0.67
D_T × D_A × ACC_t (⁠ $β_{4}$ ⁠)	0.057	0.10
Fiscal year-end month fixed effects	Yes
Industry fixed effects	Yes
N	728
R²	0.116
$β_{1}$ + $β_{2}$	−0.697^*	2.25
$β_{1}$ + $β_{3}$	−0.227	0.75
$β_{1}$ + $β_{2}$ + $β_{3}$ + $β_{4}$	−0.371	1.41
$β_{3}$ + $β_{4}$	0.326	0.82

Panel E: Falsification test
Variable	Coeff.	t-stat
ACC_t ( $β_{1}$ )	−0.495^†	−1.94
D_T × ACC_t ( $β_{2}$ )	−0.202	−0.50
D_A × ACC_t ( $β_{3}$ )	0.269	0.67
D_T × D_A × ACC_t ( $β_{4}$ )	0.057	0.10
Fiscal year-end month fixed effects	Yes
Industry fixed effects	Yes
N	728
R²	0.116
$β_{1}$ + $β_{2}$	−0.697^*	2.25
$β_{1}$ + $β_{3}$	−0.227	0.75
$β_{1}$ + $β_{2}$ + $β_{3}$ + $β_{4}$	−0.371	1.41
$β_{3}$ + $β_{4}$	0.326	0.82

Note(s): This table reports diagnostics and results of the DiD test on how exogenous changes in stock liquidity resulting from the minimum tick size decimalization affect the negative relation between accruals and future stock returns. Sample selection begins with all firms with non-missing matching variables in the pre-decimalization year (t−1) and the post-decimalization year (t+1), with t indicating the year of decimalization. On the basis of the change in stock liquidity surrounding the decimalization (ΔLIQ_HL_t−1 _{to t+1}), we sort 1,837 sample firms into three equal groups and retain only the top group with the greatest improvement in stock liquidity (the treatment group) and the bottom group with the least improvement (the control group). We match firms by using one-to-one nearest neighbor propensity score matching, without replacement. Panel A presents parameter estimates from the Probit model used to compute the propensity scores for matching. The dependent variable is 1 if the firm is in the treatment group and 0 if otherwise. The “Pre-match” column reports parameter estimates from the Probit model obtained using the sample prior to the matching. These estimates are used to generate the propensity score for matching. The “Post-match” column reports parameter estimates from the Probit model obtained using the matched observations. Panel B reports the statistical distribution of estimated propensity scores separately for matched treatment and control firms. Panel C reports comparisons of observable characteristics between matched treatment and control firms and the corresponding t-statistics. Panel D reports the DiD test results. Panel E reports results from the falsification test. In Panels A, E and F, the t-statistics are calculated by using cluster-robust standard errors clustered by firm.^**, ^* and ^† denote statistical significance at the 1%, 5% and 10% levels, respectively, using a two-tailed test

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