The impact of price limit system on the comprehensive quality of the stock market: Research on long-term and short-term effects based on submarkets

Figures & data

Table 1. Description of the main variables

Main variables			Description
Endogenous variables	Liquidity LDit	$T{R}_{it}$	The liquidity indicator, as shown in formula (1), measures the liquidity of the stock market. The larger the value of this indicator, the better the liquidity of the stock market. Additionally, i represents the stock market, and t represents time, the same below.
		$NT{R}_{it}$	The illiquidity indicator, as shown in formula (2), measures the illiquidity of the stock market. The larger the value of this indicator, the worse the liquidity of the stock market.
	Volatility BDit	$Sma{20}_{it}$	This variable measures the 20-day simple moving average standard deviation of stock daily returns, as shown in formula (3). The larger the value of this indicator, the greater the volatility of the stock market; and vice versa.
		$Garc{h}_{it}$	This variable measures the daily volatility calculated by the Garch model, as shown in formula (4). The larger the value of this indicator, the greater the volatility of the stock market, and vice versa.
	Market efficiency XLit	$ME{C}_{it}$	This variable measures the market efficiency coefficient, as shown in formula (5). The closer the market efficiency coefficient is to 1, the higher the pricing efficiency of the stock market.
Dummy variables	System change	$D_t$	This variable represents the dummy variable of system change. The value is 0 before the system change, and the value is 1 after the change.
	Stock market experiment	$D_i$	This variable represents the dummy variable of the stock market experiment. The value is 1 for the experimental group and 0 for the control group.
	Interactive item	$D_t\ast D_i$	This variable represents the interaction item of dummy variables, and the regression coefficient of the interaction term on the explained variable is the focus.
Prerequisite variables	Lagged endogenous variables	$L{D}_{it-1}$	This variable represents the first-order lag term of the liquidity indicator.
		$B{D}_{it-1}$	This variable represents the first-order lag term of the volatility indicator.
		$X{L}_{it-1}$	This variable represents the first-order lag term of the market efficiency indicator.
	Exogenous variables	$\left|R_{it}\right|$	This variable represents the absolute value of the daily return rate of the stock market.
		$P_{it}$	This variable indicates the stock index price.
		$R{f}_t$	This variable indicates the one-year time deposit benchmark interest rate of the People’s Bank of China.

Note: All variables are standardized and outliers are deleted.

Table 2. Experimental design

Test of total market
Market	Quasi-natural experiment	Before the change of price limit system	After the change of price limit system
Total market	Experimental group	No price limit	10%
Hong Kong stock market	Control group	No price limit	No price limit
Test of the Shanghai stock market
Market	Quasi-natural experiment	Before the change of price limit system	After the change of price limit system
Shanghai stock market	Experimental group	1% or 5%	No price limit
Shenzhen stock market	Control group	No price limit	No price limit
Test of the Shenzhen stock market
Market	Quasi-natural experiment	Before the change of price limit system	After the change of price limit system
Shenzhen stock market	Experimental group	0.5%	No price limit
Shanghai stock market	Control group	1%	1%

Table 3. Regression results of the difference-in-differences simultaneous model of the total market

Liquidity equation			Volatility equation			Market efficiency equation
Coefficient	TRit	NTRit	Coefficient	Sma20it	Garchit	Coefficient	MECit
Interact item	0.3520*** (15.98)	−0.2612*** (−23.54)	Interact item	−0.8310*** (−32.28)	−0.1102*** (−7.12)	Interact item	0.0112*** (2.67)
BDit	−12.5175***	5.5034***	LDit	0.0279e-03***	0.0196e-04***	LDit	0.0068e-04***
	(−21.39)	(5.47)		(32.97)	(4.03)		(6.56)
XLit	−0.2712***	0.1358***	XLit	−0.0078	−0.1835***	BDit	−0.1878**
	(−8.93)	(7.95)		(−0.27)	(−9.00)		(−1.34)
LDit-1	0.2923e-04***	0.1500e-03***	BDit-1	35.3821***	92.3441***	XLit-1	0.7229***
	(37.95)	(49.52)		(90.45)	(86.14)		(25.49)
$\left|R_{it}\right|$	−9.6645***	4.5671***	Pit	0.0069e-04*	0.0835e-05	Rft	−0.1010**
	(−31.31)	(67.02)		(1.70)	(0.32)		(−1.44)
Constant	0.1057***	0.1520***	Constant	1.7642***	0.4137***	Constant	0.2636***
	(15.98)	(12.60)		(17.89)	(11.02)		(34.30)
R^2	0.3732	0.3835	R^2	0.5162	0.6828	R^2	0.5257

Note: ***, **, and * are marked at the significance level of 1%, 5%, and 10%, respectively. “()” is the Z statistic. Some of the indicators have been treated with magnitude. The same in other tables.

Table 4. Regression results of the difference-in-differences simultaneous model of the Shanghai stock market

Liquidity equation			Volatility equation			Market efficiency equation
Coefficient	TRit	NTRit	Coefficient	Sma20it	Garchit	Coefficient		MECit
Interact item	1.0532***	−1.6374***	Interact item	0.0047***	0.0011*	Interact item		−0.1114**
	(13.62)	(−6.32)		(5.35)	(1.84)			(−2.41)
BDit	−0.4359*	4.2165**	LDit	0.0113e-05***	0.0024***	LDit		−0.0215***
	(−1.82)	(2.97)		(32.99)	(4.32)			(−2.88)
XLit	−0.0147	0.1247	XLit	0.0006*	−0.0033***	BDit		0.9076***
	(−1.61)	(1.21)		(1.67)	(−7.38)			(3.69)
LDit-1	0.8669***	0.0583e-3***	BDit-1	0.9388***	0.8964***	XLit-1		0.4184***
	(87.22)	(5.35)		(201.4)	(96.41)			(22.15)
$\left|R_{it}\right|$	2.4870***	23.5011***	Pit	0.0352e-05	3.3400e-06*	Rft		−1.6726***
	(11.89)	(25.72)		(0.52)	(2.99)			(−4.45)
Constant	0.0429	1.6975***	Constant	−0.0036***	0.0058***	Constant		0.8280***
	(0.84)	(7.90)		(−5.01)	(2.90)			(16.14)
R^2	0.4014	0.3846	R^2	0.7609	0.7397	R^2		0.2713

Table 5. Regression results of the difference-in-differences simultaneous model of the Shenzhen stock market

Liquidity equation			Volatility equation			Market efficiency equation
Coefficient	TRit	NTRit	Coefficient	Sma20it	Garchit	Coefficient	MECit
Interact item	−2.4746** (−1.57)	1.5764 (3.13)	Interact item	0.0337*** (9.59)	0.0356*** (12.90)	Interact item	−3.9823 (−1.37)
BDit	−22.7659	6.3683*	LDit	−0.0004e-1*	−0.0014e-2	LDit	0.0013
	(−0.30)	(1.03)		(−1.73)	(−0.76)		(0.06)
XLit	0.0530e-04	0.2691	XLit	−0.0701e-07	−0.0328e-07	BDit	−4.1497
	(0.66)	(0.31)		(−1.25)	(−0.74)		(−0.95)
LDit-1	0.7851***	0.2670e-4***	BDit-1	0.1128***	−0.0318e-05**	XLit-1	0.3553e-4***
	(23.26)	(5.02)		(6.57)	(−2.10)		(7.33)
$\left|R_{it}\right|$	−94.8312***	6.3226	Pit	0.0001**	0.0001***	Rft	0.0001
	(−2.61)	(0.52)		(2.19)	(3.26)		(0.045)
Constant	1.0680	3.4195***	Constant	−0.0012	0.0006	Constant	0.2323
	(0.46)	(6.22)		(−0.36)	(0.23)		(0.17)
R^2	0.4377	0.3602	R^2	0.6303	0.7032	R^2	0.2989

Table 6. Test results of trading interference effect on the Shanghai stock market before and after the change of price limit system

Window	Before setting price limit system					Window	After setting price limit system
	$\mathit{S}toc{k}_{hit}$		$\mathit{S}toc{k}_{0.9}$		$\mathit{S}toc{k}_{0.8}$		$\mathit{S}toc{k}_{hit}$		$\mathit{S}toc{k}_{0.9}$		$\mathit{S}toc{k}_{0.8}$
−10	−0.0358		0.1445		0.1525	−10	−0.2125		0.0972		0.0804
−9	0.0513		−0.4633		−0.0775	−9	0.0578	>	0.0412		−0.0246
−8	−0.0791		−0.0159		−0.0493	−8	0.1505		−0.0502		−0.0289
−7	0.0190		0.0534		−0.0844	−7	−0.1190		−0.0600		0.0260
−6	−0.0897		−0.0381		−0.0882	−6	−0.0560		−0.0233		−0.0682
−5	−0.1393	>>	0.3473		−0.0221	−5	−0.0682		−0.0163		0.0252
−4	−0.0138		0.2555		0.0156	−4	−0.0487		0.1305		0.0905
−3	0.0088		−0.3620		−0.0714	−3	0.1013		0.0321		−0.0003
−2	−0.0964	>>	0.5502		0.0742	−2	0.2477		−0.0473		−0.0315
−1	0.0122		0.3351	>>	−0.0964	−1	0.3693		0.0542		−0.1001
0	0.4208		0.1266		−0.0629	0	0.7631	>	0.1340		0.1656
1	−0.0229		−0.0614	>	−0.2055	1	−0.0917	>	−0.0099		−0.0502
2	−0.2835		−0.1556		−0.3343	2	−0.5372	>>	0.0473		−0.0473
3	−0.1084		−0.2369		−0.1911	3	−0.1226		−0.0866		−0.1692
4	−0.2761		−0.0387		−0.0629	4	0.4393		−0.0445		−0.0215
5	−0.1322		−0.0222		−0.0380	5	−0.0765		−0.0310		−0.0668
6	−0.0172		−0.0741		−0.1322	6	−0.2502		−0.0029		0.0678
7	−0.1446		−0.2161		−0.0024	7	−0.0685		0.0679	>>	−0.1734
8	−0.0614		−0.1324		−0.0594	8	−0.1142		−0.0809		−0.0557
9	−0.1398		−0.0491		−0.2212	9	−0.0954		−0.0383		−0.0288
10	−0.0614		0.0852		−0.0714	10	−0.0955		0.0541		−0.1136

Note: “>>” indicates that the data on the left are significantly larger than the data on the right at the 1% significance level; “>” indicates that the data on the left are significantly greater than the data on the right at the 5% significance level. By contrast, “<<” means that the data on the left are significantly smaller than the data on the right at the 1% significance level, and “<” means that the data on the left are significantly smaller than the data on the right at the 5% significance level. The same in other tables.

Table 7. Test results of trading interference effect on the Shenzhen stock market before and after the change of price limit system

Window	Before setting price limit system					Window	After setting price limit system
	$\mathit{S}toc{k}_{hit}$		$\mathit{S}toc{k}_{0.9}$		$\mathit{S}toc{k}_{0.8}$		$\mathit{S}toc{k}_{hit}$		$\mathit{S}toc{k}_{0.9}$		$\mathit{S}toc{k}_{0.8}$
−10	−0.1955		0.0696		0.0599	−10	−0.0468		−0.0359		0.0603
−9	0.0164		−0.1073		−0.1710	−9	0.1512		−0.0594		0.0218
−8	0.0255		0.2624		0.0420	−8	0.1144		0.1716		0.0353
−7	0.0521		0.0357		0.3357	−7	0.1175		0.0147		0.0431
−6	0.1049		0.1079		0.5884	−6	−0.0733		−0.0232		0.0264
−5	0.4278		0.1705		0.1265	−5	−0.1172		−0.0157		0.0146
−4	0.0652		0.1092		0.1813	−4	0.1753		−0.0458		−0.0895
−3	−0.0774		0.3308		0.5670	−3	−0.1259	<	0.2679	>	0.0378
−2	0.3952		0.6638		0.3095	−2	0.2635		−0.1255		−0.0341
−1	5.3299	>	0.5072	>>	0.1043	−1	0.3317		0.0851		0.0282
0	0.9240		0.0483		0.2077	0	1.0358	>	0.3446		0.2834
1	0.5558	>	−0.0661		0.2693	1	−0.1467		0.1453		0.1119
2	−0.3273		−0.0558		−0.0314	2	−0.1258		−0.1279		−0.1397
3	−0.2504		−0.0763		−0.1215	3	−0.0493		−0.0987		−0.0070
4	0.2189		0.0343		−0.0596	4	−0.0386		0.2502	>	−0.0123
5	−0.2141		−0.0633		0.0326	5	−0.1322		0.0204		−0.0194
6	0.0590		0.0906		0.0119	6	−0.0346		0.0028		0.0545
7	0.0526		−0.1485		0.2814	7	0.1334		−0.0804		−0.0442
8	−0.0226		0.0364		0.2179	8	−0.0823		−0.0204		0.0863
9	0.0362		0.0434		0.1438	9	0.0418		−0.0133		0.1123
10	−0.1866		0.0364		−0.0640	10	−0.1445		0.0963		−0.0081

Table 8. Test results of volatility spillover effects on the Shanghai stock market before and after the change of price limit system

Window	Before setting price limit system					Window	After setting price limit system
	$\mathit{S}toc{k}_{hit}$		$\mathit{S}toc{k}_{0.9}$		$\mathit{S}toc{k}_{0.8}$		$\mathit{S}toc{k}_{hit}$		$\mathit{S}toc{k}_{0.9}$		$\mathit{S}toc{k}_{0.8}$
−10	0.0025		0.0006		0.0032	−10	0.0003		0.0012		0.0003
−9	0.0028		0.0003		0.0020	−9	0.0003		0.0006		0.0005
−8	0.0014		0.0004	>>	0.0022	−8	0.0006	>	0.0002	<<	0.0005
−7	0.0025	>>	0.0001		0.0011	−7	0.0004		0.0002		0.0004
−6	0.0018		0.0007		0.0021	−6	0.0001		0.0005		0.0005
−5	0.0025		0.0009		0.0020	−5	0.0004		0.0008		0.0008
−4	0.0036		0.0009		0.0011	−4	0.0003		0.0007		0.0008
−3	0.0016		0.0008	>>	0.0027	−3	0.0010		0.0003		0.0009
−2	0.0049	>>	0.0007		0.0025	−2	0.0003		0.0003		0.0007
−1	0.0017		0.0009	>>	0.0050	−1	0.0009		0.0004		0.0016
0	0.0100		0.0051		0.0041	0	0.0006	>	0.0049	>	0.0025
1	0.0040		0.0011	<<	0.0042	1	0.0001	>>	0.0011		0.0013
2	0.0059		0.0057		0.0008	2	0.0001	<	0.0017		0.0012
3	0.0024		0.0036		0.0031	3	0.0010		0.0006		0.0007
4	0.0028		0.0098		0.0026	4	0.0008		0.0003		0.0007
5	0.0025		0.0007		0.0015	5	0.0001		0.0001	>	0.0008
6	0.0020		0.0047		0.0010	6	0.0006		0.0003		0.0011
7	0.0030	>	0.0002		0.0011	7	0.0005		0.0004		0.0008
8	0.0014		0.0052		0.0007	8	0.0004		0.0002		0.0004
9	0.0013		0.0066		0.0005	9	0.0002		0.0004		0.0008
10	0.0011		0.0019		0.0009	10	0.0004		0.0005		0.0005

Table 9. Test results of volatility spillover effect on the Shenzhen stock market before and after the change of price limit system

Window	Before setting price limit system					Window	After setting price limit system
	$\mathit{S}toc{k}_{hit}$		$\mathit{S}toc{k}_{0.9}$		$\mathit{S}toc{k}_{0.8}$		$\mathit{S}toc{k}_{hit}$		$\mathbf{S}\mathbf{t}\mathbf{o}\mathbf{c}{\mathbf{k}}_{\mathbf{0.9}}$		$\mathit{S}toc{k}_{0.8}$
−10	0.0003		0.0005		0.0015	−10	0.0008		0.0003		0.0009
−9	0.0004		0.0004		0.0017	−9	0.0008		0.0003		0.0009
−8	0.0004		0.0002		0.0011	−8	0.0006		0.0017		0.0015
−7	0.0005		0.0005		0.0011	−7	0.0003		0.0002	<	0.0015
−6	0.0002		0.0007		0.0205	−6	0.0012		0.0005		0.0012
−5	0.0012		0.0010		0.0002	−5	0.0005		0.0005		0.0017
−4	0.0018		0.0010		0.0057	−4	0.0016		0.0008		0.0017
−3	0.0021		0.0064		0.0021	−3	0.0003		0.0018		0.0016
−2	0.0037		0.0027		0.0026	−2	0.0012		0.0019		0.0015
−1	0.0173		0.0090	>	0.0012	−1	0.0022		0.0010		0.0019
0	0.0088	>>	0.0059		0.0056	0	0.0090	>>	0.0071	>>	0.0055
1	0.0050		0.0045		0.0041	1	0.0010		0.0014		0.0015
2	0.0094		0.0027		0.0033	2	0.0013		0.0011		0.0013
3	0.0007		0.0031		0.00037	3	0.0016		0.0012		0.0018
4	0.0026		0.0021		0.0009	4	0.0015		0.0014		0.0013
5	0.0021	>	0.0006		0.0006	5	0.0008		0.0014		0.0007
6	0.0031		0.0005		0.0015	6	0.0010		0.0009		0.0012
7	0.0006		0.0009		0.0008	7	0.0015		0.0013		0.0006
8	0.0009		0.0010		0.0016	8	0.0004		0.0004		0.0007
9	0.0011		0.0004		0.0015	9	0.0003		0.0011		0.0009
10	0.0010		0.0005		0.0008	10	0.0008		0.0005		0.0005

Table 10. Test results of price discovery delay effect on the Shanghai stock market before and after the change of price limit system

Before setting price limit system				After setting price limit system
Stock market uptrend	$\mathit{S}toc{k}_{hit}$	$\mathit{S}toc{k}_{0.9}$	$\mathit{S}toc{k}_{0.8}$	Stock market uptrend	$\mathit{S}toc{k}_{hit}$	$\mathit{S}toc{k}_{0.9}$	$\mathit{S}toc{k}_{0.8}$
Inertial probability	0.73	0.80	0.71	Inertial probability	0.80	0.50	0.00
Reversal probability	0.27	0.20	0.29	Reversal probability	0.20	0.50	1.00
Stock market downtrend	$\mathit{S}toc{k}_{hit}$	$\mathit{S}toc{k}_{0.9}$	$\mathit{S}toc{k}_{0.8}$	Stock market uptrend	$\mathit{S}toc{k}_{hit}$	$\mathit{S}toc{k}_{0.9}$	$\mathit{S}toc{k}_{0.8}$
Inertial probability	0.50	1.00	0.40	Inertial probability	1.00	0.71	0.38
Reversal probability	0.50	0.00	0.60	Reversal probability	0.00	0.29	0.63

Table 11. Test results of price discovery delay effect on the Shenzhen stock market before and after the change of price limit system

Before setting price limit system				After setting price limit system
Stock market uptrend	$\mathit{S}toc{k}_{hit}$	$\mathit{S}toc{k}_{0.9}$	$\mathit{S}toc{k}_{0.8}$	Stock market uptrend	$\mathit{S}toc{k}_{hit}$	$\mathit{S}toc{k}_{0.9}$	$\mathit{S}toc{k}_{0.8}$
Inertial probability	0.42	0.67	0.50	Inertial probability	1.00	1.00	0.71
Reversal probability	0.33	0.33	0.50	Reversal probability	0.00	0.00	0.29
Stock market downtrend	$\mathit{S}toc{k}_{hit}$	$\mathit{S}toc{k}_{0.9}$	$\mathit{S}toc{k}_{0.8}$	Stock market downtrend	$\mathit{S}toc{k}_{hit}$	$\mathit{S}toc{k}_{0.9}$	$\mathit{S}toc{k}_{0.8}$
Inertial probability	0.33	0.25	0.40	Inertial probability	0.80	1.00	0.57
Reversal probability	0.33	0.50	0.20	Reversal probability	0.20	0.00	0.43

Table A1. Descriptive statistical results of the total market

	Indicator	Variable	Number of observations	Average	Standard deviation	Minimum value	Maximum value
Total market (experimental group)	Liquidity	TRit	6553	0.0361	1.0102	0.0053	7.3329
		NTRit	6553	0.1711	1.4076	0.0001	8.0211
	Volatility	Sma20it	6553	0.0204	0.0262	0.0026	0.9885
		Garchit	6553	0.0232	0.0224	0.0059	0.5766
	Market efficiency	MECit	6553	0.9800	0.2390	0.0171	1.0000
Hong Kong market (control group)	Liquidity	TRit	6550	0.0251	0.0980	0.0007	5.6121
		NTRit	6468	0.1392	1.9231	0.0006	15.8952
	Volatility	Sma20it	6551	0.0150	0.0223	0.0004	1.5170
		Garchit	6450	0.0157	0.0072	0.0017	0.0901
	Market efficiency	MECit	6450	0.9321	0.2743	0.0358	1.0000

Note: As the result of the NTR indicator calculation is relatively small, for the convenience of comparison, we multiply it by 10⁹. The same in other tables.

Table A2. Descriptive statistical results of the Shanghai stock market

	Indicator	Variable	Number of observations	Average	Standard deviation	Minimum value	Maximum value
Shanghai stock market (experimental group)	Liquidity	TRit	1183	0.6566	0.8034	0.0120	1.3759
		NTRit	1181	0.7711	0.2265	0.1094	4.1728
	Volatility	Sma20it	1183	0.0395	0.0414	0.0051	0.5504
		Garchit	1183	0.0374	0.0301	0.0043	0.2591
	Market efficiency	MECit	1183	0.9234	0.5043	0.2931	1.0000
Shenzhen stock market (control group)	Liquidity	TRit	1182	0.7881	0.8749	0.0000	4.8080
		NTRit	1181	0.6655	1.0460	0.0000	12.3477
	Volatility	Sma20it	1183	0.0291	0.0131	0.0104	0.0856
		Garchit	1183	0.0288	0.0143	0.0000	0.1065
	Market efficiency	MECit	1183	0.9213	0.4890	0.2878	1.0000

Table A3. Descriptive statistical results of the Shenzhen stock market

	Indicator	Variable	Number of observations	Average	Standard deviation	Minimum value	Maximum value
Shenzhen stock market (experimental group)	Liquidity	TRit	228	0.2871	0.2722	0.0015	1.1618
		NTRit	228	0.5733	0.2230	0.0001	2.0900
	Volatility	Sma20it	228	0.0303	0.0229	0.0040	0.0832
		Garchit	228	0.0305	0.0228	0.0091	0.0995
	Market efficiency	MECit	228	0.9641	0.4240	0.4641	1.0000
Shanghai stock market (control group)	Liquidity	TRit	229	0.2143	0.2822	0.0006	1.3041
		NTRit	228	0.5350	0.8670	0.1070	1.9340
	Volatility	Sma20it	229	0.0182	0.1325	0.0051	0.1809
		Garchit	229	0.0375	0.0511	0.0063	0.0696
	Market efficiency	MECit	229	0.9375	0.5074	0.6916	1.0000