Market Efficiency and Stability Under Short Sales Constraints: Evidence from a Natural Experiment with High-Frequency Resolution

Abstract

The six short-sales constraints (SSCs) regime changes from 2002 to 2009 in the Taiwan stock market provide “natural social” experiments to examine how different SSC intensities affect price adjustment efficiency and market stability. There are three main findings. Firstly, we derive the theoretical price with put–call parity from seven series index options. Using a “threshold error correction model” (TECM), we find a more efficient price adjustment to new equilibria for upward adjustments than for downward adjustments. The SSCs impede the price adjustment downward, especially during the financial crisis of 2008. Therefore, relaxing the short-sales constraints essentially improves price efficiency. Secondly, our findings also refute the claim that tighter SSCs can help stabilize the market since the tightening of the short-sales restriction leads to increases in both market volatility and downside risk even after controlling the investor fear gauge of the Taiwan volatility index (TVIX). These results hold even when market conditions and liquidity are controlled. Finally, the evidence from our counterfactual policy analysis suggests that tighter constraints help restore market confidence even though prices may fall more sharply without short-sales bans. As a result, policymakers may practically optimize to strike a balance between the benefits of restored emerging market order and the cost of elevated market volatility.

1. Introduction

Given the recent financial crisis of 2008, academic researchers, market practitioners, and regulators are keen to understand better the highly contentious impact of short-sales policies on stability and pricing efficiency within capital markets. Stock exchanges and government supervisory bodies have found it difficult to reach any consensus on a consistent set of short-selling guidelines. As a result, short-sales regulations continue to vary widely across countries and capital markets [1]. In contrast, researchers have generally found that short-selling constraints (hereafter referred to as SSCs) will lead to a more volatile market [1,2,3,4,5,6,7,8,9,10] and market inefficiency of SSCs [11,12,13,14,15]. In contrast to the argument by Franklin and Gale [16] and Chang et al. [17], the reality appears to be an empirical puzzle since most regulators have resorted to imposing SSCs when their markets are drastically volatile. Beber and Pagano [18] studied the impact of short-sales bans in 30 countries on liquidity, price discovery, and stock prices during the 2007–2009 crisis period and found the bans slowed down price discovery but were not associated with excess returns, except for a positive and significant association in the U.S. Similar results for price inefficiency were found in Korea [19,20], in China [12], and in the U.S. [9,21].

To solve this puzzle, we investigate whether SSCs play a role in stabilizing a market when it is fragile. As the ability to short-sell affects liquidity and the adjustment toward new market equilibria, we seek to disentangle the effect of SSCs on price discovery and market efficiency. Miller [22] and several recent studies [17,20,23,24,25,26] on the relationship between short sales and stock overvaluations [1,20,22,24,26,27,28,29] have shown that the SSCs may result in overpriced securities and low subsequent returns. This, unfortunately, may be due to the lack of transaction data or models that were able to characterize the speed of price adjustments in the past and, until recently, had seldom been used to examine price adjustments in response to new information. For example, Chen and Rhee [20] present empirical evidence to show that short sales on the Hong Kong Exchange contributed to market efficiency by increasing the speed of price adjustment for private or public firm-specific and market-wide information.

In a departure from the existing literature, we examine the effects of SSCs on both the speed of price adjustment to the new equilibrium and market stabilization within a correctly identified threshold error correction model (TECM). By taking advantage of the changes in short-selling policies implemented between 2002 and 2009 in the emerging Taiwanese market, our study provides several empirical insights based on price discovery within a series of “natural social” experiments. The beauty of the model used in the context of different regimes is that we can perform direct counterfactual analysis to assess “what if” scenarios when disentangling the policy effects of SSCs.

From an equilibrium perspective, if the restrictions on short sales hinder price discovery in the underlying spot index, investors can alternatively short-sell, at an even lower cost, by writing puts or shorting calls in the options and futures markets [2,18,23,30,31,32,33,34,35,36,37]. Voluminous empirical results have suggested that the options market plays a more informative price discovery role, significantly when short-selling is restricted in the spot market. Therefore, we use the put–call parity-derived index, free from model misspecifications and biased volatility inputs [38], as a proxy for the virtual price equilibrium. We explore dynamically how mispricing is adjusted towards the new equilibrium through this cointegration linkage between the spot and derivative markets. The analysis of the effects of SSCs on adjustment speed is straightforward and uses a comprehensive TECM approach. More importantly, unlike the extant literature that employs daily or monthly data, our study hinges on the 1 min high-frequency equilibrium deviations to resolve the issue of market efficiency adjustment and issues about market stability under SSCs. These are all highlighted as the significant differences between our study and those in the recent literature.

Our main findings are as follows. First, short-sales constraints in mispricing lead to a less efficient market by creating asymmetry in both the magnitude and the speed of price adjustments. Within our TECM, the convergence rate of upward adjustments is more rapid than that of downward adjustments, even after controlling for market conditions and liquidity. Secondly, the speed of downward adjustments significantly improves after the relaxation of such constraints. Finally, we find that tighter SSCs help to retain investors’ confidence, effectively discouraging the execution of “fire sales” and saving the market from liquidity “droughts”, as verified by our counterfactual analysis of the realized equilibrium adjustments. However, tighter constraints provide little help in stabilizing market fluctuations, which are generally associated with more significant downside risk and higher volatility. Specifically, our robustness check reveals that these results hold, even after controlling for the investor “fear index” or “fear gauge”, which is proxied by the Taiwan volatility index (TVIX) obtained from the Taiwan Futures Exchange (TAIFEX) in our study.

Our empirical results shed practical economic light. The market is fragile during the financial crisis, as the market liquidity critically depends on investor confidence. The consideration of flying to safety or liquidity can further amplify the contraction of funding liquidity through the unwinding and deleveraging of positions among various market participants. Given that a loss of confidence can trigger fire sales and destabilize the financial system, the SSCs, as a policy tool, can be used to protect against these undesired scenarios. Policymakers may then take advantage of the SSCs by optimally striking a nice balance between the cost of obstructing price efficiency and the benefits of restoring investor confidence, mainly when it is scarce during a financial crisis.

The remainder of this paper is organized as follows. A description of the data and short-sales policy changes in Taiwan is presented in Section 2, followed in Section 3 by developing our hypotheses and empirical design. Section 4 presents our main empirical results along with a counterfactual analysis. Various robustness checks are provided in Section 5. Finally, the conclusions drawn from this study are presented in Section 6.

2. Data and Description of Short-Sales Policies

It can be empirically tricky, if not impossible, to identify the policy impacts of SSCs since the durations of SSCs policies implemented are often too short for meaningful examinations of the policy consequences, even for some specific developed countries. However, the experience of Taiwan provides an interesting avenue for research, as a ban on short-selling in terms of the uptick rule was superimposed in Taiwan over a long period, from 22 September 2008 to 31 December 2008.

The data analyzed in this study are intraday TAIFEX index option prices and their common underlying asset on the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) from 2002 to 2009, the details of which are available from the TEJ (Taiwan Economic Journal., Ltd., Taipei City, Taiwan) database. We chose the TAIEX index because the institutional factors within the Taiwanese market closely resemble a representative case of an emerging market with its large population of retail investors, heavy government intervention, and regulatory controls. These institutional factors are distinctly different from those in the markets of developed countries. Therefore, the impacts of such SSC policy adjustments toward market efficiency and stability are of practical relevance and informative for many emerging and developing economies.

2.1. Six SSC Policy Regimes from 2000 to 2009

The Taiwan Stock Exchange (hereafter TWSE) initially imposed an uptick rule in September 1998, allowing short-selling at least as high as the closing price for the previous trading day for all stocks eligible for short sales. SSCs, in terms of the uptick rule, are stricter in Taiwan than in the U.S., since the uptick rule in U.S. stock exchanges requires that the short-selling prices not be lower than the best current asking price. In an attempt to improve the efficiency of price discovery, the TWSE relaxed the uptick rule on 30 June 2003 for equities listed in the first exchange-traded fund (ETF), the Taiwan Top50 Tracker Fund (TTT) (ID: 0050). Starting on 16 May 2005, the component stocks of the TTT were allowed to freely short-sell. Among the largest and most actively traded stocks listed on the TWSE, these are less vulnerable to potential price manipulations. Therefore, we have the following three periods: p1, from 2 January 2002 to 29 June 2003; p2, from 30 June 2003 to 15 May 2005; and p3, from 16 May 2005 to 11 November 2007. Starting on 12 November 2007, the constituent stocks of the Taiwan Mid-Cap 100 index and the Technology Index were also exempted from the uptick rule. As a reaction to the global financial crisis, from 22 September 2008 to the end of that year, the TWSE banned the short-selling of 150 companies’ shares below their closing prices on the previous day, which marks our fourth and fifth sub-periods as p4, from 12 November 2007 to 21 September 2008, and p5, from 22 September 2008 to 31 December 2008. It should be noted that the regulators imposed a further ban on the short-selling of all stocks from 1 October to 27 November 2008, prohibiting all short-selling during that period. Finally, p6 denotes the relaxation of all SSCs from 2009 onwards. Beginning 23 September 2013, around 1200 borrowed stocks and ETFs currently eligible for margin trading have been exempted from the uptick rule and can be sold for lower than the closing price on the previous trading day. ETFs are exempt from the uptick rule, except for the short-sales ban of P5 within our data period.

As our sample period runs from January 2002 to December 2009, we divide the entire sample period into six sub-periods according to these short-sales policy changes (see Figure 1). The strength of the SSCs throughout the various periods, from the highest to lowest, is in the order of p5, p1, p2, p3, p6, and p4. Although SSCs were relaxed after the end of 2008, the basis for calculating securities borrowing and lending balances has been restricted since 22 July 2009. Hence, the weakest SSCs are in p4 rather than in p6. Although no stock or ETF was exempted from the uptick rule in p1, no stocks or ETFs were allowed to short-sell at any price level from 1 October to 27 November 2008 within p5. Hence, the highest intensity of SSCs is p5 rather than p1. Thus, these policy changes provide us with natural proxies for examining the effects of the SSCs on market stability and efficiency.

2.2. SSC Proxies

Most previous empirical studies related to SSCs rely either on various measures to characterize the strength of SSCs or on restricted samples with lending data. The former includes a variety of proxies that have been used for capturing higher SSCs or higher short-sales costs, including the lower lending supply or higher loan fees [6], lower rebate rates [4,5,37,38,39,40], negative rebate rate spread [27], and low daily short interest [26]. Some proxies for relaxed short-sales restrictions are the presence of stock options [5,23,41] the introduction of stock futures [42], the availability of short-selling [20], or the percentage of proceeds available to short-sellers [43]. Another stream uses lending data provided by one or some custodians. Geczy et al. [39] used one-year rebate data (November 1998 to October 1999) provided by a U.S. custodian bank to study borrowing costs for IPOs, whilst Ofek et al. [27] relied on the rebate rate from one of the largest dealer–brokers. Saffi and Sigurdsson [6] once argued that ten custodians obtained the average loan fee for 12,621 firms from 26 countries, representing the average lending price. However, it could be challenging to collect complete data from all custodians, and since we can never know whether custodians have different pricing strategies, such data may not be at the equilibrium lending price.

As suggested by Diether et al. [26] and Saffi and Sigurdsson [6], it is difficult to determine whether high short interest reflects either negative sentiment amongst investors regarding the stock or lower SSCs. As Diether et al. [26] have further argued that short-sellers will quickly cover their positions, the monthly short interest would be inappropriate for addressing the short-term adjustments toward a new equilibrium. These shortcomings can be avoided through the use of better proxies for SSCs. Fortunately, the short-sales policy changes in Taiwan between 2002 and 2009 provided a natural platform for examining how the market equilibrium responds to the various SSC regimes. Our paper addresses how the emerging market reacts to SSC policy changes.

2.3. The Implied Index Price and Equilibrium Deviations

The theoretical index price obtained in this study is based upon put–call parity, a simple no-arbitrage relationship for which there are no superimposed assumptions regarding agents’ preferences or return distributions [38]. There are advantages in deriving the theoretical index price from put–call parity. First, since the TAIFEX options are European-style, we can avoid the potential effects of early exercise risk on mispricing errors. Thus, the “per minute” synchronously matched data rule out the potential problem of non-synchronicity. Secondly, the options market has fewer transaction limitations than the stock market, and, as shown by Miller [22], investors prefer to trade in a less limited market where the asset prices immediately reflect new information. In the absence of arbitrage opportunities, the put–call parity suggests that the implied index price be given by:

$${\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}={\mathrm{C}}_{\mathrm{t}}-{\mathrm{P}}_{\mathrm{t}}+\mathrm{K}{\mathrm{e}}^{-{\mathrm{r}}_{\mathrm{f}}\left(\mathrm{T}-\mathrm{t}\right)},$$

(1)

where ${\mathrm{C}}_{\mathrm{t}}$ (${\mathrm{P}}_{\mathrm{t}}$) denotes the call (put) price at the time $t$ for an option contract maturing at $\mathrm{T}$ with strike price $\mathrm{K}$, ${\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}$ is the synthesized implied price as a proxy for the equilibrium price, and ${\mathrm{r}}_{\mathrm{f}}$ is the risk-free rate and $\mathrm{K}$ represents the strike price.

Given the current index price, we collect seven series of near-month option contracts with different moneyness. To remove the effect of varying moneyness, we then average the seven implied index prices over their moneyness to arrive at the final theoretical index price (${\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}$ for time t. For example, given the previous trading day’s closing price of 5678, we would round the number to 5700. We then collect option contracts with strike prices ranging from 5400 to 6000 to derive their corresponding implied indices. Each series is matched with the same strike price and the same maturity. We then average the seven implied index prices over moneyness to obtain the final theoretical index price (${\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}$) for time t. Intuitively, the logarithmic observed index value and the put–call parity implied theoretical index are cointegrated with their common trend, discernibly depicted in Figure 2a, and the formal cointegration test results are provided in

Table 1. Unit root and cointegration tests.

Measures	Statistics	Critical Values	First Difference
			t-Statistic	Critical Values
Panel A: Augmented Dickey–Fuller test statistics
$\ln {\mathrm{S}}_{\mathrm{t}}$	–1.38	–3.43019	–212.365	–2.86136
$\ln {\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}$	–1.60	–2.86136	–287.005	–2.86136
Panel B: Cointegration test
Trace test	1180.2	25.87211	–	–
Max-eigenvalue test	1176.0	19.38704	–	–

Note: For the definitions of the notations, refer to Appendix B.

.

It is interesting to explore why the positive deviations between the index price and the theoretical index price became more extensive during the short-sales ban period (as we can see from Figure 2c and Figure 3a) and whether the regulators imposed such constraints to stabilize prices while witnessing more significant fluctuations in returns, as illustrated in Figure 2b. Figure 2 illustrates the time plot for the index price, the index returns, and the price deviations between 2002 and 2009, during which there was a total of six SSC policy changes (indicated by the vertical red lines). Figure 3a presents the time plot for price deviations under different SSC pressures, Figure 3b concentrates on the tail behavior of the price deviations, and Figure 3c concentrates on the tail behavior of the index returns.

Our sample period runs from 2 January 2002 to 31 December 2009, yielding 1989 days and 539,109 one-minute intraday observations. We use high-frequency data instead of previous empirical studies that employed low-frequency data because the results indicate that short-sellers covered their positions within a few days. Diether et al. [26] found that short-sellers covered their positions in 5.4 days on the NYSE and in 4.4 days on the NASDAQ, with daily short interest rather than monthly data.

Utilizing data at a lower frequency may fail to resemble the equilibrium adjustment and hinder the price discovery occurring at a higher frequency. In the present study, we find that the average time taken to converge to equilibrium in the examined Taiwanese market between 2002 and 2009 was, on average, 26 min. Secondly, given the high proportion of day-trading activities and high turnover in the Taiwanese market, only high-frequency data may help reveal the nature of equilibrium adjustments and efficiency changes, particularly during exogenous policy changes.

2.4. Other Variables and Control Variables

Using high-frequency data avoids the potential problem of non-synchronous trading confounding the results, while index-level analysis undertaken at a market-wide aggregate level can help prevent idiosyncratic risk and analyst disagreement. Tentative explanations for price deviations include the presence of transaction costs [27,44,45], non-synchronous trading [46], market illiquidity [27,43,47], idiosyncratic risk [48], the microstructure effect [49], analyst disagreement [50] and SSC costs [27,45]. Given the potential link between price movements and other variables, such as liquidity, transaction costs, market conditions, and the microstructure effect, it is essential to control alternative concerns properly.

Saffi and Sigurdsson [6] provided controls for firm capitalization, liquidity, and transaction costs to avoid such spurious findings when examining how stock pricing efficiency and return distributions were affected by SSCs. The liquidity and transaction cost variables included total share turnover, incidences of zero weekly returns, the annual average of the weekly quoted bid–ask spread, and the Datastream free float measure. Therefore, a total of five measures are employed to control for the effects of market liquidity on price movements: (i) Num_Trades is the number of trades in the previous minute, (ii) Num_Shares denotes the number of trading shares in the previous minute, (iii) TDollar_t−1 denotes the amount of trading in the previous minute (in dollars × 1000), (iv) Daily_Turnover is calculated as the trading volume on the previous day divided by the number of outstanding shares on the previous day, and (v) Daily_Turnover/MV denotes the daily trading dollars divided by the daily market value [6]. As we can see from

Table 2. Summary statistics.

Variables	Full Sample					Sub-Period Mean Values
	Median	S.E.	Min	Max	Mean	$\mathbf{p}1$	$\mathbf{p}2$	$\mathbf{p}3$	$\mathbf{p}4$	$\mathbf{p}5$	$\mathbf{p}6$
${\mathrm{S}}_{\mathrm{t}}$	6212	1307	3846	6421	9860	5024	5931	7239	8006	4790	6463
${\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}$	6174	1308	3774	6393	9848	4995	5922	7211	7963	4705	6428
$\mathsf{\Delta }\ln {\mathrm{S}}_{\mathrm{t}}\times 10^5$	0.0000	82	–6905	0.0721	6047	−0.1304	0.1612	0.2412	−0.7021	−1.3651	0.8505
$\mathsf{\Delta }\ln {\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}\times 10^5$	0.0000	107	−12,810	0.0731	12,744	−0.1310	0.1673	0.2400	−0.7111	−1.4137	0.8723
${\mathrm{Z}}_{\mathrm{t}}$	0.0036	0.0074	−0.1132	0.0047	0.1218	0.0058	0.0016	0.0039	0.0056	0.0183	0.0058
No. of Obs.	539,019					99,186	126,557	168,020	57,994	19,241	68,021
Market liquidity
Num_Trades	2289	2807	0	152,241	2862	2434	2467	2745	3507	2690	4011
Num_Shares	11,477	17,737	0	1,063,416	14,877	12,965	14,971	14,411	16,936	12,759	17,485
TDollart−1	281	434	0	35,933	368	301	332	394	450	223	438
Daily_Turnover	0.0061	0.0030	0.0020	0.0223	0.0069	0.0082	0.0078	0.0059	0.0057	0.0048	0.0075
Daily_Turnover/MV	0.0062	0.0025	0.0021	0.0193	0.0068	0.0083	0.0070	0.0061	0.0061	0.0050	0.0074
No. of Obs.	1989					366	467	620	214	71	251
Market condition
Realized_Variance × 100	0.0101	0.0358	0.0009	0.4814	0.0186	0.0240	0.0158	0.0080	0.0272	0.0757	0.0188
${\overline{\mathrm{R}}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	0.0005	0.0021	−0.0070	0.0060	0.0003	0.0001	0.0006	0.0008	−0.0012	−0.0053	0.0014
$\mathrm{s}\mathrm{t}\mathrm{d}{\mathrm{r}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	0.0148	0.0053	0.0068	0.0270	0.0148	0.0181	0.0127	0.0100	0.0200	0.0242	0.0187
$\mathrm{s}\mathrm{k}\mathrm{e}{\mathrm{w}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	−0.1374	0.6337	−1.9077	2.2563	−0.1706	0.1864	−0.1878	−0.4167	0.1668	0.3709	−0.4920
$\mathrm{k}\mathrm{u}\mathrm{r}{\mathrm{t}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	0.8466	2.4404	−0.3963	16.2872	1.7216	0.3252	1.4754	2.4858	2.4188	0.2950	2.1374

Note: For the definitions of the notations, refer to Appendix B. The distribution of the index price, returns, price deviations, and control variables are also illustrated in Figure 2a. The average price deviation ($Z_t$) in Equation (2) is described earlier, in Figure 3a,b.

, the market was more liquid during periods when SSCs were lifted.

We also use four different methodologies to portray the market conditions. The ${\overline{\mathrm{R}}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$, $\mathrm{s}\mathrm{t}\mathrm{d}{\mathrm{r}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$, $\mathrm{s}\mathrm{k}\mathrm{e}{\mathrm{w}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$, and $\mathrm{k}\mathrm{u}\mathrm{r}{\mathrm{t}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$ are the average return, standard deviations, skewness, and kurtosis calculated from the one-minute index returns over the previous three-month period. The $\mathrm{s}\mathrm{k}\mathrm{e}{\mathrm{w}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$ variables capture the heavy tail phenomena in the index returns, while ${\overline{\mathrm{R}}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$, the average market returns over the previous three-month period, captures how bear or bull markets affect price movements.

Jiang et al. [51] deleted their sample’s first ten-minute data segments, as investors could have been overreacting to overnight news releases. Since the present study focuses on intraday return behavior, an overnight dummy variable (identifying transactions occurring at 9:00 a.m.) is included in our model to control for the overnight effect on price movements. In their analysis of the impact of the short-sales price test pilot plan on market quality in the U.S., Diether et al. [52] excluded data from 9:30 to 10:00 a.m. to avoid the undue influence of the market opening in their results. Following their merits, we also include open and closed dummies for control in this study, where Open (Close) equals one if the transactions occurred during the 9:01–9:30 (13:01–13:30) period.

3. Hypothesis Development and Empirical Design

Most of the previous theoretical or empirical studies looking at the policy effects of SSCs are concerned with the magnitude of price changes and subsequent reduced returns [1,2,22,24,27,28,29,53,54]. Saffi and Sigurdsson [6] found price efficiency increases with smaller SSCs [1,24,27,28,29,51,55,56,57,58], while they find no evidence of the relaxation of SSCs leading to price fluctuations or extreme negative returns. However, few studies, except for that of Chen and Rhee [20], have examined the speed of adjustment towards the fundamental price. This paper seeks to fill this gap.

To see this, we define the price deviation ${\mathrm{Z}}_{\mathrm{t}}$ as the natural logarithmic difference between the index price $S_t$and the theoretical index price$S_t^o$ as the error-correction term representing the possible arbitrage opportunities:

$${\mathrm{Z}}_{\mathrm{t}}=\ln {\mathrm{S}}_{\mathrm{t}}-\ln {\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}.$$

(2)

The cointegrating vector (the mispricing error or error correction term) is estimated as (1, −0.99) and is simplified to (1, −1) under the cointegration test in Table 1. Under the assumption of a perfect market, if the index price is too high relative to the fundamental value (i.e., ${\mathrm{Z}}_{\mathrm{t}}>0$), then arbitrageurs will engage in short-selling or sell the spot commodity to mitigate the discrepancy, whereas if the index price is undervalued (${\mathrm{Z}}_{\mathrm{t}}<0$), then the opposite trading strategies will occur. Both actions will ensure adjustment towards the fundamental price (${\mathrm{Z}}_{\mathrm{t}}=0$). In reality, for each SSC policy regime, we average over the unconditional number of minutes, and the price persists in being overpriced (underpriced) until it reverts to its fundamental price with a given threshold. Our preliminary results exhibit a discernible asymmetric pattern between upward and downward adjustments. The analyzed results are available upon request, and we find an overvaluation taking from 27 to 86 min to converge to equilibrium during the period with the strongest SSC, as compared to just 11 to 16 min to equilibrium for an undervaluation during the period with the fewest SSCs, after considering the transaction costs. We use the given threshold as transaction cost by 0.4425% (−0.1425%) since the explicit transaction costs of investors in Taiwan for sales (purchases) of stocks in the TWSE market are 0.4425% (0.1425%).

3.1. Price Adjustment Speed

To illustrate the effects of upward and downward price adjustments, we specifically employ the three-regime threshold error correction model (TECM) with varying upward and downward adjustment rates to identify whether any asymmetric patterns exist in the convergence speed. The TECM model has been used to describe many economic phenomena, such as government intervention in exchange rates when the market price diverges too far from the fair price (where an exchange rate is almost a random walk within thresholds). The TECM specifies the magnitude of the deviation from the theoretical price that will ultimately trigger trading and provides possible estimates for explicit and implicit transaction costs, which may prevent investors from adjusting immediately [59]. From a financial standpoint, we also care about the extent to which the deviations may be sufficiently large to cover the total costs incurred by investors, including transaction costs and risk. The nonlinear flexibility to estimate the latent decision thresholds in a TECM allows us to capture the market frictions, such as transaction costs, the tax burden, and the market microstructure.

We set out to characterize market friction and price adjustments in terms of a more general three-regime TECM. The threshold values ($c_1$, $c_2$) are estimated by following the approach of Enders and Siklos [60] and Balke and Fomby [61]. Dwyer et al. [59] showed that the estimated threshold value (c) was similar to actual world transaction costs in analyzing the non-linear dynamic relationship between S&P 500 futures and the cash indices attributable to non-zero transaction costs. The three-regime TECM is estimated using the thresholds $c_1=-0.0001$, and $c_2=0.0004$:

$$\left\{\begin{array}{l}\begin{array}{l}\Delta \ln {\mathrm{S}}_{\mathrm{t}}={\mathrm{int}}_{\mathrm{S}}+{\mathsf{\alpha }}_{\mathrm{S}}^{-}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\{{\mathrm{Z}}_{\mathrm{t}-1}\le {\mathrm{c}}_1\}}+{\mathsf{\alpha }}_{\mathrm{S}}^{\mathrm{b}\mathrm{t}\mathrm{w}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\{{\mathrm{c}}_1<{\mathrm{Z}}_{\mathrm{t}-1}<{\mathrm{c}}_2\}}\\ +{\mathsf{\alpha }}_{\mathrm{S}}^{+}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\{{\mathrm{Z}}_{\mathrm{t}-1}\ge {\mathrm{c}}_2\}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\beta }}_{\mathrm{i}}^{\mathrm{S}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\gamma }}_{\mathrm{i}}^{\mathrm{S}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}^{\mathrm{o}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{k}}}{\mathsf{\xi }}_{\mathrm{i}}^{\mathrm{S}}{\mathrm{X}}_{\mathrm{i}}+{\mathsf{\epsilon }}_{\mathrm{t}}^{\mathrm{S}}\end{array}\\ \begin{array}{l}\Delta \ln {\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}={\mathrm{int}}_{{\mathrm{S}}^{\mathrm{o}}}+{\mathsf{\alpha }}_{{\mathrm{S}}^{\mathrm{o}}}^{-}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\{{\mathrm{Z}}_{\mathrm{t}-1}\le {\mathrm{c}}_1\}}+{\mathsf{\alpha }}_{{\mathrm{S}}^{\mathrm{o}}}^{\mathrm{b}\mathrm{t}\mathrm{w}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\{{\mathrm{c}}_1<{\mathrm{Z}}_{\mathrm{t}-1}<{\mathrm{c}}_2\}}\\ +{\mathsf{\alpha }}_{{\mathrm{S}}^{\mathrm{o}}}^{+}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\{{\mathrm{Z}}_{\mathrm{t}-1}\ge \mathrm{c}2\}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\beta }}_{\mathrm{i}}^{{\mathrm{S}}^{\mathrm{o}}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\gamma }}_{\mathrm{i}}^{{\mathrm{S}}^{\mathrm{o}}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}^{\mathrm{o}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{k}}}{\mathsf{\xi }}_{\mathrm{i}}^{{\mathrm{S}}^{\mathrm{o}}}{\mathrm{X}}_{\mathrm{i}}+{\mathsf{\epsilon }}_{\mathrm{t}}^{{\mathrm{S}}^{\mathrm{o}}}\end{array}\end{array}\right.$$

(3)

where ${\mathsf{\alpha }}_{\mathrm{j}}^{+}$ (${\mathsf{\alpha }}_{\mathrm{j}}^{-}$) refers to the speed of downward (upward) adjustments, accounting for all transaction costs (such as $\mathrm{j}=\mathrm{S} \mathrm{o}\mathrm{r} {\mathrm{S}}^{\mathrm{O}}$), and ${\mathsf{\alpha }}_{\mathrm{j}}^{\mathrm{b}\mathrm{t}\mathrm{w}}$ refers to the speed of the adjustment in the interband while the other notations follow the same previous definitions. ${\mathrm{Z}}_{\mathrm{t}-1}$ is the error correction term, and the coefficient specifies the speed of adjustment towards the theoretical price, which should be negative. Within the model, $\mathrm{p}$ is the lag operator determined by the minimum Akaike information criterion (AIC) and Schwarz information criterion (SIC) compromising for white noise in ${\mathsf{\epsilon }}_{\mathrm{t}}^{\mathrm{j}}$, with $\mathrm{p}$ being set at 21. We include three categories of control variables (${\mathrm{X}}_{\mathrm{i}}$): expressed market liquidity, market condition, and microstructure effect. Since Connolly [62] noted that the conventional t-value criterion was inappropriate for large sample sizes, a size-adjusted critical t-value (3.65) is used to determine significance. We examine Hypothesis 1, which states that the adjustment speed will be more rapid for upward adjustments.

Hypothesis 1:

Upward adjustments are more rapid than downward adjustments under general SSCs.

$$\left\{\begin{array}{l}{\mathrm{H}}_0^1:\hspace{0.33em}{\mathsf{\alpha }}_{\mathrm{S}}^{-}-{\mathsf{\alpha }}_{\mathrm{S}}^{+}\ge 0\\ {\mathrm{H}}_1^1:\hspace{0.33em}{\mathsf{\alpha }}_{\mathrm{S}}^{-}-{\mathsf{\alpha }}_{\mathrm{S}}^{+}<0\end{array}\right.$$

When the SSC binds, assets can be overpriced due to the SSC impeding arbitrage activities by pessimistic traders. As a result, the adjustment period for an overvaluation should be extended. By analogy, the market will exhibit a slower downward adjustment under a tighter SSC. Given the disclosure of a significantly different adjustment period for overvaluations but no significant differences for undervaluations between the weakest and strongest SSC intensity ($\mathrm{p}4$ and $\mathrm{p}5$ periods) in our preliminary results, we proceed to examine whether the slower speed of price adjustment is more pronounced at the time in which short sales are prohibited, and whether price efficiency improves during periods of relaxed SSCs, as noted in Section 2.1.

We define ${\mathsf{\alpha }}_{\mathrm{S}}^{+,{\mathrm{p}}_5}$ (and ${\mathsf{\alpha }}_{\mathrm{S}}^{+,{\mathrm{p}}_4}$) as the average downward adjustment speed during strict (and relaxed) SSCs. We go on to extend our three-regime TECM with downward (upward) adjustment speed under the various policy changes to examine the adjustment speed between the weakest (${\mathsf{\alpha }}_{\mathrm{S}}^{+,{\mathrm{p}}_4}$) and strongest (${\mathsf{\alpha }}_{\mathrm{S}}^{+,{\mathrm{p}}_5}$) levels of SSC with the estimated thresholds of ${\mathrm{c}}_1$ and ${\mathrm{c}}_2$ as follows:

$$\left\{\begin{array}{l}\begin{array}{l}\Delta \ln {\mathrm{S}}_{\mathrm{t}}={\mathrm{int}}_{\mathrm{S}}+{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{\mathrm{S}}^{-,{\mathrm{p}}_{\mathrm{i}}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\left\{\mathrm{t}\in {\mathrm{p}}_{\mathrm{i}},{\mathrm{Z}}_{\mathrm{t}-1}\le {\mathrm{c}}_1\right\}}+{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{{\mathrm{S}}^{\mathrm{O}}}^{\mathrm{b}\mathrm{t}\mathrm{w},{\mathrm{p}}_{\mathrm{i}}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\left\{\mathrm{t}\in {\mathrm{p}}_{\mathrm{i}},{\mathrm{c}}_1<{\mathrm{Z}}_{\mathrm{t}-1}<{\mathrm{c}}_2\right\}}\\ +{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{\mathrm{S}}^{+,{\mathrm{p}}_{\mathrm{i}}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\left\{\mathrm{t}\in {\mathrm{p}}_{\mathrm{i}},{\mathrm{Z}}_{\mathrm{t}-1}\ge {\mathrm{c}}_2\right\}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\beta }}_{\mathrm{i}}^{\mathrm{S}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\gamma }}_{\mathrm{i}}^{\mathrm{S}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}^{\mathrm{O}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{k}}}{\mathsf{\xi }}_{\mathrm{i}}^{\mathrm{S}}{\mathrm{X}}_{\mathrm{i}}+{\mathsf{\epsilon }}_{\mathrm{t}}^{\mathrm{S}}\end{array}\\ \begin{array}{l}\Delta \ln {\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}={\mathrm{int}}_{{\mathrm{S}}^{\mathrm{o}}}+{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{{\mathrm{S}}^{\mathrm{o}}}^{-,{\mathrm{p}}_{\mathrm{i}}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\left\{\mathrm{t}\in {\mathrm{p}}_{\mathrm{i}},{\mathrm{Z}}_{\mathrm{t}-1}\le {\mathrm{c}}_1\right\}}+{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{{\mathrm{S}}^{\mathrm{o}}}^{\mathrm{b}\mathrm{t}\mathrm{w},{\mathrm{p}}_{\mathrm{i}}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\left\{\mathrm{t}\in {\mathrm{p}}_{\mathrm{i}},{\mathrm{c}}_1<{\mathrm{Z}}_{\mathrm{t}-1}<{\mathrm{c}}_2\right\}}\\ +{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{{\mathrm{S}}^{\mathrm{o}}}^{+,{\mathrm{p}}_{\mathrm{i}}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}_{\left\{\mathrm{t}\in {\mathrm{p}}_{\mathrm{i}},{\mathrm{Z}}_{\mathrm{t}-1}\ge {\mathrm{c}}_2\right\}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\beta }}_{\mathrm{i}}^{{\mathrm{S}}^{\mathrm{o}}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\gamma }}_{\mathrm{i}}^{{\mathrm{S}}^{\mathrm{o}}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}^{\mathrm{o}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{k}}}{\mathsf{\xi }}_{\mathrm{i}}^{{\mathrm{S}}^{\mathrm{o}}}{\mathrm{X}}_{\mathrm{i}}+{\mathsf{\epsilon }}_{\mathrm{t}}^{{\mathrm{S}}^{\mathrm{o}}}\end{array}\end{array}\right.$$

(4)

where ${\mathsf{\alpha }}_{\mathrm{j}}^{+,{\mathrm{p}}_{\mathrm{i}}}$ (${\mathsf{\alpha }}_{\mathrm{j}}^{-,{\mathrm{p}}_{\mathrm{i}}}$) is the downward (upward) adjustment speed, taking all transaction costs into account under the various policy changes ($\mathrm{i}=\mathrm{1,2},...,6,$ and $\mathrm{j}=\mathrm{S}\hspace{0.33em}\mathrm{or}{ S}^O\hspace{0.33em}$). The other notation follows previous definitions.

The three-regime TECM enables us to specify which size deviations from the theoretical price will trigger trading and resolve the puzzle of how SSC affects market efficiency. If the SSCs suppress the realization of lousy news in prices, one would expect market efficiency to improve when the SSCs are relaxed, i.e., the speed of the rigid downward adjustment to new information will be more rapid. Therefore, we construct Hypothesis 2 as follows:

Hypothesis 2:

The speed of downward adjustment will increase due to the relaxation of SSCs.

$$\left\{\begin{array}{l}{H}_0^2:\hspace{0.33em}{\alpha }_S^{+,p_4}-{\alpha }_S^{+,p_5}\ge 0\\ H_1^2:\hspace{0.33em}{\alpha }_S^{+,p_4}-{\alpha }_S^{+,p_5}<0\end{array}\right.$$

3.2. Price Stabilization Under SSCs: A Counterfactual Analysis

To shed light on the remaining puzzle regarding the short-selling policy and market stabilization, i.e., why the regulators still employ academically vicious SSCs for stabilization, we conduct an informative counterfactual analysis to see what would happen if the SSC policy is not launched (or with a zero-SSC). Recall that the option-implied theoretical price is free from SSCs. Therefore, the theoretical price should be least affected by the short-sales ban, and only the index price should be adjusted in cases of a short-sales ban. We follow Politis and Romano [63] and Hsu, Hsu, and Kuan [64] to examine whether the market price may have fallen even further without the short-sales ban based upon a counterfactual simulation and stationary bootstrap method. As the speeds of adjustment across different levels of SSC intensity are well estimated in our adopted TECM model, we simulate the market price without the short-sales ban and then examine whether the price with the short-sales ban could mitigate the price fluctuations.

Hypothesis 3:

The price without a short-sales ban may drop more than that with a short-sales ban.

$$\left\{\begin{array}{l}{H}_0^3:{price}^{with ban}-{price}^{without ban}\le 0\\ H_1^3:{price}^{with ban}-{price}^{without ban}>0\end{array}\right.$$

Short-sales activities are arguably an essential element of any discussion of market stabilization. Regulators claim that short-selling is detrimental to price stabilization. However, the academic evidence indicates that stocks with fewer SSCs have lower kurtosis [6] and lower levels of downside risk and total volatility. The volatility estimated by intraday data is more informative and a good predictor of volatility [65]. Therefore, we employe 1 min data to obtain daily return characteristics, including daily kurtosis, skewness, extreme negative (positive) return frequency, realized risk, and downside risk, which are the proxy of return volatility. Daily kurtosis captures the frequency of extreme returns, and higher negative skewness indicates a higher probability of extreme negative returns. The realized risk and downside risk capture the whole volatility and negative volatility. Based on the advantage of the market volatility with intraday data, we can test our hypothesis to examine whether higher-intensity SSCs lead to higher total risk and the downside risk, and then go on to provide some suggestions for regulators about short-sales policy.

Hypothesis 4:

Tighter SSCs, or a total ban on short sales, will not enhance the price stabilization.

$$\left\{\begin{array}{l}{H}_0^4:{DOWNSIDERISK}^{p4}-{DOWNSIDERISK}^{p5}\ge 0\\ H_1^4:{DOWNSIDERISK}^{p4}-{DOWNSIDERISK}^{p5}<0\end{array}\right.$$

4. Empirical Results

4.1. Rapid Upward and Sluggish Downward Adjustment

The price deviations are more than three times greater than all other periods during the strictest constraint period (see Table 2). As noted earlier, these policy changes, from the highest to the lowest intensity of SSCs, are in the order of $p5,\hspace{0.33em}p1,\hspace{0.33em}p2,\hspace{0.33em}p3,\hspace{0.33em}p6,\hspace{0.33em}\mathrm{a}\mathrm{n}\mathrm{d}\hspace{0.33em}p4$. Under the strictest constraints, a decline in market liquidity is found for several measures, including trading frequency, trading volume, and trading dollars per minute. Decreasing daily turnover and increasing risk are shown in $p5$ (see Table 2). The relatively high frequency of price deviations during periods of tighter SSCs is discernible in Figure 2c and Figure 3a. Figure 3 shows more positive deviations than negative deviations, particularly during p₅ (a period of tight constraints). By taking advantage of a hybrid of high-frequency data, the natural experiments, and the TECM approach, this paper addresses the gap in prior studies by characterizing how and how much the SSCs affect market efficiency. Under no-arbitrage pricing, prices will adjust immediately after their initial departure from the asset’s fundamental value; thus, theoretically, the duration of upward adjustments should be precisely the same as that of downward adjustments.

Diamond and Verrecchia [2] and Hong et al. [3] noted that SSCs delayed the effects of negative news on the price; that is, SSCs impede the propagation of bad news, with the cumulative negative momentums being too heavy to bind, which may potentially lead to a total collapse or a bubble [7,66]. Conversely, relaxing restrictions improves the dissemination of downside news disclosures [1,5,41].

To specify how much SSCs delayed the effects of negative news on the price, we construct the three-regime TECM with market friction items controlled in Equation (3). The estimated thresholds represent the barrier to trade necessary to cover all transaction costs. Following Enders and Siklos [60], the threshold values and threshold lags (denoted as $\mathrm{d}$) are obtained from the minimum mean squared error of the threshold autoregressive (TAR) model. The exact procedure used to estimate threshold values and threshold lags is shown in Appendix C. The thresholds are different under the various policy changes: −0.0003 and 0.0051 for $\mathrm{p}1$, −0.0015 and 0 for $\mathrm{p}2$, −0.0001 and 0.0001 for $\mathrm{p}3$, −0.0002 and 0.0139 for $\mathrm{p}4$, 0.0030 and 0.0270 for $p5$, and −0.0001 and 0.0006 for $\mathrm{p}6$, while the threshold lags are $\mathrm{d}=1$ in $\mathrm{p}1,\mathrm{p}4,\mathrm{p}5,\hspace{0.33em}\mathrm{a}\mathrm{n}\mathrm{d}\hspace{0.33em}\mathrm{p}6$; $d=3$ in$\mathrm{p}3$; and $\mathrm{d}=2$ in $\mathrm{p}3$. The estimation procedure follows Enders and Siklos [60], and the results are available upon request.

At the bottom of

Table 3. Three-regime TECM estimates under different policy changes.

Models	(1) (i)				(1) (ii)				(2) (i)				(2) (ii)
Variables	ΔlnSt		ΔlnSto		ΔlnSt		ΔlnSto		ΔlnSt		ΔlnSto		ΔlnSt		ΔlnSto
Intercept	−0.0000		0.0000		−0.0000	†	0.0000		−0.0000	†	−0.0000		−0.0000	†	−0.0000
αj+	−0.0011	†	0.0012	†	−0.0016	†	0.0014	†	−		−		−		−
αjbtw	−0.0007		−0.0021	†	−0.0017	†	−0.0014		–		–		–		–
αj−	−0.0100	†	0.0094	†	−0.0105	†	0.0097	†	–		–		–		–
${\mathsf{\alpha }}_{\mathrm{j}}^{+\mathrm{p}1}$	–		–		–		–		0.0041	†	0.0070	†	0.0041	†	0.0073	†
${\mathsf{\alpha }}_{\mathrm{j}}^{-\mathrm{p}1}$	–		–		–		–		−0.0055		0.0511	†	−0.0049		0.0505	†
${\mathsf{\alpha }}_{\mathrm{j}}^{+\mathrm{p}2}$	–		–		–		–		−0.0002		0.0020	†	−0.0012		0.0021	†
${\mathsf{\alpha }}_{\mathrm{j}}^{-\mathrm{p}2}$	–		–		–		–		−0.0143	†	−0.0001		−0.0157	†	0.0001
${\mathsf{\alpha }}_{\mathrm{j}}^{+\mathrm{p}3}$	–		–		–		–		0.0008		0.0009		0.0001		0.0007
${\mathsf{\alpha }}_{\mathrm{j}}^{-\mathrm{p}3}$	–		–		–		–		−0.0401	†	−0.0038		−0.0437	†	−0.0033
${\mathsf{\alpha }}_{\mathrm{j}}^{+\mathrm{p}4}$	–		–		–		–		−0.0051	†	0.0008		−0.0050	†	0.0009
${\mathsf{\alpha }}_{\mathrm{j}}^{-\mathrm{p}4}$	–		–		–		–		−0.2013	†	−0.0152		−0.2020	†	−0.0151
${\mathsf{\alpha }}_{\mathrm{j}}^{+\mathrm{p}5}$	–		–		–		–		−0.0018	†	−0.0008		−0.0018	†	−0.0006
${\mathsf{\alpha }}_{\mathrm{j}}^{-\mathrm{p}5}$	–		–		–		–		−0.0743	†	−0.0022		−0.0742	†	−0.0025
${\mathsf{\alpha }}_{\mathrm{j}}^{+\mathrm{p}6}$	–		–		–		–		0.0009		0.0017		0.0002		0.0019
${\mathsf{\alpha }}_{\mathrm{j}}^{-\mathrm{p}6}$	–		–		–		–		0.0009		0.0123	†	−0.0009		0.0124	†
${\mathsf{\alpha }}_{\mathrm{j}}^{\mathrm{b}\mathrm{t}\mathrm{w} \mathrm{p}1}$	–		–		–		–		0.0009		−0.0052		0.0011		−0.0043
${\mathsf{\alpha }}_{\mathrm{j}}^{\mathrm{b}\mathrm{t}\mathrm{w}\hspace{0.33em}\mathrm{p}2}$	–		–		–		–		−0.0136		−0.0045		−0.0148		−0.0051
${\mathsf{\alpha }}_{\mathrm{j}}^{\mathrm{b}\mathrm{t}\mathrm{w}\hspace{0.33em}\mathrm{p}3}$	–		–		–		–		0.0014		0.0748		−0.0001		0.0732
${\mathsf{\alpha }}_{\mathrm{j}}^{\mathrm{b}\mathrm{t}\mathrm{w}\hspace{0.33em}\mathrm{p}4}$	–		–		–		–		0.0017		−0.0013		0.0023		−0.0005
${\mathsf{\alpha }}_{\mathrm{j}}^{\mathrm{b}\mathrm{t}\mathrm{w}\hspace{0.33em}\mathrm{p}5}$	–		–		–		–		0.0009		−0.0009		0.0008		−0.0002
${\mathsf{\alpha }}_{\mathrm{j}}^{\mathrm{b}\mathrm{t}\mathrm{w}\hspace{0.33em}\mathrm{p}6}$	–		–		–		–		−0.0007		0.0971		−0.0335		0.0811
TDollart−1	–		–		−0.0000	†	0.0000		–		–		−0.0000		0.0000
${\overline{\mathrm{R}}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	–		–		−0.0006		0.0015		–		–		0.0008		0.0010
$\mathrm{s}\mathrm{t}\mathrm{d}{\mathrm{r}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	–		–		−0.0000	†	0.0000		–		–		−0.0000	†	−0.0000
$\mathrm{s}\mathrm{k}\mathrm{e}{\mathrm{w}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	–		–		0.0014	†	−0.0004		–		–		0.0009		−0.0002
$\mathrm{k}\mathrm{u}\mathrm{r}{\mathrm{t}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	–		–		0.0000		−0.0000		–		–		0.0000		0.0000
Overnight	–		–		0.0002	†	0.0006	†	–		–		0.0002	†	0.0006	†
Open	–		–		0.0001	†	0.0000	†	–		–		0.0001	†	−0.0000	†
Close	–		–		−0.0000		0.0000		–		–		−0.0000		0.0000
AIC	−22.6123		–		−22.6152		–		−22.6218		–		−22.6249		–
${\mathrm{H}}_0^1:{\mathrm{\alpha }}_{\mathrm{S}}^{-}-{\mathrm{\alpha }}_{\mathrm{S}}^{+}$ ≥ 0	−0.0089 ***				−0.0089 *** –				–		–		–		–
${\mathrm{H}0}_0^2:{\mathrm{\alpha }}_{\mathrm{S}}^{+,{\mathrm{P}}_4}-{\mathrm{\alpha }}_{\mathrm{S}}^{+,{\mathrm{P}}_5}$ ≥ 0			–		–		–		−0.0033 ***				−0.0032 ***–

Note: The model (1) and (2) estimates are specified in Equations (3) and (4). For the definitions of the notations, refer to Appendix B. *** Denotes significance at the 1% level. † Significantly differs from zero if its conventional t-value is greater than the sample size-adjusted critical t-value, 3.65, calculated by Connolly [62].

, the statistics provide evidence as to whether there is an asymmetric pattern in the speed of upward versus downward adjustment, and whether the speed of downward adjustment improves under strict SSCs. Since the speed differences of 0.0089 between upward (${\mathsf{\alpha }}_{\mathrm{j}}^{-}$) and downward (${\mathsf{\alpha }}_{\mathrm{j}}^{+}$) adjustments are significant in model (1) of Table 3, we can conclude that the speed of an upward adjustment to the new equilibrium is much more rapid than that of a downward adjustment, even after controlling for as much market friction as possible. These results provide strong support for Hypothesis 1. This finding is similar to that of Miller [22] and Shleifer and Vishny [67], who identified illiquidity risk and SSCs as impediments to arbitrageurs entering and trading in the spot market, so when seeking to determine the cause of more extended periods of adjustment they did so only in those cases where the spot market was overvalued. The results confirm that SSCs hinder the speed of incorporating lousy news into the price more than six times that of good news, as evidenced by the Taiwan Exchange Market from 2002 to 2009. In this case, we conjecture that the speed of downward adjustment will improve adjusting periods when the constraints are lifted, compared to during those periods with the strictest restrictions. Next, we focus on market responses to the arrival of bad news under different levels of SSCs.

4.2. How Is Market Efficiency Improved After Lifting SSCs?

We further examine whether the speed is improved for downward adjustments after the SSCs are lifted. Since the downward adjustment speeds between the lowest (${\alpha }_S^{+,p_4}$) and highest (${\alpha }_S^{+,p_5}$) SSC intensity are significantly different, as shown in model (2) of Table 3, Hypothesis 2 is strongly supported. To put it differently, interestingly, our results indicate that the relaxation of SSCs has accelerated the speed of downward adjustment by up to more than 2.7 times its original speed. In other words, lifting SSCs indeed enhances market efficiency.

4.3. Counterfactual Analysis of a Zero-SSC Scenario

In this subsection, we further try to resolve the remaining puzzle—why policymakers implemented SSCs that may have deteriorated market efficiency during the 2008 market crisis in Taiwan. The results above show that tighter SSCs give rise to market inefficiency in an asymmetric manner, as the downward adjustment is much slower, particularly during the period when short sales were banned during $P_5$. Nonetheless, suppose we interpret the evidence from the other perspective. In that case, a slower response to bad news seems to justify stabilizing market fluctuations since slower downward adjustments may lead to complacency among investors in terms of market confidence. Despite such an argument being indirectly supported by several studies that note that financial bailouts can mitigate a credit crunch problem, the related costs are huge [68,69,70]. To assess the likely state of the market index in the absence of the SSCs or a ban, we implement our counterfactual simulations with a stationary bootstrap algorithm, as shown in the procedure in Appendix A. We keep the residuals during the short-sales ban period to capture the big and random movement during financial crisis. Based on the intuition, the time-series plot for the price differences between the actual market index with the short-sales ban and the pseudo-true index without the short-sales ban is illustrated in Figure 4.

Figure 4 shows the difference between the index price with and without a short-sales ban obtained from the counterfactual analysis. We assume that only the index price will change in cases where there is no short-sales ban. A positive difference indicates that the index price with a short-sales ban helps reduce price decreases more than the situation without a short-sales ban. The blue (green) line denotes the price difference between the market index price with a short-sales ban and the mean (median) of the simulated market price without a short-sales ban. The first and second pairs of dashed lines indicate the start and end dates of the total ban on the short-selling of all stocks. The first and second pairs of dashed lines denote the start and end dates of the short-sales ban on all equities from 1 October to 27 November 2008. The positive difference between the actual and pseudo price indices indicates that the short-sales ban succeeded in halting falling prices. As we can see from Figure 4, almost all of the price differences are large and positive during the total short-sales ban period. In contrast, less positive price differences are discernible in periods when short sales were only prohibited under uptick rules. Therefore, we conclude from our counterfactual analysis that SSCs are helpful in quelling concerns among investors and preventing the execution of fire sales while also avoiding liquidity “droughts” in the market during a short-sales ban.

4.4. Tighter Constraints, Higher Total Risk, and Downside Risk

Dose a short-sales ban help to stabilize the market like regulators claimed in Taiwan? Consistent with the evidence presented by Bris et al. [1], skewness is reduced with tighter SSCs. We also find that kurtosis is increased under such strengthened constraints, which is consistent with the findings of Saffi and Sigurdsson [6]. The average daily excess kurtosis for our TAIEX intraday data is 121 on $p5$ and 96 on $p4$, whilst daily skewness is –3.01 on $p5$ and 1.06 on $p4$. Therefore, we conclude that tighter SSCs are associated with lower skewness and higher kurtosis, as shown in Table 2.

$\mathrm{E}\mathrm{x}\mathrm{t}\mathrm{r}\mathrm{e}\_\mathrm{F}\mathrm{r}\mathrm{e}{\mathrm{q}}^{-}$ ($\mathrm{E}\mathrm{x}\mathrm{t}\mathrm{r}\mathrm{e}\_\mathrm{F}\mathrm{r}\mathrm{e}{\mathrm{q}}^{+}$) denotes the daily percentage of the occurrence of extreme negative (positive) returns, defined as index returns that are less than (greater than) two standard deviations during each period of policy changes. Reading through the relevant columns, we failed to find clear evidence of short sales increasing either the frequency of extreme returns or the likelihood of a market crash. $\mathrm{R}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}\_\mathrm{V}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}$ calculated by the sum of the squared one-minute index returns represents the level of total risk every day. $\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\_\mathrm{R}\mathrm{i}\mathrm{s}\mathrm{k}$ is calculated by the sum of the squared one-minute negative index returns, representing the level of downside risk every day. As shown in the last two columns in

Table 4. Regression identification of elevated risk due to tighter SSC policy.

Panel A: The mean of daily return characterisitics calculated by 1 min data
Periods	No. of Obs.	Skew	Kurt	Extre. Freq−	Extre. Freq+	$\mathrm{R}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}\_\mathrm{V}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}$ * 100	$\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\_\mathrm{R}\mathrm{i}\mathrm{s}\mathrm{k}$ * 100
$\mathrm{p}1$	366	0.9126	56.04	0.0054	0.0063	0.0240	0.0106
$\mathrm{p}2$	467	0.8683	32.62	0.0092	0.0111	0.0158	0.0079
$\mathrm{p}3$	620	2.6429	75.12	0.0049	0.0058	0.0080	0.0034
$\mathrm{p}4$	214	1.0573	96.01	0.0031	0.0037	0.0272	0.0141
$\mathrm{p}5$	71	−3.0075	120.54	0.0032	0.0034	0.0757	0.0530
$\mathrm{p}6$	251	2.8151	75.75	0.0073	0.0071	0.0188	0.0064
Panel B: The regression of the daily return characterisitics on the SSC policy dummy
Dep. Var.		Skew	Kurt	Extre. Freq−	Extre. Freq+	$\mathrm{R}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}\_\mathrm{V}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}$ * 100	$\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\_\mathrm{R}\mathrm{i}\mathrm{s}\mathrm{k}$ * 100
Intercept		−3.0075 ***	120.5425 ***	0.0032 ***	0.0034 ***	0.0757 ***	0.0530 ***
$\mathrm{p}1$		3.9201 ***	−64.5062 ***	0.0022 **	0.0030 ***	−0.0517 ***	−0.0424 ***
$\mathrm{p}2$		3.8759 ***	−87.9231 ***	0.0060 ***	0.0078 ***	−0.0599 ***	−0.0451 ***
$\mathrm{p}3$		5.6505 ***	−45.4243 ***	0.0017	0.0024	−0.0677 ***	−0.0496 ***
$\mathrm{p}4$		4.0648 ***	−24.5364 ***	0.000003	0.0003	−0.0484 ***	−0.0389 ***
$\mathrm{p}6$		5.8227 ***	−44.7912 ***	0.0041 ***	0.0037 ***	−0.0569 ***	−0.0466 ***
No. of Obs. 1989			1989	1989	1989	1989	1989

Note: For the definitions of the notations, refer to Appendix B. ***, **, * Denote significance at the 1%, 5%, and 10% levels, with Newey–West standard errors.

, higher SSCs positively correlate with total and downside risk, with the results largely echoing those of Charoenrook and Daouk [5].

Recall that the intensity order of SSCs from high to low in Section 2.1 are in the order of $p5,\hspace{0.33em}p1,\hspace{0.33em}p2,\hspace{0.33em}p3,\hspace{0.33em}p6,\hspace{0.33em}\mathrm{a}\mathrm{n}\mathrm{d}\hspace{0.33em}p4$. Therefore, for our regression model, we apply the dummy variable, $p5$, as the benchmark to see whether lifting SSCs reduces the market volatility and negative return volatility. We can see that the mean of the realized volatility and downside risk during short-sales ban is higher than during other periods. In panel B in Table 4, we further provide the regression to see the incremental difference in market volatility compared with that during short-sales ban. In the last two columns of panel B in Table 4, our empirical results show that relaxing SSCs leads to a more stable market than a short-sales ban period (p5). The total risk and downside risk is significantly lower during a lower intensity of SSCs than during extremely strict SSCs. The results are consistent with previous studies showing that SSCs have failed to achieve the regulators’ purpose, and several studies disagree that short-selling is detrimental to price stabilization [1,5,6]. Saffi and Sigurdsson [6] found that the total risk and downside risk increased significantly for stocks with higher loan fees or low loan supply. Similar to Bris et al. [1], we found that relaxing SSCs had higher positive skewness than tighter SSCs, as shown in the first column of panel B in Table 4. A higher probability of extreme negative price movement is more easily shown under high-intensity SSCs. The higher extreme return frequency in $p5$ is shown in the kurtosis regression in panel B in Table 4. There is no significant difference of extreme return under the lightest SSC policy ($\mathrm{p}4$) versus the strictest period ($\mathrm{p}5$). That partially supports Hypothesis 3, that a short-sales ban helps investors’ fear and really stops price drops. Overall, there is no evidence of tighter SSCs being associated with enhanced price stability; on the contrary, the imposition of such SSCs is generally associated with a reduction in pricing efficiency and an increase in downside risk and total risk.

5. Robustness Checks

5.1. Further Evidence of High Short-Demand Transactions

If there are indeed some transactions in the stock market with high short demand, then the adjustment speed of such transactions should be much more rapid during periods when the constraints are relaxed. We follow Fung and Jiang [71] and Jiang et al. [51] to measure market direction using the “relative strength index” (RSI) to identify the direction of the price movements; they defined the highest 10th percentile of the RSI as transactions with “high short demand”.

$$\mathrm{R}\mathrm{S}{\mathrm{I}}_{\mathrm{t}}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{t}}^{+}}{{\mathrm{N}}_{\mathrm{t}}^{+}+{\mathrm{N}}_{\mathrm{t}}^{-}}}$$

where ${\mathrm{N}}_{\mathrm{t}}^{+}$ (${\mathrm{N}}_{\mathrm{t}}^{-}$) is the daily number of one-minute intervals in which the TWSE spot index advanced (declined).

Our observations are sorted into ten deciles, based on the daily RSI, with the highest decile representing the most positive price movements, thereby indicating a period when short-selling is more likely. We define the highest 10th percentile of the RSI as the period most likely to attract short-selling, denoted in this study as a “high propensity to short” (hereafter HPTS).

We aim to identify whether the relaxation of constraints accelerates the rate of downward adjustment for HPTS. Next, we examine the model with varying upward and downward adjustment rates in cases of HPTS with different constraint pressures, which is expressed as follows:

$$\left\{\begin{array}{l}\begin{array}{l}\Delta \ln {\mathrm{S}}_{\mathrm{t}}={\mathrm{int}}_{\mathrm{S}}+{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{\mathrm{S}}^{+\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S},\mathrm{p}\mathrm{i}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}^{+,\mathrm{p}\mathrm{i}}+{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{\mathrm{S}}^{-\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S},\mathrm{p}\mathrm{i}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}^{-,\mathrm{p}\mathrm{i}}\\ +{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{\mathrm{S}}^{\mathrm{o}\mathrm{w},\mathrm{p}\mathrm{i}}{\mathrm{Z}}_{\mathrm{t}-1}(1-{\mathrm{I}}^{+,\mathrm{p}\mathrm{i}}-{\mathrm{I}}^{-,\mathrm{p}\mathrm{i}})+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\beta }}_{\mathrm{i}}^{\mathrm{S}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\gamma }}_{\mathrm{i}}^{\mathrm{S}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}^{\mathrm{o}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{k}}}{\mathsf{\xi }}_{\mathrm{i}}^{\mathrm{S}}{\mathrm{X}}_{\mathrm{i}}+{\mathsf{\epsilon }}_{\mathrm{t}}^{\mathrm{S}}\end{array}\\ \begin{array}{l}\Delta \ln {\mathrm{S}}_{\mathrm{t}}^{\mathrm{o}}={\mathrm{int}}_{{\mathrm{S}}^{\mathrm{o}}}+{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{{\mathrm{S}}^{\mathrm{o}}}^{+\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S},\mathrm{p}\mathrm{i}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}^{+,\mathrm{p}\mathrm{i}}+{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{{\mathrm{S}}^{\mathrm{o}}}^{-\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S},\mathrm{p}\mathrm{i}}{\mathrm{Z}}_{\mathrm{t}-1}{\mathrm{I}}^{-,\mathrm{p}\mathrm{i}}\\ +{\displaystyle \sum _{\mathrm{i}=1}^6}{\mathsf{\alpha }}_{{\mathrm{S}}^{\mathrm{o}}}^{\mathrm{o}\mathrm{w},\mathrm{p}\mathrm{i}}{\mathrm{Z}}_{\mathrm{t}-1}(1-{\mathrm{I}}^{+,\mathrm{p}\mathrm{i}}-{\mathrm{I}}^{-,\mathrm{p}\mathrm{i}})+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\beta }}_{\mathrm{i}}^{{\mathrm{S}}^{\mathrm{o}}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{p}}}{\mathsf{\gamma }}_{\mathrm{i}}^{{\mathrm{S}}^{\mathrm{o}}}\Delta \ln {\mathrm{S}}_{\mathrm{t}-\mathrm{i}}^{\mathrm{o}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{k}}}{\mathsf{\xi }}_{\mathrm{i}}^{{\mathrm{S}}^{\mathrm{o}}}{\mathrm{X}}_{\mathrm{i}}+{\mathsf{\epsilon }}_{\mathrm{t}}^{{\mathrm{S}}^{\mathrm{o}}}\end{array}\end{array}\right.$$

(5)

where ${\mathrm{I}}^{+,\mathrm{p}\mathrm{i}}$ and ${\mathrm{I}}^{-,\mathrm{p}\mathrm{i}}$ denote the indicators for overvaluation and undervaluation with those transactions, with$\mathrm{R}\mathrm{S}{\mathrm{I}}_{\mathrm{t}-1}\ge 90\%$ under different SSC policies. ${\mathsf{\alpha }}_{\mathrm{j}}^{+\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S},\mathrm{p}\mathrm{i}}$ denotes the speed of downward adjustment in the case of transactions with HPTS where $\mathrm{i}=\mathrm{1,2}...,6$, $\mathrm{j}=\mathrm{S}\hspace{0.33em}\mathrm{o}\mathrm{r}\hspace{0.33em}{\mathrm{S}}^{\mathrm{o}},$and the other notations follow those provided Appendix B. The lag length p of the 1 min data is parsimoniously determined by the AIC and SIC, with the lag length p set at 21.

The results support Hypothesis 2. In

Table 5. TECM estimates with “high propensity to short” (HPTS).

MODEL	(3)			(4)			(5)			(6)
Dep. Var.	$\mathbf{\Delta }\mathbf{ln}{\mathbf{S}}_{\mathbf{t}}$	$\mathbf{\Delta }\mathbf{ln}{\mathbf{S}}_{\mathbf{t}}^{\mathbf{O}}$		$\mathbf{\Delta }\mathbf{ln}{\mathbf{S}}_{\mathbf{t}}$	$\mathbf{\Delta }\mathbf{ln}{\mathbf{S}}_{\mathbf{t}}^{\mathbf{O}}$		$\mathbf{\Delta }\mathbf{ln}{\mathbf{S}}_{\mathbf{t}}$	$\mathbf{\Delta }\mathbf{ln}{\mathbf{S}}_{\mathbf{t}}^{\mathbf{O}}$		$\mathbf{\Delta }\mathbf{ln}{\mathbf{S}}_{\mathbf{t}}$	$\mathbf{\Delta }\mathbf{ln}{\mathbf{S}}_{\mathbf{t}}^{\mathbf{O}}$
Intercept	−0.0000	0.0000	Intercept	−0.0000	0.0000	Intercept	−0.0000	0.0000	Intercept	−0.0000	−0.0000
${\mathsf{\alpha }}_{\mathrm{j}}^{\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S}}$	−0.0055 †	0.0011	${\alpha }_j^{+HPTS}$	−0.0035 †	−0.0004	${\alpha }_j^{HPTS,p1}$	−0.0026	0.0055†	${\alpha }_j^{+HPTS,p1}$	−0.0032 †	0.0026
			${\alpha }_j^{-HPTS}$	−0.0262 †	0.0174 †	${\alpha }_j^{HPTS,p2}$	−0.0023	−0.0009	${\alpha }_j^{-HPTS,p1}$	0.0129 †	0.0495 †
						${\alpha }_j^{HPTS,p3}$	−0.0051 †	−0.0025	${\alpha }_j^{+HPTS,p2}$	−0.0028	−0.0025
						${\alpha }_j^{HPTS,p4}$	−0.0083 †	−0.0002	${\alpha }_j^{-HPTS,p2}$	0.0007	0.0042
						${\alpha }_j^{HPTS,p5}$	−0.0038 †	0.0028	${\alpha }_j^{+HPTS,p3}$	−0.0035 †	−0.0029
						${\alpha }_j^{HPTS,p6}$	−0.0148 †	0.0059	${\alpha }_j^{-HPTS,p3}$	−0.0573 †	0.0060
									${\alpha }_j^{+HPTS,p4}$	−0.0050 †	−0.0007
									${\alpha }_j^{-HPTS,p4}$	−0.3309 †	0.0228
									${\alpha }_j^{+HPTS,p5}$	−0.0010	0.0025
									${\alpha }_j^{-HPTS,p5}$	−0.2231 †	0.0016
									${\alpha }_j^{+HPTS,p6}$	−0.0051	−0.0042
									${\alpha }_j^{-HPTS,p6}$	−0.0326 †	0.0241 †
${\mathsf{\alpha }}_{\mathrm{j}}^{\mathrm{o}\mathrm{w}}$	−0.0028 †	0.0028 †		−0.0025 †	0.0026 †		−0.0027 †	0.0029 †		−0.0024 †	0.0026 †
$\mathrm{T}\mathrm{D}\mathrm{O}\mathrm{L}\mathrm{L}\mathrm{A}{\mathrm{R}}_{\mathrm{t}-1}$	−0.0000 †	0.0000		−0.0000 †	0.0000		−0.0000 †	0.0000		−0.0000 †	0.0000
${\overline{\mathrm{R}}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	−0.0007	0.0028		−0.0005	0.0027		−0.0007	0.0028		0.0003	0.0029
$\mathrm{s}\mathrm{t}\mathrm{d}{\mathrm{r}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	0.0017 †	−0.0009		0.0015 †	−0.0008		0.0016 †	−0.0011		0.0012 †	−0.0007
$\mathrm{s}\mathrm{k}\mathrm{e}{\mathrm{w}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	−0.0000 †	−0.0000		−0.0000 †	−0.0000		−0.0000 †	−0.0000		−0.0000 †	−0.0000
$\mathrm{k}\mathrm{u}\mathrm{r}{\mathrm{t}}_{-3\mathrm{m}}^{\mathrm{s}\mathrm{p}\mathrm{o}\mathrm{t}}$	−0.0000	0.0000		−0.0000	0.0000		−0.0000	0.0000		−0.0000	0.0000
overnight	0.0001 †	0.0006 †		0.0002 †	0.0006 †		0.0001 †	0.0006 †		0.0002 †	0.0006 †
open	0.0001 †	−0.0000 †		0.0001 †	−0.0000 †		0.0001 †	−0.0000 †		0.0001 †	−0.0000 †
close	−0.0000	0.0000		−0.0000	0.0000		−0.0000	0.0000		−0.0000	0.0000
AIC	−22.6144			−22.6151			−22.6146			−22.6202
Asymmetry Test
${\mathrm{H}}_0:\hspace{0.33em}{\mathsf{\alpha }}_{\mathrm{S}}^{-\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S}}-{\mathsf{\alpha }}_{\mathrm{S}}^{+\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S}}\ge 0$				−0.0226 ***
Different Policy Test
${\mathrm{H}}_0:\hspace{0.33em}{\mathsf{\alpha }}_{\mathrm{S}}^{\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S},\mathrm{p}4}-{\mathsf{\alpha }}_{\mathrm{S}}^{\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S},\mathrm{p}5}\ge 0$							−0.0045 ***
Downward Adjustment Test
${\mathrm{H}}_0:\hspace{0.33em}{\mathsf{\alpha }}_{\mathrm{S}}^{+\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S},\mathrm{p}4}-{\mathsf{\alpha }}_{\mathrm{S}}^{+\mathrm{H}\mathrm{P}\mathrm{T}\mathrm{S},\mathrm{p}5}\ge 0$										−0.0039 ***

Note: The equations of models (3–5) are provided upon request, and the model (6) estimates are specified in Equation (5). For the definitions of the notations, refer to Appendix B. *** Indicates significance at the 1% level with the Newey–West standard errors. † Significantly differs from zero if its conventional t-value is greater than the sample size-adjusted critical t-value of 3.65 calculated by Connolly [62].

, we can witness that the relaxation of SSCs promotes more rapid downward adjustment for transactions with high short demand. We also find evidence supporting Hypothesis 1 in that the speed of adjustment is asymmetric, with the pace of upward adjustment being more rapid than that of downward adjustment, even in the case of HPTS. The high short-demand transactions are divided into six groups according to the policy changes to verify whether lifting constraints might speed up the convergence rate toward equilibrium. The Equations of models (3)–(5) in Table 5 are skipped to save space and can be provided upon request. The results deliver similar conclusions.

5.2. The Elevated Risk Due to Stronger SSCs

The question arises as to whether the increases in downside and total risk in the 2008 financial crisis resulted from the tightened SSCs or simply due to the increased market volatility of investment sentiment. To tease out the endogeneity from the higher market volatility, we specifically regress the $\mathrm{R}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d}\_\mathrm{V}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}$ and $\mathrm{D}\mathrm{o}\mathrm{w}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\_\mathrm{R}\mathrm{i}\mathrm{s}\mathrm{k}$ on a set of dummy variables characterizing different SSC regimes as well as the TVIX index as a hybrid control variable for market-wide sentiments and volatility during this period. The TVIX index is computed by weighted average index options with different strike prices and moneyness following the CBOE methodology and has been available since 18 December 2006. Therefore, we examine the relationship between risk, SSCs, and market sentiment from 2007 to 2009. Generally, the higher the TVIX index, the more severe the expected future volatility of the stock price index among the derivative investors. Since the TVIX describes changes in overall market sentiment, it is also known as the investor “fear index” or “fear gauge” [72].

As shown and expected in

Table 6. Regression identification of elevated risk due to tighter SSC policy after controlling for the investor fear gauge.

Dependent Variable	No. of Obs.	Intercept	$\mathbf{p}3$	$\mathbf{p}5$	$\mathbf{p}6$	TVIX
Realized_Variance * 100	768	−0.0343 *	0.0011	0.0162 **	−0.0111 *	0.0020 *
Downside_Risk * 100	768	−0.0182 *	0.0000	0.0220 *	−0.0091 *	0.0011*

Note: For the definitions of the notations, refer to Appendix B. **, * Denote significance at the 1%, 5%, and 10% levels with the Newey–West standard errors.

, the TVIX index significantly positively comoves with the risk measures examined. Surprisingly, while controlling for market-wide sentiments and volatility, the significant positive estimates for the p5 regimes in both regression equations suggest that tighter SSC intensity positively contributes to both the escalated downside risk and total risk. The marginally imparted greater downside risk and higher volatility during p5 than p4 due to tighter SSCs are non-negligible, even after controlling for the investor fear gauge, proxied by the TVIX.

6. Conclusions

The regime shifts in the regulatory uptick rules in Taiwan between 2002 and 2009 provide a sequence of natural experimental environments to examine the stock market efficiency and stability of short-sales policy changes in Taiwan. Our research arrives at three main empirical findings.

First, in the presence of mispricing, SSCs lead to a less efficient market by delivering asymmetries in the magnitudes and speed of price adjustments. Consistent with prior studies, such constraints are generally found to hinder the reflection of negative information in the price; thus, based on the TECM adopted for this study, we document that upward adjustments converge more rapidly than downward adjustments, even when controlling for market conditions and liquidity. Secondly, we find that the speed of downward adjustments is improved in periods characterized by relaxed SSCs. Market efficiency is improved during fewer SSC periods. Finally, the realized equilibrium adjustments identified through our counterfactual analysis also indicate that SSCs can indeed restore investor confidence, thereby discouraging the execution of fire sales and saving the market from further liquidity problems. However, such restrictions are of very little help in stabilizing market fluctuations. In particular, stricter short-sales restrictions are associated with more significant downside risk and higher volatility.

Our results hold, even after controlling for the investor fear gauge, which is proxied by the TVIX in this study. Interestingly, however, our findings support the academic finding that short-sales constraints generally lead to a less efficient market. Even though there is no evidence suggesting that regulators can stabilize prices by restricting short sales, such policy announcements may likely retain or restore investors’ confidence, a valuable yet scarce resource, wildly when markets are plunging. We suggest the regulators utilize the counterfactual analysis to simulate and predict the effects of short-sales policy on price movement, and then adjust the parameters of the model to improve the accuracy of predictions on SSC policy for the emerging market.