ÐÏࡱá>þÿ ¬®þÿÿÿ¨©ª«oÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿì¥Á5@ ø¿šøbjbjÏ2Ï2 –>­X­XIá ÿÿÿÿÿÿˆ˜˜˜FÞ4b b b 4– ž†ž†ž†h‡,2Œä– ¸"�&H’H’^’^’=“B“›“—™™™™™™$ÆR‚½µb h�9“=“h�h�½  ^’^’ÛrÈÂÈÂÈÂh�¨ 8^’b ^’—ÈÂh�—ÈÂÈÂæÂnåJ b ç^’� �ÿÍš�Éž†·!æ +lˆ0¸AæÔš¾Tš@ç– –     çJšb _çÌ«“Å•€ÈÂE—4y˜ï«“«“«“½½– – ¤H:Rd4dÂd– – :RThe Dynamics of Market EfficiencyJing Jiang*State University of New York (SUNY) at BuffaloJob Market PaperJan. 12, 2009AbstractMarket efficiency varies across individual stock according to stock attributes. We find prices are closer to random walk benchmarks for stocks with better liquidity provision, frequent trading, greater return volatility, higher prices, larger market capitalizations, and smaller trade sizes than in other ones. These findings suggest that liquidity stimulates arbitrage activity, which, in turn, enhances market efficiency. Market efficiency also varies with information environment. We find that stocks with greater information-based trading exhibit higher level of efficiency. Lastly, market structure influences market efficiency. NYSE stocks achieve higher level of efficiency than NASDAQ stocks do. Market efficiency improves after decimalization in both markets. Our results are robust and not driven by differences in stock attributes between the two markets or time periods. Overall, our results indicate that liquidity provision, stock attributes, market structure, and tick size exert a significant impact on the realization of market efficiency. 1. IntroductionThe study and analysis of how financial asset prices adjust to information has long been a focus of attention in the finance literature. Evidence that a market is quite efficient (Fama, 1970) over a daily horizon does not preclude inefficiencies at shorter horizons. This is because investors need time to absorb and act on new information. The empirical documentation of overreactions (DeBondt and Thaler, 1985, 1987), underreactions (Michaely et al., 1995; Bernard and Thomas, 1989) and other anomalies (for example, Jegadeesh and Titman, 1993, 2001) has led to a search for alternative theoretical models to describe the price adjustment process. A number of behavioral models have been subsequently developed to provide rationales for the empirically documented under(over) reactions by Barberis et al. (1998), Daniel et al. (1998) and Hong and Stein (1999); Fama (1998) and Hirshleifer (2001) provide excellent overviews and discussions of this topic area. Recent research on the microstructure of security markets draws attention to the role of the market's organization in the determination of security prices. It is now increasingly recognized that institutional factors-such as the brokers' handling of investors' orders, the management of the limit order book, or the existence of designated specialists entrusted with an affirmative obligation to maintain "price continuity"-affect the speed of the prices' adjustment to changing conditions. For example, Cushing and Madhavan (2000), and Chordia, Roll, and Subrahmanyam (2005) document that short horizon returns are predictable from past order flows. The determinants of this short-horizon predictability deserve a thorough investigation by finance scholars. This study extends the scope of the analysis one step further. We explicitly examine how the individual stock price efficiency is related to the market environment and stock attributes. More specifically, we examine the role of liquidity provision, stock attributes, information environment, and market structure in the realization of individual stock’s market efficiency. Amihud and Mendelson (1987) suggested a simple model of price adjustment in which observed prices noisily and partially adjust towards their intrinsic values. Along this line, a number of estimators have been subsequently developed in the literature. Damodaran (1993) and Brisley and Theobald (1996) estimate the speed of price adjustment using the partial adjustment model. Thoebald and Yallup (2004) compare the speed of price adjustments between large and small companies. Most of the previous research focuses on the improvement of the estimator and/or how the speed of price adjustment is related to the trading volume. In particular, two studies are closely related to our study. Chung et al. (2008) analyze the speed at which quotes adjust to new information, but they focus on quote width and depth. Chordia et al. (2008) suggests that market efficiency is related to liquidity, but they neither directly study the speed of price adjustment, nor directly investigate the role of liquidity provision in market efficiency. Despite its obvious importance to traders, we know very little about the dynamics of price adjustment. Prior studies offer little evidence as to the speed at which new information is impounded into the price. There is also limited evidence regarding how liquidity provision, market structure and trading protocol, such as tick size, affect the speed at which new information is incorporated into price. Using the speed of price adjustment as a proxy for individual stock efficiency, we extend our understanding of market efficiency one step further. Traders do not always immediately incorporate the new information into their prices for a number of reasons. For instance, tick size is likely to be a binding constraint or the minimum feasible quote increment is larger than the desired change implied by the new information (Hasbrouck, 1991). Furthermore, the individual efficiency is likely to be different across stocks. For example, traders may react faster to new information (and thereby move more quickly to equilibrium prices) for stocks with greater adverse-selection risks because the cost of not doing so is greater for such stocks. An important question is whether fluctuations in liquidity are related to variations in the degree of market efficiency. We believe markets are efficient because we believe arbitrage forces are constantly at work. If a particular piece of value-relevant information is not incorporated in price, there will be powerful economic incentives to uncover it, and to trade on it. Individual agents within the economy may behave irrationally, but we expect arbitrage forces in the market to keep prices right. This arbitrage trading should be more extensive and effective during times in which the market is more liquid. Finance literature documents that reductions in the minimum tick size have led to exogenous decreases in bid-ask spreads (see, for example, Bessembinder, 2003), and thus an important issue is how such liquidity improvements are related to market efficiency.In this study we address the following questions using a large sample of New York Stock Exchange (NYSE) and NASDAQ stocks: (1) How quickly does the stock price reflect new information through trading? Does the stock price on the NYSE reflect new information more quickly than that on NASDAQ? (2) How the individual stock efficiency is related to stock attributes? For example, do stocks with greater information-based trading exhibit faster price adjustments towards equilibrium value? Do stocks that are traded in less competitive markets (e.g., fewer dealers) exhibit slower adjustments? (3) Does decimal pricing result in better stock market efficiency as reflected by how the traders incorporate new information in trading? Answers to these questions would be of significant interest not only to investors and researchers, but also to stock exchanges facing increased competition from foreign markets expanding their trading hours and from the creation of new electronic communication networks (ECNs). Our study is also relevant to market regulators, who continuously respond to the technological innovation in trading environment to enhance market efficiency without favoring some market over others. We employ the partial adjustment model to analyze how quickly security prices on the NYSE and NASDAQ adjust in response to new information. We show that the overall market efficiency on the NYSE is better than that of NASDAQ. In both markets, the individual stock efficiency is higher for stocks with a larger number of trades, higher share prices, greater return volatility, larger market capitalizations, and smaller trade sizes. Our results also indicate liquidity provision and information-based trading enhance market efficiency. The level of price efficiency after decimal pricing is significantly higher than that before decimal pricing in both markets, indicating that larger tick sizes slow price discovery. Numerous studies employ variance ratio (for example, Chordia et al. (2008)) and Dimson beta regression approach to study market efficiency. As a robustness check, we develop other measures of individual stock efficiency based on Dimson beta regression and variance ratio approach and find similar results. On the whole, our study depicts a picture that liquidity provision, stock attributes, informational environment, and market structure jointly determine individual stock efficiency.The remainder of the paper is organized as follows. Section 2 presents our hypothesis. Section 3 explains our methodology. Section 4 explains data sources and presents descriptive statistics. Section 5 examines how the individual stock efficiency is related to stock attributes, adverse-selection costs, probability of information-based trading, and competition. Section 6 shows how decimal pricing affects the individual stock efficiency. Section 7 concludes the paper.2. Statement of hypothesesIn this section, we present our hypothesis on how the individual stock efficiency is determined by liquidity provision, stock attributes, informational environment, dealer competition, market structure, and tick size.2.1. Market structure and the speed of price adjustment The institutional details between the NYSE and NASDAQ are likely to affect the level of individual stock efficiency. The NYSE is an order driven continuous auction market, with individual specialist assigned to each stock. Specialists facilitate continuous trading by posting quotes for their own accounts or by reflecting the best quotes on their limit order book. Harris and Hasbrouck (1996) report that limit orders account for about 54% of all orders submitted through SuperDOT. The 1992 New York Stock Exchange Fact Book reports that The NYSE specialist participates in fewer than 20% of trades with over 80% of the liquidity provided by other traders. Chung et al. (1999) documents that only 5.9% of the posted spreads are quoted exclusively by the specialist in their sample stocks. In contrast, the Nasdaq market is based on a competing dealer system in which each dealer continually posts firm bid and ask quotes on an electronic screen. Further, Nasdaq dealers do not have access to a central limit order book. It is costly for Nasdaq market makers to constantly monitor trade arrivals and quote changes by other market-makers (perhaps because they must monitor several stocks simultaneously), it may be impossible for such market makers to respond instantly to the information contained in an arriving trade. Overall, the more centralized specialist system on the NYSE is likely to result in higher level of price efficiency as reflected by the speed at which new information is absorbed in stock price. . Dealer competition on Nasdaq is likely to diminish by the rules allowing directed order flow to preferred dealers. Chung, Chuwonganant, and McCormick (2004) show that a large portion of order flow on NASDAQ is either internalized or preferenced based on payment for order flow agreements. NASDAQ dealers who bear the risk of offering the best price, and hence facilitating the price discovery process, are not rewarded with increased order flow. This reduces dealers’ incentiveness to improve quotes and slow down price discovery. As order flow fragments, the ability of price aggregate information can be reduced, and so does the efficiency of the market. Although a part of the NYSE volume is also routed to regional exchanges according to preferencing agreements between brokers and dealers, prior studies (Bessembinder, 2003) show that NYSE specialists almost always post the most competitive quotes. Consequently, order preferencing between brokers and regional dealers may not significantly compromise price competition on the NYSE. These considerations suggest that the level of market efficiency on the NYSE is likely to be higher than that on NASDAQ.Benveniste, Marcus, and Wilhelm (1992) suggest that repeatedly dealing with the same brokers allows market makers to know when brokers exploit private information. Garfinkel and Nimalendran (2003) find insider trades are more transparent on the NYSE specialist system relative to the NASDAQ dealer system. Foucault et al. (2007) contrast two different trading mechanisms: a non-anonymous market (limit-order traders’ IDs are visible) and an anonymous market (limit-order traders’ IDs are concealed). They show that the quotes informativeness is smaller in the anonymous system if the traders have asymmetric information about future volatility. The lower degree of anonymity on the NYSE lead to liquidity providers on the NYSE are likely to respond more quickly to information-based trading than those on NASDAQ. These considerations lead to our first hypothesis.Hypothesis 1: The level of market efficiency on the NYSE is higher than that on NASDAQ.2.2. Stock attributes and price efficiency Extensive evidence indicates that trading volume and stock returns volatility are positively correlated (see e.g., Karpoff, 1987 and Gallant et al., 1992). Although many theories attempt to explain this correlation, there is no consensus on what are key factors behind the volume–volatility relation. Glosten and Milgrom (1985) develop a sequential trading model with informed and uninformed investors and find that market makers and uninformed investors experience adverse selection when trading with informed investors. By assumption, each investor is allowed to transact one unit of stock per unit of time, so price changes are completely independent of trade size. Easley and O’Hara (1987) extend this model to allow traders to transact at varying trade sizes and by introducing uncertainty in the information arrival process of the informed trader. When investors act competitively, Easley and O’Hara find that larger sized trades tend to be executed by better informed investors, so that larger trades exhibit a greater adverse selection effect. Thus, there is a positive relation between trade size and price volatility. On the other hand, theorists have observed that traders are not allowed to act strategically, which could result in large blocks being broken up into a number of smaller trades. If informed investors are allowed to strategically breakup orders as in Kyle (1985), Amati and Pfleiderer (1988), Foster and Vishwanathan (1990) and Back (1992), then the effect of trade size on price volatility is attenuated and its impact may be shifted to the number of trades. Supporting this view, Barclay and Warner (1993) report empirical evidence from the NYSE consistent with informed investors breaking up large trades to better hide their information motivated trading activity. Their evidence is based on how influential trades of various sizes are on price changes. This evidence suggests the need to investigate whether price volatility reacts differently to trades depending on their size category, and number of trades may also have significant information content for stock prices. The role of number of trades in price formation is highlighted by Easley and O’Hara (1992) who show that the presence or absence of trades may provide information to market participants. Specifically, the larger the number of trades, the higher is the probability that new information has arrived (Proposition 1, p. 587). Thus, number of trades assumes the role of the information arrival rate. In Harris and Raviv (1993), trading occurs if and only if cumulative information for a particular type of trader switches from favorable to unfavorable or vice versa. Jones, Kaul, and Lipson (1994) analyze stock price volatility on NASDAQ market and find that trade size appears to have an immaterial effect, once the number of trades is taken into account. This conclusion appears to be at variance with the prior empirical evidence. Karpoff (1987) reviews the earlier literature (prior to JKL) and reports that stock price volatility is positively related to trading volume. However, these earlier studies typically do not consider competing measures of trading activity, nor do they examine the number of trades as a measure of trading activity. JKL maintain that the occurrence of transactions per se contains all of the information pertinent to pricing securities. Their results are confirmed by Huang and Masulis (2003) using data from the London Stock Exchange.Taken above evidence as a whole, we conjecture that if trades convey information and liquidity provider update quote in response to new information, they are likely to update quotes more quickly for stocks that are actively traded and have large return volatility. These considerations lead to our second hypothesis:Hypothesis 2: The individual stock price efficiency is positively related to both the number of trades and return volatility.Chung and Chuwonganant (2002) show that low-price stocks exhibit fewer quote revisions that accompany a spread change. They interpret this result as evidence that the minimum price variation is more frequently a binding constraint on absolute spreads for low-price stocks. Chung, Charoenwong, and Ding (2004) calculate the proportion of spreads that are equal to one penny to assess the extent to which the penny tick is a binding constraint. They find that although the proportion is much smaller under decimal pricing than under $1/16 pricing, the penny tick is still a significant binding constraint for low-price stocks. We conjecture that liquidity providers make slower price adjustments towards equilibrium for low-price stocks because the binding constraint prevents them from making such revisions. These considerations lead to our next hypothesis: Hypothesis 3: The individual stock price efficiency is positively related to share price.Information about fundamentals is capitalized into stock prices in two ways: through a general revaluation of stock values following the release of public information, such as unemployment statistics or quarterly earnings, and through the trading activity of risk arbitrageurs who gather and possess private information. Roll (1988) finds that firm-specific stock price movements are generally not associated with identifiable news release, thus he argues that the second channel is especially important in the capitalization of firm-specific information. As a result, firm-specific price fluctuations are a sign of active trading by informed arbitrageurs and thus may signal that the stock price is tracking its fundamental value quite closely. Similarly, we conjecture that liquidity providers make faster quote revisions to equilibrium when competition is higher. These considerations lead to the following hypothesis:Hypothesis 4: The level of stock price efficiency is positively related to both adverse-selection risks (and costs) and dealer competition.2.3. Liquidity and stock price efficiencyPrior literature explores a link between liquidity and stock returns by way of a premium demanded by investors for trading in illiquid stocks. For example, Amihud and Mendelson (1986) and Jacoby, Fowler, and Gottesman (2000) provide theoretical arguments and empirical evidence to support the existence of liquidity premia. In addition, Jones (2001) and Amihud (2002) show that liquidity predicts expected returns in the time-series, and Pastor and Stambaugh (2003) and Acharya and Pedersen (2005) find that expected stock returns are cross-sectionally related to liquidity risk. We explore a distinctly different link between liquidity and asset prices by examining whether liquidity is associated with an enhanced degree of market efficiency. Kyle (1985) suggests that markets are illiquid because prices for buying and selling shares are different, but prices also are martingales because market makers are risk-neutral. Thus, in this model, current prices and order flows do not predict future returns. However, if market makers have limited risk-bearing capacity, persistent asymmetric orders will lead to predictable returns due to temporary deviations of prices from fundamental values. If arbitrageurs can detect such deviations and submit arbitrage trades, they may speed up the convergence of prices to fundamental values. However, the possibility of these traders to submit arbitrage orders would be negatively influenced by liquidity/illiquidity. This mechanism creates a link between liquidity and efficiency. The other possibility is that rational market maker promptly absorbs information and update quote towards optimum. Under this scenario, there would be no relationship between liquidity and price efficiency. So, our analysis may then be viewed as a test of the two competing hypotheses.Hypothesis 5: The level of stock price efficiency is positively related to liquidity provision. 2.4. Tick size and stock price efficiency Market tick is a specific form of market friction. It is an important protocol of securities markets because it affects trading costs and market quality. Bid and ask prices can move only in discrete increments of the tick. When the tick is large, there is a discernible jump. When the tick is small, prices adjust almost continuously. This would attract more frequent participation of informed traders and thus stimulate price competition. Although there is extensive literature on the effect of tick size on market quality, there is little evidence on how tick size affects the stock price efficiency. We analyze the impact of tick size on stock price efficiency using data before and after decimal pricing. We conjecture that the level of stock price efficiency is higher under decimal pricing because the penny tick is less likely to be a binding constraint than the pre-decimal tick size (i.e., $1/16) and thus it would attract more informed trading. This is consistent with Chordia, Roll, and Subrahmanyam (2005). Also note that a smaller tick size results in greater price competition because it implies a smaller cost of both front running by sell-side intermediaries and stepping ahead of the existing queue by buy-side traders. This is another reason why we expect higher level of stock price efficiency under decimal pricing. These consideration lead to the following hypothesis:Hypothesis 6: The level of stock price efficiency during the post-decimalization period is higher than that during the pre-decimalization period.3. Methodology In this section, we present how we measure the individual stock price efficiency. 3. 1 Partial adjustment model. We use the following partial adjustment model to measure the speed of price adjustment: EMBED Equation.3  (1) EMBED Equation.3  (2)where  EMBED Equation.3  is the change in the actual (or observed) price (with  EMBED Equation.3  the change operator), expressed in natural logarithms,  EMBED Equation.3 , is the speed of adjustment coefficient, which will be within the range [0, 2] for non-explosive processes.,  EMBED Equation.3  a white noise term,  EMBED Equation.3  the change in logarithmic intrinsic values,  EMBED Equation.3  the mean of the intrinsic value random walk process and  EMBED Equation.3  the innovations in logarithmic intrinsic values which will be serially uncorrelated in efficient markets. The speed of adjustment coefficient,  EMBED Equation.3 , will equal one when prices fully and unbiasedly adjust while it will be greater (less) than one where over(under) reactions occur.We can derive from equation (1)  EMBED Equation.3  (3)Substituting equation (2) into equation (3) EMBED Equation.3  (4)The autocorrelations induced by under/overreactions are reflected as an ARMA(1,1) process. However, the speed of price adjustment coefficient, À, is not a direct stock price efficiency measure in that it s not a monotonic measurement. We employ an alternative measure (»ar) defined by the following equation: EMBED Equation.3 ; (5)where À is the partial adjustment coefficient estimated from Eq. (4). Note that if À is equal to one (i.e., when liquidity providers fully incorporate concurrent information into quote midpoint), »ar would also be equal to one. If À is either greater or less than one, »ar would range between zero and 1. The closer is »ar to one, the more efficient the stock price is in the sense that the stock price moves quickly towards its equilibrium value to incorporate the new information. Also note that » is equal to À whenever À is smaller than or equal to one. 3.2 Dimson Beta regressionAs a robustness check, we construct another measure of stock price efficiency based on contemporaneous and lagged betas from Dimson beta regressions.  EMBED Equation.3  (6)where  EMBED Equation.3  is the daily return on the stock,  EMBED Equation.3  is the daily return on the market index, and  EMBED Equation.3  is the beta with respect to the market return at lag k. We use the NYSE/AMEX equal-weighted market index as a proxy of the market portfolio. For simplicity, consider a Dimson beta regression with just one lag and one lead. In the comparing the speed of adjustment of two stocks A and B, returns of stock B are said to adjust faster to common information than do returns of stock A if and only if stock B’s contemporaneous beta,  EMBED Equation.3 , is greater than stock A’s contemporaneous beta,  EMBED Equation.3 , and stock B’s lagged beta,  EMBED Equation.3 , is less than stock A's lagged  EMBED Equation.3 . Chordia and Swaminathan (2000) construct the delay measure based on the Dimson beta regression: EMBED Equation.3  (7)where EMBED Equation.3  (8)The DELAY measure is a modification of the measure proposed by McQueen et al. (1996), which has several appealing properties. However, one serious problem is that it is still not a monotonic measurement of the price efficiency. One can not simply say the larger the DELAY measure, the more efficient the price is because when the DELAY measure is over 0.5, we have the over-reaction case. Therefore, we modify the DELAY measure in the following way to make it a monotonic measurement of the stock price efficiency: EMBED Equation.3  (9)3.3 Variance ratio testThis approach is based on the observation that for a random walk price process, the variance of long-horizon returns is q times the variance of short horizon returns, where q is the number of short horizon intervals in the longer horizon. Deviations from a random walk (efficient-market) benchmark can arise because of various reasons, for example, inventory control activity can induce return serial correlation (Grossman and Miller, 1988). We consider the ratio of mid quote return variances computed from five-minute intervals and from open-to-close of trading days. In computing this variance ratio, the five-minute return variance is multiplied by the number of five-minute intervals in a trading day. For a random walk, this scaled variance ratio would converge to one in large samples. For the same reason as the other two efficiency estimators, we apply the following transformation in order to make the variance ratio estimator a monotonic measurement.  EMBED Equation.3  (10)4. Data sources and sample characteristicsWe obtain trade and quote data for the three-month period from Feb 2007 to Apr 2007 from the NYSE’s Trade and Quote (TAQ) database. We eliminate stocks with average share prices under $2. We omit the following trades and quotes to minimize data errors: quotes with an ask price or bid price less than or equal to zero; quotes with an ask size or bid size less than or equal to zero; quotes with bid-ask spreads greater than $5 or less than zero; quotes associated with trading halts or designated order imbalances; before-the-open and after the-close trades and quotes; trades and quotes involving errors or corrections; trades with price or volume less than or equal to zero; trade price, pt, if |(pt – pt-1)/pt-1| > 0.10; ask quote, at, if |(at – at-1) /at-1| > 0.10; and bid quote, bt, if |(bt – bt-1)/bt-1| > 0.10. We construct national best bids and offers (NBBOs) using quotes from all exchanges. We obtain data required for calculation of market capitalizations from CRSP. Our final sample includes 4,138 stocks, of which 1,868 NYSE stocks, and 2,270 NASD stocks.We partition each trading day into 78 successive five-minute intervals to calculate the variables used in partial adjustment approach. We measure share price by the quote midpoint at the end of each interval and return volatility by the standard deviation of quote-midpoint returns during each interval. We measure trading frequency by the number of trades during each interval and trade size by the size of the last trade in each interval. We measure the quoted spread of each stock at time t by (Askt – Bidt)/Mt; where Askt is the ask price, Bidt is the bid price, and Mt is the mean of Askt and Bidt. The quoted spread is the implicit trading cost for market orders when a trade occurs at the quoted price with no price improvement. To measure the cost of trading when it occurs at prices inside the posted bid and ask quotes, we also measure the effective spread at time t by 2Qt (Pt – Mt)/Mt; where Pt is the transaction price at time t, Mt is the midpoint of the most recently posted bid and ask quotes for the stock, and  EMBED Equation.3 equals 1 for buyer-initiated trades and –1 for seller-initiated trades. We estimate Qt using the Lee and Ready (1991) algorithm as modified by Bessembinder (2003) to classify a trade as either a buy or sell. We then calculate the mean values of these variables for each stock during the study period. We calculate those variables with daily average in order to proceed with the Dimson beta approach. Panel A of Table 1 shows daily descriptive statistics on our study sample of 1,868 NYSE stocks and 2,270 NASDAQ stocks that have complete data required for our empirical analyses. The average share price is $36.85 for the NYSE sample and $20.46 for the NASDAQ sample. The average trade size and average number of trades are $15,596.78 and 4,102.68 for the NYSE sample, and $5,539.28 and 2,444.68 for the NASDAQ sample. The average standard deviation of quote midpoint returns is 0.0005 for the NYSE sample and 0.0011 for the NASDAQ sample. The average market capitalizations for our NYSE and NASDAQ stocks are $7,911.65 million and $1,562.71 million, respectively. The average quoted and effective spreads for NYSE stocks are smaller than those of NASDAQ stocks. On the whole, NYSE stocks have higher share prices, larger trade size and number of trades, lower return volatility, larger market capitalization, smaller spreads, and smaller depths.5. Empirical findings In this section, we present the empirical results regarding our hypotheses 1 through 6 described in Section 2. 5.1. Market structure versus price efficiencyWe estimate Eq. (4) for each stock in our study sample using the five-minute interval data from Feb 2007 to Apr 2007. We estimate Eq. (6) for each stock in our study sample using daily observation in the same period. We calculate the mean value of À for our NYSE and NASDAQ stocks, respectively, together with t-statistics for testing the equality of the mean. Because estimates of the partial adjustment coefficient for certain stocks are less meaningful (i.e., smaller t-values) than those for other stocks, we calculate the weighted average of À using the reciprocal of the standard error (SE) of each estimated coefficient as weight. We consider this approach sensible because it assigns greater weight to the more precise estimates, thereby reducing the effect of measurement errors on our inferences. Similarly, we compare the mean values of »ar between our NYSE and NASDAQ stocks.Panel A of Table 2 shows that the mean value of partial adjustment coefficient estimates is 0.8530 for the NYSE sample and 0.7219 for the NASDAQ sample, and the difference between the two figures is statistically significant at the 1% level. These results indicate that liquidity providers in both markets only partially reflect the newly arrived information. The mean value of »ar estimates for the NYSE sample is 0.6155, which is significantly greater than the corresponding figures, 0.5090, for the NASDAQ sample. These results indicate that liquidity providers on the NYSE make faster price adjustments towards the equilibrium than their counterparts on NASDAQ. We find qualitatively similar results for the Dimson beta model (i.e., Eq. (6)). These results support our hypothesis 1. As shown in Panel A of Table 1, the stock attributes between NYSE and NASDAQ are quite different, for example, NYSE stocks have larger transaction sizes than NASDAQ stocks. Furthermore, NYSE stocks have much larger market capitalizations than NASDAQ stocks. Thus, differences in price efficiency could be simply due to differences in stock attributes. As a robustness check, we obtain matched samples of NYSE and NASDAQ stocks that are similar in trade size, price, return volatility, and market capitalization. We first calculate the matching score (MS) for each NYSE stock against each of the 1,614 NASDAQ stocks in our study sample: MS =  EMBED Equation.3 , where Xi represents one of the four stock attributes, superscripts N and T refer to NYSE and NASDAQ, respectively; and £ denotes the summation over i = 1 to 4. Then, for each NYSE stock, we select the NASDAQ stock with the smallest MS. Once we match a NASDAQ stock with a NYSE issue, that particular NASDAQ stock is no longer considered for subsequent matches. This procedure results in 686 pairs of NASDAQ and NYSE stocks with similar attributes.Panel B of Table 1 shows descriptive statistics on the matched sample. The average share price for the NYSE sample is $21.39 and the corresponding figure for the NASDAQ sample is $19.22. The average trade size for the NYSE sample is $8,635.14 and the corresponding figure for the NASDAQ sample is $11,158.22. The mean value of the standard deviation of quote midpoint returns is 0.0009 for the NYSE sample and 0.0010 for the NASDAQ sample. The average market value of equity for our NYSE and NASDAQ firms is $6,767.92 million and $4,861.74 million, respectively. The average quoted (effective) spread of NYSE stocks is 0.0315 (0.0017) whereas the corresponding figure for NASDAQ stocks is 0.0374 (0.0025). The average quoted depth (16.78 round lots) for NYSE stocks is larger than the corresponding figure (9.12 round lots) for NASDAQ stocks.Panel D of Table 2 shows the price adjustment speed comparison results for the matched sample, which still support our conjecture that NYSE liquidity providers make faster price adjustment than NASDAQ dealers do, although the results based on Dimson beta approach is weaker. One possible explanation is that the Dimson beta measure can be more viewed as a test on the semi-strong form market efficiency in the sense that it measures the speed with which prices reflect public announcements, while the partial adjustment approach directly tests the strong form efficiency of the stock market. Hence we conclude that at least our results on the strong form market efficiency are not driven by differences in stock attributes between the two markets.5.2. Stock attributes and price efficiency5.2.1. Model specification and the measurement of the variables To examine how the price efficiency is related to stock attributes, we estimate the following cross-sectional regression model using data for our study sample of 1,868 NYSE stocks and 2,270 NASDAQ stocks (we omit stock subscript for notational simplicity):  EMBED Equation.3  (11)where »ar and »d are the price efficiency measures,  EMBED Equation.3  (i = 1 to 5) is one of the five stock attributes (i.e., NTRADE, TSIZE, PRICE, RISK and MVE), £ denotes the summation over i = 1 to 5, ²0 through ²9 are regression coefficients, and  EMBED Equation.3  is the error term. GKN is the adverse-selection component of the spread estimated from the method in George, Kaul, and Nimalendran (1991), GH is the adverse-selection component of the spread estimated from the method in Glosten and Harris (1988), PIN is the probability of information-based trading, and MM is the number of marketmakers (for NASDAQ stocks). George, Kaul, and Nimalendran (1991) use the following regression model to estimate the adverse-selection component: 2(TRt – MRt) = Á0 + Á1sq(Qt  Qt-1) + µt; (12) where TRt is the transaction return at time t, MRt is the quote midpoint return calculated from the quote midpoint immediately following the transaction at time t, sq is the percentage bid-ask spread, Qt equals 1 for buyer-initiated trades and  1 for seller-initiated trades, Á1 measures the order-processing component, (1  Á1) measures the adverse-selection component, and µt is the error term.Glosten and Harris (1988) use the following regression model to estimate the adverse-selection component:  EMBED Equation.3  (13)where EMBED Equation.3 is the transaction price at time t,  EMBED Equation.3 is the number of shares traded at time t,  EMBED Equation.3 is the error term that captures both the rounding error and the arrival of public information, and  EMBED Equation.3 equals 1 for buyer-initiated trades and –1 for seller-initiated trades. We use the Lee and Ready (1991) algorithm as modified by Bessembinder (2003) to classify a trade as either a buy or sell. We estimate the adverse-selection component by Z0 = 2(z0 + z1Vt) and the transitory component by C0 = 2(c0 + c1Vt). Because the bid-ask spread in the GH model is the sum of Z0 and C0, we measure the adverse-selection component (as a proportion of the spread) by EMBED Equation.3 /[ EMBED Equation.3 ]. We use the algorithm in Easley, Hvidkjaer, and O’Hara (2002) to measure the probability of information-based trading (PIN).5.2.2. Regression results We estimate Eq. (11) using the weighted regression procedure to reflect the statistical significance of À estimates. We use the reciprocal of the standard error of partial adjustment coefficients (i.e., À) from the first-pass regressions as weight in the second-pass regression (i.e., Eq. (11)). This approach assigns smaller weights to À estimates that are less meaningful (i.e., smaller t-values). We use the log of number of trades, trade size, share price, market value of equity, and MM in the regression.Panels A and B of Table 3 show the results of the second-pass regressions using »ar and »d values that are estimated from the partial adjustment model and Dimson beta model. In each panel, the first four columns show the results for NYSE stocks, the next four columns show the results for NASDAQ stocks, and the last four columns show the results for the combined sample of NYSE and NASDAQ stocks.Panel A shows that both price efficiency measures are significantly and positively related to the number of trades and share price for both NYSE and NASDAQ stocks in most regressions. The results on the return volatility weakly support our hypothesis. These results are generally consistent with our hypotheses 2 and 3 and support the idea that trades convey information and the penny tick is more likely a binding constraint on the spreads of low-price stocks. Our results show that »ar and »d are significantly negatively related to trade size in most regressions. Because of the ambiguity involved in the relation between trade size and information content, however, it is unclear what drives this relation. Both »ar and »d are positively related to the adverse-selection component of the spread (i.e., GKN/GH), although only the results on the GH measurement are significant. The results on probability of information-based trading (PIN) are mixed and significant only when it’s positively related to the price efficiency. These results are generally consistent with hypothesis 4, supporting the idea that liquidity providers make faster price adjustments in response to new information when they face greater adverse-selection costs. Both »ar and »d are positively related to the market value of equity in all regressions. This result is consistent with a number of prior research, for example, Lin and Rozeff (1995), Chordia et al. (2008). We interpret the results as evidence that information is less available for small firm. Both »ar and »d are not significantly related to the number of market makers for NASDAQ stocks. We interpret this result as evidence that the prevalence of order preferencing on NASDAQ leads to incompetent NASDAQ dealer. Both »ar and »d are negatively related to the percentage quoted spread in all regressions. We interpret the results as strong evidence that illiquidity hinders arbitrage activity, thus slows down price discovery. The results of the second-pass regressions regressing »ar and »d on effective spread model (see Panel B) are generally similar to those in Panel A. For example, both »ar and »d are positively related to number of trade, share price, return volatility, and adverse selection costs, but negatively related to trade size, and effective spread. These results indicate that our results are not sensitive to how we measure the illiquidity, i.e., whether we measure spreads using quoted prices or actual transaction prices. 5.3. Relative price efficiency between NYSE and NASDAQ stocks: a robustness check In the last section, we showed that the price efficiency of NYSE stocks is higher than that of NASDAQ stocks and attributed this result to the differences in market structure between the NYSE and NASDAQ. However, it’s possible that the difference in the price efficiency across the stock markets is simply due to the differences in stock characteristics across the two markets. For example, as we have shown in section 4, NYSE stocks have higher share prices, larger trade size and number of trades, lower return volatility, larger market capitalization, smaller spreads, and smaller depths.In this section, we examine whether the result can be explained by differences in stock attributes between the two markets. To test whether price efficiency are higher on the NYSE after controlling for differences in stock attributes between the two markets, we estimate the following cross-sectional regression model using the pooled sample of NYSE and NASDAQ stocks:  EMBED Equation.3 ; (14)where NYSE is a dummy variable which equals one for NYSE stocks and zero for NASDAQ stocks and all other variables are the same as previously defined.The last four columns of Table 3 show the regression results. Panels A and B show that estimated coefficients on the NYSE dummy variable are positive and significant in all but one regression, indicating that prices are more efficient on NYSE than that on NASDAQ. This result confirms our earlier finding that the different price efficiencies between NYSE and NASDAQ stocks are not entirely due to differences in stock attributes between the two samples. At least part of the difference could be due to the structural differences (such as order preferencing on NASDAQ and NYSE specialists’ interaction with floor traders and NYSE’s central order book) between the two markets.5.4. Tick size versus price efficiency To examine our hypothesis 6, we perform an event study with the decimalization as the study event. For NYSE stocks, we consider the three-month period from May 28, 2000 to August 27, 2000 as the pre-decimal period and January 30, 2001 to April 29, 2001 as the post-decimal period. For NASDAQ stocks, we consider the three-month period from December 12, 2000 to March 11, 2001 as the pre-decimal period and April 10, 2001 to July 9, 2001 as the post-decimal period. For each NYSE and NASDAQ stock, we first estimate the partial adjustment coefficients (À) during the pre- and post-decimal periods, with the partial adjustment approach and Dimson beta approach, respectively. We then calculate the mean partial adjustment coefficient during the pre- and post-decimal periods within each market and each approach. Similarly, we calculate the mean value of »ar and »d during the pre- and post-decimal periods within each market.Table 4 shows that for NYSE stocks, the mean partial adjustment coefficient (À) in the partial adjustment (Dimson beta) model is 0.8815 (0.3921) during the pre-decimal period and 0.8821 (0.5015) during the post-decimal period. The differences are significant at the 1% level for the Dimson beta model. For NASDAQ stocks, the mean partial adjustment coefficients in the partial adjustment (Dimson beta) model is 0.5911 (0.4284) during the pre-decimal period and 0.7724 (0.4564) during the post-decimal period. The differences are all significant at the 1% level. Similarly, the mean price efficiency measures (»d and »ar) during the post-decimal period are significantly greater than the corresponding figure during the pre-decimal period for both NYSE and NASDAQ stocks. These results indicate that liquidity suppliers in both markets make faster price adjustments after decimalization, which supports our hypothesis 6.Although the results in Table 4 suggest greater price efficiency after decimalization, it is possible that the results are driven by differences in the trading environments between the two periods rather than different tick sizes per se. To examine this possibility, we estimate the following regression model: EMBED Equation.3 (15)where " denotes the difference between the post- and pre-decimal values (post  pre) and all other variables are the same as previously defined. If the increases in the price adjustment speed shown in Table 4 are indeed due to the smaller tick size (rather than due to concurrent changes in stock attributes), we expect the estimated intercept (i.e.,  EMBED Equation.3 ) in regression model (14) to be positive and significant.Panel A of Table 5 shows the results of regression model (15) for NYSE stocks and Panel B shows the results for NASDAQ stocks. In both panels, the first four columns show the regression results using percentage spread to measure illiquidity. The next four columns show the regression results using effective spread to measure illiquidity. As in Table 3, we estimate the model using the weighted regression procedure, where the weight is the mean value of the reciprocal of the standard error of partial adjustment coefficients from the pre-decimal period and the corresponding value from the post-decimal period. The results show that the estimated intercepts are all positive and significant in most regressions for both the NYSE and NASDAQ samples. Thus, greater price efficiency during the post-decimal period cannot be attributed to the differences in trading environments between the pre and post decimal periods. We interpret this result as indirect evidence that illiquidity create market frictions and delay price discovery because tick size reduction enhances liquidity.5.5 Variance ratio test: a robustness checkIn this section, we present our results on the variance test as a robustness check. As we illustrate in section 3, the variance of long-horizon returns is q times the variance of short horizon returns, where q is the number of short horizon intervals in the longer horizon. In computing this variance ratio, the five-minute return variance is multiplied by the number of five-minute intervals in a trading day. For a random walk, this scaled variance ratio would converge to one in large samples. Table 6 shows the correlation among our three price efficiency estimator. They are all strongly positively correlated with each other. It’s of interest to explore the patterns in the liquidity–efficiency relations across groups categorized by firm liquidity. Table 7 shows results for subsamples formed by ranking firms by their liquidity measurement, for example, percentage spread, dividing the ranked firms into thirds. We find that all of the three price efficiency estimators show a monotonic decline with the decline in the liquidity measurement, indicating that the prices for the most liquid firms conform more closely to random walks. The evidence is consistent with our hypothesis that deviations from random walk benchmarks should be reduced when markets are more liquid. 6. Summary and concluding remarksThe present study expands the literature by providing evidence on how liquidity, market structure, tick size, and stock attributes jointly determine individual stocks’ price efficiency. We employ two distinct approaches, partial adjustment model and Dimson beta model, to investigate the price efficiency. We show stocks with better liquidity provision, more frequent trading, greater return volatility, higher prices, larger market capitalizations, and smaller trade sizes exhibit higher level of market efficiency. Market efficiency also varies with information environment. We find that stocks with greater information-based trading exhibit higher level of efficiency. NYSE stocks achieve higher level of efficiency than NASDAQ stocks do. Market efficiency improves after decimalization in both markets. We interpret this result as indirect evidence that illiquidity create market frictions and delay price discovery because tick size reduction enhances liquidity. 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We measure firm size by the average market value of equity during the study period. We measure the dollar quoted spread of each stock at time t by Askt – Bidt, and percentage spread by (Askt – Bidt)/Mt; where Askt is the ask price, Bidt is the bid price, and Mt is the mean of Askt and Bidt. The quoted spread is the implicit trading cost for market orders when a trade occurs at the quoted price with no price improvement. To measure the cost of trading when it occurs at prices inside the posted bid and ask quotes, we also measure the effective spread at time t by 2Qt (Pt – Mt)/Mt; where Pt is the transaction price at time t, Mt is the midpoint of the most recently posted bid and ask quotes for the stock, and  EMBED Equation.3 equals 1 for buyer-initiated trades and –1 for seller-initiated trades. We measure the quoted depth of each stock by the combined quoted depth at the bid and ask in round lots. Panel B shows descriptive statistics on 686 matched pairs of NYSE and NASDAQ stocks. We obtain matched samples of NYSE and NASDAQ stocks that are similar in trade size, price, return volatility, and market capitalization. We first calculate the matching score (MS) for each NYSE stock against each of the 2,270 NASDAQ stocks in our study sample: MS =  EMBED Equation.3 , where Xi represents one of the four stock attributes (i.e., PRICE, MVE, TSIZE and RISK), superscripts N and T, refer to NYSE and NASDAQ, respectively; and £ denotes the summation over i = 1 to 4. Then, for each NYSE stock, we select the NASDAQ stock with the smallest MS. Panel A: Whole sample____________________________________________________________________________________________________________________________________ Percentile Standard ________________________________________________________________ Exchange Mean deviation 5 25 50 75 95 ____________________________________________________________________________________________________________________________________Share price NYSE 36.85 37.86 7.99 17.28 29.86 47.69 82.23(PRICE) NASDAQ 20.46 20.13 3.33 7.95 15.90 27.23 50.91Number of trades NYSE 4,102.68 6,732.36 42.49 565.56 1,909.20 4,527.89 16,624.26(NTRADE) NASDAQ 2,444.68 6,509.48 42.93 211.56 747.24 2,009.33 9,661.59Trade size ($) NYSE 15,596.78 16,077.87 2,887.36 6,150.59 10,505.87 19,018.07 43,779.02(TSIZE) NASDAQ 5,539.28 34,365.40 1,298.80 3703.43 4,068.59 7,163.40 20,269.40Risk NYSE 0.0005 0.0005 0.0001 0.0002 0.0003 0.0006 0.0014(RISK) NASDAQ 0.0011 0.0012 0.0002 0.0004 0.0007 0.0014 0.0035Market value (in million) NYSE 7,911.65 23,739.03 147.48 6,07.59 1,741.16 5,220.38 31,012.70(MVE) NASDAQ 1,562.71 8,744.85 46.74 166.39 374.81 857.90 4,299.04 Quoted spread NYSE 0.0260 0.0430 0.0107 0.0138 0.0184 0.0276 0.0552 (QS) NASDAQ 0.0363 0.0547 0.0105 0.0158 0.0236 0.0401 0.0905Percentage spread NYSE 0.0011 0.0010 0.0002 0.0004 0.0006 0.0014 0.0031(PS) NSADAQ 0.0029 0.0033 0.0004 0.0009 0.0017 0.0036 0.0095Effective spread NYSE 0.0005 0.0004 0.0002 0.0003 0.0004 0.0007 0.0016(ES) NASDAQ 0.0026 0.0023 0.0005 0.0009 0.0018 0.0036 0.0071Depth NYSE 18.06 46.57 5.05 6.65 8.77 14.94 45.05 (DEPTH) NASDAQ 27.10 185.49 4.11 5.82 8.18 13.76 66.17 Panel B: Matched sample____________________________________________________________________________________________________________________________________ Percentile Standard ___________________________________________________________________ Exchange Mean deviation 5 25 50 75 95 ____________________________________________________________________________________________________________________________________Share price NYSE 21.39 15.57 5.42 11.93 16.58 26.42 50.52(PRICE) NASDAQ 19.22 13.69 5.34 10.57 15.84 23.80 45.33Trade size ($) NYSE 8,635.14 10,304.52 1,925.51 4,171.32 6,327.15 9,317.96 23,288.22(TSIZE) NASDAQ 11,158.22 14,397.11 1,998.60 4,405.12 7,374.81 12,032.18 34,207.04Risk NYSE 0.0009 0.0006 0.0003 0.0005 0.0007 0.0011 0.0020(RISK) NASDAQ 0.0010 0.0006 0.0003 0.0006 0.0009 0.0012 0.0020Market value (in million) NYSE 6,767.92 7,624.75 943.67 2,261.30 4,175.01 8,417.51 22,326.27(MVE) NASDAQ 4,861.74 5,288.84 939.47 2,063.51 3,154.31 5,408.94 14,975.06Quoted spread NYSE 0.0315 0.0237 0.0118 0.0174 0.0253 0.0371 0.0705 (QS) NASDAQ 0.0374 0.0368 0.0129 0.0198 0.0274 0.0427 0.0837Percentage spread NYSE 0.0019 0.0013 0.0005 0.0010 0.0016 0.0024 0.0044(PS) NSADAQ 0.0024 0.0017 0.0007 0.0013 0.0019 0.0029 0.0054Effective spread NYSE 0.0017 0.0009 0.0008 0.0011 0.0015 0.0020 0.0032(ES) NASDAQ 0.0025 0.0014 0.0008 0.0013 0.0022 0.0032 0.0049Depth NYSE 16.78 33.68 5.15 7.21 10.77 19.59 35.79(DEPTH) NASDAQ 9.12 11.79 3.94 5.19 6.73 9.22 20.56____________________________________________________________________________________________________________________________________ Table 2Price efficiency for NYSE and NASDAQ stocksThis table shows the mean values of partial adjustment coefficients (À) and the mean values of price adjustment speeds, and whether the difference in the mean value between NYSE and NASDAQ stocks is statistically significant. We estimate À and » using the ARMA model and Dimson beta approach, respectively. Panels A shows the results from the whole study sample of NYSE and NASDAQ stocks and Panel B shows the results from the matched sample of NYSE and NASDAQ stocks. Panel A: Whole sample _____________________________________________________________________________________________________________________________________________ ARMA model Dimson Beta model ______________________________________________________________________________________________________________________________________________ NYSE NASDAQ Difference (t-value) NYSE NASDAQ Difference (t-value) ______________________________________________________________________________________________________________________________________________ EMBED Equation.3  0.8530 0.7219 0.1311** (8.09) 0.4942 0.5061 -0.0119* (-2.00) » 0.6155 0.5090 0.1065** (9.85) 0.3840 0.3422 0.0418** (10.21) Panel B: Matched sample _____________________________________________________________________________________________________________________________________________ ARMA model Dimson Beta model ______________________________________________________________________________________________________________________________________________ NYSE NASDAQ Difference (t-value) NYSE NASDAQ Difference (t-value)______________________________________________________________________________________________________________________________________________ EMBED Equation.3  0.8743 0.6608 0.2135** (9.07) 0.5126 0.4960 0.0166 (1.45) » 0.7676 0.4657 0.3019** (18.20) 0.3463 0.3387 0.0076 (0.99) **Significant at the 1% level.*Significant at the 5% level. Table 3Price efficiency and stock attributesThis table shows the results of the following regression model:  EMBED Equation.3 Where »d/ »ar are the measures of the price efficiency, EMBED Equation.3  (i = 1 to 5) is one of the five stock attributes (i.e., NTRADE, TSIZE, PRICE, RISK and MVE), measured daily or in five-minute interval, respectively, £ denotes the summation over i = 1 to 5, ²0 through ²9 are the regression coefficients, and  EMBED Equation.3  is the error term. GKN denotes the adverse-selection component of the spread estimated from the method in George, Kaul and Nimalendran (1991), GH denotes the adverse-selection component of the spread estimated from the method in Glosten and Harris (1988), PIN is the probability of information-based trading, PS and ES denote percentage quoted spread and effective spread respectively, and MM is the number of marketmakers for NASDAQ stocks. We estimate the model using the weighted regression procedure, in which the weight is the reciprocal of the standard error of the partial adjustment coefficient. Panel A shows the results of the second-pass regressions using »d and »ar values that are estimated from the percentage quoted spread model, Panel B shows the results of the second-pass regressions using »d and »ar values that are estimated from the effective spread model. Within each panel, the first four columns show the results for NYSE stocks, the next four columns show the results for NASDAQ stocks, and the last four columns show the results for the combined sample of NYSE and NASDAQ stocks. Numbers in parentheses are t-statistics. Table 3 (continued)Price efficiency and stock attributesPanel A: Quoted percentage spread model______________________________________________________________________________________________________ NYSE NASDAQ Combined »d »d »ar »ar »d »d »ar »ar »d »d »ar »ar Intercept 0.2601** 0.1174* 0.4056** 0.7045** 0.1542* 0.0408* 0.2565 0.3889 0.2054** 0.0389 -0.0865 0.0271 (8.12) (2.08) (6.59) (9.04) (2.53) (0.59) (0.92) (1.37) (6.86) (1.03) (-0.94) (1.78)Log(NTRADE) 0.0278** 0.0370* 0.0637** 0.0296** 0.0043 0.0087 0.0510** 0.0489** 0.0152** 0.0216** 0.0684** 0.0455** (8.75) (10.78) (3.29) (3.09) (0.73) (1.44) (3.83) (3.65) (5.84) (7.90) (5.60) (3.44)Log(TSIZE) -0.0374** -0.0241** -0.0828** -0.1101** -0.0022 -0.0003 -0.1111** -0.1140** -0.0106** -0.0076** -0.0900** -0.0994** (-6.82) (-4.17) (-10.33) (-12.18) (-0.40) (-0.05) (-8.92) (-9.04) (-3.64) (-2.59) (-16.59) (-17.15)Log(PRICE) 0.0389** 0.0143* 0.2221** 0.1198** 0.0104 -0.0048 0.1709** 0.1585** 0.0250** 0.0059 0.1695** 0.1243** (6.43) (2.02) (13.18) (5.21) (1.43) (-0.57) (10.37) (8.27) (6.12) (1.21) (15.46) (8.44)RISK 3.10 31.95 15.44 9.41 3.93 -9.23 89.86** 101.14** 11.41 4.26 38.84** 58.14** (0.19) (1.95) (0.62) (0.38) (0.35) (-0.77) (4.53) (4.66) (1.35) (0.49) (2.62) (3.78)Log(MVE) 0.0023 0.0066 0.0065 0.0030 0.0228** 0.0279** 0.0731** 0.0694** 0.0067* 0.0129** 0.0422** 0.0341** (0.66) (1.84) (0.65) (0.30) (3.06) (4.81) (6.13) (5.67) (2.24) (4.21) (6.04) (4.76)GKN 0.0020 0.0090 0.0037 -0.0021 0.0003 0.0053 (1.25) (1.81) (0.80) (-0.18) (0.21) (1.13)GH 0.3527** 0.8908** 0.2537** 0.1852 0.3093** 0.4691** (6.62) (6.42) (3.45) (1.28) (7.18) (4.62)PIN 0.0259 0.0568 -0.0141 -0.1306 0.0553 -0.0158 0.3069** 0.2883** 0.0066 0.0406 0.1657* 0.1013 (0.68) (1.50) (-0.13) (-1.25) (1.21) (-0.33) (3.06) (2.84) (0.22) (1.34) (2.33) (1.40)Log(MM) 0.0331* 0.0359* 0.0115 0.0077 (1.97) (2.14) (0.32) (0.21)PS -4.78** -19.95* -45.66** -53.62** -7.67* -3.59 -10.47 -13.72 -9.20** -3.59 -1.84* -6.77** (-3.56) (-2.31) (-2.93) (-3.47) (-2.11) (-0.94) (-1.58) (-1.93) (-3.17) (-1.21) (-2.34) (-3.24)NYSE 0.0068* 0.0048** 0.1756** 0.1800** (2.16) (2.84) (15.09) (15.46)F–value 37.26** 43.42** 134.00** 141.63** 27.71** 29.11** 103.00** 103.26** 61.44** 68.00** 235.43** 238.91**Adjusted R2 0.1395 0.1594 0.3766 0.3898 0.1072 0.1122 0.3170 0.3175 0.1254 0.1372 0.3607 0.3641 **Significant at the 1% level.*Significant at the 5% level. Table 3 (continued)Price efficiency and stock attributesPanel B: Effective spread model______________________________________________________________________________________________________ NYSE NASDAQ Combined »d »d »ar »ar »d »d »ar »ar »d »d »ar »ar Intercept 0.3649** 0.1485** 0.4482** 0.6258** 0.1951** 0.0710 0.4092 0.4175 0.2159** 0.0459 -0.0823 0.0051 (8.34) (2.70) (7.03) (9.37) (3.24) (0.99) (0.87) (0.83) (7.27) (1.20) (-0.90) (1.84)Log(NTRADE) 0.0286** 0.0342** 0.0641** 0.0035 0.0079 0.0107 0.0517** 0.0513** 0.0181** 0.0227** 0.0678** 0.0440** (8.21) (9.58) (3.34) (0.16) (1.33) (1.78) (3.88) (3.80) (6.54) (8.03) (5.56) (3.31)Log(TSIZE) -0.0366** -0.0229**-0.0627** -0.0886** -0.0037 -0.0012 -0.1151** -0.1151** -0.0135** -0.0088** -0.0896** -0.0980** (-6.77) (-3.98) (-7.50) (-9.61) (-0.65) (-0.12) (-9.04) (-9.04) (-4.49) (-2.89) (-15.92) (-16.55)Log(PRICE) 0.0374** 0.0091 0.2070** 0.1028** 0.0132 0.0028 0.1599** 0.1584** 0.0305** 0.0084 0.1685** 0.1216** (7.14) (1.32) (13.36) (4.60) (1.90) (0.33) (10.13) (8.26) (7.85) (1.69) (15.99) (8.25)RISK 8.54 5.06 5.1227 12.03 1.41 6.84 39.46* 40.29* 6.72 5.53 37.92** 51.47** (0.75) (0.44) (0.26) (0.60) (1.17) (0.77) (2.49) (2.41) (1.03) (0.82) (3.15) (4.16)Log(MVE) 0.0017 0.0069 0.0018 0.0115 0.0215** 0.0269** 0.0718** 0.0713** 0.0054 0.0123** 0.0420** 0.0334** (0.45) (1.84) (0.18) (1.15) (3.85) (4.64) (6.04) (5.82) (1.83) (4.00) (6.04) (4.66)GKN 0.0020 0.0098* 0.0037 0.0021 0.0003 0.0053 (1.31) (1.98) (0.81) (0.18) (0.19) (1.13)GH 0.3280** 0.8794** 0.2384** 0.0207 0.3040** 0.4589** (6.22) (6.41) (3.27) (0.15) (6.98) (4.56)PIN 0.0569 0.0548 0.0812 0.0358 0.0179 0.0066 0.2371* 0.2364* 0.0210 0.0514 0.1724* 0.1203 (1.45) (1.44) (0.77) (0.34) (0.37) (0.14) (2.24) (2.23) (0.68) (1.66) (2.32) (1.61)Log(MM) 0.0449** 0.0427* 0.0070 0.0069 (2.66) (2.54) (0.19) (0.19)ES -3.58** -3.12** -77.48** -79.54** -10.30** -6.76 -14.43 -14.12 -9.85** -4.12* -2.07* -5.78** (-2.71) (-3.61) (-5.85) (-6.08) (-2.82) (-1.77) (-1.90) (-1.80) (-3.67) (-2.48) (2.37) (-4.01)NYSE 0.0092 0.0.059* 0.1757** 0.1810** (1.57) (2.01) (15.23) (15.64)F–value 37.29** 42.68** 139.14** 146.71** 28.14** 29.40** 103.19** 103.19** 61.88** 68.09** 235.43** 238.82**Adjusted R2 0.1396 0.1571 0.3856 0.3983 0.1087 0.1132 0.3174 0.3174 0.1262 0.1373 0.3607 0.3640 **Significant at the 1% level.*Significant at the 5% level. Table 4Comparisons of price efficiency between the pre- and post-decimal periodsThis table shows the mean value of partial adjustment coefficients (À) and the mean value of price adjustment speeds for our study sample of NYSE and NASDAQ stocks, respectively, and the results of t-tests on whether the difference in the mean value between the pre- and post-decimal periods within each market is statistically significant. Panel A shows the results for NYSE stocks and Panel B shows the results for NASDAQ stocks. For NYSE stocks, we consider the three-month period from May 28, 2000 to August 27, 2000 as the pre-decimal period and January 30, 2001 to April 29, 2001 as the post-decimal period. For NASDAQ stocks, we consider the three-month period from December 12, 2000 to March 11, 2001 as the pre-decimal period and April 10, 2001 to July 9, 2001 as the post-decimal period. Panel A: NYSE ______________________________________________________________________________________________________________________________________________ ARMA model Dimson Beta model ______________________________________________________________________________________________________________________________________________ Pre Post Difference (t-value) Pre Post Difference (t-value) ______________________________________________________________________________________________________________________________________________ EMBED Equation.3  0.8815 0.8821 0.0006 (0.05) 0.3921 0.5015 0.1094** (11.41) » 0.7297 0.7302 0.0005 (0.06) 0.2695 0.3456 0.0761** (12.79) Panel B: NASD _____________________________________________________________________________________________________________________________________________ ARMA model Dimson Beta model ______________________________________________________________________________________________________________________________________________ Pre Post Difference (t-value) Pre Post Difference (t-value) ______________________________________________________________________________________________________________________________________________ EMBED Equation.3  0.5911 0.7724 0.1813** (7.73) 0.4284 0.4564 0.0280** (3.55) » 0.3680 0.5185 0.1505** (10.70) 0.3252 0.3301 0.0049 (0.93) **Significant at the 1% level.*Significant at the 5% level. 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h�rmhÔ:r>*B*CJaJph#h�rmhÔ:r>*B*CJH*aJph%N'N+N.N0N4N=NyNzN{N’N¢N£NÍNÎNïSðSïÞͼ«Íœ�~ocToH9*h�rmhÔ>B*CJaJphh�rmhÔ>B*CJaJphh«0B*CJaJphh�rmh$âB*CJaJphh$âB*CJaJphh�rmh…OÌB*CJaJphh�rmh…OÌB*CJaJphh�rmh«0B*CJaJphh�rmh«0B*CJaJph h�rmh¦,¥>*B*CJaJph h�rmh‹$¥>*B*CJaJph h�rmhÔ:r>*B*CJaJph h�rmh>A>*B*CJaJph h�rmh0bp>*B*CJaJphðST‘TªTµTˆVŠV°V²V´V¶VÀVÄVÌVÚVâVòVüVWWWW&W.WFWPWVW`WxW€WŽWðáÒÇÒ²¡„m²¡Ò^Ò^Ò^Ò^ÒOÒOÒOÒOÒ^Òh�rmhÞ0ÃB*CJaJphh�rmh}B*CJaJph-jFnh�rmhBø5�B*CJEHúÿUaJph8j?j_I h�rmhBøB*CJPJUVaJnHphtH h�rmhBø5�B*CJaJph)jh�rmhBø5�B*CJUaJphh�rmhBøCJaJh�rmhBøB*CJaJphh�rmh8C±B*CJaJphh�rmh…OÌB*CJaJphŽW–WªW®W²W´W¸WÀWÎWÖWâWæWXX XXÑXÜXÖZØZþZ[[[[Z[f[n[v[~[˜[¢[¦[®[Â[ \\\\ðáðÒðáðáÒáÒáÒáÒáËá¶¥ˆq¶¥ðábábábábáðábáh�rmh×]ñB*CJaJph-j:ph�rmhBø5�B*CJEHúÿUaJph8j?j_I h�rmhBøB*CJPJUVaJnHphtH h�rmhBø5�B*CJaJph)jh�rmhBø5�B*CJUaJph h�rmhBøh�rmhÞ0ÃB*CJaJphh�rmhBøB*CJaJphh�rmh}B*CJaJph&X,X»XéXˆYÝY¶[;\<\[\y\ƒ\Ó\Ô\]-]´§¶§öíÜÓÂÓ½¬£½½½½žžž½gdÔ>„äÿ]„äÿgd$jJ„äÿ&dPÆÿ]„äÿgd$jJgd$jJ„àþ„P„ ]„àþ^„P`„ gd"y„àþ]„àþgd$jJ„çþ„ „ ]„çþ^„ `„ gd"y„Sÿ]„Sÿgd$jJ„Lÿ]„Lÿgd$jJ\\+\1\2\6\;\<\y\z\ \°\±\Ó\Ô\]])]*]+],]°^ðáðáðáÒôè™Ã�~j~T>j~*j.rh�rmhÔ>B*CJEHäÿUaJph+j¾}áK h�rmhÔ>CJKHPJUVaJ&jh�rmhÔ>B*CJUaJphh�rmhÔ>B*CJaJphh…OÌB*CJaJphh�rmh$âB*CJaJphh$âB*CJaJphh�rmh…OÌB*CJaJphh�rmh…OÌB*CJaJphh�rmhBøB*CJaJphh�rmhBøB*CJaJphh�rmh×]ñB*CJaJph°^´^¶^¾^ _"_H_J_L_N_` ^ ` t v À  è ê ì î Ȧ̦ΦÖ¦²§ðáðáÍᮘÍá–á…á…áÍáfPÍáðáðá*jËwh�rmhÔ>B*CJEHúÿUaJph<jÂ_I h�rmhÔ>B*CJKHPJUVaJnHphtH h�rmhÔ>B*CJH*aJphU*jÆuh�rmhÔ>B*CJEHöÿUaJph<j³_I h�rmhÔ>B*CJKHPJUVaJnHphtH&jh�rmhÔ>B*CJUaJphh�rmhÔ>B*CJaJphh�rmhÔ>B*CJaJphVE), £ denotes the summation over i = 1 to 5, ²0 through ²9 are the regression coefficients, and EMBED Equation.3 is an error term. GKN denotes the adverse-selection component of the spread estimated from the method in George, Kaul and Nimalendran (1991), GH denotes the adverse-selection component of the spread estimated from the method in Glosten and Harris (1988), PIN is the probability of information-based trading, PS and ES denote percentage quoted spread and effective spread respectively, and MM is the number of market-makers for NASDAQ stocks. We estimate the model using the weighted regression procedure, in which the weight is the reciprocal of the standard error of the partial adjustment coefficient. Panel A shows the results for NYSE stocks and Panel B shows the results for NASDAQ stocks. In each panel, we show the regression results using »d/ »ar values that are estimated from ARMA model, and the Dimson Beta model. Numbers in parentheses are t-statistics Table 5 (continued)Effects of decimalization on price efficiency for NYSE stocks and NASDAQ stocksPanel A: NYSE stocks__________________________________________________________________________________________ Quoted percentage spread model Effective spread model »d »d »ar »ar »d »d »ar »ar Intercept 0.0454** 0.0615** 0.0507* 0.0860** 0.0462** 0.0622** 0.0503* 0.0852** (4.40) (6.92) (2.55) (5.02) (4.50) (7.04) (2.54) (4.99)  EMBED Equation.3 Log(NTRADE) 0.0207 0.0163 0.0418 0.0324 0.0213 0.0169 0.0410 0.0317 (1.46) (1.15) (1.53) (1.19) (1.51) (1.20) (1.51) (1.17)  EMBED Equation.3 Log(TSIZE) 0.0034 0.0038 -0.0191 -0.0184 0.0034 0.0038 -0.0191 -0.0184 (0.33) (0.36) (-0.95) (-0.91) (0.32) (0.36) (-0.94) (-0.90)  EMBED Equation.3 log(PRICE) -0.0285 -0.0323 0.1719* 0.1631* -0.0268 -0.0309 0.1710* 0.1616* (-0.76) (-0.86) (2.39) (2.24) (-0.72) (-0.82) (2.38) (2.22)  EMBED Equation.3 RISK 0.6874* -0.1973 -0.3546 0.7314 0.6976** -0.2007 -0.3602 0.7346 (2.46) (-0.78) (-0.66) (1.50) (2.49) (-0.79) (-0.67) (1.50)  EMBED Equation.3 Log(MVE) 0.0537 0.0564 -0.0648 -0.0586 0.0558 0.0579 -0.0648 -0.0601 (1.35) (1.41) (-0.84) (-0.76) (1.40) (1.45) (-0.84) (-0.78)  EMBED Equation.3 GKN 0.2611** 0.5786** 0.2630** 0.5797** (4.16) (4.78) (4.18) (4.78)  EMBED Equation.3 GH 0.1461** 0.3278** 0.1466** 0.33272** (3.01) (3.49) (3.02) (3.49)  EMBED Equation.3 PIN -0.0272 -0.0315 -0.0311 -0.0407 -0.0285 -0.0324 0.0311 -0.0397 (-0.57) (-0.66) (-0.34) (-0.44) (-0.60) (-0.67) (-0.34) (-0.43)  EMBED Equation.3 PS -0.4189 -0.6446 1.2802 0.7797 (-0.28) (-0.43) (0.44) (0.27)  EMBED Equation.3 ES -0.5769 -0.4366 2.9546 0.7189 (-0.15) (-0.11) (0.39) (0.10) F value 3.75** 2.71** 6.05* 4.69** 3.74** 2.68** 6.05** 4.69** Adjusted R2 0.0196 0.0123 0.0354 0.0262 0.0196 0.0121 0.0354 0.0261 **Significant at the 1% level.*Significant at the 5% level. Table 5 (continued)Effects of decimalization on price efficiency for NYSE stocks and NASDAQ stocksPanel B: NASDAQ stocks__________________________________________________________________________________________ Quoted percentage spread model Effective spread model »d »d »ar »ar »d »d »ar »ar Intercept 0.0333** 0.0307** 0.0051 0.0077 0.0330** 0.0304** 0.0009 0.0032 (3.84) (3.42) (0.33) (0.49) (3.80) (3.37) (0.06) (0.20)  EMBED Equation.3 Log(NTRADE) -0.0079 -0.0137 0.0470* 0.0708** -0.0096 -0.0158 0.0451 0.0690** (-0.59) (-1.04) (2.01) (3.04) (-0.73) (-1.21) (1.95) (3.01)  EMBED Equation.3 Log(TSIZE) -0.0070 -0.0072 -0.0083 -0.0082 -0.0066 -0.0069 -0.0075 -0.0074 (-0.86) (-0.89) (-0.59) (-0.57) (-0.81) (-0.84) (-0.53) (-0.52)  EMBED Equation.3 log(PRICE) 0.0095 0.0184 0.0605 0.0339 0.0094 0.0192 0.0574 0.0323 (0.20) (0.38) (0.72) (0.40) (0.21) (0.40) (0.68) (0.38)  EMBED Equation.3 RISK -26.63 -22.57 50.83* 33.18 -25.46 -20.81 64.27** 44.07 (-1.96) (-1.68) (2.13) (1.41) (-1.88) (-1.57) (2.71) (1.89)  EMBED Equation.3 Log(MVE) 0.0245 0.0196 -0.0597 -0.0489 0.0251 0.0201 -0.0592 -0.0493 (0.52) (0.41) (-0.72) (-0.59) (0.53) (0.42) (-0.71) (-0.59)  EMBED Equation.3 GKN 0.0135 -0.2364 0.0219 -0.2748* (0.18) (-1.77) (0.28) (-2.02)  EMBED Equation.3 GH -0.2092 0.3664 -0.2118 0.3094 (-1.06) (1.06) (-1.08) (0.89)  EMBED Equation.3 PIN 0.0608 0.0600 0.0103 0.0128 0.0607 0.0599 0.0118 0.0140 (1.44) (1.42) (0.14) (0.17) (1.44) (1.42) (0.16) (0.19)  EMBED Equation.3 PS -7.7729** -6.8288* 5.8739 2.0553 (-2.68) (-2.36) (1.15) (0.40)  EMBED Equation.3 ES -17.74** -15.17* 22.47 11.93 (-2.58) (-2.24) (1.86) (1.00)  EMBED Equation.3 MM -0.0148 -0.0105 -0.0239 -0.0285 -0.0110 -0.0073 -0.0289 -0.0295 (-0.28) (-0.20) (-0.26) (-0.31) (-0.21) (-0.14) (0.31) (-0.32) F value 1.54 1.67 1.69 1.46 1.49 1.61 1.93* 1.56 Adjusted R2 0.0045 0.0056 0.0057 0.0039 0.0041 0.0051 0.0077 0.0047 **Significant at the 1% level.*Significant at the 5% level. Table 6Correlation among the three price efficiency estimatorsThis table shows how the correlation among the three price efficiency estimators. Number in the parenthesis shows the associated p-value. _______________________________________________________________________________ »d »ar »var_______________________________________________________________________________»d 0.1685** 0.1818** (0.0001) (0.0001)»ar 0.1685** 0.1123** (0.0001) (0.0001)»var 0.1818** 0.1123** (0.0001) (0.0001)_______________________________________________________________________________ **Significant at the 1% level. Table 7 Liquidity-efficiency relationsThis table shows the price efficiency patterns in liquidity categorized subsamples. We first rank our whole sample according the percentage spread into three groups. Then we calculate the mean values of the three price efficiency measures within each group, respectively, and the results of t-tests on whether the difference in the mean value between the three liquidity ranked subsamples is statistically significant. ______________________________________________________________________________________________________________________________________________ Most liquid firms Liquid firms Illiquid firms______________________________________________________________________________________________________________________________________________ Coefficient Difference (t-value) Coefficient Difference (t-value) Coefficient Difference (t-value)______________________________________________________________________________________________________________________________________________ »d 0.4521 0.0203** (8.01) 0.4318 0.0689++ (16.38) 0.3629 0.0892## (22.71)»ar 0.7065 0.1280** (12.38) 0.5785 0.0133 (1.25) 0.5652 0.1413## (14.05)»var 0.7215 0.2106** (5.73) 0.5109 0.1701++ (3.01) 0.3408 0.3807## (7.83)______________________________________________________________________________________________________________________________________________ ** 1% significant between the most liquid firms and the liquid firms++ 1% significant between the liquid firms and the illiquid firms## 1% significant between the illiquid firms and the most liquid firms*Contact information: Department of Finance & Managerial Economics, State University of New York, Buffalo, NY 14260. E-mail:  HYPERLINK "mailto:jjiang2@buffalo.edu" jjiang2@buffalo.edu. I am especially indebted to Kee Chung for many years of fruitful collaboration, discussion, and guidance. I am also grateful to Kenneth Kim, Joseph Ogden, Hao Zhang, Yang Cao for helpful comments and advice. All remaining errors are mine. © 2009 by Jing Jiang. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit is given to the source.  Beja and Goldman (1980) analyze the dynamics of asset prices using a partial adjustment model. Jones and Lipson (1999) show that quotes in NYSE- and AMEX-listed stocks adjust more quickly to the information contained in order flow than quotes in NASDAQ-listed stocks. Theissen (2000) finds that transaction prices in call and continuous auction markets are more efficient than prices in dealer markets. In contrast, Masulis and Shivakumar (2002) show that price adjustments are faster on NASDAQ than on the NYSE. Benveniste, Marcus, and Wilhelm (1992) note that NYSE specialists have continuous face-to-face contact with floor brokers while such contact is not available to NASDAQ dealers because NASDAQ operates on an electronic screen-based system. None of our study sample of stocks violated this condition. When it s greater than one, it falls into over-reaction scenario. Specifically, we multiply each estimated coefficient by the ratio of its own 1/SE to the sum of 1/SE across all NYSE (or NASDAQ) stocks in our study sample and then add up these  weighted coefficients across stocks in each market.  Our results also indicate that the mean value of À (») estimates is significantly different from one for partial adjustment model and 0.5 for Dimson beta model, for both NYSE and NASDAQ stocks Although NASDAQ uses the same volume counting rules as the NYSE, the reported number of trades on NASDAQ is not directly comparable to that on the NYSE because there are many interdealer trades and dealer-to-customer interactions on NASDAQ. Hence, we do not use the number of trades as a matching variable. Bessembinder (2003a) shows that making no allowances for trade-reporting lags is optimal when assessing whether trades are buyer or seller initiated. A trade at the quote mid-point is classified as seller-initiated if the mid-point moved down from the previous trade, and buyer-initiated if the mid-point moved up. If there were no price movements from the previous price, we apply the above algorithm to as many as four additional previous quotes. If we still could not determine the trade direction, we exclude the trade from the sample. The NYSE initiated a pilot decimalization program on August 28, 2000 and converted all 3,525 listed issues to decimal pricing on January 29, 2001. The NASDAQ Stock Market began its decimal test phase with 14 securities on March 12, 2001, followed by another 197 securities on March 26, 2001. All remaining NASDAQ securities converted to decimal trading on April 9, 2001. 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