Juan C Reboredo
email: juancarlos.reboredo@usc.es

Lluís Brú

José M Ortiz Repiso

José A Pérez

Roberto Pascual

Mikel Tapia

The Switch from Continuous to Call Auction Trading in Response to a Large Intraday Price Movement

Keywords: price volatility, Call auction trading, price discovery, volatility auctions Call auction trading, price discovery, price volatility, volatility auctions

Some European exchanges (e.g. Euronext, Frankfurt and Madrid) make use of a mechanism to moderate price volatility that was proposed by Madhavan (1992, Journal of Finance, 47(2) 607-641) as preferable to a trading halt in times of market stress. It consists of a temporary switch from continuous to call auction trading in an individual security whenever its price moves beyond predetermined limits. This paper studies whether this mechanism sharpens the information content of prices, dampens volatility, and normalizes trading volume and intensity. Taking intraday data for the Madrid order-driven continuous market, I find post-switch improvements in the information content of prices and reductions in volatility, especially for thinly traded stocks. Trading volume and intensity peaked around auctions, but soon returned to pre-event levels.

Introduction

Most stock exchanges around the world, and all continuous trading systems, make use of market control mechanisms devised to moderate excessive price volatility, allow the fair distribution of information to all market participants, and maintain an orderly market. 1 Informational asymmetries and/or diversity of opinion can be pronounced with the arrival of new information in the market, or even when there is a marked imbalance between supply and demand. The most widespread control mechanism is a temporary halt in trading of an individual stock, which can be triggered discretionally by a supervisory committee in response to the stock's market conditions (e.g. violation of exchange rules, rumour, news releases or order imbalance), or automatically whenever an attempt is made to trade the stock at a price outside a pre-determined percentage or point variation from the previous day's close. 2 The former approach is employed by the New York Stock Exchange (NYSE) and Nasdaq, the latter by Tokyo, Taiwan and US futures markets.

The effects of suspending trade in individual stocks, however the trading halt is triggered, have been extensively discussed in the literature. Greenwald andStein (1988, 1991) argue that, in a continuous trading system, an abnormal increase in price volatility discourages traders from participating in the market, and that trading halts should restore normality by facilitating price discovery. In keeping with this hypothesis, [START_REF] Corwin | Order flow and liquidity around NYSE trading halts[END_REF] found that during NYSE trading halts investors adjust their positions by submission and cancellation of orders. Similarly, [START_REF] Edelen | The role of trading halts in monitoring a specialist market[END_REF] found that trading halts, which were preceded by increased informational asymmetry between the exchange and specialists regarding the quoted price schedule, reduced agency costs associated with the organization of the exchange market. [START_REF] Kodres | The existence of Pareto superior price limits[END_REF] argue that imposing limits on price movements can reduce investment risk, since in times of marked 1 See [START_REF] Galper | Management of market volatility: A report to the FIBV working committee for the focus group study[END_REF] 2 For reviews of the trading halt literature see [START_REF] Kyle | Trading halts and price limits[END_REF], [START_REF] France | A review of regulatory mechanisms to control the volatility of prices[END_REF], [START_REF] Harris | Circuit breakers and program trading limits: What we have learned?[END_REF], and [START_REF] Kim | What makes circuit breakers attractive to financial markets? A survey[END_REF]. 5 rather than price jumps. There are several potentially important differences between the temporary auction and the temporary trading halt. First, unlike trading halts, auctions do not suspend trading altogether, and should thus avoid delay in price discovery in circumstances in which sufficient information is available but is initially unevenly distributed. Second, discretionary trading halts can be imposed in anticipation of relevant news before prices become jumpy; indeed, most NYSE trading halts occur before news events [START_REF] Lee | Volume, volatility, and New York Stock Exchange trading halts[END_REF][START_REF] Corwin | Order flow and liquidity around NYSE trading halts[END_REF], whereas temporary auctions seem often to occur as a result of price jumps following news events (see Section 3 below). Third, the switch to auction trading is rule-based and is therefore predictable.

Fourth, the duration of temporary auctions is fixed and much shorter than that of trading halts (between 5 and 5½ minutes in Madrid), which is likely to affect the behaviour of investors both during and following the call auction. Related to this, fifth, the temporary auction does not limit the daily movement of prices, at least in Madrid, where the price limits triggering it are updated when it ends. Notwithstanding, it should be borne in mind that some of these differences can be blurred in mixed systems; on the NYSE, for example, call auctions are held at the end of trading halts before continuous trading recommences.

Theoretical studies suggest that, relative to continuous trading systems, pure call auction systems enhance price discovery [START_REF] Economides | Electronic call market trading[END_REF][START_REF] Handa | How best to supply liquidity to a securities market[END_REF], reduce volatility (as order arrival time does not affect prices) [START_REF] Schwartz | The call auction alternative[END_REF], and in conditions of informational asymmetry result in liquidity traders incurring lower adverse selection costs [START_REF] Kyle | Continuous auctions and insider trading[END_REF][START_REF] Pagano | Transparency and liquidity: A comparison of auction and dealer markets with informed trading[END_REF]. These predictions are supported by the results of simulations [START_REF] Schnitzlein | Call and continuous trading mechanisms under asymmetric information: An experimental investigation[END_REF][START_REF] Theissen | Market structure, information efficiency and liquidity: An experimental comparison of auction and dealer markets[END_REF]. Empirically, call auctions have been found to be efficient price discovery mechanisms by [START_REF] Amihud | Volatility, efficiency and trading: Evidence from the Japanese stock market[END_REF], [START_REF] Stoll | Stock market structure and volatility[END_REF], [START_REF] Amihud | Stock market microstructure and return volatility: Evidence from Italy[END_REF], and [START_REF] Pagano | A closing call's impact on market quality at Euronext Paris[END_REF]. However, there has been little empirical evidence concerning the effectiveness of temporary call auction trading as a mechanism to F o r P e e r R e v i e w 6 control a primarily continuous market. The validity of the above results in this situation is in practice not immediately obvious, because price-triggered temporary call auctions are often "blind", i.e. they are conducted without letting traders see other orders or the evolution of the market-clearing price, so forcing them to obtain information from outside the order book. This paper examines empirically the impact of the switch to call auction trading on market quality for stocks traded on the Spanish Stock Exchange (SSE), a computerized, order-driven continuous market in which attempted sharp price movements trigger short, blind call auctions termed "volatility auctions". Specifically, I study a series of 543 such auctions to determine whether this mechanism delays or favours price discovery, whether it exacerbates or dampens volatility and bid-ask spread, and whether it affects trading volume and intensity. To this end I compare the data for these auctions with those of a series of reference events in which a price movement approached the auction-triggering limit but did not quite reach it. I find evidence that pre-auction continuous trading prices are biased estimators of the value of the security, whereas the auction and post-auction prices of less-liquid stocks show no statistically significant bias and, like those of more-liquid stocks, are more stable than those of reference events. In keeping with this result, I find that the volatility of stocks as measured by absolute price changes and price standard deviation is significantly more depressed after call auctions than after reference events (which contrasts with the persistent high levels of volatility reported to follow trading halts on the NYSE [START_REF] Lee | Volume, volatility, and New York Stock Exchange trading halts[END_REF][START_REF] Fong | New York Exchange trading halts and volatility[END_REF][START_REF] Corwin | Order flow and liquidity around NYSE trading halts[END_REF], intraday trading halts on Nasdaq [START_REF] Christie | Nasdaq trading halts: The impact of market mechanisms on prices, trading activity, and execution cost[END_REF], and the execution of price limits on the Tokyo exchange [START_REF] Kim | Price limit performance: Evidence from the Tokyo Stock Exchange[END_REF]. The finding that bid-ask spread is unusually wide in the minutes immediately preceding a volatility auction but not in the minutes preceding reference events suggests that triggering volatility auctions by price is more or less equivalent to triggering them by bid-ask spread, as originally proposed by [START_REF] Madhavan | Trading mechanisms in securities markets[END_REF]. Finally, share trading volume and the number of transactions, which tend to increase rapidly F o r P e e r R e v i e w 7 prior to volatility auctions and reference events, appear to return to normal more smoothly following an auction than following a reference event.

The rest of this paper is organized as follows: Section 2 sketches the operational organization of the SSE and its volatility auctions, Section 3 describes the data used, Section 4 describes methodology and reports and discusses results. Section 5 concludes.

SSE operational details

The SSE is a computerized, order-driven continuous market in which liquidity is provided by an open limit order book. The market operates 3 from 08:30 to 17:35 hours, Monday to Friday, opening with a half-hour call auction during which orders can be placed, modified or cancelled but not executed. Three types of orders are permitted: market orders, which are dealt with by walking up or down the book until totally executed; limit orders, which are executed by walking the order book subject to the specified limit, any unexecuted remnant being left on the order book with the same limit; and best price orders, which are executed at the best price available when placed, any unexecuted remnant being left on the order book with that price as limit. During the opening call auction the order book is not made public to market participants, but for each stock the marketclearing price (the price at which trading volume would be greatest) 4 is updated and publicized in real time together with the associated virtual trading volume. The auction terminates at a random instant within a 30-second period, after which orders are matched at the current market-clearing prices (which are taken as the day's opening prices) and continuous trading commences, all orders Volatility auctions replaced price limits as a market control mechanism on 14 May 2001, as part of the harmonization of trading systems in Europe. According to the Spanish Market Control Commission, their purpose is to ensure that significant price fluctuations only occur with the involvement of a large number of market participants. Accordingly, they are designed to give market participants time to digest information without closing down trade altogether. They are triggered whenever an attempt is made to trade a security at a price outside either of two publicly assigned price ranges (hereinafter "price collars"). The "dynamic" price collar of a stock is centred on the price of the latest trade, and its width (1%, 1.5%, 2%, 2.5%, 3%, 3.5%, 4% or 8% of that price) is revised every six months on the basis of the history of intraday price fluctuations of the stock. This collar prevents large intraday discontinuities in price. The "static" price collar is centred on the price arising from the latest call auction (be it the opening auction or a volatility auction), and its width (4%, 5%, 6%, 7%, 8% or 10% of that price) is likewise revised every six months, but on the basis of the history of day-to-day price fluctuations. This collar thus limits price movements relative to the Volatility auctions last 5 minutes plus the usual random end period of up to 30 seconds.

During the auction traders can submit, cancel or modify orders, but no trade is executed, and traders do not have access to the order book, the current virtual market-clearing price, or the trading volume.

They thus receive no feedback on the impact of their orders on price, a provision which, together with the short duration of the auction, is intended to minimize the temptation to try to distort the information content of the resolution price by submitting fake orders that are later withdrawn. At the end of the volatility auction, orders are matched at the consensus market-clearing price, the collars are updated, and continuous trading resumes.

Data

I studied 543 volatility auctions that occurred between May 2001 and January 2002. Since the intraday pre-auction and post-auction behaviour of these stocks were to be examined, only auctions preceded and followed by 30 minutes' uninterrupted continuous trading were considered (in particular, all auctions considered occurred between 09:30 and 17:00 hours). For each auction, the following information was obtained: its date; the times (to the second) of its commencement and termination; the resulting consensus price and associated trade volume; the opening and closing prices of the stock concerned on that day; and the bid and ask prices, transaction prices and volumes, and static and dynamic collars of the stock in the half-hours preceding and following the auction. For each volatility auction, two sets of analogous reference data were assembled for the purposes of comparison. One, intended to capture the normal trading behaviour of the stock involved (and hereinafter referred to as the "normal reference set"), consisted of data for it for the same 65-minute periods of the 10 days preceding and the 10 days following the day of the auction. The other comprised data for that occasion, within the same month as the auction, on which the price of the stock had most nearly breached one of its collars without actually doing so (in case of ties, the occasion that was closest to the auction in date and time of day was used). For the sake of brevity, in most of this paper only results obtained using this second, "volatile" reference sample are presented; results obtained with the normal reference sample (available upon request) lead to conclusions consistent with those based on the volatile reference sample. All data were provided by the Market Control Commission of the SSE.

To characterize the volatility auctions in terms of the causes of the volatility triggering them, four kinds of cause were considered: uncertainty prior to the announcement of firm-specific news (the commonest cause of trading halts on the NYSE [START_REF] Lee | Volume, volatility, and New York Stock Exchange trading halts[END_REF][START_REF] Corwin | Order flow and liquidity around NYSE trading halts[END_REF]; uncertainty in the wake of "official" firm-specific news announced by the Spanish stock market regulatory body, the National Stock market Commission; uncertainty in the wake of other publicly announced firm-specific news; and uncertainty of a market-wide nature, such as might be generated by macroeconomic announcements. About 50% of auctions were classified as due to market-wide uncertainty because they occurred on the same day as, or on the day following, news of macroeconomic relevance; most of these auctions occurred in September 2001 in the aftermath of the attack on the Twin Towers (see Fig. 1A). Another 40% of auctions were regarded as due to uncertainty following "unofficial" firm-specific news because they occurred on the same day as, or the day following, the appearance of a relevant announcement in at least one of the two major Spanish financial newspapers. A much smaller number of auctions, 6%, were classified as due to 11 uncertainty generated by "official" firm-specific news because they occurred on the same day as an announcement concerning the firm in question by the National Stockmarket Commission; and only 0.2% were attributed to pending news because they occurred on the day before a firm-specific National Stockmarket Commission announcement. Finally, about 4% of auctions satisfied none of the above criteria; the attempted price movements triggering these auctions may have been due to order imbalance, large uninformed orders, or even typing mistakes. We assume that the distribution of reference events by apparent cause is similar to that of the auctions.

Most of the stocks involved in volatility auctions (63%) were not contributors to IBEX-35, the market index based on the most actively traded SSE stocks. Some 58% of auctions were triggered by attempted excursion outside the static price collar, and 42% by attempted excursion outside the dynamic price collar. There were greater numbers of auctions on Monday and Friday than on mid-week days (Fig. 1B), which may be attributed to the effect of weekend stock return variations, and proportionately more auctions in the first half-hour or so following 09:30, i.e. during the post-opening peak in market activity, than at other times of day (Fig. 1C).

[INSERT FIGURE 1 HERE]

To investigate whether pre-and/or post-auction stock behaviour might depend on various characteristics of the stocks or market circumstances, analyses were performed both for the whole sample and for various subsamples. Specifically, the subsamples considered were auctions involving Table 1 summarizes, for both the whole sample and the IBEX-35 subset, the statistical distributions of the associated closing price, the inside bid-ask spread immediately before the switch, and the number of shares traded and number of transactions on the day of the switch. As expected, the most liquid values have a narrower bid-ask spread (by about a factor of 2) and are more active in terms of both the number of shares and the number of trades. Also, the distribution of various characteristics of the stocks involved in an auction shows that there is a considerable variation among them.

[INSERT TABLE 1 HERE]

Methods and Results

Price Discovery

To analyse whether volatility auctions facilitate price discovery, in this section I examine prices P t before and after auctions and reference events. 7 Specifically, I examine the last price in successive 5-minute intervals measured backwards from the time of the auction start or reference event (t = -6,...,-1) and forward from the resumption of continuous trading or reference event (t = 1,...,6) (in the case of auctions, the re-opening price is also considered). Like [START_REF] Biais | Price discovery and learning during the preopening period in the Paris Bourse[END_REF] in their study of price discovery and learning during the opening call auction on the Paris Bourse, I identify the equilibrium price to be discovered on day T with the closing price (P T ), take 6 Parallel analyses were also carried out for subsamples defined by whether the auction-resolving price was higher or lower than the price in the last transaction before the auction. No asymmetry was found between these two subsamples as regards the behaviour of price discovery, price volatility, bid-ask spread or trading volume and intensity (results available on request). 7 Unfortunately it has not been possible to gain access to data allowing analysis of the progress of learning during volatility auctions. 13 the previous day's closing price (P T-1 ) as a proxy for the pre-session expectation of the equilibrium price, and consider returns from the previous close rather than raw prices so as to correct for heteroscedasticity. I first examine, for each t, whether the approximate return from the previous close, x t = ln(P t /P T-1 ) differed significantly from the approximate close-to-close return x T = ln(P T /P T-1 ), to which end I apply the signed-rank test to the set of 543 return ratios y i,t = x i,t /x i , T (i = 1,...543) for the null hypothesis

H 0 : M t = 1, (1)
where M t is the population median return ratio at time t. If the call auction leads to price discovery, H 0 should not be rejected for t ≥ 0, but might be for t < 0. Even if H 0 were rejected for all t, a degree of price discovery would be indicated by the estimate of M t being significantly closer to unity for t ≥ 0 than for t < 0. If H 0 were rejected for t ≥ 0 but not for t < 0, the inference would be that the call auction distorts price discovery.

Figure 2, which plots the sample medians of the y i,t , shows that return ratios y i,t generally underwent a substantial increase as a result of the volatility auction, which suggests that the auction led to price learning. Furthermore, return ratios remained stable and close to unity in the half-hour following the auction, showing the continued validity of what had been learnt. By contrast, they differed appreciably from unity during most of the half-hour preceding the auction, though they did tend to rise towards the end of this period. The signed rank test results listed in Column 2 of Table 2 (Panel A) endorse these observations, H 0 (eq. 1) being rejected at all times prior to the switch but not in the quarter-hour following the resumption of trading (and although H 0 is rejected between 20 and 30 minutes after resumption, absolute z values remain smaller than before the switch). Panels B and C of Column 2 confirm that return ratio medians differed significantly in all before-after comparisons (including comparison of mean-over-time pre-auction y i,t with mean-over-time postresumption y i,t ; see Panel C), and also during the pre-auction period, but not during the post- As was noted in the previous section, most of the volatility auctions in the sample occurred following the announcement of macroeconomic or firm-specific news. The pre-and post-auction behaviour pattern described above suggests that, in general, the new information was successfully incorporated into prices by the end of the auction. However, since price discovery actually appears to have begun before the auction (see Fig. 2), the question arises whether it would have been just as efficient, or perhaps even more so, in the absence of the latter. Analysis of the data for reference events (Table 3) shows: 1) that return ratios half-an-hour before the event were significantly less than unity but greater than half-an-hour before auctions; 2) that during the half-hour preceding the event return ratios rose steadily to nearly unity (whereas pre-auction return ratios rose to a median value of 0.84); and 3) that during the following half-hour return ratios remained close to unity on average, but fluctuated much more than after auctions. This behaviour suggests that larger, auctiontriggering price jumps occurred in the final phases of a faster, accelerating process of information assimilation, and that although auctions certainly did not interrupt this process, their chief effect was to dampen subsequent uncertainty.

F

[INSERT TABLE 3 HERE]

As a rather different test of the existence of price discovery, I also performed a regression analysis based on the same assumption as was made by [START_REF] Biais | Price discovery and learning during the preopening period in the Paris Bourse[END_REF]

ε δ β ω δ β α +         + - +         + = ∑ ∑ = - - = (2)
where i denotes the switch event (i = 1,...543), D t is a dummy variable taking the value 1 if t < 0 and zero otherwise, and δ t is a dummy variable taking the value 1 at t and zero otherwise. A non- significant β t for all t < 0 means that before the call auction the information content of prices remains constant and equal to α, the return ratio 30 minutes before the switch. Similarly, a non-significant β t for all t > 0 means that after the call auction the information content of prices remains constant and equal to ω, the return ratio arising from the call auction. To determine whether prices at time t differed from the true value of the stock, the hypotheses tested were

H 0 : α + β t = 1 (t < 0) and H 0 : ω + β t = 1 (t > 0) (3)
Table 4, Column 3 shows that H 0 was rejected before the call but not after the resumption of continuous trading. The results of an analogous analysis of the reference data are likewise consistent with the results shown in Table 3 and commented on above.

[INSERT TABLE 4 HERE]

The above results show rapid price adjustment and subsequent stability in the 30 minutes following the resolution of call auctions. This finding contrasts with the evidence of erratic prices following trading halts in markets such as Nasdaq [START_REF] Christie | Nasdaq trading halts: The impact of market mechanisms on prices, trading activity, and execution cost[END_REF].

To check on the scope of the above results, their validity was investigated for subsamples representing various different conditions of liquidity, market volatility and time of day, and for the subsamples composed of auctions triggered by static and dynamic price collars (see Tables 234).

Although the returns on IBEX-35 shares differed significantly from the close-to-close returns at all times except immediately before and immediately after the auction, they rose during the preauction period and throughout the post-auction period remained stable at about 15% below the closeto-close returns (Table 2,Column 3 return to have already occurred, to within statistical significance, prior to the auction, and to have been maintained thereafter, although the means of the y i,t were slightly depressed by the auction and did not regain values close to unity until 10 minutes later.

In September and October 2001 the market was especially volatile. However, comparison of Columns 2 and 4 of Tables 2 and4, shows that this general volatility hardly influenced the behaviour of the return ratios of auctioned shares in the half-hours preceding and following volatility auctions.

Comparison of Columns 5, 6 and 7 of Table 2 shows that the return ratios of shares involved in pre-midday volatility auctions were considerably more depressed, prior to the auction, than those auctioned later in the day, and were more benefited by the auction. Returns following pre-midday auctions were stable, but median values remained 10-15% below the close-to-close return. The returns of shares involved in auctions between midday and mid-afternoon were much better predictors of close-to-close return: the median return ratios rose from 0.68 to 0.84 before the auction, and after it remained within 5% of unity (within 2%, once the first 10 minutes had elapsed). The statistical behaviour of the returns of shares involved in auctions later than mid-afternoon was very similar to that of the full sample (Column 2). These trends are echoed by the regression results (Table 4, Columns 8-13): of all the subsets of the full sample considered in Table 4, the pre-midday auctions are the only ones for which some of the post-auction β t differ significantly from zero.

The main return ratio trends commented on above (a rise before auctions and as the result of the auction, followed by the maintenance of values near unity over the next half hour) were also independent of whether it was the static or dynamic collar of the share that was responsible for the auction being triggered (see the final columns of Tables 2 and4). However, when the auction was triggered by the dynamic collar, post-auction return ratios were considerably smaller than when it was triggered by the static collar, around 0.86 as against 0.96.

Price Volatility

In this subsection I analyse the impact of the call auction on volatility. [START_REF] Economides | How to enhance market liquidity[END_REF] and [START_REF] Schwartz | The call auction alternative[END_REF] argue that concentrating liquidity at a single point in time reduces volatility because order arrival time does not affect prices. SSE call auctions, which are triggered during continuous trading as a result of large price changes, provide an opportunity to test this conclusion.

I measure price volatility in the half-hours preceding and following the switch in terms of a) the absolute percentage change between the first and last trading prices, and b) the standard deviation of trading prices. First, for both the auction sample and the reference sample, I compare pre-and post-event price volatility by applying the signed rank test to the after/before ratio; I then evaluate the statistical significance of differences between the two samples by applying the same test to the ratio of ratios.

According to both measures of price volatility, volatility was significantly less in the halfhour following volatility auctions than in the half-hour preceding them (Table 5, Column 2). Median post-event volatility was also less than pre-event volatility in the reference sample, but in this case the difference was not statistically significant. Furthermore, in keeping with the above results on price discovery, the proportional decrease in volatility following auctions was significantly greater than the proportional decrease following reference events (third lines of Panels A and B of Table 5).

This behaviour contrasts with reports that volatility rises to anomalously high and persistent levels following trading halts on the NYSE [START_REF] Lee | Volume, volatility, and New York Stock Exchange trading halts[END_REF][START_REF] Fong | New York Exchange trading halts and volatility[END_REF][START_REF] Corwin | Order flow and liquidity around NYSE trading halts[END_REF], intraday trading halts on Nasdaq [START_REF] Christie | Nasdaq trading halts: The impact of market mechanisms on prices, trading activity, and execution cost[END_REF], and the execution of price limits on the Tokyo exchange [START_REF] Kim | Price limit performance: Evidence from the Tokyo Stock Exchange[END_REF].

Similar behaviour was shown by the various subsamples considered. In particular, although for IBEX-35 stocks the before-after difference for reference events was statistically significant (this difference from the full sample probably being attributable to the greater liquidity of the market F o r P e e r R e v i e w 18 index stocks), the reduction in liquidity for these stocks was, as in the full sample, significantly greater following auctions than following reference events.

[ INSERT TABLE 5 HERE]

Bid-ask Spread

The effect of volatility auctions on bid-ask spread was investigated by examining the normalised bid-ask spread in successive 5-minute intervals in the half-hours preceding and following the auction. Normalized bid-ask spread was defined as (P ask -P bid )/0.5(P ask +P bid ), where P ask and P bid are the best ask and bid prices on the limit order book at the end of the 5-minute period in question.

Figure 3 shows that median normalized 5-minute bid-ask spreads tended to rise in the 10 or 15 minutes preceding a volatility auction and became even higher immediately following the auction.

Though they tended to fall thereafter, half-an-hour after the auction they were still considerably higher than half-an-hour before it.

[INSERT FIGURE 3 HERE]

To evaluate the statistical significance of the above trends, the panel data model Panel A of Table 7 lists the results of signed rank tests confirming that the bid-ask spread was relatively large immediately before and after auctions but not at other times. Specifically, spread was significantly greater in the 5 minutes preceding the auction than half-an-hour earlier, and significantly greater in the 5 minutes following the auction than 15 or 30 minutes after the resumption of continuous trading; but there was no significant difference between immediately preand post-auction spread values, or between values recorded 15 or 30 minutes before and after the auction.

Fig. 3 shows that bid-ask spreads were relatively stable before reference events and slightly higher immediately following them. To compare this behaviour with that seen around volatility auctions, a paired-sample signed rank test was performed for each 5-minute interval. The results (values in parentheses in Panel B of Table 7) show that, compared with reference values, spreads were significantly larger immediately before auctions and throughout the following half hour. In fact, spreads narrowed more slowly after auctions than after reference events, as is shown by the median excess values

Auction value Reference value

Reference value 100

  -      
(the values not shown in parentheses in Panel B), spreads narrowed more slowly after auctions than after reference events.

In general, the behaviour described above was also exhibited by the various subsamples that were considered: in almost all cases, bid-ask spread was wider in the 5 or 10 minutes prior to the auction than at earlier times, and remained wide or even increased during at least the first 5 minutes following the auction, after which it narrowed (Tables 6 and7). In the "normal" reference sample, The pre-auction rise in bid-ask spread suggests the effect of an information shock, and means that the volatility auctions considered here, which were triggered by attempted excursion of trading prices outside their constraining collars, would also have been activated by triggers defined in terms of the bid-ask spread exceeding a threshold based on trading volume and the bid-ask spread history of the stock, as proposed by [START_REF] Madhavan | Trading mechanisms in securities markets[END_REF].

Trading Volume and Intensity

The abnormally high trading volumes observed in the 30 minutes following trading halts on Nasdaq and the NYSE [START_REF] Lee | Volume, volatility, and New York Stock Exchange trading halts[END_REF][START_REF] Corwin | Order flow and liquidity around NYSE trading halts[END_REF][START_REF] Christie | Nasdaq trading halts: The impact of market mechanisms on prices, trading activity, and execution cost[END_REF] suggest that medium-run trading vigour is unaffected by the halt mechanism regardless of market structure. In this subsection I employ the same tests as in the analysis of bid-ask spread to study whether trading vigour, as reflected by the total volume of shares traded and the number of transactions (both expressed as a percentage of the totals for the day), is affected by volatility auctions on the SSE.

Share trading volume tended to increase rapidly in the 15-20 minutes prior to volatility auctions, especially in the immediately preceding 5 minutes, but within half-an-hour returned to levels similar to those observed half-an-hour before the auction (Fig. 4). This rise and fall in trading volume around the switch is corroborated by the pairwise comparisons of volume listed in Table 8 (Column 2, Panel A) and by the regression test results (Table 9, Column 2), although the increase in volume was only statistically significant during the auction and in the preceding 5 minutes. Much the same trends were observed in the various subsamples considered, except that the peak in trading Median reference values fluctuated widely on a 10-20-minute time scale both before and after the reference event (Fig. 4). The nearly auction-triggering price jump constituting the event was associated with a particularly high median trading volume peak, but this peak did not stand out much from the general large variability, which contrasted both with the smooth rise and fall of median trading volume that was seen around auctions, and with the behaviour of the "normal" reference sample, in which median trading volume remained throughout close to the values shown by the auction sample half-an-hour before and after the auction (results available on request). Except at the re-opening of continuous trading, paired-sample signed rank tests showed either no significant difference between the auction sample and the volatile reference sample, or that auction sample volumes were significantly lower than reference volumes (Table 8, Panel B); in particular auction sample volumes were significantly lower than reference volumes throughout the 20 minutes before the auction.

When trading activity is measured in terms of the number of trades, the same patterns are observed as when the measure is trading volume (see Fig. 5 and Tables 10 and11).

In keeping with the results on price discovery and volatility, these results suggest that the assimilation of new information via auctions results in smoother trading behaviour than its assimilation in the absence of an auction.

[

Conclusions

The above analysis of data for 543 five-minute, price-triggered switches from continuous to call auction trading on the SSE shows that these events are preceded by an abnormal widening of bid-ask spread. In general, they would therefore have been equally triggered by this parameter, which was the switch-activating trigger originally proposed by Madhavan.

When the day's closing price is used as a proxy for equilibrium price, comparison of price discovery data around volatility auctions with those for reference events (in which auctions were almost but not quite triggered) suggests that auctions are triggered when a rush to capitalize on new information makes its assimilation into prices especially rapid, and that the chief effect of auctions is to dampen subsequent nervousness. In keeping with this interpretation, the proportional decrease in volatility following volatility auctions is significantly greater than following reference events, and the evolution of trading volume and the number of transactions is smoother around auctions than around reference events.

The above trends contrast with those observed in connection with trading halts on the NYSE and Nasdaq [START_REF] Lee | Volume, volatility, and New York Stock Exchange trading halts[END_REF][START_REF] Corwin | Order flow and liquidity around NYSE trading halts[END_REF][START_REF] Christie | Nasdaq trading halts: The impact of market mechanisms on prices, trading activity, and execution cost[END_REF], where price volatility, bid-ask spread and trading volume all tend to remain high following trading halts. However, these differences in behaviour are difficult to interpret because the structural and operational differences between these exchanges and the SSE are numerous. Median normalized bid-ask spreads, (P asked -P bid )/0.5(P asked + P bid ), in successive 5-minute intervals in the half-hours preceding and following the auction, measured backwards from its start and forward from the resumption of continuous trading. The sample comprised 543 switch events that occurred on the SSE between May 2001 and January 2002. Analogous data for the reference sample are also shown. Median traded share volume (% of day's total) in successive 5-minute intervals in the half-hours preceding and following volatility auctions and reference events, measured backwards from the start of the auction or reference event and forward from the resumption of continuous trading. Median number of transactions (% of day's total) in successive 5-minute intervals in the half-hours preceding and following volatility auctions and reference events, measured backwards from the start of the auction or event and forward from the resumption of continuous trading.

ε δ β ω δ β α +         + - +         + = ∑ ∑ = - - =
, where i indexes the switch event (i = 1,…,543), t denotes successive 5-minute intervals in the half-hours preceding (t = -1,…,-6) and following the auction ( t = 0,1 , … , 6 ; the auction ends at t = 0), D t is a dummy variable taking the value 1 if t < 0 and zero otherwise, and t δ is a dummy variable taking the value 1 at t and zero otherwise. The dependent variable is the ratio ln(P t /P T-1 )/ln(P T /P T-1 ), where P t is the last trading price, P T is the closing price and

  auction that have not been executed remaining on the order book. Trading during the opening auction amounts to about 3% of total daily trade.During the continuous trading regime, which prioritizes orders primarily by price and secondarily by submission time (as, for example, at Frankfurt, Paris, Toronto and Tokyo), the five best positions of the order book on either side are accessible to market participants. Except for the 5-minute volatility auctions mentioned in the Introduction and described in detail below, continuous trading proceeds until 17:30 hours, when the day's closing prices are established by a 5-minute call auction similar to the opening auction (and likewise terminated at random within a period of 30 seconds).

  mediated consensus. By construction, the static price collar is always wider than the dynamic collar.5

  IBEX-35 stocks, to investigate the influence of liquidity; auctions occurring in September and October 2001, to investigate the influence of general market volatility, the market having been especially volatile in the aftermath of the Twin Towers attack; morning, early afternoon and late to investigate the influence of time of day; and auctions triggered by static and dynamic price collars, to investigate the influence of the scale of price fluctuations.6

  ). The regression results show convergence to the close-to-close

  ask spread remained throughout close to the value shown by the auction sample half-an-hour before the auction (results available on request).

  volume was comparatively flat and broad for IBEX-35 stocks (Column 3) and, to a lesser extent, in the static price collar (Column 8); while, on the contrary, the peak was confined to the auction itself in auctions triggered by the dynamic collar (Column 9), and to the 5 minutes preceding the auction in late afternoon events (Column 7), although trading volume in the latter was in fact quite irregular throughout the hour surrounding the auction.[INSERT FIGURE 4 HERE][INSERT TABLES 8 AND 9 HERE]

Figure 1 :Figure 2 :Figure 3 :

 123 Figure 1: Temporal Distribution of Volatility Auctions.

Figure 4 :

 4 Figure 4: Share Trading Volume Around Volatility Auctions and Reference Events.

Figure 5 :

 5 Figure 5: Number of Trades Around Volatility Auctions and Reference Events.

  , denotes the spread at time t in switch event i (i = 1,…,543; t as in Fig.3), d t is a dummy variable taking the value 1 at t and zero otherwise, β t is the slope coefficient at t, i is the error term. Significant values of the β t indicate significant changes in bid-ask spread. Column 2 of Table6shows that, by this criterion, bid-ask spread was significantly larger than pre-event values in the 10 minutes preceding and the 5 minutes following volatility auctions, but did not differ significantly from pre-event values at earlier or later times.

	[INSERT TABLES 6 AND 7 HERE]
	F o r
	P
	e
		e r
							R
									e
	y	, i t	=	α	i	+	t t	=-≠ ∑ 6 5 0	t t d β	, i t v ε + i e	(4)
	was fitted, where t i y α is the w
	fixed effect parameter, and t i,
							19

ε

Table 1 :

 1 Summary Statistics for Stocks involved in Volatility AuctionsDistribution quantiles of volatility auctions on the SSE (May 2001-January 2002) with regard to four characteristics of the stocks involved: closing price on the day of the switch (€), immediately pre-switch inside bid-ask spread (normalized by division by the midpoint of the spread), shares traded on the day (thousands), and transactions on the day.

	Page 33 of 44		Submitted Manuscript
		Price (€)	Bid-Ask Spread	Share Volume	Trades per Day
	Full Sample (n = 543)
	10 th Percentile	1.32	0.0022	22	24
	25 th Percentile	2.77	0.0028	63	51
	Median	7.75	0.0089	278	155
	75 th Percentile	13.65	0.0219	1,138	603
	90 th Percentile	20.02	0.0329	3,861	1,977
	Market Index Stocks (n = 203)
	10 th Percentile	4.65	0.0008	278	358
	25 th Percentile	6.42	0.0011	406	455
	Median	11.36	0.0038	1,238	710
	75 th Percentile	17.15	0.0101	3,861	1,954
	90 th Percentile	22.25	0.0175	26,716	4,466

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 2 :

 2 Results of Statistical Tests of Price Discovery Around Volatility Auctions.Panel A lists median values of the ratio ln(P t /P T-1 )/ln(P T /P T-1 ), where P T is closing price, P T-1 the previous closing price and P t the last trading price in successive 5-minute intervals in the half-hours preceding and following the auction, measured backwards from the time of its start and forward from the resumption of continuous trading; together with signed rank z values (asterisks indicate values that are significantly different from unity at the 5% level). Panel B lists signed rank z values for comparisons of the ratio ln(P t /P T-1 )/ln(P T /P T-1 ) at the pairs of times indicated in Column 1. Panel C lists median values of the mean ln(P t /P T-1 )/ln(P T /P T-1 ) ratio in the half hours preceding and following the auction, together with signed rank z values (asterisks indicate that post-auction values are significantly greater than pre-auction values at the 5% level). The sample consisted of 543 volatility auctions on the SSE between May 2001 and January 2002.

					Submitted Manuscript			Page 34 of 44
	Period	Full Sample (n = 543)	Market Index Stocks (n = 203)	September and October (n = 354)	Time of day: 9:30-12:00 (n = 201)	Time of day: 12:00-15:00 (n = 204)	Time of day: 15:00-17:00 (n = 138)	Triggered by Static Collar (n = 315)	Triggered by Dynamic Collar (n = 228)
	Panel A
	-6	0.58 (-10.32)*	0.59 (-6.10)*	0.57 (-7.50)*	0.42 (-6.54)*	0.68 (-5.16)*	0.57 (-6.22)*	0.60 (-10.37)*	0.56 (-4.04)*
	-5	0.59 (-10.10)*	0.62 (-5.30)*	0.59 (-7.32)*	0.45 (-6.75)*	0.67 (-5.16)*	0.63 (-5.47)*	0.62 (-9.58)*	0.56 (-4.27)*
	-4	0.63 (-9.65)*	0.69 (-4.60)*	0.63 (-7.07)*	0.50 (-6.51)*	0.70 (-4.96)*	0.68 (-5.04)*	0.64 (-9.65)*	0.63 (-3.91)*
	-3	0.67 (-8.38)*	0.69 (-4.52)*	0.68 (-5.74)*	0.55 (-5.44)*	0.76 (-4.29)*	0.73 (-4.72)*	0.69 (-8.43)*	0.63 (-3.27)*
	-2	0.75 (-7.06)*	0.78 (-3.39)*	0.75 (-4.71)*	0.60 (-4.25)*	0.80 (-3.86)*	0.79 (-3.94)*	0.75 (-7.49)*	0.78 (-2.40)*
	-1	0.84 (-4.24)*	0.87 (-1.58)	0.82 (-3.05)*	0.70 (-2.94)*	0.84 (-2.14)*	0.90 (-1.97)*	0.84 (-4.31)*	0.80 (-1.54)
	Switch
	Reopening	0.93 (-1.88)	0.86 (-1.70)	0.90 (-1.20)	0.87 (-2.04)*	0.95 (-0.19)	0.93 (-0.95)	0.96 (-0.80)	0.85 (-1.77)
	1	0.94 (-1.49)	0.82 (-2.45)*	0.94 (-0.76)	0.87 (-1.31)	0.97 (-0.27)	0.95 (-0.98)	0.97 (-0.43)	0.86 (-1.54)
	2	0.94 (-1.90)	0.84 (-2.17)*	0.94 (-1.09)	0.89 (-1.92)	0.99 (-0.46)	0.94 (-0.77)	0.99 (-0.88)	0.85 (-1.65)
	3	0.94 (-1.77)	0.84 (-2.28)*	0.94 (-0.90)	0.84 (-2.07)*	0.99(-0.21)	0.97 (-0.58)	0.96 (-0.94)	0.84 (-1.43)
	4	0.93 (-2.37)*	0.83 (-2.40)*	0.88 (-2.12)*	0.85 (-2.26)*	0.98 (-0.70)	0.92 (-0.98)	0.95 (-1.62)	0.86 (-1.71)
	5	0.94 (-2.35)*	0.86 (-2.40)*	0.90 (-1.78)	0.86 (-2.36)*	0.99 (-0.54)	0.95 (-1.04)	0.96 (-1.84)	0.88 (-1.42)
	6	0.94 (-2.01)*	0.84 (-2.79)*	0.88 (-1.45)	0.85 (-2.15)*	1.00 (-0.46)	0.94 (-0.61)	0.96 (-1.35)	0.88 (-1.43)
	Panel B
	-1,-3	(8.52)*	(6.29)*	(7.85)*	(5.03)*	(6.31)*	(6.11)*	(10.15)*	(2.59)*
	-1,-6	(10.77)*	(7.63)*	(8.63)*	(5.26)*	(6.96)*	(6.65)*	(10.99)*	(3.91)*
	1,3	(0.21)	(-0.13)	(0.07)	(0.26)	(0.54)	(-0.44)	(1.20)	(-0.96)
	1,6	(0.98)	(1.03)	(1.08)	(1.11)	(0.36)	(0.11)	(1.22)	(-0.78)
	1,-1	(3.77)*	(0.38)	(3.46)*	(1.17)	(3.52)*	(2.05)*	(2.91)*	(0.27)
	3,-3	(9.49)*	(5.29)*	(7.43)*	(4.16)*	(6.92)*	(5.63)*	(7.93)*	(2.84)*
	6,-6	(10.17)*	(6.39)*	(7.54)*	(4.91)*	(6.55)*	(6.50)*	(8.98)*	(3.80)*
	Panel C
	Mean test (after-before)	0.92-0.67 (9.47)*	0.85-0.71 (5.13)*	0.92-0.68 (7.20)*	0.84-0.56 (3.96)*	0.95-0.71 (6.84)*	0.94-0.71 (6.03)*	0.95-0.67 (10.78)* 0.84-0.69 (2.47)*
	Obs.	7059	2639	4602	2613	2652	1794	4095	2964

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 3 :

 3 Results of Statistical Tests of Price Discovery for the Reference Sample.Analyses analogous to those of Panel A of Table2.

	Period	Full Sample (n = 543)	Market Index Stocks (n = 203)	September and October (n = 354)	Time of day: 9:30-12:00 (n = 201)	Time of day: 12:00-15:00 (n = 204)	Time of day: 15:00-17:00 (n = 138)	Triggered by Static Collar (n = 315)	Triggered by Dynamic Collar (n = 228)
	-6	0.81 (-6.49)*	0.77 (-3.85)*	0.80 (-4.31)*	0.81 (-4.67)*	0.68 (-3.66)*	0.83 (-2.58)*	0.80 (-4.38)*	0.83 (-4.93)*
	-5	0.82 (-6.27)*	0.75 (-3.18)*	0.80 (-4.21)*	0.79 (-4.58)*	0.68 (-3.70)*	0.83 (-2.26)*	0.84 (-4.05)*	0.81 (-4.91)*
	-4	0.85 (-4.57)*	0.72 (-2.01)*	0.76 (-3.51)*	0.77 (-3.93)*	0.70 (-2.11)*	0.84 (-1.72)	0.90 (-2.76)*	0.82 (-3.82)*
	-3	0.89 (-3.25)*	0.83 (-0.90)	0.88 (-1.57)	0.88 (-3.01)*	0.78 (-1.67)	0.93 (-0.79)	0.95 (-1.88)	0.90 (-2.90)*
	-2	0.93 (-1.20)	0.81 (0.73)	0.86 (-0.44)	0.88 (-1.41)	0.81 (-0.68)	0.96 (0.29)	1.01 (-0.29)	0.91 (-1.65)
	-1	0.99 (1.21)	0.92 (-3.04)*	0.95 (1.42)	0.96 (0.17)	0.90 (0.92)	1.05 (3.12)*	1.12 (2.07)*	0.98 (0.83)
	1	1.10 (2.92)*	0.92 (-3.75)*	0.98 (1.37)	1.13 (2.36)*	1.05 (2.25)*	1.07 (5.16)*	1.09 (3.04)*	1.07 (2.47)*
	2	0.96 (-2.08)*	1.05 (-3.40)*	1.09 (4.32)*	0.93 (-1.98)*	0.95 (-2.26)*	1.20 (3.34)*	1.04 (3.38)*	0.96 (1.89)
	3	0.95 (-2.07)*	0.91 (-2.51)*	0.95 (-2.63)*	0.93 (1.94)	0.95 (-1.62)	1.02 (2.58)*	1.01 (2.55)*	0.94 (1.18)
	4	0.97 (1.71)	0.92 (-2.84)*	0.95 (-2.13)*	0.98 (0.30)	0.99 (1.95)	1.03 (2.45)*	1.02 (1.86)	0.96 (0.78)
	5	0.94 (-2.69)*	0.95 (1.16)*	1.01 (3.96)*	0.94 (-2.02)*	0.95 (-2.28)*	1.06 (2.75)*	1.05 (2.55)*	0.94 (0.91)
	6	1.00 (1.01)	0.90 (-2.35)*	0.95 (-2.20)*	1.01 (0.48)	1.01 (2.02)*	1.02 (2.25)*	1.03 (2.26)*	0.99 (-0.36)

Page 35 of 44 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	F o r P e e r R e v i e w
	36

Table 4 :

 4 Results of the Regression Test of Price Discovery Around Volatility Auctions. This table summarizes the results of fitting the panel data regression model

				1					6
	i y	,	t	t D	t	t	1 (	t D	)	t	t	i	,	t
				t	5				t	1

Page 38 of 44 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  P T-1 is the previous day's closing price. The table reports the estimated coefficients and the results of statistical tests of the null hypothesis that the return ratio y it, equals unity (F tests of H 0 : Asterisks indicate rejection of the null hypothesis at the 5% level using White robust standard errors.

									Submitted Manuscript
	H 0 : Panel B + t β ω for t=0). Period 1 = for 0 > t ; t tests of H 0 : 1 = α for t=-6 and of H 0 : 1 = ω Full Sample (n = 543) Market Index Stocks (n = 203) September and October (n = 354) Time of the day: 9:30-12:00 (n = 201) (H 0 : y i,t =1) (H 0 : y i,t =1) (H 0 : y i,t =1) (H 0 : y i,t =1) α 0.595 (-5.75)* 0.649 (-2.97)* 0.516 (-5.76)* 0.583 (-5.27)* 5 -β 0.035 (24.45)* 0.152 (3.95)* 0.021 (24.88)* -0.014 (33.22)* 4 -β 0.062 (21.11)* 0.157 (3.86)* 0.038 (23.23)* 0.030 (26.69)* 3 -β 0.094 (17.30)* 0.178 (3.23) 0.121 (15.48)* 0.062 (22.55)* 2 -β 0.204 (7.23)* 0.249 (0.50) 0.221 (8.14)* 0.138 (13.84)* 1 -β 0.269 (4.31)* 0.289 (0.20) 0.311 (3.92)* 0.232 (6.09)* 1,-1 (0.05) (1.38) (0.21) (-2.22)* 3,-3 (0.66) (1.46) (0.44) (-0.40) 6,-6 (0.92) (1.06) (-0.54) (-2.76)* -6 7.45 (1.12) 4.96 (1.04) 2.55 (1.30) 8.04 (2.32)* -5 5.65 (1.19) 5.65 (0.66) 3.99 (1.13) 6.60 (1.30) -4 7.17 (0.61) 6.18 (0.22) 6.62 (0.73) 9.80 (1.45) -3 7.42 (0.80) 5.20 (0.61) 5.41 (0.73) 8.16 (1.91) -2 7.54 (2.48)* 7.20 (0.64) 7.08 (1.28) 8.05 (1.97)* -1 7.52 (2.37)* 8.10 (1.66) 7.59 (2.01)* 11.15 (2.68)* Switch 1 7.67 (2.90)* 5.91 (2.17)* 8.35 (2.42)* 11.32 (3.04)* F o r P e e r R e v i e w Time of the day: 12:00-15:00 (n = 204) Time of the day: 15:00-17:00 (n = 138) (H 0 : y i,t =1) (H 0 : y i,t =1) 0.759 (-3.11)* 0.566 (-5.54)* -0.012 (12.10)* 0.022 (22.16)* -0.021 (12.91)* 0.077 (16.77)* -0.006 (11.45)* 0.173 (8.98)* 0.085 (4.47)* 0.233 (5.36)* 0.138 (1.97) 0.335 (1.29) (-2.22)* (1.05) (-0.40) (1.22) (-2.76) (0.81) 8.15 (-0.63) 7.10 (1.05) 6.61 (-0.33) 5.87 (0.19) 8.91 (0.21) 7.54 (0.20) 8.49 (1.05) 7.17 (0.81) 8.52 (1.84) 7.42 (0.66) 8.55 (1.86) 7.61 (0.11) 7.86 (2.43)* 7.67 (1.63)	1 Triggered by = + t β α Static Collar (n = 315) (H 0 : y i,t =1) 0.494 (-7.89)* for 0.034 (51.18)* 0.058 (46.72)* 0.152 (17.30)* 0.214 (21.67)* 0.293 (12.74)* (4.07)* (0.14) (-0.50) 0.15 (-0.91) 2.10 (-1.20) 3.46 (-0.45) 3.25 (0.27) 2.07 (1.16) 4.73 (4.41)* 4.29 (2.02)*	t	1 5 -,..., -Triggered by , and of Dynamic Collar = (n = 228) (H 0 : y i,t =1) 0.708 (-3.24)* -0.039 (14.17)* -0.002 (11.21)* 0.054 (7.37)* 0.142 (3.88)* 0.136 (3.29) (-3.61)* (0.75) (0.88) 7.07 (1.87) 5.87 (1.06) 7.06 (2.15)* 6.35 (1.59) 7.51 (3.32)* 7.52 (4.18)* 7.33 (6.17)*
	2 Switch ω 3	11.56 (2.98)* 0.954 (-0.51) 10.04 (2.18)*	7.98 (1.65) 0.888 (-0.77) 8.01 (1.15)	12.09 (2.38)* 0.936 (-0.64) 8.39 (2.55)*	12.06 (2.63)* 0.922 (-1.01) 13.10 (10.72)*	10.49 (2.67)* 1.072 (0.71) 11.29 (2.45)*	9.16 (1.34) 0.965 (-0.40) 9.95 (1.16)	5.01 (2.46)* 1.001 (-0.51) 3.62 (0.25)		9.44 (5.28)* 0.855 (-1.37) 10.28 (4.87)*
	1 4 β 2 β 5 3 β 6	0.021 10.39 (2.34)* (0.06) 0.010 (0.15) 10.27 (2.29)* 0.032 (0.02) 8.87 (2.34)*	-0.045 (0.73) 8.24 (0.41) 0.119 (0.20) 7.92 (0.47) 0.108 (0.01) 7.67 (0.69)	0.021 9.33 (3.08)* (0.16) -0.001 (0.37) 9.05 (2.51)* 0.025 (0.13) 6.97 (1.82)	0.060 12.30 (2.45)* (0.70) -0.035 (3.37) 12.51 (2.12)* -0.007 (1.90) 9.05 (1.53)	-0.027 8.85 (1.56) (0.58) -0.019 (0.77) 9.83 (1.59) -0.016 (0.53) 10.22 (2.43)*	-0.027 9.41 (1.20) (0.70) -0.019 (0.51) 9.38 (1.80) -0.016 (0.46) 9.24 (1.12)	0.046 1.93 (0.20) (0.33) -0.022 (0.69) 3.17 (0.69) 0.031 (0.15) 4.36 (0.78)		0.061 10.57 (4.24)* (0.72) 0.099 10.27 (3.36)* (0.26) 0.114 (0.16) 9.05 (3.54)*
	β	4	0.013	(0.12)	0.098 (0.04)	0.010	(0.26)	-0.040 (3.86)*	-0.021	(0.34)	-0.021	(0.56)	-0.052	(0.38)		0.076	(0.50)
	β	5	0.004	(0.21)	-0.007 (0.42)	-0.006	(0.44)	-0.027	(3.08)	0.010	(0.44)	0.010	(0.10)	-0.060	(0.51)		0.175	(0.15)
	β	6	0.050	(0.02)	0.050	(0.11)	0.043	(0.32)	-0.054 (4.84)*	-0.004	(0.43)	-0.004	(0.25)	0.002	(0.01)		0.165	(0.10)
	Obs.		7059		2639		4602		2613		2652		1794		4095		2964
										39

Table 7 :

 7 Results of the Regression Test of Bid-Ask Spread Around Volatility Auctions. This table summarizes the results of fitting the panel data regression model , denotes the spread recorded in event i (i = 1,…,543) in the t-th 5-minute interval preceding the auction (t = -1,…,-6) or following it (t = 1 , … , 6 ), d t is a dummy variable taking the value 1 at t and zero otherwise, and t i, ε is the error term. The sample comprised 543 volatility auctions on the Spanish Stock Exchange between May 2001 and January 2002. Student's t-statistics are shown in parentheses; * denotes statistical significance at the 1% level.

	y	, i t	=	α	i	+	t t	6 ∑ =-5 ≠ 0	t t d β	+	ε	, i t

Page 42 of 44 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript F o r P e e r R e v i e w 43 Page 43 of 44 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript F o r P e e r R e v i e w 44Table 11 :

 11 Results of the Regression Test of the Number of Transactions Around Volatility Auctions. This table summarizes the results of fitting the panel data regression model , denotes number of transactions (% of the daily total) in the t-th 5-minute interval preceding (t = -1,…,-6) or following ( t = 1 , … , 6 ) the i-th auction (i = 1,…,543); d t is a dummy variable taking the value 1 at t and zero otherwise; and t i, ε is the error term. The sample comprised 543 volatility auctions on the Spanish Stock Exchange between May 2001 and January 2002. Values of t-statistics are given in parentheses; * denotes statistical significance at the 1% level.

													Page
									y	, i t	=	α	i	+	t t	6 ∑ =-5 ≠ 0	t t d β	+	ε	, i t
	where y Period i	t	Full Sample (n = 543)	Market Index Stocks (n = 203)	September and October (n = 354)		Time of day: 9:30-12:00 (n = 201)	Time of day: 12:00-15:00 (n = 204)	Time of day: 15:00-17:00 (n = 138)	Triggered by Static Collar (n = 315)	Triggered by Dynamic Collar (n = 228)
	β	-	5		-0.0013 (-0.94)	-0.0003 (-0.44)	-0.0016 (-1.01)	-0.0022 (-1.05)	-0.0007 (-0.35)	-0.0003 (-0.13)	-0.0010 (-0.62)	-0.0016 (-0.74)
	β	-	4		-0.0001 (-0.21)	0.0002 (0.58)	-0.0004 (-0.46)	-0.0005 (-0.47)	0.0008 (0.72)	0.0001 (0.09)	-0.0001 (-0.18)	-0.0005 (-0.34)
	β	-	3		-0.0008 (-0.65)	0.0001 (0.21)	-0.0009 (-0.72)	-0.0014 (-0.76)	-0.0001 (-0.10)	0.0002 (0.12)	-0.0004 (-0.27)	-0.0015 (-0.76)
	β	-	2		0.0013 (0.92)	0.0019 (2.20)*	0.0004 (0.27)	0.0011 (0.51)	0.0023 (1.13)	0.0014 (0.49)	0.0014 (0.74)	0.0010 (0.42)
	β	1 -		0.0049 (4.20)*	0.0033 (4.41)*	0.0036 (2.89)*	0.0056 (3.07)*	0.0055 (3.17)*	0.0060 (3.02)*	0.0063 (4.22)*	0.0051 (2.82)*
	Switch
	β	1		0.0070 (7.10)*	0.0032 (4.51)*	0.0052 (4.51)*	0.0058 (3.61)*	0.0087 (5.45)*	0.0077 (3.96)*	0.0080 (5.84)*	0.0053 (3.16)*
	β	2		0.0013 (1.13)	0.0017 (2.33)*	-0.0003 (-0.23)	0.0005 (0.29)	0.0019 (1.05)	0.0031 (1.53)	0.0022 (1.57)	0.0004 (0.23)
	β	3		0.0002 (0.13)	0.0001 (0.40)	-0.0004 (-0.54)	-0.0007 (-0.63)	0.0021 (1.80)	0.0010 (0.71)	0.0001 (0.09)	-0.0003 (-0.22)
	β	4		0.0001 (0.04)	0.0004 (0.54)	-0.0006 (-0.44)	-0.0013 (-0.75)	0.0004 (0.24)	0.0029 (1.27)	0.0010 (0.68)	-0.0011 (-0.55)
	β	5		-0.0011 (-0.96)	-0.0003 (-0.42)	-0.0017 (-1.34)	-0.0033 (-1.97)*	0.0004 (0.26)	0.0019 (0.95)	-0.0003 (-0.22)	-0.0020 (-1.06)
	β	6		-0.0001 (-0.01)	0.0008 (1.15)	-0.0002 (-0.16)	-0.0019 (-1.04)	-0.0001 (-0.09)	0.0033 (1.46)	0.0005 (0.34)	-0.0011 (-0.61)
	Adj. R 2		0.55	0.22	0.56				0.54	0.58	0.50	0.53	0.56
	F-Statistic	11.60	4.12	12.38				10.35	11.75	9.90	10.94	10.83
	Obs.		6516	2436	4248				2412	2448	1656	3780	2736

44 of 44 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

The static and dynamic price collars are also used to control opening and closing auctions. When the final virtual resolution price of the auction lies outside one of the collars (the static collar in the case of opening auctions, and either the static or the dynamic collar in that of closing auctions), the auction is extended for 2 minutes. However, no such extension of volatility auctions is possible.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

I thank the Spanish Stock Exchange for providing the database, and Rafael Villar for research assistance. I am very grateful for partial financial support from the Spanish Stock Exchange in the form of the Best Research Paper on Stock Markets Prize (2004). I am also grateful for financial support from the Center for Economic and Financial Research (CIEF) of the Caixa Galicia Foundation, from the Xunta de Galicia (under contract PGIDIT06PXIB201002PR and INCITE09201042PR), and from research grant MTM2008-03010.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

The table lists, for both the auction sample and the reference sample, median values of the ratio between post-and pre-event volatility as measured by the absolute percentage first-last price change and price standard deviation; and also, median values of the ratio of the auction and reference sample ratios. Values of z for signed rank comparisons with unity are shown in parentheses (asterisks indicate values that are significant at the 5% level).


Terry Robinson
email: terry.a.robinson@mbs.ac.uk

An Empirical Note on Fan Loyalty

Keywords: attendance, football, stability

This paper attempts to investigate empirically the strength of intra-city football club support and seeks to test the commonly held belief among the sports community that supporters will not switch allegiance between city rivals very readily.

To test this phenomenon, data on the attendances of five English and two Italian city rival clubs is used to conduct a cointegration analysis. The results imply that a stable relationship does not exist between the attendance series which throws doubt on the proposition that supporters of a team are unlikely to switch their support to a rival club. To test the possibility that this result could be due to fickle supporters ceasing to attend, a sensitivity analysis is conducted between attendances and performance.

Introduction

The subject of fan loyalty and partisanship in sport has received attention from cultural historians [START_REF] Russell | Football and the English: A social history of association football in England, 1863-1995[END_REF], sociologists [START_REF] Connor | The Sociology of Loyalty[END_REF][START_REF] Armstrong | Fear and Loathing in World Football[END_REF] marketers [START_REF] King | The End of the Terraces: The Transformation of English Football in the 1990s[END_REF] and economists [START_REF] Morley | Attendance demand and core support: evidence from limited-overs cricket[END_REF][START_REF] Barajas | A model to explain support in Spanish football[END_REF][START_REF] Depken | Fan loyalty and stadium funding in professional baseball[END_REF][START_REF] Dimeo | Team Loyalty Splits the City into Two[END_REF] 2 . This is not surprising since team loyalty and partisanship are significant determinants of demand in professional sport.

In North America, it is common for sports franchises to move from one city to another in response to a lack of demand 3 . It follows that the size and loyalty of a franchises fan base can dictate in which city professional sports franchises and clubs locate. In European leagues where promotion and relegation exist, a significant relationship between market size, or "fan base" and performance has been identified by [START_REF] Babatunde | Freedom of Entry, Market Size, and Competitive Outcome: Evidence from English Soccer[END_REF]. The loyalty of a team's supporters will clearly be a factor in the size of the fan base and hence may affect performance and revenue. The subject of fan loyalty is, then, one of obvious importance for the sports industry, with implications for financial solvency and location of teams/franchises.

The general view of the characteristics of sports attendance is that there are a significant number of "core" supporters who will follow their clubs fortunes irrespective of the usual determinants of attendance such as price, opponents, etc. The sociology of football attendance supports this view. [START_REF] Dobson | The Economics of Football[END_REF] provide case studies on FC Barcelona and the two Glasgow clubs, Rangers and Celtic which suggests that social, cultural, political and historical tradition strongly influence the support for clubs in a given city. However, these authors also suggest that these 2 These latter papers make up part of the voluminous literature on the economics of sport. The fact that a recent special issue (Vol. 41, Issue 25) of this journal was devoted to this subject demonstrates it's growing importance. 3 There are too many instances of this to list. A recent example is the move of the NFL's Cleveland Browns to Baltimore in 1995 to become the Ravens. (Dobson & Goddard (2001, p. 318). Conversely, in his survey of the historiography of football and culture, [START_REF] Russell | Football and the English: A social history of association football in England, 1863-1995[END_REF] Anecdotal evidence would suggest that team allegiance is formed early and is unlikely to alter during a supporting career. This view is reinforced by [START_REF] Parker | The West Ham Syndrome[END_REF] who, in their research on brand loyalty in football, strongly emphasise the importance of parental influences on football support. Indeed, the subject of fan loyalty has received considerable attention in the sociology and marketing literature. [START_REF] Wakefield | The effects of team loyalty and selected stadium factors on spectator attendance[END_REF] investigate fan loyalty in US college football by means of direct surveys to acquire self-revealed levels of fan loyalty. They conclude that a greater degree of fan loyalty does increase the attendance to a college's home football games. [START_REF] King | The End of the Terraces: The Transformation of English Football in the 1990s[END_REF] suggests that key elements of both brand community and consumption as subculture4 may be present in fan loyalty. [START_REF] Mahony | The effects of individual levels of selfmonitoring on loyalty to professional football teams[END_REF] adapt this idea and investigate the effects of "self-monitoring"5 on fan loyalty relating to American football teams. This work is particularly relevant for this study since it deals with the likelihood that supporters will switch their loyalties to make themselves more socially attractive. They found that there was a negative relationship between self-monitoring and number of years as a fan of the currently supported team and a positive relationship between self-monitoring and the total number of teams a fan has supported. The conclusion is that high self-monitors have a marked predisposition to switching their support between teams. [START_REF] Richardson | Football Supporters and Football Team Brands: A Study in Consumer Brand Loyalty[END_REF] partially replicate Mahony et al's study for the English Premiership using a survey of 161 soccer fans They similarly find that self-monitoring is an important influence on fan loyalty with reference to Premiership teams.

In the economics of sport literature, the demand for attendance has been one of the most-researched subjects, but few economists have investigated the issue of fan loyalty explicitly. [START_REF] Depken | Fan loyalty and stadium funding in professional baseball[END_REF][START_REF] Depken | Research Notes: Fan Loyalty in Professional Sports: An Extension to the National Football League[END_REF] is an exception. Using data from Major League Baseball (MLB) he estimates an equation of attendance demand developed in the stochastic frontier literature which incorporates "inputs" to the attendance decision. The equation employs a half-normal error term which is decomposed into a measure of inefficiency that is interpreted as a measure of fan loyalty. Rankings of fan loyalty are then constructed for MLB franchises. This technique is then extended to the National Football League [START_REF] Depken | Research Notes: Fan Loyalty in Professional Sports: An Extension to the National Football League[END_REF].

A distinction has been drawn between "core" and "floating" support. [START_REF] Morley | Attendance demand and core support: evidence from limited-overs cricket[END_REF]; [START_REF] Peel | The Demand for Football: Some Evidence on Outcome Uncertainty[END_REF]; [START_REF] Kuypers | The beautiful game: an econometric study of why people watch football[END_REF]). It is argued that attendees are made up of a committed core who support the club whatever its results and 'floaters', or 'theatregoers' [START_REF] Borland | The Demand for Australian Rules Football[END_REF], whose presence depends on the appeal of the event. Most economists, however, have approached fan loyalty from the perspective of habit persistence [START_REF] Simmons | The Demand for Spectator Sports[END_REF] in which habit is treated as a component of the demand function. [START_REF] Borland | Attendance at Australian Rules football: a panel study[END_REF] suggest that learning about a game from previous visits increases the marginal utility of current and future attendance. In an attempt to incorporate this idea in economic models Peel andThomas (1992, 1996) used attendance data for a team's previous game, and for A methodology that has been frequently employed by the small number of researchers who include a variable to allow for a habit component in their models is to include a lagged dependent variable in a dynamic adjustment model. This approach has its critics however, [START_REF] Dawson | Measuring habit persistence effects in attendance at professional sports encounters: a cautionary note[END_REF], who propose that there is a big difference between partial adjustment and habit persistence.

The main problem for researchers attempting to include "core" support, or "habit" in any analysis of attendance is the difficulty of acquiring data containing information on those spectators who pay at the gate separately from season tickets holders. [START_REF] Paton | Attendance at County Cricket: an Economic Analysis[END_REF], and [START_REF] Morley | Attendance demand and core support: evidence from limited-overs cricket[END_REF] do include such information for English cricket, but we are not aware of any such studies pertaining to English football.

In an effort to obviate these difficulties a time-series method is used here which to some extent by-passes the problems of modelling the demand for attendance encountered by many economists 6 (see Borland & Macdonald, (2003) for a wideranging survey). Whilst it is has been well established that the demand for attendance in football is determined by many factors other than loyalty 7 , the assumption here is that, in the long-run, many of these factors, such as income, social trends, competitive balance, etc. will affect both teams in a single city in the same way. Hence the only other factor left is the relative fortunes of each club. So if we consider attendance for Team A and Team B in a city as two variables, and if loyalty, partisanship and habit 6 Depken (2000) suggests that sales of merchandise could be used as an indicator of fan loyalty. But as he says this data is not readily available. 7 See [START_REF] Dobson | The Economics of Football[END_REF] for a survey of attendance demand studies in football F o r P e e r R e v i e w 6 persistence were a significant factor, then if one club in the city was doing well we would not expect to see supporters from that club switching allegiance to the other club, hence sending these two variables away from each other. In other words, we would expect to observe a long-run equilibrium relationship between the variables.

Attempting to test this possibility is somewhat complicated by the nature of sports attendance as discussed above. To reiterate, core supporters will attend their team's matches no matter what. Floaters are more fickle. They will attend more often during period of success, but may not attend when things are not going so well. This characteristic of the football fan means that if the attendance of Team A increases by one, this does not necessarily mean that the attendee has switched from Team B. This fan could be a "floater". We attempt to incorporate this feature of football supporters by looking at the relationship between performance and attendance 8 .

Methodology & Results

This paper firstly investigates the stability of the relationship between the attendances of rival football clubs in several large English and two Italian cities. To do this we need to establish whether a long-run equilibrium relationship has existed between the attendances of clubs in a single market or city. If there has, it would provide some tentative long-run evidence that supporters do not switch allegiance for any length of time.

8 A well-known problem in the empirical literature is the fact that football attendance is made up of two types of ticket holders -season tickets and game-specific tickets bought sometimes on the day of the game. Clearly, the factors motivating these two groups will be different, given the "sunk cost" nature of the season ticket (Dobson and Goddard (2001), pp. 317-318). Historical season ticket data is notoriously difficult to obtain and was not available to us for this study. However, since we are using seasonal average attendances we can assume that both types of ticket buyers will base their decision to purchase to some extent on the previous season's league position. (Figures 1 to 7 here please) 9 Information on football rivalries was gathered from the following sources: [START_REF] Harvey | The Offbeat Guide To The 92 League Clubs[END_REF], [START_REF] Goodhead | Us vs Them -Journeys to the World's Greatest Football Derbies[END_REF], and www.footballderbies.com 10 Due to the suspension of League football during the Second World War the attendance data ends after the 1938-9 season and starts again in 1946-47. 11 Several of the selected cities host some smaller clubs although these are usually based in the suburbs. For example, Tranmere Rover's stadium is technically in the Merseyside area along with Everton and Liverpool but is actually in the town of Birkenhead not Liverpool. None of the London clubs are included in the analysis due to the sheer number of them. At the time of writing no less than five clubs from the English Premier League are based in London. Turin respectively. Whilst there is evidence in the charts of a stable relationship between the attendances of these clubs at certain periods the patterns represented are inconclusive. A more robust statistical method is required. An obvious candidate is cointegration analysis which is designed to identify exactly the type of long-run relationship we are investigating here.

Before testing for cointegration, the integrational properties of each of the variables needs to be established. This is done by applying using the standard Dickey-Fuller tests and by applying the test from [START_REF] Kwiatkowski | Testing the null hypothesis of stationarity against the alternative of a unit root[END_REF], hereafter KPSS. The KPSS test differs from the rest of unit-root testing procedures in that the data series is assumed to be stationary under the null hypothesis.

(Table 1 here please) Table 1 presents the results of stationary tests for each of the club series expressed in logarithmic terms. The Dickey-Fuller tests suggest that a unit-root exists in all the series except that for Manchester City whilst the KPSS tests imply rejection of the null hypothesis of level and trend stationarity for only five of the fourteen series.

However, when the series are differenced, the null hypothesis of stationarity cannot be rejected at the 10% level using the KPSS test. Overall, the combined results suggest that all the series are integrated of order one.

The most popular tests for cointegration are those proposed by [START_REF] Engle | Cointegration and Error correction: Representation, Estimation and Testing[END_REF] and [START_REF] Johansen | Statistical Analysis of Cointegration Vectors[END_REF]. When, as in this case, two variables are subject of testing for the stationarity of the residuals defined by the linear combination of nonstationarity variables that comprise the regression. This is the method adopted here.

(Table 2 here please) Table 2 shows the results of the Dickey-Fuller tests for cointegration between the attendances of clubs in each of the seven cities. In each case the null hypothesis of no cointegration between the series cannot be rejected at the five per cent level of significance. The results of the above cointegration tests suggest that a long-run equilibrium relationship between the attendances of these city rivals does not, in fact, exist. This conclusion suggests that there are significant periods in which the attendances of these city rivals drift away from each other 12 .

For clubs with greatly varying fortunes on the field over this period this is not a surprising finding. The two Nottingham clubs are a good example. During our period Nottingham Forest were far more successful in terms of league position than Notts County in addition to being successful in European competitions during the 1970s.

Less committed supporters of Notts County would drift away and marginal and new supporters would be attracted to Nottingham Forest. Even if Notts County supporters did not migrate to Nottingham Forest, the two attendance variables would move away from an equilibrium position. However, the fortunes of the clubs in the other four 12 To test the possibility of a structural break in the attendance data after the end of the Second World War, a dummy variable was included in the cointegrating regressions for the British clubs defined as zero up until 1939 and 1 afterwards. The dummy was not significant and therefore was not included in the main analysis. As mentioned above, the issue of "core" and "non-core" support is well established in the literature. The basis of this division is the belief that a proportion of a club's supporters are fickle in the sense that they will only attend when the team are doing well. The possibility that supporters are not switching between city rivals but are, in fact, not attending the matches of their favourite team when they are performing poorly is difficult to establish empirically. However, one thing that can be investigated is the extent to which attendance depends on the performance of a team.

Most studies of attendance demand in football find that performance; however this is defined, has a significant attendance effect on attendance 13 . Dobson andGoddard (1995, 1996), [START_REF] Simmons | The demand for English league football: a club-level analysis[END_REF] and [START_REF] Szymanski | The English Football Industry, Profit, Performance and Industrial Structure[END_REF] all include the team's final league position in their multiple regression equations to control for team performance. All of them find this variable to be a highly significant determinant of annual attendance. However, for the reasons given above about the commonality of most of the independent variables for these clubs a sensitivity analysis is performed here between attendance and performance for the British clubs. We define seasonal performance here as the finishing league position of the club. The possibility that attendance in season t could be affected by performance in season t-1 because of behavioural lags is also incorporated in the analysis.

(Table 3 here please) 13 See [START_REF] Dobson | The Economics of Football[END_REF] Chapter 7 for a comprehensive review. 3 gives the results of the sensitivity analysis. The results suggest a significant relationship between attendance and league position for all our ten clubs bar one, Everton. League position in the previous season also affects attendance in the current season for six of the ten clubs. However the explanatory power of these regressions is very poor with a maximum R 2 of 54 per cent and a minimum of 6 per cent. This suggests that, on average, attendances are not very well explained by league position.

These findings are inconclusive in the sense that they do not provide any evidence on the fickleness of supporters one way or the other.

Conclusion

This paper has attempted to investigate the extent of fan loyalty by using time series techniques rather than the survey-based or multiple regression methods employed by previous researchers. The objective was to determine whether a long-term equilibrium relationship was present the between the attendances of rival clubs in seven large These findings do not provide support for the view that supporters will stick by their team "through thick and thin". The empirical work above implies that there were significant periods in which the attendance variables of these teams drifted apart.

Moreover this occurred even when the performance of the clubs in terms of league position was similar. It is acknowledged that variations in attendance may not be due to supporters switching from one team to another, but may be due to variations in (1996)).

The KPSS stationarity test was used both with intercept only and with intercept and time trend on first differences of the series. The critical values at the 10% level are, for the model with intercept and time trend 0.12, and for the model only with intercept 0.35 [START_REF] Kwiatkowski | Testing the null hypothesis of stationarity against the alternative of a unit root[END_REF] The 95% critical value for the Dickey-Fuller statistic is -3.49

.

  relatively unimportant in shaping the attendances of individual English clubs

  the same season, whereas Kuypurs (1996) employed a clubs average home attendance for the prior three seasons.

  version of fan loyalty, we investigate the relationship between the attendances of ten football clubs in five large English cities -Manchester, Birmingham, Liverpool, Sheffield and Nottingham; and four clubs in two large Italian cities -Milan and Turin. Each pair of clubs are widely recognised as intense sporting rivals 9 . If, therefore, loyalty and partisanship is a factor driving football attendances, we would expect to see it exhibited in this context. We use seasonal average attendance data. The English data is for seasons 1919-1999 and was collected from[START_REF] Tabner | Football through the Turnstiles …Again[END_REF] 10 ; the Italian data is for 1963-2006 and was collected from www.european-football-statistics.co.uk These cities were selected because they contain two large clubs thereby making the empirical analysis more straightforward 11 . Although many other intra-city rivalries exist in european football it was not possible to obtain a sufficient quantity of data to undertake a meaningful time series analysis. The English clubs operated mainly in the top two tiers of the English Football League during this period. The top tier became the English Premier League in 1992. The Italian clubs played almost exclusively in Serie A, the top tier of Italian football.

  Figures 1 to 7 show the attendances for the fourteen rival clubs plotted by city of

  Engle and Granger technique is the simplest since it merely involves

  similar which makes it more surprising that a long-run equilibrium relationship is not evident.

  English and Italian cities. Cointegration analysis was used with annual average attendance data for each team. The cointegration tests suggest that no such equilibrium relationship exists between the attendances of Manchester City and Manchester United; Liverpool and Everton; Aston Villa and Birmingham City; Sheffield United and Sheffield Wednesday; Nottingham Forest and Notts County; AC Milan and Inter Milan; and Juventus and Torino.

  support. This was investigated by using a sensitivity analysis on attendance and league position, which showed that this may indeed be what is happening, but were inconclusive. Further research possibly in the form of extensive survey work and match-by-match analysis is required before more authoritative judgements can be made on the nature of fan loyalty.

  Figure 1: Manchester United and Manchester City attendances 1919-1999

  demurs from this view; "In general, it would appear that geographical and organisational factors rather than social, political or cultural ones, structured patterns of club allegiances in cities and large towns." (op.cit p. 66).

Table 1 :

 1 Unit root tests

	/	ADF(1) no	ADF(1) with	KPSS no	KPSS with
		trend	trend	trend	trend
	Man Utd	-1.95	-2.77	0.71	0.15
	Man City	-3.50	-3.58	0.17	0.09
	Aston Villa	-2.50	-2.53	0.26	0.08
	B'ham city	-2.00	-2.19	0.44	0.12
	Everton	-3.01	-3.06	0.24	0.20
	Liverpool	-2.41	-2.81	0.53	0.15
	Sheff Utd	-2.37	-2.85	0.50	0.11
	Sheff weds	-2.49	-2.47	0.11	0.11
	Notts C	-2.08	-2.67	0.61	0.07
	Notts F	-2.94	-3.04	0.54	0.17
	AC Milan	─2.15	─2.84	0.52	0.09
	Inter Milan	─ 2.77	─3.95	0.57	0.09
	Juventus	─ 3.20	─2.91	0.33	0.11
	Torino	─ 2.20	─2.53	0.34	0.20
	Note: The ADF no trend critical values are -3.52 at the 1% level, -2.90 at the 5%
	level and -2.59 at the 10% level. The with trend values are ─4.09 at the 1% level,
	─3.47 at the 5% level, and ─3.16% at the 10% level. (According to MacKinnon

Table 2 :

 2 , Table 1, p. 166). Cointegration tests

	Regression of:	DF Test Stat on residuals ADF Test Stat on
			residuals
	Manchester United on	-1.84	-1.69
	Manchester City
	Aston Villa on	-3.22	-2.89
	Birmingham City
	Liverpool on Everton	-2.89	-2.47
	Sheffield United on	-2.66	-2.72
	Sheffield Wednesday
	Nottingham forest on	-2.23	-2.19
	Notts County
	AC Milan on Inter Milan	─2.70	─2.33
	r o F Juventus on Torino ─2.35	─2.51
		P
		e
		e r
		R
		e
		v i e
			w

Table 3 :

 3 Attendance-League Position Sensitivity Estimates Estimated equations: ATT it = α + βPOS it and ATT it = α + θPOS it-1 . ATT is average attendance in season t. POS is league position in season t defined as distance from 1 st position in the Football League (including the Premier League). Estimated tvalues are in parentheses. Significance at the 5% level is denoted by *. Number of club is 74. The R 2 value reported is for the equation ATT it = α + βPOS it

		β	θ	R 2
	Aston Villa	-141.78*	-64.34	0.06
		(-2.01)	(-0.89)
	Birmingham City	-384.03*	-283.58*	0.34
		(-6.04)	(-3.99)
	Everton	-145.86	51.92	0.02
		(-1.21)	(0.423)
	Liverpool	-296.09*	-245.94*	0.12
		(-3.09)	(-2.52)
	Manchester Utd	-840.62*	-731.15*	0.54
		(-9.13)	(-6.99)
	Manchester City	-221.90*	-98.30	0.15
		(-3.42)	(-1.41)
	Notts C	-110.88*	-78.21	0.10
		(-2.88)	(-1.97)
	Notts F	-296.80*	-213.51*	0.33
		(-6.22)	(-4.00)
	Sheff Utd	-214.03*	-184.03*	0.25
		(-4.85)	(-4.01)
	Sheff Weds	-211.69*	-137.47*	0.18
		(-4.03)	(-2.45)
	Notes:

"Brand communities and consumption subcultures share common values, rituals and traditions, they also typically have strong sense of who is an authentic user of a brand and who is not." King, 1998 p.

The term "self-monitoring" refers to how individuals are motivated by what others think of them. SeeMahony (1999) et. al. p44

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript