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Dual capacity trading and the quality of the market

Röell, A.A.

Publication date:1991

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Citation for published version (APA):Röell, A. A. (1991). Dual capacity trading and the quality of the market. (Reprint series / CentER for EconomicResearch; Vol. 63). Unknown Publisher.

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88231991

omic Research II III I III I I I IIII I I II II III II I I '~ II II I I III I I I II IIIDual-Capacity Trading andthe Quality of the Market

byAilsa Roell

Reprinted from Journal of FinancialIntermediation, Vol. 1, No. 2, 1990

~~,~Q ,,~'.~' Reprint SeriesJ,.írí;~~JQ~~ no. 631~0i

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ISSN o9z4-7874

1991

forEconomic Research

Dual-Capacity Trading andthe Quality of the Market

byAilsa Roell

Reprinted from Journal of FinancialIntermediation, Vol. 1, No. 2, 1990

Reprint Seriesno. 63

)f1URNnI fll" rINAN(~Inl INIrRMChIn~11f,N 1, I11~-124 (tYrHt)

Dual-Capacity Trading and the Quality of the Market~

Alt.sn Riirl-1.

Londnn Sfltnnl n~Frnnr)mics, HouRlrlnn ,Srrenr, Lnndnrt W(7A 2AE, Urlirrd KinRJ~nr

l his ~a~er considers a securities market in which orders are channcled throughprofcssion:,l hrokcr-dealcrs such as London's market makers or the large bankso~eraling on continental exchanges. If these dual-capacity dealers can judge Ihemolives behind their cuttomers' or(lers, Ihey can trade profitahly on their nwnaccount teven if they cannot "front run," that is, lrade on Ihcir own accounlbefore execuling a customer order). 11 is shown thal the dealers have an incenliveto catisfy roughly half of Iheir cuslomers' order~ from Ihcir own invenlory if theyare sure that order~ are liquidity-mrttivated and nol based on inside information.ns a result of dual-capacily dealing, transaction costs for liquidity-motivatedIraders in Ihe aggregate fall, but they rise for those traders who are unable toconvince any dealer Ihal Ihey have no in5ide informalion. The liquidily of themain market worsens, even though its effective liquidity for cuslnmers whoseorders are parlly filled from broker-dcaler inventories improves. Jr,rrrrrnf ojf;f-n-nomif l.ile~rnnrrr Cl:lssificatinn Nlnnhcrs: 020. .llll, ?2(l. ~~ 14'NI AcaJcmic Prc... IM.

I. INTRODUCTION

This paper considers the role of dual-capacity traders in an auctionmarket for securities. Dual-capacity traders act both as brokers who bringclients' orders to the market and as dealers who trade on their own ac-count. Examples that come to mind are London's market makers after the"Big Bang" of 1986, Chicago's tloor tradcrs, and the major banks incontinental Europe.

This paper does not focus on the obvious conflict of interest inherent indetermining a price when a dealer can execute clients' orders against his

' l hc author lhanks Anal Admali,lurgen 1)ennert, Marco P:Ig:mo. 1'ete Kyle. Ihe partici-~ants in thc (.Ih F.uro~can Mccting on the Fconomics of Inform:dinn. and Ihc annnymousrcfcrccs of this jonrnal G,r many hcl~ful commcnts :Ind discussiuns. -) hc .Il~~nrt of IhcC~enlcr for F'.conomic Rcscarch :,1 Tilhurg Univcrsily is gralcfully acknawtc(IFcd.

If1511142-9571IY(1 SZ.INI

('~Myri~hl r~ IY'Mrby AcarMmK 11c~r. 1~.All riphla ur repnrlrw'IHm in any frnm rr.crvrd

106 nt~sn tt~it;t.t-

own (or an associate's) book. Most exchanges have rules safeguardingagainst abuses, although the recent scandals in Chicago suggest that theyare far from watertight. Instead, it will be taken for granted that dealerskeep to rules designed to ensure fair pricing. In London, for example,market makers may satisfy brokerage orders in-house provided that the"best execution" is obtained: the price must be the best one quoted in themarket. Similarly, in Italy banks that fill customer orders from their owninventory must do so at the market price reigning in the first followingstock exchange batch auction in Milan.

Even so, in ltaly it is commonly argued that banks are able to manipu-late prices and take advantage of ordinary traders and that this may be aprincipal cause of the poor liquidity of the main market. Along similarlines, in London it has been argued that British market makers with astrong customer base have an unfair advantage over their (American)rivals and that the current stock exchange rule changes (which reduce tlievisibility of true available prices and recent lrading history,' turning backthe clock on some of the changes introduced at the time of the Big Bang)exacerbate this problem.

In this paper I attempt to model dual-capacity trading in a market wheredealers are risk neutral and competitive, and orders are placed both byuninformed agents trading for liquidity purposes and by traders with somemeasure of inside information. Dual-capacity traders' competitive advan-tage rests in their ability to identify at least some of their brokeragecustomers as liquidity traders and to use this information in taking profit-able positions.2

2. A MODEL WHERE DEALERS KNOW 'I'HEIRBROKERAGE CUSTOMERS

The setting investigated in this paper is one where broker-dealers areable to identify the customer who places an order with them andjudge hismotives for wishing to trade. This might stem from a long-standing rela-tionship with the customer or a detailed knowledge of his current financialneeds, so that the dealer can infer with some degree of certainty that hiscustomer's wish to buy or sell does not stem from inside information.

For simplicity, it is assumed that the dealer either knows for sure that aparticular customer is an uninformed liquidity trader or knows nothing at

' Market makcrs are now allowed to execute small orders in-house al the best quotedmarket price even if they themselves are not quoting that price on-screen. nlso, the publica-tion of large lrades omscreen is to be delayed.

' This paper dces not consider a second potential source of profit for broker-dealers:"front running," that is, trading on their own account after receiving customer orders butbefore executing those orders.

ount.-cnrnctrv rRnt~lNC~ nNt) MnRtcFr Qunt.rrr IO7

all about him (in practice, of course, intermediate degrees of knowledgcarc likefy to prcvail). Moreover, any given uninformcd customcr has atmosl onc, if any, brokcr-dcalcr :lvailahlc whrt knows that hc is ttnin-formed. (This assumption is rel:txed in Section 4, where competitiunamong broker-dealers is examincd.)

Suppose that aggregate liquidity traders' demand ri is a mean-zero nor-m:tlly distributed variable with variance rT~. There are N risk-neutralhroker-dealers, each of whom has a customer base which allows him toidentify a portion of uninformed traders' demand rr; ihat has variance ~?,for i- 1, ..., N. For ease of computation it is assumed that all dealershave an equally large (identifiably uninformed) customer base, so that v?- rrz for all r. Individual traders' demands are independent, so that

rT~} rr j f ... f- tr N- tr ~.

where the indcx i- 0 refers to that portion of liquidity trading demandwhich none of the broker-dealers can certify as such (Q,~, - 0 is not ruledout). Such demand might be channeled through single-capacity (agency-only) brokers; or it might be placed via broker-dcalers who are ignorant ofthe identity and motives of the agents placing the orders.

The broker-dealers submit net demand schedules on their own accountof Z;(u;, p), i- 1, ..., N.

For simplicity let ihere he just one risk-neutral informed trader. Thisinsider observes the best estimate of the security's value v, while all othermarket participants have a prior on u distributed normally with mean u„and variance V.'

It is assumcd that there is a large enough number of competing marketmakers or "uninformed speculators" who submit price-quantity sched-ules to ensure that in equilihrium, the market price is equal to the ex-pected value of the security, given aggregate net demand and public infor-mation.' Total market demand (y) submitted to this group of competitivesingle-capacity market makers comes from the three main groups ofagents identified ahove, the insider(s), the noise traders, and the noisetradcrs' broker-dealers:

' tVote Ihat we need nol excludc any furthcr uncertainty ahout Ihc security's value Isay.ils liquidalion value is v} e, where r. is a fur~her random variable whosc conditional valuegiven v is zerol. Such addilional uncertainty Joes not affect the behavior of the agenls in ourmoclel, who are all presumed lo he risk-neulral.

' Kyle (19R9) shows that in a model with M uninformed imperfectly competitive constantri~k-averse market makers, there is a linear equilibrium in which each one provides a supplyproportional to (p - v„). The efficienl pricing assumed in our model emerges as Ihe limit asM-~ ~(so that txith incentives for imperfectly competitive behavior and total market makersector risk aversion vanish). Our assumption ofcompetitive risk-neutral markel making is amatter of convenience that docs not drive the basic qualitative results obtained.

108 nn.sn tc~ii:~ i.

IY N

y-~ ~~; f~ ~;(~,;. n) } x(u. r~).

Only y, but not its separate components, is observable to the marketmakers, or, more precisely, revealed by the market price in equilibrium.Perfect competition then ensures that the market is efficient in the sense[hat

n - El~l3~l.

An eqriilihri~~m consists of demand schedules T.;(ir;, p) and X(u, p) forthe broker-dealers i- 1, ..., N and the insider, respectively, such thateach of these agents maximizes expected profit, realizing that his tradingaffects the market price; and a price function P(y) formulated by a com-petitive risk-neutral market making sector.

Pttorosn ioN I. 7he u~rique línear ey~iilihrium njrlre nrndc~l de.cc~rihc~daboue i.c Riuen hy

f'(y)-u~t~yx(u, n) - R(u - n)

z;(~,,, n) - -sr.; - y(n - ~~), i - I, . . . , N,

where S is rhe unique real rnor (jor v~ ~ 0) nj

(I - S)' (2N - I) QZ - (I - S)z (N - I) Q~ -f 2(I - S) ~r~ - cro - 0.

When a-~ - 0, rhere are r~t~o roors, S- NI(2N - I) a,td S- I. Nore rlrar ~~ S s I and S--~ } a.c N --~ ~. Ciuen S c I, rhe nrher parameler.c jnlln~~~jrnm

v,~, f N( I- S)'Q~R- V

y-1-2SQI - S

I I - S~- Q 1- S- N( I- 2S )'

Pr~iuf. Sce Appendix.

l)unt.-cnPn('1 I Y'1 Rnl)1N(~ nNl) MAFtKf lOUnLI 1 Y

Oh~crvc that in cquilihrium, hrcikcr-dcalcrs xupply ahout half` of thciridcntifiably uninformcd customcrs' ordcrs fmm thcir own inventory: inthc proof of Proposition I, it is shown that ~ s R s NI(2N - I). In effect,the hroker-clealers act rather like ordinary monopolists facing a lincardemand curve. Suppose a broker-dcaler receives a huy order from acustomcr whom he knows is a liquidity tradcr. Hc knows thc ordcr con-veys no information about the security's value. However, if the order ispassed through to the market in full, it will drive up the market price; themarket at large does not know whether it is liquidity-based or not, andtherefore revises upward its estimate of the security's value. The broker-dcaler takes advantage of this discrepancy between the market price andhis own hetter estimate of value by satisfying part of the customer's ordcrfrom his own inventory. Since the broker-dealer realizes that his sale willpush the market pricc hack down, he does not satisfy the customer'sordcr in full. If he did, the net order hrought to thc market from himselfand his customer would be zem, the market rrice would not rise above hisestimate of the security's best value, and he would make zero expectedprofit. Instead, rather like an ordinary monopolist who supplies half thequantity that drives lhe price down to marginal cost, he fills ahout half theorclcr.

Note also that y c 0: hroker-dealcrs' demand on their own accountincrcases with thc market price. When main markct dcmand y increases,thc uninformed market makcrs revisc thcir estimate of u, and p, upwardbecause they believe that tlle change may be due to trading by the insideras well as to liquidity trading. Each broker-dcaler, however, is able tocheck that the increase in y~ is not caused by his own liquidity customers.He therefore attaches a relatively higher probahility lo the possibility thatinsider trading is responsible for ihe change in y. He therefore revisesupward his estimate of v by a little more than the market makers do, and,accordingly, buys more of the security.

The somewhat unrealistic case where tT~ - 0 deserves special mention.Hcre the broker-dealers as a group are able to identify ihe entire liquiditytracling demand i~. In that case there is always the following somewhatdegenerate equilibrium. The insider formulates an infinitely elastic de-mand-supply schedule at price p- v. The market making sector providesno liquidity whatsoever (~ -~). The broker-dealers each satisfy, inelasti-cally, their liquidity customers' demand (7; --n;, i.e., S- I, y- 0) and

' In a simpler model in which duat-capacity traders are presumeJ to submit market ordersor price-inelastic net demands (i.e., y- 0), we oblain h-~ exactly, (3 - (o~ f JNrr~)IV ,and J~ - U~. [3ecause dual-capacity traders are professional speculalors who play a centralrolc in the market, it seems more reas~nable lo model them as adjusting their demand tomarket conditions by setting price-quantity schedules.

provide no further liquidity. It is readily verificd that the insider, thebroker-dealers, and the market makers are unable to obtain positiveprofits in this equilibrium. Transaction costs are zero. The main marketprovides no liquidity; all liquidity demand is satisfied by the broker-deal-ers.

When N- 1, this is the only equilibrium for v~ - 0. When N 1 1, thereis in addition an equilibrium at which the market price does not perfectlyreveal aggregate noise trading demand r~ - ui f... t rrN. Here S- NI(2N - I) and the insider and broker-dealers make positive profits, so thattransaction costs for liquidity traders are nonzero.

At this point it seems appropriate to make some comments justifyingour assumptions concerning the nature of the information exploited by ihedual-capacity dealers.

Why need we assume that dealers know something about the identity ofthe traders who place the order flow? In our static model, where frontrunning by dcalers is excluded, the anonymous order flow to each dealerwill not in itself convcy any useful information over and above the aggre-gate order flow. If the main market and dealers I... N were to recciveindependent anonymous components of the uninformcd ordcr Ilow, rr„ -rr,w, f . . . -t- rr„n, with standard dcviations .~,N,, . . . , .c„n,, rcspcctivcly,then it can be shown that in equilibrium a profit-maximizing insider woulddivide his total market order among the dealcrs in proportion to thcsestandard deviations. Individual dealers' order flow would then convey noinformation on the insider's total trade that is not expressed in the aggre-gate order flow (a sufficient statistic for the insider's trade), and hence inthe competitive market price. Thus dual-capacity dealers would not bcable to trade profitably, and would simply take on thc status of unin-formed speculators. In short, as far as demand from unidentified agents isconcerned, it makes no difference whether it is submitted to the msirketdirectly or via a broker-dealer.

Why not have the dual-capacity dealers identify insider orders ratherthan liquidity trading orders, and thus deduce some exclusive informationabout security value from [heir order flow? If able to identify an insiderorder, the dealer would have an incentive to trade in the same direclion.This competition would spoil the market for the insider. Hence insidershave every incentive to hide behind anonymous intermediaries andlor toplace orders directly on the main market via single-capacity (agency-only)brokers. In contrast, identifiable liquidity traders benefit from iheir dcal-er's trading from their own inventory, because it reduces adverse pres-sure on the market price.

Throughout this paper, the broker-dealer who knows that his clicnl isuninformcd is also assumcd to scc thc sizc of his clicnt's total nct dcmand.If not, the client can profit at the dealer's expense by behaving strategi-

OUAL-CnPnCI 1 Y 7 RAbIN(; ANp MARKf? r QUnLITY I I I

calty. Suppose that his true net demand is rr, . He can place an order for alarge multiple Ilu,. (H 7 I) of his desired trade with his broker-dealer andreverse ihe excessive demand by a direct order of ( I - If )rr, elsewhere. Ifthc broker-dealer supplies a proportion fi of the announced order, the netdemand to the main market from the client and the broker-dealer togetherwill be

Hrr,. f (I - H)n,. - Slfrir -( I - SH)rr,..

Clearly, this strategy yields a better execution price, the higher the an-nounced trade Hrr~. The broker-dealer suffers and, in fact, loses money ifH ~ Ilfi because the market price is driven down by the combined orderswhile he is selling from his own inventory. If the broker-dealer suspectsthat a client may cheat him in this way, he will not wish to trade on hisown account, and the client's order flow will appear in our model as acomponcnt of the anonymous order flow rr„ rathcr than of rr for i? I.

Thus, for the effects studied in our model to emerge, the broker-dealernot only needs to know that some of his clients are uninformed but alsoneeds to be able to gauge their total order flow. This could be because thebroker-dealer is able to monitor the client's total order flow to somedegree, through contacts with other market professionals. Or perhaps heknows enough about his client to judge his trading needs. Or perhaps hesimply irusts him. Last, observe that the relationship between the broker-dealer and a trusted client is of mutual benefit. By "cheating," the clientrisks his reputation and hence the recurring benefits of a long-term rela-tionship.

3. COMPARISON OF MARKET EQUILIBRIUM WITH ANDWITHOUT DUAL-CAPACITY DEALING

Let us compare the results obtained in Proposition I with the situationin which dual-capacity trading is hanned. in that case, our model coin-cides with a limiting case discussed in Section R of Kyle (19R9). Setting S- y- 0 in Eq. ( I) and (4) of the proof, we readily obtain

Q,- ~~fN~ZV

~,~ - ~~ - VI3 rr~ f N~2

Thus, in the absence of dual-capacity trading, the insider trades some-what more vigorously ( ~3 is greater) in response to his information.

I12 n((.sn rciiia.(.

The presence of dual-capacity trading does harm the liquidity of themain market. Intuitively, dual-capacity tradcrs offsct a rroportion Fi -~ oftheir liquidity customers' demand by supplying from their own inventory.This means that total liquidity trading on the main market is sparser. Thenany order placed directly on the main market will have a greater impact onprices.

To see this, the price impact of an order from an anonymous liquiditytrader (who does not have a relationship of trust with any broker-dcaler)can be calculated. Solving the equilibrium conditions for the price interms of exogenous variablcs, using Proposition I, wc ohtain

n-

n- ~n -

N

i-~O -S)ll;f-~3lu-p)-Ny(n-uo));

ÁI f~tR f Ny) ~Illl t

N

~, (I - f1)ll; f ~~U - UII)),N

2~ ~IIp f ~ tI - fI)Ili~ f 1 tU - UII).` i I ~

dp J~ 1clrln - I f~1(3 t!Vy) - 2~.

(1)

Hence the average transaction costs of the liquidity traders, E~(p - v„)uo~uo], are equal to (I12~3) Iro.~

Similarly, in a market without dual-capacity trading

~n' 1li„ - Z~.

Since ~3~ ~(3, dpldll„ ? clp~`Idn. Thus an ordcr from a customcr whocannot convince a dealer thal he is uninformed moves the market pricemore than it would in the absence of dual-capacity trading. However,liquidily traders who are able to convince a broker-dealer that they havcno information are betler off. Their orders do not exert as much rricepressure because Ihe hroker-dealcr will satisfy roughly one-half of Ihcirorder from his own inventory:

" With linear schedules, E1p - u~u;j -(dpldu;)u,. Nence expected transac~ion cosis xregiven by (dpldu,)Q?, for r - 0, I, ..., N.

1)Unl.-(~nPnCl l Y l RnDING AND MnRK1:.I QUAI.I I Y ~ ~ 3

dn- 1 (i-s)~~1; iR1 v

- 2 (~r~l(I - S)-) f Nrrz

I VC 2 (cr~ ~- Nlr')

dP~- v,l -

Thus thcse agcnts trade on hetter terms than thcy would in thc absence ofdual-capacity trading. Their total transaction costs are (Il2R) (I - S)NIr2.

We also calculate the ex ante (before observing u nr rl;) expected profitsof the insider and the dual-capacity traders.

lnsider profit - (u - p)x- R(~ - n)2

I 1 N 2

- R~2 (U - Up) - 2R ~Up ~ ~ (Í - ~i)1li~~

using Eq. ( I ).

Ex ante expected insider profit

- 4 R(V f ~Z (~~ f N(1 - S)ZQZ)1

- ~ Ryi

using the expression for R given in Proposition 1.

Broker-dealers' total profit

-(U-~,(,~Z;)r N N

- I-(U - Up) - 'p ~flp f- ~ (1 -Ó)ui~Jl-s ~ UjLLZ 2N i-1 1~1

1 1 ( N lll-Ny(2 (u - up) f ?R `up } ~ (1 - S)u`ll J

114 ntt.sn rtiita.t.

N-2~(~-~„)-;~~,,,,t ~(I -í,)„i)lf -2Ny(~-~„)N

- 2y IIp - (S t( I - S) ~Y~ ~ II; I.R Q i I

Ex ante expected broker-dealers' profit

- Ny (-V t ~o t(I - S)Z N~zl t~ I- S)S Nv24 Rz J 2R (

- (1 - S)S N~z.2R

Adding up, total cxpected profits of insidcr and brokcr-dcalcrs

- ZR (cr; t (I - S)Ncr').

This expression is, of course, equal to the total transaction cost to liquid-ity traders of both kinds. To see that total transaction cost is smaller thanit would be in the absence of dual capacity, observe that

Transaction cost with dual capacityTransaction cost without dual capacity

(I12j3) (vó t (I - S)N~z)( I 12~3') (cr; t NQZ)

(Q~ t (I - S)Ncrz)'- (~ó t( I- S)ZN~Z)(~ó t N~~) ~ I if S 1 0.

(2)

Thus the profits of the dual-capacity traders are more than offset by thereduction in insider profits, and transaction costs to liquidity traders fall.Intuitively, the overall quality of the market improves because less of theorder flow "noise" is brought to the main market, to be exploited by theinsider who hides his trading behind the noise. Liquidity traders whoare known to a broker-dealer see a proportion S of their order satisfied atzero transaction cost from the broker-dealers' inventories. The remain-der of their orders, together with the anonymous liquidity orders, arebrought onto the main market where transaction costs, as in Kyle(1985), are roughly proportional to the standard deviation of the orderflow.

DUA1,-CAPA('l l Y l Rnl)1N(i nND MnRKP.I QUnl.l l Y I I S

'fhc effects of greater concentration in hroker-dcaling can also he exam-ined in our model. HoWing constant Nrr' and ~r ;(~0), Ihe respective totctlvarianccs of Ihe liquidity trading dcmand that is and is not idcntifiahlc sls~uch by the broker-dealer sector, it can he shown that as N increases,total transaclion costs of liquidity lraders rise. (In expression (2), thedenominator is equal to the numcrator plus a Ierm Fi'Nrr'-rr ;. Totallydiffcrentiating the cuhic expression for ~i givcn in Proposition 1 with re-spcct to N and S, holding N~r'- conetant, wc find lhat R is decrcasing in N.Thcn il is rcadily shown ihal exprctsion (2) iti incrcasing in N whcn Ncr'- isheld constant.) Intuitively, as their numher N increaties, individual hro-ker-dealcrs' information concerning the composition of total market de-mand is less superior to that of the markct making scctor. Therefore, thcyspeculate less aggressively: both Fi and Ny, their comhined responsive-ncss to the market price, fall in ahsolute valuc. Insider profit increaseswith N while hroker-dealers' joint profit falls (or stays constant in the case.r; - 0, Fi - I), but by less. Total transaction costs rise.'

Rclated work by Cripps (1989) and Fishman and Longstaff (1989) con-siders a many-period model where broker-dealers may inherit inside in-formation about the sectlrity's valtle directly by observing the ordersplaced by i~tforrned clients. These models (for Cripps, just the model ofSection 5) are immune to our critique of Section 2 above (that the in-formed client would want to remain anonymous to prevent the broker-dealer from driving up the price against him by his trading) because thebroker-dealers are effectively constrained not to trade on the informationuntil one period after thc client's order has been fillcd. Dealers are ablc toprofit from the information only because the insider naively places a one-shot trade instead of exploiting his information optimally by trading re-peatedly. Thus the profits of the broker-dealers are, in effect, profits theinsider could have captured for himself by a dynamic trading strategy ofthe type studied by Kyle (1985). Since the broker-dealer profits stemmingfrom observing the insider's traders are not obtained at the expense of theinsider (when the insider trades first), they musr be offset by increasedtransaction costs. In the Fishman and Longstaff model, in addition, thebroker-dealers are able to identify uninformed traders, thus to some ex-tent reducing the scope for insider profits and hence transaction costs, asin our model. The total impact on liquidity traders' transaction costs thenbecomes ambiguous, depending on which of the two effects dominates.

' Note, from footnote S, that changes in N, holding Nvr constant, have no etTecl in amrtdel where broker-dealers submit market orders. As they do not speculate in rcsponse tochanges in the market price, the accuracy of Iheir inferences with regard to variables otherthan lheir own customers' ordcr flow is irrelevant. In effect the equilibrium of the modelwith broker-dealers placing only price-inelastic market orders can be regarded as the limilingcase N -~ ~ of our main modcl.

nn.Sn Rti1.I I

Wc havc shown that hoth thc cutitomcr and Ihc hrokcr-dcalcr will hcnc-fit from lhc lattcr's knowlcdgc of thc formcr's liyuidity-motivated tr:ulingdemand. What is crucial is this information, rather than the clicnt-brokerrelationship that gives risc to it. For examplc, suppose Ihat thc hrokcr-dealer knows about the client's trade, but the latter channels his orderthrough another broker-dealer who knows nothing about him. Then theoriginal broker-dealer will still trade as described in our model, while thebroker-dealer who executes the order has no incentive to trade becausehc has no information ovcr and ahove Ihat of the market at large. "I'hismeans that, once the division of information ahout clients and their ordershas been fixed (and our model takes it as exogenous), there is no scope foreither the broker-dealer or the client to hargain for a largcr share of theirjoint surplus. The threat of breaking the customcr-agent relationship isineffective as it does not alter the outcome.

However, in the longer term it is possible to influence the allocation ofthe information about thc clicnt, and thcre is room to ncgotiatc thc divi-sion of the gains. For example, there should bc ncgotiation at the timc ofsetting up long-tcrm rclationship which will cvcntually allow thc hrokcr-dealer to judge the client's trading motives and needs. In particular, ifbroker-dealing is competitive, one would expect the client to be ablc toextract a contract for inexpensive below-cost relaled services from thebroker-dealer, in anticipation of the lattcr's futurc profits from the rcla-tionship. Our model does not endogenize information gathering and dis-semination by broker-dealers and thcir clients. !t should he viewed as abuilding block for such a wider framcwork.

In general, our model focuses on expected gains and losses to theagents modeled but does not address ihe distortionary effects of suchchanges in rewards. For example, the reduction in insider profits meansthat ihere is less of an incentive to gather information. This may reducethe informational efficiency of the market. Our model is not completeenough to address the question of whether the current situation providesover- or underinvestment in information gathering. Indeed, it also fails toconsider the distortionary effect of high transaction costs~ liquidity trad-ers' demand is taken to be exogenous and price-inelastic.

4. THC ROLE OF COMPC;TI"TION AMONGDUAL-CAPACI"I'Y DEALERS

In the modcl analyzed so far, it has been assumcd that each liyuielitytrader can find only one, if any, broker-dealer whom he can convince Ihathe is uninformed.

What happens when more than one broker-dealer knows th:it a p:~rticu-lar segment of the order flow is pure liquidity trading? We consider one

f)UAI -('AI'A('ll Y 1 RAI)IN(~ ANI) MANKP.I QUAI I 1 Y I t~

such sctting in which thcrc arc N sc);mcnl~ of liquiclity tlcman(1, ahoutc:tch of which K diffcrcnt du:tl-car:tcily traclcrs arc infonnc(I. I:or sim~lic-ity it is astiumcd that c:tch (lual-ca~acity traclcr has only onc ~iccc of suchinform:ttion," so lhat there are in tot:tl NK dual-ca~acity lra(lers withsomc information.

PrtoroslTwN 2. When cr~ ~ 0, !he uniqne linc~nr eqrrilihrircnt Uf Ihemndc I d~s(~rihed ahoue is kiuen b}~

P( ~' ) - ut~ f ~~,

x(u, n) - R(~ - ~~)7;;(r,;. n) - -Scr;-y( p - un). i - I. . . . . N..i - I. . . . , K,

tt~here S i.c !he uniqrre renl rciol (fi)r cr~ ~ 0) oJ

((K f I)N - I) (I - KS)' cr2 -(N - I) (1 - KS)z crz f

(K -~ I) (I - KFi) ~r~~ - ~r11 - 0.

Nu)r ~lrcr~ I I( K ~ I)~ R~- NIf( K t I) N- I 1`" I I K rrncl Irc~rrc c~ S 1 I I( Kf I ) fur Inr~,~c' N.'' 7hc' utlrc~r ~~urnnrc~lc~r.c rnr

(cr~~ f N( I - KSI'rr'-~ - V

(I-(Kf I)Sy-~` I - KFi ~

I I-KFi~-Jil -KR-KNII -IK-t I)R)'

I'rur,~. Not shown. (;xactly analogous to thc mcthocl uscJ in rruvingProrosition I.

" In a moJel wilh ~ricc-inelastic Jual-capacity traJer JemanJs, thi~ assumption woulJhave no effecl un Ihe outcome.

" II can he shown that with price-inelaslic Jual-capacity traJcr JemanJ, fi- II( I t K) asin Ihe lincar Cournot-Nash model. 'fhen any uninfiirmeJ tradcr identifieJ as such by KJr.ilcr~ will sce a pro~ortion K~(K F I) rif his order satisfieJ from Jealers' inventories. withonly a proporlion U(K f I) going lo Ihe main market. Hence,

( I l ~rró t `K f t l rri I

Q- V~ , A-á.

IIR nn.sn R ii~,i.i.

Ohscrve that as K incrcascs 11 - KR) -- II(K ~ I) dccrcascs. ns Ihcnumbcr of compcting dcalcrs who know that a p:~rlicular Uadc is liyuiclily-motivatcd incrcases, thc prciporlion not supplicd dircctly from clcalcrs'invcntory dccreascs. l,iquidity tradcrs havc an inccntivc lo convincc asmany dealcrs as possihlc that thc ordcr lhat thcy plan lo placc is nc~lmotivatcd hy insidc informalian. "Sunshinc trading," in which agcnlspuhlicly announcc in advancc thcir intcntion to makc a I:u-gc clcal, is ancxamplc discusscd in furlhcr dctail and in Ihc contcxt uf a compctitivcmodcl with risk-aversc agcnls hy Admati and Pflcidcrcr (19~N1) and alsa hyGcnnolte and I,cland ( I~0). In practicc such announccmcnls oflcn fail loachieve the desired effect for two reasons. First, market professionalsmay not believe that the proposed deal is not information-generated. Sec-ond, such an announcement may not be credible for reasons discussed atthe end of Section 2: even bona fide liquiciity traders have an incentive toannounce a very large intended trade, and then place a smaller actualorder. Dcalers who trade hased on the announcement thcn take losses.

In our model, the market price is more responsive to unidentified liquid-ity demand then to identified liquidity demand:

~P~dP -1-Kfi~lclr~; d1i~

(--. 0 as K ~~).

This result mirrors lhc findings of Gcnnotlc and Lcland ( I~0) in a ccim-pctitive modcl with risk-averse agents. In thcir moclcl thc markct priccalso becomcs substantially less responsive to the order flow whcn morcagents are informcd that il is liquidity-driven.

In the limit, as K-~ ~, a situation where only the anonymous compo-nent of the order flow determines market liquidity is achieved:

~V

~~ácl - sx~ -~ o.

Here main market liquidity is minimal, but certified liquidity traders exertno pressure on prices and thus trade at near-zero transaction cost. Bro-ker-dealers are too competitive to make profits, and insider protïts areminimal. Thus aggregate transaction costs to liquidity traders as a groupare minimized; however, they are borne entirely by those liquidity traderswho are unahle to convince the market professionals that they are unin-formed.

I~UnI--CAPnCII'Y 1 RnhINO nNU MARKti"T (JUAI.tI Y I 19

In theory, much the same effect may be achieved indirectly if dual-capacity firms are forced to announce their price-quantity schedules pub-licly during the auction market tatonnement. The outcomes described inPropositions I and 2 would then no longer be an equilibrium because theschedules Z,{u;, p) reveal {rrl, . .., uN} publicly to all other marketparticipants, who adjust their behavior accordingly. Instead, the limitingoutcome described above would be an equilibrium.

Thus with dual-capacity firms forced to reveal their price-quan-tity schedules for proprietary trading, the equilibrium that fully revealstr; f... f nN) could emerge:

N

P(y)-u~fa~y-~rr-~,- l

X(u, P) - Q(u - p)

Z,(u;,P)-0, i- I,...N,

where

7~his eyuilihrium minimizes total transaction costs for liquidity traders.t"London's market makers are an example of a group of dual-capacity

dealers who are to some degree forced to publicize their trading strategyin the form of electronically displayed on-screen bid and ask quotes.However, these quotes are not fully informative because they are bindingonly for small trades (for large trades, as suggested by our model, marketmakers prefcr to negotiate a price that dcpends on the identity of thcircounterparty). Moreover, now dual-capacity firms are allowed to satisfysmall orders from their own inventory at will at the best price quoted inthe market even if they themselves are not quoting that price. Hence there

'" In Ihis eyuilibrium the agenls who have private information (the dual-capacity dealers)havc no incentive to trade and thus express Iheir information (the u,) in the final equilibrium;see Itellwig (1980) for a discussion of this problem in the conlext of a competitive rationalexpectations equilibrium. Presumably the information is conveyed during the precedingtatonnement process, in which dealers have no ineentive to holJ back information (giventhat in the final equilibrium they will be held to zero trading on lheir own account anyway)hul also no incentive to reveal it.

12O nn sn aiiet.l.

is now even more score for adorting a rroprictary trading ~olicy that isnot visible to other markct particirants via the hid-atik qurncs. 'fhisshould thus lead to higher transaction costs for liquidity traders in theaggregate.

5. POLICY IMI'LICATIONS

In our model dual-ca~acity trading reduces total transaction costs forliquidity iraders. True, the liquidity for anonymous ordcrs on thc mainmarket deteriorates. But this effcct is more than offset by hcncfits tocustomers of dual-capacity firms which partly fill orders from thcir owninventory, resulting in less price rressure and im~mved exccution qual-ity. A Chicago Mercantile Exchange Panel defended dual-caracity trading( W~ll Slree~ Jnrirncil, A~ril 20, 19R9) on these grouncls: "f)ual trading isneeded ... to maintain enough liquidity."

Our model identifies two potential disadvantages associated with dual-capacity trading. First, it may he considcrcd unfair th;tt somc tradcrs'transaction costs actually risc though thc total falls. f;qual trcatment of allpotential investors is a rrinciple on which many current rulcs arc h;tscd."Second, insiders' profits are reduced. This might he undersir;tble if themarket currently provides insufficient incentives for gathering informa-tion.

In Section 4 it was shown ihat these effecls are ~articularly sU-ong ifliquidity traders can convince multiple competing hroker-dcalers Ihatthey have in mind a trade that is not information-drivcn, ur if hroker-dealers are forced to make puhlic their price-quantity schedules.

One final word of caution: Our modcl does not explore thc full range ofeffects associated with dual-capacity trading. In rarticular, our static ap-proach precludes an analysis of "front running" wherehy dual trader~trade on their own account in advance of customer order execution. Wealso do not address one of thc rrimc practical reasons why brokcr-dcalcrsin continental Europe have diverted order flow away from the main cx-change: fixed brokerage commissions. When these exceed order process-ing costs, there is a strong incentive to cross orders in-house or fill themfrom their own inventory. This particular motive for in-house executionshould disappear once commission rates are left to be determined hycompetitive market forces.

" For example, Ihe London and NnSt)AQ rule reyuiring market makcrs to yuote "lirm"prices ( at which they are ohliged to trade with all comerc) for deals up to a certain size meansthat it is difficult to take advantage of inexperienced traderc. tiut il also means that marketmakers are less ahle to protect themselves against known inziders and must lherefore chargehigher average spreads.

1)Unl.-C'nPACI'I Y I Rnl)IN(~ ANU MnRKI:.I QUnLI lY ~Z~

APPENDIX: PROUF OF PROPOSITION I

We look for a Nash equilibrium in trading strategies. A justification forthe method used is given in Section ï of Kyle (1989).

I. 'I~he irrsi~lc-r chooses a net demand schedule X(u, p) that maximizeshis exrected rrofits, given Ihat he knows u, the value of the security, andinfcrs (from the m~,rket Price) the noise traders' demand net of the result-ing supply from broker-dcalcrs:

m:ix (u - p) x, whcre P- u„ f J~(W - Ny( p- u„) f.r) and Wt~i

N

- ri - Fi ~ ri; .

Suhtitiluting in for ~, ancl taking Ihc lirst-urdcr condition~, wc uhtain

.r - 1}`~ Ny ( u- uu) - Z W

I } ), Ny.r- ~ (u-~,)

~3 -I ~- 1` Ny

II. Rrukr-r-clc~rrkv. i maximires cxPcctcd Pro(its, givcn n; and thc mar-kct Pricc ( from which hc infcrti K- ri„ f ~j~i 11 - S)ri; ~~i(u - u„)):

max l:~lu - p)z,~,i:,i

whcrcp-u„fJ~(u;t K-J3(p-u„1

-~Y(P-uu)-FZ;).

Substituting in for p, taking the first-order condition, and rewriting interms of p, we obtain

z;

E3ut

It~Qf)`(N- I)y- ~ (E~u-un~-(P-uo)).

~~r,-u„~ri„}~(~ - s),i;~~(~-~„)-K~;-.- ~~- azV f cro f(N - I)(I - S)zQ2 K

122 nn sn R~iei.i.

QV~3zV ~- .r~ f (N - I)(I - S)z?i

fl txpf(N- I)y 1I ~ (P - vo) - n; -Z; I .

Hence

QV I f~Qf(N-I)ylI f QzV f Q~ f(N - I)(I - S)z~rz ~ I 7;

I f l~p ~~(N - I)y (( QV~ I`~3z V f rr,z, f(N- I)( I-

I f- ~~i -~ ( N- I)y -1)( P- ~n)~

( R~ l-`~3zV f cr~ f(N - I)(I - S)zcrz~~~'J

y-

S-

1 ~ ~(3 } ~(N - 1)y~

1- 1 f aQ f ~(N - I)y QV~ QzV f ~o f(N - I)( I- S)z~z

l~lf~(3f~(N-I)Y QV~ (3zV f rr,z, f(N - I)(I - S)z?z

1 f l~p f J~(N - 1)y RV~ QzV f ~~ f( N - 1)( I- g)z~z

1~ 1 f~Q f J~(N - I)y QVJ~ (3z V f~~ -~ (N - I)( I - S)z~r z

(2)

(3)

(II. Semrslrn~tA marke~ ~ffrc~iency. A competitive group of marketmakers or speculators ensures that

N

- ~i f~3( v - n)- Ny( p- vo) -~, Fi~i;I

S)z~r z

Vn-"" - QzV f ~r; a N(I - s),?z (y }(Q } Ny)(r - ~~~))

DUnI.-CAPACIIY I RAI)IN(~ AND MARKf 1 QUnl.l"IY 123

RVn- u" t~~ t N( I- S)z~rz -~iVNy y

RV~ -

v,z, t N(I - S)zrrz -RVNy.

y - (2p - y)( I - 2S).

1V. Solution of eq~~atíon system (1) ~o (4). Inserting ( 4) into (I), wehave

Qó t N(1 - S)zQZ -RVNy(3 - R V t Ny

RzV - Qo t N(I - S)z~z,

and using (I) and (3) in (2),

Hence

y-R (1 - 2S)

and from (3), using (I),

1 - S - 1

(4)

(5)

I t (2p - y) pV2~ó t (2N - 1)(I - S)z~z

Using (tí) and (5) to eliminate y and R in this equation, we obtain the cubicexpression for S:

(I - S)' (2N - I) ~z - (l - S)z (N - I) vz f 2(I - S) ~ó - vó - 0.

Since the sum of the first two terms must be opposite in sign to the sum ofthe last two terms, it is readily verified that the cubic equation's real rootsmust lie in the interval [}, I]; indeed, more precisely, S E [}, NI(2N - I)J.Inside that interval, the slope with respect to (1 - S),

3(I - S)z (2N - 1)~rz - 2(I - S) (N - I)~rz t 2~ri,

must be positive whenever the cubic expression equals zero, since thatevent (1 - S)` (2N - I)oz -(1 - S)z (N - Orrz 7 0 (given that 2(I - S)cr,z,- R~ ~ 0). Hence, there is only one real root when Q„ ~ 0. The expres-sions for Q, ~, and y follow directly. ri

124 nll.sn R~ir.l.l.

REFERENCESAriMntt, A. R., nNti 1't t nnrrtrrt, P. (19~N11. Sunchinc Ir:~ding: Ihc cffcclc ~if ~rcannuuncc-

mcnl on Iradcn' wclfarc and on ~rice variahility, unpuhlieheJ, Graduatc SchMil cif liuci-nesc, Stanford Univercity, rcviced vcrcion.

CRtrrs, M. (19R9). hc.Jer hehaviour and price volatility in aacel markcts, un~uhlichcJ.f)c~artment of F,conomics, Warwick Universily.

FISHMAN, M. .I., AND LoN~srnrr, F. A. (19R9). hual Uading in futurec markclc, un~uh-lished, Kellogg Graduate School of Management, Northwectcrn Univercily, Niwcmhcr.

(inNNrrnc, (i., nNn I.r.t.nNti. II. E. 11'riNll. Markct IiyuiJity, hcdginF and cra~hcc. ~nuv.liran. Rt~u. R0, 999- I11? I.

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Kvt e. A. S. (19R51. Continuciua aucli~nc and incidcr Irading. f:rrornrn~~rirn Si, 171c-~13C.Kvt t. A. S. (19R91. InformeJ ti~cculati~in with im~crfcct com~ctiti~~n, Rru. l:i.rn. ,~n~d. S6,

317-iSS.

Reprínt Series, CentER, Tilburg Uníversity, 7he Netherlands:

No. 1 G. Marini and F. van der Plceg, Monetery and fiscal policy !n anoptimising model with capital eccwulation and finite lives,The Econwic Journal, vol. 98, no. 392. 1988. PP. 772 - 786.

No. 2 F. ven der Plceg, International policy coordinetion in ínterdependentmonetary economiea, Journal of International Economics, vol. 25,1988. PP. 1 - 23.

No. 3 A.P. Barten, The history of Dutch macroeconomic modelling(1936-1986), in W. Driehuís, M.M.G. Fese end H. den Nartog (eds.),Challen es for Macroeconomic Modellin , Contributiona to EconomicMalyais 17 , Amsterdam: North-Holland, 1988, pp. 39 - 88.

No. 4 F. van der Plceg, Disposable income, unemployment, inflation andatate apending in a dynamic political-economic model, Public Choice.vol. 60. 1989. PP. 211 - 239.

No. 5 Th. ten Raa and F. van der Ploeg, A atatiatical epproach to theproblem of negetives in input-output analyais, Economic Mode111nR,vol. 6, no. 1, 1989. PP. 2- 19.

No. 6 E. van Demme, Renegotiation-proof equilibria in repeated prisoners'dilemma, Journal of Economic Theory, vol. 47, no. 1, 1989,PP. 206 - 217.

No. 7 C. Mulder and F. van der Plceg, Trade unions, inveatment andemployment in e amall open economy: e Dutch perspective, !n J.Muyaken and C. de Neubourg ( eda.), Unemployment in Europe, London:The MacMillan Presa Ltd, 1989. PP. 2~ - 229.

No. 8 Th. ven de Klundert and F. van der Plceg, Wage rigidity end capitalmobility in an optimizing model of a emall open economy, De Economiat137. nr. 1, 1989. PP. 47 - 75.

No. 9 G. Dhaene end A.P. Barten, When it all began: the 1936 Tinbergenmodel revisíted, Economic Modelling, vol. 6, no. 2, 1989,PP. 203 - 219.

No. 10 F. van der Ploeg and A.J. de Zeeuw, Conflict over arms accumulationin market and command economiea, in F. ven der Plceg and A.J. deZeeuw (eds.), D emic Polic Games in Economics, Contributions toEconomic Analyais 1 1, Amsterdam: Elsevier Science Publishers B.V.(North-Holland). 1989. pP. 91 - 119.

No. 11 J. Driffill, Macrceconomic policy gamea with incomplete information:some extensiona, in F. van der Plceg end A.J. de Zeeuw (eds.),Dynemíc Policy Games in Economics, Contributiona to Economic Malysís181, Amsterdam: Elaevier Science Publishera B.V. (North-Holland),1989. PP. 289 - 32z.

No. 12 F. van der Plceg, Towerds monetary integration in Europe, in P. DeGreuwe e.e., De Euro ae Monetaire Inte ratie: vier viaiea,Wetenschappelijke Raad voor het Regeringsbeleíd V 6, 's-Gravenhege:SDU uitgeveri~, 1989, pp. 81 - 1G6.

No. 13 R.J.M. Alesaie and A. Kapteyn, Consumption, savings end demogrephy,in A. Wenig, K.F. Zimmermann ( eds.), Demographic Change end EconomicDevelopment, Ber1ln~Heidelberg: Springer-Verlag, 1989. PP. 272 - 305.

No. 14 A. Hoque, J.A. Megnus and 8. Peseran, The exect multi-period mean-aquare forecest error for the first-order autoregressive model,Journel of Econometrics, vol. 39. no. 3. 1988. PP. 327 - 3~~6.

No. 15 R. Alessie, A. Kapteyn and B. Melenberg, The effects of liquidityconstraints on consumption: estimation from household penel data,EuroPean Economic Review 33, no. 2~3, 1989. PP. 5~~7 - 555.

No. 16 A. Holly end J.R. Magnus, A note on instrucental variables andmaximum likelihood eatímation procedurea, Mnnlea d'Économie et deStatistigue, no. 10, April-June, 1988, pp. 121 - 13 .

No. 17 P. ten Hacken, A. Kapteyn and I. Wolttiez, Unemployment benefits andthe labor merket, a micro~macro epproach, in A.A. Qustafason and N.Mdera Klevmarken (eda.), The Politícal Econosy of Sociel Security,Contributiona to Economic Analyaís 179, Amsterdam: Elsevíer SciencePubliahera B.V. (North-Holland), 1989. PP. 143 - 164.

No. 18 T. Wansbeek and A. Kapteyn. Estimation of the error-components modelwith incomplete penels, Journal of Econometrica, vol. 41, no. 3,1989. pp. 341 - 361.

No. 19 A. Kepteyn, P. Kooreman end R. Willemae, Some methodological issuesin the implementation of aub~ective poverty definitions, The Journalof Human Resources, vol. 23, no. 2, 1988, pp. 222 - 242.

No. 20 Th. ven de Klundert and F. van der Plceg, Fiscal policy end finitelives in interdependent economies with real and nominal wagerigidity, Oxford Econoaic Papers, vol. 41, no. 3. 1989. PP. 459 -489.

No. 21 J.R. Magnus and 8. Pesaran, The exact multi-period mean-squareforecast error for the fírat-order autoregresaive model with enintercept, Journal of Econometrics, vol. 42, no. 2, 1989,PP. 157 - 179.

No. 22 F. van der Plceg, Two easays on political economy: (i) The politíceleconomy of overvaluatíon, The Econoeic Journal, vo1. 99. no. 397.1989, pp. 850 - 855; ( 11) Election outcomes and the stockearket.European Journal of Political Economy, vol. 5, no. 1, 1989, pp. 21 -30.

No. 23 J.R. Magnue and A.D. Woodland, On the maximum likelihood estimationof multiveriate regresaion modela containing serielly correletederror componenta, International Economic Review, vol. 29, no. 4,1988. PP. 707 - 725.

No. 24 A.J.J. Talman and Y. Yasamoto, A simpliciel algorithm for stationarypoint problema on polytopes, Mathematica of Operetiona Research, vol.14, no. 3. 1989. pp. 383 - 399.

No. 25 E. ven Demme, Stable equilibrie and forwerd induction, Journal ofEconomic Theory, vol. 48, no. 2, 1989, pp. 476 - 496.No. 26 A.P. Barten and L.J. Bettendorf, Price foroetion of fiah: Anapplication of an inverae demand ayatem, European Economíc Review,

vol. 33. no. 8. 1989, PP. 1509 - 1525.

No. 27 0. Noldeke end E. van Demme, Signalling in a dynamíc lnbour merket,Review of Economic Studiea, vol. 57 (1), no. 189, 1990, pp. 1- 23

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No. 29 F. ven der Plceg end A.J. de Zeeuw, Perfect equilibrium in a model ofcompetitive erma accumulation, International Economic Review, vol.31, no. 1, 1990, pp. 131 - 146.

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No. 31 F. van der Plceg, International interdependence end policycoordination in economiea with real end nominal wage rigidity, GreekEconomic Review, vol. 10, no. 1, June 1988, pp. 1- 48.

No. 32 E. van Damme, Signaling and forwerd inductlon in a market entrycontext, 0 rationa Reaearch Proceedin s 1 8, Berlin-Heídelberg:Springer-Verlag, 1990, pp. 5- 59.

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No. 35 Th, ven de Klundert, On sociceconomic causea of 'weit unemployment',Eucopean Economic Review, vol. 34, no. 5, 1990, pp. 1011 - 1022.

No. 36 R.J.M. Alesaie, A. Kapteyn, J.B. ven Lochem end T.J. Wanabeek,Indivldusl effecta in utility conaiatent modela of demand, in J.Hartog, 0. Ridder and J. Theeuwes (eds.), Panel Data and LaborMarket Studiea, Amaterdam: Elsevier Science Publiahera B.V. (North-Hollana), 1990, pp. 253 - 278.

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No. 41 A. ven Scest, I. Noittiez and A. Kepteyn, Labor supply, income taxes,end houra restrictions in the Netherlends, Journal of HumanReaourcea, vol. 25, no. 3. 1990. PP- 517 - 558.

No. 42 7Ti.C.M.J. van de Klundert and A.B.T.M. ven Schalk, Unemploymentperaistence and loss of productive capacity: a Keynesien eDProach,Journel of Macrceconomica, vol. 12, no. 3, 1990. PP. 363 - 380.

No. 43 Zh. Níjman and M. Verbeek, Estimation of time-dependent parameters inlinear modela using cross-sectíons, penels, or both, Journal ofEconometrica, vol. 46, no. 3. 1990. PP. 333 - 346.

No. 44 E. ven Damme, R. Selten nnd E. Winter, Alternating bid bargainingwith e amalleat money unit, Oames and Economic Behavior, vol. 2,no. 2. 1990. PP. 188 - 201.

No. 45 C. Dang, 1'he D 1 -trianguletion of Rn for aimpliciel elgorithms forcomputing soluiiona of nonlinear equationa, Methematics of OperationsReseerch, vol. 16, no. 1, 1991, pp. 148 - 161.

No. 46 T1i. Ni~men end F. Palm, Predictive eccurecy gein from disaggregateeempling in ARIMA modela, Journal of Businesa R Economic Statiatics,vol. 8, no. 4, 1990. DP- 405 - 15.

No. 47 J.R. Magnus, On certain moments relating to retios of quadratic formsin normel variablea: further resulta, Sankhye: The Indian Journal ofStatiatica, vol. 52, aeries B, pert. 1, 1990, pp. 1- 13.

No. 48 M.F.J. Steel. A Beyeeían enelysis of aimulteneous equation models bycosbining recuraive analytical and nusericnl epproaches, Journal otEconometrice. vol. 48, no. 1~2, 1991, pp. 83 - 117.

No. 49 F. van der Plceg end C. Withagen, Pollution control end the remaeyproblem, Environmentnl end Resource Economica, vol. 1, no. 2, 1991,pp. 215 - 236.

No. 50 F. van der Plceg, Money and cepital in interdependent econoaies withoverlapping generations, Econosica, vol. 58, no. 230. 1991,pP. 233 - 256.

No. 51 A. ICapteyn and A. de Zeeuw, Chenging incentivea for economic reseerchin the Netherlanda, Buropean Economic Review, vol. 35, no. 2~3, 1991.PP. ~3 - 611.

No. 52 C.O. de Vriea, On the reletíon between OARCH and stable processes,Journal of Econometrica, vol. 48, no. 3, 1991, pp. 313 - 324.

No. 53 R. Alessie and A. Kapteyn, Habit formation, interdependent prefer-ences and demographic effects in the almost ideal demand system, TheEconomic Journal, vol. 101, no. 406, 1991, pp. 404 - 419.

No. 54 W. van Grcenendasl and A. de Zeeuw, Control, coordination endconflict on international commodity markets, Economic Modelling, vol.8, no. 1, 1991, pp. 90 - 101.

No. 55 F. van der Plceg end A.J. Markink, Dynamic policy in linear modelswith rational expectations of future events: A computer package,Computer Science in Economics and Management, vol. 4, no. 3, 1991,pp. 175 - 199.

No. 56 H.A. Keuzenkamp and F. van der Plceg. Savings, ínvestment, governmentfinance, and the current account: The Dutch experience, in C.Alogoskoufis, L. Papademos and R. Portes (eds.), External Constraintson Macroeconomic Policy: The European Experience, Cambridge:Cambridge University Press, 1991, pp. 219 - 263.

No. 57 Th. Nijman, M. Verbeek and A. van Scest, The efficiency of rotating-panel designs in en enalysis-of-variance model, Journal ofEconometrics, vol. 49, no. 3, 1991. PP. 373 - 399.

No. 58 M.F.J. Steel and J.-F. Richard, Bayesian multivariate exogeneityenalysis - an applícation to a UK money demand equation, Journal ofEconometrics, vol. 49, no. 1~2, 1991. pp. 239 - 274.

No. 59 Th. Nijman and F. Palm, Generalized least squares estimation oflinear models containing rational future expectations, InternationalEconomic Review, vol. 32, no. 2, 1991. PP. 383 - 389.

No. 60 E. van Damme, Equilibrium selection in 2 x 2 games, Revista Espanolade Economia, vol. 8, no. 1. 1991. pp. 37 - 52.

No. 61 E. Bennett and E. van Damme, Demand commitment bargaining: the caseof apex games, in R. Selten (ed.), Game uilibrium Models III -Strategic Bargaining, Berlin: Springer-Verlag, 1991, pp. 118 - 1 0.

No. 62 W. GUth and E. van Damme, Gorby games - a game theoretic analysis ofdisarmament campaigns and the defense efficiency - hypothesia -, inR. Avenhaus, H. Karkar and M. Rudnianski (eds.), Defense DecisionMaking - Analytical Support and Crisis Management, Berlin: Springer-Verlag, 1991, pp. 215 - 240.

No. 63 A. Roell, Dual-capacity trading and the quality of the market,Journal of Financial Intermediation, vol. 1, no. 2. 1990,pp. 105 - 124.

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