Tilburg University

Empirical tests of a simple pricing model for sugar futures

Nijman, T.E.; Beetsma, R.M.W.J.

Publication date:1993

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Citation for published version (APA):Nijman, T. E., & Beetsma, R. M. W. J. (1993). Empirical tests of a simple pricing model for sugar futures.(Reprint series / CentER for Economic Research; Vol. 131). Unknown Publisher.

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imi i iu ii u i u i i ii im i um i~i i u m i u i u iEmpirical Tests of a Simple Pricing

Model for Sugar Futures

byTheo E. Nijman

and Roel Beetsma

Reprinted from Annales d'Économieet de Statistique,

No. 24, 1991

Reprint Seriesno. 131

CENTER FOR ECONOMIC RESEARCH

BoardIlarry BarkemaHelmut BesterEric van Damme, chairmanFrank van der Duyn Schoutenleffrey James

ManagementEric van Damme ( graduate education)Arie Kapteyn (scientific director)Marie-Louise Kempertnan ( administration)

Scientific CouncilAnton BartenEduard BomhoffWillem BuiterJacques DrèzeTheo van de KlundertSimon KuipersJean-Jacques LaffontMerton MillerStephen NickellPieter RuysJacques Sijben

Université Catholique de LouvainErasmus University RotterdamYale UniversityUniversité Catholique de LouvainTilburg UniversityGroningen UniversityUniversité des SciencesUniversity of ChicagoUniversity of OxfordTilburg UniversityTilburg University

Residential FellowsLans BovenbergWerner GiithJan MagnusShigeo MutoTheodore 'roKarl Wí;merydKarl-Erik Wíirneryd

Research CoordinatorsEric van DammeFrank van der Duyn SchoutenHany fluizingaArie Kapteyn

Sociales de Toulouse

CentER, Erasmus University RotterdamUniversity of FrankfurtCentER, LSETohoku UniversityUniversity of PittsburghStockholm School of EconomicsStockholm School of Economics

Address : Warandelaan 2, P.O. Box 90153, 5000 LE Tilburg, The NetherlandsPhone : t31 13 663050Telex : 52426 kub nlTelefax : f31 13 663066E-mail : "centerna htikub5.bitnet"

ISSN 0924-7874

1993

forEconomic Research '-.~-;""~ ~~.U,B.í;.,;, ,.,

, :í,'I,'ïj ~fji fi: ;;,~ i,~ BtF3l~I(JTHEEK~r'~ TILBURC

~~ -EmpircTTests of a Simple Pricing

Model for Sugar Futures

byTheo E. Nijman

and Roel Beetsma

Reprinted from Annales d'Économieet de Statistique,

No. 24, 1991

Reprint Seriesno. 131

ANNALES D'ÉCONOMIE ET DE STATISTIQUE. - N' 24 - 1991

E m p i r i ca I Testsof a

Simple Pricing Modelfor Sugar Futures

Theo E. NIJMAN, Roel BEETSMA "

ABSTRACT. - In this paper we test the empirical implicationsof a simple pricing model for commodity futures for the marginalprocess of prices of sugar futures. According to the pricing model,the futures price bias depends linearly on the conditionalvariance. We find significant coefficients, from monthly as wellas daily data, if the conditional variahce is modelled using theGARCH-M model. These estimates imply contango in the futuresmarked and a net hedging demand on the long side of it.

Tests empiriques d"un modèle de prix pour descontrats à terme de sucre

RÉSUMÉ. - Dans cet article, nous testons un modèle de déter-mination des prix pour des contrats à terme concernant le sucre.Selon ce modèle, la déviation des prix prévisionnels dépend linéai-rement de la variance conditionnelle. En utilisant le modèle deGARCH-M pour la variance conditionnelle, nous trouvons descoefficients significatifs, à partir des données aussi bien mensuellesque quotidiennes. Ces estimations impliquent un ~~ contango~ surle marché et une demande nette de diminution des risques du cótédes acheteurs.

' T. E. NIJMAN et R. BEETSMA: Department of Economics, Tilburg University, P.O.Box 90153. 5000 LE Tilburg, The Netherlands and Center for Economic Research,Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands respectively.Helpful comments by Henk van Stokkom and Rene van Rooyen of Limako BrokerageN.V. in Breda, by Hidde Smit and Franz Palm and by seminar participants at ErasmusUniversity. Rotterdam, are gratefully acknowledged. The data were kindly provided byLimako Brokerage N. V.

1 Introduction

Many models consider relations between prices of futures contracls andcorresponding spot prices (see e. g. ANnERSON and DnN-r}~iN~ [1983], I{IRSCH-~rtr-eR [1989, 1990]). In this paper, we test whether a simple special caseof lhesc models, which is discussed at length e. g. in the recent textbook hyDuFFir [1989], is relevant for the futures market for sugac Qecause of datalimitations the tests are directcd lowards the implications for the marginalprocess of the futures prices only. According to the model under considera-tion, tlie futures price bias depends linearly on the conditional variance. Astraightforward gencralization of the ARCH-M model proposed in GNC~r.r,LtueN and RoarNS [1987] is used to model the condilional variance. Resultson monthly data from January 1972 to June 1989 as well as from dailydata since 1979 are reported. The GARCH-M models yield significantcoefticicnts for the conditional variance, which imply contango in the sugarfutures market and a net hedging demand on the long side of the market.

'The plan of this papcr is as follows. [n section 2 we present the pricingmodel under consideration. The stylized facts in thc data are described insection 3. The significance of lhe estimates of the monthly conditionalvariance is tested in seclion4. Daily data are analyzed in sec[ion5, whilcsection 6 concludes.

2 A Simple Pricing Model

Consider the demand for commodity futures contracts of agents withmean variance utility functions, who possibly have positions on next periodsspot market for the commodity under consideration. Assume that theagents can trade the corresponding futures contract as well as a stvckmarket portfolio. Let y,'„ denote agent i's next period's spot rnarketposition, whilc s,~, denotes next periods spot príce. We make the simplify-ing assump[ion that q,'~ 1 is known in period ~, which can be motivated bythe observation that the uncertainty in y,'t, is probably small compared tothe price-uncertainty. if furthermore f,kt denotes the price of the corre-sponding futures contract k periods before expiration, [3;'~ is the amountinvested in the stock market portfolio and r,t, is the return on the stockmarkel portfolio, the wealth of agenti in the subseyuent pcriod, W;;,, canbe expressed as

(I) W~'~ -Q"r(Ifr )f t'~ s -f- r~"(jtk-~t-ft"~),r-Ft r rtt qr.t~r~t )r rrt r

122

where r;" denotes the agent's futures position in period r. Note that it isassumed that are no margin requirements in cash. Moreover we assumefor simplicity thal the returns on the stock market portfolio are uncorrelatedwith thc spot and futures prices, which is not in conflict with the empiricalevidcncc for commodity futures ( DUSAK [1973]). Every agent is assumedto choose his posi[ion in the futures marke[ by maximizing a utility functiondefined over the expected value and the variance of' end-of-period wealthWrt~~ i.e.

(~) y~'~.-argmax U~~t { Er [W~'t i), Varr [W~~t,] i.yS"

whcre U~'t is the utility function of agent i and E, [. ] and Var, [. J denotethe conditional expectation and conditional variance respectively. One wayto motivate ( 2) is to assume utility functions with constant absolute riskaversion for ull agents as well as lognormality of wealth ( sce e.g f)t:A~oNand Mueu.tiAUeR [1980, p.403]. Note that the ugcnts are allowed to huvcdifferent degrees of risk aversion, but that homogeneity of expectations isassumcd throughout. Differcntiation with respect to y,'' in (2) after substitu-tion of ( I) yields the first order condition

(3) t.~,i'-0.5{ Er[i~t,'~]-.~;k~~~{ Varr~l~: ~it]r Poi }

-~~rrt I COVr 1~1r t 1~fi t I' ~l~Varr lfrk- 1 r~1~

where p"'- - UZ'~U1't is the risk aversion coefficienl. "The Iirst and seconclterm in ( 3) are known as the pure speculative demand and the pure hedgedemand respectively, as the second tenn vanishes for speculators (y;"-0)while thc fírst term vanishes if p"~ --. oc. Equilibrium on the futures markctrey uires

(4)N

~ y;'t - 0~-i

where N is the number of agents in [he economy. From ( 3) and (4) onecan essily derive the following expression for the futures price bias

~kt-E jk-Ij~t rUttl ]~

(5) ErU~t~lt]-~~kt-2P9rt~Covr[.5'rt~,.~~:~'~,

where

p-~ ~ (p7-'~N

N

is the markets risk aversion and q,t ~- ~ y,'; ~~N is thc nct hedging pressure~-i

on the market. Two additional assumptions will bc imposed to ubtain aunivariate model which can be estimated from data on tLtures pricesonly. Admittedly, these two assumptions are crude approximations at thebest and they can be avoided in a multivariate model. The first additionalassumption is that in every period a futures con[ract expires witli exactly

~-i

SUGAR PUTURF.S 123

thc spcciliculions (placc of dclivcry, yualily ctc.) which thc hcclgcrsrequire. Using an arbitragc argument this assumption of [he absence ol'basis risk implics Cov, [.r, t~,.~; ~~'r] - Var, [ ~;;~'t]. 'Thc sccond additionalassumption is Ihat net hedging pressure docs not vary over lime:q, ~~-y. If thesc assumptions are made eyualion (5) yields testablc implica-tions on the marginal process for ~J;t r-.~;t~'~-J;kr,

(6) Qli .r 1-~1 Vari t~~~ t I J} F~ t 1~

where S-2pq and where s,a r is indcpendent of past rcalizations of4~;,.~. CnkirH eruL [1983] have considered a model similar to (5) andavoided the assumption of a constant net hedging pressure by making useof data on the percentage of speculators who were net along. GRir:R e~nl.(1983) howcvcr ,rssumcd rnnditional homoskedasticity.

The basic modcl that is outlined above has been re(incd by many aulhors(SEe C.g. ANDP.RSUN and 1)AN"ï111NG [1983] and HIRSrIILrtFeR [1989, 1990])taking into account e. g. production uncertainty and covariance of commod-ity prices with the market portfolio. fn this paper we will restrict ourselvesto testing the relevance of the basic model for sugar futures.

3 Some Stylized Facts on SugarFutures

Sugar-I I contracts which expire in January, March, May. July, Septemberand October are traded on the New York Coffee, Sugar and Cocoa Exch-ange (NYCSCE). A da[a-series of daily observations on price changes inthe contract which is closest to expiration (excluding last month observationsto avoid potenlial delivery obligations) will be analyzed in sections 4 and 5in order to test the pricing model that was presentcd in the previoussection. The series of monthly changes which is constructed from thisdata-set is presented in figure I. Throughout the paper all prices are indollars per IO.OOOIbs. Two pcriods of bad weather (1973~1974 and1979~1980) caused high international sugar prices ( see Fno [1985]), whichare evidently rellected in the futures prices. Figure I also clearly showsthat volatility of the sugar futures prices is titne varying and that themargina) distribution of the price changes is fat tailed. Thesc are wcllknown stylized facts, which hold true for many futures (campare e. g.Tnvr.oR [1986]). The kurtosis of the monthly serics is cstimated as I1.9,while lhe standard Lagrange Multiplier test statistic for sixth ordcr ARCHyields lhe very significant value of 63.6. The LM test for sixth arderautocorrelation yields a value of 17.6 which is close to the I"~o criticalvalue of a x2-distribution with six degrees of freedom. Note howcver thatstandard lests for serial correlation in the mean will be biascd upward inthe presence of conditional heteroskedasticity ( see c. g. Drr.nor.n ( 1987]) and

124

Ili;uRr. I

Chunges in ILlunthlt~ Sugur FuJurrs Prices

1453.6

726.5060

,868Ar

-665,5A88

-1331, A I~.u72M2

DF

thus Icad to over-rejection. In figure 2 the monthly price dianges areplotted for the sub-sample from .lanuary 1982 to June 1989 during whichperiod the sugar prices were much more stable. For this sub-period Iheestimated kurtosis is 3.8 and the LM tests for ARCH and autocorrelationyield Ihe insigniticant values of 2.8 and 5.7.

FIrURE ~

Chunges in MonthlJ~ Sugur Futures Prices

345, eeae

76M6 86K18 85M2 89l15

172, seee

-119,5866

-239.B6A682N1 83M11 85M9 87M7 89M5m

The two daily series, which will be analyzed in section 5, are plotted infigures 3 and 4. The conditional heteroskedasticity is obviously even morepronounced for the full sample than it is for the less volatile sub-sample. Note that, according to [he results on temporal aggregation of

SUGAR FUTURES 125

i'IGURI' 3

Dailv Price Differences for Sugar Frrlures 72-89

v' 400.00

v- -400.00

F~cuRE 4

Daily Price DiJ'ferencesfor Sugar Futures 82-89

iso.oo

e3 84 Bs B6

v~ -aso.oo

87 B6 m

Í26

GARCH processes in DROST and Nun~nN [1990], the conditional hetero-skedas[icity in [Ile daily data in the subsamplc is not cunllicliug with the:apparent homoskedasticity of the monthly data.

4 Tests Based on Monthly Data

According to the pricing model discussed in section 2, the futures pricebias depends linearly on the conditional variance. As the conditionalvariance is unobservable, estima[ion of the parameter S in (6) requiresestimates of this conditional variance. At least two approaches to deriveestimates of the monthly conditional variance have been proposed in theliterature. A first suggestion (see e.g. PoreROn and SuMMeRS [1986] or1'RENCH, SCHWERT 8nd STAMBAUGH [19~7]) IS the Use Of a n70Ving averageof squared daily returns. We have computed estimates of lhe monthlyconditional variance in this way and subsequently estimated (6) usingordinary and generalized least squares for various subsamples. The esti-mates of S, which are reported in NuwtnN and BEETSMn [1990], tend to benegative but insignificant. We do nut report the estimates here because ofspace limitations, but also because this approach is valid only if the dailyexpected return can be assumed to be negligible. Another drawback ofthis approach is that it can not be used to generate daily variance forecastsfrom daily data.

A second approach to the estimation of the conditional variance whichhas been taken in [he literature is the use of the GARCH model propusedby BOLLERSLC-V [1986]. The simplest GARCH model, the GARCH(l,l)mudel, assumes that the conditional variance depends with exponentiallydedining weights on squared unexpected changes in the futures price. Ifin addition to the GARCH(l,l) assumption normality of the conditionaldistribution is imposed the complete model reads as

(7) Af,-Sh,t~,h,

(8) ~~~~~-1,~~-z,. . . -N(0, I)z

(~) h~-~f Í~11~-1 fa~,-.1Ir,-,.

The model in (7), (8) and (9) is a straightforward generalization of theARCH-M (ARCH in mean) modcl proposed by ENGLe, LILICN and RontNs[1987]. The parameters in the GARCH-M model can be estimated bynumerical maximization of the likelihood. The consistency of the max-imom likelihood estimator in this model, which has long been a mereconjecture, has been recently proved by BOLLERSLEV and WnULnRll~cr.[ I 990].

Estimates of (7)-(9) from monthly data are presented in table 1. Thenumbers in pan;ntheses are !-statistics derived from estima[es of thc large

SUGAR FUTURES 127

s.rmlilc variancc which arc roulincly comhutcd Ironr lhc I Icstii,rn c~l Ihe Ic~g-likelihood. -1'he numbcrs in square brackets are the ~-statistics proposedby Wr..iss [1986], which are mbust to departures from normalily in therescaled innovations ~, in GARCH models. We conjecture thal thcse ~-statistics are also more reliable in GARCH-M models if conclitional norm.rl-ity does not hold. The divergencc from normality can be judged from theestimate of the kurtosis of the rescaled disturbances in the last column ofthe tahle. Finally thc sixth colum of the tablc prescnts the Lagrangemultiplier test, LM~, for up to sixth order autocorrclatiun on thc rescaledresiduals.

Ta,ur.t~ 1

A4on~hly GARCH-M mndels

Sampte ~ a (i S li LM~ K

72-I 89-6 2~24 0.43 0.52 - O.IR)0 55 16.R 4.9(3.21) (5.73) ( 7.44) ( - 3.62)(3.37] (zt7] [to.os) (-3.63J

72-I 81-12 2 35R 0.44 0.51 - 0.OD(154 18.9 6.0(2.38) (5.88) (7.24) ( - 3.13)12.12j (B.SSJ [10.41] (- 2.85)

82- I 89-6 2 789 0.12 0.G0 - 0.000 G4 5.0 3.6(0.64) (0.55) (I.01) ( - 0.51)[0.37J [0.25] ( 0.53J [-0.48J

72-I 89-6 2320 0.43 O.í2 -Q.00053 - o.W43 17.0 4.5(3.22) (5.74) ( 7.45) (-3.04) (- r1.50)[3.26) (G.99j (9.90] [ - 2.87J [ - 0.45J

The cs[imates of S in table I are negative, which suggests a net hcdgingdemand on lhe long side of the market: The hedging dernand from buycrson the spot market exceeds the hedging demand of sellers. The order ofmagnitude of the estimates of S in table I does not differ from the resultswhich are obtained if estimates of the monthly conditional variance arederived from squared daily excess returns, but the important point to notehere is that for both the full sample (January 1972-June 1989) and the highvolalility subsample (January 1972-December 1981) the impact ofthe conditional variance on the futures price bias appears to besignificant. Note however that the Lagrange Multiplier test autocorrela-tion, LM~, indicates some autocorrelation in the disturbances, which mightresult in biased t-ratio's. Under the null hypothesis of no autocorrelationthis test statistic is asymptotically centrally xz distributed with 6 degrees offreedom. The critical values of this distribution at the 5 and I"~" level are12.6 and 16.8 respectively.

Attempts to estimate a GARCH-M model for January 1982-June 1989failed as the assumption of no persistence in variance (a -t- ~ ~ I) which isimposed by the software was violated, which probably has to do with erraticobservations in the beginning of the sample and a sma(I sample size. (f thesample is chosen as .lanuary 1984-June 1989 convergence is achieved. As inthis case the estimated variance parameters are insignificant, it is notsurprising to tind an insigni(icant estimate of lhe mean pararneter as

128

wcll. ln ordcr W show thal thc evid~nce on the time varying risk premiumis nut causcd by the presence of a constant risk prcmium xnd absence of aconstant in (7), we have also estimated the model including the possibi[ityof a time-invariant risk premium, denoted by Et. As shown in the final rowof table 1 this parameter is insignificant and does not affect the signiticanceof thc remaining paramelers.

5 Tests Based on Daily Data

In thc prcvious scction the GARCH-M modcl, whidt was molivated bythe pricing model presented in section 2, was estimated for monthly data. Itis not cle~~r from the pricing model, however, how long the appropriatetime periods are. If the agents solve a simple single period optimizationproblem, as they do in section 2, the use of monthly data already appearsto imply a short planning horizon. On the other hand, however, the agentsobviously have access [o high freyuency information un the underlyingvariables and have incentives to use this information. This argument sug-gests the use of high frequency, e. g. daily, data. Moreover, the behavior ofagents who in fact maximize a mu[tiperiod additively separable mean vari-ance criterion function, can probably be closely mimicked by the behaviourof myopic agents if subsequent changes in asset prices are uncon-elated,which is roughly the case for the sugar futures (cumpare also 1NGERSOLL[1987], pp.2S5-258). This implies that the GARCH-M model might wellbe a valid specification at the daily frequency as well.

Estimates of the daily GARCH-M model arc presented in table 2. Becauseof limitatiuns of our software, daily observations have only been analyzed

T.aHI e 2

Duil~~ GARCEI-h1 ncudel~~

--Samplc-- - -- ~-------~- --~----5- -

ti LM.~ ~

-- - 780101 ----- - 6.14 --- 0.084 0.906 - Q000 8 -- ----- -- - 8.6 4.5(4.22) (9.75) (96.9) ( - 2.10)

890601 (3.02) [6.60j [65. I ] ( - 2.021820 I U I I U.41 0.081 0.90(1 - U.0112 5 3.6 4.7

(3.36) (7.27) (63.5) ( - 2.70)890601 [2.21) [4.60] [41.0] (-2.53)780101 6.07 0.085 0.906 -0.0005 -0.72 8.S 4.S

(4.20) (9.75) (96.8) (- I.01) (- t.74)890601 [3.00[ [6.63] [65.3J [ - 0.911 [ - I .70]8201 U I I U.44 0.081 0.900 - 0.002 6 U.059 3.6 4.7

- (3.30) (7.25) (62.8) ( - 2.12) (0.14)890601 (2.23J [4.53] [39.8j ( - 2.08] [0.21 ]

SUGAR FUTURES 129

from January I, 197R onwards. '[~he estimates for thc I'ull samplc imply(once more) a significant ncgalive impact of the conditional variance onthe futures price bias. Moreover the estimate of S that is obtained is closeto the estimates from monthly data. As suggested by the resulls on tempo-ral aggregation of GARCH processes in DROST and NuMnrv [1990], thedaily model is close to integration in variance and the estimate of (3 fromdaily dala exceeds the estimates from monthly data, while the opposite istrue for the estimates ofa. For the subsample from 820101-890601 similarresults are oblained, although the estimate of S is somewhat small. Forthe full sample the problem of multicollinearity between a time-variantand a time-invariant component of the risk premium reappears. For thesubsarnple, however, the significance of the conditional variance term is notaffected by the presence of a constant in (7).

6 Concluding Remarks

[n this paper we have tested the empirical implications for the marginalprocess of prices of Sugar futures of a simple pricíng modeL A significantimpact of the conditional variance on the change in futures prices wasoblained in monthly as well as daily GARCH-M models. Thcse estimatesimply contango in the futures markets and a net hedging demand on thelong side of the futures market. Moreover our resulls suggest that thesimple pricing model points at at least one important aspect of the pricingof Sugar futures: the risk premia depend on the time varyingvolatility. Tests of the more detailed pricing models which have beenproposed in the literature are left for future research.

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NuMAN, T. E. and BeersMA, R. -"Empirical Tesls of a Simpl(: Pricing Mudel lurSugar Futures", Center (Ilscussion puprr 9068, Tilburg Univcrsity.

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SUGAR I:UTURES 131

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No. 1 G. Marini and F. van der Ploeg, Monetary and fiscal policy in an optimising modelwith capital accumulation and finite lives, 7he Ecatomic Journal, vol. 98, no. 392,1988, PP. 772 - 786.

No. 2 F. van der Plceg, International policy coordination in interdependent monetaryeconomies, Jortrnal of buentational Ecortomics, vol. 25, 1988, pp. 1- 23.

No. 3 A.P. Barten, The history of Dutch macroeconomic modelling (1936-1986), in W.Driehuis, M.M.G. Fase and H. den Hartog (eds.), Challeitges for MacroecononticModellir:g, Contributions to Economic Analysis 178, Amsterdam: North-Holland,1988, pp. 39 - 88.

No. 4 F. van der Plceg, Disposable income, unemployment, inFlation and state spending ina dynamic political-economic model, Public Cltoice, vol. 60, 1989, pp. 211 - 239.

No. 5 Th. ten Raa and F. van der Plceg, A statistical approach to the probfem of negativesin input-output analysis, Econornrc Modelling, vol. 6, no. l, 1989, pp. 2- 19.

No. 6 E. van Damme, Renegotiation-proof equilibria in repeated prisoners' dilemma,Jottrrurl ojEcono~tic 77teory, vol. 47, no. 1, 1989, pp. 206 - 217.

No. 7 C. Mulder and F. van der Plceg, Trade unions, investment and employment in asmall open economy: a Dutch perspective, in J. Muysken and C. de Neubourg ( eds.),Utternployntertt in Europe, London: The Macmillan Press Ltd, I989, pp. 200 - 229.

No. 8 Th. van de Klundert and F. van der Plceg, Wage rigidity and capital mobility in anoptimizing model of a small open economy, De Economrst, vol. 137, nr. 1, 1989, pp.47 - 75.

No. 9 G. Dhaene and A.P. Barten, When it all began: the 1936 Tinbergen model revisited,Econotnic Modelling, vol. 6, no. 2, 1989, pp. 203 - 219.

No. 10 F. van der Ploeg and A.J. de Zeeuw, Conflict over arnu accumulation in market andcommand economies, in F. van der Plceg and A.J. de Zeeuw (eds.), Dynamic PolicyGmnes in Econanics, Contributions to Economic Analysis 181, Amster- dam:Elsevier Science Publishers B.V. (North-Holland), 1989, pp. 91 - l l9.

No. ll 1. Driffill, Macrceconomic policy games with incotnplete information: someeztensions, in F. van der Plceg and A.J. de Zeeuw (eds.), Dyrtatnic Policy Gantes inEconornics, Contributions to Economic Analysis 181, Amsterdam: Elsevier SciencePublishers B.V. (North-Holland), 1989, pp. 289 - 322.

No. 12 F. van der Ploeg, Towards monetary integration in Europe, in P. De Grauwe et al.,De Europese Mortetaire Integratie: vier visies, Wetenschappelijke Raad voor hetRegeringsbeleid V 66, 's-Gravenhage: SDU uitgeverij, 1989, pp. 81 - 106.

No. 13 R.1.M. Alessie and A. Kapteyn, Consumption, savings and demography, in A.W enig, K. F. Zi mmermann (eds. ), Demograpl:ic Changeand Economic Developtnettt,Berlin~Heidelberg: Springer-Verlag, 1989, pp. 272 - 305.

No. 14 A. Hoque, 1.R. Magnus and B. Pesaran, The exact multi-period mean-square forecasterror for the first-order autoregressive model, Journa[of Ecottonretrics, vol. 39, no.3, 1988, pp. 327 - 346.

No. 15 R. Alessie, A. Kapteyn and B. Melenberg, The effects of liquidity cotutraints onconsumption: estimation from household panel data, European Economic Revieiv, vol.33, no. 213, 1989, pp. 547 - 555.

No. 16 A. Holly and J.R. Magnus, A note on instrumental variables and maximum likeli-hood estimation procedures, Altltales d'Écouomie er de Statistique, no. 10,April-June, 1988, pp. 12l - 138.

No. 17 P. ten Hacken, A. Kapteyn and I. Woittiez, Unemployment benefits and tlie labormarket, a microlmacro approach, in B.A. Gustafsson and N. Anders Klevmarken(eds.), 7he Po(itical Econo~tv of Socia! Security, Contributions to Economic Analysis179, Amsterdam: Elsevier Science Publishers B.V. (North-Holland), I989, pp. 143- 164. '

No. IS T. Wansbeek and A. Kapteyn, Estimation of the error-components model withincomplete panels, Journa!of Ecatanetrics, vol. 41, no. 3, 1989, pp. 34l - 361.

No. 19 A. Kapteyn, P. Kooreman and R. Willemse, Some methodological issues in theimplementation of subjective poverty definitions, The Jourual of Hmnau Resources,vol. 23, no. 2, 1988, PP. 222 - 242.

No. 20 Tli. vatl de Klundert and F. van der Ploeg, Fiscal policy and finite lives ininterdependent economies with real and nominal wage rigidity, Osford EconomicPapers, vol. 4l, no. 3, 1989, pp. 459 - 489.

No. 2l J.R. Magnus and B. Pesaran, The exact multi-period mean-square forecast error forthe first-order autoregressive model with an intercept, Journa! of Econometrics, vol.42, no. 2, 1989, pp. 157 - 179.

No. 22 F. van der Ploeg, Two essays on political econotny: (i) Tlie political economy ofovervaluation, The Ecottomic Jountal, vol. 99, no. 397, 1989, pp. 850 - 855; (ii)Election outcomes and the stockmarket, Europeanlournalof Politica! Econonty, vol.5, no. l, 1989, pp. 21 - 30.

No. 23 J.R. Magnus and A.D. Woodland, On the maximum likelihood estimation ofmultivariate regression models containing serially correlated error components,btternational Economic Review, voL 29, no. 4, 1988, pp. 707 - 725.

No. 24 A.1.J. Talman and Y. Yamamoto, A simplicial algorithm for stationary pointproblems on polytopes, Mathematics of Operatiotu Researclt, vol. 14, no. 3, I989,pp. 383 - 399.

No. 25 E. van Damme, Slable equilibria and forward induction, Journa!ojEconanic 77teory,vol. 48, no. 2, 1989, pp. 476 - 496.

No. 26 A.P. Barten and L.J. Bettendorf, Price formation of fish: An application of an inversedemand system, European Ecortomic Review, vol. 33, no. 8, 1989, pp. 1509 -] 525.

No. 27 G. Noldeke and E. van Damme, Signalling in a dynamic labour market, Revietv ojEcaromic Snrdies, vol. 57 (1), no. 189, 1990, PP. 1- 23.

No. 28 P. Kop Jansen and Th. ten Raa, The choice of model in the construction ofinput-output ccefficients matrices, Intentatiortal Economic Review, vol. 3l, no. 1,1990, pP. 213 - 227.

No. 29 F. van der Ploeg and A.l. de Zeeuw, Perfect equilibrium in a model of competitivearms accumulation, Interna[ionalEcormmic Review, vol. 3l, no. l, 1990, pp. l31- 146.

No. 30 J.R. Magnus and A.D. Woodland, Separabilityand aggregation, Econontica, vol. 57,no. 226, 1990, pp. 239 - 247.

No. 31 F. van der Ploeg, International interdependence and policy coordination in economieswith real and nominal wage rigidity, Greek Ecatomic Review, vol. 10, no. 1, June1988, pP. 1 - 48.

No. 32 E. van Damme, Signaling and forward induction in a market entry contezt,Operations Researclt Proceedings 1989, Berlin-Heidelberg: Springer-Verlag, 1990,pp. 45 - 59.

No. 33 A.P. Barten, Toward a levels version of the Rotterdam and related detnand systenu,Contributiars to Operations Research and Econornics, Cambridge: M1T Press, 1989,pp. 441 - 465.

No. 34 F. van der Ploeg, International coordination of monetary polícies under alternativeezchange-rate regimes, in F. van der Plceg (ed.), Advanced Lectures in QuanritativeEconomics, London-0rlando: Academic Press Ltd., 1990, pp. 91 - 121.

No. 35 Th. van de Klundert, On socioeconomic causes of 'wait unetnployment', EuropeanEconomic Review, vol. 34, no. 5, 1990, pp. 101! - 1022.

No. 36 R.J.M. Alessie, A. Kapteyn, J.B. van Lochem and T.J. Wansbeek, Individual effectsin utility consistent models of demand, in J. Hartog, G. Ridder and 1. Tlieeuwes(eds.), Pmtel Dnta and Labor Market Studies, Amsterdam: Elsevier SciencePublishers B.V. (North-Holland), 1990, pp. 253 - 278.

No. 37 F. van der Ploeg, Capital accumulation, inflation and long-run conflict ininternational objectives, Oxjord Economic Papers, vol. 42, no. 3, 1990, pp. 501 -525.

No. 38 Th. Nijman and F. Paltn, Parameter identification in ARMA Processes in thepresence of regular but incomplete sampling, Journalof Time Series Analysis, vol.I1, no. 3, 1990, pp. 239 - 248.

No. 39 Th. van de Klundert, Wage differentials and employment in a two-sector model witha dual labour market, Metroecortomica, vol. 40, no. 3, 1989, pp. 235 - 256.

No.40 Tlt. Nijman and M.F.I. Steel, Exclusion restrictions in instrumental variablesequations, Ecottotnetric Reviews, vol. 9, no. l, 1990, pp. 37 - 55.

No. 4l A. van Soest, l. Woittiez and A. Kapteyn, Labor supply, income taxes, and hoursrestrictions in the Netherlands, Jourual of Htuttau Resottrces, vol. 25, no. 3, 1990,pp. 517 - 558.

No. 42 Th.C.M.J. van de Klundert and A.B.T.M. van Schaik, Unemployment persistenceand loss of productive capacity: a Keynesian approach, JoranalojMacro- economic.r,vol. l2, no. 3, 1990, pp. 363 - 380.

No. 43 Th. Nijman and M. Verbeek, Estimation of time-dependent parameters in linearmodels using cross-sections, panels, or both, Jourttal of Econometrics, vol. 46, no.3, I990, pp. 333 - 346.

No. 44 E. van Danune, R. Selten and E. Winter, Alternating bid bargaining with a smallestmoney unit, Games and Ecatomic Beleavior, vol. 2, no. 2, 1990, pp. 188 - 201.

No. 45 C. Dang, The Di-triangulation of R" for simplicial algorithms for computing solutíonsof nonlinear equations, Marhentmics of Operations Research, vol. 16, no. 1, 1991,PP. l48 - I61.

No. 46 Th. Nijman and F. Palm, Predictive accuracy gain from disaggregate sampling inARIMA models, Journalof Business Rc Econotnic Statistics, vol. 8, no. 4, 1990, pp.405 - 415.

No. 47 J.R. Magnus, On certain moments relating to ratios of quadratic forms in nonnalvariables: further results, Sanklrya: T7te Iitdian Journa!of Statistics, vol. 52, seriesB, part. L, 1990, PP. 1- 13.

No. 48 M.F.J. Steel, A Bayesian analysis of simultaneous equation models by combiningrecursive analytical and numerical approaches, Journalof Econon:etrics, vol. 48, no.l l2, 1991, pp. 83 - 117.

No. 49 F. van der Plceg and C. Withagen, Pollution control and the ramsey problem,Eirviron~nental atd Resoterce Ecottontics, vol. 1, no. 2, 1991, pp. 215 - 236.

No. 50 F. van der Ploeg, Money and capital in interdependent economies with overlappinggenerations, Econonrica, vol. 58, no. 230, 1991, pp. 233 - 256.

No. Sl A. Kapteyn and A. de Zeeuw, Changing incentives for economic research in theNetherlands, Europemt Economic Review, vol. 35, no. 213, 1991, pp. 603 - 611.

No. 52 C.G. de Vries, On the relation between GARCH and stable ptocesses, Journal ofEcottontetrics, vol. 48, no. 3, 1991, pp. 313 - 324.

No. 53 R. Alessie and A. Kapteyn, Habit formation, interdependent preferences anddemographic effects in the almost ideal demand system, The Economic Journal, vol.101, no. 406, 1991, pp. 404 - 419.

No. 54 W. van Groenendaal and A. de Zeeuw, Control, coordination and conflict oninternational commodity markets, Economic Modelling, vol. 8, no. t, 1991, pp. 90- IOI.

No. 55 F. van der Ploeg and A.1. Markink, Dynamic policy in linear models with rationalexpectations of future events: A computer package, Computer Science in Economicsand Management, vol. 4, no. 3, 1991, pp. 175 - 199.

No. 56 H.A. Keuzenkamp and F. van der Plceg, Savings, investment, govemment finance,and the current account: The Dutch ezperience, in G. Alogoskoufis, L. Papadetnosand R. Portes (eds.), External Constraints on Macroeconomic Policy: The EuropeanExperience, Cambridge: Cambridge University Press, 1991, pp. 219 - 263.

No. 57 Th. Nijman, M. Verbeek and A. van Soest, The efficiency of rotating-panel designsin an analysis-of-variance model, Journal of Econometrics, vol. 49, no. 3, 1991, pp.373 - 399.

No. 58 M.F.I. Steel and J.-F. Richard, Bayesian multivariate ezogeneity analysis - anapplication to a UK money demand equation, ]ournal of Econometrics, vol. 49, no.112, 1991, PP. 239 - 274.

No. 59 Th. Nijman and F. Palm, Generalized least squares estimation of linear modelscontaining rational future expectations, International Economic Review, vol. 32, no.2, 1991, pp. 383 - 389.

No. 60 E. van Damme, Equilibrium selection in 2 x 2 games, Revista Espanola deEconomia, vol. 8, no. l, 1991, pp. 37 - 52.

No. 61 E. Bennett and E. van Damme, Demand commitment bargaining: the case of apexgames, in R. Selten (ed.), Game Equilibrium Models III - Strategic Bargaining,Berlin: Springer-Verlag, 1991, pp. I18 - I40.

No. 62 W. Giith and E. van Damme, Gorby games - a game theoretic analysis ofdisarmament campaigns and the defense efficiency - hypothesis - , in R. Avenhaus,H. Karkar and M. Rudniatuki (eds.), Defense Decision Making - Analytical Supportand Crisis Managetnent, Berlin: Springer-Verlag, 1991, pp. 215 - 240.

No. 63 A. Roell, Dual-capacity trading and the quality of lhe market, Jottntal of FittmtcialIrUennediarion, vol. 1, no. 2, 1990, pp. l05 - 124.

No. 64 Y. Dai, G. van der Laan, A.J.J. Talman and Y. Yamamoto, A simplicial algorithmfor the nonlinear stationary point problem on an unbounded polyhedron, 5imtt Jounta!of Optirrtizatiort, vol. l, no. 2, 1991, pp. I51 - 165.

No.65 M. McAleer and C.R. McKenzie, Keynesian and new classical models ofunemployment revisited, 77te Economic Joarnal, vol. lOl, no. 406, 1991, pp. 359- 381.

No. 66 A.J.I. Talman, General equilibrium programming, Niettw Archief voor Wisktotde, vol.8, no. 3, I990, pp. 387 - 397.

No. 67 ].R. Magnus and B. Pesaran, The bias of forecasts from a ftrst-order autoregression,Economerric 77eeory, vol. 7, no. 2, 1991, pp. 222 - 235.

No. 68 F. van der Ploeg, Macroeconomic policy coordination issues during the variousphases of economic and monetary integration in Europe, Etrropean Economy - 7heEconomics of EMU, Commission of the European Corrununities, special edition no.1, 1991, pp. l36 - 164.

No. 69 H. Keuzenkamp, A precursor to Muth: Tinbergen's 1932 model of rationalexpectations, 77te Economic Jourrml, vol. 101, no. 408, 1991, pp. 1245 - 1253.

No. 70 L. Zou, The target-incentive system vs. the price-incentive system under adverseselection and the ratchet effect, Jottrttalof Public Economics, vol. 46, no. l, 1991,pp. 51 - 89.

No. 7l E. Bomhoff, Between price reform and privatization: Eastern Europe in transition,FinanZmarkt und Portfo[io Managemetu, vol. 5, no. 3, 1991, pp. 241 - 251.

No. 72 E. Botnhoff, Stability of velocity in the major industrial countries: a Kalman filterapproach, lrttentatiorta! Monetary Futtd Staff Papers, vol. 38, no. 3, 1991, pp. 626- 642.

No. 73 E. Bomhoff, Currency convertibility: when and how? A contribution to the Bulgariandebate, Kredit und Kapital, vol. 24, no. 3, 1991, pp. 4l2 - 431.

No. 74 H. Keuzenkamp and F. van der Ploeg, Perceived constraints for Dutch unemploymentpoliey, in C. de Neubourg (ed.), T7ie Art of Full Employment - Unemployntent Policyin Open Economies, Contributions to Economic Analysis 203, Amsterdam: ElsevierScience Publishers B.V. (North-Holland), 1991, pp. 7- 37.

No. 75 H. Peters and E. van Damme, Characterizing the Nash and Raiffa bargainingsolutions by disagreement point axions, Matl:ematics of Operatiotts Research, vol. 16,no. 3, 1991, pp. 447 - 461.

No. 76 P.J. Deschamps, On the estimated variances of regression coef6cients in misspecifiederror components models, Econometric Theory, vol. 7, no. 3, 1991, pp. 369 - 384.

No. 77 A. de Zeeuw, Note on 'Nash and Stackelberg solutions in a differential game modelof capitalism', Journa! of Economíc Dyrtatnics a~ui Control, vol. 16, no. I, 1992, pp.l39 - 145.

No. 78 J.R. Magnus, On the fundamental bordered matrix of linear estimation, in F. van derPloeg (ed.), Advattced Lectures in Quantitative Eca:onrics, London-Orlando:Academic Press Ltd., 1990, pp. 583 - 604.

No. 79 F. van der Ploeg and A. de Zeeuw, A differential game of international pollutioncontrol, Systems and Contro! Le[ters, vol. 17, no. 6, 1991, pp. 409 - 414.

No. RO Th. Nijman and M. Verbeek, The optimal choice of controls and pre-experimen- talobservations, Jounta! of Econometrics, vol. 51, no. 112, 1992, pp. 183 - 189.

No. 81 M. Verbeek and Th. Nijman, Can cohort data be treated as genuine panel data?,Empirica! Economics, vol. 17, no. 1, 1992, pp. 9- 23.

No. 82 E. van Damme and W. Gáth, Equilibrium selection in the Spence signaling game, inR. Selten (ed.), Game Equilibriunt Models !I - Methods, Morals, and Markets,Berlin: Springer-Verlag, 1991, pp. 263 - 288.

No. 83 R.P. Gilles and P.H.M. Ruys, Characterization of economic agents in arbitrarycommunication structures, Nieuw Archiej voor Wiskrtnde, vol. 8, no. 3, I990, pp.325 - 345.

No. 84 A. de Zeeuw and F. van der Ploeg, Difference games and policy evaluation: aconceptual framework, O~tford Ecottomic Papers, vol. 43, no. 4, 1991, pp. 612 -636.

No. 85 E. van Damme, Fair division under asymmetric information, in R. Selten (ed.),Ratiana! Inleraaio~ - Essays in Honor oj Jol:n C. Harsattyi, BerlinlHeidelberg:Springer-Verlag, 1992, pp. 121 - 144.

No. 86 F. de 1ong, A. Kemna and T. Klcek, A contribution to event study methodology withan application to the Dutch stock market, Jountal ojBanking and Finance, vol. 16,no. l, 1992, pp. 11 - 36.

No. 87 A.P. Barten, The estimation of mized demand systems, in R. Bewley and T. VanHoa (eds. ), Comributions to Consroner Denuutd andEconometrics, Essays itt HonourojHenri 77tei1, Basingstoke: The Macmillan Press Ltd., 1992, pp. 31 - 57.

No. 88 T. Wansbeek and A. Kapteyn, Simple estimators for dynamic panel data models witherrors in variables, in R. Bewley and T. Van Hoa (eds.), Contributions to CottsrnnerDemand and Econometrics, Essays in Honour oj Henri Thei[, Basingstoke: TheMactnillan Press Ltd., 1992, pp. 238 - 251.

No. 89 S. Chib, J. Osiewalski and M. Steel, Posterior inference on the degrees of freedomparameter in multivariate-t regression models, Econontics Leners, vol. 37, no. 4,1991, pp. 391 - 397.

No. 90 H. Peters and P. Wakker, Irtdependence of irrelevant alternatives and revealed grouppreferences, Econometrica, vol. 59, no. 6, 1991, pp. I787 - 1801.

No. 9l G. Alogoskoufis and F. van der Ploeg, On budgetary policies, growth, and externaldeficits in an interdependent world, Journal of the Japanese mtd InternationalEcortonties, vol. 5, no. 4, 1991, pp. 305 - 324.

No. 92 R.P. Gilles, G. Owen and R. van den Brink, Games with permission structures: Theconjunctive approach, Internatiotta! Jourrta! of Game 73teory, vol. 20, no. 3, 1992,PP. 277 - 293.

No. 93 J.A.M. Potters, I.1. Curiel and S.H. Tijs, Traveling salesman games, Mathe~taticaJProgramming, vol. 53, no. 2, 1992, pp. 199 - 211.

No. 94 A.P. 1urg, M.1.M. lansen, J.A.M. Potters and S.H. Tijs, A symmetrization for finitetwo-person games, Zertschrift fur Operarions Research - Methods and Models ofOperations Research, vol. 36, no. 2, 1992, pp. 111 - 123.

No. 95 A. van den Nouweland, P. Borm and S. Tijs, Allocation rules for hypergraphcommunication situations, Interrtatíortal Journal oj Game 7heory, vol. 20, no. 3,1992, pp. 255 - 268.

No. 96 E.1. Bomhoff, Monetary reform in Eastern Europe, Ertropeart Econorrric Review, vol.36, no. 213, 1992, pp. 454 - 458.

No. 97 F. van der Ploeg and A. de Zeeuw, International aspects of pollution control,Environmenta! and Resource Econontics, vol. 2, no. 2, 1992, pp. 1 17 - 139.

No. 98 P.E.M. Borm and S.H. Tijs, Strategic claim games corresponding to an NTU-game,Games and Ecortanic Behavior, vol. 4, no. 1, 1992, pp. 58 - 71.

No. 99 A. van Soest and P. Kooreman, Coherency of the indirect translog demand systemwith binding nonnegativity constraints, Jonrna! oj Econometrics, vol. 44, no. 3,1990, pp. 39l - 400.

No. !00 Th. ten Raa and E.N. Wolff, Secondary products and the measurement ofproductivity growth, Regiortal Science and Urban Ecortanics, vol. 21, no. 4, 1991,pp. 581 - 615.

No. l01 P. Kooreman and A. Kapteyn, On the empirical implementation of some gametheoretic models of household labor supply, 77re Joarrta! of Human Resources, vol.25, no. 4, 1990, pp. 584 - 598.

No. I02 H. Bester, Bertrand equilibrium in a differentiated duopoly, Intentotlonaf EconomicRevierv, vol. 33, no. 2, 1992, pp. 433 - 448.

No. 103 J.A.M. Potters and S.H. Tijs, The nucleolus of a ntatrix game and otlier nucleoli,Matlrernatics of Operatioru Researci:, vol. 17, no. 1, 1992, pp. 164 - 174.

No. l04 A. Kapteyn, P. Kooreman and A. van Soest, Quantity rationing and concavity in aftexible household labor supply model, Review of Econornics artd Statistics, vol. 72,no. l, 1990, pp. 55 - 62.

No. 105 A. Kapteyn and P. Kooreman, Household Iabor supply: What kind of data can tellus how many decision makers there are7, European Economic Review, vol. 36, no.213, 1992, pp. 365 - 371.

No. 106 Th. van de Klundert and S. Smulders, Reconstructing growth theory: A survey, DeEconomist, voL 140, no. 2, 1992, pp. 177 - 203.

No. 107 N. Rankin, Imperfect competition, expectations and the multiple effects of monetarygrowth, 71re Econontic Jonrnal, vol. 102, no. 413, 1992, pp. 743 - 753.

No. l08 J. Greenberg, On the sensitivity of von Neumann and Morgenstern abstract stablesets: The stable and the individual stable bargaining set, Ltternational Jourrta! ofGrrrne 7Jteory, vol. 21, no. I, 1992, pp. 41 - 55.

No. 109 S. van Wijnbergen, Trade reform, policy uncertainty, and the current account: Anon-expected-utility approach, Arnerican Econornic Review, vol. 82, no. 3, 1992, pp.626 - 633.

No. 110 M. Verbeek and Th. Nijman, Testing for selectivity bias in panel data models,Irtten~atiortal Eco~tomic Review, vol. 33, no. 3, 1992, pp. 681 - 703.

No. I 1 l Th. Nijman and M. Verbeek, Nonresponse in panel data: The impact on estimates ofa life cycle consumption function, Journal of Applied Econontetrics, vol. 7, no. 3,1992, pP. 243 - 257.

No. l 12 l. Bomze and E. van Damme, A dynamical characterization of evolutionarily stablestates, Annals of Operatiorts Research, vol. 37, 1992, pp. 229 - 244.

No. 113 P.]. Deschamps, Ezpectations and intertemporal separability in an empirical modelof consumption and investment under uncertainty, Empirical Economics, vol. 17, no.3, 1992, pp. 419 - 450.

No. l14 K. Kamiya and D. Talman, Simplicial algorithm for computing a core element in abalanced gatne, Jourrta!of the Operations Research, vol. 34, no. 2, 1991, pp. 222 -228.

No. 115 G.W. lmbens, An efficient melhod of moments estimator for discrete choice modelswith choice-based sampling, Econornetrica, vol. 60, no. 5, 1992, pp. 1187 -1214.

No. 116 P. Borm, On perfectness concepts for bimatriz games, OR Spektnint, vol. 14, no.l, 1992, pp. 33 - 42.

No. I 17 A.P. Jurg, I. Garcia Jurado and P.E.M. Borm, On modifications of the concepts ofperfec[ and proper equilibria, OR Spektrum, vol. 14, no. 2, 1992, pp. 85 - 90.

No. 1 18 P. Borm, H. Keiding, R.P. McLean, S. Oortwijn and S. Tijs, The compromise valuefor NTU-gatnes, Intentational Jountal of Game Theory, vol. 21, no. 2, 1992, pp.175 - 189.

No. t 19 M. Maschler, J.A.M. Potters and S.H. Tijs, The general nucleolus and the reducedgame property, buernatiotuil Journalof Game 77teory, vol. 21, no. l, 1992, pp. 85 -

106.

No. 120 K. Wíirneryd, Communication, correlation and symmetry in bargaining, EconomicsLerters, vol. 39, no. 3, 1992, pp. 295 - 300.

No. 121 M.R. Baye, D. Kovenock and C.G. de Vries, I[ takes two to tango: equilibria in a

model of sales, Games artd Economic Behat~or, vol. 4, no. 4, 1992, pp. 493 - 510.

No. l22 M. Verbeek, Pseudo panel data, ín L. Mátyás and P. Sevestre (eds.), lheEcwiometrics of Panel Data, Dordrecht: Kluwer Academic Publishers, 1992, pp. 303- 315.

No. 123 S. van Wijnbergen, Intertemporal speculation, shortages and the political economyof price reform, The Econornic Jountal, vol. 102, no. 415, 1992, pp. 1395 - 14(Xi.

No. 124 M. Verbeek and Th. Nijman, Incomplete panels and selection bias, in L. Mátyás andP. Sevestre (eds.), 71te Econometrics oj Panel Data, Dordrechr. Kluwer AcademicPublishers, 1992, pp. 262 - 302.

No. 125 J.J. Sijben, Monetary policy in a game-Iheoretic framework, JalrrbiicáerfurNatiorraldkonorrrie utrd Statistik, vol. 210, no. 314, 1992, pp. 233 - 253.

No. 126 H.A.A. Verbon and M.J.M. Verhoeven, Decision making on pension schemes underrational expectations, Journa! of Econanics, vol. 56, no. 1, 1992, pp. 71 - 97.

No. l27 L. Zou, Ownership structure and eCficiency: An incentive mechanism approacli,Jortnra! of Conrparatève Ecorromics, voL 16, no. 3, 1993, pp. 399 - 431.

No. l28 C. Fershtman and A. de Zeeuw, Capital accumulation and eutry deterrence: Aclarifying note, in G. Feichtinger (ed.), DV~ramic Econon:ic MOdels and OptimalControl, Amsterdam: Elsevier Science Publishers B.V. (North-Holland), 1992, pp.281 - 296.

No. 129 L. Bovenberg and C. Petersen, Public debt and pension policy, Fisca! Sn~dies, vol.l3, no. 3, 1992, pp. 1- 14.

No. 130 R. Gradus and A. de Zeeuw, An employment game between government and firms,Optimal Corrtro[Apptications ~ Methods, vol. 13, no. 1, 1992, pp. 55 - 71.

No. 131 Th. Nijman and R. Beetsma, Empirical tests of a simple pricing model for sugarfutures, Anirales d'Écotromie et de Statistique, no. 24, 1991, pp. 121 - 131.

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