• Non ci sono risultati.

On ants and markets

N/A
N/A
Protected

Academic year: 2021

Condividi "On ants and markets"

Copied!
32
0
0

Testo completo

(1)

EUROPEAN UNIVERSITY INSTITUTE, FLORENCE

DEPARTMENT O F ECONOMICS

F

o r k i n g p a p e r n o

. 88/351

; AND MARKETS by

Alan

K I R M A N

BADIA FIESOLANA, SAN DOMENICO (F I)

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(2)

All rights reserved. No part of this paper may be reproduced in any form without

permission of the author.

(C) Alan Kirman Printed in Italy in June 1988 European University Institute

Badia Fiesolana - 50016 San Domenico (Fi) -

Italy © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(3)

ON ANTS AND MARKETS 1:

A lar. P. KIRMAN

European University Institute 50016 San Domenico di Fiesoie. Itaiv

Man has long been intrigued by the behaviour of social

insects and the rationale for their apparently complicated

behaviour. The observed complex patterns may sometimes be

derived from rather simple individual behavioural rules and

the interaction between the individuals involved. This

paper describes some counterintuitive phenomena observed in

certain species of ants, provides a simple mathematical

model to explain these phenomena and then suggests how these

phenomena may be reinterpreted to explain market behaviour

which seems to correspond to many observed features and yet.

is difficult to explain with standard models. Whilst the

paper probably generates more questions than answers. it

suggests an underlying mechanism very different from those

incorporated in more conventional models, which may prove a

useful way of looking at certain market features. In

particular the model used generates endogenous market,

fluctuations which, whilst not chaotic in the standard

sense, exhibit certain features which seem to coincide with

some empirical behaviour.

Ants: The empirical evidence

j I an greatly indebted to Hans Follmer who provided the basic insight as to the nature of the stochastic process

involved here. We are pursuing joint work on the issues

^ raised in this paper. X am also grateful to Michael

Woodford for his helpful comments. The usual disclaimers apply. 1 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(4)

In a recent article Pasteels et al (1987) describe the

following phenomena:

Two identical sources of food piles. A and B. were

placed near to an ants' nest and were constantly replenished

so that they remained at the same level. When an ant finds

one of the sources he returns with food to the nest and lays

a chemical trail which increases the probability that

another ant emerging from the nest and searching

stochastically will find that pile. Since both heaps were

always found and exploited, the natural question to ask is

how did the ants distribute themselves between the two

heaps. Instead of finally settling, as one might have

expected, to an equal concentration at each heap the ants

would be heavily concentrated on say pile A and then there

would be a sudden switch to heap B and this switch would

occur from time to time. Pasteels et al (1987) constructed a

model of the ants' behaviour which reduces to a system of

differential equations for which the numerical solution gave

two steady states when the number of ants was large enough.

The two solutions are asymmetric in that each involves a

large proportion of ants feeding at one pile and a small

number at the other. Although such a model would explain

the asymmetric division of the ants it would not explain how

a switch in the intensity of exploitation from one pile to

the other would occur as does the model presented here.

For economists two remarks made by the entomologists in

question (Pasteels et al 1987) are of particular interest.

2 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(5)

"Without falling into naive anthropomorphism, the

study of social insects has greatly benefitted from

distant analogies with human behaviour and economics"

and they also remark in connection with the stochastic

nature of individual behaviour:

"However it is remarkable that a mathematical model

based on these simple premises is able to generate

the coherent collective behaviour observed in the

experiments. We do not believe that more classical

approaches, such as a reductionist analysis of

communication or models based on optimisation theory

could have achieved this goal".

The economist' objection to the second observation must

be that there is something less than coherent about a

society which splits its resources between two identical

sources and in fact has some "lost ants" who find neither.

The defense is that the behaviour involved is efficient in

nature where there is always a likelihood of a food source

drying up and therefore society must always be on the

lookout for new sources. Presumably if the sources were

replenished over a sufficiently long period and there were

some learning 2 ) there would eventually be complete

concentration on the productive sources. Nevertheless as

our model shows the concentration would be asymmetric.

We will take here as the major features of our model

interaction and stochastic "recruiting" and try to reverse

2 Paradoxically Pasteels et al (1987b) in another paper look at the learning problem but consider it at the purely

individualistic level. 3 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(6)

the trend observed by the entomologists by applying evidence

from insects to human behaviour.

A . s i m p l e f o r m a l , m o d e l

First we describe a simple mathematical model in which

individuals (ants) are recruited to one of two sources,

or as another interpretation to anticipate what follows,

there are two prevalent views in the world and when two

individuals with different views meet there is some

probability of one of them being converted to the other's

v i e w .

More formally, consider N (ants) people belonging to

one of two groups. The state of the system is defined as

the number of (ants) people k in group 1 .

i.e. k £ (0, 1, --- N)

Now the dynamics of the system are given by the following.

Choose one person at random then choose another. Let the

first be converted to the second’s group with probability l-£.

(He will otherwise change group with probability -§7 .

In a finite group the importance of this is obvious). The

pfocess may then be described as follows.

+

1

With p r o b a b i l i t y (1-;;) ( f + (1 - £ ) “ T )

y/l N 2 N-l

(1 ) k

^ k - 1 with p r o b a b i l i t y ^ ( f + (1 - £) ^ ^ )

N 2 N - l

There are two special cases:

a) £ = 1 (no interaction, the first person chooses his

group by flipping a coin). This is the Ehrenfest urn model

with an equilibrium distribution which is binomial.

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(7)

n

(k = 0, ...n) (k)

b) £ = 0 (total interaction, the first person moves to the

second’s group I. In this case the state k performs a

martingale with final absorption in k = 0 or k = N. with

Prob [absorption in k = N | initial state =kQ J = _£

In general the eouillbrium distribution p(k), (k = 0,

...n) of the Markov chain P (k, A. ) defined by (1) is

defined by

p(k) = I 1>U) W

1=0 ,.. .n

,c-V*C \

and can be explicitly calculated via the detailed.balanced

condition p(k) P(k, l) = ti(i) P ( i , k ), i . e . p(k) •“o p(0) ii (k) ji(k-l) ii(l) u(0) " ci( aiil 1 + t 1 ii(0 ) i=i 11 (k) n(k-l) ii (1 ) . . p ( i - l ) ) where 5 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(8)

u(k-t-l) _ P(k - k+IL p(k) P0<+1 - M

( L -

5

) (f

(1

~ c)

>

( § + (1-eH1 * n=I

))-Now let us look at the asymptotic form when N-?*> and = M

for some OC > 0 . Let x =-^£[0. T\

When N is large p can be approximated by a distribution on

the interval [Jo, l] with density fix). Thus for N large we

have. f- -i /£ '■ V (k+l) - V (k) ^ f (N + N) - f(N j p(k) ~ 1/N f (k) ^ N j f’ lx)

But as N — ? 00 the right hand term is just '

Furthermore as S - ? 1® we have assumed Therefore we

have

f'(x) _ (j*-l)(l-2x)

f(x) X (1-x)

and that:

f is the density of a symmetric Beta distribution, l.e.

fix) = const, x**'"* ll-x) " - ' 1_____

The shapes of the distributions for different values of

£ are illustrated in figure 1. The time evolution of the

state x for N=50 and different values of £ is illustrated

in figure 2 . © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(9)

Equilibrium.distribution for the model with state space £o.

1 ...nJ respectively , 1/N... 1^ with different.

values of £. and N = 1 0 0 .

Figure 1.

It is of interest to note that this is also related to

Polya's urn model a classical model for contagious effects,

which evolves as follows: Two groups of (people) ants, with

s ants each,start at time t = 0 and then at period t+l,c new

ants arrive, meet one randomly chosen ant from the old

population and follow it to its group.

The state at time t of the process, i.e. k ants in

crowd no. 1 changes to ktc with probability --- . The

2s + c . t

proportion of ants in crowd no. 1 which is^-t- converges

c . t

almost surely to a limiting value which has a Beta

s distribution with p a r a m e t e r - . 7 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(10)

n « 50 epsilon = .001

Time evolution of the state x = "# ants in crowd No.i"

for n = 50, with starting value x = 25, for

e = .001, with

y

- corresponding equilibrium distribution.

e = 0.9 , with | | = corresponding equilibrium distribution.

Figure 2 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(11)

Some, observations fin...foreign-exchange markets

The first question. it we are to apply the model

developed above, that is natural to pose, is to what extent

are people in financial markets, tor example, influenced by

communicating with each other'? Do they not simply observe

market signals as a large part of the literature would have

us believe? If this were the case, the very basis on which

the model presented here is founded would be undermined.

However there is accumulating evidence that a great deal of

information is transmitted in this way and that, trading in

particular shares may often be prompted by a conversation

with another trader. Shiller and Pound ( 1 9 8 6 1 in a recent

article give substance to what is a long-standing feature of

market lore. Interestingly enough they explicitly refer to

the epidemic phenomenon and cite such standard texts on this

subject as Bailey (1975) and Kermack and McKendrick (1927).

The second question is to what extent does the market

reflect empirical features which would cast doubts on

existing explanations. Goodhart (1987) putting together

empirical evidence and knowledge of institutions points out

many of the weaknesses of existing theoretical models.

"Overshooting" is rarely observed and the responsiveness to

shocks is muted, in particular the impact of "unanticipated"

interest rate changes on spot exchange rates was

undetectable, the random walk with its persistence cannot be

easily rejected for nominal spot foreign exchange rates for

example, but seems to correspond to shorter rather than to

longer term views.

9 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(12)

Goodhart (1987) is led to the belief that, the market

reflects a fundamental tug-of-war between two groups of

individuals, those who extrapolate and those who believe

that "fundamentals" play a determining role. A possibility

is that individuals are themselves schisophrenic, adopting

the extrapolatory view for their short term transactions and

the fundamentalist point of view for their longer term

positions. We shall take a simpler point of view and adopt

a model derived from one of Frankel and Froot (1986) in

which two views are held by individuals. In their model

actual trades are made by portfolio managers who attach

weights to the two different market views prevailing,

changing these weights in such a way as to forecast

correctly the current changes. But as they say:

"In any case one could interpret the two groups as

taking positions in the market directly rather than

merely issuing forecasts for the portfolio managers

to read".

Indeed Figlewski (1978, 1982) considers a model in which the

private information or views of individuals are transmitted

to the market through the market price and these views are

weighted by the relative wealth of the individuals.

In our model the important point is that agents change

their views by discussing with others whom they meet at

random. Now a problem raised by Michael Woodford 3) is that

3 In private correspondence. He suggests an alternative model in which agents of the two types are in fixed proportions and their demand is derived from a utility

function of the mean and variance of wealth. This model has

interesting features but involves individuals having fixed views as to the variance of future spot prices which would not be consistent with our model.

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(13)

at. first, glance the process of conversion from one type to

another does not seem to be related to how the individuals

of each type are faring. In fact if there are many agents

of one type in the market, the probability of being converted

to that type is quite high. However, since these agents

dominate, the market reflects their view, and to maintain

the other view is losing behaviour. Thus there is a close

relation between conversion to a type and the fact. that, that

type’s view is economically correct. What is very important,

to note is that when there are large numbers of agents

plays almost no role in the conversion, the dominant part of

the probability is the relative size of the popoulation.

Thus it is the prevailing view that matters rather than

epsilon and this makes economic sense. We now give the.

details of our model.

A simple model of exchange rate determination

Modifying Frankel and Froot’s (1986) model as

suggested we consider a model in which there are two types

of agents. Firstly there are "fundamentalists" f who

believe that the change in the exchange rate st at time t

will tend to bring it back to an underlying equilibrium s

and whose forecast change is expressed by

A

3[+1

» V(S - Sfc)

and secondly there are "chartists" who extrapolate naively

11 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(14)

^t+l ” st ■ st-l

The “market, view" cari then be expressed as

* s t + l = " t “ t + l + (1 - w =t + l

where if k is the number of and there are N agents, then

fundamentalists in the market

The dynamics of kt. are given as described before by the

random meeting of agents.

The market actually evolves as follows:

ill n

s t = CASt + l + 2t

where Zt is some index of fundamental economic variables.

Frankel and Froot justify this model in different ways but

of course have a different dynamic for w+ . If we solve this

simple model and assume "rationality',' zt = s we obtain

(£) Sj. = [l+cwtV - c+cwt]-1 [Cltcw t V) s - c ( l - w , J st - 1 ]

Looking at the simple case in which c = 1, which depends

naturally on the underlying model, it is clear that i f ( l -

wt ) J(l + V) wtj - 1 > 1 the system becomes unstable.

Precisely this happens when the model is simulated as

can be seen in figure 3. It remains close to s for a long

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(15)

Fundamentalists and Chartists,

Figure 3

time and then explodes. However, it is important to note

that the way in which the market evolves is highly dependent

on the number of meetings that take place between each price

change. The stability of the process is closely related to

this and it is interesting to reflect on the consequences of

the change from periodic fixing of prices with an opportunity

for discussion between price fixings to a system with

"continuous" price changes.

13 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(16)

In fact, although our system "explodes" it would

eventually return to the fundamentalist equilibrium and

would thus exhibit the creation and extinction of bubbles.

The size and duration of these bubbles depends essentially

on the relative frequency of meetings and price changes.

Some intuition as to the evolution of s^ with can be

derived from looking at the derivative.

This can be contrasted with Frankel and Froot’s results

in that they have to introduce a further feature to induce

the eventual collapse of a bubble, whereas, in our case, the

evolution of w t guarantees this.

An alternative model is one in which there are two

types of fundamentalists believing respectively that the

exchange rate will return to i i , or s z .

In this case we have

__ t = _ [l+CW V - C + C W t 3wt T -]"2 [cv+c] ai+cwtv) s-c(l-w) V l + [1+CW,.V - c+ c w t l 1 [CVS + and we obtain ri(sl " st) + (1 - w) (S2 - st) 14 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(17)

Now if we let. c = 1 and s

we obtain

st = [1+ w ^ + ( l -w t ) v 2] 1 (wt V s + ( ( l - w t ) v2 + i2

Now given the stochastic process governing w^. we can examine

the evolution of st and compare it with the results of

simulations in the previous case. This is illustrated in

figure 4.

Two Fundamentalists.

Figure 4 15 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(18)

There is movement between the two equilibria and visual

examination would suggest the existence of "regimes" and

rapid shifts from one to the other. As mentioned before the

relationship between the frequency of meetings and of price

fixing plays a significant role in determining the pattern

of the exchange rate over time.

In this case the movements of the exchange rate are

characterised by shifts from one regime to the other whilst

in the first case the exchange rate remained at a given

level, then is characterised by a period of explosive

activity before returning to that level.

A different approach would be to suggest that people

appreciate that when their views are minority ones, markets

will not reflect these views. Thus, although having their

own opinions, they behave in line with the prevailing view.

However when the percentage of people agreeing with them

rises, they begin to anticipate a market change and switch

their behaviour. This would lead to more dramatic changes

in market prices than those in the model above, in which

people always behave according to their own views.

In this paper we have provided an account of a

mechanism which may be useful in explaining some features of

markets which seem to defy simple theoretical analysis of

the standard type. Here the important features are the

existence of different views of the market, stochastic

16 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(19)

encounter between the individuals in the market and the

possibility of changing view. A natural question is why do

individuals change view so radically and not progressively.

In our second example the answer is clear. If the market

fluctuates between two levels and spends very little time at

intermediate values, the individual must forecast either the

high rate or the low rate and it never makes sense to

forecast some intermediate rate. The essential problem for

the agent is to anticipate the switch between regimes.

Finally it is worth underlining again the simple

coherence of the model. When one view predominates, the

evolution of the market reflects that view, and thus

justifies those holding it. This situation, as is only

reasonable, corresponds with a high probability of the

minority being converted to the prevailing view. Thus

although conversion is stochastic, the probability of being

converted to a view is dependent on how accurate that view

of the market i s .

A particularly interesting problem raised by the model

is that of the relationship of the number of encounters

between price changes to the stability of the evolution of

prices.

However the essential lesson to be learned here from

the behaviour of ants is the importance of individual

interaction and its consequences for the aggregate behaviour

of the system. Whilst this problem preoccupies other

scientists and social scientists it is one to which

economists tend only to allude.

17 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(20)

References

Bailey. N .T .J .. f19751 The Mathemati,ca1 Theory of Infactioug

Diseases. London. Griffith.

Denenbourg J.-L., S. Goss, J.M. Pasteels, D. Fresneau and

J.P. Lachaud (19871 "Self organization mechanisms in ant

societies (II): Learning in foraging and division of

labour", in J.M. Pasteels and J.-L. Denenbourg (eds.). Fro®

Individual to._Collective___ Behaviour_in ,Social__ Insects,

Birkhauser, Basel.

Figlewski S. (1978) "’Market efficiency' in a market with

heterogeneous information". Journal of Political_.Economy,

v o l . 8 6 , pp. 581-597.

Figlewski S. (1982) "Information diversity and market

behaviour", Journal_of.Finance. p p . 87-102. March.

Frankel J. and K. Froot (1986) "The dollar as a speculative

bubble: a tale of fundamentalists and chartists". National

Bureau of Economic Research Working Paper n o . 1854.

Goodhart C. (1987), "The foreign exchange market: a random

walk with a dragging anchor", London School__q£_.Economics

Fin.anc.ial Markets GrouE_Warking.Paper no. l.

Kermack, W.O. and A.G. McKendrick (1927) "Contributions to

the mathematical theory of epidemics", Proceedings _0.f__the

Royal....Society, p p- 700-21.

Pasteels J.M., J.-L. Denenbourg and S. Goss (1987a) "Self­

organization mechanisms in ant societies (I): Trail

recruitment to newly discovered food sources", in J.M.

Pasteels and J.-L. Denenbourg (eds.), From__ Inhiyid.U.al__tC

Shiller R.J. and J. Pound (1986) "Survey evidence of

diffusion of interest among institutional investors",

, Birkhauser, Basel. no. 1851. © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(21)

WORKING PAPERS ECONOMICS DEPARTMENT

86/206: Volker DEVILLE Bibliography on The European Monetary System and the European Currency Unit.

86/212: Emil CLAASSEN Melvyn KRAUSS

Budget Deficits and the Exchange Rate

86/214: Alberto CHILOSI The Right to Employment Principle and Self-Managed Market Socialism: A Historical Account and an Analytical Appraisal of some Old Ideas

86/218: Emil CLAASSEN The Optimum Monetary Constitution: Monetary Integration and Monetary Stability

86/222: Edmund S. PHELPS Economic Equilibrium and Other Economic Concepts: A "New Palgrave" Quartet

86/223: Giuliano FERRARI BRAVO Economic Diplomacy. The Keynes-Cuno Affair

86/224: Jean-Michel GRANDMONT Stabilizing Competitive Business Cycles

86/225: Donald A.R. GEORGE Wage-earners' Investment Funds: theory, simulation and policy

86/227: Domenico Mario NUTI Michal Kalecki's Contributions to the Theory and Practice of Socialist Planning 86/228: Domenico Mario NUTI Codetermination, Profit-Sharing and Full

Employment

86/229: Marcello DE CECCO Currency, Coinage and the Gold Standard

86/230: Rosemarie FEITHEN Determinants of Labour Migration in an Enlarged European Community

86/232: Saul ESTRIN Derek C. JONES

Are There Life Cycles in Labor-Managed Firms? Evidence for France

86/236: Will BARTLETT Milica UVALIC

Labour Managed Firms, Employee Participa­ tion and Profit Sharing - Theoretical Perspectives and European Experience. 86/240: Domenico Mario NUTI Information, Expectations and Economic

Planning

86/241: Donald D. HESTER Time, Jurisdiction and Sovereign Risk

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(22)

2 -86/242: Marcello DE CECCO 86/243: Pierre DEHEZ Jacques DREZE 86/244: Jacques PECK Karl SHELL

86/245: Domenico Mario NUTI

86/246: Karol Attila SOOS

86/247: Tamas BAUER 86/257: Luigi MONTRUCCHIO 87/264: Pietro REICHLIN 87/265: Bernard CORNET 87/267: Edmund PHELPS 87/268: Pierre DEHEZ Jacques DREZE 87/269: Marcello CLARICH 87/270: Egbert DIERKER Wilhelm NEUEFEIND 87/276: Paul MARER 87/277: Fe'lix FITZROY 87/279: Darrell DUFFIE Wayne SHAFER 87/280: Martin SHUBIK

Financial Innovations and Monetary Theory

Competitive Equilibria with Increasing Returns

Market Uncertainty: Correlated Equilibrium and Sunspot Equilibrium in Market Games

Profit-Sharing and Employment: Claims and Overclaims

Informal Pressures, Mobilization, and Campaigns in the Management of Centrally Planned Economies

Reforming or Perfecting the Economic Mechanism in Eastern Europe

Lipschitz Continuous Policy Functions for Strongly Concave Optimization Problems

Endogenous Fluctuations in a Two-Sector Overlapping Generations Economy

The Second Welfare Theorem in Nonconvex Economies

Recent Studies of Speculative Markets in the Controversy over Rational Expecta­ tions

Distributive Production Sets and Equilibria with Increasing Returns

The German Banking System: Legal Foundations and Recent Trends

Quantity Guided Price Setting

Can Joint Ventures in Hungary Serve as a "Bridge" to the CMEA Market?

Efficiency Wage Contracts, Unemployment, and Worksharing

Equilibrium and the Role of the Firm in Incomplete Markets

A Game Theoretic Approach to the Theory of Money and Financial Institutions

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(23)

3

-87/283: Leslie T. OXLEY Donald A.R. GEORGE

Perfect Foresight, Non-Linearity and Hyperinflation

87/284: Saul ESTRIN Derek C. JONES

The Determinants of Workers' Participation and Productivity in Producer Cooperatives

87/285: Domenico Mario NÜTI Financial Innovation under Market Socialism

87/286: Felix FITZROY Unemployment and the Share Economy: A Sceptical Note

87/287: Paul HARE Supply Multipliers in a Centrally Planned Economy with a Private Sector

87/288: Roberto TAMBORINI The Stock Approach to the Exchange Rate: An Exposition and a Critical Appraisal

87/289: Corrado BENASSI Asymmetric Information and Financial Markets: from Financial Intermediation to Credit Rationing

87/296: Gianna GIANNELLI On Labour Market Theories

87/297: Domenica TROPEANO The Riddle of Foreign Exchanges: A Swedish-German Debate (1917-1919)

87/305: G. VAN DER LAAN A.J.J. TALMAN

Computing Economic Equilibria by Variable Dimension Algorithms: State of the Art

87/306: Paolo GABELLA Adverse Selection and Intermediation

87/307: Jean-Michel GRANDMONT Local Bifurcations and Stationary Sunspots

87/308: Birgit GRODAL Werner HILDENBRAND

Income Distributions and the Axiom of Revealed Preference

87/309: Eric PEREE Alfred STEINHERR

Exchange Rate Uncertainty and Foreign Trade

87/312: Pietro REICHLIN Output-Inflation Cycles in an Economy with Staggered Wage Setting

87/319: Peter RAPPOPORT Lucrezia REICHLIN

Segmented Trends and Nonstationary Time Series

87/320: Douglas GALE A Strategic Model of Labor Markets with Incomplete Information

87/321: Gianna GIANNELLI A Monopoly Union Model of the Italian Labour Market: 1970-1984 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(24)

4 -87/322: 87/323: 87/324: 88/329: 88/330: 88/331: 88/332: 88/333: 88/335: 88/337: 88/338: 88/339: 88/340: 88/341: 88/344: 88/345: Keith PILBEAM Alan KIRMAN Andreu MAS-COLELL Dalia MARIN Milica UVALIC David CANNING Dalia MARIN Keith PILBEAM

Sterilization and the Profitability of UK Intervention 1973-86

The Intrinsic Limits of Modern Economic Theory

An Equivalence Theorem for a Bargaining Set

Assessing Structural Change: the Case of Austria

"Shareholding" in Yugoslav Theory and Practice

Convergence to Equilibrium in a Sequence of Games with Learning

Trade and Scale Economies. A causality test for the US, Japan, Germany and the UK.

Fixed versus Floating Exchange Rates Revisited.

Felix FITZROY Piece Rates with Endogenous Monitoring: Komelius KRAFT Some theory and evidence

Domenico Mario NUTI On Traditional Cooperatives and James Meade's Labour-Capital Discriminating Partnerships

Government Debt and Equity Capital in an Economy with Credit Rationing

The EMS with the ECU at Centerstage: a proposal for reform of the European rate system

Frederick VAN DER PLOEG Monetary and Fiscal Policy in Inter­ dependent Economies with Capital

Accumulation, Death and Population Growth Pietro REICHLIN

Paolo SICONOLFI

Alfred STEINHERR

David CANNING Optimal Monetary Policy in an Economy without a Forward Market for Labour

Joerg MAYER Intervention Mechanisms and Symmetry in the EMS

Keith PILBEAM Exchange Rate Management and the Risk Premium © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(25)

5

-88/348: Milica UVALIC The Investment Behaviour of the Labour- Managed Firm: an econometric analysis

88/351: Alan P. KIRMAN On Ants and Markets

88/352: Gianna GIANNELLI Labour Demand, Pricing and Investment Decisions in Italy: An econometric Analysis

88/353: Niall O'HIGGINS The Progressivity of Government Taxes and Benefits in Ireland: a comparison of two measures of redistributive impact

Spare copies of these working papers and/or a complete list of all working papers that have appeared in the Economics Department series can be obtained from the Secretariat of the Economics Department.

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(26)

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(27)

m

EUI

B o : WORKING

i

PAPERS

EUI Working Papers are published and distributed by the European University Institute, Florence.

A com plete list and cop ies of Working Papers can be obtained free of charge - depending on the availability of stocks - from:

T h e P u b lic a tio n s O ffic e r E u ro p e a n U niv e rsity Institute

B a d ia Fie so la n a

I - 50016 San D o m e n ico di F ie s o le (FI) Italy

Please use order form overleaf

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(28)

PU B LIC A T IO N S OF T H E E U R O P E A N U N IV ER SITY IN STITU TE

T o T h e P u b lic a tio n s O ffic e r E u ro p e a n U n iv e rsity Institute B a d ia F ie so la n a

I - 50016 San D o m e n ico di F ie s o le (FI) Italy

From N a m e ... A d d re s s ...

P lea se se n d me:

□ a com plete list of EUI Working Papers □ the following EUI Working Paper(s):

Author, title: Date: Signature: © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(29)

21

PUBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE JUNE 1988 87/300: A. ELZINGA, P. NABER,

R. CIPPOLLINI, F. FACCIOLI, T. PITCH

Decision-Making About Girls by the Criminal Justice System in Holland and Italy

87/301: S. LEES, J. SHAW, K. REISBY

Aspects of School Culture and the Social Control of Girls

87/302: Eleanor MILLER, Rosa ANDRIEU-SANZ and Carmen VAZQUEZ ANTON

Becoming a Teenage Prostitute in Spain and the U.S.A.

87/303: Mary EATON and Lode WALGRAVE

A comparison of crime and its

treatment amongst girls in Britain and Belgium

87/304: Annie HUDSON Edna OPPENHEIMER

Towards an effective policy for delinquent girls

87/305: G. VAN DER LAAN and A.J.J. TALMAN

Computing, Economic Equilibria by Variable Dimension Algorithms: State of the Art

87/306: Paolo C. GARELLA Adverse Selection and Intermediation 87/307: Jean-Michel GRANDMONT Local Bifurcations and Stationary

Sunspots 87/308: Birgit GRODAL/Werner

HILDENBRAND

Income Distributions and the Axiom of Revealed Preference

87/309: Eric PEREE/Alfred STEINHERR

Exchange Rate Uncertainty and Foreign Trade

87/310: Giampaolo VALDEVIT American Policy in the Mediterranean: The Operational Codes, 1945-1952 *

87/311: Fede r i co ROMERO United States Policy for Postwar European Reconstruction: The Role of American Trade Unions *

87/312: Pietro REICHLIN Output-Inflation Cycles in an Economy with staggered wage setting

87/313: Neil KAY,

Jean-Philippe ROBE and Patrizia ZAGNOLI

An Approach to the Analysis of Joint Ventures *

87/314: Jane LEWIS Models of Equality for Women: The Case of State Support for Children in 20th Century Britain

rWorking Paper out of print

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(30)

22

PUBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE JUNE 1988 87/315: Serge NOIRET Nuovi motivi per studiare i meccanismi

delle leggi elettorali. Una

riflessione metodologica a proposito della legge del 1919 in Italia 87/316: Alain GOUSSOT Les sources internationales de la

culture socialiste italienne à la fin du 19e siècle et au début du 20e siècle. Problèmes de la composition de l'idéologie du PSI et ses rapports avec la circulation des idées en Europe

87/317: Eamonn NOONAN Württtemberg's exporters and German protection, 1931-36

87/318: Jean-Pierre CAVAILLE Theatrum Mundi. Notes sur la théâtralité du Monde Baroque. 87/319: Peter RAPPOPORT and Segmented Trends and Nonstationary

Lucrezia REICHLIN Time Series

87/320: Douglas GALE A Strategic Model of Labor Markets with Incomplete Information

87/321: Gianna GIANNELLI A Monopoly Union Model of the Italian Labour Market

87/322: Keith PILBEAM Sterilization and the Profitability of UK Intervention 1973-86

87/323: Alan KIRMAN The Intrinsic Limits of Modern Economic Theory

87/324: Andreu MAS-COLELL An Equivalence Theorem for a Bargaining Set

88/325: Angela GROPPI "La classe la plus nombreuse, la plus utile et la plus précieuse".

Organizzazione del lavoro e conflitti nella Parigi rivoluzionaria.

88/326: Bernd MARIN Qu'est-ce que c'est "Le Patronat"? Quelques enjeux théoriques et observations empiriques

88/327: Jean BLONDEL Decision-Making Processes, Conflicts, and Cabinet Government

88/328: Ida KOPPEN The European Community's Environment Policy.

From the Summit in Paris, 1972, to the Single European Act, 1987

îWorking Paper out of print

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(31)

23

PUBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE JUNE 1988

88/330: Milica UVALIC

88/331: David CANNING

88/332: Dalia MARIN

88/333: Keith PILBEAM

88/334: Hans Ulrich Jessurun d'OLIVEIRA

of Austria

"Shareholding" in Yugoslav Theory and Practice

Convergence to Equilibrium in a Sequence of Games with Learning

Trade and Scale Economies. A causality test for the U.S., Japan, Germany and the UK

Fixed versus Floating Exchange Rates Revisited

Die EWG und die Versalzung des Rheins

88/335: Felix Fitzroy and Kornelius Kraft

Piece Rates with Endogenous Monitoring Some Theory and Evidence

88/336: Norbert LORENZ

88/337: Domenico Mario NUTI

88/338: Pietro REICHLIN and Paolo SICONOLFI 88/339: Alfred STEINHERR

Die Ubertragung von Hoheitsrechten auf die Europaischen Gemeinschaften - verfassungsrechtliche Chancen und Grenzen einer europaischen Integration erlautert am Beispiel der

Bundesrepublik Deutschland, Frankreichs und Italiens

-On Traditional Cooperatives and James Meade's Labour-Capital Discriminating Partnerships

Government Debt and Equity Capital in an Economy with Credit Rationing The EMS with the ECU at Centerstage: A proposal for reform of the European Exchange rate system

88/340: Frederick VAN DER PLOEG

88/341: David CANNING

88/342: Gunther TEUBNER

88/343: Jean BLONDEL

Monetary and Fiscal Policy in Interdependent Economies with Capital Accumulation, Death and Population Growth

Optimal Monetary Policy in an Economy without a Forward Market for Labour

"And God Laughed..."

Indeterminacy, Self-Reference and Paradox in Law

Ministerial Careers in Western European Governments

:Working Paper out of print

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

(32)

24

PUBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE JUNE 1998

88/344: Joerg MAYER Intervention Mechanisms and Symmetry in the EMS

88/345: Keith PILBEAM Exchange Rate Management and the Risk Premium

88/346: Efisio ESPA The Structure and Methodology of International Debt Statistics

88/347: Francese MORATA and and Jaume VERNET

Las Asambleas Régionales en Italia y Espaha: Organizacion Institucional y Réglas de Funcionamiento

88/348: Milica UVALIC The Investment Behaviour of the Labour-Managed Firm: An Econometric Analysis

88/349: Massimo PANEBIANCO Latin-American Identity in the International and Economic Structure

88/350: Gregorio ROBLES La Cour de Justice des CE et les Principes Gânàraux du droit

88/351: Alan KIRMAN On Ants and Markets

88/352: Gianna GIANNELLI Labour Demand, Pricing and Investment Decisions in Italy: An Econometric Analysis

88/353: Niall O'HIGGINS The Progressivity of Government Taxes and Benefits in Ireland: A Comparison of Two Measures of Redistributive Impact

88/354: Christian JOERGES Amerikanische und deutsche Traditionen der soziologischen Jurisprudenz und der Rechtskritk

88/355: Summary of Conference debates and abstracts of selected interventions

The Future Financing Df the EC Budget EPU Conference 16-17 October 1987

:Working Paper out of print

© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

Riferimenti

Documenti correlati

e di Biblioteca Astense, Centro studi Renato Bordone sui Lombardi sul credito e sulla banca, Diocesi di Asti, Istituto per la storia della Resistenza e della Società contemporanea

The products of the Publishing Committee of Biblioteca di Studi di Filologia Moderna: Collana, Riviste e

Angiotensin II and vascular endothelial growth factor in the vitreous fluid of patients with diabetic macular edema and other retinal disorders. Effects of soluble CD14

and without using optical amplifiers, which can support higher number of users (higher splitting ratio) and/or longer reach; b) ultra dense WDM detection (6.25 GHz spacing) enabled

However, using proper scheduling technologies, coupled with proper performance modelling techniques, it is possible to deploy virtualised

• Forme minori di organizzazione del territorio nell'Italia dei comuni: i comitatus e altri distretti dello Stato della Chiesa, in La provincia feretrana (secoli XIV-XIX) (Atti

introdotte dal significativo preambolo: «In nomine sancte et individue Trinitatis. Ob statum Cartusiensis Ordinis in sancta religione conservandum visitationis per omnes domus eiusdem