Department of Sociology, University of Surrey, Guildford, GU2 5XH

 Originally written, March 1995. Revised November 1995

This research is part of Project L122-251-013 funded by the ESRC under their Economic

Beliefs and Behaviour Programme

This paper considers the meaning of the term ``simulation'' as it is commonly used in economics. A distinction is made between the relatively mechanical task of simulating a pre-existing mathematical model and the far more difficult task of building a simulation of some social process. It is argued that economists almost always use simulation in the first sense and, consequently, find it rather unimportant. Some economic objections to simulation are criticized, because they depend on a restricted understanding of the term, which has not itself been justified. Within a broader understanding of simulation, many of these objections can be shown to be unfounded. In addition, the paper describes a number of phenomena which are more amenable to simulation, in the broader sense, than to the usual type of mathematical economic modelling. The final part of the paper considers one particular, methodologically based, objection to simulation, that the process of developing deductive economic theories has a superior claim to ``scientific rigour''. It is argued that, even taking the economic definition of rigour as given, simulation is actually more rigourous than mathematical modelling in several important respects.

The commonest form of economic modelling is deductive. Deductive

modelling involves following through the logical or mathematical

implications of a series of axioms to produce predictions about

behaviour that can be compared with what is observed in a social

process. Modification of the model involves altering or generalising

these axioms of behaviour in the light of failures of prediction or

``common sense'' objections to the axiom system. In practice, the

commonest deductive technique appears to be the solution of sets of

differential equations. Beginning with some initial conditions and a

set of equations, deduction, in the form of manipulation of the

equations, produces one or more solutions which are intended to

represent social behaviours. (1)

Following this approach to modelling, it is possible to use

``simulation'' for a purely instrumental purpose, to replace the

economist using pencil and paper with a computer program, thus

automating the process of deduction for a particular model. In this

case, the computer is not simulating a social process, but carrying

out a process of deduction. It is the axiom system or mathematical

model which is intended to represent the social process. The use of

the computer is instrumental because the choice between hand

calculation and computer calculation is irrelevant to the correct

answer. (Of course, it is unlikely to be irrelevant to whether we

obtain that answer and how long it takes, but that is a

different matter.) There are obvious practical advantages to the

instrumental use of computers in modelling. Automated deduction will

certainly be faster and possibly more reliable than that carried out

by hand. However, seen in this light, simulation can only serve as a

supportive tool for the ``main task'' of economics, the production of

mathematical models.(2)

Such a view of simulation seems to imply that mathematical models are

the most suitable representations for social processes. This position

is seldom defended explicitly. Instead, it tends to be argued that

although simulation may be capable of dealing with socially

important behaviours that cannot be described mathematically, it tends

to produce models that are either practically or methodologically

unsatisfactory when it does so. (In some cases, the economic theory

may also be used to disparage the importance of the behaviours

themselves, though seldom with reference to empirical data.) For this

reason, it appears that non instrumental simulations are seldom

accepted into the economic mainstream.(3)

In the course of this paper, I shall argue that all of these

implications are false. Firstly, there are a number of situations in

which mathematical representation of the dynamics of social action is

at least limiting, and in some cases impossible, given our current

level of mathematical knowledge. Secondly, computer simulation can

assist in the practical modelling of these social processes. Finally,

there need be nothing non rigorous or unscientific about the resulting

simulations. In fact, simulation may actually increase the amount of

``real'' or useful rigour in models. (One important difference between

simulation and mathematical representation is that difficulties with

simulation models often turn out to be ``practical'', involving the

need for more data or faster computers. By contrast, mathematical

models often reveal inherent tensions or inconsistencies at the

theoretical level which are far harder to resolve.) In the process of

rehearsing some of these arguments, the importance of posing and

answering methodological and practical objections separately should

become clear.

By contrast to the instrumental view, this paper urges that simulation

should be seen not simply as a tool for deduction in mathematical

models, but as a technique in its own right, capable of representing a

broader class of starting conditions and deductive rules than the sort

of mathematics commonly used in economic modelling. Instead of being

restricted to representing mathematical models of social processes,

there is no reason why simulation should not enable us to represent

the processes themselves. It seems appropriate to refer to simulations

of this sort as descriptive and contrast them with the

process of instrumental simulation discussed at the beginning of this

section.

In descriptive simulation, it is no longer merely a matter of

speed and convenience whether we use a system of equations or a

computer program to represent a social process. Not everything that

can be expressed in one way can be expressed in the

other. (This distinction takes the current level of knowledge as given. New mathematical

techniques for representing social processes will undoubtedly arise in future. Given a particular

level of mathematical knowledge, however, the distinction is between processes that can be

modelled faster or more competently by a program and those which cannot yet be modelled by

any other means. Doubtless, the representational capacity of programs will also continue to

increase.) If there are justifications for preferring the mathematical representation over the

computational (4) one, these need to be made more

explicit than they have been. In any event, they are not

justifications based on instrumental concerns of speed or efficiency

in achieving the same goal, but rather disputes over what the goals of

scientific modelling should be. The distinction between arguments

about means and arguments about ends is important and should not be

blurred. Towards the end of the paper, some of these traditional

disputes over the role of simulation are examined in more detail.

One possible explanation of the preference for instrumental simulation

in economics is the unusually resistant ``protective

belt'' (Lakatos, 1970, 1976) which insulates methodology and theory

from the continuing discrepancy between model predictions and

empirical data. At the methodological level, the discipline is still

committed to utilitarianism as a basis for modelling behaviour. At the

theoretical level, this commitment is almost invariably implemented by

designing models in which individual decision involves optimal choice

over a set of known alternatives. (It is interesting to trace the

course of generalisations to utility theory and observe the ways in

which they have retained this core assumption. Economics models risk,

but largely ignores uncertainty (Knight, 1921). In the same way, it

models routine technical progress, but largely ignores

innovation (Sahal, 1983). Neither of these choices appears to be

justified by empirical considerations, that is by the extent to which

research and uncertainty are significant features of economic

behaviour.) The class of models resulting from rational choice

theories can be represented and solved using differential calculus. In

cases where the calculus proves difficult, there is an instrumental

role for simulation, but it appears to have no descriptive role in

building models which reject the utilitarian framework, because such

models are still considered theoretically and methodologically

unacceptable. (5)

It is plain that the acceptability of such a subsidiary role for

simulation depends heavily on one's faith in the traditional economic

methodology. If one feels able to reject utilitarianism or optimising

choice as the sole basis for model building, then it is no longer

clear why simulation should be limited to the efficient solution of

equation systems. Indeed, it is even possible that simulation may

prove superior to mathematical representation in some respects.

Certainly, once one ceases to take the instrumental nature of

simulation for granted, possibly as a consequence of methodological

and theoretical preconceptions, the functional similarities between

equation systems and simulation programs become more apparent. In each

case, a combination of empirical observation and theory, structured by

methodology, is represented in a formal language. A set of

initial statements in that language undergo transformations according

a set of rules and the end result is either a ``solution'' to a static

system or an unfolding dynamic process in one or more variables. In

each case, the end results of the operation of the model can be

compared with some corresponding social process which the model is

intended to represent. In the case of a mathematical representation of

a model, the deductions are carried out by the theorist, according to

the ``rules of mathematics''. In the case of a computational

representation, they are carried out by the computer according to the

grammar of the programming language, or some grammar written by the

theorist in that language.

Having drawn a distinction between descriptive and instrumental uses

of simulation, and attempted to explain the dominance of instrumental

simulation in economics, we now turn to a more detailed consideration

of the task of representing theories so that they may be tested.

In the last section, it was suggested that economics regards

simulation as instrumental to mathematical modelling of social

processes, rather than as a (descriptive) modelling technique in its

own right. The explanation put forward for this view was that

economics had an unusually strong commitment to a single methodology

and approach to theory building, based on utilitarianism implemented

theoretically as individualistic rational

choice.(6) Given this methodological commitment,

simulation can only play a supporting role in the solution of

mathematical models. It cannot demonstrate its advantages, because the

sorts of models which this would require are themselves regarded as of

doubtful merit. In this section, the advantages and disadvantages of

computer simulation and mathematical modelling are discussed.

Once we have accepted that sets of equations and computer programs can

both be used to represent a social theory in a form suitable for

testing, we can ask what the advantages and shortcomings of the two

representations are. Having admitted that there are multiple

representations --- the verbal description of a model is another ---

we are by no means committed to saying that each is of equivalent

value for the tasks of social science, whatever these are taken to be.

There is a long tradition in economics which views the mathematical

representation as in all respects superior to the verbal

one. (7) This tradition, which values simplicity

and analytical solubility more highly than generality and complexity,

arose at a time when the verbal description of models was the only

alternative. Such verbal descriptions were even more subject to

incompleteness, errors and omissions than their mathematical

equivalents. It was all too easy to take advantage of the ambiguity of

everyday language to obscure the weaknesses of a poor argument. In

mathematical modelling, deduction is based on the manipulation of

fixed symbols according to fixed rules carried out by hand. In verbal

models, neither the symbols nor the rules have an agreed

interpretation. Thus the increasing standardisation of the rules of

deduction can be seen as a sort of progress towards greater

formalism. (8)

The reasons for the ``mathematical turn'' in economics are difficult

to trace, because the superiority of mathematical representation is

seldom justified explicitly. However, in addition to its relevance for

a utilitarian methodology, a number of other explanations have been

proposed for the continuing dominance of mathematical modelling. In

the early stages of economics, there was considerable enthusiasm for

the elegance of Newtonian mechanics as a scientific metaphor. This

seems to have resulted in the development of theories in which atomic

social actors, lacking any internal structure, collide only briefly in

trade, driven by the reversible and smoothly acting laws of supply and

demand. This Newtonian view seems to underpin mainstream economics

despite the impact of Quantum Mechanics, Thermodynamics and Relativity

which have fundamentally changed the understanding of physics on which

it was originally based. (9), but it is only recently that models

based on these ideas have taken new impetus from new developments in

the study of complexity, chaos and path dependent processes.

Interestingly, the resulting models are often even more abstract and

mathematical than other developments in

economics (Anderson, Arrow and Pines, 1988, Batten, Casti and Johansson, 1987).

Economics has also been obliged to carve itself a niche as a respectable academic discipline

and that purpose could also be served by increasing formality, for example, by

association with high status physics rather than the other low status

social sciences. Finally, there are a number of ``selection''

arguments asserting that if formal purity and mathematical precision

were favoured in the academic environment, for whatever reason, those

who were most mathematically able would advance themselves and also,

being inclined to value their own skills most highly in others,

perpetuate the process. The possibility of self selection by the

economics profession (Clander and brenner, 1992) and the socialisation of students

by the teaching process have both been remarked

upon (Frank, Gilovitch and regan, 1993, Marwell and Ames, 1981). (10)

In fact all of these explanations probably have a part to play, and

additional explanations are possible, but two important points should

be noted. Firstly, all the explanations provided address the value of

the mathematical representation to economics as a professional

discipline, rather than as a useful and realistic representation of

social behaviour. Secondly, and more importantly, where they

do relate to the task of producing realistic models, we may

question whether comparisons that were relevant in the past are still

relevant. An economics based on the Newtonian clockwork can be

challenged by pointing out that physics has itself moved on and no

longer regards such models as adequate or complete. Similarly, we may

challenge the superiority of mathematical representation, originally

contrasted to verbal representation, by asking whether additional

possibilities for representation are now available. I have already

suggested that mathematical representation could be seen as superior

to verbal representation because it made use of symbols with fixed

meanings and a broadly agreed set of transformational rules. Even in a

purely instrumental use, simulation of a particular model can be seen

to complete the process of formalisation by automating and formalising

deduction as well. However, in the remainder of this paper, I shall

consider a number of ways in which the descriptive use of simulation

can go still further in providing rigorous models of social processes.

Unfortunately, one obvious method of comparison between different

representations is surprisingly difficult to implement. It is by no

means straightforward to compare the predictive quality of models

based on the different representations. (11) There are a number of reasons for this.

One difficulty is that descriptive simulation is extremely new, and it

would be unreasonable to compare it with an approach that has had two

hundred years to develop and refine its methods. Even if descriptive

simulations were able to predict better, it could be argued that they

had simply adopted the mechanisms of traditional models in an

instrumental fashion and then developed them a little further. Of

course, there would be nothing to stop mathematical models from doing

the same thing using mechanisms arising from simulation. Although this

paper argues for the richness of simulation, it may turn out that

certain social processes can be described extremely well by simple

mathematical relationships. However, this fact needs to be discovered

rather than simply asserted. (12)

Even supposing that a comparison between predictions could

legitimately be made, it would be extremely hard to decide which

predictions to compare. Although certain economic models have improved

considerably in predictive power, the consumption function for

example (13), there are others which have not, such as prediction of

investment behaviour. There are even predictive relationships like the

Phillips Curve that seem to have collapsed altogether. (It is not

clear whether these relationships were spurious to begin with or have

simply broken down, but in either case the problem of comparison

remains.)

Finally, there are no straightforward criteria for comparing the

social or theoretical importance of predicting different variables and

no simple way of measuring the parsimony of a diverse set of different

models. How does one compare a model that predicts total consumption

badly, with one that predicts alcohol consumption very well, but

cannot be generalised to any other form of consumption? (In such

cases, the success of a representation might simply result from a

judicious choice of subject matter rather than any genuine insight.)

Simplistic approaches, such as counting explanatory variables, are not

only theoretically unsatisfactory, but may not be relevant to non

mathematical representations. (In fact, for a fair test we would need

to compare the same set of predictions for each model based on the

same data set. Then we would face the equally difficult problem of

measuring the relative parsimony of the two processes transforming

data into predictions. Such issues have also arisen in judging the

significance of comparing predictions by neural networks with those

made by other methods (Chattoe, 1993). Because the model is distributed

over the nodes of the network, one cannot count variables.)

If we cannot assess the relative merits of model representations by

comparing their predictive power, what other criteria can we use to

decide between them? One possibility is to show that simulation

encompasses (14) the mathematical representation. In this case, everything

which can be expressed in the mathematical representation can also be

expressed in simulation, but in addition, it is possible to express

things in the simulation which cannot be expressed mathematically. (Of

course, it would not be sufficient simply to define a mathematical

notation for a given situation. There would also have to be a set of

deductive rules available which could be applied to that notation to

produce testable deductions.)

In one sense, demonstrating this encompassing is trivial. Any computer

language contains many commands which are not arithmetic operators or

involved solely in the construction of those operators. However, for

the purposes of modelling social processes, this ``argument'' is

plainly not sufficient. Perhaps all the additional commands are simply

irrelevant to the modelling of social processes. In the next section I

shall provide examples which suggest that this is not the case.

One final point to bear in mind, is that although verbal descriptions

may be unsuitable for describing testable models, it does not follow

that they are unsuitable for describing theories or hypotheses. In

economics, it is relatively common for the credibility of a verbal

theory to be judged by the extent to which it can be translated into a

mathematical model. This is an effective technique for filtering out

behaviours which reveal the weaknesses or inconsistencies of

utilitarianism. (As has already been remarked, utility theory is

neutral on the issue of whether utility functions are individualistic

or not, but in practice there is almost no investigation of

non-individualistic functions. Such concepts as need and altruism have

also fallen foul of their unsuitability for utilitarian treatment.

Instead of arguing that such concepts are irrelevant to our

understanding of social processes, which might prove difficult,

economics simply disregards them without discussion.) It seems that

the verbal representation may be more compatible with the

computational than either is with the mathematical

representation. Everyday language is very good at dealing with many

different types of ambiguity, uncertainty, fuzziness, self-reference

and reflexivity. (15) Computer programs, like everyday languages, can express a rich variety of

ideas and describe complex chains of interaction and causation.

Because economics appears to be wary of hypotheses that cannot be

fitted into its methodology, it appears to be doubly wary of the

reports of economic actors who are not trained as economists.

(Qualitative analysis of everyday economic action is still

surprisingly rare. In cases where it has been carried out, the results

often differ considerably from the findings of the corresponding

theory (Hall and Hitch, 1939.) The practices of real economic actors are

often dismissed as ``rationalisations'', ``approximations'' or ``rules

of thumb'' even when the practices they are asserted to approximate

are almost impossible to carry out. Given the potential richness of

verbal representations, and a capability to simulate the descriptions

of economic actors directly, we may at least question the value of

mathematics as a suitable representation for models of social action.

Verbal descriptions, particularly by active participants in a social

practice, may reveal subtleties that are far beyond the scope of

mathematical formulation while proving tremendously important in the

determination of behaviour. In the next section I shall turn to some

practical illustrations of the hypothesis that simulation can

encompass mathematical modelling in a useful and revealing way.

In this section, I will discuss some of the limitations of

mathematical representation which simulation is able to address, thus

supporting the claim that simulation encompasses mathematical

modelling.

The first difficulty in using sets of equations to represent social

processes is to clarify the relationship between the equations and

agents of causality in the world. Two obvious kinds of relationship

suggest themselves. (16), which simply assumes the relationship away,

arguing that appropriate mechanism is irrelevant if prediction

occurs. Firstly, it may be questioned how good this prediction needs

to be. Secondly, it appears that prediction in economics is seldom

good enough to justify such an approach, assuming any substantial

predictive power is required. Thirdly, such a view seems to deny all

descriptive relevance to social science. It is hard to see what use

a perfectly predictive, but completely non explanatory, model of the

economy would involve, if such a model can even be conceived of. It

would be rather like the Delphic Oracle.

To return to an earlier point, models must be explanatory as well as predictive otherwise we

cannot tell which situations they apply to. The first possibility is that the agents are themselves

using equations as the basis for their decisions. For example, one reason why total consumption

might be observed to be a linear function of total income would be that each

individual in the economy was determining their consumption as a

linear function of individual income. Such a view immediately

dispenses with the problem of aggregation as all variability is

restricted to the individual linear coefficients in the shared model.

However, the hypothesis that everyone uses the same decision process

is an extremely strong one, which ought really to receive equally

strong empirical support. Such support is not forthcoming. As a

result, the econometric testing of equation systems is actually

involves an enormous joint hypothesis: that all individuals have the

same model of the world, and that this model is the one that the

economist has chosen. It is not surprising that such models fail to

predict, or that such a complicated joint hypothesis provides little

information about what is wrong with the model and how it may be

corrected.

The second possibility is that individual agents do not use

the same model as their decision process, but that there is some

mechanism at work which means that it is ``as if'' they do. This is

not a claim that many agents follow the model approximately, that

would be a hypothesis of the first sort. Rather, it is supposed that

some higher level process organises the agents in such a way that

their behaviour appears to follow a simple model. An example is

provided by the argument that although firms may use very different

models of the market to decide their price setting behaviour,

selection pressure based on profitability will bankrupt all those

firms who are not in fact maximising their profits (Friedman, 1953).

Apart from the fact that this argument appears to be

mistaken (Chiappori, 1984, Witt, 1986), it does not provide much useful

support for the hypothesis of profit maximisation. Postulating a

universal higher level organizing principle like selection simply

pushes the problem of justification back a step, where it may be

harder to address. It is no longer sufficient to demonstrate that most

firms do profit maximise. That might be a relatively simple

empirical task, at least in principle. Instead, it must be shown that

the appropriate ordering mechanism is at work and, in fact, leads to

the hypothesised outcome. (Some selection mechanisms might select

firms that displayed other traits than profit maximisation. More

generally, experience of biological systems suggests that it would be

unusual to expect selection to result in the strict dominance of any

single behavioural trait.) If the outcome of the ordering mechanism

is conditional, for example, on the values of certain model

parameters, then it must also be shown that, empirically, these have

the relevant values.

In addition to the practical problems of aggregation, both of these

views involve deeper assumptions that can be questioned. To what

extent can agents acquire common knowledge of the ``correct''

model of the world? To what extent can an external organising

principle like selection legitimately be ``naturalised'' rather than

seen as a negotiable institution itself resulting from social

decisions. (The extent to which the market selects profit

maximisation is dependent on the political views of voters and

lawmakers who influence the rules by which competition is to take

place. Furthermore, it is well known that firms are often able to

circumvent the ``laws'' of the market.) One purpose of this paper is

to demonstrate that simulation has the potential to address these

issues by representing agents with genuinely differing models of the

world as well as the processes by which these models are

developed and shared.

Be all this as it may, it does not appear that either of these

positions adequately justifies the assumption that the behaviour of a

large number of individuals can be captured by a small number of

quasi-behavioural equations. Either strong evidence must be provided

that agents do in fact have extremely similar ways of making

decisions, or the mechanism by which the net result occurs should be

made explicit. (The burden of proof rests on the users of these models

because their predictive power has remained rather poor.) It does not

appear that agents with systematically different models of the world

can be represented using current mathematical techniques. If such

representations do exist, they have not, to my knowledge, been used in

economics. The relatively rare models which explicitly simulate a

mechanism of convergence for the behaviour of systematically different

agents are exclusively based on computer

simulation (Dixon, Wallis and Moss, 1994, Dosi, Marengo, Bassanini and Valente, 1993).

Although these methodological concerns are important, there are also a

number of quite concrete limitations to mathematical representation.

Several of these can be illustrated by considering the common practice

of describing economic interactions in terms of sets of equations

linking the values of variables in discrete time periods. We will

suppose for now that the use of discrete time is a convenient (and

realistic) simplification, and, to avoid the difficulties of

aggregation discussed above, that each equation explicitly represents

the behaviour of a single agent or institution. The difficulties of

such a representation fall into two complementary classes: those

caused by an unrealistic treatment of time and those resulting from an

attempt to represent multiple agency as an ordered sequence of

individual actions. These difficulties are complementary because the

unrealistic treatment of time is both a consequence and a partial

cause of the unrealistic treatment of multiple agency.

I shall deal with the representation of time first. Prima facie it may

appear that equations linking time periods in models are representing

``real time'' and it is commonly implied that this is the case. In

fact they often reflect either ``econometric time'' (the availability

of new data) or ``theory time'' (the requirement that the output of

one equation should always be available before it is needed as input

for the next). Both of these senses of time cannot easily be

reconciled with standard ``clock'' time. Econometric time obliges us

to leave unmodelled any processes that take place between

announcements of new data.

The only way that we can improve such

models is by collecting data more frequently and this may be very

costly. (17) Because of this difficulty, it is hard to argue that mathematical models of this sort

are telling us very much about the social processes which give rise to

aggregate behaviour, except for the very broadest trends. Agents are

not, typically, making decisions on the basis of the same data as

economists, in fact, they are generating, through their individual

models of the world, the data that economists use to build aggregated

models. (18) It seems extremely unlikely that stable constants linking economic variables

should persist over periods of years unless these can be grounded in

the actual decision-making processes of individuals and the reasons

for their stability. Furthermore, these potentially

ungrounded macroeconomic constants are themselves theory constructs,

so we are again testing a joint hypothesis about both constants and

variables in a given system of equations.

Hendry (1987) has argued that we must judge ``constants'' in terms of their functional

behaviour, for example the fact that they are observed to be

stable over time and produce errors in the residuals that are randomly

distributed. Under this view, constants must be established rather

than asserted. It is clear that this process cannot just involve

econometric data since relationships between variables are also

allowed to vary. Independent support for particular decision variables

can only come from addressing the problems of individual

decision-making and its relationship to aggregate data head on.

The main difficulty with theory time is, appropriately, one of

representation. The system of equations is indeterminate with regard

to the order in which the behaviour summarised by the equations is

executed. The ``move structure'' of the system must be imposed and

executed by the modeller. Typically, this is not done with regard to

the realistic modelling of social interaction, but rather to the

requirements of mathematical tractability. (19) In particular, the move structure is

designed so that the output from one equation is always available when

it is required as input for another. In turn, this is necessary

because the equations effectively represent fixed rules of action

which involve no discretion or choice. If a piece of information is

unavailable the equation produces no result, and the system of

equations fails altogether from that time on.

As a representation of

individual behaviour, such equations are therefore plainly

unrealistic. We are often forced to act before our ideal decision

process is ready to use, sometimes before we have any

decision process available. The imposition of a move structure also

conflicts strongly with the individualistic basis of economics. If one

equation fails, they all do. Such a system lacks the everyday

robustness of human interaction. It must be protected by the

``invisible hand'' of the modeller. (The same difficulties apply if

the equations are considered to represent aggregates, though there are

additional complications arising from the lack of robustness in

variables over time.) The assumption of a common move structure can

perhaps be seen as a corollary of the assumption that all agents share

a common model. However, it has already been remarked that this

assumption requires considerably more empirical support than it

receives. If agents are using different models of the world, there

seems no reason to suppose that they will cooperate by moving in an

agreed order.

Real time, unlike econometric time or theory time can be defined more

or less independently of the actions which take place within

it. (20) By contrast theory time is designed to make the

actions of individuals appropriately sequential and econometric time

to relate available data. Actors operating in ``real time'' are not

obliged to ensure that others have sufficient information on which to

act before acting themselves. (That is not to say that we do not

cooperate to take turns, for example in conversation, but we are not

obliged to do so. Even when we do, the move structure cannot easily

be represented as a strict sequence. Turn taking can operate on very

different time scales and ``change gear'' within single interactions.

Consider the organisation of an academic conference with an audience

and speakers and, within a particular speaker session, the shifts from

a lecture punctuated with questions to a free discussion and then an

argument. The lack of realism in strictly sequential models is not

removed simply by making the time period very short.) The

representation of real time also obliges us to consider how

information is transmitted and processed. If there is a fixed move

structure, we can simplify matters by assuming that everything that

has already happened is known, but without such a structure, what has

``already happened'' is inextricably connected with the way in which

information and materials move from place to

place. (21)

In real time, agents can act simultaneously. If they do, neither can

decide ``rationally'' what to do, because that would involve knowing

what the other agent would do. Since the other agent is in the same

position, this results in infinite regress. Nevertheless agents

do act and their actions have real effects even if they are

simultaneous. Similarly, an agent or group of agents can be involved

in a positive or negative feedback process independently of the rest

of society, but that process may still affect the society at large and

be affected by it. A simple example is provided by the escalation of

an argument in the playground which can only be stopped by the

teacher. (Equation based representations must either avoid feedbacks

or model them as processes which cannot be stopped from ``outside''.

Theory time does not allow the independent action of some system that

could constitute such an outside.)

These examples lead us towards the complementary limitation arising

from the restrictive representation of time, that of representing

multiple agency as a sequence of individual actions. The modeller who

arranges an equation system to guarantee its solubility does so

because he or she must solve it sequentially, it is not feasible for

certain processes to be carried out ``in the background'' or for the

actions of several agents to be revised at once. Thus only one agent

can act at a time in such models. Everyone else must freeze while

this action is taking place. The richness of the environment is thus

restricted to suit the attention of the modeller. This is plainly

unrealistic. In practice agents are acting simultaneously and

independently all the time. This allows for the possibility of action

over different time scales, feedbacks and simultaneity.

Multiple agency also has two important corollaries which are similarly

neglected in economics. The first is the more or less independent

agency of the world, which follows its own laws to make hot coffee go

cold, ultimately regardless of our efforts. (22) The second is that we

cannot make sense of the world without our own models of agency.

Because the world will not present itself to us as a series of

snaphots, our mental models must involve an understanding of the

dynamics of action. For example, consider another case of multiple

agency, the ``retry''. (One way in which our behaviour is more robust

than that of an equation system is that if we find some data is

missing, we may wait and try again rather than simply seizing up.)

An

example of a retry occurs when a person repeatedly phones someone who

is already on the phone. Such a situation requires a representation of

independent action that cannot simply be reduced to a sequential

process. Whether the person gets through depends on whether the other

is still talking, but the decision to try again cannot simply be a

function of whether the phone is engaged or not. If it were, there

would be a danger that the person would never try again or ring

forever if the phone was broken. What protects us from this impasse is

that we decide not only on the basis of the engaged tone but also as a

result of our model of the world and other agents and objects, that

the telephone might be broken, or that it might be better to ring a

busy person again at the weekend or send a letter.

Multiple agency also arises in the individual agent, who must

reconcile different data from the senses, from inside the body, from

memory, from reason and from feelings. These different sources of

information cannot be accessed in an imposed ``order'' and it does not

seem likely that they can be represented in a single metric as utility

theory suggests. The irreducibility of multiple agency also suggests

the necessity for agents to develop dynamic models of the world based

on coherence between different sorts of information, rather than on

any static and unitary notion of ``truth''.

In this section I have argued that equation based models are

restricted to an unrealistic representation of sequential time and

single agency by the inability of the modeller to solve models with

genuine multiple agency in real time. The relaxation of the resulting

restrictions on agent behaviour discussed above suggests that we might

replace the deterministic and reactive optimising agent with one who

is cognitive, creative and adaptive. In doing so, we are also obliged

to replace the simple environment resulting from the behaviour of

deterministic agents with a profoundly and continuously uncertain one.

(23)

This shift of perspective also has an appealing symmetry. Economic

agents can only make sense of a world where everyone is very much the

same as they are. Having pursued a ``destructive'' programme in this

section, deconstructing the economic views of time and agency, the

subsequent sections offer a ``constructive'' view of the ways in which

simulation may help to rebuild them. The next section addresses the

practical concern that a research programme calling for simulations of

complex interactions by multiple agents may not be feasible. The

following section considers whether such a programme is useful in

meeting the methodological goals currently set out for mathematical

economic modelling.

After the highly critical discussion in the previous sections, it

would be quite acceptable to object. Many of these criticisms are not

particularly novel, and the practicalities of economic model building

have not apparently been taken into account. If one suggests that

every agent has a different model of the world, and can interact in a

variety of ways in real time, how can we possibly build tractable

models of human behaviour?

This question needs to be addressed on a number of levels. In the

first place, there is no point in continuing to build tractable models

that work very poorly. After a certain amount of time, it is valid to

question whether building more models of the same type is really a

worthwhile exercise, or whether it is time for something different. It

has already been remarked that progressive ``improvement'' in the

quality of economic models is by no means obvious. In some cases, like

the movement of stock prices, it has not even be demonstrated that the

best models predict better than a random walk.

Secondly, the suggestion is only that we need a representation in

which every agent might have a different model and act at any

time, not that this is in practice the case, or even that we must

build models in which it is. In fact, agents possess precisely the

same difficulty in making sense of the world as theorists, though the

latter suffer it in a more acute form because of their more ambitious

objectives. This gives the simulation approach a pleasing symmetry

with its subject matter. Both scientists and everyday actors are

extremely anxious to reduce uncertainty and to predict the world in

order to operate within it. The scientists view of the world is not

intrinsically privileged, but only to the extent that his or her model

can make more sense of the world than the folk models. (It is in this

sense that prediction may be regarded as the acid test of a model.)

The countless mechanisms by which agents ``agree'' to make their

environments more stable form a rich field for study and a source of

evidence for the extent to which agent models and behaviours do in

fact converge. (The market seems to be one such institution.) However,

such convergence must be part of our empirical data, not a theoretical

assumption. If the representation we choose for our models is only

suitable for certain empirical possibilities, it will be extremely

tempting to ignore those which don't fit.

Finally, we need to consider the use of the term ``tractability''. If

this term is intended to mean that the model produces convergence or

optimality in some formal system, then that model building criterion

requires some justification. On the other hand, if it means that the

model should not be unwieldy, then we should provide a more respectful

answer, depending on the form of unwieldiness involved.

One possibility is that a simulation of such complexity is too big or

too slow to run. It is certainly true that such models have little

predictive use in real time, but they may still be validated. (The

distinction is between data in and out of sample, rather than between

past and future after all.) If the simulation predicts well, then it

appears that reality simply is that complex, and a larger computer

will be required. (Rejecting a model because it runs too slowly is not

much different from rejecting it because it won't converge. It

confuses objectives of different sorts.)

This comment does not apply

to proofs that various economic decision processes are non computable

since that suggests that no computer, including the human mind,

could ever perform the computation fast

enough.(24) Instead it reflects the fact that a computer simulation often models the decision

processes of hundreds of agents while in reality, most agents only

deal in detail with their own decision processes and perhaps those of

a few others. (The ways in which social institutions and the

individual ability to abstract permit modelling at this level of

simplicity is an important topic of study.) The task of social

science is considerably more computationally expensive, but this is

not surprising when we reflect on its nature.

Another claim is that simulations are unwieldy because they require

extensive ``tweaking''. Most simulations have so many parameters, it

is claimed, that the designer can use them to produce almost any

desired result. (25)In part, this is an inevitable

consequence of the greater levels of complexity attainable in

simulation. It is much less clear that simulations have an

``unreasonable'' or ``inappropriate'' number of parameters. They may

simply be drawing attention to the amount of data actually required

for social understanding. In any event, this problem also arises in

mathematical models and is typically solved by endogenising as many

variables as possible. However, as Engle, Hendry and Richard point

out exogeneity is something that should be measured, not something

that can simply be assigned (1983). It seems that a useful

distinction can be made between parameters that are genuinely

exogenous, and those which are simply unmodelled. An exogenous

parameter should not be susceptible to tweaking, because it should be

one which is not being estimated within the framework of the model.

For example, a model that includes an exogenous rate of forgetting

should use psychological literature to narrow down the range of the

parameter. If the parameter is so poorly defined that it proves

impossible to assign a value to it, or even to design an experiment by

which the value might be determined, it may not be a suitable part of

any model. It is definitional of an exogenous variable that

its value is determined outside (and therefore free of) the model to

which it is exogenous.

Processes which are unmodelled are also unavailable for ``tweaking''

in the derogatory sense of the term. The relations between them can

only reflect empirical probabilities of particular transitions between

states if these are available. (It often seems to be assumed that data

made available to social scientists must be sufficient to their

purposes but there is an important distinction between a practical

inability to get more data and whether or not that data is needed.)

For example, a minimal simulation is that event B follows event A one

quarter of the time. Here event B is unmodelled, in the sense that no

causal mechanism is incorporated into the simulation to explain how it

comes about. Event A can be chosen arbitrarily, perhaps because the

transition probability between A and B is already well known. (It may

not even be supposed that A is particularly relevant to the fact that

B occurs.) Each time event A occurs, the simulation program ``rolls a

dice'' and considers whether to set an instance of event B in motion.

In fact, event B could follow event C invariably, or even be caused by

it, but that fact has not yet been established either in the

simulation or in the world.

In the process of developing a model of

``how'' event B arises, a simple probability (or model of ``what'') is

replaced by a series of causal or process links, but in no case is it

clear that the simulator has a free hand in adjusting the model to get

some desirable outcome. (In fact, accusations of ``tweaking'' reflect

complaints from both mathematical modellers and economists. In the

former case, there is a practical problem of model refinement to solve

and an incentive to demonstrate that you can solve it. In the latter

case, there is often an extra-theoretical goal like convergence to be

satisfied. Social simulation, in its attempts to avoid both

instrumental and ideological modelling should ideally only use data to

distinguish between models. It would simply reject convergence as a

criterion for parameter adjustment unless convergence was observed to

be involved in the social process.)

It is certainly true that simulators do adjust the parameters

of their models, but their motivation for doing so is obviously

important. It may be possible to show, by a sort of interactive

sensitivity analysis that certain variables can be treated as

completely exogenous, or that they are relatively unimportant in that

the model still behaves in a similar way whatever value they are set

to. (Strict exogeneity is rare, but the empirical determination of

relative unimportance with respect to a given system is probably the

most promising basis for theoretical abstraction. It also seems

compatible with the sort of approximate definition of systems used by

real actors.) This raises the issue of the systematic ``reduction'' of

models (Gilbert, 1986, Hendry, 1987, Hendry and Richard, 1982). It is very important to

distinguish between a modeller who is attempting to reduce a complex

simulation to a simpler one (or possibly even a mathematical model) at

the expense of a known loss of precision, from a mathematical modeller

who is unable to establish just how restrictive an arbitrarily

selected model is. (One of the advantages of model encompassing as a

progressive strategy is that it becomes possible to see just how much

of a special case the encompassed model was. Economics seems to be a

special case of dynamic interaction where agents' models are

fundamentally identical and move structures and interaction patterns

are fixed. Put in these terms, the plausibility of models based on

such assumptions is placed in grave doubt.)

Having addressed these concerns about the practical feasibility of

simulation, it is relatively easy to see how simulation might address

some of the difficulties outlined in the last section. Independent

agency can be implemented by genuine parallelism or the representation

of an independent environment in which time is monitored independently

of the actions of particular agents. (Note that such a system

could be simulated by a human, probably in a very error-prone

and uncomfortable way, but not solved mathematically.) Individual

activities can interact over very different timescales, through

interactions with the environment, and the models which agents use to

understand the world can be refined and transmitted. The simulation

can record and, if necessary, ``compile'' statistical data at a number

of levels. (For example, it can both record all the individual models

of the world at each point in clock time and total up the number of

sales made by a firm in any arbitrary period.) In principle, there is

no reason why the environment should not provide this compiled data to

individual agents as a basis for subsequent decision. (This draws

attention to another important consequence of multiple agency, the

possibility of wholly different types of agents such as

banks, firms, consumers and governments, each with a different

internal structure and goals.)

In the next section, a number of the advantages of simulation will be

discussed further. It will be argued that not only do these advantages

make simulation superior to mathematical representation, for practical

reasons considered already, but that they also provide additional

methodological advantages in the pursuit of ``rigour''.

So far, we have considered the representational advantages of

simulation and answered a number of practical objections to simulation

as a technique. However, there is a final objection which needs to be

addressed, namely that simulation models do not adequately fulfill

some methodological criterion of scientific ``rigour''. (It is not

always easy to separate methodological objections from practical ones

so this section may overlap somewhat with the previous one.)

The economic view of the scientific method appears to be that we

develop a theory by some means, make appropriate deductions from the

premises of the theory, test these deductions using the available data

and then modify the premises or (much more rarely) the deductive

techniques as a basis for further modelling. One difficulty with

implementing this view is that mathematical theories are not

appropriately ``modular''. It is not typically feasible to ``throw

away'' those parts of a mathematical theory that are malfunctioning.

For one thing, if the model is not adequately grounded in actual

causal processes, it may be unclear which pieces these are. In a

poorly specified system, it will be very hard to link sections of an

equation to particular behaviours, particularly when aggregation is

problematic. (There may be coefficients in the model representing a

collection of different factors. It has already been remarked that in

many cases econometric modelling involves the testing of extremely

complex joint hypotheses. In some cases, the integrity of the

variables may be as questionable as that of the constants.)

Secondly,

the mathematical representation is not itself modular. Even if the

appropriate part of an equation, or system of equations can be

identified, replacing it with a more complex or realistic functional

form may simply render the whole system insoluble or indeterminate.

(This is a common progression in economic research. A simple model

producing a definite conclusion is criticised and replaced by a more

general model producing a range of outcomes depending on the value of

some parameter. No empirical evidence is provided for the actual

value of the parameter, and more importantly, no guidance concerning

how it could be measured. If the matter is pursued

econometrically at all, the additional theory or assumptions required

to proxy such parameters make it hard to determine whether the theory

can still be falsified. (26)) Thirdly, it is seldom possible

to reconcile or aggregate theories that use different sorts of

mathematical representations. (Econometric modelling actually avoids

this difficulty by limiting itself to models in separable terms. These

can be aggregated easily, but it is unrealistic.)

For these reasons, it is very hard for the development of mathematical

models to take place progressively, and there is a strong and observed

tendency for the development of overarching and competing models that

each explain some proportion of the phenomenon but are presented as

the whole explanation. The inability of each model to deal with other

aspects of a social process is not addressed. Instead, the importance

of those recalcitrant aspects is simply minimised, often by supporting

verbal handwaving. Examples are provided by competing theories of

investment, consumption and the speed of market clearing. In each

case the competing theories provide a partial explanation but it has

proved quite difficult to reconcile them within the mathematical

framework. Perhaps the deepest division of all is that between the

microeconomic and macroeconomic representations of economic activity.

At the microeconomic level, agents and firms are modelled as making

optimising decisions in markets. At the macroeconomic level, causal

connections are deduced by reference to models that do not have any

connection with individual optimisation. Clearly there are agents

whose microeconomic behaviour gives rise to macroeconomic aggregates

and conversely there are organisations like governments, which attempt

to influence individual behaviour by controlling these aggregates.

However, there is currently no realistic and unified mathematical

representation within which the links between the two levels can be

made explicit.

The limitations of mathematical representation also affect the process

of theory development. Because only certain extensions to the theory

prevent it from becoming intractable, there is a tendency to filter

new data with this in mind. Certain sorts of behaviour, like altruism,

learning and morality have become almost unrecognisable when

translated into economic theory. Ideally, theories should be

represented in a language which actually encourages the incorporation

of new and diverse data by ensuring that this process does not make

the resulting models impossible to handle.

The final difficulty with mathematical representation concerns the

social effect it has on the accessibility of models to other

practitioners and critics. Both the representation and solution of

mathematical systems require considerable technical skill and the

``reinterpretation'' of economic phenomena for mathematical

tractability makes the resulting models even harder to compare with

everyday experience. Even among practitioners, the tendency to make

assumptions ``in passing'' while solving mathematical systems makes it

very hard to replicate the results of econometric studies. In addition

to these technical difficulties with sharing econometric models, there

are also theoretical difficulties. The simplification of time and move

structure is such that there is very little ``emergent'' behaviour in

mathematical models that can be checked by subsequent investigators.

Apart from detecting errors of calculation or using the models with a

``better'' or different data set, there are no implications in the model

other than those made explicit by its solution.

Taking the economic view of scientific progress as the correct one, we

may ask whether simulation or mathematical modelling is better adapted

to this sort of activity. Simulation is capable of representing

properly grounded theories directly. Individual agents, with their

respective models of the world, are represented exchanging information

and materials in real time.

Any processes resulting in the generation

of aggregate data involved in individual decision-making can be

represented explicitly, for example the generation of statistical data

by banks.(27) Thus macroscopic data does not ``float

free'' in such models, though it may turn out to be less important

than previously supposed. At the same time, the kind of abstractions

that individual actors make in dealing with the world also provide

valuable information about the possibility of modular simulation. If

the process of government is either predicted or taken as exogenous by

agents, without the need to refer to the internal workings of

government, then this sort of decision-making may allow the modelling

of government policy as a ``black box'' or statistical process. (Of

course, it may be that agents are being insufficiently sophisticated

in taking this view. However, we can judge this by the extent to which

they view this model as satisfactory.) Nonetheless, it seems that the

everyday understandings of agents, or at least aggregates which are

not too far removed from them, may provide a better ontology for

models than abstract theory. This sort of modelling is made possible

by the richness of computer languages, which, though by no means as

rich as everyday language, is still far less restrictive than

mathematics. (In any event, the linkage between objects or actions and

talk about them is itself something that agents may be able to

explain.)

Simulations can be developed in a modular fashion when the

descriptions of transformations and processes are not primarily

theoretical, but reflect the movements of actual goods and information

in the economy. This is again made possible by the fact that

simulation can keep track of multiple processes. Although the

observation of these variables may be more or less problematic, their

characterisation is relatively straightforward. As a result, it should

be possible to pose research questions in relatively simple language

and leave the investigation of different subsystems to different

researchers or disciplines with appropriate skills. (28)

However, once this individual research has been

done, it is still capable of being reconciled within the same

simulation. For example, it is possible to regard an agent as a black

box, in the economic fashion, with preferences as inputs and decisions

as outputs. However, within a simulation it is no longer

theoretically necessary to do so. Furthermore, the neglect

of factors influencing preference such as education and advertising

becomes apparent once the processes by which agents interact are

modelled explicitly. (Curiously, economic theories of advertising have

proposed almost every theory of its function except that it

is intended to alter preference.) These factors were previously the

province of psychology, but are clearly important to economic

behaviour too. Simulation provides a framework within which

traditional economic models can be reconciled with psychological ones,

at least in principle. Thus it enables progressive research through

the development of increasingly rich models, and modularity, through

the exercise of collecting data about the ontology which agents

actually use in decision making. (29)

Such complex models of interacting agencies also produce large amounts

of emergent data which retains its everyday interpretation. By

contrast, for example, intermediate iterations of a mathematical model

do not necessarily have any obvious real world interpretation. The

amount of emergent data produced by a system is likely to be a

function of the number of agencies involved and their ability to act

independently of each other. For example, in a model of firm

interaction, all that need be simulated is the pricing decisions of

individual firms and their survival or bankruptcy according to

profitability and the workings of the market. The age profile of

firms comprises an independent emergent piece of data

resulting from the independent actions of many firms, which is not

designed into the simulation and can be compared with the age profile

of actual firms.

A ``complex object'' like a simulation provides a

rich mixture of new effects for investigation and comparison with

empirical data, as well as suggesting the need for new theories and

data. Unmodelled features, simply simulated as probability

distributions, can be ``unpacked'' and linked to other features within

a simulation over time. The very complexity of simulated data,

provided it is based on everyday rather than theoretical

understandings, allows us to make use of our excellent cognitive

skills as pattern recognisers to develop understandings of the future

needs of the simulation. The use of everyday understandings also

allows us to present the simulation, in a suitably user friendly form,

to non technical practitioners. (30)For example, suppose that a manager is

presented with the opportunity to ``play'' an interactive simulation

of firms in a market, taking the role of one firm. She is amazed at

the difficulty of representing the pricing decision process she

actually uses within the current framework of the simulation, both in

terms of information provided and techniques available to process it.

She explains: ``If I had to make pricing decisions on that information

alone, I'd always err on the side of caution. But of course, we do it

rather differently.'' When the simulation prices are observed to be

systematically too low, having been compared to those in real markets,

such comments suggest not only what might be wrong, but what ought to

be done about it. Furthermore, such comments need not be limited to

the internal workings of the firm, but may also be used to refine the

environment if the manager reports ``I've never seen price fluctuate so

much as that''.

Finally, just as simulation makes a model more accessible to non

specialised critics, it also makes it more accessible to specialised

ones. A well designed program is relatively portable and contains a

record of assumptions far more complete than that involved in

mathematical modelling. As such, it is far harder for

non-comparability of results to go unchallenged as an invitable

consequence of the different subsidiary assumptions that result when

people attempt to solve systems of equations. At the same time, the

amount of emergent data produced by a simulation is such that it is

actually rewarding and interesting to investigate a simulation

further. By contrast, the simplicity of mathematical systems reduces

secondary analysis to the rather menial and potentially negative task

of looking for errors. In addition, the complexity and variety of

emergent data makes it far harder to manipulate parts of the model,

consciously or unconsciously, to produce ``acceptable'' results.

Adjusting one section of the model is likely to influence the nature

of a large number of other parts of the model, all of which can be

evaluated independently for plausibility. Within a simulation, it is

also possible for this plausibility to take richer forms that a simple

comparison of variable values. Not only can the simulation deal with

such features as the distribution of individuals, but, as has already

been mentioned, it can address the reconciliation of different sorts

of data and different methods of obtaining it, for example that the

simulation is consistent not only with the observed pricing decisions

of firms based on supermarket observations, but with the descriptions

of managers based on interviews. (31)The existence of independent sources of

data also means that the testing of models need not involve impossibly

complicated joint hypotheses. It may prove possible to establish that

some subsystem has been substantially understood before moving on to

deal with the next. (Such a view still requires a certain amount of

realism about the world and our ability to develop a common way of

talking about it, but it is not a simplistic realism, rather it is

predicated on our socialisation as language users in a shared

environment.)

Of course, this is an idealised picture of the possibilities of

simulation, but one that itself deals in concrete objectives. We do

not yet know how to model the human ability to abstract and develop

models, for example, but we can be reasonably confident that it will

be capable of representation in simulation. We can have no

corresponding confidence about the mathematical representation when we

already seem to be pushing at some of its limits which are described

above. Because we are discussing methodology, all arguments must be

qualified as being ``in principle'', but if we take the scientific

objectives of economics as given, it does not seem that simulation is

any less rigorous than mathematical representation and may actually be

more so. This development has a cost. Simulation will require more

data and more equipment than mathematical modelling, but these

``practical'' costs seem far more agreeable and rewarding than the

self inflicted costs of inconsistency and ambiguity which result

from the arbitrary restriction of models by their mathematical

representation. It is the difference between climbing a mountain and

digging a pit.

This paper addresses the three main classes of objections that have

been levelled at simulation in economics. Firstly that it is

unecessary, except as a technique for solving mathematical models,

because these models are the best representation of social processes

we have. Secondly, that even if simulation is a better potential

representation of these processes, the models it tends to produce are

either practically or methodologically unacceptable. I have challenged

the first argument by suggesting two major areas in which the

mathematical representation is restrictive, in its representation of

time and multiple agency. I have also suggested a number of concrete

examples in which these limitations are manifested such as

simultaneous action, retries and external control of feedback systems.

I have challenged the second and third arguments by unpacking them and

addressing a number of individual methodological complaints. There are

other objections, but I have tried to deal with all the commonest and

most important ones. In each case, I have not challenged the goals of

economics or its view of scientific method directly, but have

attempted to show that even given those goals, simulation is still

potentially superior to mathematical modelling. (In fact, I think it

is possible to go further and argue that simultion is compatible with

a richer and more contemporary view of the philosophy of science.

However, that is too big a task for a single paper.) Generally, the

attempt to separate different sorts of objection may prove valuable in

subsequent attempts to clarify appropriate responses. Methodological

complaints require different responses to practical ones.

The broader purpose of the paper has been to address the relationship

between methodology, theory and models which differs between the

simulation approach and the more traditional methods of economics. It

seems that economics confuses methodology and theory, which determine

the subject matter of interest and the ways of representing and

investigating it, with models, which present the results of these

investigations in a form suitable for testing. Simulation attempts to

use the widest possible representation language, allowing it to be

agnostic about what data matters. By contrast economics takes a very

particular view of what data is required. This seems to be forced on

it by the prescriptive choice of a representation language which

narrows the range of model possibilities in an arbitrary way. The

paper attempts to show that the deductive approach, favoured by

economics, and the inductive one, suggested by the capabilities of

simulation, may not prove equally satisfactory.

(1) Paradigm cases of this research rogramme are provided in consumer theory (Deaton and

Muelbauer, 1980) and the theory of the firm (Koutsoyiannis, 1979).

(2) This view of the role of simulation seems to predominate in the literature of

Computational Economics (Pau, 1986, Roos, 1987).

3) In a survey of evolutionary models in economics, discussed in Chattoe (1994) the

proportion of simulations describing processes that could not be solved mathematically was found

to be very small. Furthermore, it is generally acknowledged that evolutionary modelling is far

more sympathetic to simulation than other branches of economics.

(4) A simulation, which consists of a computer program, can be seen as a set of starting

conditions and rules for change in the same way that a system of equations can. Thus we may talk

about a computational representation of a social process.

(5) The relatively rare examples of descriptive simulation in economics are almost invariably

found where traditional theory has proved particularly unsuccessful (Witt, 1986), or where its

assumptions are questioned by individual economists (Alchian, 1950, Witt and Perske, 1982). In

all cases, until extremely recently, this work was seldom followed up, rarely quoted for practical

use and restricted to less prestigious publications. In many cases, this cannot easily be explained

by its lower intellectual quality.

(6) Utilitarianism does not imply individualism. Economics text books often contain

``entertaining'' examples of joint utility functions (Deaton and Muelbauer, 1980, page 126).

However, these are quite rare in economic modelling generally, I suspect because they are so

hard to solve analytically. This does not mean, however, that they do not represent important

social processes with which theory should be expected to cope.

(7) This view has been criticised by Leontief (1977).

(8) Interestingly, a residue of the era of verbal theories is still with us. Even in the most

rigorous mathematical models, the variables used, for example `capital', `unemployment' and

`profit', commonly have interpretations which neither correspond to everyday usage nor bear

close theoretical examination. (For an example of the ``deconstruction'' of the investment

variable, see the last chapter of Nickell (1978). At the very least, they turn out to encapsulate

some very controversial technical assumptions about the possibility of aggregation.

(9) A number of authors have pointed out the economic importance of changes in physical

science (Georgescu-Roegen, 1971, Mirowski, 1989).

(10) The phenomenon of ``heresy'' among Nobel Laureates also reveals something about

the social conditions prevailing within the economics profession. When, but largely only when,

academics reach an untouchable professional position, they lose faith in mathematical modelling

of rational choice as a progressive methodology and begin to criticise it. (Such methodological

criticisms should not be confused with objections to specific assumptions from within the rational

choice framework.) Sadly, these critics have often lost their direct influence on teaching and

research policy by this point. The objections by Leontief have already been referred to, but other

such ``heretics'' are Kenneth Arrow and John Hicks. There are also interesting cases like Ronald

Coase and Herbert Simon who have found their ``heretical'' objections re-absorbed into the

optimising framework. The theoretical awkwardness that has resulted from this process arises

from the requirement that optimising choice should be retained as an assumption.

(11) One may also question whether this comparison would be useful in any event. The

success of a representation is measured by its ability to represent, almost regardless of the quality

of the models it represents. This distinction is not absolute. No-one would recommend a

representation that was suitable only for palpably ridiculous models. Nonetheless, we do not yet

know enough about which models are plausible to use prediction as the main criterion of

representational quality.

(12) The fact that different representations can be used to describe the same phenomenon

makes it important that they should be associated with theories possessing adequate heuristic

fertility. This is the capability to progress by generating new models for testing. When economics

is presented with new findings in the other social sciences, it often responds by observing that the

behaviour concerned can be represented, after the event, by some utility function. However, this

is not the same as anticipating that behaviour in the first place. Pure utilitarianism implies nothing

about what people actually derive utility from. Taken alone therefore, it does provide a suitable

basis for the development of economic theories. Furthermore, if almost any behaviour can be

represented by a utility function, though not necessarily a soluble one, we need some method to

help us decide which behaviours actually occur and which utility function might be appropriate

in a given situation. The possibility that utility theory might be non-falsifiable, because it lacks

such a method, is discussed further in Chattoe (1995a)

(13) However, it may be significant that many of the most successful models involve

predicting the current value using a set of past values, a strictly econometric process that has no

starting point.

(14) The idea of encompassing originates in econometrics (Hendry, 1988), where it applies

to the comparison of model predictions rather than representations. Nonetheless, using it in this

new sense does not seem to distort the original meaning unduly.

(15) One might argue that this richness reflects our need to talk about our own mental

processes and those of others, an understanding of which is clearly vital to the modelling of social

behaviour for reasons discussed shortly.

(16) There is a third approach, proposed by Friedman (1953).

(17) Econometric time may also encourage the use of the ``lowest common denominator''

of data. If one has three monthly data on one variable and yearly data on another, one cannot

make any effective use of the additional three monthly data. One can average the three monthly

data or interpolate the yearly data, but both processes introduce uncertainties of their own.

(18) Unsurprisingly, attempts to control individual behaviour by altering these aggregates has

met with mixed results. The causal link between micro and macro data is not equally rigid in both

directions. There may be instances where individuals use macro data in their decision-making, for

example the interest rate, but the extent of such behaviour has not been demonstrated.

(19) This is sometimes referred to as the ``problem of simultaneity'' in econometrics (Hendry,

1993).

(20) This is not possible in an absolute sense, but is possible in practice through the social

institution of time-keeping.

(21) Abstracting from time in economics also seems to produce abstraction from space in

most models.

(22) The extent to which our bodies also act according to laws independent of the minds

embedded in them has also been neglected.

(23) This raises a number of other issues, for example the possibility that additional

information may be harmful rather than helpful and that it may be very hard to make rational

comparisons between past and present situations because so much is changing.

(24) However, given a proof that a decision process was not computable, nobody would

presumably build a simulation which represented agents as using that decision process!

(25) This claim may simply be false. The purpose of sensitivity analysis is to establish

whether outcomes are independent of the values of some parameters. One could certainly argue

that a model capable of producing any outcome was simply a poor model but it does not follow

that this is a necessary feature of the simulation approach.

(26) A good example of this progression is to be found in the development of the

Modigliani-Miller Theorem in the corporate finance literature.

(27) Such representations may ultimately need to model the role of simulators themselves!

This serves as an appropriate reminder that social systems can also be influenced by attempts to

measure and understand them.

(28) In fact, the extent to which these research questions can be phrased in common terms

is a useful measure of the extent to which they might reflect the decision processes and actions

of common people. If they only make sense in the terminology of one discipline, they may not

be very useful.

(29) One interesting consequence of this view of multiple processes is that different

techniques are also available to elicit different sorts of data and can be used to cross-check

simulated behaviour in a rich way. Techniques such as interviewing may allow us to establish how

agents really take decisions. Thus far, it has proved possible to transfer suitably abstracted data

between disciplines but there has been comparatively little transfer of techniques.

(30) It is true that the skills for building simulations are at least as rare as those for building

mathematical models, but because the behaviour of a simulation is more than simply the listing

of the program which produces it, it is possible for a person to use a simulation she doesn't

``understand'' in a way which has no analogy in the case of a set of equations.

(31) Such reconciliation is necessary in any event, unless we have great confidence in any one

source of data. Economists often reject interview data because agents are not ``motivated'' to tell

the truth, though the conception of motivation involved is rather attenuated. By contrast,

they are happy with official statistics, though these presume that both the reporters and the

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