1 Some characteristics of structural change

For purposes of this paper (and as a cock-shy), I will take structural change to mean some alteration in the components and relationships among the components of a coherent system. I will say that a system is coherent if it can be represented formally by a mathematical network in such a way that, for every pair of nodes there is either a path between them or a path to some common node. On this definition, structural change would be either a change in the set of edges or a change in the path algebra determining the value or cost of traversing any path or achange in the node set (requiring, self-evidently, a change in the edgeset) or, most likely, some combination of these.

The structures with which most of us are concerned are the transition (or emerging-market) economies of the CEE countries, the EU with its convergence issues or changes in organizational structures with the associated issues of downsizing and flattening, etc.

I am simply going to assert here that such changes entail changes in behavioural and other norms prevailing within the system and that not all agents respond in the same way to structural changes. Moreover, in practice new norms emerge more or less gradually as the agents within the system continue to learn about the effects of these changes. They learn by building up their own views of the new relationships which affect them both directly and indirectly. The learning is partly a result of observing the effects of their own actions and the actions of others. It is natural to suppose as a working presumption that the changes in relationships will depend on the behavioural changes in all of the different agents. Consequently, the emergence of new norms will reflect the changing behaviour of the agents who make up the system and how these changing behavioural processes interact.

In short, structural change is a process of emergent and distributed behaviour. I am going to argue in this note that emergent, distributed behaviour (and therefore the process of structural change) is best and most naturally modelled within a declarative modelling framework. I am also going to argue that the properties of preferred outcomes from structural changes are best and most naturally modelled within a procedural modelling framework. To coin an aphorism, declarative representations support models of what we can have while procedural representations support models of what we want to have.

2 Defining the terms

Modelling can be either imperative or declarative. Imperative modelling states what will happen. Declarative modelling states what is "true". If an imperative model includes statements about how to make something happen, it is that particular kind of imperative model that we call procedural.

Mainstream economic models, in most cases that I know, represent agent behaviour procedurally - by constrained-optimization algorithms, by Bayesian updating procedures or by algorithms for choosing gametheoretic strategies. Some models from outside the mainstream of economics are imperative but not procedural. The classic examples ofthese models are those of Nelson and Winter as discussed below.

Declarative representations assert a statement which are known to betrue either axiomatically or inferentially. All logics are declarative though not all declarative modelling will conform to a logic. The general point here is that a declarative representation is one which specifies the immediate implications of a given set of conditions. Such implications could amount to actions but they need not do so. It is natural for such implications to amount to beliefs or the creation of knowledge which had not previously existed.

Declarative modelling is the natural choice for the analyst who is concerned with the ways in which behaviour can emerge from a given state of affairs. Procedural/imperative modelling is the natural choicefor the analyst who wants to know the best possible reaction to a state of affairs or the best possible state of affairs which can be reachedfrom the current state. In general, procedural modelling is the natural technique for analysing sequences of states while declarative modelling is the natural technique for analysing the processes which emerge from an initial state.

The repeated use of the word "natural" here is intended to emphasise that declarative modelling techniques can be used to capture theprocesses from which states emerge and imperative modelling techniques can be used to capture the processes that emerge from given states. It is easier and more efficient to do it the other way round.

For concreteness, I give some examples from analyses of technological change. The Solow growth model and model of technical change has it that there is a production function and that shifts in the production function are the consequences of technical change. Explanations of the shifts in that production function involve inputs of, for example, investment in human capital to produce those production-function shifts. Some relation between human capital and production function shifts is specified and indirectly estimated. This is a procedural representation of technological change since the position occupied on the production function and the investments in human capital aredetermined by some optimization procedure which is specified in advance.

The Nelson-Winter models of evolutionary growth depend on individualagents competing in part by moving along a technological trajectory. The representation of their behaviour is by means of rules which state that, in a given set of conditions, the agent will undertake aspecified action such as investing in one unit of capital if profits are positive and the realization of a random number in U[0,1] isgreater than (say) 0.5. The process which leads to this relation is not specified so that we would call the representation imperative even though it is not procedural.

In one of our own technical reports, Bruce Edmonds, Helen Gaylard and I represented technological possibilities as a network and R&D as a network search. The agents would search the network in order not onlyto improve their technological positions, but also to learn about whichR&D strategies were effective and which were not. The process of R&D takes the form of building models of the effects of different search heuristics and then applying the search heuristics in which the agents have the most confidence. The models are built up by the assertion of statements implied by previously determined true statements and rules of inference. Thus, R&D is represented as a logic-like process of proving the analytic truth of statements in a way which amounts toinformation-processing, model-building and then decision-making.

I believe that imperative (including procedural) representations require the relationships between conditions and actions and between actions and outcomes to be specified in advance while declarative representations allow these relationships to emerge. I accept that this belief might not be correct and, so, I hope that there can be some discussion of this assertion.

3 Defining the issues

In general, procedural representations of agent behaviour are better suited to modelling emergent states since the behaviour is pre-determined while declarative representations are better suited to modelling emergent processes and agent behaviour. In this section I address three issues raised by this difference: the rigour of the two approaches to analysis, the generality of each approach and whether the two approaches are in conflict.

Rigour

Conventional economic models are rigorous in the sense that they rely on the axioms and rules of inference of various branches of mathematics. The rigour is complemented by modularity and reusabilityof results in the sense that the modeller can always use results established previously and in different applications without having to prove those results from scratch. Although there is no shortage of procedural simulation models (such as computable general equilibrium models), prior to the advent of the PC the bulk of procedural models were formal and, even if explicated by means of examples, were not implemented as simulation models.

Imperative models have typically been implemented as simulation models. As such, there was typically no particular claim to rigour and, in one case at least, such claims were simply wrong. (See Moss, 1990a, 1990b;Winter, 1990.)

Because declarative systems assert statements inferred from previouslyasserted statements and rules, they are relatively easy to relate to formal logics. For example, the research team in the Centre for Policy Modelling has developed a programming language which is optimised for representing behaviour of and among individual agents declaratively -hence it is called SDML for strictly declarative modelling language. This language has been implemented as a strict superset of Konolige's autoepistemic logic. The details of this logic are not relevant here.What is relevant is that, because models in SDML can be made conformable with the axioms, rules of inference and access relations ofa particular modal logic, such models are not obviously less rigorous than models that conform to the axioms and rules of inference of oneparticular branch or mathematics or another.

This discussion does raise a further, I think interesting, question about the relationship between rigour and relevance.

There are many formal logics including a variety of mathematical systems (e.g. Euclidian and non-Euclidian geometries). Godel proved in his second inconsistency theorem that no formalism proved its own internal consistency. Such proofs have to appeal to somemeta-formalism. And the meta-formalisms can only be proved consistent by appeal to some meta-meta-formalism, and so one without limit. My point is that no one formalism is unambiguously more rigorous than any other. Absolute rigour is simply not to be had. It seems reasonable on these grounds to assert that Konolige's autoepistemic logic is neithermore nor less rigorous than the mathematical formalisms relied upon by economists.

The implication of these remarks is that the choice of a logical formalism in which to represent the structure and behaviour of anysystem is a matter for the judgement of the modeller who ought to be able to describe the virtues of the chosen formalism for the problem being considered. In light of the discussion in the previous section, I would argue that appropriate formalisms for modelling emergent behaviour will support declarative representations while the appropriate formalisms for modelling emergent states and sequences of such states forming trajectories will support procedural representations.

Generality

I have identified rigour with logical formalism to suggest that declarative simulation models in general need not be logically any weaker than formal, procedural or imperative models. This leaves open the question of generality. I raise here two concepts of generality: generality in relation to a formalism (analytic generality) and generality in relation to conditions of application (synthetic generality). I guess that most of us would identify analytic generality with the proof that, within a formalism, a well formulated set of conditions are necessary and sufficient for a particular result to be realized. In a declarative model, the result would normally be some aspect of emergent behaviour while, in a procedural model the result would normally be some characteristic of emergent states. One virtue of a modelling environment such as SDML is that the analytic generality of the results of simulation models can sometimes be proved within, inthis case, Konolige's autoepistemic logic. The simulations themselvesare useful in suggesting which propositions to try to prove and also to provide some indication of the synthetic generality of the beliefs and views of domain experts which are, in our work, captured in the models.

Compatibility

So far, I have been distinguishing between the natural spheres of application of declarative and of procedural modelling. I simply suggest here that the use of procedural modelling to determine optimal trajectories and final states can be supplemented by declarative representations of behaviour to determine the conditions in which the optimal paths/states would emerge. In effect, I am suggesting that the declarative formalisms and the procedural formalisms yield perspectives on different aspects of the same problems. Neither requires the other yet procedural models can provide a benchmark for the declarative representations (how close does behaviour come to whatever is optimal) and declarative representations can support a discussion of the plausibility of the results obtained with procedural representations of behaviour.

4 Distributed, emergent behaviour in conditions of structural change

Declarative (e.g. logic) modelling techniques are the natural means of describing emergent behaviour for the reasons given above. It is not always (or perhaps often) the case that an individual's behaviour emerges either independently of the behaviour of all other agents or in the same way as that of all other agents. Different agents engage indifferent activities and learn in different ways about different things. These differences can themselves be crucial to the emergence of new norms. If economists recognize this statement as code for rejecting the modern concept of the representative agent, then they would be correct. But even rejection can be constructive.

In this final section of my note, I offer an example of the construction of a declarative model and the distributed nature of the emergent behaviour.

The problem was to model the phenomenon of rapidly increasinginter-enterprise debt together with high and increasing rates of inflation as found in the Russian Federation and in Beloruss. We set up a three production-sector model with, in addition, a household sector. The decision variables and their determination reflected the understanding of domain experts as collected by my colleague, Olga Kuznetsova. The details of the model are available from our Web site (http://www.fmb.mmu.ac.uk/cpm/).

Individual enterprises were modelled as agents who learn by specifying models of other agents' behaviour and the relationship between their own decisions and the success of the enterprise in terms of eithersales or cash holdings. The very earliest versions of the model yielded the sorts of increase in inter-enterprise debt that we observe in these emerging-market economies. What seemed difficult to get was a pattern of high and rising rates of price inflation. It simply was not enough in our models for agents to develop models of the effects of changing individual decision variables or collections of decision variables in order to learn that increasing prices will increase cash flows. It was also a feature of the model that price increases would not immediately affect sales because there were no efficient information flows built into the model (because they are not believed to characterise the economies in question) to support the identification of the lowest-price supplies.

Without increasing the information-processing and computational capacities of the simulated enterprises, we found that an inflationary pattern became established when each enterprise imitated the enterprises that it identified as being the most successful it knew. We assumed that an enterprise would identify its best suppliers as those who supplied what the enterprise ordered and its best customers as those who paid their bills in a timely way. The public information about these enterprises was limited to the prices they charged for their outputs. This model generated a pattern of price inflation which had a high and rising trend rate but the time series was extremely volatile and marked by occasional and substantial falls in the rate of price inflation. When we subsequently obtained such actual price data as exists (and as distinct from statements of common perception), we found that the series for Russian inflation rates exhibited the same characteristics as the series we generated with our later simulation models.

The development of this one model entailed specifications of behavioural principles based partly on plausibility and partly on evidence from domain experts. The numbers which emerged from the model were the result of emergent and interactive, distributed behaviour. These numbers could be taken to be predictions of the nature of the price inflation in the Russian Federation - predictions which, on this occasion, were not disconfirmed. The model was rigorous in the sense that it entailed the axioms, the rules of inference and the access relations of a particular modal logic. It left not only numerical outputs to compare with actual data series but also a set of behavioural principles which can be tested by interview and survey for their empirical relevance. All we claim for this model is that it is both rigorous and its realism is testable. The modelling process is not at an end and, within the limits of rigour, its realism can be enhanced yet further. Moreover, it yields numerical outputs which can be assessed for conformity with the statistical record by means of standard descriptive statistics.

What the model and its results do not do is to tell us what would be optimal in any sense. However, just as we were able to develop the model to yield results which have a clear correspondence with the statistical record, we could develop the model to identify behavioural norms and principles which, in one policy regime or another, support trajectories identified by, for example, optimal control theoretic or computable general equilibrium models.