Models and exploration

It is a fact of economics that models are explored. A quick look at any survey ar- ticle on a certain topic would reveal this fact. Generally, an influential model built on observations about the phenomenon under consideration, on knowledge of other areas of research and on knowledge available tools suggests something new. Other economists, then, go on to study this model. Some check whether the same conclusion holds under different assumptions, some check whether the model is in agreement with data, or whether the model works when other disturbing factors are introduced, some others instead may test the model with real individuals (i.e. conduct an experiment). It seems that there is no single way, or methodology, to study a model and its implications. For models of unintended social phenomena, availability of data and historical records restrict the possible ways in which one can explore and test a model. Yet we have seen in Chapter 6 that this does not prevent researchers from testing the existing models or hypotheses concerning unintended consequences of human action.

It has been argued that a good invisible-hand explanation should suggest a novel way to look at the real world. Our story of exploration can then begin from there. Consider the chequerboard model. It suggests that mild discriminatory preferences may bring about segregation. More properly, the chequerboard model tests this hypothesis and suggests that it is plausible, and that we may expect to see the depicted individual mechanisms to interact in the real world as they do in the model. Of course, we have every right to be suspicious about this claim, or at least about the possible range of conditions under which it may hold. And if we are, we may test it. For example, we may ask whether the hypothesis holds under extreme conditions, such as when everyone strictly prefers a mixed neighbour-hood to any other mixture. Pancs and Vriend (2003) present an example of this. They test the chequerboard model under the conditions of strict preference43 for perfect integration and conclude that Schelling’s results hold even if this assump- tion is made. What they do is not to increase the realisticness of the model, or to test it with available data. They simply question the strength of Schelling’s conclusions. They partially test the chequerboard model in the abstract.

Alternatively, we may introduce new factors to the chequerboard model. We may change the definition of the neighbourhoods, the number of agents, the way in which individuals are initially distributed, we may add certain other specifica- tions to the agents and all that. There are numerous possibilities, and all can help us to understand the strength of Schelling’s argument, and to have a better idea of the implications of the chequerboard model. Two examples of this approach are presented by Epstein and Axtell (1996) and Zhang (2004a). They simulate the chequerboard city by way of changing the number of agents and by setting a certain limit on the lifetime of agents. Again, these simulations are not any closer to the real world than the chequerboard model. They test it under different con- ditions, or with specific parameters. Both Epstein and Axtell (1996) and Zhang (2004a) show that Schelling’s initial hypothesis holds under these conditions for a variety of initial starting points.

Another possibility is to integrate some factual information to the chequerboard model and hence see whether it holds when some external factual constraints are introduced. For example, Sander et al. (2000a,b) and Zhang (2000) use survey data to determine the preferences of different types of agents in the chequerboard city. That is, their assumptions are consistent with real individuals’ preferences. The survey data suggest that individuals are tolerant to mixed neighbourhoods, but that whites are less tolerant than blacks. By way of integrating this infor- mation, Sander et al. (2000a,b) and Zhang (2000) demonstrate that Schelling’s insights hold.

It should be noted that the survey data by themselves suggest that Schelling’s insights may be true and that they need further examination. Bobo and Zubrinsky (1996) and Farley (1997) argue that many individuals are highly tolerant to mixed neighbourhoods. This indicates that the individual mechanisms (i.e. tendencies) depicted in Schelling’s model actually exist. Maybe more importantly, they suggest that strong discriminatory preferences alone cannot explain residential segregation. This should give us reasons to examine how tolerant individuals contribute to the emergence (or persistence) of segregation in particular cities, that is, examining the way in which individual mechanisms interact with each other as well as with others (e.g. economic mechanisms). We have argued that Schelling’s model is valuable because it suggests new explanatory mechanisms (i.e. the interaction of individual mechanisms). To be able to utilise this sugges- tion we need to examine the way in which these mechanisms interact with others in particular cases.

Introducing into the chequerboard world the factors that were isolated is another way in which we may explore and test it. In fact, Sander et al. (2000a,b) pursue this strategy in combination with others. They assume larger neighbourhoods and integrate housing costs and costs of moving into the model. Moreover, they use survey data to give shape to the preference functions of the individuals. The ac- tual discriminatory preferences of blacks and whites are represented in the model by defining, consistently with survey data, three types of agents of each group. Sander et al. then simulate the model under some ‘what-if’ scenarios to see how different factors (e.g. housing costs, moving costs, discriminatory preferences) may be related to each other. What we have in this case is confrontation with data as well as further conjectural scenarios. Yet another thing to do is to confront a certain aspect of Schelling’s models with statistical data. This is exemplified by Clark (1991). By studying statistics for certain particular segregated cities, he confirms that integrated equilibria (i.e. mixed neighbourhoods) are not stable.

Of course, there are other ways to explore and test Schelling’s model. Ap- pendix III presents a brief survey of the literature concerning the chequerboard model in order to give a better idea of the different ways in which models may be explored and tested. Nevertheless, exploration is not (and cannot be) a well- defined concept. There is no single way in which we can examine the plausibility of a certain hypothesis or its implications. Economists (and other scientists) test the available hypotheses in different ways. They sometimes test them partially, sometimes test their implications, sometimes their premises. But the important idea is that they explore the existing models to assess their plausibility. Moreover, they also entertain new hypotheses and test their plausibility in different ways by way of building models (Figure 7.4). In this sense, models are like thought experiments:44 when models are confronted with the real world, they come close to ‘real’ experiments.

The relation between thought experiments and ‘real’ experiments can be cap- tured by distinguishing between two types of isolation. Mäki (1992a) identifies two subspecies of isolation: material and theoretical. In material experiments the laboratory environment is materially isolated to test a certain hypothesis. ‘Theo- retical isolation is based on “thought experiments” instead of laboratory experi- ments: isolation takes place in one’s ideas, not in the real world’ (Mäki 1992a: 325). Morgan (2000) and Boumans and Morgan (2001) suggest that we may dis- tinguish between different types of experiments by way of studying the material- ity of the intervention. In a thought experiment, the intervention is immaterial. We simply make assumptions about the model entities (e.g. about the way in which they change). In a material experiment, however, we physically intervene in the process under consideration. For example, if we want to know how changes in X (e.g. temperature) affect Y (e.g. a certain material), we materially intervene to change the physical temperature of the laboratory environment. Morgan (2000) suggests that there are also quasi-material experiments where the intervention is only partially material.

Figure 7.4 Conceptual tools for model building (adapted from Boumans 1999: 93).

If we are allowed to use this terminology, we may say that models of unin- tended social phenomena may also be tested by way of conducting quasi-material experiments, if not with material experiments. For example, we may test whether real individuals behave in the way the model theoretic agents behave under cer- tain conditions. Most economic experiments are considered to fall under this cat- egory. There may be different reasons for conducting such experiments. We may be interested in seeing whether individuals behave according to the predictions of the model, or we may want to check whether our hypothesis is valid if we let real individuals ‘play the game’. Such experiments bring the model close to the real world for they connect the model world with the real world. We have seen an example of this in Duffy and Ochs (1999). They have created a laboratory environment within which they let real individuals behave (see Chapter 6). The environment was artificial in that real individuals had to assume they were behav- ing in an imaginary world, yet Duffy and Ochs have controlled the environment by way of changing some of the parameters.

All the complex ways in which new models are constructed and explored can- not be pictured easily. Some of the possible ways to explore and test existing models on a certain topic or about a certain phenomenon are listed below. Note that this list merely indicates some of the possibilities.

Assume that Model A suggests and supports a certain hypothesis, H(0). H(0), or its premises [H(a0), H(b0), etc.] or its implications [H(0a), H(0b), etc.] may be tested:

  1. By using a specific version of Model A, and by examining what happens under certain parameter values (e.g. by changing the number of agents, goods or neighbourhoods).
  2. By trying to construct a more coherent / consistent / robust model with restricted (i.e. more unrealistic) assumptions (i.e. by way of applying further isolations to Model A).
  3. By trying to construct a more coherent / consistent / robust model with some relaxed and some restricted assumptions (i.e. partially more realistic and partially more unrealistic compared to Model A).
  4. By trying to construct a more realistic model with relaxed assumptions.
  5. By adding some other relevant factors to the model and by examining how they interact.
  6. By testing the existing model against real-world data, or by conducting (quasi-)material experiments.

Most of the models we have seen in the previous chapters may be considered as thought experiments concerning a certain hypothesis. When the experiment results are positive, then the thought experiment renders our initial hypothesis (or a modified version of it) a plausible conjecture about the real world. Like material experiments, thought experiments may be conducted under different conditions. The rationale behind this is that this may help us see how plausible our initial con- jecture is. Abstract models help us to check the logical coherence / consistency of certain hypotheses and the robustness of our models. Quasi-material experiments help us connect the model with the real world. If they support the hypothesis, we gain more confidence about its plausibility. Yet these models cannot go beyond alerting us to certain possibilities unless the suggested individual mechanisms are found to interact in the way the model suggests for particular cases.

Source: Aydinonat N. Emrah (2008), The Invisible Hand in Economics: How Economists Explain Unintended Social Consequences, Routledge; 1st edition.

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