Assessing the Use of Agent-Based Models for Tobacco Regulation (2015) / Chapter Skim
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Appendix B: Agent-Based Models for Policy Analysis--Lawrence Blume
Appendix B: Agent-Based Models for Policy Analysis--Lawrence Blume
Pages 195-216
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From page 195... ...
is a computational simulation model of a many-agent system that captures the behaviors of the system's autonomous agents and their interactions with each other. An ABM is a computational instantiation of a complex adaptive system (CAS)
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The CAS describes a probability distribution on outcomes for every vector of inputs x and equation parameters p, and the ABM simulates the probability distribution. Each run of the program yields a random draw from the CAS's outcome distribution, and so the empirical distribution of many draws approximates the CAS's outcome distribution.
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describe a stochastic process, a joint probability distribution of the collection of random variables {S ( t )
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Emergent properties of the CAS have to do with the behavior of aggre gates, such as the number of susceptibles. This CAS is a Markov process that has a single absorbing state in which no one is infected; that is, the disease has died out.
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The aggregate behavior of the simple CAS can be usefully approximated for large N and small h over finite time horizons by the differential equation system 1, and a similar system approximates the multitype version when there are many more people than types. If the social structure of the networked model is something regular, like a lattice, it is possible to approximate the system with a partial differential equation if the large-N question is posed the right way.
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The large-scale properties of the heroin market are likely to be measurable only with great difficulty, so using a simulation model that is based on more easily observed individual behavior patterns is a clever idea. One's confidence in the model's macro-level predictions depends on one's confidence in the internal validity of the model, that is, how well it matches the ethnographic data and how well the ethnographic data capture the fine details of the agent interactions on which the model most sensitively depends.
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The model has three components: an urban transportation component, a detailed epidemiological model of smallpox transmission, and a model of disease detection. The urban transportation simulation model is used to simulate the daily movements of individuals across locations.
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The "representative contact graph" derived from the urban transportation model calibrated to data from a smallpox-free Portland might look very different from a graph of social contacts in a Portland where smallpox is rampant. I will argue below that ABMs that are complex enough to demonstrate or describe possible policy effects in interesting environments will almost certainly fail to measure causal effects to the satisfaction of at least some social science communities.
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The SIS CAS is a structural model. Its equations describe how individuals meet and transmit a disease and how they are cured -- a combination of social and biologic rules.
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In contemporary macroeconomics, the phrase Lucas critique, in honor of Robert Lucas (1976) , is often applied to claims that the behavioral equations of some models are not invariant under alternative macroeconomic policies, that is, that they fail Marschak's stability requirement.
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history. Descriptive output validation matches computationally generated output with preexisting data on the process being modeled; for example, one might fit the SIS ABM to data on chickenpox by choosing parameter values to match data on the time path of chickenpox incidence in a given location and year.
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Input validation alone is reasonable for demonstration purposes but not for proof of concept.11 The problem of parameter stability is often discussed in the context of estimating structural models, but it is even more critical for models that have externally validated, "input-validated" parameters. Before turning to issues of ABM parameter estimation, I want to mention a fundamental question about the choice of parameter values for policy evaluation: What does it mean to have good parameter estimates?
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DSGE modelers choose descriptive output validation over input validation; this has implications for the predicted distribution of income. 13 The derivation is described formally in the annex to this appendix.
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Simple ABMs pose no unusual identification problems. For example, in the simple SIS model, up to a change in time scale, the stochastic behavior of the model is completely described by the ratio β/γ, and things that we might measure, such as the number of susceptibles or infecteds at a given time t, are stochastically increasing or decreasing, respectively, in this parameter.
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In a truly complex model, one would have to simulate with the ABM across the entire parameter space to trace out the different observables distributions, and this is often not practical. PseudoComplexity There is often less to ABMs than meets the eye.
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Following conventional method-of-moments techniques, one can search across the parameter space with the goal of minimizing the distance (measured according to a prespecified metric) between moments or other statistics of the simulated observables distribution and those of the empirical distribution from the data.
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There are few general principles to apply, and any asymptotic analysis of a given ABM may depend on fine details of the model's structure that are not readily accessible in the computational algorithm. Other Paths My theme, in summary, is that the very complexity that makes ABMs useful for exploratory analysis creates difficulties when the task is to pin down the nature of the actual environment sufficiently to determine good policies.
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From page 212... ...
Decision theory is the economist's lever. For example, the traditional economic model is expected welfare maximization, which makes use of probabilistic forecasts generated by the structural model and accounts for parameter uncertainty by positing an a priori subjective probability distribution on the set of parameters, which can be revised in light of new information.
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Note that the unobservables of the system, such as the states of individual agents, do not appear directly in this description. They gener ate the randomness that is captured in the probability distributions that F produces; if everything is observable, the probability distributions will be trivial -- the system is deterministic.
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Emergent properties have to do with aggregates, such as the population mean and variance of behavior, and other less obvious functions of the observables. For example, in the SIS CAS, the extinction time is an emergent property.
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1972. Markov processes and learning models.
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