Abstract
There is considerable controversy whether a population’s extent of income inequality (not just individual income levels) affects a population’s health. Very provocative evidence is provided by a comparison of Canadian and US cities. There is a clear correlation in the US between city-level income inequality and working age mortality. But highly comparable data for Canada show no correlation. One hypothesis is that this major observed difference is due to greater income segregation (in turn highly correlated with racial segregation) in US cities compared to Canada. In this chapter, we develop and present an agent-based model called the Theoretical Health Inequality Model (THIM). THIM embodies a theory of this correlation wherein it is contingent on a range of factors that are plausibly important, and that differ between Canada and the US in empirically verifiable ways. Drawing on both empirical evidence and various social science theoretical work, we posit a formal algorithmic structure for THIM, and then a set of parameters reflecting the “stylized facts” for Canada and the US. The focus of this chapter is on the development of THIM as an agent-based model, including its conceptualization, and the realization of these concepts as a virtual in silico laboratory for simulation experiments and hypothesis exploration.
“an aggregate relation between income inequality and health is not necessary — associations are contingent”
(Lynch et al. 2000)
This research was developed as part of the NIH-funded Network on Inequality, Complexity and Health (NICH) led by George Kaplan (NIH 2010). We are deeply indebted to NICH colleagues for many valuable discussions, and to Nate Osgood and Chris Dutchyn for invaluable collaboration in refining the algorithm specifications throughout THIM. Much of the NICH work is published in Kaplan et al. (2016).
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Notes
- 1.
To be precise, the US data are referring to Standardized Metropolitan Statistical Areas (SMSAs), with the data for the other countries specifically constructed by the authors to be as close as possible in concept and definition.
- 2.
No analysis has been done to compare the strength of the Gravelle artefact hypothesis across countries. However, given its rather small effect among US states as estimated by Wolfson et al. (1999), any such differences are unlikely to be material.
- 3.
If A affects B, and B affects A, then a different value for A will result in a different effect on B, and a different value for B will result in a different effect on A. Thus, if transitions in A are simulated in discrete time before the probabilities of transitions in B are computed, the possible outcomes for A and B can be different than if B’s transitions are simulated first. For example, in THIM, if a change in location were simulated before changes in income, there could be a different move than if income change were simulated first.
- 4.
Of course, other THIM users might judge differently in this case and many others. If so, the source code is available and these kinds of modification to THIM can be made given some programming knowledge and experience.
- 5.
Indeed, even if a sim has aged into an “overcrowded” neighbourhood, and there are other candidate neighbourhoods, but none of these is less discrepant in terms of income, the sim remains in its current neighbourhood.
- 6.
Note that this formulation embodies a symmetry assumption – that sims with both high and low income relative to their neighbourhood average income are equally likely to want to move to another neighbourhood. This assumption may not be that realistic, but it was judged adequate for the experiments planned for THIM.
- 7.
Strictly speaking, the median share should not be called an inequality measure because it need not be consistent with the partial ordering of income distributions induced by the criterion of Lorenz domination, i.e. that one Lorenz curve is everywhere closer to (or everywhere further from) the 45* line (Atkinson 1970).
- 8.
Note that these measures need not be rank order correlated, and in fact are not for the YBase distributions used as inputs. Such situations are typically associated with crossing Lorenz curves (Atkinson 1970).
- 9.
Further details on the model, including parameters, source code, and an executable version are available from the authors (mwolfson@uottawa.ca).
- 10.
These stochastic elements also give rise to Monte Carlo error. The THIM results presented have been assessed to ensure that this source of error is not material.
- 11.
Not all age groups are shown; of those shown, for example, “40–45” indicates all sims at least exact age 40 and less than exact age 45.
- 12.
As in Fig. 17.10, the simulation spans 500 years, and only selected decades over this 500-year span that have been graphed.
- 13.
While the vertical axes in the three graphs are identical, the horizontal axis scales are specific to each measure.
- 14.
LE and HALE are computed in THIM as in usual real world practice using cross-sectional data from overlapping birth cohorts and the Sullivan (1971) method.
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Wolfson, M., Gribble, S., Beall, R. (2017). Exploring Contingent Inequalities: Building the Theoretical Health Inequality Model. In: Grow, A., Van Bavel, J. (eds) Agent-Based Modelling in Population Studies. The Springer Series on Demographic Methods and Population Analysis, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-32283-4_17
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