Pollution and infectious diseases

• Author: David Desmarchelier,Stefano Bosi
• Published date: 01 December 2018
• DOI: http://doi.org/10.1111/ijet.12157
• Date: 01 December 2018

doi: 10.1111/ijet.12157

Pollution and infectious diseases

Stefano Bosi∗and David Desmarchelier†

Recent empirical contributions highlight the negative impact of pollution on labor supply. This

relationship is explained bytwo mechanisms: first, pollution modifies agents’ work–leisure trade-

off as it deteriorates their working conditions (incentive effect); and second, a pollutedenviron-

ment is likelyto generate more frequent epidemic outbreaks and to affect agents’ immune systems

(health effect). Bosi et al. (2015) explore the aggregate consequences of the incentive effect and

show that it can generate endogenous fluctuations in the economic activity. The present paper

focuses on the health effect as we study a Ramsey model augmented with the spread of infectious

disease. We find that industrial pollution may generate limit cycles around an endemic steady

state. More precisely, the economicsystem may undergo a transcritical bifurcation followed by

two Hopf bifurcations near this steady state.

Key wor ds pollution, SIS model, Ramsey model, Hopf bifurcation, transcritical bifurcation

JEL classification D9, Q5, I1

Accepted 17 May2016

1 Introduction

Recent empirical contributions highlight the negative effect of pollution on labor supply (Carson

et al. 2011; Graff Zivin and Neidell 2014; Hanna and Oliva 2015). By studying a database on industrial

activities in MexicoCity, Hanna and Oliva (2015) find thata1percentincrease in air pollution reduces

the number of worked hours by 0.61 percent. On theoretical grounds, two mechanisms contribute

to explaining this negative impact: first, an incentive effect through which pollution affects people’s

work–leisure trade-off by deteriorating their working conditions (Bosi et al. 2015); and second, a

health effect, through which pollution weakens agents’ immune systems and increases the likelihood

of epidemic outbreaks (Caren 1981). The consequences of the health effect on economic activities

are potentially important, as illness is recognized as one of the main causes of work absenteeism

(Akazawa et al. 2003).

In their study of the incentiveeffect, Bosi et al .(2015) use a discrete-time Ramsey model in which

pollution and labor are non-separable variables of the utility function. In this model, periodic cycles

may arise around the steady state through a flip bifurcation when pollution increases labor disutility.

Departing from this result, we propose to address the issue of endogenous cycles when the afore-

mentioned health effect operates. Intuition indeed suggests that if pollution affects agents’ immune

systems, then labor supply should decrease, which, in turn, should lead to a smaller production and

∗EPEE, University of Evry,Evry, France.

†Bureau of Theoretical and Applied Economics (BETA), UMR 7522, National Centre for Scientific Research (CNRS),

University of Lorraine, Lorraine, France. Email: david.desmarchelier@gmail.com

Wewould like to thank Julien Arino for helpful comments about the SIS model. This research has been conducted as part

of the LABEX MME-DII (ANR11-LBX-0023-01) project.

International Journal of Economic Theory 14 (2018) 351–372 © IAET 351

International Journal of Economic Theory

Pollution and infectious diseases Stefano Bosi and David Desmarchelier

so on. This potential rationale for macroeconomic volatility is grounded on a solid body of medical

evidence on the effect of pollution immune systems (Caren 1981; Bauer et al. 2012).

In mathematical epidemiology, the spread of disease is usually represented by a dynamicsystem

describing the evolution of healthy and unhealthy populations (Hethcote 2009). The most funda-

mental of these models is the SIS model (susceptible–infected–susceptible). It explains the spread of

an endemic disease for which recovery does not confer immunity: individuals move from the sus-

ceptible class (S) to the infective class (I), and then go back to the susceptibleclass (S). SIS dynamics

notably succeed in describing the spread of gonorrhea, Chagas disease or Rocky Mountain spotted

fever (Hethcote and Van den Driessche 2000).

Interdisciplinary contributions, mixing models of disease spread with microeconomic founda-

tions, often produce interesting and counterintuitive results. For instance, a conventional view in

mathematical epidemiology suggests that a higher ratio of HIV infected individuals implies more

new infections in later periods, while Geoffard and Philipson (1996), by allowing agents to perform

microeconomic trade-offs, argue that this larger ratio could in fact generate a drop in new infec-

tions, as it provides a strong incentive for condom adoption. Delfino and Simmons (2000) study the

evolution of infected and healthy individuals in a Lotka–Volterra system, augmented with parameter

functions of economic variables. They show that, in these conditions, multiple steady states arise.

Gersovitz and Hammer (2004) focus on a dynamic cost–benefit analysis between public prevention

and therapeutic efforts, and they compare the centralized and the decentralized solutions. They

recommend that government levy taxes for maximizing social welfare.

One of the first attempts to introduce infectious diseases in capital accumulation models is pro-

vided by Goenka and Liu (2012). They embed an SIS model in a discrete-time Ramsey economy

with endogenous labor supply. While labor force is exclusively composed of healthy individuals, the

latter tune their labor supply via a consumption–leisure arbitrage. Studying the aggregate dynamics

of the model, they find that periodic cycles and chaotic dynamics arise for highly infectious dis-

eases. Goenka et al. (2014) develop a continuous-time version of this model, augmented to take into

account optimal health expenditures. Inthis version of the model, labor supply is inelastic, and there-

fore, the aggregate labor supply inherits the dynamics of the susceptible class. Goenka et al. (2014)

assume that spending on public health affects the parameters of infection, namely the probability of

being infected and the time to recovery. The study also focuses only on the social planner solution.

Through a local analysis, Goenka et al. (2014) exclude the possibility of endogenous cycles.

We challenge the latter conclusion by considering an economy in which pollution deteriorates

the household’s immune system. Our model is similar to that used by Goenka et al. (2014) in the

sense that it is a continuous-time Ramsey economy where only healthy individuals work. However,

we focus on a competitive economy rather than on a planned one. In our model, pollution is an

externality generated by production. It increases both the probability of being sick and the time to

recovery. The economyexhibits one or two steady states: a disease-free one and/or an endemic one.

When studying the local dynamics around these steady states, we find two limit cycles (stable and

unstable) near the endemic steady state when pollution becomes excessive.Thus, contrary to Goenka

et al. (2014), we find similarities between the health effect and the incentive effect (Bosi et al. 2015),

as both situations generate endogenous macroeconomic cycles around the steady state.

The rest of the paper is organized as follows. We introduce the model and derive the dynamic

system in Sections 2 and 3. In Section 4 we compute the steady stateand we formulate the conditions

for its existence and uniqueness. Section 5 provides general conditions for local bifurcations and

indeterminacy of a three-dimensional system. We also consider the dynamics around the disease-

free and endemic steady states. We then provide a numerical illustration in Section 6. Section 7

concludes.

352 International Journal of Economic Theory 14 (2018) 351–372 © IAET