Life Expectancy and the Environment(In co-authorship with Fabio Mariani (UCL) and Natacha Raffin (Paris 1))

SALISES 11th Annual ConferencePort of Spain

Trinidad and TobagoMarch 24-26, 2010

Agustın Perez-Barahona

agperez@grignon.inra.frhttp://sites.google.com/site/agustinperezbarahona/

INRA and Ecole Polytechnique (France)

Motivation:

1.- Two-way causality between life expectancy and environmental quality:(John and Pecchenino (1994), Ono and Maeda (2001) and Jouvet et al. (2007)).

2.- Stylized facts:

Environmental quality : Environmental Performance Index (EPI) (YCELP (2006)).Life expectancy : Life expectancy at birth (2005) (UN (2007)).

Stylized 1 (SF1): Environmental quality is positively correlated with life expectancy.Correlation coef. 0.66 (statistically significant at the 1% level).

30 40 50 60 70

4050

6070

80

correlation

EPI

Life

exp

ecta

ncy

ALB

DZA

AGO

ARG

ARM

AUSAUT

AZE

BGD

BEL

BEN

BOL

BRABGR

BFA

BDI

KHM

CMR

CAN

CAF

TCD

CHL

CHN COL

COG

CRI

CIV

CUBCYP

CZE

COD

DNK

DOM

ECU

EGYSLV

ETH

FINFRA

GABGMB

GEO

DEU

GHA

GRC

GTM

GIN

GNB

HTI

HND

HUN

ISL

IND

IDN

IRN

IRLISR ITA

JAM

JPN

JOR

KAZ

KEN

KGZ

LAO

LBN

LBR

MDG

MWI

MYS

MLI

MRT

MEX

MDA

MNG

MAR

MOZ

MMR

NAM

NPL

NLD NZL

NIC

NERNGA

NOR

OMN

PAK

PAN

PNG

PRYPER PHL

POL

PRT

ROU

RUS

RWA

SAU

SEN

SLE

SVK

SVN

ZAF

KOR

ESP

LKA

SDN

SUR

SWZ

SWECHE

SYR

TJK

TZA

THA

TGO

TTO

TUN

TUR

TKM

UGA

UKR

ARE GBRUSA

UZB

VEN

VNM

YEM

ZMB ZWE

corr.coeff = 0.66

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Stylized fact 2 (SF2): Environmental quality and life expectancy are bimodallydistributed. Hartigan’s dip test (Hartigan and Hartigan (1985)).

bandwidth=3.9EPI (2006)

Den

sity

30 40 50 60 70 80

0.00

00.

005

0.01

00.

015

0.02

00.

025

0.03

00.

035

bandwidth=4.3Life expectancy (2005)

Den

sity

30 40 50 60 70 80

0.00

0.01

0.02

0.03

0.04

Environmental trap: low life expectancy / low environmental quality.

Examples of environmental traps: linked with a reduction in life expectancy.

• Africa or ex-USSR: McMichael et al. (2004) and Patz et al. (2005).

• Easter Island: Diamond (2005) and de la Croix and Dottori (2008).

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Benchmark model: theoretical framework (OLG) that allows us to reproduce SF1and SF2.

a) Two-way causality:

• Environmental conditions affect the survival probability: endogenous life ex-pectancy (π(et)).

• Agents invest in environmental quality depending on how much they expect tolive.

b) Environmental trap:

• Relationship between environmental quality and life expectancy: ecologicalthreshold effects (convex-concave π(et)).

– Natural sciences: Cakmak et al. (1999) and Scheffer et al. (2001).

– Economics: Baland and Platteau (1996) and Dasgupta and Maler (2003).

• Multiple steady state equilibria: initial conditions do matter.

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1.- Preferences:

U(ct, et+1) = ln ct + πtγ ln et+1, with γ > 0 (1)

• πt = π(et), such that π′(et) > 0, limet→0 π(et) = π, limet→∞ π(et) = π and 0 < π <π ≤ 1 (medical and epidemiological literature).

2.- Budget constraint: wt is assumed to be exogenous (benchmark model).

wt = ct +mt (2)

3.- Law of motion of environmental quality: (John and Pecchenino (1994) andOno (2002)).

et+1 = (1− η)et + σmt − βct − λQt (3)

• β, σ, λ > 0 and 0 < η < 1. λQt > 0 (< 0): total impact of a harmful (beneficial)external effect (exogenous). et: inherited environmental quality.

• Agents cannot improve their own survival probability (crucial role of early lifehealth): Blackburn and Cipriani (2002), de la Croix and Licandro (2007), andCase and Paxson (2008).

4

4.- Agents problem: maximize (1) subject to (2), (3), ct > 0, mt > 0, et > 0, andwt and et are taken as given ⇒ FOC.

5.- Dynamics: FOC into (3) (for the sake of simplicity: wt = w and Qt = Q).

et+1 =γπ(et)

1 + γπ(et)[(1− η)et + σw − λQ] ≡ φ(et) (6)

Graphical example:

0 et

et+1

e∗L e∗He

φ(et)

5

6.- Environmental trap: A convex-concave φ(et) might be generated by a convex-concave π(et) (Blackburn and Cipriani (2002)).

Analytical illustration: long term exposure to bad environmental conditions (Evansand Smith (2005).

π(et) =

{π if et < eπ if et ≥ e

(7)

et+1

et0

A

B

B′

φ(et) = et

e∗L e∗He

6

Main results: two-way causality between life exp. and env. quality + SF1 + SF2.

1.- Escaping the trap (1/2): medical technological progress: improvement inmedicine effectiveness (de la Croix and Sommacal (2008)).

– European Environment and Health Action Plan 2004-2010.

2.- Escaping the trap (2/2): reduction of harmful external effects on theenvironment (oil slicks, Chernobyl disaster, etc).

– Implementation of international agreements that promotes a worldwidereduction of pollution: Kyoto Protocol.

3.- Welfare analysis: environmental taxes:

– Inter-generational externality: external effects of agent choices on futuregenerations ⇒ (decentralized) economy is under-investing in environmentalmaintenance.

– Environmental taxes ⇒ optimal allocation (social planner solution).

– Social planner solution may imply the elimination of the environmental trap.

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Conclusions:

1.- A model with: two-way causality between the life expectancy and the environ-mental quality + multiple equilibria.

2.- Environmental trap: convex-concave π(e)

• Benchmark model: low life expectancy / poor environmental quality.

• Model with physical or human (education) capital accumulation: de la Croixand Doepke (2003, 2004).

– Human capital: inter-generational altruism.

– Low life expectancy / poor environmental quality / low physical orhuman capital.

Extentions:

1.- Heterogeneous agents: environmental tastes.

2.- Demography: endogenous fertility and environmental quality.

3.- Fiscal policy: environmental taxes.

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