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William Fallon
May 08, 2012
Brown University
Department of Economics
A Theoretical and Empirical Analysis of Cross-Country Welfare
Objectives
Evaluate the relative level well-being of individuals between nations around the world.
• Improve upon the shortcomings of simple accounts of GDP or consumption per capita
• Address the failures of Jones and Klenow (2009): summary measure of welfare from consumption, inequality, health, and leisure
• Develop a theoretical framework for comparing welfare across countries
• Analyze the empirical implications of the theoretical model in a large number of nations around the world
Modeling Welfare
Desirable characteristics of a comparative welfare model:
• Minimal normative judgment or calibration• Avoid “weighting” of input parameters – Human Development Index
• Grounding in economic theory and established practice• Avoid arbitrary aggregation of factors impacting well-being - HDI
• Simple and Intuitive• Widely available and reliable component data
• Evaluating relative well-being in developing and least-developed nations is particularly interesting.
Jones and Klenow (2009)
“Beyond GDP? Welfare across Countries and Time”
• Primary motivation for the framework developed here• Utilitarian model of welfare• Consider a hypothetical individual to be born into a nation:
• He “lives” with probability, where e is life expectancy in years• When he lives, he obtains utility from living• Consumption provides utility equal to • Leisure provides utility equal to • Inequality impacts the expected consumption utility of individuals
Jones and Klenow (2009)
The cardinal values of utility provide no insight to the relative levels of well-being across countries, however.
• Equivalent Variation and Compensating Variation
• What levels of consumption make individuals indifferent in utility expectation between countries?
• Lambda captures the relative level of well-being
Jones and Klenow (2009)
Primary Results:
• Welfare measure highly correlated with GDP, but the typical deviation is significant
• Western European nations have higher welfare than GDP per capita suggests• High leisure and low inequality increase well-being relative to U.S.
• Least developed nations are generally worse off than income alone can indicate – their poor life expectancy contributes to far lower levels of relative well-being.
Jones and Klenow (2009)
The JK framework is problematic, however …
• Treatment of life expectancy• Scaling utility by simple life expectancy is theoretically weird• Survivorship data exists for most nations – why not use it?
• Ignorance of variation across age groups• Model makes no distinction between utility of newborns and elderly
• Ignorance of income dynamics and sustainability• Income/consumption growth unaccounted for• Welfare in developing nations is likely to be underestimated by
models ignoring expectations of future growth
Theoretical Model
The welfare model presented here improves upon the shortcomings of the JK framework.
• Accounts for life expectancy with actual survivorship data• More precise, intuitive, and theoretically sound
• Identifies relative utility levels for individuals of all ages• Aggregates these utilities according to country-level demographics
• Discounts future utility flows to the present• A DPV method of accounting for lifetime utility provides a more
precise snapshot of individual well-being in each nation
Theoretical Model
Demographics and Life Expectancy:
• Let represent the age of individuals, • Let be the population distribution in each nation• Let equal the probability an individual is alive at age
conditional on being born. Thus, the probability that an individual lives from age to is
Theoretical Model
Individuals:
• Assume individual preferences are homogeneous• Utility of an individual aged years is a concave function
of expected consumption, denoted by • Thus, instantaneous (annual) individual utility is given by
• However, we are interested in the expected discounted value of all current and future utility flows …
Theoretical Model
Individuals (cont.)
• Assume there is an annual discount factor, • Incorporating the impact of the survivorship function, the
expected lifetime utility of an individual in nation is
• Note that utility is normalized to zero when the individual ceases to live
• Note also that utility remains a function of age,
Theoretical Model
Inequality:
• We would like next to account for the impact of inequality on individuals’ expected utility from consumption• Higher inequality will reduce utility because of preference concavity
• Gini coefficients measure the degree of income inequality in a large set of countries.
• Assume that consumption is well approximated by the log-normal distribution• This allows us to deduce the standard deviation of consumption
from Gini coefficients
Theoretical Model
Inequality (cont.)
• Let the standard deviation of consumption in nation be given by
• Let the current level of mean consumption be • Since consumption is log-normally distributed,
Theoretical Model
Cross-Country Variation:
• Once again, the cardinal utility values provide no insight• This work also uses the method of equivalent and
compensating variation described in JK (2009).• However, the calculation within this work allows for variation in the
“lambdas” across each age group• Let and be the equivalent and compensating variation values that
satisfy the following equations for each nation and each age within each nation.
Theoretical Model
Cross-Country Variation (cont.)
• Lastly, one can solve for the values of lambda that make the above equalities hold true:
Theoretical Model
Country Level Welfare:
• Last, utility must be aggregated across age groups• Since the goal is to measure the average well-being of
individuals in each society, the utility is aggregated according to the population distribution
• To reconcile the differences in CV and EV approaches, the empirical results follow JK (2009) by reporting
Theoretical ModelAccounting for Future Economic Growth
• Suppose one could project the growth in consumption in each nation into the future. We could, then, augment the model to account for the expected future levels of consumption individuals will experience in each future year of life.
• Let represent the cumulative growth rate of consumption in nation in years from the present. Empirical results presented later assume that income and consumption growth are identical.
• Then, the individual welfare function becomes
• CV and EV analysis is not changed meaningfully by adding growth.
Empirical Results
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
0.2
0.4
0.6
0.8
1
1.2
1.4
ALBDZAARM
AUSAUT
AZE
BHS
BGD
BLR
BEL
BENBOL
BIH
BWA
BRABGR
BFABDIKHMCMR
CAN
CAF
CHL
CH2COL
CRI
CIV
HRV
CYPCZE
DNK
DJI
DOM
ECUEGYSLV
EST
FJI
FIN
FRA
GMBGEO
GER
GHA
GRC
GTM
GINGNBGUY
HTIHND
HUN
ISL
INDIDNIRN
IRLISR
ITA
JAM
JPN
KAZLAO
LVA
LSO
LTU
LUX
MKD
MWI
MYS
MLI
MLT
MRT
MUSMEX
MDAMNGMOZ NAMNPL
NLD
NZL
NOR
PAK
PAN
PNGPRYPHL
POL
PRT
ROMRUS
RWASENSLE
SGP
SVK
SVN
ZAF
KOR
ESP
LKASWZ
SWE CHE
TZATHA
TTO
TUN
TUR
TKMUGA
GBR
USA
UZB
VEN
VNMYEMZMB
Baseline Model vs. GDP Per Capita
GDP Per Capita : USA 2000 GDP = 1.0
Bas
elin
e M
od
el -
No
Lei
sure
Empirical Results
0 0.2 0.4 0.6 0.8 1 1.2 1.40
0.2
0.4
0.6
0.8
1
1.2
1.4
ALBDZAARM
AUS AUT
AZE
BHS
BGD
BLR
BEL
BENBOL
BIH
BWA
BRABGR
BFABDIKHMCMR
CAN
CAF
CHL
CH2COL
CRI
CIV
HRV
CYPCZE
DNK
DJI
DOM
ECUEGYSLV
EST
ETH
FJI
FIN
FRA
GMBGEO
GER
GHA
GRC
GTM
GINGNBGUYHTIHND
HUN
ISL
INDIDNIRN
IRLISR
ITA
JAM
JPN
JORKAZKENKGZLAO
LVA
LSO
LTU
LUX
MKD
MDGMWI
MYS
MLI
MLT
MRT
MUSMEX
MDAMNGMOZNAMNPL
NLD
NZL
NICNERNGA
NOR
PAK
PAN
PNGPRYPERPHL
POL
PRT
ROMRUS
RWASENSLE
SGP
SVK
SVN
SOMZAF
KOR
ESP
LKASWZ
SWECHE
TJKTZATHA
TTO
TUN
TUR
TKMUGA
UKR
GBR
USA
UZB
VEN
VNMYEMZMBZWE
Baseline Model vs. JK Model
Year 2000, Jones and Klenow "lambda" Welfare Measure; US = 1
Bas
elin
e M
od
el W
elfa
re M
easu
re;
US
= 1
Empirical Results
The empirical results of the improved theoretical model demonstrate at least three important deviations from recent studies of country level well-being.
• (1) The overly simplistic accounting of life expectancy in Jones and Klenow (2009) results in a disproportional underestimation of welfare in the least developed nations (in addition to being intuitively and theoretically weak)
Empirical Results
0 20 40 60 80 100 120 140 160
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Series1
Figure 1: JK Underestimation of LDC Welfare - Age-Specific and De-mographic Impacts
Rank of Countries According to JK 2000 Welfare Computation
Lo
g R
atio
Wel
fare
Im
pro
vem
ent
fro
m A
ge
+ D
emo
gra
ph
ic
Co
nsi
der
atio
ns
Empirical Results
0 20 40 60 80 100 120 140 160
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Series1
ZMB
Figure 2: JK Underestimation of LDC Welfare - Age-Specific and Demographic Impacts w/ Zero Time Discounting
Rank of Countries According to JK 2000 Welfare Computation
Lo
g R
atio
Wel
fare
Im
pro
vem
ent
fro
m A
ge
+ D
emo
gra
ph
ic
Co
nsi
der
atio
ns
Empirical Results
• (2) Accounting for projected income and consumption growth in quickly developing economies has a significant positive impact on current national well-being that fails to be captured in recent work and simple income accounts.
• For instance, China’s income per capita is only 18.7% of that in the United States, but its growth-adjusted relative welfare today is 28.2% of the U.S. level.
Empirical Results
0 0.2 0.4 0.6 0.8 1 1.20
0.2
0.4
0.6
0.8
1
1.2
1.4
Australia
Brazil
Canada
China
France
Germany
India
Indonesia
Italy
Japan
Mexico
Nigeria
RussiaSouth Africa
South Korea
Spain
Turkey
United Kingdom
United States
Vietnam
Figure 9: Impact of Growth Projections on Cross-Country Welfare
2009 GDP Per Capita - US = 1
2009
Bas
elin
e (n
o L
eisu
re)
Wel
fare
Fra
mew
ork
w/
Wo
rld
Ban
k G
row
th P
roje
ctio
ns
Empirical Results
0 0.2 0.4 0.6 0.8 1 1.20
0.2
0.4
0.6
0.8
1
1.2
1.4
Australia
Brazil
Canada
China
France
Germany
India
Indonesia
Italy
Japan
Mexico
Nigeria
RussiaSouth Africa
South Korea
SpainTurkey
United Kingdom
United States
Vietnam
Figure 10: Baseline Framework with Growth Projections vs. Jones and Klenow (2009) Welfare
Jones and Klenow (2009) Measure of Cross-Country Welfare - US = 1
2009
Bas
elin
e (n
o L
eisu
re)
Wel
fare
Fra
mew
ork
w/
Wo
rld
Ban
k G
row
th P
roje
ctio
ns
Empirical Results
• (3) The welfare of the youngest individuals in many of the fastest growing nations today remains significantly underestimated by recent welfare estimates and measures of simple income.
Empirical Results
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 990
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Figure 11: Age-Specific Relative Welfare, Baseline Model w/ Growth Pro-jections (US =1)
Australia Brazil Canada China
France Germany India Indonesia
Italy Japan Mexico Nigeria
Russian Federation South Africa Republic of (South) Korea Spain
Turkey United Kingdom Viet Nam
Empirical Results
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 990
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Figure 12: Age-Specific Relative Welfare, Baseline Model w/ Growth Pro-jections (US =1)
Brazil China India Indonesia Mexico Nigeria Turkey Viet Nam
Summary• Recent work to measure country level welfare has found
that well-being in the least developed nations is actually worse than measures of income can alone indicate
• The results found in this work find roughly similar results• However, the plight in LDC’s seems slightly overstated in
JK 2009 due to improper treatment of life expectancy.• Furthermore, the theoretical framework and empirical
results presented here consider future growth projections which suggest that individuals in quickly developing nations may actually be far better off than indicated by income or the recent efforts of Jones and Klenow.
Thank You!
