William Fallon May 08, 2012 Brown University Department of Economics

1. A Theoretical and Empirical Analysis of Cross-Country Welfare William Fallon May 08, 2012 Brown University Department of Economics

2. 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

3. 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.

4. 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

5. 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

6. 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.

7. 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

8. 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

9. 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

10. 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 …

11. 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,

12. 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

13. 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,

14. 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.

15. Theoretical Model Cross-Country Variation (cont.) • Lastly, one can solve for the values of lambda that make the above equalities hold true:

16. 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

17. Theoretical Model Accounting 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.

18. Empirical Results

19. Empirical Results

20. 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)

21. Empirical Results

22. Empirical Results

23. 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.

24. Empirical Results

25. Empirical Results

26. 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.

27. Empirical Results

28. Empirical Results

29. 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.

30. Thank You!