1. Discussion of Welfare Consistent Country Comparisons: The Geary-Allen World Accounts Marshall Reinsdorf, discussant May 13, 2011 University of Groningen, Netherlands

2. bea.gov 2 Nonparametric Methods  Want to compare levels of material welfare across countries.  Methods that don’t require model fitting include GEKS and Geary.  GEKS averages all possible bases for comparison via Fisher index.  Welfare interpretation of GEKS requires us to assume homotheticity.  Geary (GK) uses fixed reference price vector known as “world prices” based on the axiom that the world expenditure share vector at world prices equal a weighted average of country-specific share vectors where countries are weighted by their real consumption levels.  Use of fixed prices causes substitution bias (aka Gershenkron effect).

3. bea.gov 3 GAIA Method  To measure real consumption of country i, substitute expenditure function e(p*,u i ) for p*  q i where p* is the world price vector.  This cures the substitution bias problem of the Geary method.  To solve for GAIA prices, modify the equations used to solve for Geary world prices by replacing q i with Hicksian quantities.  Can model preferences as non-homothetic, so less restrictive assumptions required than for GEKS.  But of course, need to model preferences is not so convenient and makes results dependent on specification assumptions.

4. bea.gov 4 Adjusting Country Weights for Population  Geary weights countries by their aggregate real consumption, not their average consumption.  Don’t want a country to double its weight by splitting in two.  So the authors propose the GAIAp estimator:

5. bea.gov 5 Nonhomotheticy and Aggregation  Aggregate demands of a group of nonhomothetic individuals facing common set of prices generally not a function of aggregate income.  Assuming QUAIDS, aggregate shares a function of weighted average of the log y j and [ log y j ] 2

6. bea.gov 6 GAWA  Treat each household as a kind of country.  Country k’s real consumption is measured by cost to a social planner of giving every households its observed utility at world prices, and solution for GAWA world prices is consistent with this:

7. bea.gov 7 Satisfying Second Order Conditions Globally  To results to have a sensible welfare interpretation, demands must satisfy WARP at every point in observed sample space.  Translog and its progeny don’t have this property.  So authors assume a kind of nested average of Cobb-Douglas and CES functions that has fairly flexible Engel curves.  But strong separability is a restrictive assumption for substitution patterns.

8. bea.gov 8 My Thoughts on the Paper  Authors implement a model-based approach to international comparisons in a way that captures key features of the problem.  Population weighting is the logical way to extend the Geary to allow for substitution behavior.  Quadratic Engel curves imply need to replace representative consumer approach with explicit aggregation over households.  Good attention to regularity conditions.  These are important steps forward.

9. bea.gov 9 Suggestions  Aten & Reinsdorf (2010) had population weighted version of GAIA.  Restrictive model of substitution behavior probably causes bias in income effect parameter estimates.  But overall an excellent paper.