Transcript Slide 1

Discussion of
Welfare Consistent Country
Comparisons: The Geary-Allen
World Accounts
Marshall Reinsdorf, discussant
May 13, 2011
University of Groningen,
Netherlands
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).
bea.gov
2
GAIA Method
 To measure real consumption of country i, substitute expenditure
function e(p*,ui ) for p*qi 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 qi 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.
bea.gov
3
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:
bea.gov
4
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 yj and [log yj]2
bea.gov
5
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:
bea.gov
6
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.
bea.gov
7
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.
bea.gov
8
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.
bea.gov
9