Discussion of

Welfare Consistent Country Comparisons: The Geary-Allen World

AccountsMarshall Reinsdorf, discussant

May 13, 2011University of Groningen,

Netherlands

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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).

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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.

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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:

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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

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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:

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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.

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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.

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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.