Welcome to the GAIA Homepage

Maintained by Peter Neary, Department of Economics, University of Oxford



Introduction to GAIA

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Real incomes are routinely compared internationally using methods which "correct" for deviations from purchasing power parity. The most widely used of these is the Geary method which, though theoretically suspect, underlies the Penn World Table. The objective of this research programme is to provide a theoretical foundation for the Geary method which I call the GAIA ("Geary-Allen International Accounts") System. The GAIA system yields a set of index numbers which equal the real incomes of a group of countries, taking account of differences in purchasing power parities (i.e., allowing for differences in price levels between countries) and at the same time maintaining consistency with economic theory. As its name suggests, each GAIA index is a "true" or utility-based index in the tradition of R.G.D. Allen: the real income of country i relative to country j is the ratio of the minimum expenditures needed to obtain country i's and country j's utility levels, both evaluated at common prices. The common prices, in turn, are hypothetical "world" prices in the tradition of R.C. Geary. Measured in world prices, the matrix of commodities consumed in each country adds up to a consistent set of international accounts.

The GAIA index was introduced in reference [1] (see list of Research Papers at bottom of page); a pilot application was given in [2]; an account of Geary's work is in [3]; while paper [4] presents a full theoretical justification and an empirical application, based on estimates of a QUAIDS ("Quadratic Almost Ideal Demand System") model for 60 countries. Further details can be found in the papers. Using the GAUSS programs below, it should be possible to replicate the results in [4] and to reestimate the QUAIDS model and the corresponding GAIA indexes with a user-provided data set.


Gauss Files

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Each of the following program and data files is stored as a text file (with extension ".txt"). After down-loading them to your own machine, change the extension to that indicated below. You will need the commercially-available Gauss package to run the programs.

Programs:
  1. BASICS.GAU Calculates Laspeyres, EKS, CCD and Geary real incomes and writes results to disk.
  2. QUAIDEST.GAU Estimates the semiflexible QUAIDS ["Quadratic Almost Ideal System"] model, for a particular value of a user-specified parameter Nsystem: = 1 for HAIDS (Homothetic AIDS); =2 for AIDS; and =3 for QUAIDS; and for all values of k (the rank of the Slutsky substitution matrix, which is restricted to be symmetric negative semi-definite) between zero and a user-specified value (not greater than n-1, where n is the number of commodity groups).
  3. GAIAQUAI.GAU Reads QUAIDS parameters (for a particular value of NSystem), and calculates Geary and GAIA real incomes.
  4. SUMMARY.GAU Reads indexes from disk and prints summary table and figures.
  5. GEARYLIB.SRC This file contains miscellaneous procedures (sub-routines) used by the above programs.
  6. GEARYLIB.LCG This library file lists the procedures defined in GEARYLIB.SRC.


Data Files

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  1. 80p-60.prn Price data for 60 countries and 11 commodity groups in 1980
  2. 80q-60.prn Quantity data for 60 countries and 11 commodity groups in 1980
  3. Pop1980.prn Population data for 60 countries in 1980
  4. Excel.zip A zip file containing Excel files with the raw data. Refer to p. 9 of the Appendix below for details.


Input and Output for GAUSS files

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To run the programs without changes, the following directory structure must be available on your hard disk:
  1. C:\ME\RESEARCH\GEARY2\GAUSS\
    Contains all the .GAU files and GEARYLIB.SRC
  2. C:\ME\RESEARCH\GEARY2\EMPIRICS\GAUSSIN\
    Contains all the data files
  3. C:\ME\RESEARCH\GEARY2\EMPIRICS\GAUSSOUT\ALL\
    Contains output from BASICS.GAU, needed as input to SUMMARY.GAU
  4. C:\ME\RESEARCH\GEARY2\EMPIRICS\GAUSSOUT\HAIDS\
    Contains output from QUAIDEST.GAU; input to and output from GAIAQUAI.GAU (for NSYSTEM=1); and input to SUMMARY.GAU
  5. C:\ME\RESEARCH\GEARY2\EMPIRICS\GAUSSOUT\AIDS\
    Contains output from QUAIDEST.GAU; input to and output from GAIAQUAI.GAU (for NSYSTEM=2); and input to SUMMARY.GAU
  6. C:\ME\RESEARCH\GEARY2\EMPIRICS\GAUSSOUT\QUAIDS\
    Contains output from QUAIDEST.GAU; input to and output from GAIAQUAI.GAU (for NSYSTEM=3); and input to SUMMARY.GAU
  7. C:\GAUSS\LIB\
    Contains the library file GEARYLIB.LCG
  8. C:\GAUSS\
    Contains the Gauss program files.


Research Papers

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  1. "Theoretical foundations of the 'Geary Method' for international comparisons of purchasing power and real incomes," Economic and Social Review, 27:2, January 1996, 161-179.
  2. (J.P. Neary and B. Gleeson) "Measuring the wealth of nations: Reference prices and multilateral real income indexes," Economic and Social Review, 28:4, October 1997, 401-421.
  3. "R.C. Geary's contributions to economic theory,", in D. Conniffe (ed.): Roy Geary, 1896-1983: Irish Statistician, Dublin: Oak Tree Press and ESRI, 1997, 93-118.
  4. "Rationalising the Penn World Table: True multilateral indices for international comparisons of real income," American Economic Review, 94:5, December 2004, 1411-1428. [Published version]
  5. Appendix to "Rationalising the Penn World Table: True multilateral indices for international comparisons of real income," mimeo, University College Dublin, April 2003.
  6. (with Ian Crawford) Testing for a reference consumer in international comparisons of living standards, American Economic Review, 98:4, September 2008, 1731-1732. [Published version]


Links to Other Resources on Index Numbers

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