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An Econometric Approach to the Construction of Complete Panels of Purchasing Power Parities: Analytical Properties and Empirical Results

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D.S. Prasada Rao, Alicia Rambaldi, Howard E. Doran

Outline

Introduction Motivation The Problem Basic Information and Sources

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Econometric model Data Empirical Results Future work

Purchasing Power Parities (PPPs)

PPPs are amounts of currencies, of different countries, that have the same purchasing power as one unit of a reference currency (e.g. US$) with respect to a selected basket of goods and services.

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goods and services.

Big Mac Index PPPs from the International Comparison Program – World Bank, OECD, EUROSTAT Agricultural Sector PPPs – FAO, UN Manufacturing Sector PPPs 1 Groningen

PPPs 1 some celebrated examples

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Manufacturing Sector PPPs 1 Groningen PPPs for Global and Regional Poverty Measurement – World Bank Penn World Tables (PWT) – a panel of PPPs covering more than 150 countries and 50 years

PPPs are essentially spatial price index numbers – interregional comparisons PPPs are used for real income comparisons

WDI and HDI; regional and global inequality

Growth and convergence studies

Necessary to have panels of real incomes – nominal incomes

PPPs 1 basic uses

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Necessary to have panels of real incomes – nominal incomes adjusted for temporal and spatial price differences

Growth and productivity studies

Computing TFP measures, decomposition to technical change and efficiency change

PPPs are very useful for cross1country analyses by researchers, industries and international organisations.

PPPs from ICP 2005

Country

• Exch. Rate

PPP

PLI% (US=100)

P.R. China Hong Kong India 8.19 7.78 44.10 3.56 5.86 15.15 43 75 34

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India Australia Japan Switzerland Ethiopia 44.10 1.31 110.22 1.25 8.67 15.15 1.39 129.55 1.75 2.33 34 106 118 140 27

Source: World Bank, 2005 ICP Report

Estimates of real per capita income 1 2005

Country

• Exch. Rate

ICP1PPP

HDR, 2006

P.R. China Hong Kong India Australia 1,720 26,121 708 34,774 3,957 34,660 2,060 32,798 6,757 34,833 3,452 31,794

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Australia Japan Switzerland Ethiopia 34,774 35,607 49,675 154 32,798 30,293 35,520 571 31,794 31,267 35,633 1,055

• ICP1 PPPs refer to 2005 benchmark comparisons
• HDR, 2006 estimates are based on extrapolations of PPPs from 1996

benchmark results compiled by the World Bank

Estimated No. of poor 1 $1/day poverty line

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Source: Chen and Ravallion (2007)

These estimates are based on extrapolated PPPs for Consumption from the 1993 benchmark comparisons.

Global and regional poverty estimates

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Source: Chen and Ravallion (2008)

• PPPs from ICP benchmark studies
• Compiled periodically, roughly once in 5 years
• The latest round for 2005 has been completed.

Penn World Tables – “gold standard”

• Available since 1980’s
• Covers 150 countries and a 501year period

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• Covers 150 countries and a 501year period
• Extrapolations of benchmark PPPs

− Mainly uses the latest benchmark available − Uses movements in national price levels

• Latest version, 6.3 (version 7.0 has recently been

released)

• Summers and Heston (1991) – most cited
• Ad hoc procedures

ICP Benchmarks – country participation

ICP Phase

Benchmark year No. of participating

countries

I II III 1970 1973 1975 10 16 34

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III IV V VI VII 1975 1980 1985 1993 2005 34 60 64 117 146

OECD and Eurostat compile PPPs for their member countries every three years

Research Problem

• Consider the available PPPs and real income data

from ICP as an “incomplete” tableau of information.

• Information starts from 1970, but ideally one would

like extrapolations back to 1950

• Long gaps between benchmarks
• India’s participation in ICP prior to 2005 was in 1985

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• India’s participation in ICP prior to 2005 was in 1985

and P.R. China never participated in ICP before.

• The main objective is to construct a complete panel
• f PPPs.
• To provide measures of reliability associated with the

predicted PPPs.

Current Econometric Practice

The Methodology of Construction of the Penn World Tables:

• 1. Extrapolate to non1participating countries

Based on predictions from a price level regression

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regression Version 6.3 based on 1996 benchmarks – for some countries other benchmarks were used

• 2. Use “derived growth rates” in prices to

extrapolate over time

Using the published National Accounts data on GDP Deflators

• Use all available benchmark information –

an unbalanced panel

• Set up an econometric model to predict
• Our Approach

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• Write it in a state1space form
• Use a Kalman filter and smoother to

produce predictions and associated standard errors

Sources of information for !"

1. ICP Benchmark PPPs: Observation of the variable of interest contaminated with noise 2. A Model Derived from the Theory of Price Levels: Links national level data to variable of interest.

Combining Theory and Noisy Data

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interest. 3. Derived growth rates from movements in national price levels: Links national accounts data to variable of interest 4. Reference Country Definition: A restriction that must hold, #= 0

• Surveys are very resource intensive,

– Carried out by national statistical agency of those countries that participate in the ICP. – Internationally comparable basket is priced

• We can then write

Combining Theory and Noisy Data (Source 1)

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• We can then write

1

• ξ

= +

• where,
• ICP benchmark observation for participating country at time

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ξ is a random error accounting for measurement error.

Theory and Cross1Country Relationships

The Theory of Price Levels

• National price level ratio or “E$

$%:

• =

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ER exchange rate of currency of country at time ,

(Kravis and Lipsey 1983 and 1986; Clague, 1988; Bergstrand, 1996)

• =
• Most developed countries & ≈ unity

Most developing countries & << unity.

The Theory of Price Levels National Price Level differences (or exchange rate deviation index – PPP/Xr) are due to:

productivity differences in traded and non)traded goods sectors across developed and developing countries.

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Some of the primary drivers of Price Levels:

Size of the agriculture sector in the economy, openness, educational attainment, share of exportable services (such as tourism), resource abundance, size of the population, trade balance.

Proposed Methodology

Combining Theory and Noisy Data (Source 2)

, ln( / ); a set of conditioning variables

• ′

= x

• ′

= + x β

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a vector of parameters a random disturbance with specific distributional characteristics

• β

We obtain a prediction

ˆ ˆ = + ln( )

• ′

x β

• We assume some measurement error exists in

national accounts and thus use

• to define:

Combining Theory and Noisy Data (Source 3)

,[ 1, ] , , 1 ,[ 1, ]

• −

− −

= ×

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• to define:

where,

,[ , 1] ,[ , 1]

c ln

• −

−

  =       η is a random error accounting for measurement error in the growth rates

, )1

• η

= + +

• The definition of PPP requires a choice

reference country.

• The reference country is defined to have a

PPP = 1 for all time periods. Combining Theory and Noisy Data (Source 4)

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PPP = 1 for all time periods.

• US is taken as the reference country, so

, = 0

Econometric Model 1 Assumptions

a) The errors in the regression relationship (4) are assumed to be spatially correlated b) measurement errors in the observation of benchmark are heteroskedastic

=

• φ

+ u Wu e

1 φ < and ( ) × W is a spatial weights matrix

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c) measurement error in the growth rates are heteroskedastic

here

2 ξ

σ is a constant of proportionality

2 2 1

( )

• ξ

ξ σ =

( )

2 2

Ε

• η

η σ =

2 η

σ is a constant of proportionality

# is an inverse measure of development of country

A State1Space Representation

We can combine the model and sources of information into a state1space model:

• 1. Observation Equations

= + +

• θ ζ

y Z B X

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• 2. Transition Equations

Show the evolution of the state variable over time

= + +

• θ ζ

y Z B X

A State1Space Representation 1 continued

– The Transition Equations:

)1

• =

+ + p p c η

( )

2 t

Ε =

• η

σ ′ ≡ η η Q V

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V is diagonal and captures the extent of measurement error in the national accounts More developed countries are assumed to collect the data more accurately.

Definitions

Benchmark Years

=

y

= Z

1

ˆ

• 

         S p S p

• 1

    S S

• Refer. country

constraint

Other Years

1

    S S

1

ˆ       S p

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=

Z

• =

Z

=

H

1

• 

       S S

1

• 

         S

2 1 1 2

• ξ

σ σ ′     ′     ′     S SS S VS

constraint Regression

ICP

1

      S

1

    S

2 1 1

• σ

′     ′     S SS

Main Features and some Analytical Results

1. Constrain to make the PPP estimates track benchmark PPPs (Section 4) – we use benchmark PPP data as a set of linear restrictions. Then Kalman Filter predictions of PPPs satisfy the restrictions. 2. Constrain to produce estimates that track the movements in implicit price deflators .

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3. Use regression information only at benchmark years: Under this simplified model, the resulting estimates are weighted averages of the benchmark1year PPPs of the given country with weights determined by the error structure of the model. 4. The method is invariant to the choice of reference country. Demonstrated using an empirical illustration. Proof of the result is under construction and will be included in the next version of the paper. (Proof in Appendix A).

Empirical Application

Country coverage: 138 COUNTRIES Period: 1970 – 2004 and the new benchmark 2005 is included Benchmark years: 1975,1980, 1985, 1990, 1993, 1996, 1999, 2002, and 2005 Regression variables: Data are compiled for 61 variables (including an array of dummy variables) – Sources of data

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(including an array of dummy variables) – Sources of data include the WDI; UN; IMF; PWT 6.3; FAO; and other sources '( Spatial Correlation (Wt): Based on a measure of socio1 economic distance Accuracy of data collection (V): (real GDP per capita)11

Predictions from different models and PWT Australia

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Predictions from different models and PWT China

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Predictions from different models and PWT India

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Website for the New PPP Data 1 “UQICD”

As per the Australian Research Council funding arrangements, we have established a website to disseminate the PPP Extrapolations generated using our data. The website can be accessed by googling “uqicd”. The URL for the website is: ww.uqicd.economics.uq.edu.au The website has a lot of useful information apart from panel

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The website has a lot of useful information apart from panel

• f PPPs.

Extrapolated PPPs (unconstrained) with SE’s Extrapolated PPPs with deflator constrained with SW’s Population, exchange rates Real GDP per capita at current prices using PPPs Nominal GDP (in local currency) at current and constant prices

Please check the website, download data and send your comments.

Future work

The model produces PPPs and realincomes at current

• prices. Work is underway to extend this to compile real

incomes and PPPs at constant prices. The next step is to develop models to work at a

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The next step is to develop models to work at a disaggregated level – Consumption, Government and Investment and create panels of PPPs for each component.