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An Econometric Approach to the Construction of Complete Panels of Purchasing Power Parities: Analytical Properties and Empirical Results D.S. Prasada Rao, Alicia Rambaldi, Howard E. Doran ������������������� ���������������������������� 1

Outline � Introduction � Motivation � The Problem � Basic Information and Sources � Econometric model � Data � Empirical Results � Future work 2

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. goods and services. 3

PPPs 1 some celebrated examples � Big Mac Index � PPPs from the International Comparison Program – World Bank, OECD, EUROSTAT � Agricultural Sector PPPs – FAO, UN � Manufacturing Sector PPPs 1 Groningen � 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 4

PPPs 1 basic uses � 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 � 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. 5

PPPs from ICP 2005 PLI% Country Exch. Rate PPP (US=100) P.R. China 8.19 3.56 43 Hong Kong 7.78 5.86 75 India India 44.10 44.10 15.15 15.15 34 34 Australia 1.31 1.39 106 Japan 110.22 129.55 118 Switzerland 1.25 1.75 140 Ethiopia 8.67 2.33 27 Source: World Bank, 2005 ICP Report 6

Estimates of real per capita income 1 2005 HDR, 2006 Country Exch. Rate ICP1PPP P.R. China 1,720 3,957 6,757 Hong Kong 26,121 34,660 34,833 India 708 2,060 3,452 Australia Australia 34,774 34,774 32,798 32,798 31,794 31,794 Japan 35,607 30,293 31,267 Switzerland 49,675 35,520 35,633 Ethiopia 154 571 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 7

Estimated No. of poor 1 $1/day poverty line Source: Chen and Ravallion (2007) These estimates are based on extrapolated PPPs for Consumption from the 1993 benchmark comparisons. 8

Global and regional poverty estimates Source: Chen and Ravallion (2008) 9

�������������������� � 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 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 10

ICP Benchmarks – country participation ICP Phase Benchmark year No. of participating countries I 1970 10 II 1973 16 III III 1975 1975 34 34 IV 1980 60 V 1985 64 VI 1993 117 VII 2005 146 OECD and Eurostat compile PPPs for their member countries every three years 11

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 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 of PPPs. � To provide measures of reliability associated with the predicted PPPs. 12

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 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 13

Our Approach � Use all available benchmark information – an unbalanced panel � Set up an econometric model to predict ��� � ����������������������������������� ��������������������� ��������������������� � Write it in a state1space form � Use a Kalman filter and smoother to produce predictions and associated standard errors 14

Combining Theory and Noisy Data 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. 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 15

Combining Theory and Noisy Data (Source 1) • 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 • We can then write = + ξ � � � �� �� 1 �� where, � ICP benchmark observation for participating country � at time � � �� ξ is a random error accounting for measurement error. 1 �� 16

Theory and Cross1Country Relationships The Theory of Price Levels • National price level ratio or “E $������� �������������������$% : ��� � = = � �� �� �� �� �� 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. 17

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. 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. 18

Proposed Methodology Combining Theory and Noisy Data (Source 2) ′ = + � x β � �� �� �� �� ����� , ′ = � ln( ��� / �� ); x a set of conditioning variables �� �� �� �� �� �� �� �� β a vector of parameters �� � a random disturbance with specific �� distributional characteristics We obtain a prediction � ˆ ′ ˆ = � x β + ln( �� ) �� �� �� �� 19

Combining Theory and Noisy Data (Source 3) • We assume some measurement error exists in national accounts and thus use ������ − = × � � ,[ 1, ] � ��� ��� − � � , � � , 1 ������ − �� � ,[ 1, ] � • to define: • to define: = + + η � � � �� � � , )1 �� �� where,   ������ − = � � � ,[ , 1] c ln     �� ������   − �� ,[ , � � 1] η �� is a random error accounting for measurement error in the growth rates 20

Combining Theory and Noisy Data (Source 4) � The definition of PPP requires a choice reference country. � The reference country is defined to have a PPP = 1 for all time periods. PPP = 1 for all time periods. � US is taken as the reference country, so � , = 0 �� � 21

Econometric Model 1 Assumptions a) The errors in the regression relationship (4) are assumed to be spatially correlated φ + u = Wu e φ < and × 1 W ( � � ) is a spatial weights matrix � � � � b) measurement errors in the observation of benchmark ��� �� are heteroskedastic ξ = σ 2 2 � ( ) � σ 2 here is a constant of proportionality ξ ξ 1 �� �� c) measurement error in the growth rates are heteroskedastic ( ) η = σ 2 2 σ is a constant of proportionality 2 Ε � η η �� �� � ��#� is an inverse measure of development of country � 22