Review of data variability as it affects aggregation of PPPs Frederic Vogel 3rd Regional Coordinating Agencies meeting October 28-30, 2015 Washington, DC

Purpose of Presentation Aggregation methods include 148 countries FOC review suggests “Elimination of weak links through countries with different price and expenditure structures” which includes Bilateral aggregation of basic heading PPPs using Laspeyres/Paasche to get Fisher PPPs for 148 countries Binary PPPs used to compute direct PPP of each country with the US and all 144 indirect links to compute aggregated PPPs Are there weak links—especially indirect PPPs across regions? Are weak links result of different price and expenditure structures or the result of poor quality data?

Overview Review sources of variability at each step Conclusions Basic Heading Linking Factors Global Basic Heading PPPs—after linking Aggregation—L/P ratios Aggregation—GEKS direct and indirect PPPs Conclusions Recommendations

Table 1. Variability of Basic Heading Linking factors Matrix of linking factors 154 basic heading between region PPPs for Africa, Asia, Eurostat-OECD, Latin America, Western Asia– with Eurostat-OECD = 1.00 Within region, computed 95 % confidence interval of basic heading linking factors Compared confidence interval with maximum and minimum linking factors within region Identified basic headings very extreme with maximum and minimum values

Table 1. Variability of Basic Heading Linking factors Region 95 % Confidence interval of linking factors (geomean) Maximum linking factor Minimum linking factor Max/Min ratio Africa 0-12.41 (5.23) 28.01* .70# 39.81 Asia 0-12.50 (5.88) 22.60** 1.67## 13.50 Eurostat/OECD -- 1.00 Latin America 0-3.21 (1.57) 4.65*** .249### 18.65 Western Asia 0-.491 (.206) 2.00**** .031#### 64.16 *Electricity & gas **Gas & domestic services ***Jams & Honey, & Electricity **** Eggs & Pork #Transport by RR ##Bicycles ###Compensation of employees #### Outpatient services

Tables 2 and 3 Variability of global basic heading PPPs For each country calculated the ratio—maximum PPP/minimum PPP Within each region calculated the 95% confidence interval of the max/min ratios Examined the countries in each region with largest max/min ratios and their basic headings with the largest and smallest PPPs

Table 2. Variability of Global Basic Heading PPPs by region   Geo Mean Max/min ratios* 95% confidence interval max/min ratios Largest Max/min ratio in region Country in region with largest Max/min ratio Smallest Max/min ratio in region Country in region with smallest Max/min ratio Africa 36 2-70 93 Equatorial Guinea 13 Botswana Asia 50 1-126 141 Indonesia 14 Hong Kong CIS 1-208 258 Tajikistan Russia Eurostat OECD 9 1-27 53 Albania 1 US Latin America** 35 1-161 275 Venezuela Uruguay Caribbean 27 1-69 101 Grenada Virgin Islands Western Asia 38 1-96 124 Kuwait 15 United Arab Emirates *Geo mean of country max/min ratios **Does not include Cuba with Max/min ratio =583

Table 3. Countries with greatest variability in BH PPPs, max/min ratio, and basic headings with largest and smallest PPPs Country Max/min ratio Basic Headings with largest PPPs Basic Headings with smallest PPPs Equatorial Guinea 93 Eggs Out Patient svcs Indonesia 141 Wine Medical svcs Lao 113 Education Mynmar 118 Other fuels Nepal 107 Motor Cars Vietnam 112 Tajikistan 258 Transport by air Compensation of employees Albania 53 Venezuela 275 Frozen & preserved fruit Fuels/lubricants Grenada 101 Tools & Equipment Kuwait 124 Other services Electricity

Table 4—L/P ratios from aggregation Matrix of 148x148 binary Fisher indexes, Laspeyres and Paasche aggregations and L/P ratios. For each country, started with the L/P ratio with each other country and calculated the geomean of the respective ratios and the standard deviation Identified country pair with the largest L/P ratio

Table 4. Countries with largest L/P ratios Country Geomean of L/p ratios +/- 2 Stdev Max L/p Country pair with max L/P ratio Burundi 1.51 .46 3.03 Venezuela Comoros 1.57 .44 3.45 Bahrain Gambia 1.45 .38 3.01 Madagascar 1.32 .35 Rwanda 1.73 3.69 Uganda 1.42 .36 3.05 Cambodia 1.39 2.76 Japan .34 2.63 1.91 .42 1.70 Data—Matrix of 148x148 binary Fishers, Laspeyres and Paasche PPPs, and L/P Ratios across all countries (Venezuela expenditures example: housing 72% of motor cars, 90% transport by road, 30% catering services

Table 5. Variability of direct and indirect PPPs from the GEKS method Matrix of 148 x 148 countries. For each country have column of direct PPP to the US and 146 indirect PPPs through each other country For each country computed the ratio of the largest indirect PPP to the smallest indirect PPP—max/min ratio For each region computed geo mean and standard deviation of the country max/min ratios Identified country in each region with largest Max/min ratio For that country, identified countries with largest and smallest indirect PPPs

Table 5. Variability in direct and indirect bilateral PPPs—148 countries—measured by ratio of maximum PPP to minimum PPP for each country Region Geomean of max/min PPPs in region +/- 2 Stdevs of country max/min values Country in each region with largest Max/min ratio* Country with largest indirect PPP with col (c) Country with smallest indirect PPP with col (c) (a) (b) (c) (d) (e) Africa 1.61 .20 Burundi 1.87 Lithuania Liberia Asia 1.43 .22 Nepal 1.68 Luxembourg Sierra Leone Eurostat/OECD 1.32 .16 Albania 1.48 Kuwait Latin America 1.37 Nicaragua 1.51 Venezuela Western Asia 1.45 .18 Yemen 1.54 Mauritania The ratio of the largest indirect PPP to the smallest PPP for Burundi was 1.87 The indirect PPP through Lithuania was the largest indirect PPP for Burundi and Liberia the smallest PPP for Burundi

Conclusions Significant basic heading outliers for linking factors and global PPPs Electricity, gas serious problem in three regions Significant L/P outliers in aggregation to Fisher PPPs Venezuela, Bahrain, Comoros, Rwanda More robust results for GEKS method—direct-indirect PPPs Need close look at Liberia Consider there is more of a data quality problem than “weak links”

Recommendations Basic Heading regional linking factors Review electricity and gas & other BHs with largest values Global Basic Heading PPPs Do same analysis of BH PPPs within region before linking Aggregation—L/P ratios Do same analysis within regions GEKS—Variability in direct-indirect PPPs—within regions: Remaining questions Are global PPPs more variable than within region PPPs before linking? Need to consider criteria identifying “weak links” but only after reviewing data quality in more detail.