Estimation of PPPs for non-benchmark economies for the 2005 ICP round

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1 Estimation of PPPs for non-benchmark economies for the 25 ICP round This note provides a brief explanation on the imputation method used to estimate PPP rates at the GDP and private consumption level for economies that did not participate in the 25 ICP round. Although these non-benchmark economies account for only a small share of the global output and population, it is important to include them in any comprehensive measurements of economic size and international poverty. The ICP 25 Final Report includes a discussion of the regression models used in the previous (993) ICP round to impute PPP rates at GDP level. The specifications were used to impute PPPs for the 25 round. Estimated values for non-benchmark countries can be found at page 64 of the Final Report. Afterwards, a search for better regression model was undertaken and an alternative model was found to yield better estimates. The new model uses the price level index (PLI) as the dependent variable. The PLI is the ratio of a PPP to a corresponding market exchange rate. The PLI with the United States = is modeled as: PLI i = a + b*x i + e i () The explanatory variables, X i, included GDP per capita in US$ at market prices, imports as share of GDP, exports as share of GDP, the age dependency ratio, dummy variables for Sub-Saharan African economies, OECD economies, island economies, and landlocked developing economies, as well as the interaction terms of GDP per capita and dummy variables. Data came from the ICP 25 and WDI databases, supplemented by other official data sources in a small number of cases. Figure : Price level index increases with GDP per capita in US$ PLI at GDP level PLI at private consumption level lgdpd lgdpd Color representation: yellow - OECD; blue - Sub-Sahara Africa; black-latin America and Caribbean; red - all others International Comparison Program, Global Purchasing Power Parities and Real Expenditures, (Washington, DC: The World Bank, 28).

2 Because the USA is the base country in the multilateral comparison, by definition its PPPs are always and its PLIs are always. So it is necessary to add an explicit constraint on the equation () to force those values. If the constraint can be written as PLI usa = a + b*x usa (2) Substitute (2) into (), the equation becomes: PLI i - PLI usa = b*(x i - X usa ) + e c (3) Both dependent variable and explanatory variables are normalized by the corresponding values of the United States. Note in regression, all continuous variables are in natural log. There are two regressions one for PLI at GDP level and one for PLI at private consumption level. Two regressions are run together using Zellner's Seemingly Unrelated Regression method. The regression results are presented in the following table. Dependent variable Table : Regression results Eq #: PLI at GDP level (N=43) Eq #2: PLI at private consumption level (N=43) coefficient standard standard coefficient error error GDP pc (US$) Export as % of GDP Imports as % of GDP.7.22 Age dependency ratio GDP pc (US$)*SSA dummy GDP pc (US$)*island economy dummy GDP pc (US$)*landlocked developing economy dummy OECD dummy SSA dummy Island economy dummy Landlocked developing economy dummy Regression summary 2 R 2 RMSE R 2 RMSE Figure 2 below plots residuals against fitted values in each regression and Figure 3 plots imputed PPPs for non-benchmark countries and actual PPPs for benchmark countries against GDP per capita in US$. Figure 4 compares the predicted PPPs with the actual 2 Both regressions exclude constant term as the equation (3) indicates. The same regressions are run with constant term and a joint test of both constant term being zero gives chi2(2) =6.6.

3 PPPs for benchmark countries using the previous method reported in the ICP final report and using the method presented here. Clearly the average deviation for both PPPs are smaller using the new method. Figure 2: Residuals against predicted values Eq # Eq #2 Residuals: # Residuals: # Residuals: # Residuals: # Residuals: #2 Residuals: #2 Color representation: brown Latin America and Caribbean; blue all other countries Figure 3: Imputed and actual PPPs against GDP per capita in US$ PPP at GDP level PPP at private consumption level igdpd igdpd ipli icpli Color representation: yellow - ICP benchmark countries; blue - non-benchmark countries in Latin America and Caribbean; black other non-benchmark countries

4 Figure 4: Imputed PPP against actual PPPs old method new method Color representation: blue PPP at GDP level; red- PPP at private consumption Level

5 Table 2: Imputed PPP estimates for non-benchmark economies Exchange PPP for Rate GDP Region (LCU/US$) (LCU/PPP$) PPP for private consumption (LCU/PPP$) Country United Arab Emirates Bahamas, The..886 Micronesia, Fed. Sts. EAP Kiribati EAP Myanmar EAP Papua New Guinea EAP Solomon Islands EAP Timor-Leste EAP Tonga EAP Vanuatu EAP Samoa EAP Turkmenistan ECA Uzbekistan ECA Antigua and Barbuda LAC Belize LAC Barbados LAC Costa Rica LAC Dominica LAC Dominican Republic LAC Grenada LAC Guatemala LAC Guyana LAC Honduras LAC Haiti LAC Jamaica LAC St. Kitts and Nevis LAC St. Lucia LAC Nicaragua LAC Panama LAC El Salvador LAC Suriname LAC Trinidad and Tobago LAC St. Vincent and the Grenadines LAC Algeria MNA Libya MNA West Bank and Gaza MNA Afghanistan SAS Eritrea SSA Seychelles SSA