The 2005 International Comparison Program's (ICP) estimates of economy-wide purchasing power parity (PPP) are based on parity estimates for 155 basic expenditure headings, mainly estimated using country product dummy (CPD) regressions. The estimates are potentially inefficient and open to omitted variable bias for two reasons. First, they use average prices across outlets as the left-hand-side variable. Second, quality-adjusted prices of non-comparable replacements, required when products in outlets do not match the required specifications, cannot be effectively included. This paper provides an analytical framework based on panel data and hedonic CPD regressions for ameliorating these sources of bias and inefficiency.