Divisia indexes, money and welfare

We suggest the use of a particular Divisia index for measuring welfare losses due to interest rate wedges and in‡ation. Compared to the existing options in the literature: i) when the demands for the monetary assets are known, closed-form solutions for the welfare measures can be obtained at a relatively lower algebraic cost; ii) less demanding integrability conditions allow for the recovery of welfare measures from a larger class of demand systems and; iii) when the demand speci…cations are not known, using an index number entitles the researcher to rank di¤erent vectors of opportunity costs directly from market observations. We use two examples to illustrate the method.

Purchasing power parity: the choice of price index

Looking closely at the PPP argument, it states that the currencies purchasing power should not change when comparing the same basket goods across countries, and these goods should all be tradable. Hence, if PPP is valid at all, it should be captured by the relative price indices that best Öts these two features. We ran a horse race among six di§erent price indices available from the IMF database to see which one would yield higher PPP evidence, and, therefore, better Öt the two features. We used RER proxies measured as the ratio of export unit values, wholesale prices, value added deáators, unit labor costs, normalized unit labor costs and consumer prices, for a sample of 16 industrial countries, with quarterly data from 1975 to 2002. PPP was tested using both the ADF and the DFGLS unit root test of the RER series. The RER measured as WPI ratios was the one for which PPP evidence was found for the larger number of countries: six out of sixteen when we use DF-GLS test with demeaned series. The worst measure of all was the RER based on the ratio of foreign CPIs and domestic WPI. No evidence of PPP at all was found for this measure.