## Thursday, 8 September 2011

### Daily Consumer Price Index - Part 3

Daily Consumer Price Index - Part 3

“The UF is now a lagged daily interpolation of the monthly consumer price

index. The formula for computation of the UF on day t is:

UF t = UF t–1 × (1+ π) to the power 1/d

where π is the inflation rate for the calendar month preceding the calendar month in which t falls if t is between day ten and the last day of the month (and d is the number of days in the calendar month in which t falls), and π is the inflation rate for the second calendar month before the calendar month in which t falls if t is between day one and day nine of the month (and d is the number of days in the calendar month before the calendar month in which t falls).”

Robert J. Shiller, Indexed Units of Account: Theory and Assessment of Historical Experience, Cowles Foundation Discussion Paper No 1171, 1998, p3.
The above formula applies to the UF in Chile where the CPI for the current calendar month used to be available on the 10th of the next calendar month. The general case formula can be stated as follows:
On day t
DI t = DI t–1 X (1 + π) to the power 1/d

where π is the monthly inflation rate for the second calendar month before the calendar month in which t falls if t is on or between day one and the day of publication of the CPI of the previous calendar month (and d is the number of days in the calendar month before the calendar month in which t falls), and π is the monthly inflation rate for the calendar month preceding the calendar month in which t falls if t is on or between the day the CPI for the previous calendar month is published and the last day of the month (and d is the number of days in the calendar month in which t falls).

The monthly inflation rate for a calendar month is calculated using the CPI for that month and for the preceding month. The DCPIs within a given calendar month thus depend on the CPI for each of the three preceding months. For example, the July DCPIs depend before the day the June CPI is published on the CPI for April and May, and starting with the day the June CPI is published on the CPI for May and June.

A DCPI is very similar to, but, not exactly the same as a monetized daily indexed unit of account, e.g. the UF in Chile. The UF is monetized; i.e. it is stated in terms of the Chilean peso. That is not the case with a DCPI. A DCPI is not automatically monetized.
“The UF was and is an amount of currency related to the Indice de Precios al Consumidor (IPC), the consumer price index for Chile.” (Shiller, 1998, p3)

A DCPI is, like the monthly CPI on which it is based, a non–monetary index value. Monetization depends on generally accepted monetary practices in an economy: see the UF in Chile. A DCPI can be monetized and used as a monetized daily indexed unit of account with payments being made in the national monetary unit depending on users in an economy. Monetization is not a necessity.
“An exchange rate between the unit (the UF) and the true money or legal tender, in Chile the peso, is defined using an index number (such as the consumer price index), and payments are executed in money. Thus, the indexed units of account facilitate payments that are tied to the index number, without being a means of payment.” (Shiller, 1998, p2)

A DCPI is not a unit of account just like the CPI is not a unit of account for accounting purposes. The US Dollar, Euro, Yen, Yuan, etc are the nominally fixed monetary units of account, unstable in real value, used in their respective countries as the national monetary unit of account for accounting purposes during inflation, deflation and hyperinflation. The US, EU, Japanese and Chinese CPIs are not units of account for accounting purposes. They are non–monetary general price level indices. So are their DCPIs. Prices are not quoted in CPIs or in DCPIs – although they can be.

DCPIs based on the UF formula for Portugal and South Africa are available on this blog as from 1st July, 2011.

Nicolaas Smith