Daily Consumer Price Index – DCPI
(i) Introduction
Today the economic values of all economic items are stated in terms of unstable money. Prices are expressed in unstable monetary units. Unstable money is the generally accepted unstable monetary unit of account used to value and account all economic activity by entities applying the stable measuring unit assumption as part of the traditional Historical Cost Accounting model under which they implement financial capital maintenance in fixed nominal monetary units with unstable real values in the world economy during inflation, deflation and hyperinflation.
Unstable money is not fixed in constant real value. Unstable money is fixed in nominal value in economies subject to inflation, deflation and hyperinflation. Unstable money is a fixed nominal unit of account with a daily changing real value (purchasing power). Financial capital maintenance in nominal monetary units, although approved in IFRS and by the United States Financial Accounting Standards Board (US FASB) and implemented worldwide, is a very popular accounting fallacy not yet extinct because it is impossible to maintain the real value of capital in nominal monetary units per se during inflation and hyperinflation.
Bank notes and bank coins cannot currently be inflation–indexed or deflation–indexed which makes it impossible for money or the monetary unit of account to be a perfectly stable unit of constant real value during inflation, deflation and hyperinflation.
(ii) Unidad de Fomento
Notwithstanding or despite the above, monetary items in the form of certain time deposits – not the actual bank notes and coins – and other monetary items, e.g. certain government capital market bonds, have been inflation–indexed in Chile since 1967 by means of the Unidad de Fomento which is now a monetized daily indexed unit of account.
The UF´s value in Chilean escudos was originally (1967) updated every quarter which would be the official rate for the following quarter. The UF´s original value of 100 has never been rebased like most CPIs. It was updated monthly from October 1975, with the currency changeover to pesos, till 1977. Since July 1977 it was calculated daily by interpolation between the 10th of each month and the 9th of the following month, according to the monthly variation of the Indice de Precios al Consumidor (IPC), the Chilean Consumer Price Index. The Banco Central de Chile has calculated and published the UF´s value daily since 1990. The UF is a lagged daily interpolation of the Chilean CPI. The IPC is independently calculated and published monthly by the Chilean National Statistical Institute.
Most bank deposits in Chile are 30–day non–indexed deposits or 90–day indexed deposits whose rates are expressed in terms of the UFs. Interest rates on the indexed deposits are expressed as a premium over the UFs. On maturity, the deposits are converted back to pesos at the current UF rate. Shiller, 1998, p3.
(iii) Definition: Daily Consumer Price Index
Daily inflation–indexing monetary items is thus not a new concept. Chile is the country which is closest to inflation–indexing its entire money supply. 30–Day deposits are not currently inflation–indexed in Chile. 90–Day deposits and various other monetary items are inflation–indexed daily resulting in 20 to 25% of Chile´s broad M3 money supply being inflation–indexed on a daily basis in terms of the UF according to the Banco Central de Chile.
The Consumer Price Index is an example of a non–monetary general price level index. The annual percentage change in the CPI indicates the annual rate of inflation. The CPI for a particular calendar month is normally published in the second or third week of the next calendar month.
A daily instead of a monthly general price–level index is required to implement financial capital maintenance in units of constant purchasing power during inflation and deflation (Constant Item Purchasing Power Accounting). Using the CPI published monthly may result in sudden increases or decreases in values on the date the new monthly CPI is published. A Daily CPI, which is a lagged daily interpolation of the monthly–published CPI, solves this problem. The UF is a very successful monetized daily indexed unit of account used in Chile during the last 44 years and was copied by Ecuador, Mexico and Columbia. (See Shiller, 1998, p6.)
Financial capital maintenance in units of constant purchasing power during hyperinflation would require measurement in either a daily parallel hard currency exchange rate – normally the daily US Dollar parallel rate – or a Brazilian style Unidade Real de Valor daily non–monetary index primarily based on the US Dollar daily parallel rate. The URV was an excellent daily non–monetary index published by the government during hyperinflation in Brazil because it was mainly based on the US Dollar parallel rate (a hard currency parallel rate is essential during hyperinflation which is an exceptional circumstance according to the IASB), but, the CPI was also included in the formula.
Implementing IAS 29 does not result in financial capital maintenance in units of constant purchasing power during hyperinflation. IAS 29 simply requires restatement of Historical Cost or Current Cost financial statements in terms of the period–end monthly CPI during hyperinflation. Inflation–adjusted financial statements in terms of IAS 29 are not a departure from, but, an extension to HCA during hyperinflation.
Definition
A Daily Consumer Price Index is a lagged daily interpolation of the CPI
The DCPI is based on the formula to calculate the daily price of a government inflation–indexed bond in a particular country, e.g., the formula to calculate the daily price of TIPS in the US, or the formula used to calculate the Unidad de Fomento in Chile.
Every country which issues inflation–indexed government bonds has a Daily Consumer Price Index based on the respective CPI. In practice, a DCPI is used to inflation–adjust monetary items, to update historical variable items and to measure constant items in units of constant purchasing power on a daily basis under Constant Item Purchasing Power Accounting; i.e. financial capital maintenance in units of constant purchasing power during low inflation and deflation as authorized in International Financial Reporting Standards (IFRS) in the original Framework (1989), Par 104 (a).
The Unidad de Fomento in Chile is the most successful monetized daily indexed unit of account to date.
A DCPI is calculated and published daily, for example, the UF published daily by the Banco Central de Chile. The monthly published CPI for the first day of any month is only available – at the earliest – round–about the tenth of the next month: up to 41 days later. The SA CPI for the first day of a calendar month can become available up to the 24th of the next calendar month: i.e. up to 55 days later. This is very impractical for daily financial capital maintenance in units of constant purchasing power.
(iv) Formula
“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).” See Shiller, 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 for a UF–based DCPI is 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 general price–level 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.” (See 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 unstable 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.
Nicolaas Smith
Copyright (c) 2005-2011 Nicolaas J Smith. All rights reserved. No reproduction without permission.
