Daily CPI compared to daily monetized indexed unit of account
Updated on 1-9-11
Unstable money is the unstable medium of exchange, unstable store of value and unstable unit of account in the economy. Pre-monetary economies had units of account without money being available in the economy.
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 constant nominal unit of account with a continuously changing real value (purchasing power). Financial capital maintenance in nominal monetary units, although approved in IFRS and by the US FASB and implemented worldwide, is still a very popular accounting fallacy not yet extinct since it is impossible to maintain the real value of capital constant in nominal monetary units per se during inflation, deflation and hyperinflation.
Bank notes and bank coins cannot currently be indexed which makes it impossible for money held (currency) or the monetary unit of account to be a constant indexed unit of account or a perfectly stable unit of constant real value during inflation, deflation and hyperinflation.
However, notwithstanding or despite the above, monetary items in the form of bank deposits - not the actual bank notes and coins - have been inflation-indexed in, for example, Chile since 1967 by means of the
Unidad de Fomento which is now a monetized daily indexed unit of account.
The Central Bank of Chile translates the “Unidad de Fomento” on their site to An Inflation-Indexed Accounting Unit and CPI-Indexed Unit of Account (UF). The UF´s value in Chilean escudos was originally updated every quarter which would be the official rate for the following quarter. 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 IPC. The Chilean Central bank has calculated and published its value daily since 1990. The UF is a lagged daily interpolation of the Chilean consumer price index (IPC).
The UF daily rate is available at the
Central Bank of Chile
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
Treasury Inflation-Protected Securities (TIPS) are inflation-adjusted or indexed money loans to the US government. The principle or capital amount of the loan is indexed on repayment. On maturity, the loans are converted back to US Dollars at the current CPI rate. Interest is paid on TIPS. Inflation-indexed loans which are monetary item securities or investments are available in other countries too. Inflation-indexing monetary items is thus not a relatively new concept. Chile is the country which is closest to inflation-indexing its entire money supply although 30-day deposits are still not indexed. Money outside the banking system is not indexed.
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 is published monthly.
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 (CIPPA). Using the CPI published monthly may result in sudden increases or decreases in values on the date the new CPI is published. A lagged CPI smoothed by means of the formula used to calculate the UF 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.)
Constant Purchasing Power Accounting (CPPA) during hyperinflation requires either a parallel hard currency exchange rate – normally the US Dollar parallel rate - or a Brazilian style Unidade Real de Valor daily index primarily based on a parallel hard currency. The URV was an excellent daily non-monetary index during hyperinflation in Brazil because it was mainly based on the US Dollar parallel rate (a hard currency parallel rate essential during hyperinflation which is an exceptional circumstance), but, the CPI was also included in the formula.
The CPI is the weighted average index value of a typical basket of consumer goods purchased by a typical consumer statistically stated as a non-monetary initial index value of 100 at the start date. The CPI is thus fixed in real terms.
An example is the harmonized consumer price index of the Euro Zone stated as the non-monetary index value of 100 in 2005. This fixed internal unit of real value is then compared to the weighted average price of the typical basket of consumer goods and services a year later in order to determine the annual rate at which inflation is eroding the real value of only money and other monetary items in only the monetary economy or deflation is creating real value in only money and other monetary items in only the monetary economy. Inflation and deflation have no effect on the real value of non-monetary items. The same is true for hyperinflation.
The stable measuring unit assumption (not inflation and hyperinflation) erodes the real value of constant items never maintained constant (never measured in units of constant purchasing power in a double-entry accounting model where the real value of capital is equal to the real value of net assets) during inflation and hyperinflation under the HC paradigm. Similarly, it is not deflation, but, the stable measuring unit assumption that creates real value in constant items never maintained constant (qualified as per the previous sentence) during deflation under HCA.
The annual percentage change in the CPI indicates the annual rate at which only the real value of the national (or monetary union, e.g. the European Monetary Union) monetary unit and other monetary items is being eroded by the economic process of inflation / hyperinflation or being increased by the economic process of deflation.
The Daily Consumer Price Index (DCPI) is a lagged daily interpolation of the CPI based on the formula used to calculate the UF. In practice, the DCPI is used to inflation-adjust monetary items, to update historical variable items and to measure constant items in units of constant purchasing power when an entity implements financial capital maintenance in units of constant purchasing power during inflation and deflation (CIPPA) because there is no stable measuring unit assumption under this IFRS-authorized accounting model.
The DCPI is calculated and published daily. The monthly published CPI for the first day of any month is only available round-about the tenth of the next month: up to 41 days later. The UF is a monetized daily index of account.
“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 is 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 annual 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), and π is the annual 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 falls).
The inflation rate for a calendar month is calculated using the CPI for that month and for the preceding month. The DIs within a given calendar month thus depend on the CPI for each of the three preceding months. For example, the July DIs 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.
The 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 the DCPI. The 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. The DCPI can be used as a monetized unit of account with payments being made in the national monetary unit depending on users in an economy.
“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 unit of account for accounting purposes during inflation, deflation and hyperinflation. The US, EU, Japanese and Chinese CPI´s are not units of account for accounting purposes. They are non-monetary general price level indices. Prices are not quoted in CPIs or in DCPIs – although they can be.
The DCPIs for Portugal and South Africa are available on this blog.
Inflation-adjusting or indexing the entire money supply with all the money in the banking system eliminates the cost of inflation (not inflation in the monetary unit) completely, only in the money supply; i.e. the monetary economy.
Financial capital maintenance in units of constant purchasing power during inflation and deflation under which all constant items are always and everywhere valued and accounted in units of constant purchasing power by means of a DCPI because there is no stable measuring unit assumption under this accounting model eliminates the entire cost of the stable measuring unit assumption (which is not the cost of inflation) from only the constant item economy. This amounts to hundreds of billions of US Dollars per annum of the real value of constant items never maintained constant in the world´s constant item economy which are currently being eroded unnecessarily by the implementation of the stable measuring unit assumption (not inflation) as it forms part of the traditional HCA model that would be maintained constant under CIPPA.
When all variable items are also measured in terms of specific IFRS with all historical variable items updated in terms of a DCPI because there is no stable measuring unit assumption under financial capital maintenance in units of constant purchasing power during inflation and deflation as authorized in IFRS, then CIPPA automatically maintains the constant purchasing power of capital constant forever in all entities that at least break even during inflation and deflation – ceteris paribus.
Nicolaas Smith Copyright (c) 2005-2011 Nicolaas J Smith. All rights reserved. No reproduction without permission.
