Price index

A price index measures how have changed the prices of goods of a basket of goods, such as the consumer price index or the import price index. With its help, a statement about the level of inflation or deflation will be met in an economic sector. For this purpose, it is determined how to change the prices of the goods, a representative for the agricultural industry basket, over time.

Price indices can be distinguished according to subject matter and formation algorithm. After the subject of a whole set of price indices is determined in the price statistics. The following considerations are made ​​for simplicity ( consumer price index for Germany, for example ) for a purchase price index.

There are two concepts of the formation of price indices widely used:

A price adjustment with the so-called chain indices (chain prices ) made ​​- In the national accounts, however, is in accordance with international conventions - in Germany from 2005.

• 6.1 Laspeyres index
• 6.2 Paasche index
• 6.3 Fisher index

Alternative definitions

" Consumer Price Index ( CPI) [ ... ] calculated the cost of a detailed list of goods and services in Euro ( formerly known as a price index for Living ) "

" Measures the average price change of all goods and services purchased by households for consumption purposes "

" Price indices are, in simple terms, functions that aggregate prices and price changes and combine them into a measuring number that allows a conclusion about future prices as a whole. "

Classification

An important economic policy objective has always been price stability. To check if a price level is constant, or what is its change, an inflation rate is calculated:

So, for example,

With and.

Only an exponential behavior of the CPI results in a constant rate of inflation.

Primary is interesting to see how changes the purchasing power of money the consumer over time. Therefore, the consumer price index is calculated in practice, mainly because of this, only those goods and services acquired, which are intended for private households. The consumer price index (CPI ) is calculated monthly by the Federal Statistical Office. Other possible price indices are, for example, the index of import and export prices, the index of producer prices of agricultural or industrial products as well as the index of gross domestic product. Also statements about regional differences in price levels can be expressed by a price index, which is then built up in a manner analogous to the temporal price index. Such price indices are rarely determined.

In a temporal price index, which will be considered in more detail below, it is first of all necessary to determine two points in time at which the price of the basket of goods to be determined. These are called " base year " (or " base period " ) and the reporting year. Here, the base year is the year to which the investigation relates ( the starting point of the analysis) and the year the year in which the price index is created (so to speak the current year, or the end point of view). In determining changes in a price index, a base year equal to 100%. It should always be chosen so that it is as good as possible in the current trend of development.

The price of a basket of goods is the sum of the individual goods prices, which it contains. These are multiplied by the respective quantities consumed of goods, ie " Weighted by their share in the total expenditure of the household. " Come from what year these weights distinguishes the Laspeyres index and the Paasche index.

Laspeyres index

When calculating the price index by Étienne Laspeyres the selected weights derived (ie, the consumption quantities ) from the base year. The index determines the price of a basket of goods in the composition of the base year relative to commodity prices of the year on the price of the same basket of goods (same consumption rates ) for freight base-year prices. This is expressed as a ratio:

With respect to the reporting year = prices = prices with respect to base year = consumption with respect to the base year.

The Laspeyres index is thus a weighted arithmetic mean of price relatives digits

Where the weights are the shares of sales of various goods from the base year.

It is therefore examines what the old cart (consumption quantities in the base year ) would cost in the reporting year (eg today ) ( prices of the year ) and what had to be paid for the same basket in the base year (old prices and quantities in the base year ). It is assumed that the quantities and qualities of goods in the basket over time are constant, so that changes in the index can only result from changes in the prices of goods.

The practical advantage of Laspeyres indices is that the weights must be determined for the base year and then remain unchanged. So that they can still be considered as representative for the current price action, they will be in the official statistics - as well as the composition of the basket - regularly (usually every year, to 2005 every 5 years) updated. However, the constant consumption volumes have the advantage that the individual price indices that were created with the same base year, very well comparable.

The determination of the consumer price index is made in Germany using a Laspeyres index.

Paasche index

In contrast to the Laspeyres index the selected weights in the calculation of the price index by Hermann Paasche from the current reporting year, not from the base year were taken. It compares the price of a basket of goods in the composition of the reporting year to commodity prices of the year with the price of the same basket of goods (current consumption rates of the year ) to commodity prices of the base year. This can also be expressed as the ratio:

With respect to the reporting year = prices = prices with respect to base year = consumption with respect to the reporting year.

The Paasche index is thus a weighted harmonic mean of price relatives digits

Where the weights are the shares of sales of various goods from the reporting year.

It is therefore examines what a current shopping cart cost (current prices and quantities of the year ) and what for the same basket (consumption quantities of the year ) in the base year would have to be paid ( prices of the base year ).

A (pure ) Paasche price index is often calculated by the official statistics, since it is resource and time consuming due to the necessary periodic updates of consumption and the ever-changing weights negative effect on the comparability of individual years. It is however required when deflating sales trends to get "real" volume trends as Laspeyres quantity indices.

"If the Paasche index a similar dilemma as the Laspeyres index is - long time series with high information content about the rate of inflation, but problematic configuration ( Laspeyres ) or an exact quantity structure, but low predictive value of the inflation rate ( Paasche ) -, it is consistently to choose the less expensive Laspeyres index. "

Other indexes

Paasche and Laspeyres In addition, there are further indices.

Fisher - Price Index

The Fisher price index (named after Irving Fisher) is the geometric mean of the Laspeyres and Paasche price indices. The Fisher price index is referred to in statistics as " Fisher's ideal price index ":

For Fisher index is worth mentioning that this calculates the real inflation with unusual accuracy compared to the indices Laspeyres and Paasche. This is because he chooses the middle between the two, bearing in mind that the Laspeyres index indicates the true inflation tends to be high, while the indication Paasche tends to understatement.

The fact that the Fisher index yet could hardly prevail in statistical practice, is primarily because he is too little illustrative of the general population, difficult to understand and to communicate from public office only with difficulty.

Chain price index

Chain price indexes (chain prices ) determine each year how much the purchased goods in the previous year in the current year cost ( in the Laspeyresform ) or have cost how much the goods purchased in the current year in the previous year ( in the Paascheform ). This is another cart as a basis and shall take into account the current consumption habits in the determination of price changes for each year. Disadvantage of the method is that the results from year to year are not directly comparable, since the cart has always paved, and longer-term considerations only by chaining - hence the name of the index - the annual results are possible.

The harmonized consumer price index is computed as a chain index ( Laspeyresform ). It shall be collected within the EU by all Member States. This allows the development of prices across countries to compare.

Examples

Carts:

(Prices in GE, consumption in ME)

The representative cart is exemplified here consist of only four goods, ie only these four items will be purchased in the amounts indicated to the prices of the consumer typically. As seen from the table, the quantities consumed basket of goods from 1995 to 2000 had to be adjusted in order to continue to be representative. This is due to changing consumer habits.

Laspeyres index

Paasche index

Fisher index

The deviation between the top two types of calculation of 0.9 % is averaged by the Fisher index:

Assessment

The price index can be accurately given only for items that do not change their "quality", that is, their price-determining characteristics. Change these properties whose estimated price influence must be eliminated in order to face the same price for like can. As for some goods, the quality is rapidly transforming itself and the price index in this case is highly dependent on (subjective) estimates, the statistical offices are increasingly about to raise hedonic prices. However, there are still other internationally recognized and recommended quality adjustment methods ( eg equipment cleanup ), with the help of quality changes can be eliminated. As a rule, certain procedures for specific groups of goods especially recommended, that is, no quality adjustment methods are general statements for all goods equally suitable.

The significance of a price index is several issues that are connected with his determination perspective:

• It is not individual social groups of the population that may be affected to different degrees of price level changes, differentiated
• Although the formation of different index households increases the accuracy, but these indices represent only refined mean values ​​that do not necessarily correspond with the actual individual consumption habits of individual households
• The actual consumption structure may change over time, while the composition of the basket of goods used to fixing a new base year for reasons of comparability remains unchanged ( at Laspeyres )
• No account of price elasticities
• Permanent structural changes in the supply of goods

Because of these factors that affect the price index and lead to inaccuracies, it is necessary to define a tolerance range within which still prevails monetary stability. In Germany it is estimated by the Bundesbank with one to two percent, ie varies a price index less it is considered constant.

International comparison

" The MUICP is used among others by the European Central Bank ( ECB) as a main indicator for monetary policy management in the euro zone. " The U.S. central bank ( Federal Reserve System) uses to measure inflation the personal consumption expenditures price index. Since 2008, the Swiss Federal Statistical Office ( FSO ) is also calculated in addition to the national index of consumer prices to the EU harmonized consumer price index.

Indices by subject

Depending on the object of study can be divided arbitrarily the economy horizontally and vertically. Often considered or published indices on:

• Commodity prices - CRB Index, CCI, DJ UBSCI, RICI, S & P GSCI, oil prices, gold prices, silver prices, platinum prices, palladium price
• Wages
• Producer prices, which require the manufacturer (of the wholesale or business customers ); to be distinguished from the cost. Agricultural prices (agricultural producer prices ) - FAO Food Price Index