What is a price index and how is it calculated?

Main types of price indices

The most common are the following indices :

consumer prices (CPI);
gross domestic product (deflator);
industrial products;
producer prices;
cost of living, etc.

Different price indices are intended to define different classes of goods and for different purposes :

consumer prices are measured by the Consumer Price Index (CPI);
production prices are measured separately and correspond to production costs;
stock indices provide insight into the price of productive assets;
the construction cost index or rent benchmark measures the dynamics of housing prices, etc.

An individual price index means the price level for a specific product in the base period and reporting year.

The consolidated price index expresses the price level for those categories of goods that were sold in the reporting period, calculated in prices of the base period and in actual prices.

The producer price index reflects the dynamics of wholesale prices of companies for a specific period of time. The price level in this index is measured at the production stage or at the wholesale stage. This index is widely used in the business sector.

The cost of living index shows the dynamics of prices for a fixed set of goods and services included in the consumer basket of specific categories of the population.

To measure the rate of price growth, the rate or rate of inflation . It describes the comparative fluctuations in the price level. To do this, the price level in the current year must be divided by the price level in the previous year and multiplied by 100%.

Index number theory[edit]

Price index formulas can be evaluated based on their relationship to economic concepts (such as the cost of living) or on their mathematical properties. Several different tests of such properties have been proposed in the index theory literature. We Dyworth summarized past studies into a list of nine such tests for a price index, where and are vectors giving prices for the base period and the reference period at that time and give values for those periods. [12] I ( P t 0 , P tm , Q t 0 , Q tm ) {\displaystyle I(P_{t_{0}},P_{t_{m}},Q_{t_{0}},Q_{ t_{m}})} P t 0 {\displaystyle P_{t_{0}}} P tm {\displaystyle P_{t_{m}}} Q t 0 {\displaystyle Q_{t_{0}}} Q tm {\displaystyle Q_{t_{m}}}

Identity check: I ( ptm , ptn , α ⋅ qtm , β ⋅ qtn ) = 1 ∀ ( α , β ) ∈ ( 0 , ∞ ) 2 {\displaystyle I(p_{t_{m}},p_{t_{n }},\alpha \cdot q_{t_{m}},\beta \cdot q_{t_{n}})=1~~\forall (\alpha ,\beta )\in (0,\infty )^{ 2}} Identity testing basically means that if prices remain the same and quantities remain in the same proportion to each other (each quantity of a good is multiplied by the same factor for either the first period or a later period), then the index value will be equal to one. α {\displaystyle \alpha } β {\displaystyle \beta }
Proportionality test: I ( ptm , α ⋅ ptn , qtm , qtn ) = α ⋅ I ( ptm , ptn , qtm , qtn ) {\displaystyle I(p_{t_{m}},\alpha \cdot p_{t_{ n}},q_{t_{m}},q_{t_{n}})=\alpha \cdot I(p_{t_{m}},p_{t_{n}},q_{t_{m}} ,q_{t_{n}})} If each price in the initial period increases by α times, then the index should increase by α times.
Test of invariance to scale changes: I (α ⋅ ptm, α ⋅ ptn, β ⋅ qtm, γ ⋅ qtn) = I (ptm, ptn, qtm, qtn) ∀ (α, β, γ) ∈ (0, ∞) 3 {\displaystyle I(\alpha \cdot p_{t_{m}},\alpha \cdot p_{t_{n}},\beta \cdot q_{t_{m}},\gamma \cdot q_{t_{n }})=I(p_{t_{m}},p_{t_{n}},q_{t_{m}},q_{t_{n}})~~\forall (\alpha ,\beta ,\ gamma )\in (0,\infty )^{3}} The price index should not change if prices in both periods increase by a factor and quantities in both periods increase by another factor. In other words, the magnitude of the quantities and prices should not affect the price index.
Test of commensurability: The index should not be affected by the choice of units used to measure prices and quantities.
Symmetrical treatment of time (or, in the case of parity, symmetrical treatment of place): I ( ptn , ptm , qtn , qtm ) = 1 I ( ptm , ptn , qtm , qtn ) {\displaystyle I(p_{t_{n}}, p_{t_{m}},q_{t_{n}},q_{t_{m}})={\frac {1}{I(p_{t_{m}},p_{t_{n}}, q_{t_{m}},q_{t_{n}})}}} Reversing the order of time periods should reverse the index value. If the index is calculated from the most recent time period to an earlier time period, it must be the reciprocal of the index found when moving from the earlier to the later period.
Symmetrical Treatment of Commodities: All commodities should have a symmetrical impact on the index. Different permutations of the same set of vectors should not change the index.
Monotonicity test: I ( ptm , ptn , qtm , qtn ) ≤ I ( ptm , ptr , qtm , qtr ) ⇐ ptn ≤ ptr {\displaystyle I(p_{t_{m}},p_{t_{n}}, q_{t_{m}},q_{t_{n}})\leq I(p_{t_{m}},p_{t_{r}},q_{t_{m}},q_{t_{r} })~~\Leftarrow ~~p_{t_{n}}\leq p_{t_{r}}} The price index for lower prices in a later period must be lower than the price index for higher prices in later periods.
Test of Mean: The overall relative price implied by the price index must lie between the lowest and highest relative price for all items.
Roundness test: I ( ptm , ptn , qtm , qtn ) ⋅ I ( ptn , ptr , qtn , qtr ) = I ( ptm , ptr , qtm , qtr ) ⇐ tm ≤ tn ≤ tr {\displaystyle I(p_{t_ {m}},p_{t_{n}},q_{t_{m}},q_{t_{n}})\cdot I(p_{t_{n}},p_{t_{r}},q_ {t_{n}},q_{t_{r}})=I(p_{t_{m}},p_{t_{r}},q_{t_{m}},q_{t_{r}}) ~~\Leftarrow ~~t_{m}\leq t_{n}\leq t_{r}} Given three ordered periods , , , a price index for periods and times a price index for periods and must be equivalent to a price index for periods and . tm {\displaystyle t_{m}} tn {\displaystyle t_{n}} tr {\displaystyle t_{r}} tm {\displaystyle t_{m}} tn {\displaystyle t_{n}} tn {\displaystyle t_ {n}} tr {\displaystyle t_{r}} tm {\displaystyle t_{m}} tr {\displaystyle t_{r}}

GDP deflator

The GDP deflator is the ratio of nominal GDP to real GDP. It takes into account the prices of all final goods and services: consumer and investment. It also takes into account the goods and services produced within a country's economic territory and uses a new set of goods each year.

It is calculated using the Paasche index using the following formula. This is the ratio of nominal GDP to real GDP, the numerator being the sum of the current year's price multiplied by the quantity of goods. The denominator is the sum of the base year price multiplied by the quantity of goods.

Purpose of the indicator

The CPI is used in determining inflation. Another indicator is involved in this process – the GDP deflator. It includes all goods and services that were produced in Russia during the reporting period and in one way or another affected GDP. Unlike the CPI, the deflator takes into account only domestic products produced in the Russian Federation.

Using the price index, the state monitors changes in the cost of living of citizens, makes decisions on increasing social benefits, and indexing the salaries of public sector employees. The Central Bank studies the dynamics and decides to increase or decrease the key rate. And this, in turn, leads to changes in interest rates on loans and deposits.

Investors also monitor changes in the CPI, trying to build a forecast of inflation, the exchange rate of the national currency and predict the actions of the Central Bank to regulate monetary policy. If we continue to talk about investments, then information about changes in consumer prices will help predict the situation regarding the cost of bonds.

Adjustment of economic parameters taking into account the effect of inflation

A change in the price level indicates a change in the purchasing power of the state currency. In life, it is very often necessary to adjust economic parameters taking into account changes in the purchasing power of money caused by the effect of inflation.

The process of adjusting the amounts of payments under contracts or obligations, depending on changes in the price level, is called indexation.

The purchasing power of funds must also be taken into account when calculating the level of interest rates. The interest rate without taking into account inflation is the nominal interest rate, and taking into account inflation it is the real interest rate. The real interest rate is the difference between the nominal interest rate and the inflation rate. The nominal interest rate demonstrates the level of growth of an amount over the year (for example, deposits in a bank), and the real rate is the actual growth in the purchasing power of a given amount.

Adjustment of nominal income can be carried out taking into account the Fisher equation , according to which the nominal interest rate is equal to the real interest rate multiplied by the level of expected inflation.

Changes in quantity

Quantity changes are also included in the price comparison. For example, if a supplier reduces the packaging size of a product while keeping the price constant, this is considered a price increase in price statistics.

Remember, the period when instead of a liter of milk in bags they began to sell only 900 milliliters. To maintain statistical significance, calculations must consider a single volume—a liter of milk. Accordingly, the price must be recalculated.

Model changes, as well as changes in contract terms, may be accompanied by changes in quality, which may be reflected in the price, but should not completely determine the price difference between the old and new product. In these cases, the price difference caused by quality differences is quantified and subtracted from the index definition. Without such quality adjustment, improvements or deteriorations in the quality of goods would be reflected entirely in price indices.

Consumer price index

This index is the ratio of the cost of the consumer basket in current prices to the cost of the consumer basket in basic prices. The index reflects only the prices of consumer goods and services. It takes into account the prices of both domestic consumer goods and services and imported ones. It is calculated for a constant set of goods and services. It can be calculated using the Laspeyres formula (in the numerator - the prices of the studied and base periods, in the denominator - the number of goods of the base period).

Sometimes, as a kind of compromise between these two indices, the so-called Fisher index is calculated, which is the square root of the product of the consumer price index and the GDP deflator.

Statistics committees of different countries monthly calculate the CPI, which characterizes the level of inflation in the country. The CPI reflects changes over time in the average price level for a fixed basket of goods and services purchased by the population for personal consumption.

Marshall-Edgeworth Index

Alfred Marshall (1842-1924) was an English economist considered by many to be the father of modern neoclassical economics. Marshall's Principles of Economics (1890) is one of the most influential textbooks in the history of economic thought. Francis Isidro Edgeworth (1845-1926) was an Anglo-Irish economist and philosopher. Edgeworth was an early proponent of the use of statistics to analyze economic issues.

The Marshall-Edgeworth price index formula is as follows:

Where:

L (P): Laspeyres Price Index
P (P): Paasche Price Index

The Marshall-Edgeworth Price Index is the arithmetic mean (simple average) of the Laspeyres Price Index and the Paasche Price Index.

Difficulties in calculation

Unfortunately, the described process is quite complicated to implement. Yes, key competitors can be identified in 15 minutes, but the preparatory stage takes much longer.

Most often, difficulties for retailers arise at the data collection stage. To work with a price index, you need fresh, cleaned and repeatedly verified data about competitors. It is necessary to collect data both on aggregators and on competitors’ websites, as well as arrange multiple quality checks of the collected information - retailers do not always do this and, as a result, work with poor data.

However, even when the issue of obtaining quality data is resolved, problems arise with their processing, analysis and use. Errors caused by the human factor can occur at any stage of work: during data collection, their combination, work with them, analysis, revaluation of goods...

At the same time, all the described difficulties in collecting and processing data can be solved if you use a solution for optimizing pricing, which anticipates and eliminates all possible errors (here is a detailed case about the implementation of such a solution by a large retailer) when collecting data, automates the process of their analysis and revaluation.

Links[edit]

^ a b Chance, 108.
↑
Chance, 108–9
^ abc Peter Hill. 2010. "Low's Indices", chapter 9, pp. 197-216 in W.E. Diverta, B.M. Balka, D. Fixler, K.J. Fox and A.O. Nakamura's Price and Performance Measurement: Volume 6 - Index Number Theory
. Trafford Press
https://www.bls.gov/pir/journal/gj14.pdf, citing paragraphs 1.17-1.23 of the International Labor Office (2004).
https://www.statcan.gc.ca/pub/62-553-x/2014001/chap/chap-6-eng.htm
https://www.statisticalconsultants.co.nz/blog/different-ways-of-measuring-the-cpi.html
Post-Laspeyres: The Case for a New Formula for Calculating Consumer Price Indices, IMF Working Paper WP/12/105 by Paul Armknecht and Mick Silver
Bert M. Balk. Lowe's and Cobb-Douglas consumer price indices and their substitution bias (on jstor). Jahrbücher für Nationalökonomie und Statistik / Journal of Economics and Statistics. 230:6, Themenheft: Index Number Theory and Price Statistics (December 2010), pp. 726-740.
Lapedes, Daniel N. (1978). Physics and mathematics dictionary. McGraw - Hill. paragraph 367. ISBN 0-07-045480-9.
Statistics New Zealand; Glossary of General Terms
, "Paasche Index". Archived May 18, 2017, at the Wayback Machine.
Statistics New Zealand; Glossary of General Terms
, "Laspeyres Index". Archived February 6, 2012 at the Wayback Machine.
Dywerta (1993), 75-76.
Commercial knowledge ensures this
Triplett (2004), 12.
Triplett (2004), 18.
Triplett (2004), 34.
Triplett (2004), 24-6.

Index performance during inflation

The indicator under consideration is of high importance when conducting economic analysis . We have already noted above that when making calculations it is necessary to take into account the current level of inflation. Below we suggest that you familiarize yourself with the specifics of the consumer price index.

Main factors of inflation processes

An increase in the CPI indicates changes in the exchange rate of the national currency. The growth of this indicator indicates that the current level of inflation has a negative impact on the country's economy. In such a situation, there is a need to take strict monetary measures. The Central Bank, which is responsible for developing a strategy for correcting this course, must take into account the following factors:

actual CPI value;
predicted dynamics.

Workers who believe in rising prices for basic necessities are demanding higher wages. Increasing wages forces manufacturing companies to increase the cost of their goods. However, rising inflation contributes to an increase in investment flow. This means that increased consumption of food products is more beneficial for the state’s economy.

Negative consequences

The monetary strategy of the authorities responsible for regulating the CPI is usually aimed at reducing the level of inflation. The growth of this indicator indicates economic difficulties in the country. It is important to note that low prices for commercial products pose an immediate danger to the economy. This fact is explained by the fact that people stop investing free funds in various investment projects.