Back Matter

## Abstract

A joint production by six international organizations, this manual explores the conceptual and theoretical issues that national statistical offices should consider in the daily compilation of export and import price indices. Intended for use by both developed and developing countries, it replaces guidance from the United Nations that is now more than a quarter-century old and thus badly outdated. The chapters cover many topics; they elaborate on the different practices currently in use, propose alternatives whenever possible, and discuss the advantages and disadvantages of each alternative. Given its comprehensive nature, the manual is expected to satisfy the needs of many users in addition to national statistical offices and international organizations, particularly businesses, policymakers, and researchers.

## Glossary of Terms

### Accrual accounting

The recording of the value of a purchase or other transaction at the time the obligation to pay is incurred, as distinct from the time payment is made. For an XPI and an MPI, this means that the prices of goods are generally recorded at the time of shipment and the prices of services at the time of delivery.

At current prices, the value of an aggregate is equal to the sum of its components. Additivity requires this identity to be preserved for the extrapolated values of the aggregate and its components when their current values in some period are extrapolated using a set of interrelated quantity indices; or, alternatively, when the current values of the aggregate and its components in some period are deflated using a set of interrelated price indices. See also “consistency in aggregation.”

### Aggregate

A set of transactions relating to a specified flow of goods and services, such as the total exports produced by resident establishments in a given period or the total imports of intermediate inputs made by resident establishments in a given period. The term “aggregate” is also used to mean the value of the specified set of transactions.

### Aggregation

The process of combining different sets of transactions to obtain a larger set of transactions. The larger set is described as having a higher level of aggregation than the sets of which it is composed. The term “aggregation” includes the process of adding the values of lower-level aggregates to obtain higher-level aggregates. In the case of price indices, it means the process by which price indices for lower-level aggregates are averaged, or otherwise combined, to obtain price indices for higher-level aggregates.

### ASYCUDA

Automated System for Customs Data. A computer system designed by UNCTAD (United Nations Conference on Trade and Development) for the immediate verification of customs declarations. It ensures that declarations contain all information required, including quantity information, in order to receive customs clearance. The system also validates customs values by matching the unit values on the declarations against those for a predetermined list of commodity prices.

### Asymmetric index

An index that does not treat the two periods being compared in a symmetric or balanced way by attaching equal importance to the price and value data in both periods. For example, the Laspeyres price index, the Paasche price index, and the Palgrave price index are asymmetrically weighted price indices: the Laspeyres because it uses the value shares of the base period, the Paasche and Palgrave because they use the value shares of the current period.

### Axiomatic approach

The approach to index number theory that determines the choice of index number formula on the basis of its mathematical properties. A list of tests is drawn up, each test requiring an index to possess a certain property or satisfy a certain axiom. The choice of index is made on the basis of the number of tests satisfied. Not all tests may be considered equally important, and the failure to satisfy certain key tests may be considered sufficient grounds for rejecting an index. An important feature of the axiomatic approach is that prices and quantities are considered as separate variables and no account is taken of possible links between them. Also known as the “test approach.”

### Base period

The base period is generally understood to be the period with which other periods are compared. However, the term is not a precise one and may be used to mean rather different things. Three types of base period may be distinguished:

• The price reference period—the period that provides the prices to which the prices in other periods are compared. The prices of the price reference period appear in the denominators of the price relatives used to calculate the index.

• The weight reference period—the period, usually one or more years, whose values serve as weights for the index. When the values are hybrid (that is, the quantities of one period are valued at the prices of some other period), the weight reference period is the period to which the quantities refer.

• The index reference period—the period for which the index is set equal to 100.

The three reference periods may coincide but frequently do not.

### Base-weighted index

See “Laspeyres price index.”

### Basic price

The amount received by the producer from the purchaser for a unit of good or service produced as output. It includes subsidies on products and other taxes on production. It excludes taxes on products, other subsidies on production, supplier’s retail and wholesale margins, and separately invoiced transport and insurance charges. Basic prices are the prices most relevant for decision making by suppliers.

A specified set of quantities of goods and services for which prices are collected for the purpose of compiling an index.

See “Lowe index” and equation (G.1) in the Appendix.

### BEC

Classification by Broad Economic Categories. An internationally agreed classification that groups commodities according to their main end use: consumption goods, intermediate goods, capital goods, dual-purpose goods (motor spirit, passenger motor cars), and military and other goods not elsewhere classified. The categories and subcategories of the classification are defined in terms of SITC Rev.3 basic headings.

### Bias

A systematic tendency of the calculated index to diverge from some ideal or preferred index. Bias can arise for a number of reasons, including the design of the sample selected, the price measurement procedures followed, the data processing methods used, and/or the index number formula employed.

### Bilateral price index

The value ratio decomposition approach to index numbers involves breaking down the value ratio between two periods into two numbers: one representing the price change between the two periods and the other representing the quantity change between the two periods. The resulting price index is called a “bilateral price index.” “Bilateral” refers to the assumption that the price index depends only on price and quantity data pertaining to the two periods being compared.

### Book price

See “list price.”

### Bouncing

The fluctuation or oscillation of prices up and down in a persistent pattern.

### BPM6

Balance of Payments and International Investment Position Manual, Sixth Edition. An internationally agreed set of accounts summarizing the economic relationships between residents of an economy and the rest of the world. The accounts provide an integrated framework for recording an economy’s international current, capital, and financial account transactions, and the financial assets and liabilities of its residents vis-à-vis nonresidents. See also “EBOPS.”

A register or list of enterprises or establishments involved in productive activities that is maintained by countries, often by their national statistical institutes, to provide the frame for carrying out their economic censuses and surveys. Such registers usually contain information on location, economic activity, size (employment, payroll, annual production, or turnover), contact persons, links with tax and other administrative registers, etc.

### Carli price index

An elementary price index defined as the simple, or unweighted, arithmetic average of the current to base period price relatives.

${P}_{C}\equiv \frac{1}{n}\mathrm{\Sigma }\left(\frac{{p}^{t}}{{p}^{0}}\right)$

### Carry forward

The situation in which a missing price for a product in the current period is imputed as being equal to the last price observed for that product.

### Chain index

An index number series for a long sequence of periods obtained by linking together index numbers spanning shorter sequences of periods, each with their own weights. The linking may be made as frequently as the weights change and the data permit, or at specified intervals, such as every five or ten periods. Each link in the chain consists of an index comparing each period with the previous period. See also equation (G.6) in the Appendix.

Splicing together two consecutive sequences of price indices that overlap in one or more periods. When the two sequences overlap by a single period, the usual procedure is simply to rescale one or another sequence so that the value in the overlap period is the same in both sequences and the spliced sequences form one continuous series. More complex methods may be used to link indices that overlap by more than one period. Also known as “chaining” or “linking.”

See “drift.”

### Characteristics

The physical and economic attributes of a good or service that serve to identify it and enable it to be classified.

### C.i.f. price

Cost, insurance, and freight price. The price of a good delivered at the customs frontier of the importing country or the price of a service delivered to a resident. It includes any insurance and freight charges incurred to that point. It excludes any import duties or other taxes on imports and trade and transport margins within the importing country.

### Circularity

An index number property such that the algebraic product of the price index comparing period i with period j and the price index comparing period k with period j is equal to the price index that compares period k directly with period i. The property is also known as “transitivity.” When the axiomatic approach is used, a price index number may be required to satisfy the “circularity test.”

### COLI

Cost of living index. An index that measures the change between two periods in the minimum expenditures that would be incurred by a utility-maximizing consumer, whose preferences or tastes remain unchanged, in order to maintaining a given level of utility (or standard of living or welfare). Because consumers may be expected to change the quantities they consume in response to changes in relative prices (the “substitution effect”), the COLI is not a fixed-basket index. COLIs cannot be directly calculated but may be approximated by superlative indices. A conditional cost of living index is one that assumes that all the factors that may influence the consumer’s utility or welfare other than prices (such as the physical environment) do not change.

### Commensurability test

See “invariance to changes in the units of measurement test.”

### Commodity

A generic term for a good or a service, interchangeable with the term “product.” Commodities or products are the result of production. They are exchanged and used for various purposes: as inputs in the production of other goods and services, as final consumption, or as investment. Individual sampled commodities or products are often described as “items.”

### Commodity reversal test

A test under the axiomatic approach that requires that, for a given set of products, the price index should remain unchanged when the ordering of the products is changed.

### Comparison period

See “current period.”

### Compensation of employees

The total remuneration, in cash or kind, payable by enterprises, to employees in return for work done by the latter during the accounting period. Includes employers’ actual and imputed social contributions.

### Consistency in aggregation

An index is said to be consistent in aggregation when the index for some aggregate has the same value whether it is calculated directly in a single operation, without distinguishing its components, or it is calculated in two or more steps by first calculating separate indices, or subindices, for its components, or subcomponents, and then aggregating them, the same formula being used at each step. See also “additivity.”

### Constant elasticity of substitution index

A family of price indices that allows for substitution between products. The Lloyd-Moulton index is such an index.

### Constant prices test

See “identity test.”

### Consumption of fixed capital

The reduction in the value of the fixed assets used in production during the accounting period resulting from physical deterioration, normal obsolescence, or normal accidental damage.

### Continuity

The property whereby the price index is a continuous function of its price and quantity vectors.

### Contract escalation

See “indexation of contracts.”

### Contract price

A general term referring to a written sales instrument that specifies both the price and shipment terms. A contract may include arrangements for a single shipment or multiple shipments. Usually it covers a period of time in excess of one month. Contracts are often unique in that all the price-determining characteristics in one contract are not repeated exactly in any other contract.

### Coverage

The set of goods and services whose prices are actually included in the index. For practical reasons, coverage may have to be less than the scope or domain of the index. In other words, the set of goods and services covered by the index may be narrower than the set of goods and services that the compliers of the index would prefer to include if it were feasible.

### CPA

Statistical Classification of Products by Activity within the European Economic Community. The classification of goods and services by originating activity favored by the European Union. Originating activities are those defined by NACE.

### CPC

Central Product Classification. An internationally agreed classification of goods and services based on the physical characteristics of goods or on the nature of the services rendered. Each type of good or service distinguished in the CPC is defined in such a way that it is normally produced by only one activity as defined in ISIC.

### CPI

Consumer price index. A monthly or quarterly price index compiled and published by an official statistical agency that measures the changes in the prices of consumption goods and services acquired or used by households. Its exact definition may vary from country to country.

### CSWD index

Carruthers, Sellwood, Ward, Dalén index. A geometric average of the Carli index and the harmonic mean of price relatives index.

${P}_{CSWD}\equiv \sqrt{{P}_{C}×{P}_{HR}}$

### Current period

In principle, the current period should refer to the most recent period for which an index has been computed or is being computed. However, the term is widely used to refer to any period that is compared with the base period or index reference period. It is also widely used simply to mean the latter of the two periods being compared. The exact meaning is usually clear in the context. Also referred to as the “comparison period.”

### Current-weighted index

See “Paasche price index.”

### Cutoff sampling

A sampling procedure in which a predetermined threshold is established with all units in the universe at or above the threshold being included in the sample and all units below the threshold being excluded. The threshold is usually specified in terms of the size of some known variable, the largest sampling units being included and the rest given a zero chance of inclusion. For XMPIs, size is usually defined in terms of export or import values or shares.

### Deflation

The division of the current value of some aggregate by a price index—described as a “deflator”—in order to revalue its quantities at the prices of the price reference period or to revalue the aggregate at the general price level of the price reference period.

### Discount

A deduction from the list or advertised price of a good or service that is available to specific customers under specific conditions. Examples include cash discounts, prompt payment discounts, volume discounts, trade discounts, and advertising discounts.

### Divisia approach

A price or quantity index that treats both prices and quantities as continuous functions of time. By differentiation with respect to time, the rate of change in the value of the aggregate in question is partitioned into two components, one of which is the price index and the other the quantity index. In practice, the indices cannot be calculated directly, but it may be possible to approximate them by chain indices in which indices measuring changes between consecutive discrete periods are linked together.

### Domain

An alternative term for the scope of an index. See “scope” and “coverage.”

### Drift

A chain index is said to drift if it does not return to unity when prices in the current period return to their levels in the base period. Chain indices are liable to drift when prices fluctuate or “bounce” over the periods they cover. Also known as “chain linking bias.”

### Drobisch price index

A price index defined as the arithmetic average of the Laspeyres price index and the Paasche price index. It is a symmetric index and a pseudo-superlative index.

${P}_{DR}\equiv \frac{1}{2}\left({P}_{L}+{P}_{P}\right)$

### Dutot index

An elementary price index defined as the ratio of the unweighted arithmetic average of the prices in the current period to the unweighted arithmetic average of the prices in the base period.

${P}_{D}=\frac{\frac{1}{n}\mathrm{\Sigma }{p}^{t}}{\frac{1}{n}\mathrm{\Sigma }{p}^{0}}$

### EBOPS

Extended Balance of Payments Services Classification. An extension to the BPM6 classification of international trade in services. It is primarily a product classification and as such is defined in terms of the CPC. However, in line with the BPM6, it includes some classes that are not compatible with the CPC or with other international product classifications such as the CPA. It also includes various supplementary items and alternative groupings that are intended to provide additional information on the transactions recorded in the system.

### Economic approach

The approach to index number theory that assumes that the quantities are functions of the prices and not independent variables. The observed price and quantity data are assumed to be generated as solutions to various economic optimization problems. Also known as the “microeconomic approach.”

### Economic territory (of a country)

The economic territory of a country consists of the geographical territory administered by a government within which persons, goods, and capital circulate freely. It includes (1) the air space, territorial waters, and continental shelf lying in international waters over which the country enjoys exclusive rights or over which it has, or claims to have, jurisdiction with respect to the right to fish or to exploit fuels or minerals below the sea bed; (2) territorial enclaves in the rest of the world (clearly demarcated areas of land that are located in other countries and that are used by the government for diplomatic, military, scientific, or other purposes with the formal political agreement of the government of the country in which they are physically located); and (3) any free zones, or bonded warehouses or factories operated by offshore enterprises under customs control (these form part of the economic territory of the country in which they are physically located).

### Economically significant prices

Prices that have a significant influence on the amounts producers are willing to supply and on the amounts purchasers wish to buy.

### Editing

The process of scrutinizing and checking the prices reported or collected for the price index. Checks may be carried out by computers using statistical programs written for the purpose. See “input editing” and “output editing.”

### Elementary aggregate

The lowest level of aggregation for which value data are available and used in the calculation of the price index. The values of elementary aggregates are used to weight the elementary price indices associated with them to obtain indices for higher-level aggregates. Elementary aggregates usually cover a relatively narrow range of goods or services. They also serve as strata for the sample of products selected for pricing.

### Elementary item

One of the individual goods or services that make up an elementary aggregate. An individual good or service selected for pricing from among the various goods or services comprising an elementary aggregate. Often referred to as an “item.”

### Elementary price index

A price index for an elementary aggregate. Value weights cannot usually be assigned to the price relatives for sample products within an elementary aggregate, although other kinds of weighting may be explicitly or implicitly introduced into the calculation of elementary indices. Three examples of elementary index number formulas are the Carli, the Dutot, and the Jevons indices.

### Enterprise

An institutional unit in its capacity as a producer of goods and services consisting of one or more establishments. An enterprise may be a corporation, a quasi-corporation, a nonprofit institution, or an unincorporated enterprise.

### Error

The difference between the observed value of an index and its “true” value. Errors may be random or systematic. Random errors are generally referred to as “errors.” Systematic errors are called “biases.”

### Establishment

An enterprise, or part of an enterprise, that is situated in a single location and in which a single nonancillary productive activity is carried out or in which the principal productive activity accounts for most of the value added. Also referred to as “LKAU” or “local kind of activity unit.” An establishment should be capable of providing basic accounting information on the prices and quantities it produces and the inputs it uses during an accounting period. This is often not the case in practice, particularly when an establishment is one of a number of production units belonging to an enterprise. In these circumstances, an establishment is defined either as the enterprise itself or in terms of the smallest subsets of production units for which the enterprise (or the subsets themselves) is able to supply accounting information on inputs and outputs for the time period under consideration.

### Evolutionary goods

Goods that are similar to or extensions of existing goods. They are typically produced on the same production line using production inputs and processes that are largely the same as those used to produce existing goods. It is possible, at least in theory, to adjust for any quality differences between an evolutionary good and an existing good.

A direct estimate of how much of the change in price of a product is attributable to changes in its physical or economic characteristics. It requires an evaluation of the contributions of the differences in particular characteristics to the differences in the observed prices of two products. It includes quality adjustments based on hedonic methods. See also “quality adjustment” and “implicit quality adjustment.”

### Factor reversal test

Suppose the prices and quantities in a price index are interchanged to yield a quantity index of exactly the same functional form as the price index. Under the axiomatic approach, the factor reversal test requires that the product of this quantity index and the original price index should be identical with the proportionate change in the value of the aggregate in question. Also known as the “product test.”

### Factory gate price

A basic price with the “factory gate” as the pricing point.

### FEPI

Final expenditure price index. A measure of the changes in prices paid by consumers, businesses, and government for final purchases of goods and services. Intermediate purchases are excluded.

### FIOPI

Fixed-input output (export) price index. The theoretical model for an XPI for resident producers based on the assumption of fixed technology and inputs. It requires the index to reflect changes in revenue resulting from the export of the same products—although not necessarily the same mix of products—produced under the same circumstances and sold under the same terms. In other words, changes in the index arise solely from changes in export prices and are not influenced by changes in inputs. Revenue maximizing behavior is assumed on the part of the exporting producer.

### Fisher price index

A price index defined as the geometric average of the Laspeyres price index and the Paasche price index. It is a symmetric and superlative index.

${P}_{F}\equiv \sqrt{{P}_{L}×{P}_{P}}$

The traditional conceptualization of a price index. The index measures the change in value of a fixed set of quantities—commonly described as a “fixed basket of good and services”—between two periods. Because the quantities or weights remain fixed, any change in the index is due to price changes only. In principle, there is no restriction on the quantities that make up the basket. They may be those of one of the two periods being compared, they may refer to the quantities in some third period, or they may constitute a hypothetical basket such as an average of the quantities in the two periods. Moreover, the quantities may refer to a much longer period of time than the periods of the index: for example, quantities exported or imported over a period of a year or more may be used for a monthly or quarterly XPI or MPI. A fixed-basket index is sometimes described as a “pure price index.” Also known as a “fixed-weight price index.”

A test under the axiomatic approach that requires that if all the quantities remain unchanged (that is, the sets of quantities in both periods are identical), the price index should equal the proportionate change in the value of the aggregate. Also known as the “constant quantities test.”

### F.o.b. price

Free on board price. The price of a good delivered at the customs frontier of the exporting country or the price of a service delivered to a nonresident. It includes the freight and insurance charges incurred to that point and any export duties or other taxes on exports levied by the exporting country.

### FOIPI

Fixed-output input (import) price index. The theoretical model for an MPI for resident producers based on the assumption of fixed technology and outputs. It requires the index to reflect changes in costs resulting from the import of the same inputs—although not necessarily the same mix of inputs—purchased under the same terms in order to produce the same output with the same technology. In other words, changes in the index arise solely from changes in import prices of inputs and are not influenced by changes in outputs. Cost minimizing behavior is assumed on the part of the importing producer.

### Formula bias

Bias arising from the index number formula used to calculate the index. See “bias” and “substitution bias.”

### GDDS

General Data Dissemination System. A system designed by the IMF to promote the development and dissemination of comprehensive macroeconomic, financial, and socio-demographic data sets in line with international methodology and good practice. It enables official statistical agencies to identify and prioritize improvements to their statistics in a thorough and systematic way.

### Geometric Laspeyres price index

A price index defined as the weighted geometric average of the current to base period price relatives using the value shares of the base period as weights. Also known as the “logarithmic Laspeyres price index.”

${P}_{GL}\equiv \mathrm{\Pi }{\left(\frac{{p}^{t}}{{p}^{0}}\right)}^{{s}^{0}}\text{where}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{\hspace{0.17em}}{s}^{0}\equiv \frac{{p}^{0}{q}^{0}}{\mathrm{\Sigma }{p}^{0}{q}^{0}}$

### Geometric Paasche price index

A price index defined as the weighted geometric average of the current to base period price relatives using the value shares of the current period as weights. Also known as the “logarithmic Paasche price index.”

${P}_{GP}\equiv \mathrm{\Pi }\left(\frac{{p}^{t}}{{p}^{0}}{\right)}^{{s}^{t}}\text{where}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{\hspace{0.17em}}{s}^{t}\equiv \frac{{p}^{t}{q}^{t}}{\mathrm{\Sigma }{p}^{t}{q}^{t}}$

### Goods

Physical objects for which a demand exists, over which ownership rights can be established, and whose ownership can be transferred from one institutional unit to another by engaging in transactions on the market. They are in demand because they may be used to satisfy the needs or wants of households or the community or used to produce other goods or services.

### Harmonic mean of price relatives

An elementary index that constitutes the harmonic average counterpart to the Carli index.

${P}_{HR}\equiv \frac{1}{\frac{1}{n}\mathrm{\Sigma }\left(\frac{{p}^{0}}{{p}^{t}}\right)}$

### Harmonic means price index

See “ratio of harmonic means of prices.”

### Hedonic method

A regression technique in which observed prices of different qualities or models of the same generic good or service are expressed as a function of the characteristics of the goods or services in question. It is based on the hypothesis that products can be treated as bundles of characteristics and that prices can be attached to the characteristics. The characteristics may be non-numerical attributes that are represented by dummy variables. The regression coefficients are treated as estimates of the contributions of the characteristics to the overall prices. The estimates may be used to predict the price of a new quality or model whose mix of characteristics is different from that of any product already on the market. The hedonic method can therefore be used to estimate the effects of quality changes on prices.

### Higher-level index

A term used to describe an index for an aggregate at a higher level of aggregation than an elementary aggregate. An index constructed from elementary or lower-level indices. Weights are used to combine them. Also referred to as an “upper-level index.”

### Homogeneity tests

Four tests under the axiomatic approach, namely: the proportionality in current prices test, the inverse proportionality in base prices test, the invariance to proportional changes in current quantities test, and the invariance to proportional changes in base quantities test.

### HS

Harmonized Commodity Description and Coding System or Harmonized System. An internationally agreed commodity classification providing the basis for customs tariffs and for the compilation and dissemination of statistics on international merchandized trade. Goods are classified primarily according to the component material or the type of product, degree of processing, function, and economic activity. The HS was introduced in 1988 as a replacement for the SITC. It is updated every four to six years to take account of changing conditions of international trade. It was last revised in 2007 (HS07). There is full correspondence between the six-digit subheadings of HS07 and the five-digit basic headings of SITC Rev.4.

### Hybrid (export or import) index

A price index that combines price indices for some of the elementary aggregates covered by the index with unit value indices for the other elementary aggregates covered by the index. Price indices are used for heterogeneous elementary aggregates with unacceptable levels of unit value bias. Unit value indices are used for homogeneous elementary aggregates with acceptable levels of unit value bias. See “price dispersion test” and “quantity proportionality test.”

### Hybrid values

Hypothetical values in which quantities are valued at a different set of prices from those at which they were actually bought or sold. For example, when the quantities purchased in an earlier period are valued at prices prevailing in a later period.

### ICP

International Comparison Programme. A worldwide statistical program that compares the price and volume levels of GDP and its component expenditures across participating countries. Comparisons are made every five or so years. Before such comparisons can be made, it is first necessary to express the GDPs of participating countries—which are in national currencies and valued at national price levels—in a common currency at a uniform price level. Purchasing power parities (PPPs) are used to do this. The PPPs are calculated with price and expenditure data collected from participating countries. The price and expenditure data collected cover the whole range of final goods and services included in GDP.

### Identity test

A test under the axiomatic approach that requires that if the prices remain unchanged between the two periods (that is, the sets of prices are identical), the price index should equal unity. Also known as the “constant prices test.”

Inferring indirectly the change in the quality of a product whose characteristics change over time by estimating, or assuming, the pure price change that has occurred. For example, if the pure price change is assumed to be equal to the average for some other group of products, the implied change in quality is equal to the actual observed price change divided by the assumed pure price change. If the whole of the observed price change is assumed to be pure price change, there is assumed to be no change in quality. See also “quality adjustment” and “explicit quality adjustment.”

### Imputed price

The price assigned to a product for which the price is missing in a particular period. The term “imputed price” may also refer to the price assigned to a product that is not sold on the market, such as a good or service produced for own consumption, including housing services produced by owner-occupiers, or one received as payment in kind or as a free transfer from a government or nonprofit institution.

### Index number problem

How to combine the relative changes in the prices and quantities of various products into (1) a single measure of the relative change of the overall price level and (2) a single measure of the relative change of the overall quantity level. Or, conversely, how a value ratio pertaining to two periods can be decomposed into a component that measures the overall change in prices between the two periods—that is, the price index—and a component that measures the overall change in quantities between the two periods—that is, the quantity index.

### Index reference period

The period for which the value of the index is set at 100. See also “base period.”

### Indexation

The periodic adjustment of the money values of some regular scheduled payments based on the movement of a nominated price index such as the CPI or another similar price index. The payments may be wages or salaries, social security or other pensions, other social security benefits, rents, interest payments, etc. The purpose of indexation is to protect the recipients of the payments against inflation. Also known as “index linking.”

### Indexation of contracts

A procedure whereby a long-term contract for the provision of goods or services includes a periodic adjustment to the prices paid for the goods or services based on the increase or decrease in the level of a nominated price index, such as the PPI, the XPI, or the MPI. The purpose of the indexation is to take inflationary risk out of the contract. Also known as “contract escalation.”

### Industry

A general term to describe a group of establishments engaged in the same, or similar, kinds of production activity. Also a specific term used to describe establishments engaged in mining and quarrying, manufacturing, electricity, gas, and water (Sections C, D, and E of ISIC, Rev. 3).

### Input editing

The process of analyzing the prices reported by an individual respondent and querying price changes that are above a specified level or are inconsistent across product lines. An important objective of the process is to ensure that actual transaction prices are reported and to detect any changes in the specifications.

### Institutional unit

A national accounts concept defined as an economic entity that is capable, in its own right, of owning assets, incurring liabilities, and engaging in economic activities and transactions with other entities. Enterprises are institutional units. Other kinds of units include households and governments.

A basket derived as the average of the baskets of two time periods, usually the base and current periods. The average can be arithmetic, as in the Marshall-Edgeworth price index, or geometric, as in the Walsh price index.

### Intermediate consumption

The value of goods and services used or consumed as intermediate inputs by a process of production.

### Intermediate inputs

Goods and services, other than primary inputs and fixed assets, used as inputs into the production process of an establishment, which are produced elsewhere in the economy or are imported. They may be either transformed or used up by the production process. Also called “intermediate products.”

### Intra-company transfer price

The value assigned on a per unit or per shipment basis to goods transferred from one establishment of an enterprise to another. It may or may not be economically significant. However, it is not a market price because ownership of the good does not change hands. See “transfer price.”

### Invariance or symmetry tests

Five tests under the axiomatic approach, namely: the commodity reversal test, the commensurability test, the time reversal test, the quantity reversal test, and the price reversal test.

### Invariance to changes in the units of measurement test

A test under the axiomatic approach that requires that the price index does not change when the units of quantity to which the prices refer are changed: for example, when the price of some drink is quoted per liter rather than per pint. Also known as the “commensurability test.”

### Invariance to proportional change in current or base quantities test

A test under the axiomatic approach that requires that the price index remains unchanged when all the base period quantities, or all the current period quantities, are multiplied by a positive scalar.

### Inverse proportionality in base prices test

A test under the axiomatic approach that requires that if all base period prices are multiplied by the positive scalar λ, the new price index is 1/λ times the old price index.

### ISIC

International Standard Industrial Classification of All Economic Activities. An internationally agreed classification that allows enterprises and establishments to be classified according to economic activity based on the class of goods produced or services rendered.

### Item

An individual good or service in the sample of products selected for pricing. Also referred to as an “elementary item.”

### Item or product rotation

The deliberate replacement of a sampled item, or product, for which prices are being collected, by another product before the replaced product has disappeared from the market or individual establishment. It is designed to keep the sample of products up to date and reduce the need for forced replacements caused by the disappearance of products. See “replacement product.”

### Item or product substitution

The deliberate or forced replacement of a sampled item, or product, for which prices are being collected, by a new product because it is about to disappear or has disappeared from the market or specific establishment. See “replacement product.”

### ITRS

International Transactions Reporting System. An ITRS measures individual balance of payments cash transactions passing through the domestic banks and foreign bank accounts of enterprises, noncash transactions, and stock positions. Statistics are compiled from forms submitted by domestic banks and from forms submitted by enterprisers to the compiler.

### Jevons price index

An elementary price index defined as the unweighted geometric average of the current to base period price relatives also equal to the ratio of geometric means of the current to base period prices.

${P}_{J}\equiv \mathrm{\Pi }{\left(\frac{{p}^{t}}{{p}^{0}}\right)}^{1/n}\text{\hspace{0.17em}}=\frac{\mathrm{\Pi }{\left({p}^{t}\right)}^{1/n}}{\mathrm{\Pi }{\left({p}^{0}\right)}^{1/n}}$

### Laspeyres price index

A price index defined as a fixed-basket, or fixed-weight, index that uses the basket of goods and services of the base period. The base period serves as both the weight reference period and the price reference period. It is identical to a weighted arithmetic average of the current to base period price relatives using the value shares of the base period as weights. Also called a “base-weighted index.”

${P}_{L}\equiv \frac{\mathrm{\Sigma }{p}^{t}{q}^{0}}{\mathrm{\Sigma }{p}^{0}{q}^{0}}=\mathrm{\Sigma }{s}^{0}\left(\frac{{p}^{t}}{{p}^{0}}\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{where}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{s}^{0}\equiv \frac{{p}^{0}{q}^{0}}{\mathrm{\Sigma }{p}^{0}{q}^{0}}$

### List price

The price of a product as quoted in the seller’s price list, catalogue, Internet site, etc. The gross price exclusive of all discounts, surcharges, rebates, and the like that apply to an actual transaction. Also known as the “book price.”

### LKAU

Local kind of activity unit. See “establishment.”

### Lloyd-Moulton price index

A particular case of a constant elasticity of substitution price index. In its unweighted form, the Lloyd-Moulton formula is

${P}_{LM}\equiv {\left[\mathrm{\Sigma }\frac{1}{n}{\left(\frac{{p}^{t}}{{p}^{0}}\right)}^{1-\mathrm{\sigma }}\right]}^{\frac{1}{1-\mathrm{\sigma }}}.$

In its weighted form, the Lloyd-Moulton formula is

${P}_{LM}\equiv \left[\mathrm{\Sigma }{s}^{0}\left(\frac{{p}^{t}}{{p}^{0}}\right){}^{1-\mathrm{\sigma }}\right]{}^{\frac{1}{1-\mathrm{\sigma }}}\text{\hspace{0.17em}}\text{where}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{s}^{0}\equiv \frac{{p}^{0}{q}^{0}}{\mathrm{\Sigma }{p}^{0}{q}^{0}}.$

### Lowe price index

Although called a “Lowe price index” after the index number pioneer who first proposed this general type of index, it is not a single index but a family of basket price indices, each of which measures the proportionate change between periods 0 and t in the total value of a specified basket of goods and services.

$\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{}\mathrm{}\begin{array}{c}{P}_{LO}\equiv \frac{\mathrm{\Sigma }{p}^{t}{q}_{n}}{\mathrm{\Sigma }{p}^{0}{q}_{n}}\text{where the terms}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{q}_{n}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{are the specified}\\ \text{quantities.}\hfill \end{array}$

The family of Lowe indices includes the Laspeyres index, the Paasche index, the Marshall-Edgeworth index, and the Walsh index. See equation (G.1) in the Appendix.

In practice, official statistical agencies frequently use a Lowe price index with a quantity basket of period b, where b denotes some period before 0, and hybrid value shares valued at prices in period 0, the price reference period. The share-weighted Lowe index is

${P}_{LO}\equiv \mathrm{\Sigma }{s}^{b0}\left(\frac{{p}^{t}}{{p}^{0}}\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{where}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{\hspace{0.17em}}{s}^{b0}\equiv \frac{{p}^{0}{q}^{b}}{\mathrm{\Sigma }{p}^{0}{q}^{b}}.$

### Lower-level index

See “elementary price index.”

### Market price

The amount of money a willing buyer pays to acquire a good or service from a willing seller. The actual price for a transaction agreed by the transactors. The net price inclusive of all discounts, surcharges, and rebates applied to the transaction. From the seller’s point of view, the market price is the basic price; from the buyer’s point of view, the market price is the purchaser’s price. Also referred to as “transaction price.”

### Marshall-Edgeworth price index

A price index defined as the weighted arithmetic average of the current to base period price relatives that uses the quantities of an intermediate basket as weights. The quantities of the intermediate basket are arithmetic averages of the quantities of the base and current periods. It is a symmetric index and a pseudo-superlative index.

${P}_{ME}\equiv \frac{\mathrm{\Sigma }{p}^{t}\left({q}^{t}+{q}^{0}\right)/2}{\mathrm{\Sigma }{p}^{0}\left({q}^{t}+{q}^{0}\right)/2}$

### Matched models or products method

The practice of pricing exactly the same model or product in two or more consecutive periods. It is designed to ensure that the observed price changes are not affected by quality change. The change in price between two perfectly matched models or products is described as a “pure” price change.

### Mean value tests

Three tests under the axiomatic approach, namely: the mean value test for prices, the mean value test for quantities, and the Paasche and Laspeyres bounding test.

### Mean value test for prices

A test under the axiomatic approach that requires that the price index lies between the smallest price relative and the largest price relative.

### Mean value test for quantities

A test under the axiomatic approach that requires that the implicit quantity index lies between the minimum and maximum rates of growth of the individual quantities.

### Merchanting

The purchase of goods by a resident from a nonresident combined with the subsequent resale of the goods to another nonresident without the resident taking physical possession of the goods. In other words, the goods do not pass through the economic territory in which the resident resides.

### Microeconomic approach

See “economic approach.”

### Mid-period or midyear price index

A price index that utilizes either the quantity or value weights from an intermediate period that lies between the base period and the current period when the number of periods between them is odd, or the average of the quantity or value weights for two consecutive intermediate periods that lie between the base period and the current period when the number of periods between them is even.

### Mirror price index

An XPI for a country constructed as the weighted average of the corresponding MPIs of the countries to which it exports. An MPI for a country constructed as the weighted average of the corresponding XPIs of the countries from which it imports.

### “Modified,” “short-term change,” or “two-stage” Laspeyres price index

These often-used descriptions of the Laspeyres index have at least three meanings:

As a short-run modified Laspeyres index. This is an index with weight reference period b and price changes between periods 0 and t where the latter are decomposed into price changes between period 0 and t ̶ 1 and period t ̶ 1 and t.

${P}_{MLAS}\equiv \mathrm{\Sigma }{s}^{b}\left(\frac{{p}^{t-1}}{{p}^{0}}\right)\text{\hspace{0.17em}}\left(\frac{{p}^{t}}{{p}^{t-1}}\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{where}\text{\hspace{0.17em}}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{s}^{b}\equiv \frac{{p}^{b}{q}^{b}}{\mathrm{\Sigma }{p}^{b}{q}^{b}}$

The decomposition helps deal with changes in the sampled products. In the absence of changes in the sample, PMLAS reduces to a Young index between t and 0 with weight reference period b.

${P}_{MLAS}\equiv \mathrm{\Sigma }{s}^{b}\left(\frac{{p}^{t}}{{p}^{0}}\right)={P}_{Y}$

As a price-updated version of a Young index. This is a fixed-weight index in which the quantities are those of the weight reference period b, but the price reference period is a later period 0 preceding the current period t. The implicit expenditure weights are obtained by revaluing the quantities of the weight reference period b at the prices of the price reference period 0, a procedure described as “price updating.” This modified Laspeyres index between periods 0 and t can be interpreted as a weighted average of the price relatives between 0 and t, using the price-updated expenditure weights. Its definition is

$\mathrm{\Sigma }\left(\frac{{s}^{b}\left({p}^{0}/{p}^{b}\right)}{\mathrm{\Sigma }{s}^{b}\left({p}^{0}/{p}^{b}\right)}\right)\text{\hspace{0.17em}}\left(\frac{{p}^{t}}{{p}^{0}}\right)$

and corresponds to a Lowe price index between periods 0 and t with weight reference period b. See also “price updating” and “Lowe price index.”

As a two-stage Laspeyres index. The two-stage procedure decomposes a Laspeyres price index between b and t into a Laspeyres price index between b and 0 and a Lowe price index between 0 and t.

$\frac{\mathrm{\Sigma }{p}^{t}{q}^{b}}{\mathrm{\Sigma }{p}^{b}{q}^{b}}=\frac{\mathrm{\Sigma }{p}^{0}{q}^{b}}{\mathrm{\Sigma }{p}^{b}{q}^{b}}\frac{\mathrm{\Sigma }{p}^{t}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{q}^{b}}{\mathrm{\Sigma }{p}^{0}{q}^{b}}$

### Monotonicity in prices

The property whereby if any current period price increases or any base period price decreases, the price index increases.

### Monotonicity in quantities

The property whereby if any current period quantity increases or any base period quantity decreases, the implicit quantity index that corresponds to the price index increases.

### Monotonicity tests

Four tests under the axiomatic approach that test for monotonicity in current prices, in base prices, in current quantities, and in base quantities.

### MPI

Import price index. See “XMPIs.”

### Multi-factor productivity

See “total factor productivity.”

### NACE

The acronym from the French for General Industrial Classification of Economic Activities within the European Communities. The classification is basically a more detailed version of ISIC appropriate to European circumstances.

### Net exports

The value of exports of goods and services less the value of imports of goods and services. Also known as the “balance of exports and imports.”

### New good problem

Difficulty in comparing prices between two periods when a product enters the basket only in period 2, so that a price for the product does not exist in period 1.

### New goods

See “evolutionary goods” and “revolutionary goods.”

### Non-probability sampling

Selection in which establishments or products do not have a known non-zero probability of selection. Also known as “non-random sampling.” It includes the deliberate selection of a sample of establishments and products on the basis of the knowledge or judgment of the person responsible. Also known as “purposive sampling” and “judgmental sampling.”

### Nonresident

An institutional unit whose center of economic interest is not in the economic territory of the country.

### Non-response bias

The bias that arises when those who do not respond have different price experiences than those who do respond.

### Non-sampling error

An error in sample estimates that cannot be attributed to sample variation. It can arise from any number of different sources, including defects in the sampling frame and/or in the selection of sample units, faulty demarcation of sample units, mistakes in the collection of data owing to misunderstandings or dishonesty on the part of the enumerator and/or the respondent, and mistakes during the processing of data.

### Observation

The price collected or reported for a sampled product or item.

### Order price

The price quoted at the time the order is placed by the purchaser.

### Other subsidies on production

The subsidies that resident enterprises may receive as a consequence of engaging in production; for example, subsidies on payroll or workforce, or subsidies to reduce pollution. They do not include subsidies on products.

### Other taxes on production

The taxes that resident enterprises may pay as a consequence of engaging in production. They mainly consist of current taxes on the labor or capital employed in the enterprise, such as payroll taxes or current taxes on vehicles or buildings. They do not include taxes on products.

### Outlier

A term that is generally used to describe any extreme value in a set of survey data. In an XMPI context, it is used for an extreme value of price or price relative that requires further investigation or that has been verified as being correct.

### Output

The goods or services that are produced within an establishment that become available for use outside that establishment, plus any goods and services produced for own final use.

### Output editing

The process of comparing the price levels and price movements of similar products between different respondents and querying any outliers.

### Paasche and Laspeyres bounding test

A test under the axiomatic approach that requires that the price index lies between the Laspeyres price index and the Paasche price index.

### Paasche price index

A price index defined as a fixed-basket, or fixed-weight, index that uses the basket of goods and services of the current period. The current period serves as the weight reference period and the base period as the price reference period. It is identical to a weighted harmonic average of the current to base period price relatives using the value shares of the current period as weights. Also called a “current weighted index.”

${P}_{p}\equiv \frac{\mathrm{\Sigma }{p}^{t}{q}^{t}}{\mathrm{\Sigma }{p}^{0}{q}^{t}}={\left[\mathrm{\Sigma }{s}^{t}{\left(\frac{{p}^{t}}{{p}^{0}}\right)}^{-1}\right]}^{-1}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{where}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{\hspace{0.17em}}{s}^{t}\equiv \frac{{p}^{t}{q}^{t}}{\mathrm{\Sigma }{p}^{t}{q}^{t}}$

### Palgrave price index

A price index defined as the weighted arithmetic average of the current to base period price relatives using the current period value shares as weights.

${P}_{Pal}\equiv \mathrm{\Sigma }{s}^{t}\left(\frac{{p}^{t}}{{p}^{0}}\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{where}\mathrm{}\mathrm{}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{\hspace{0.17em}}{s}^{t}\equiv \frac{{p}^{t}{q}^{t}}{\mathrm{\Sigma }{p}^{t}{q}^{t}}$

### Point-in-time prices

Transaction prices prevailing on a particular day of the month.

### Positivity

The property whereby the price index and its constituent vectors of prices and quantities are positive—that is, greater than zero.

### PPI

Producer price index. A measure of the change in the prices of goods and services either as they leave their place of production or as they enter the production process. A measure of the change in the prices received by domestic producers for their outputs or of the change in the prices paid by domestic producers for their intermediate inputs.

### PPPs

Purchasing power parities. Spatial deflators and currency converters that eliminate the effects of the differences in price levels between countries, thus allowing volume-level comparisons and price-level comparisons of GDP and its components.

### PPS

Probability proportional to size. A sampling procedure whereby each unit in the universe has a probability of selection proportional to the size of some known variable. In the case of XMPIs, size is usually defined in terms of export or import values or shares.

The price index nominated to determine the periodic adjustments to regular scheduled payments or to prices of long-term contracts required under indexation. See “indexation” and “indexation of contracts.”

### Price dispersion test

A test to determine whether the individual unit values for an elementary aggregate (defined as the lowest level of the customs commodity classification by destination or source country) are sufficiently uniform for the overall unit value to be used as a surrogate price in a hybrid XPI or MPI. The test involves computing unit values for every transaction covered by the elementary aggregate for a given month or quarter (depending on the frequency of the index) and measuring their statistical variance. A low variance measurement indicates that the overall unit value for the elementary aggregate could be included in the index. Before doing so, the test is repeated for a number of months or quarters to verify that the low variance measurement persists over time. See also “quantity proportionality test.”

### Price index

A measure reflecting the average of the proportionate changes in the prices of the specified set of goods and services between two periods of time. Usually a price index is assigned a value of 100 in some selected base period, and the values of the index for other periods are intended to indicate the average percentage change in prices compared with the base period.

### Price reference period

The period with whose prices the prices in the current period are compared. The period whose prices appear in the denominators of the price relatives. See also “base period.”

### Price relative

The ratio of the price of an individual good or service in one period to the price of that same good or service in some other period. Also referred to as a “price ratio.”

### Price reversal test

A test under the axiomatic approach that requires that the quantity index remains unchanged after the price vectors for the two periods being compared are interchanged.

### Price updating

A procedure whereby the quantities of an earlier period are revalued at the prices of a later period. The resulting values are hybrid. In practice, the price-updated values may be obtained by multiplying the original values by price relatives or price indices. Also known as “value updating.”

### Pricing point

The point in the production or distribution process to which the price refers. For an exported good, it is the customs frontier of the exporting country; for an imported good, it is the customs frontier of the importing country. For an exported service, it is the place of delivery to a nonresident; for an imported service, it is the place of delivery to a resident.

### Pricing to constant quality

See “specification pricing.”

### Primary inputs

Land, labor, and capital.

### Probability sampling

The random selection of a sample of units, such as establishments or commodities, in such a way that each unit has a known non-zero probability of selection. It ensures that the units are selected in an impartial and objective fashion and permits the measurement of the quality of survey results through estimates of the variance or sampling error. Also known as “random sampling” or “scientific sampling.”

### PRODCOM

The acronym from Production Communautaire, the name in French for the European Union’s system for the collection and dissemination of statistics on the production of manufactured goods. Manufactured goods are those produced by the mining, quarrying, and manufacturing industries. The system is based on a product classification—the Prodcom List—with about 4,500 headings relating to manufactured products.

### Producer’s index

An index constructed from price data supplied by producers—that is, by exporters in the case of XMPIs.

### Producer’s price

The amount received by the producer from the purchaser for a unit of good or service produced as output. It excludes any VAT (or similar deductible tax on products) invoiced to the purchaser. It also excludes supplier’s retail and wholesale margins and separately invoiced transport and insurance charges. (A producer’s price for a product is the basic price plus any nondeductible tax on products paid by the producer less any subsidies on products received by the producer.)

See “commodity.”

### Product line

A group, class, or category of products that is relatively homogeneous in use and price behavior.

### Product line specification

A statement of the characteristics of the range of products included in a product line. Its purpose is to provide the frame within which individual products may be selected as part of the sample for pricing. It may also describe the products included in a subindex. See “SPD.”

### Product specification

A detailed list of the characteristics that identify an individual sampled product. Its purpose is to ensure that a consistent price is collected from period to period relating to a consistent product with the same terms of sale in each period. Hence, the characteristics listed cover both the product (name, serial number, description, etc.) and the transaction (class of customer, size of shipment, discounts, payment terms, delivery details, etc.).

### Product test

See “factor reversal test.”

### Production

An activity that transforms or combines material inputs into other material outputs—as in agricultural, mining, manufacturing, or construction activities—or transports materials from one location to another. Production also includes storage activities—which in effect transport materials in the same location from one time period to another—and the creation of services of all types.

### Proportionality in current prices test

A test under the axiomatic approach that requires that if all current period prices are multiplied by the positive scalar λ, the new price index is λ times the old price index.

### Pseudo-superlative index

An index that approximates any superlative index to the second order around an equal price and quantity point.

### Purchaser’s index

An index constructed from price data supplied by purchasers—that is, by importers in the case of XMPIs.

### Purchaser’s price

The amount paid by the purchaser in order to take delivery of a unit of a good or service at the time and place required by the purchaser. It excludes any VAT (or similar deductible tax on products) that the purchaser can deduct from his own VAT liability with respect to VAT invoiced to his customers. It includes supplier’s retail and wholesale margins, separately invoiced transport and insurance charges, and any VAT (or similar deductible tax on products) that the purchaser cannot deduct from his own VAT liability. (A purchaser’s price for a product is the producer’s price plus supplier’s retail and wholesale margins, separately invoiced transport and insurance charges, and nondeductible taxes on products payable by the purchaser.) Purchasers’ prices are the prices most relevant for decision making by buyers.

### “Pure” price change

The change in the price of a good or service whose characteristics are unchanged; or the change in the price after adjusting for any change in quality.

### “Pure” price index

A price index that measures “pure” price change. A price index that is based on pricing a fixed basket of products and product quantities at the prices of the base period and at the prices of the current period. Because the products and their quantities remain constant, any change in the index is due to price changes only. Also called an “unequivocal price index.”

### “Pure” quantity change

The change in the quantity of a good or service whose characteristics are unchanged.

### “Pure” quantity index

A quantity index that measures “pure” quantity change. A quantity index that is based on a fixed basket of products where the quantities of the base period and the quantities of the current period are both valued with the same set of prices. Because the products and their prices remain constant, any change in the index is due to changes in quantities only. Also called an “unequivocal quantity index.”

### Purposive sampling

See “non-probability sampling.”

An adjustment to the change in the price of a product whose characteristics change over time that is designed to remove the contribution of the change in the characteristics to the observed price. In a price index context, an adjustment is needed when the price of a replacement product has to be compared with the price of the product it replaces. In practice, the required adjustment can only be estimated. Different methods of estimation, including hedonic methods, may be used in different circumstances. See “explicit quality adjustment” and “implicit quality adjustment.”

### Quality change bias

Systematic error arising from the application of inappropriate or no quality adjustments.

### Quantity index

A measure reflecting the average of the proportionate changes in the quantities of a specified set of goods and services between two periods of time. Usually a quantity index is assigned a value of 100 in some selected base period, and the values of the index for other periods are intended to indicate the average percentage change in quantities compared with the base period. See “volume index.”

### Quantity proportionality test

An elementary aggregate (defined as the lowest level of the customs commodity classification by destination or source country) may fail the price dispersion test, yet its overall unit value may still be suitable for inclusion as a surrogate price in a hybrid XPI or MPI if the quantities of the various transactions covered by the elementary aggregate remain in fixed proportions over time. The quantity proportionality test is used to verify whether or not this is the case. It involves computing the average quantities transacted across quantiles of the transaction values for a number of months or quarters (depending on the frequency of the index) and comparing the relatives of the average quantity transacted between months or quarters for each quantile. If the quantity relatives are roughly the same across quantiles, this adds support to the proposition that quantity proportions have not changed over time. See also “price dispersion test.”

### Quantity relative

The ratio of the quantity of a specific good or service in one period to the quantity of the same good or service in some other period.

### Quantity reversal test

A test under the axiomatic approach that requires that the price index remains unchanged after the quantity vectors for the two periods being compared are interchanged.

### Quantity weights

Weights defined in terms of physical quantities, such as the number or total weight of goods or the number of services. Quantity weights are feasible only at the detailed product level because meaningful aggregation of product weights requires them to be commensurate. Values rather than quantities act as weights for price relatives. See “value weights.”

### Random sampling

See “probability sampling.”

### Ratio of harmonic means of prices

An elementary index that constitutes the harmonic average counterpart to the Dutot index. Also known as the “harmonic means price index.”

${P}_{RH}\equiv \frac{\mathrm{\Sigma }n/{p}^{0}}{\mathrm{\Sigma }n/{p}^{t}}$

### Real GDI

Real gross domestic income. A real income measure defined as the volume of GDP plus the trading gain or loss resulting from changes in the terms of trade.

### Rebasing

Rebasing may have different meanings in different contexts. It may mean

• changing the weights used for a series of indices,

• changing the price reference period used for a series of indices, or

• changing the index reference period for a series of indices.

The weights, the price reference period, and the index reference period may be changed separately or at the same time.

### Rebate

A discount paid to the customer after the transaction has occurred.

### Replacement product

The product chosen to replace a product previously sampled, either because it has disappeared completely from the market or because its market share has fallen either in a specific establishment or in the market as a whole.

### Representative product

A product, or product line, that accounts for a significant proportion of the total trade within an elementary aggregate, and/or for which the average price change is expected to be close to the average for all products within the aggregate.

### Representativity bias

Bias in a basket index that results from the use of products that are not representative of those in the two periods being compared; that is, the bias that arises from the use of products whose aggregate price change systematically diverges from the average price change in the two periods.

### Resident

An institutional unit whose center of economic interest is in the economic territory of the country.

### Rest of the world

All nonresident institutional units that enter into transactions with resident units or have economic links with resident units.

### Revenue

The value of output sold. The value of invoiced sales of goods or services supplied to third parties during the reference period.

### Revenue weights

Weights or shares based on the value of output sold in the weight reference period. See “value weights.”

### Revolutionary goods

Goods that are significantly different from existing goods. They are generally produced on entirely new production lines using production inputs and processes that are considerably newer than those used to produce existing goods. It is virtually impossible, both in theory and in practice, to adjust for any quality differences between a revolutionary good and any existing good.

### Reweighting

Replacing the weights used in an index with a new set of weights.

### Rolling year indices

A monthly series of indices that compares successive non-calendar years, each of 12 consecutive months, with a base calendar year. The monthly indices are constructed by comparing each month in the non-calendar year with the corresponding month in the base calendar year. The resulting indices can be regarded as seasonally adjusted price indices. For example, if the base calendar year is 2000, the index for January 2001 will refer to the non-calendar year February 2000 to January 2001: February 2000 will be compared with February 2000, March 2000 with March 2000, . . . . . . . . . ., December 2000 with December 2000, and January 2001 with January 2000. The index for February 2001 will refer to the non-calendar year March 2000 to February 2001: March 2000 will be compared with March 2000, April 2000 with April 2000, . . . . . . . . . ., January 2001 with January 2000, and February 2001 with February 2000, and so on for each month in the series.

### Sample augmentation

Maintaining and adding to the sample of establishments in the survey panel to ensure that it continues to be representative of the population of establishments. A fixed sample of establishments tends to become depleted as establishments cease producing or stop responding. Recruiting new establishments also facilitates the inclusion of new commodities in an XPI or an MPI.

### Sample rotation

Limiting the length of time that establishments and/or commodities are included in price surveys by dropping a proportion of them, or possibly all of them, after a certain period of time and selecting a new sample of establishments and/or commodities. Rotation is designed to keep the sample up to date. It also helps to alleviate the problems caused by sample depletion.

### Sampling error

A measure of the chance of a difference between the results obtained from the units sampled and the results that would have been obtained from a complete enumeration of all units in the universe.

### Sampling frame

The list of the units in the universe from which a sample of units is to be selected. It provides for each unit the details, such as the unit’s location, size, value, and type of exports and/or imports, required to pick the sample. Also referred to as the “survey frame.”

### Sauerbeck price index

A price index defined as the weighted arithmetic average of the current to previous period price relatives using the values of the base period as weights. The price reference period is the previous period (that is, the period immediately before the current period), and the weight reference period is some other fixed period before the previous period. A time-series index is derived by chaining, which, because the weight reference period remains fixed, can result in a serious upward drift in the index when price changes are large and erratic.

### Scope

The set of goods and services or transactions for which the index is intended to measure the price changes. In practice, certain goods and services may have to be excluded because it is too difficult, time-consuming, or costly to collect the required data on values or prices. The coverage of an index denotes the actual set of goods and services included, as distinct from the intended scope of the index. Also referred to as “domain.”

### Seasonal products

Products that either (1) are not available on the market during certain seasons or periods of the year or (2) are available throughout the year but with regular fluctuations in their quantities and prices that are linked to the season or time of year. A product that satisfies (1) is said to be “strongly seasonal.” A product that satisfies (2) is said to be “weakly seasonal.”

### Sector

A general term used to describe a group of establishments engaged in similar kinds of economic activity. A sector can be a subgroup of an economic activity—as in “coal mining sector”—or a group of economic activities—as in “service sector”—or a cross-section of a group of economic activities—as in “informal sector.” Also a specific term used in the SNA to denote one of the five mutually exclusive institutional sectors that group together institutional units on the basis of their principal functions, behavior, and objectives, namely: nonfinancial corporations, financial corporations, general government, nonprofit institutions serving households, and households.

### Services

Outputs produced to order and that cannot be traded separately from their production. Ownership rights cannot be established over services, and by the time their production is completed they must have been provided to the consumers. However, as an exception to this rule, there is a group of industries, generally classified as service industries, some of whose outputs have characteristics of goods. These are the industries concerned with the provision, storage, communication, and dissemination of information, advice, and entertainment in the broadest sense of those terms. The products of these industries, where ownership rights can be established, may be classified as either goods or services depending on the medium by which these outputs are supplied.

### Shipment price

The price at the time the order is delivered to the purchaser.

### SITC

Standard International Trade Classification. An internationally agreed commodity classification for the compilation and dissemination of statistics on international merchandised trade. SITC commodity groupings reflect (1) the nature of the product and the materials used in its production, (2) the stage of processing, (3) marketing practices and the uses of the product, (4) the importance of the product in world trade, and (5) technological changes. The original SITC was published in 1951 and has been revised periodically. It was last revised in 2006 (SITC Rev.4). There is full correspondence between the five-digit basic headings of SITC Rev.4 and the six-digit sub-headings of HS07.

### SNA 2008

System of National Accounts, 2008. A coherent, consistent, and integrated set of macroeconomic accounts, balance sheets, and tables based on a set of internationally agreed concepts, definitions, classifications, and accounting rules. The system first appeared in 1953 and since then has evolved, going through major revisions in 1968 and 1993. SNA 2008 is an update of SNA 1993, the version currently adhered to by most countries.

### SPDs

Structured product descriptions. The generic product descriptions used to define the product specifications to be priced for the ICP. An SPD refers to a product cluster. It lists the technical and economic characteristics that products constituting the cluster can possess. A product cluster usually covers a narrow range of homogeneous products, but variation in their common set of characteristics is to be expected. A product can therefore be distinguished from others in the cluster by identifying its specific subset of characteristics. The subset provides the basis for a product specification should the product be selected for pricing. See “product line specification.”

### Specification

A description or list of the characteristics that can be used to identify an individual sampled product to be priced. A tight specification is a fairly precise description of an item intended to narrow the range of items from which a price collector might choose, possibly reducing it to a unique item, such as a particular brand of television set identified by a specific code number. A loose definition is a generic description of a range of items that allows the price collector some discretion as to which particular item or model to select for pricing, such as color televisions sets of a particular screen size.

### Specification pricing

The pricing methodology whereby a manageable sample of precisely specified products is selected, in consultation with each reporting establishment, for repeat pricing. Products are fully defined in terms of all characteristics that influence their transaction prices. The objective is to price to constant quality in order to produce an index showing pure price change.

### Splicing

Introducing a replacement item and attributing any price change between the replacement item in the period it is introduced and the replaced item in the period prior to the introduction to the change in quality.

### Spot market price

A generic term referring to any short-term sales agreement. Generally it refers to single-shipment orders with delivery expected in less than one month. Goods sold on this basis are usually off-the-shelf and not subject to customization. Spot market prices are subject to discounting and directly reflect current market conditions.

### Stage of processing

The classification of goods and services according to their position in the chain of production. However, unlike the classification by stage of production, a product is allocated to only one stage even though it may occur in several stages. Goods and services are classified as either primary products, intermediate products, or finished products.

### Stage of production

The classification of goods and services according to their position in the chain of production, but allowing for the multi-function nature of products. Unlike the classification by stage of processing, a product is allocated to each stage to which it contributes and not assigned solely to one stage. Goods and services are classified as primary products, intermediate products, and/or finished products.

### Stochastic approach

The approach to index number theory that treats the observed price relatives as if they were a random sample drawn from a defined universe for which the mean can be interpreted as the general rate of inflation. The sample mean provides an estimate of the rate of inflation.

### Subsidies on products

The subsidies on goods or services produced as the outputs of resident enterprises that become payable as the result of the production of those goods or services. They are payable per unit of good or service produced.

### Subsidized prices

Prices that differ from market prices in that some significant portion of variable and/or fixed costs are covered by a revenue source other than the selling price.

### Substitution bias

The bias that results when a fixed basket index is used. By definition, the quantities of the goods and services in the basket to be priced are fixed, and so the index cannot take into account the effects of substitutions made by exporters or importers in response to changes in relative prices. Exporters seeking to maximize revenue may shift to exporting items with above-average relative price increases and, as a result, an XPI with base period quantities will systematically understate average price increases. Importers seeking to minimize costs may shift to importing items with below-average relative price increases and, as a result, an MPI with base period quantities will systematically overstate average price increases. The direction of the bias will be reversed if current period quantities are used—that is, the XPI will systematically overstate average price increases and the MPI will systematically understate them. See “FIOPI,” “FOIPI,” and “true index.”

### Superlative index

An index that is “exact” for a “flexible aggregator.” A flexible aggregator is a second-order approximation to an arbitrary cost, production, utility, or distance function. Exactness implies that a particular index number can be derived directly from a specific flexible aggregator. The Fisher price index, the Törnqvist price index, and the Walsh price index are superlative indices. Superlative indices are generally symmetric indices.

### Surcharge

An addition to the list price of a good or a service. It is generally of short duration, reflecting unusual cost pressures affecting the producer; for example, a fuel surcharge for transport operators.

### Survey frame

See “sampling frame.”

### SUTs

Supply and use tables. SUTs are in the form of matrices that record how supplies of different kinds of goods and services originate from domestic industries and imports and how those supplies are allocated between various intermediate and final uses, including exports.

### Symmetric index

An index that treats the two periods being compared symmetrically by attaching equal importance to the price and value data in both periods. The price and value data for both periods are entered into the index number formula in a symmetric or balanced way. The superlative price indices of Fisher, Törnqvist, and Walsh are symmetric indices, as are the pseudo-superlative price indices of Drobisch and Marshall-Edgeworth.

### Target index

The theoretical index that compilers would choose to calculate in the ideal hypothetical situation in which they have complete information about prices and quantities in the two periods being compared. In practice, the target index is likely to be an economic index as approximated by a superlative price index (such as a Fisher, Törnqvist, or Walsh) or a basket or Lowe index (usually a Laspeyres) that has a clear meaning and can be easily explained to users.

### Taxes on products

The taxes on goods or services produced as the outputs of resident enterprises that become payable as the result of the production of those goods or services. They are payable per unit of good or service produced.

The ratio of the export price index to the import price index: XPI/MPI. A terms of trade index shows the relationship between the prices at which a country sells its exports and the prices it pays for its imports. If the prices of a country’s exports rise relative to the prices of its imports, its terms of trade are said to have moved in a favorable direction, because, in effect, it now receives more imports for each unit it exports.

### Test approach

See “axiomatic approach.”

### Time aggregation problem

How to define and obtain the basic price and quantity for a precisely specified product included in a price index given that, during the time period under consideration, individual buyers may buy the same product at different prices and an individual seller may sell the same product at different prices.

### Time reversal test

A test under the axiomatic approach that requires that if the prices and quantities in the two periods being compared are interchanged, the resulting price index is the reciprocal of the original price index. When an index satisfies this test, the same result is obtained whether the direction of change is measured forward in time from the first to the second period or backward from the second to the first period.

### Törnqvist price index

A price index defined as the weighted geometric average of the current to base period price relatives in which the weights are the simple unweighted arithmetic averages of the value shares in the two periods. It is a symmetric index and a superlative index. Also known as the “Törnqvist-Theil price index.”

$\begin{array}{ll}\text{In}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{P}_{T}\equiv \mathrm{\Sigma }\frac{1}{2}\left({s}^{0}+{s}^{t}\right)\mathrm{I}\mathrm{n}\left(\frac{{p}^{t}}{{p}^{0}}\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{where}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{s}^{j}& \equiv -\frac{{p}^{j}{q}^{j}}{\mathrm{\Sigma }{p}^{j}{q}^{j}};\\ \hfill j& =t,0.\\ \text{Also written as}\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}{P}_{T}\equiv \mathrm{\Pi }{\left(\frac{{p}^{t}}{{p}^{0}}\right)}^{\frac{\left({s}^{0}+{s}^{t}\right)}{2}}.& \end{array}$

### Total factor productivity

Relates a measure of output to a measure of combined primary inputs. Rates of change of multi-factor productivity are typically measured residually as that change in output that cannot be accounted for by the change in combined inputs.

### Transaction

The buying and selling of a good or service on terms mutually agreed by the buyer and seller.

### Transaction price

See “market price.”

### Transfer price

A price adopted for bookkeeping purposes that is used to value transactions between affiliated enterprises integrated under the same management at artificially high or low levels in order to effect an unspecified income payment or capital transfer between those enterprises. See “intra-company transfer price.”

### Transitivity

See “circularity.”

### “True” index

A theoretically defined index that lies between the Laspeyres price index and the Paasche price index. For a theoretical XPI, the Laspeyres price index is the lower bound and the Paasche price index is the upper bound. For a theoretical MPI, the situation is reversed: the Paasche price index is the lower bound and the Laspeyres price index is the upper bound. See “FIOPI,” “FOIPI,” and “substitution bias.”

### Unequivocal price index

See “‘pure’ price index.”

### Unequivocal quantity index

See “‘pure’ quantity index.”

### Unilateral price index

One approach to index numbers involves decomposing a value aggregate for one period into two numbers: one representing the price level in the period and the other representing the quantity level in the period. The resulting price index is called a “unilateral price index.” “Unilateral” refers to the assumption that the price index depends only on price and quantity data of the period under consideration. It is also called an “absolute index number.”

### Unique product

A product that is manufactured only once to the specification of an individual customer.

### Unit value bias

The ratio of a unit value index to a price index calculated with an acceptable index number formula such as the Fisher price index. The term “bias” assumes a systematic divergence. If the divergence is not systematic, then the term “error” is more appropriate. See “bias.”

### Unit value index

An index that measures the change in the average unit value of items comprising an individual commodity class. The items may not be homogeneous, and the unit value index may therefore be affected by changes in the mix of items (compositional quality and quantity changes) as well as by changes in their prices. Unit value indices are not price indices, but serve as surrogates for price indices. A unit value elementary index, PU, is given for a price comparison between the current period 1 and reference period 0 over m = 1, . . . . , M items in period 1 and over n = 1, . . . , N items in period 0 by:

${P}_{U}\equiv \left(\frac{\underset{m=1}{\overset{M}{\mathrm{\Sigma }}}{p}_{m}^{1}{q}_{m}^{1}}{\underset{m-1}{\overset{M}{\mathrm{\Sigma }}}{q}_{m}^{1}}\right)/\left(\frac{\underset{n=1}{\overset{N}{\mathrm{\Sigma }}}{p}_{n}^{0}{q}_{n}^{0}}{\underset{n=1}{\overset{N}{\mathrm{\Sigma }}}{q}_{n}^{0}}\right)\phantom{\rule[-0.0ex]{0.2em}{0.0ex}}\text{where prices and}$

quantities are given respectively as ${p}_{m}^{1}$ and ${q}_{m}^{1}$ for period 1, and ${p}_{n}^{0}$ and ${q}_{n}^{0}$ for period 0.

### Unit value “mix” problem

That the change in the value of a unit value index, thereby implying a “price change,” arises from a change in the relative quantities of the items covered without any change in their prices.

### Universe

For an XPI, the population of exporters and exports to be sampled. For an MPI, the population of importers and imports to be sampled.

### Upper-level index

See “higher-level index.”

### Value

At the level of a single homogeneous good or service, value is equal to the price per unit of quantity multiplied by the number of quantity units of that good or service. Unlike price, value is independent of the choice of quantity unit. Values are expressed in terms of a common unit of currency and are commensurate and additive across different products. Quantities, on the other hand, are not commensurate and additive across different products even when measured in the same kind of physical units.

Gross value added is the value of output less the value of intermediate consumption. It is a measure of the contribution to GDP made by an individual producer, industry, or sector. It is the source from which the primary incomes of the SNA are generated. Net value added is the value of output less the values of both intermediate consumption and consumption of fixed capital.

### Value updating

See “price updating.”

### Value weights

The measures of the relative importance of products in the index. The weight reference period values or shares of the various elementary aggregates covered by the index. Being commensurate and additive across different products, value weights can be used at aggregation levels above the detailed product level. See “quantity weights.”

### VAT

Value-added tax. A wide-ranging tax usually designed to cover most or all goods and services. It is collected in stages by enterprises that are obliged to pay to government only the difference between the VAT on their sales and the VAT on their purchases for intermediate consumption or capital formation. VAT is not usually charged on exports.

### Virtual corporation

A partnership among several enterprises sharing complementary expertise created expressly to produce a product with a short–prospective life span, with the production of the product being controlled through a computerized network. The corporation is disbanded upon the conclusion of the product’s life span.

### Volume index

The weighted average of the proportionate changes in the quantities of a specified set of goods and services between two periods of time. The quantities compared must be homogeneous, while the changes for the different goods and services must be weighted by their economic importance as measured by their values in one or both periods.

### Walsh price index

A price index defined as the change in the value of a fixed intermediate basket of quantities. The quantities of the intermediate basket are geometric averages of the quantities of the base and current periods. It is a symmetric index and a superlative index.

${P}_{w}\equiv \frac{\mathrm{\Sigma }{p}^{t}{\left({q}^{t}{q}^{0}\right)}^{\frac{1}{2}}}{\mathrm{\Sigma }{p}^{0}{\left({q}^{t}{q}^{0}\right)}^{\frac{1}{2}}}$

### Weight reference period

The period of which the value shares serve as weights for a Young index, or of which the quantities make up the basket for a Lowe index. It does not have to have the same duration as the periods for which the index is calculated, and in the case of XMPIs is typically longer, a year or more, rather than a month or quarter. There may be no weight reference period when the value shares for the two periods are averaged, as in a Törnqvist index, or when the quantities are averaged, as in a Marshall-Edgeworth index and a Walsh index. See also “base period.”

### Weights

A set of numbers summing to unity that are used to calculate averages. Value shares sum to unity by definition and are used to weight price relatives or elementary price indices when these are averaged to obtain price indices or higher-level indices. Although quantities are frequently described as weights, they cannot serve as weights for the prices of different types of products whose quantities are not commensurate and that use different units of quantity that are not additive. The term “quantity weights” is generally used loosely to refer to the quantities that make up the basket of goods and services covered by an index and included in the value weights. See “quantity weights” and “value weights.”

### Wholesale price index

A measure that reflects changes in the prices paid for goods at various stages of distribution up to the point of retail. It can include prices of raw materials for intermediate and final consumption, prices of intermediate or unfinished goods, and prices of finished goods. The goods are usually valued at purchasers’ prices. For historical reasons, some countries call their PPI a “wholesale price index,” even though the index no longer measures changes in wholesale prices.

### XMPIs

Export and import price indices. The export price index (XPI) measures the average change over time in the prices of the goods and services supplied by residents of the economic territory of a country and used by non-residents (the rest of the world). The import price index (MPI) measures the average change over time in the prices of goods and services supplied by nonresidents (the rest of the world) and used by residents of the economic territory of a country.

### XPI

Export price index. See “XMPIs.”

### Year-over-year indices

Year-over-year monthly indices: Indices in which a given month in the current period is compared with the corresponding month in the base period. For example, if the current period is 2001 and the base period is 2000, January 2001 would be compared with January 2000, February 2001 with February 2000, March 2001 with March 2000, etc. There are in effect 12 separate series of indices, one for each month of the year. Year-over-year monthly indices are a means of dealing with seasonal variation. It is assumed that the patterns of seasonal variation remain the same month by month, year after year.

Year-on-year annual indices: The weighted average of the 12 year-over-year monthly indices. The weights are monthly value (revenue) shares of the base year or the current year or the average of the two, depending on the index number formulation.

### Young index

This manual specifically refers to the Young price index as a weighted arithmetic average of price ratios between the current period t and the price reference period 0, where the weights are value shares in a (usually) preceding period b.

${P}_{YO}\equiv \mathrm{\Sigma }{s}^{b}\left(\frac{{p}^{t}}{{p}^{0}}\right).$

More generally, a Young index can be defined as a weighted arithmetic average of price ratios between the current period t and the price reference period, where the weights are value shares (sn) that sum to 1. The Young index is thus defined as

${P}_{YO}\equiv \mathrm{\Sigma }{S}_{n}\left(\frac{{p}^{t}}{{p}^{0}}\right).$

Special cases include the Laspeyres index when ${S}_{n}={S}^{0}=\frac{{p}^{0}{q}^{0}}{\mathrm{\Sigma }{p}^{0}{q}^{0}}$ and the Paasche index when sn are hybrid weights using period t quantities valued at period 0 prices, that is, ${S}_{n}={S}^{0t}\equiv \frac{{p}^{0}{q}^{t}}{\mathrm{\Sigma }{p}^{0}{q}^{t}}.$

## Appendix: Some basic index number formulas and terminology

1. A basket price index (called here a Lowe price index after the index number pioneer who first proposed this general type of index) is an index of the form1

$\begin{array}{cc}\frac{\mathrm{\Sigma }{p}_{n}^{t}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}},& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\mathrm{G}.1\right)\end{array}$

which compares the prices of period t with those of (an earlier) period 0, using a certain specified quantity basket. The family of Lowe indices includes some well-known indices as special cases:

• When ${q}_{n}={q}_{n}^{0},$, we get the Laspeyres index;

• When ${q}_{n}={q}_{n}^{t},$, we get the Paasche index;

• When ${q}_{n}=\left({q}_{n}^{0}+{q}_{n}^{1}\right)/2,$, we get the Marshall-Edgeworth index; and

• When ${q}_{n}={\left({q}_{n}^{0}{q}_{n}^{t}\right)}^{1/2},$, we get the Walsh index.

In practice, official statistical agencies frequently work with a Lowe index in which ${q}_{n}={q}_{n}^{b}$, where b denotes some period before 0.

2. A useful feature of a basket price index for period t relative to period 0 is that it can be decomposed, or factored, into the product of two or more indices of the same type: for instance, as the product of an index for period t – 1 relative to period 0 and an index for period t relative to period t – 1. Formally,

$\begin{array}{cc}\frac{\mathrm{\Sigma }{p}_{n}^{t}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}}=\frac{\mathrm{\Sigma }{p}_{n}^{t-1}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}}\frac{\mathrm{\Sigma }{p}_{n}^{t}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{t-1}{q}_{n}}.& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\mathrm{G}.2\right)\end{array}$

The index on the right side of equation (G.2) is described as a “two-stage index.” It is identical to the single-basket index that compares period t directly with period 0, provided the same set of prices is available and used in all three periods, 0, t – 1, and t.

In particular, when ${q}_{n}={q}_{n}^{0},$, equation (G.2) turns into

$\begin{array}{cc}\frac{\mathrm{\Sigma }{p}_{n}^{t}{q}_{n}^{0}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}^{0}}=\frac{\mathrm{\Sigma }{p}_{n}^{t-1}{q}_{n}^{0}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}^{0}}\frac{\mathrm{\Sigma }{p}_{n}^{t}{q}_{n}^{0}}{\mathrm{\Sigma }{p}_{n}^{t-1}{q}_{n}^{0}}.& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\mathrm{G}.3\right)\end{array}$

The left side of equation (G.3) is a direct Laspeyres index. Note that only the first of the indices that make up the “two-stage Laspeyres” index on the right side is itself a Laspeyres index, the second being a Lowe index for period t relative to period t – 1 that uses the quantity basket of period 0 (not t – 1). Some official statistical agencies describe the two-stage Laspeyres index given in equation (G.3) as a “modified Laspeyres” index.

3. In a time-series context, say when t runs from 1 to T, the series

$\begin{array}{cc}\frac{\mathrm{\Sigma }{p}_{n}^{1}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}},\frac{\mathrm{\Sigma }{p}_{n}^{2}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}},......,\frac{\mathrm{\Sigma }{p}_{n}^{T}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}}& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\mathrm{G}.4\right)\end{array}$

is termed a series of fixed-basket price indices. In particular, when ${q}_{n}={q}_{n}^{0},$, we get a series of Laspeyres indices.

4. At period T, one could change to a new quantity basket q’ and calculate from this period onward

$\begin{array}{cc}\frac{\mathrm{\Sigma }{p}_{n}^{T+1}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{T}{q}_{n}},\frac{\mathrm{\Sigma }{p}_{n}^{T+2}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{T}{q}_{n}},\frac{\mathrm{\Sigma }{p}_{n}^{T+3}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{T}{q}_{n}},.....& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\mathrm{G}.5\right)\end{array}$

To relate the prices of periods T + 1, T + 2, T + 3, . . . . to those of period 0, chain linking can be used to transform (G.5) into a series of the form

$\begin{array}{cc}\frac{\mathrm{\Sigma }{p}_{n}^{T}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}}\frac{\mathrm{\Sigma }{p}_{n}^{T+1}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{T}{q}_{n}},\frac{\mathrm{\Sigma }{p}_{n}^{T}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}}\frac{\mathrm{\Sigma }{p}_{n}^{T+2}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{T}{q}_{n}},& \\ \frac{\mathrm{\Sigma }{p}_{n}^{T}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}}\frac{\mathrm{\Sigma }{p}_{n}^{T+3}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{T}{q}_{n}},......\hfill & \begin{array}{c}\phantom{\rule[-0.0ex]{4.0em}{0.0ex}}\left(\mathrm{G}.6\right)\end{array}\end{array}$

This could be termed a series of chain-linked fixed-basket price indices. In particular, when ${q}_{n}={q}_{n}^{0}$ and, ${q}_{n}={q}_{n}^{T}$ we get a series of chain-linked Laspeyres indices. Because the basket was changed at period T, the adjective “fixed” applies literally over only a certain number of time intervals. The basket was fixed from period 1 to period T and is fixed again from period T + 1 onward. When the time intervals during which the basket is kept fixed are of the same length, such as one, two, or five years, this feature can be made explicit by describing the index as an annual, biannual, or five-yearly chain-linked fixed-basket price index.

5. A weighted arithmetic2-average(-type) price index (called here a Young price index after another index number pioneer) is an index of the form

$\begin{array}{c}\begin{array}{cc}\mathrm{\Sigma }{w}_{n}\left({p}_{n}^{t}/{p}_{n}^{0}\right)& \begin{array}{c}\phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\mathrm{G}.7\right)\end{array}\end{array}\end{array}$

which compares the prices of period t with those of period 0, using a certain set of weights adding up to 1. Note that any basket price index in the form of equation (G.1) can be expressed in the form of equation (G.7), because

$\begin{array}{cc}\frac{\mathrm{\Sigma }{p}_{n}^{t}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}}=\mathrm{\Sigma }\frac{{p}_{n}^{0}{q}_{n}}{\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}}\frac{{p}_{n}^{t}}{{p}_{n}^{0}}.& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\mathrm{G}.8\right)\end{array}$

In particular, when

$\begin{array}{cc}\left(i\right)\text{\hspace{0.17em}}{w}_{n}={s}_{n}^{0}\equiv {p}_{n}^{0}{q}_{n}^{0}/\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}^{0},& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\begin{array}{c}\left(\mathrm{G}.9\right)\end{array}\end{array}$

that is, period 0 value shares, equation (G.7) turns into the Laspeyres index. When

$\begin{array}{cc}\left(ii\right)\text{\hspace{0.17em}}{w}_{n}={p}_{n}^{0}{q}_{n}^{t}/\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}^{t},& \begin{array}{c}\phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\mathrm{G}.10\right)\end{array}\end{array}$

that is, hybrid period (0, t) value shares, we get the Paasche index. One could also think of setting

$\begin{array}{cc}\left(iii\right)\text{\hspace{0.17em}}{w}_{n}={S}_{n}^{b}\equiv {p}_{n}^{b}{q}_{n}^{b}/\mathrm{\Sigma }{p}_{n}^{b}{q}_{n}^{b},& \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\mathrm{G}.11\right)\end{array}$

that is, period b value shares.3

Instead of working with equation (G.11), one frequently works with

$\begin{array}{ccc}\hfill \left(iv\right)\text{\hspace{0.17em}}{w}_{n}& ={S}_{n}^{b}\left({p}_{n}^{0}/{p}_{n}^{b}\right)/\mathrm{\Sigma }{S}_{n}^{b}\left({p}_{n}^{0}/{p}_{n}^{b}\right)\hfill & \\ & ={p}_{n}^{0}{q}_{n}^{b}/\mathrm{\Sigma }{p}_{n}^{0}{q}_{n}^{b},\hfill & \phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\left(\mathrm{G}.12\right)\hfill \end{array}\phantom{\rule{0ex}{0ex}}$

that is, price-updated period b value shares.

Note that hybrid value shares, such as equation

(G.10) or (G.12), typically are not constructed by multiplying sums of prices of one period times quantities of another period. They must be constructed using price relatives and actual expenditure shares, as in the first part of equation (G.12).

6. In a time-series context, when t runs from 1 to T, the series

$\begin{array}{cc}\mathrm{\Sigma }{w}_{n}\left({p}_{n}^{1}/{p}_{n}^{0}\right),\text{\hspace{0.17em}}\mathrm{\Sigma }{w}_{n}\left({p}_{n}^{2}/{p}_{n}^{0}\right),\text{\hspace{0.17em}}......,\hfill & \\ \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\phantom{\rule[-0.0ex]{3.0em}{0.0ex}}\phantom{\rule[-0.0ex]{3.0em}{0.0ex}}\mathrm{\Sigma }{w}_{n}\left({p}_{n}^{T}/{p}_{n}^{0}\right)\text{\hspace{0.17em}}& \phantom{\rule[-0.0ex]{3.0em}{0.0ex}}\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\left(\mathrm{G}.13\right)\hfill \end{array}\phantom{\rule{0ex}{0ex}}\text{\hspace{0.17em}}$

is termed a series of fixed weighted arithmetic-average price indices. In particular, when the weights are equal to the period 0 expenditure shares, we get a series of Laspeyres indices, and when the weights are equal to the price-updated period b expenditure shares, we get a series of Lowe indices in which the quantities in the basket are those of period b.

7. In period T, one could change to a new set of weights w’, and calculate from this period onward

$\text{\hspace{0.17em}}\begin{array}{cc}\hfill \mathrm{\Sigma }w{\prime }_{n}\left({p}_{n}^{T+1}/{p}_{n}^{T}\right),\mathrm{\Sigma }w{\prime }_{n}\left({p}_{n}^{T+1}/{p}_{n}^{T}\right),& \\ \hfill \mathrm{\Sigma }w{\prime }_{n}\left({p}_{n}^{T+3}/{p}_{n}^{T}\right),....,& \phantom{\rule[-0.0ex]{4.0em}{0.0ex}}\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\left(\mathrm{G}.14\right)\end{array}$

or, using linking to relate the prices of periods T + 1, T + 2, T + 3, . . . . to those of period 0,

$\begin{array}{cc}\mathrm{\Sigma }{w}_{n}\left({p}_{n}^{T}/{p}_{n}^{0}\right)\mathrm{\Sigma }w{\prime }_{n}\left({p}_{n}^{T+1}/{p}_{n}^{T}\right),\text{\hspace{0.17em}}\hfill & \\ \mathrm{\Sigma }{w}_{n}\left({p}_{n}^{T}/{p}_{n}^{0}\right)\mathrm{\Sigma }w{\prime }_{n}\left({p}_{n}^{T+2}/{p}_{n}^{T}\right),......\hfill & \phantom{\rule[-0.0ex]{5.0em}{0.0ex}}\left(\mathrm{G}.15\right)\end{array}\phantom{\rule{0ex}{0ex}}$

This could be termed a series of linked fixed-weighted arithmetic-average price indices. In particular, when ${w}_{n}={s}_{n}^{0}$ and ${w}_{n}={S}_{n}^{T},$, we get a series of chain-linked Lowe indices. When ${w}_{n}={s}_{n}^{b}\left({p}_{n}^{0}/{p}_{n}^{b}\right)/\mathrm{\Sigma }{S}_{n}^{b}\left({p}_{n}^{0}/{p}_{n}^{b}\right)$ and ${w}_{n}={S}_{n}^{b}\left({p}_{n}^{T}/{p}_{n}^{b}\right)/\mathrm{\Sigma }{S}_{n}^{b}\left({p}_{n}^{T}/{p}_{n}^{b}\right)$ for some later period b’, we get a series of chain-linked Laspeyres indices.

8. Again, because the weights were changed at period T, the adjective “fixed” applies literally over only certain time intervals. The weights were fixed from period 1 to period T and are again fixed from period T + 1 onward. When the time intervals during which the weights are kept fixed are of the same length, this feature can be made explicit by adding a temporal adjective, such as biannual or five-yearly. When the intervals are annual, the term “chain-linking” is used.

The sums are understood to be running over all items n.

To distinguish from geometric or other kinds of average.

This manual specifically refers to this as a Young index.

## Bibliography

• Abraham, Katherine G., John S. Greenlees, and Brent R. Moulton, 1998, “Working to Improve the Consumer Price Index,” Journal of Economic Perspectives, Vol. 12 (Winter), pp. 2736.

• Export Citation
• Aczél, J., 1987, A Short Course on Functional Equations: Based Upon Recent Applications to the Social and Behavioral Sciences (Dordrecht, Netherlands: Reidel).

• Export Citation
• Aizcorbe, Ana, Carol Corrado, and Mark Doms, 2001, “Constructing Price and Quantity Indexes for High Technology Goods” (Washington: Industrial Output Section, Division of Research and Statistics, Board of Governors of the Federal Reserve System, July). Also available asWhen Do Matched-Model and Hedonic Techniques Yield Similar Measures?Federal Reserve Bank of San Francisco Working Paper No. 2003-14. Available via the Internet: http://www.frbsf.org/publications/economics/papers/index.php?2005.

• Export Citation
• Allen, Robert D., and W. Erwin Diewert, 1981, “Direct Versus Implicit Superlative Index Number Formulae,” Review of Economics and Statistics, Vol. 63 (August), pp. 43035.

• Export Citation
• Alterman, William, 1991, “Price Trends in U.S. Trade: New Data, New Insights,” in International Economic Transactions, NBER Studies in Income and Wealth Vol. 55, ed. by Peter Hooper and J. David Richardson (Chicago: University of Chicago Press).

• Export Citation
• Alterman, W.F., W. Erwin Diewert, and Robert C. Feenstra, eds., 1999, International Trade Price Indexes and Seasonal Commodities (Washington: Bureau of Labor Statistics).

• Export Citation
• Alterman, William, David S. Johnson, and John Goth, 1987, “BLS Publishes Average Exchange Rate and Foreign Currency Price Indexes,” Monthly Labor Review (December), pp. 4749.

• Export Citation
• Anderson, Richard G., Barry E. Jones, and Travis Nesmith, 1997, “Building New Monetary Services Indexes: Concepts, Data and Methods,” Federal Reserve Bank of St. Louis Review, Vol. 79 (January/February), pp. 5383.

• Export Citation
• Angermann, Oswald, 1980, “External Terms of Trade of the Federal Republic of Germany Using Different Methods of Deflation,” Review of Income and Wealth, Vol. 26 (December), pp. 36785.

• Export Citation
• Archibald, Robert B., 1977, “On the Theory of Industrial Price Measurement: Output Price Indexes,” Annals of Economic and Social Measurement, Vol. 6, No. 1, pp. 5772.

• Export Citation
• Arguea, N.M., C. Hsiao, and G.A. Taylor, 1994, “Estimating Consumer Preferences Using Market Data—An Application to U.S. Automobile Demand,” Journal of Applied Econometrics, Vol. 9 (January–March), pp. 118.

• Export Citation
• Armknecht, Paul A., Walter F. Lane, and Kenneth J. Stewart, 1997, “New Products and the U.S. Consumer Price Index,” in The Economics of New Goods, NBER Studies in Income and Wealth Vol. 58, ed. by Timothy F. Bresnahan and Robert J. Gordon (Chicago: University of Chicago Press), pp. 37591.

• Export Citation
• Armknecht, Paul A., and Fenella Maitland-Smith, 1999, “Price Imputation and Other Techniques for Dealing with Missing Observations, Seasonality and Quality Change in Price Indices,” IMF Working Paper 99/78 (Washington: International Monetary Fund).

• Export Citation
• Armknecht, Paul A., and Fenella Maitland-Smith, 2002, “Spurious Inflation: The Legacy of Laspeyres and Others,” Quarterly Review of Economics and Finance, Vol. 42 (Autumn) pp. 52942.

• Export Citation
• Australian Bureau of Statistics, 1995, “Producer and International Trade Price Indexes,” Catalogue No. 6419.0 (Canberra). Available via the Internet: www.abs.gov.au.

• Export Citation
• Australian Bureau of Statistics, 2001, “Stages of Production Producer Price Indexes,” Australia, Catalogue No. 6426.0 (Canberra). Available via the Internet: www.abs. gov.au.

• Export Citation
• Baldwin, Andrew, 1990, “Seasonal Baskets in Consumer Price Indexes,” Journal of Official Statistics, Vol. 6 (September), pp. 25173.

• Export Citation
• Baldwin, Andrew, 2002, “The Redesign of the Farm Product Price Index: Questions and Answers” (Ottawa: Industry Measures and Analysis Division, Statistics Canada, May).

• Export Citation
• Balk, Bert M., 1980a, Seasonal Products in Agriculture and Horticulture and Methods for Computing Price Indices, Statistical Studies No. 24 (The Hague: Netherlands Central Bureau of Statistics).

• Export Citation
• Balk, Bert M., 1980b, “Seasonal Commodities and the Construction of Annual and Monthly Price Indexes,” Statistical Papers, Vol. 21 (June), pp. 11016.

• Export Citation
• Balk, Bert M., 1980c, “A Method for Constructing Price Indices for Seasonal Commodities,” Journal of the Royal Statistical Society, Series A, Vol. 143, No. 1 pp. 6875.

• Export Citation
• Balk, Bert M., 1981, “A Simple Method for Constructing Price Indices for Seasonal Commodities,” Statistical Papers, Vol. 22 (March), pp. 7278.

• Export Citation
• Balk, Bert M., 1983, “Does There Exist a Relation Between Inflation and Relative Price-Change Variability? The Effect of the Aggregation Level,” Economics Letters, Vol. 13, (No. 2–3), pp. 17380.

• Export Citation
• Balk, Bert M., 1985, “A Simple Characterization of Fisher’s Price Index,” Statistical Papers, Vol. 26 (December), pp. 5963.

• Balk, Bert M., 1989, “Changing Consumer Preferences and the Cost-of-Living Index: Theory and Nonparametric Expressions,” Journal of Economics, Vol. 50 (June), pp. 15769.

• Export Citation
• Balk, Bert M., 1994, “On the First Step in the Calculation of a Consumer Price Index,” paper prepared for the International Conference on Price Indices, First Meeting hosted by Statistics Canada, Ottawa, October 31–November 4.

• Export Citation
• Balk, Bert M., 1995, “Axiomatic Price Index Theory: A Survey,” International Statistical Review, Vol. 63, pp. 6993.

• Balk, Bert M., 1996a, “A Comparison of Ten Methods for Multilateral International Price and Volume Comparison,” Journal of Official Statistics, Vol. 12 (June), pp. 199222.

• Export Citation
• Balk, Bert M., 1996b, “Consistency-in-Aggregation and Stuvel Indices,” Review of Income and Wealth, Vol. 42 (September), pp. 35363.

• Export Citation
• Balk, Bert M., 1998a, Industrial Price, Quantity, and Productivity Indices: The Micro-Economic Theory and an Application (Boston: Kluwer Academic).

• Export Citation
• Balk, Bert M., 1998b, “On the Use of Unit Value Indices as Consumer Price Subindices,” paper prepared for the International Conference on Price Indices, Fourth Meeting hosted by the Bureau of Labor Statistics, Washington, April 22–24.

• Export Citation
• Balk, Bert M., 2000a, “Divisia Price and Quantity Indexes 75 Years After” (unpublished; Voorburg, Netherlands: Department of Statistical Methods, Statistics Netherlands).

• Export Citation
• Balk, Bert M., 2000b, “On Curing the CPI’s Substitution and New Goods Bias,” Research Paper 0005 (Voorburg, Netherlands: Department of Statistical Methods, Statistics Netherlands). Presented at the Fifth Meeting of the International Working Group on Price Indices, 25–27 August 1999, Reykjavik; at the Joint ECE/ILO Meeting on Consumer Price Indices, 3–5 November 1999, Geneva; and at the Fourth Conference on Methodological Issues in Official Statistics, 12–13 October 2000, Stockholm.

• Export Citation
• Balk, Bert M., 2001, “Aggregation Methods in International Comparisons: What Have We Learned?” Report Series Research in Management ERS-2001-41-MKT, Erasmus Research Institute of Management (Rotterdam: Erasmus University). Available via the Internet: www.rsm.nl/portal/pls/portal/xopus_public.download_document?p_ guid=298255C5FD4A09A2E0401BAC4D010CA9.

• Export Citation
• Balk, Bert M., 2004, “Decompositions of Fisher Indexes,” Economics Letters, Vol. 82 (January), pp. 10713.

• Balk, Bert M., 2005, “Price Indexes for Elementary Aggregates: The Sampling Approach,” Journal of Official Statistics, Vol. 21 (December), pp. 67599.

• Export Citation
• Balk, Bert M., and W. Erwin Diewert, 2001, “A Characterization of the Törnqvist Price Index,” Economics Letters, Vol. 72 (September), pp. 27981.

• Export Citation
• Balk, Bert M., and H.M.P. Kersten, 1986, “On the Precision of Consumer Price Indices Caused by the Sampling Variability of Budget Surveys,” Journal of Economic and Social Measurement, Vol. 14, pp. 1935.

• Export Citation
• Bartik, Timothy J., 1988, “Measuring the Benefits of Amenity Improvements in Hedonic Price Models,” Land Economics, Vol. 64 (May), pp. 17283.

• Export Citation
• Barnett, William, 1978, “The User Cost of Money,” Economics Letters, Vol. 1, No. 22, pp. 14549.

• Barnett, William, 1980, “Economic Monetary Aggregates: An Application of Index Number and Aggregation Theory,” Journal of Econometrics, Vol. 14 (September), pp. 1148.

• Export Citation
• Bean, L.H., and O.C. Stine, 1924, “Four Types of Index Numbers of Farm Prices,” Journal of the American Statistical Association, Vol. 19 (March), pp. 3035.

• Export Citation
• Becker, Gary S., 1965, “A Theory of the Allocation of Time,” Economic Journal, Vol. 75 (September), pp. 493517.

• Bénabou, Roland, and Robert Gertner, 1993, “Search with Learning from Prices: Does Increased Inflationary Uncertainty Lead to Higher Markups?Review of Economic Studies, Vol. 60 (January), pp. 6994.

• Export Citation
• Berndt, Ernst R., 1983, “Quality Adjusted Prices, Hedonics, and Modern Empirical Demand Theory,” in Price Level Measurement: Proceedings from a Conference Sponsored by Statistics Canada, ed. by W. Erwin Diewert and C. Montmarquette (Ottawa: Statistics Canada), pp. 81763.

• Export Citation
• Berndt, Ernst R., 1991, The Practice of Econometrics: Classic and Contemporary (Reading Massachusetts: Addison–Wesley).

• Berndt, Ernst R., Linda T. Bui, David H. Lucking-Reiley, and Glen L. Urban, 1997, “The Roles of Marketing, Product Quality, and Price Competition in the Growth and Composition of the U.S. Antiulcer Drug Industry,” in The Economics of New Goods, NBER Studies in Income and Wealth Vol. 58, ed. by Timothy F. Bresnahan and Robert J. Gordon (Chicago: University of Chicago Press), pp. 27732.

• Export Citation
• Berndt, Ernst R., Zvi Griliches, and Neal J. Rappaport, 1995, “Econometric Estimates of Price Indexes for Personal Computers in the 1990’s,” Journal of Econometrics, Vol. 68 (July), pp. 24368.

• Export Citation
• Berndt, Ernst R., Zvi Griliches, and Joshua G. Rosett, 1993, “Auditing the Producer Price Index: Micro Evidence from Prescription Pharmaceutical Preparations,” Journal of Business and Economic Statistics, Vol. 11 (July), pp. 25164.

• Export Citation
• Berndt, Ernst R., Margaret K. Kyle, and Davina C. Ling, 2003, “The Long Shadow of Patent Expiration: Generic Entry and RX-to-OTC Switches,” in Scanner Data and Price Indexes, NBER Studies in Income and Wealth Vol. 64, ed. by Robert C. Feenstra and Matthew D. Shapiro (Chicago: University of Chicago Press), pp. 22973.

• Export Citation
• Berry, Steven, James Levinsohn, and Ariel Pakes, 1995, “Automobile Prices in Market Equilibrium,” Econometrica, Vol. 63 (July), pp. 84190. Also published as NBER Working Paper No. 4264, July 1996 (Cambridge, Massachusetts: National Bureau of Economic Research). Available via the Internet: www.nber.org/papers/w4264.

• Export Citation
• Blackorby, Charles, Daniel Primont, and R. Robert Russell, 1978, Duality, Separability, and Functional Structure: Theory and Economic Applications (New York: Elsevier North-Holland).

• Export Citation
• Bodé, Ben, and Jan van Dalen, 2001, “Quality-Corrected Price Indexes of New Passenger Cars in the Netherlands, 1990–1999,” paper prepared for the International Conference on Price Indices, Sixth Meeting, hosted by the Australian Bureau of Statistics, Canberra, April 2–6.

• Export Citation
• Bortkiewicz, L.v., 1923, “Zweck und Struktur einer Preisindexzahl,” Nordisk Statistisk Tidskrift, Vol. 2, pp. 369408.

• Boskin, Michael J.S., chair, 1996, “Toward a More Accurate Measure of the Cost of Living,” Final Report to the Senate Finance Committee, Advisory Commission to Study the Consumer Price Index, Washington, December 4.

• Export Citation
• Boskin, Michael J.S., chair, Ellen R. Dulberger, Robert J. Gordon, Zvi Griliches, and Dale W. Jorgenson, 1998, “Consumer Prices, the Consumer Price Index, and the Cost of Living,” Journal of Economic Perspectives, Vol. 12 (Winter), pp. 326.

• Export Citation
• Bowley, Arthur L., 1899, “Wages, Nominal and Real,” in Dictionary of Political Economy, Vol. 3, ed. by R.H. Inglis Palgrave (London: Macmillan), pp. 64051.

• Export Citation
• Bowley, Arthur L., 1901, Elements of Statistics (London: P.S. King & Son).

• Bowley, Arthur L., 1919, “The Measurement of Changes in the Cost of Living,” Journal of the Royal Statistical Society, Vol. 82, pp. 34372.

• Export Citation
• Bowley, Arthur L., 1921, “An Index of the Physical Volume of Production,” Economic Journal, Vol. 31 (June), pp. 196205.

• Bowley, Arthur L., 1922, “The Definition of National Income,” Economic Journal, Vol. 32 (June), pp. 111.

• Bradley, Ralph, 2005, “Pitfalls of Using Unit Values as a Price Measure or Price Index,” Journal of Economic and Social Measurement, Vol. 30, No. 1, pp. 3961.

• Export Citation
• Bradley, Ralph, Bill Cook, Sylvia G. Leaver, and Brent R. Moulton, 1997, “An Overview of Research on Potential Uses of Scanner Data in the U.S. CPI,” paper prepared for the International Conference on Price Indices, Third Meeting, hosted by Statistics Netherlands, Voorburg, April 16–18.

• Export Citation
• Bresnahan, Timothy F., 1997, “Comment” on Jerry R. Hausman’sValuation of New Goods under Perfect and Imperfect Conditions,” in The Economics of New Goods, NBER Studies in Income and Wealth Vol. 58, ed. by Timothy F. Bresnahan and Robert J. Gordon (Chicago: University of Chicago Press).

• Export Citation
• Bucknall, Robert, Markus Sova, and John Wood, 2005Estimating Standard Errors of Movements in Producer Price Indices,” in Proceedings of the GSS Methodology Conference 2005 (London: Office for National Statistics). Available at www.statistics.gov.uk/events/gss2005/agenda.asp.

• Export Citation
• Bureau of the Census, 2002, “U.S. Goods Trade: Imports and Exports by Related Parties; 2001,” United States Department of Commerce News, Economics and Statistics Information, Bureau of the Census, May 7. Available via the Internet: www.census.gov/foreign-trade/Press-Release/2001pr/aip/rp01.pdf.

• Export Citation
• Burns, Arthur F., 1930, “The Measurement of the Physical Volume of Production,” Quarterly Journal of Economics, Vol. 44 (February), pp. 24262.

• Export Citation
• Carli, Gian-Rinaldo, 1804, “Del valore e della proporzione de’ metalli monetati,” in Scrittori classici italiani di economia politica, Vol. 13, by Domenico di Gennaro Cantalupo, Giovanni Rinaldo Carli, Pietro Verri (Milan: G.G. Destefanis), pp. 297366. Originally published in 1764.

• Export Citation
• Carruthers, A.G., D.J. Sellwood, and P.W. Ward, 1980, “Recent Developments in the Retail Prices Index,” The Statistician, Vol. 29 (March), pp. 132.

• Export Citation
• Cas, Alexandra, and Thomas K. Rymes, 1991, On Concepts and Measures of Multifactor Productivity in Canada 1961–1980 (London: Cambridge University Press).

• Export Citation
• Cassel, Eric, and Robert Mendelsohn, 1985, “On the Choice of Functional Forms for Hedonic Price Equations: Comment,” Journal of Urban Economics, Vol. 18 (September), pp. 13542.

• Export Citation
• Caves, Douglas W., Laurits R. Christensen, and W. Erwin Diewert, 1982a, “Multilateral Comparisons of Output, Input and Productivity Using Superlative Index Numbers,” Economic Journal, Vol. 92 (March), pp. 7386.

• Export Citation
• Caves, Douglas W., Laurits R. Christensen, and W. Erwin Diewert, 1982b, “The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity,” Econometrica, Vol. 50, (November), pp. 13931414.

• Export Citation
• Cecchetti, Stephen G., 1997, “Measuring Short-Run Inflation for Central Bankers,” Federal Reserve Bank of St. Louis Review, Vol. 79 (May/June), pp. 14355.

• Export Citation
• Christensen, Laurits R., Dale W. Jorgenson, and L.J. Lau, 1971, “Conjugate Duality and the Transcendental Logarithmic Production Function,” Econometrica, Vol. 39 (July), pp. 25556.

• Export Citation
• Clements, Kenneth W., and H.Y. Izan, 1981, “A Note on Estimating Divisia Index Numbers,” International Economic Review, Vol. 22 (October), pp. 74547.

• Export Citation
• Clements, Kenneth W., and H.Y. Izan, 1987, “The Measurement of Inflation: A Stochastic Approach,” Journal of Business and Economic Statistics, Vol. 5 (July), pp. 33950.

• Export Citation
• Cobb, Charles W., and Paul H. Douglas, 1928, “A Theory of Production,” American Economic Review, Vol. 18 (March), pp. 13965.

• Cochran, William G., 1977, Sampling Techniques (New York: Wiley; 3rd ed.).

• Cockburn, Iain M., and Aslam H. Anis, 1998, “Hedonic Analysis and Arthritic Drugs,” NBER Working Paper No. 6574 (Cambridge, Massachusetts: National Bureau of Economic Research). Available via the Internet: www.nber.org/papers/w6574.

• Export Citation
• Coggeshall, F., 1886, “The Arithmetic, Geometric, and Harmonic Means,” Quarterly Journal of Economics, Vol. 1 (October), pp. 8386.

• Export Citation
• Commission of the European Communities (Eurostat), International Monetary Fund, Organisation for Economic Cooperation and Development, United Nations, and World Bank, 1993, System of National Accounts 1993 (New York: United Nations).

• Export Citation
• Commission of the European Communities, International Monetary Fund, Organization for Economic Cooperation and Development, United Nations, and World Bank, 2008, System of National Accounts 2008, Volume 1 (New York: United Nations). Available via the Internet: http://unstats.un.org/unsd/sna1993/draftingphase/ChapterList.asp.

• Export Citation
• Cope, Ian, and David Freeman, 1998, “Improving the Quality of the Producer Price Index,” Economic Trends, No. 541, pp. 6374.

• Copithorne, L., 1976, “La théorie des prix des transfert internes des grandes sociétés,” L’actualité économique, Vol. 52, pp. 32452.

• Export Citation
• Court, Andrew T., 1939, “Hedonic Prices with Automobile Examples,” in The Dynamics of Automobile Demand (New York: General Motors Corporation), pp. 99117.

• Export Citation
• Court, L.M., and H.G. Lewis, 1942–43, “Production Cost Indices,” Review of Economic Studies, Vol. 10 (Winter), pp. 2842.

• Cropper, Maureen L., Leland B. Deck, and Kenneth E. McConnell, 1988, “On the Choice of Functional Form for Hedonic Price Functions,” Review of Economics and Statistics, Vol. 70 (Nov), pp. 66875.

• Export Citation
• Crump, Norman, 1924, “The Interrelation and Distribution of Prices and Their Incidence upon Price Stabilization,” Journal of the Royal Statistical Society, Vol. 87 (March), pp. 167219.

• Export Citation
• Curry, Bruce, Peter Morgan, and Mick Silver, 2001, “Hedonic Regressions: Misspecification and Neural Networks,” Applied Economics, Vol. 33 (April), pp. 65971.

• Export Citation
• Czinkota, Michael R., and Ilkka Ronkainen, 1997, “International Business and Trade in the Next Decade: Report from a Delphi Study,” Journal of International Business Studies, Vol. 28 (December), pp. 82744.

• Export Citation
• Dalén, Jörgen, 1992, “Computing Elementary Aggregates in the Swedish Consumer Price Index,” Journal of Official Statistics, Vol. 8 (June), pp. 12947.

• Export Citation
• Dalén, Jörgen, 1994, “Sensitivity Analyses for Harmonising European Consumer Price Indices,” paper presented at the International Conference on Price Indices, First Meeting, hosted by Statistics Canada, Ottawa, October 31–November 4.

• Export Citation
• Dalén, Jörgen, 1997, “Experiments with Swedish Scanner Data,” paper presented at the International Conference on Price Indices, Third Meeting, hosted by Statistics Netherlands, Voorburg, April 16–18.

• Export Citation
• Dalén, Jörgen, 1998, “On the Statistical Objective of a Laspeyres’ Price Index,” paper prepared for the International Conference on Price Indices, Fourth Meeting, hosted by the Bureau of Labor Statistics, Washington, April 22–24.

• Export Citation
• Dalén, Jörgen, 2001, “Statistical Targets for Price Indexes in Dynamic Universes,” paper presented at the International Conference on Price Indices, Sixth Meeting, hosted by the Australian Bureau of Statistics, Canberra, April 2–6.

• Export Citation
• Davies, George R., 1924, “The Problem of a Standard Index Number Formula,” Journal of the American Statistical Association, Vol. 19, pp. 18088.

• Export Citation
• Davies, George R., 1932, “Index Numbers in Mathematical Economics,” Journal of the American Statistical Association, Vol. 27, pp. 5864.

• Export Citation
• de Haan, Jan, 2001, “Generalised Fisher Price Indexes and the Use of Scanner Data in the CPI,” paper presented at the International Conference on Price Indices, Sixth Meeting, hosted by the Australian Bureau of Statistics, Canberra, April 2–6.

• Export Citation
• de Haan, 2003, “Direct and Indirect Time Dummy Approaches to Hedonic Price Measurement,” paper presented at the International Conference on Price Indices, Seventh Meeting, hosted by INSEE, Paris, May 27–29.

• Export Citation
• de Haan, 2004, “Estimating Quality-Adjusted Unit Value Indexes: Evidence from Scanner Data,” paper presented at the Seventh EMG Workshop, Sydney, December 12–14. Also presented at the SSHRC International Conference on Index Number Theory and the Measurement of Prices and Productivity, Vancouver, June 30–July 3.

• Export Citation
• de Haan, 2007, “Hedonic Price Indexes: A Comparison of Imputation, Time Dummy, and Other Approaches,” paper presented at the International Conference on Price Indices, Tenth Meeting, hosted by Statistics Canada, Ottawa, October 9–12. Available at: www.ottawagroup2007.ca/ogo_r003_e.htm.

• Export Citation
• de Haan, and Eddy Opperdoes, 1997, “Estimation of the Coffee Price Index Using Scanner Data: The Choice of the Micro Index,” paper presented at the International Conference on Price Indices, Third Meeting, hosted by Statistics Netherlands, Voorburg, April 16–18.

• Export Citation
• de Haan, and Eddy Opperdoes, and C.M. Schut, 1999, “Item Selection in the Consumer Price Index: Cut-Off Versus Probability Sampling,” Survey Methodology, Vol. 25 (June), pp. 3144.

• Export Citation
• Debreu, Gérard, 1952, “A Social Equilibrium Existence Theorem,” Proceedings of the National Academy of Sciences, Vol. 38 (October 15), pp. 88693.

• Export Citation
• Debreu, Gérard, 1959, Theory of Value: An Axiomatic Analysis of Economic Equilibrium (New York: Wiley).

• Decoster, Renaud, 2003a, “Import and Export Price Indices: A Comparison of Import Unit Value Indices and Import Specific Price Indices for Four EU Member States,” Second Report, Study Performed for Eurostat Unit C-4: Methodology, Nomenclature and Statistics of External and Intra-Community Trade (Paris: PLANISTAT Europe).

• Export Citation
• Decoster, Renaud, 2003b, Import and Export Price Indices: Final Report, Study Performed for Eurostat Unit 0074 C-4: Methodology, Nomenclature and Statistics of External and Intra-Community Trade (Paris: PLANISTAT Europe).

• Export Citation
• Denny, M., 1974, “The Relationship Between Functional Forms for the Production System,” Canadian Journal of Economics, Vol. 7 (February), pp. 2131.

• Export Citation
• Diewert, W. Erwin, 1973, “Functional Forms for Profit and Transformation Functions,” Journal of Economic Theory, Vol. 6 (June), pp. 284316.

• Export Citation
• Diewert, W. Erwin, 1974a, “Applications of Duality Theory,” in Frontiers of Quantitative Economics, Vol. II, ed. by M.D. Intrilligator and D.A. Kendrick (Amsterdam: North-Holland), pp. 10671. Available via the Internet: www.econ.ubc.ca/diewert/theory.pdf.

• Export Citation
• Diewert, W. Erwin, 1974b, “Functional Forms for Revenue and Factor Requirements Functions,” International Economic Review, Vol. 15 (February), pp. 11930.

• Export Citation
• Diewert, W. Erwin, 1974c, “Intertemporal Consumer Theory and the Demand for Durables,” Econometrica, Vol. 42 (May), pp. 497516.

• Diewert, W. Erwin, 1976, “Exact and Superlative Index Numbers,” Journal of Econometrics, Vol. 4 (May), pp. 1145.

• Diewert, W. Erwin, 1978, “Superlative Index Numbers and Consistency in Aggregation,” Econometrica, Vol. 46 (July), pp. 883900.

• Diewert, W. Erwin, 1980, “Aggregation Problems in the Measurement of Capital,” in The Measurement of Capital, NBER Studies in Income and Wealth Vol. 45, ed. by Dan Usher (Chicago: University of Chicago Press), pp. 433528.

• Export Citation
• Diewert, W. Erwin, 1983a, “The Theory of the Output Price Index and the Measurement of Real Output Change,” in Price Level Measurement: Proceedings from a Conference Sponsored by Statistics Canada, ed. by W.E. Diewert and C. Montmarquette (Ottawa: Statistics Canada) pp. 10491113.

• Export Citation
• Diewert, W. Erwin, 1983b, “The Treatment of Seasonality in a Cost of Living Index,” in Price Level Measurement: Proceedings from a Conference Sponsored by Statistics Canada, ed. by W. Erwin Diewert and C. Montmarquette (Ottawa: Statistics Canada), pp. 101945.

• Export Citation
• Diewert, W. Erwin, 1985, “Transfer Pricing and Economic Efficiency,” in Multinationals and Transfer Pricing, Croom Helm Series in International Business, ed. by A.M. Rugman and L. Eden (London: Croom Helm), pp. 4781.

• Export Citation
• Diewert, W. Erwin, 1990, “The Theory of the Cost-of-Living Index and the Measurement of Welfare Change,” in Price Level Measurement, Contributions to Economic Analysis 196, ed. by W. Erwin Diewert (Amsterdam: North-Holland), pp. 79147.

• Export Citation
• Diewert, W. Erwin, 1992a, “Fisher Ideal Output, Input and Productivity Indexes Revisited,” Journal of Productivity Analysis, Vol. 3 (September), pp. 21148.

• Export Citation
• Diewert, W. Erwin, 1992b, “Exact and Superlative Welfare Change Indicators,” Economic Inquiry, Vol. 30 (October), pp. 56582.

• Diewert, W. Erwin, 1993a, “The Early History of Price Index Research,” in Essays in Index Number Theory, Vol. 1, ed. by W. Erwin Diewert and A.O. Nakamura (Amsterdam: North-Holland), pp. 3365.

• Export Citation
• Diewert, W. Erwin, 1993b, “Duality Approaches to Microeconomic Theory,” in Essays in Index Number Theory, Vol. 1, ed. by W. Erwin Diewert and A.O. Nakamura (Amsterdam: North-Holland), pp. 10575.

• Export Citation
• Diewert, W. Erwin, 1993c, “Symmetric Means and Choice Under Uncertainty,” in Essays in Index Number Theory, Vol. 1, ed. by W. Erwin Diewert and A.O. Nakamura (Amsterdam: North-Holland), pp. 355433.

• Export Citation
• Diewert, W. Erwin, 1993d, “Overview of Volume 1,” in Essays in Index Number Theory, Vol. 1, ed. by W. Erwin Diewert and A.O. Nakamura (Amsterdam: North-Holland), pp. 131.

• Export Citation
• Diewert, W. Erwin, 1995a, “Axiomatic and Economic Approaches to Elementary Price Indexes,” Discussion Paper No. 95–01 (Vancouver: Department of Economics, University of British Columbia).

• Export Citation
• Diewert, W. Erwin, 1995b, “On the Stochastic Approach to Index Numbers,” Discussion Paper No. 95–31 (Vancouver: Department of Economics, University of British Columbia).

• Export Citation
• Diewert, W. Erwin, 1996a, “Price and Volume Measures in the System of National Accounts,” in The New System of National Accounts, ed. by J. Kendrick (Norwell, Massachusetts: Kluwer Academic), pp. 23785.

• Export Citation
• Diewert, W. Erwin, 1996b, “Seasonal Commodities, High Inflation and Index Number Theory,” Discussion Paper 96-06 (Vancouver: Department of Economics, University of British Columbia).

• Export Citation
• Diewert, W. Erwin, 1997, “Commentary on Matthew D. Shapiro and David W. Wilcox: ‘Alternative Strategies for Aggregating Price in the CPI,’Federal Reserve Bank of St. Louis Review, Vol. 79 (May/June), pp. 12737. Available via the Internet: http://research.stlouisfed.org/publications/review/97/05/9705ned.pdf.

• Export Citation
• Diewert, W. Erwin, 1998a, “Index Number Issues in the Consumer Price Index,” Journal of Economic Perspectives, Vol. 12 (Winter), pp. 4758.

• Export Citation
• Diewert, W. Erwin, 1998b, “High Inflation, Seasonal Commodities and Annual Index Numbers,” Macroeconomic Dynamics, Vol. 2 (December), pp. 45671.

• Export Citation
• Diewert, W. Erwin, 1999a, “Index Number Approaches to Seasonal Adjustment,” Macroeconomic Dynamics, Vol. 3 (March), pp. 4868.

• Diewert, W. Erwin, 1999b, “Axiomatic and Economic Approaches to Multilateral Comparisons,” in International and Interarea Comparisons of Income, Output, and Prices, NBER Studies in Income and Wealth Vol. 61, ed. by Alan Heston and Robert E. Lipsey (Chicago: University of Chicago Press), pp. 1387.

• Export Citation
• Diewert, W. Erwin, 2000, “Notes on Producing an Annual Superlative Index Using Monthly Price Data,” Discussion Paper No. 00-08 (Vancouver: Department of Economics, University of British Columbia).

• Export Citation
• Diewert, W. Erwin, 2001a, “The Consumer Price Index and Index Number Purpose,” Journal of Economic and Social Measurement, Vol. 27, No. 3–4, pp. 167248.

• Export Citation
• Diewert, W. Erwin, 2001b, “Which (Old) Ideas on Productivity Measurement Are Ready to Use?in New Developments in Productivity Analysis, NBER Studies in Income and Wealth Vol. 63, ed. by C.R. Hulten, E.R. Dean and M.J. Harper (Chicago: University of Chicago Press), pp. 85101.

• Export Citation
• Diewert, W. Erwin, 2002a, “The Quadratic Approximation Lemma and Decompositions of Superlative Indexes,” Journal of Economic and Social Measurement, Vol. 28 (November), pp. 6388.

• Export Citation
• Diewert, W. Erwin, 2002b, “Similarity and Dissimilarity Indexes: An Axiomatic Approach,” Discussion Paper No. 02-10 (Vancouver: Department of Economics, University of British Columbia).

• Export Citation
• Diewert, W. Erwin, 2002c, “Harmonized Indexes of Consumer Prices: Their Conceptual Foundations,” Swiss Journal of Economics and Statistics, Vol. 138 (December), pp. 547637.

• Export Citation
• Diewert, W. Erwin, 2002d, “Notes on Hedonic Producer Price Indexes” (unpublished; Vancouver: Department of Economics, University of British Columbia, January 5).

• Export Citation
• Diewert, W. Erwin, 2002e, “Hedonic Producer Price Indexes and Quality Adjustment,” Discussion Paper No. 02-14 (Vancouver: Department of Economics, University of British Columbia).

• Export Citation
• Diewert, W. Erwin, 2002f, “Hedonic Regression: A Review of Some Unresolved Issues” (unpublished; Vancouver: Department of Economics, University of British Columbia).

• Export Citation
• Diewert, W. Erwin, 2003, “Hedonic Regressions: A Consumer Theory Approach,” in Scanner Data and Price Indexes, NBER Studies in Income and Wealth, Vol. 64, ed. by Robert C. Feenstra and Matthew D. Shapiro (Chicago: University of Chicago Press), pp. 31748.

• Export Citation
• Diewert, W. Erwin, 2005a, “On Measuring Inventory Change in Current and Constant Dollars,” Discussion Paper No. 05–12 (Vancouver: Department of Economics, University of British Columbia). Available via the Internet: www.econ.ubc.ca/discpapers/dp0512.pdf.

• Export Citation
• Diewert, W. Erwin, 2005b, “Weighted Country Product Dummy Variable Regressions and Index Number Formulae,” Review of Income and Wealth, Vol. 51 (December), pp. 56170.