| Acquisitions approach | An approach to consumer price indices (CPIs) in which consumption is identified with the consumption of goods and services acquired by a household in some period (as distinct from those wholly or partially used up for purposes of consumption). Depending on the intended scope of the CPI, acquisitions may include not only goods and services purchased but also those acquired by own-account production or as social transfers in kind from government or nonprofit institutions. |
| Additivity | At current prices, the value of an aggregate is identical to the sum of the values 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 an aggregate and its components in some period are deflated using a set of interrelated price indices. |
| Aggregate | A set of transactions relating to a specified flow of goods and services, such as the total purchases made by resident households on consumer goods and services in some period. The term “aggregate” is also used to mean the value of the designated set of transactions. |
| Aggregation | The process of combining, or adding, different sets of transactions to obtain larger sets 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” is also used to mean the process of adding the values of the 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. |
| Axiomatic, or test 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. An index number may then be chosen based on the number of tests satisfied. Not all tests may be considered to be equally important and the failure to satisfy one or two key tests may be considered sufficient grounds for rejecting an index. |
| Average of price relatives | See Carli index. |
| Base period | The base period is usually understood to mean the period with which all the other periods are compared. The term, however, has different meanings in different contexts. Three types of base periods may be distinguished:
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| Basket | A specified set of goods and services and their quantities. In a CPI context, the set may comprise the actual quantities of consumption goods or services acquired or used by households in some period, or may be made up of hypothetical quantities. |
| Basket price index | A price index that measures the proportionate change between periods 0 and t in the total value of a specified basket of goods and services: that is, ∑ptq / ∑p0q, where the term q is the quantities of the specified goods and services. See Lowe index. |
| Bias | A systematic tendency for the calculated CPI to diverge from some ideal or preferred index, resulting from the method of data collection or processing, or the index formula used. See Cost of living bias and Representativity bias. |
| Bilateral indices | A type of index that measures the aggregate price change between two periods based on prices observed in these two periods only. Depending on the index formula, the underlying quantities purchased or expenditures can be from the price reference period (for example, Laspeyres), the current period (for example, Paasche), the price reference and the current periods (for example, Fisher, Walsh, Törnqvist), or any other past period (for example, Lowe, Young). |
| Bouncing | A situation in which the set of prices for the second period is simply a reordering of the set of prices for the first period, the price relatives thus being obtained by matching each price in the first period with another price from the same set of prices. |
| Carli price index | An elementary price index defined as a simple, or unweighted, arithmetic average of the sample price relatives. |
| Carryforward | A situation in which a missing price in some period is imputed as being equal to the last price observed for that item. |
| Central product classification | An internationally agreed-upon classification of goods and services based on the physical characteristics of goods or on the nature of the services rendered. |
| Chain index | An index number series for a long sequence of periods obtained by linking together index numbers spanning shorter sequences of periods. See Linking; see also equation 6 of Appendix 6 to the Manual. |
| Chaining/chain linking | The construction of a continuous price series by multiplying together price indices that have been constructed using different weight reference periods. The resulting index is referred to as a “chain index.” |
| Characteristics | The physical and economic attributes of a good or service that serve to identify it and enable it to be classified. Some characteristics will help determine price and are commonly referred to as price-determining characteristics. |
| Circularity (transitivity) | An index number property such that, if jIk denotes a particular kind of price index that measures the change between periods j and k, then jIl ≡ jIk.kIl where the indices jIl and kIl are of the same type. When an index is transitive, the index that compares periods j and l indirectly through period k is identical with the index that compares j and l directly. One test that might be required under the axiomatic approach is that the index number should be transitive. |
| COICOP | The Classification of Individual Consumption by Purpose. It is the internationally preferred classification for CPIs, household budget surveys, and the International Comparison Program. |
| Commensurability | See Invariance to changes in the units of measurement test. |
| Commodity reversal test | A test that might be used 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. |
| Component | A subset of the goods and services that make up some defined aggregate. |
| Conditional cost of living index | A conditional cost of living index measures the change in the cost of maintaining a given utility level, or standard of living, on the assumption that all the factors, except the prices covered by the index, that influence the consumer’s utility or welfare (for example, the state of the physical environment) remain constant. See Cost of living index. |
| 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 whether 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. |
| Consumer price index (CPI) | An official indicator constructed to measure the changes over time in the general level of prices for consumer goods and services that households acquire, use, or pay for consumption. Its exact definition may vary from country to country. |
| Consumption | Consumption of goods and services is the act of completely using up the goods and services in a process of production or for the direct satisfaction of human needs or wants. The activity of consumption consists of the use of goods and services for the satisfaction of individual or collective human needs or wants. Additionally,
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| Consumption of own production | Goods or services that are consumed by the same household that produces them. The housing services consumed by owner-occupiers fall within this category. If goods and services produced and consumed within the same household are to be included in CPIs, prices must be estimated for them. Their inclusion or exclusion depends on the intended scope of the CPI. It should be noted that activities undertaken by households that produce services for their own use are outside of the scope of the System of National Accounts (SNA) production boundary, except for services provided by owner-occupied dwellings and services produced by employing paid domestic staff. The own-account production of all goods that are retained by their producers for their own final consumption or gross capital formation is included in the SNA production boundary. |
| Continuity | The property whereby the price index is a continuous function of its price and quantity vectors. |
| Cost of living bias | An alternative term used to describe Substitution bias. |
| Cost of living index | An index that measures the change between two periods in the minimum expenditures that would be required to achieve a constant standard of living (that is level of utility or economic well-being). As consumers may be expected to change the quantities they consume in response to changes in relative prices (see Substitution effect), the cost of living index is not a basket index. The quantities and expenditures made in one or other, or possibly both, periods cannot usually be observed in a timely manner. Cost of living indices cannot be directly calculated but may be approximated by superlative indices. See Conditional cost of living index. |
| Coverage | The set of goods and services of which the prices are actually included in the index. For practical reasons, coverage may have to be less than the ideal scope of the index, that is, the set of goods and services that the compilers of the index would prefer to include if it were feasible. |
| Current period, or comparison period | In principle, the current period should refer to the most recent period for which the index has been compiled or is being compiled. The term is widely used, however, to mean the comparison period; that is, the period that is compared with the base period, usually the price reference or index reference period. It is also widely used simply to mean the later of the two periods being compared. The exact meaning is usually clear in the context. |
| Current prices | The actual prices prevailing in the period in question. |
| Current value | The actual value of some aggregate in the period in question: the quantities in the period multiplied by the prices of the same period. |
| 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 with regard to the size of some relevant variable, the largest sampling units being included and the rest given a zero chance of inclusion. |
| 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. |
| Democratic index Discount | A form of CPI in which the expenditure proportions of each household are given equal weight in the calculation of the index, irrespectively of the size of its expenditures. See Plutocratic index. A deduction from the list or advertised price of a good or a 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 index | A price or quantity index that treats both prices and quantities as continuous functions of time. By differentiating 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 the changes between consecutive periods are linked together. |
| Domain | An alternative term for the scope of an index. See Scope. |
| Domestic concept | The use of weights covering all consumption expenditure on the national territory, regardless of the nationality or normal residence of the consumer. See National concept. |
| 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 over the periods they cover. |
| Drobisch price index | The arithmetic average of the Laspeyres price index and the Paasche price index. |
| Durable consumer good | A consumer good that can be used repeatedly or continuously for purposes of consumption over a period of one year or more. |
| Dutot index | An elementary price index defined as the ratio of the unweighted arithmetic averages of the prices in the two periods compared. |
| Economic approach | The economic approach to index number theory assumes that the quantities are functions of the prices, the observed data being generated as solutions to various economic optimization problems. In the CPI context, the economic approach usually requires the CPI to be some kind of cost of living index. |
| Edgeworth price index | A basket price index in which the quantities in the basket are simple arithmetic averages of the quantities consumed in the two periods. |
| Editing | The process of scrutinizing and checking the prices reported by price collectors. Some checks may be carried out by computers using statistical programs written for the purpose. |
| Elasticity of substitution | A measure of the extent to which one product is substituted for another in response to relative price changes. A zero elasticity of substitution means that there is no substitution. |
| Elementary aggregate | The lowest level of groups of goods or services for which expenditure weights are assigned and held constant for a period of one year or more. An elementary aggregate should consist of relatively homogeneous set of goods or services, with similar end-uses and similar expected price movements. More detailed weights to reflect the relative importance of individual price observations within elementary aggregates may be applied and updated more frequently. The elementary aggregates are the building blocks for the calculation of the higher-level indices. |
| Elementary price index | In general, an elementary index is a price index for an elementary aggregate, but it can also refer to a price index for a more detailed level below the elementary aggregate. Expenditure weights cannot usually be assigned to the price relatives for the sampled products within an elementary aggregate, although other kinds of weighting may be explicitly or implicitly introduced into the calculation of elementary indices. For example, scanner data could be used to develop a more detailed weighting program within an elementary aggregate. Three examples of unweighted elementary index number formulae are the Carli, the Dutot, and the Jevons. |
| Expenditure weights | See Weights. |
| Explicit (or direct) quality adjustment | A direct estimate of the value of the quality difference between the old and new product used to adjust one of the prices accordingly. Pure price change is then estimated as the difference in the adjusted prices. See 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 to the proportionate change in the value of the aggregate in question. |
| Fisher price index | The geometric average of the Laspeyres price index and the Paasche price index. It is a symmetric index and a superlative index. |
| Fixed-basket indices | A time series of basket indices that all use the same basket; see equation 4 of Appendix 6 to the Manual. In a CPI context, the fixed basket usually consists of the total quantities of goods and services consumed by the designated set of households over a period of a year or more. |
| Fixed-weight indices | An abbreviated description for a series of weighted averages of price relatives that all use the same weights; see equation 13 of Appendix 6 to the Manual. The weights are usually either actual or hybrid expenditure shares. |
| Geometric Laspeyres index | A weighted geometric average of the price relatives using the expenditure shares of the price reference period as weights. Also called Logarithmic Laspeyres index. |
| Goods | Physical, produced objects for which a demand exists, over which ownership rights can be established and for which ownership can be transferred between institutional units by engaging in transactions on the market. |
| Hedonic method | A regression model in which the market prices of different products are expressed as a function of their characteristics. Nonnumerical characteristics are represented by dummy variables. Each regression coefficient is treated as an estimate of the marginal contribution of that characteristic to the total price. The estimates may be used to predict the price of a new product for which the 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 | An aggregate index as distinct from an elementary index. |
| Household budget surveys | Sample surveys of households in which the households are asked to provide data on, or estimates of, the value of the goods and services acquired, paid, and used for consumption as well as other purposes over a given period of time. Also referred to household income and expenditure surveys. |
| Household final consumption expenditure | It consists of the expenditure, including expenditure whose value must be estimated indirectly, incurred by resident households on individual consumption goods and services, including those sold at prices that are not economically significant and including consumption goods and services acquired abroad. They exclude expenditures incurred by governments or nonprofit institutions on goods or services provided to households as free social transfers in kind. |
| Households | A household is a group of persons who share the same living accommodation, who pool some, or all, of their income and wealth and who consume certain types of goods and services collectively, mainly housing and food. Most countries choose to exclude groups of persons living in large institutional households (barracks, retirement homes, and so on) from the scope of their CPIs. |
| Hybrid values or expenditures | Hypothetical values, or expenditures, in which the 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, such as b, are valued at the prices prevailing in a later period, such as 0. |
| Hybrid weights | Weights defined as hybrid value, or hybrid expenditure, shares. |
| Identity test | A test under the axiomatic approach that requires that, if each and every price remains unchanged between the two periods, the price index must equal unity. |
| Implicit (or indirect) quality adjustment | Estimating the pure price change component of the price difference between the old and new products based on the price changes observed for similar products. The difference between the estimate of pure price change and the observed price change is considered as change due to quality difference. See Explicit quality adjustment. |
| Imputed price1 | The price assigned to a variety for which the price is missing in a particular period. The term “imputed price” may also refer to the price assigned to an variety 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. |
| Indexation | The periodic adjustment of the money values of some regular scheduled payments based on the movement of the CPI or some other price index. The payments may be wages or salaries, social security or other pensions, other social security benefits, rents, interest payments, and so on. |
| Index reference period | The period for which the value of the index is set at 100. |
| Institutional unit | 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. Households are institutional units. Other kinds of units include enterprises and governments. |
| Institutional households | A group of individuals staying in an institution for long periods of time, such as retirement homes, military accommodation, and boarding schools, and sharing resources. Such people are treated as belonging to private “institutional” households. |
| 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. This test is also described 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 year prices test | A test that may be invoked under the axiomatic approach that requires that, if all the base period prices are multiplied by the positive scalar l, the new price index is 1/l times the old price index. |
| 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 outlet. 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. |
| Jevons price index Laspeyres price index | An elementary price index defined as the unweighted geometric average of the sample price relatives. A basket index in which the basket is composed of the actual quantities of goods and services in the earlier of the two periods compared, the price reference period; see equation 3 of Appendix 6 to the Manual. It can also be expressed as a weighted arithmetic average of the price relatives that uses the expenditure shares in the earlier period as weights; see equations 7–10 of Appendix 6 to the Manual. The earlier period serves as both the weight reference period and the price reference period. |
| Linking | Splicing together two consecutive sequences of price observations, or 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 the other sequence so that the value in the overlap period is the same in both sequences and the spliced sequences form one continuous series. See equation 6 of Appendix 6 to the Manual. |
| Lowe index | A price index that measures the proportionate change between periods 0 and t in the total value of a specified basket of goods and services; that is, ∑ptq / ∑p0q, where the term q is the specified quantities. The basket does not necessarily have to consist of the actual quantities in some period. See Appendix 6 to the Manual. This type of index is described in the Manual as a Lowe index after the index number pioneer who first proposed this general type of index. The class of indices covered by this definition is very broad and includes, by appropriate specification of the terms q, the Laspeyres, Paasche, Edgeworth, and Walsh indices. Lowe indices are widely used for CPI purposes, the quantities in the basket typically being those of some weight reference period b, which precedes the price reference period 0. |
| Lower-level index | An elementary index as distinct from an aggregate index. |
| Matched products or models | The practice of pricing exactly the same product in two or more consecutive periods. It is designed to ensure that the observed price changes are not affected by the quality change. The change in price between two perfectly matched products is described as a pure price change. |
| Model | A specific variety whose characteristics are regularly updated. See Variety. |
| Mean value test for prices | A test under the axiomatic approach, which requires that the price index should lie between the smallest price relative and the largest price relative. |
| Modified Lowe index | A version of the Lowe index that compiles the index based on short-term price changes rather than long-term changes. This approach makes it easier for national statistical offices to introduce replacement varieties in the sample when a sampled variety disappears. The short-term approach also facilitates quality adjustments because only the current and previous period prices are needed in order to introduce a new variety into the index. See Lowe index. |
| Modified Young index | A version of the Young index that compiles the index based on short-term price changes rather than long-term changes. This approach makes it easier for national statistical offices to introduce replacement varieties in the sample when a sample variety disappears. The short-term approach also facilitates quality adjustments because only the current and previous period prices are needed in order to introduce a new variety in the index. See Young index. |
| Multilateral indices | A type of index that measures the aggregate price change between two periods based on prices observed in multiple periods including the two comparison periods. Multilateral indices were developed for price comparisons across countries (purchasing power parities) and have been adapted to compare prices over time. For price comparisons over time, multilateral index formulas are mainly used with scanner data. In this context, their main advantage is to avoid chain drift. The most common multilateral index formulas in CPIs are the Gini–Eltetö–Köves–Szulc, the Geary–Khamis, and the time product dummy. See Chapter 10 for further details. |
| National concept | The use of weights covering the expenditure of residents of a country, regardless of whether the expenditure is made within or outside of the country. See Domestic concept. |
| Nonprobability sampling | The deliberate (that is, nonrandom) selection of a sample of outlets and products on the basis of the knowledge or judgment of the person responsible. Also known as purposive sampling and judgmental sampling. |
| Outlier | A term that is generally used to describe any extreme value in a set of survey data. In a CPI 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. |
| Owner-occupied housing | Dwellings owned by the households that live in them. The dwellings are fixed assets that their owners use to produce housing services for their own consumption, these services being usually included within the scope of the CPI. The value of the services provided may be imputed by the rents payable on the market for equivalent accommodation or by user costs. See Rental equivalence and User cost. In the System of National Accounts (SNA) framework, the production of housing services for their own final consumption by owner-occupiers has always been included within the production boundary in national accounts, although it constitutes an exception to the general exclusion of own-account service production. |
| Paasche price index | A basket index in which the basket is composed of the actual quantities of goods and services in the later of the two periods compared. The later period serves as the weight reference period and the earlier period as the price reference period. The Paasche index can also be expressed as a weighted harmonic average of the price relatives that uses the actual expenditure shares in the later period as weights. See equations 7–11 of Appendix 6 to the Manual. |
| Plutocratic index | A form of CPI in which the weights are based on total aggregated expenditure values rather than average household expenditure proportions. |
| Price reference period | The period of which the prices appear in the denominators of the price relatives. See Base period. |
| Price relative | The ratio of the price of a variety in one period to the price of that same variety in some other period. |
| Price updating | A procedure whereby the quantities in an earlier period are revalued at the prices of a later period. The resulting expenditures are hybrid. In practice, the price-updated expenditures may be obtained by multiplying the original expenditures by price relatives or price indices. |
| Probability proportional to size sampling | A sampling procedure whereby each unit in the universe has a probability of selection proportional to the size of some known variable, such as the value of the sales of an outlet. |
| Probability sampling | The random selection of a sample of units, such as outlets or products, in such a way that each unit in the universe has a known nonzero probability of selection. |
| 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. |
| Purchaser’s price | The purchaser’s price is the amount paid by the purchaser, excluding any value-added tax or similar tax deductible 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. The purchaser’s price of a good includes any transport charges paid separately by the purchaser to take delivery at the required time and place. |
| Pure price change | The change in the price of the same variety; or the change in the price after adjusting for any change in quality. |
| Quality adjustment | An adjustment to the price of a variety of which the characteristics have changed over time. Quality adjustments are designed to remove the part of the observed price that is due to differences in the price-determining characteristics. In a CPI context, the adjustment is needed when the price of a replacement variety must be compared with the price of the variety 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. |
| Quantity relative | The ratio of the quantity of a product in one period to the quantity of that same product in some other period. |
| Quantity weights | A term sometimes used to describe the quantities in the basket. However, expenditures rather than quantities act as weights for price relatives. See Weights. |
| Quota sampling | Sample selection using judgmental procedures with respect to known characteristics such as product group or outlet type. The sample is drawn so as to contain the same proportions as in the total population of products, items, or outlets. |
| Ratio of averages | See Dutot index. |
| Rebasing | It refers to changing the weight reference period, price reference period, or index reference period. The weight reference period, price reference period, and index reference period may be changed separately or at the same time. |
| Reference population | The set of households included within the scope of the index. |
| Rental equivalence | The estimation of the imputed rents payable by owner-occupiers on the basis of the rents payable on the market for accommodation of the same type. |
| Replacement variety | A variety chosen to replace a variety for which prices have been collected previously, either because the previous variety has disappeared altogether or because it accounts for a diminishing share of the sales of the outlet, or the expenditures within the elementary aggregate. |
| Representative variety | A variety, or category of varieties, that accounts for a significant proportion of the total expenditures within an elementary aggregate, and for which the average price change is expected to be close to the average for all varieties within the aggregate. |
| Representativity bias | Bias in a basket index that results from the use of quantities that are not representative of the two periods compared; that is, that systematically diverge from the average quantities consumed in the two periods. For example, representativity bias may result from the use of an old, out-of-date basket which deviates systematically from the baskets in both the periods compared. In practice, representativity bias tends to be similar to substitution bias, as it is attributable to the same economic factors. |
| Reweighting | Replacing the weights used in an index by a new set of weights. |
| Revision | Often refers to changing index weights and implementing new calculation or compilation methodologies. |
| Sample augmentation | Maintaining and adding to the sample of outlets, items, and varieties in the survey panel to ensure that they continue to be representative of the population of outlets. A fixed sample of outlets tends to be depleted over time, as outlets cease trading or stop responding. Including new outlets also tends to facilitate the inclusion of new products in the CPI. |
| Sampled price | The price collected for a sampled product in a specific outlet at a specific time, sometimes described as a price quote. |
| Sample rotation | Limiting the length of time that outlets and products are included in the 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 outlets and products. Rotation is designed to keep the sample up to date. |
| Sampling frame | A list of the units in the universe from which a sample of units can be selected. The list may contain information about the units, which may be used for probability proportional to size sampling. Examples of lists that may be used for retail outlets are business registers, telephone directories (“yellow pages”), local authority records, or trade directories. Such lists may not cover all the units in the designated universe and may also include units that do not form part of that universe. |
| Scanner data | Detailed data on sales of products obtained by scanning the bar codes for individual varieties at electronic points of sale in retail outlets. The data can provide detailed information about quantities, characteristics, and values of varieties sold, as well as their prices. Scanner data constitute a rapidly expanding source of data with considerable potential for CPI purposes. |
| Scope | The set of products for which the index is intended to measure the price changes. The scope of a CPI will generally be defined with regard to a designated set of consumption goods and services purchased by a designated set of households. In practice, certain goods and services or households may have to be excluded because it is too difficult, time-consuming, or costly to collect the relevant data on expenditures or prices: for example, illegal expenditures. The coverage of an index denotes the actual set of products included, as distinct from the intended scope of the index. |
| Seasonal products | They are products that either are not available on the market during certain seasons or periods of the year or are available throughout the year but with regular fluctuations in their quantities and prices that are linked to the season or time of the year. |
| Services | They are the result of a production activity that changes the conditions of the consuming units or facilitates the exchange of products or financial assets. |
| Specification | A description or list of the characteristics that can be used to identify an individual sampled variety to be priced. A tight specification is a fairly precise description of an item intended to narrow the range of varieties from which a price collector might choose, possibly reducing it to a unique variety, such as a particular brand of television set identified by a specific code number. A loose specification is a generic description of a range of items that allows the price collector some discretion as to which particular variety or model to select for pricing, such as color television sets of a particular size. |
| 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. |
| Substitute | A product of which the characteristics are similar to those of another product and that can be used to meet the same kinds of consumer needs or wants. |
| Substitution | The replacement of products by substitutes, typically in response to changes in relative prices. Rational utility-maximizing consumers, as price takers, typically react to changes in relative prices by reducing, at least marginally, their consumption of goods and services that have become relatively dearer and increasing their consumption of substitutes that have become relatively cheaper. Substitution results in a negative correlation between the quantity and price relatives. |
| Substitution bias | This is generally understood to be the bias that results when a basket index is used to estimate a cost of living index, because a basket index cannot take account of the effects on the cost of living of the substitutions made by consumers in response to changes in relative prices. In general, the earlier the period of which the basket is used, the greater the upward bias in the index; see Representativity bias. |
| Substitution effect | The effect of substitution on the value of an index. |
| Superlative index | A type of index formula that can be expected to approximate to the cost of living index. An index is said to be exact when it equals the true cost of living index for consumers whose preferences can be represented by a particular functional form. A superlative index is then defined as an index that is exact for a flexible functional form that can provide a second-order approximation to other twice-differentiable functions around the same point. The Fisher, the Törnqvist, and the Walsh price indices are examples of superlative indices. Superlative indices are generally symmetric indices. |
| Symmetric index | An index that treats both periods symmetrically by attaching equal importance to the price and expenditure data in both periods. The price and expenditure data for both periods enter into the index formula in a symmetric way. |
| System of National Accounts (SNA) | A coherent, consistent, and integrated set of macroeconomic accounts, balance sheets, and tables based on a set of internationally agreed-upon concepts, definitions, classifications, and accounting rules. Distribution and use of income accounts and household final consumption expenditure form part of the SNA. The expenditure data are some of the sources that are used to estimate expenditure weights for CPI purposes. |
| Time reversal | An index number property such that, if j Ik denotes a particular kind of price index formula that measures the change from period j to period k, then j Ik ≡ 1/kIj where k Ij measures the change from period k to period j. When an index has this property, the change is the same whether it is measured forward from the first to the second period or backward from the second to the first period. An index may be required to satisfy the time reversal test under the axiomatic approach. |
| Törnqvist price index | A symmetric index defined as the weighted geometric average of the price relatives in which the weights are simple arithmetic averages of the expenditure shares in the two periods. It is a superlative index. Also known as the Törnqvist–Theil price index. |
| Transitivity | See Circularity. |
| Unit value or average value | The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities. It is therefore a quantity-weighted average of the different prices at which the product is purchased/sold. Unit values may change over time as a result of a change in the mix of the products sold at different prices, even if the prices do not change. |
| Updating | Changing the index weights. See Revision and Rebasing. |
| User cost | The cost incurred over a period of time by the owner of a fixed asset or consumer durable as a consequence of using it to provide a flow of capital or consumption services. User cost consists mainly of the depreciation of the asset or durable (measured at current prices and not at historic cost) plus the capital, or interest, cost. |
| Uses approach | An approach to CPIs in which the consumption in some period is identified with the consumption goods and services actually used up by a household to satisfy their needs and wants (as distinct from the consumption goods and services acquired). In this approach, the consumption of consumer durables in a given period is measured by the values of the flows of services provided by the stocks of durables owned by households. These values may be estimated by the user costs. |
| Value | Price times quantity. The value of the expenditures on a set of homogeneous products can be factored uniquely into its price and quantity components. Similarly, the change over time in the value of a set of homogeneous products can be factored uniquely into the change in the unit value and the change in the total quantities. There are, however, many different ways of factoring the change over time in the value of a set of heterogeneous products into its price and quantity components, a phenomenon that gives rise to the index number problem. |
| Variety | The individual product for which prices are collected during the collection period. It includes the detailed specification of the product or item observed. |
| Walsh price index | A basket index in which the quantities are geometric averages of the quantities in the two periods; see Appendix 6 to the Manual. It is a symmetric index and a superlative index. |
| Weight reference period | The period of which the expenditure shares serve as the weights for a Young index, or of which the quantities make up the basket for a Lowe index. There may be no weight reference period when the expenditure shares for the two periods are averaged, as in the Törnqvist index, or when the quantities are averaged, as in the Walsh index. See Base period. |
| Weighted arithmetic average index | An index defined as a weighted arithmetic average of the price relatives: namely, Σw(pt / p0), where the weights w sum to unity. |
| Weights | A set of numbers summing to unity that are used to calculate averages. In a CPI context, the weights are generally actual or hybrid expenditure shares that sum to unity by definition. They are used to average price relatives or elementary price indices; see Appendix 6 to the Manual. Quantities of different kinds of products are not commensurate and not additive. They cannot be used to average elementary price indices. The quantities that make up a basket should therefore not be described as quantity weights. |
| Young index | A Young index is a weighted arithmetic average of the price relatives, Σw(pt / p0), in which the terms w refer to the actual expenditure shares of period b, the weight reference period; that is, w = sb = pbqb / Σpbqb. It is a weighted version of the Carli index. |
| Acquisitions approach | An approach to consumer price indices (CPIs) in which consumption is identified with the consumption of goods and services acquired by a household in some period (as distinct from those wholly or partially used up for purposes of consumption). Depending on the intended scope of the CPI, acquisitions may include not only goods and services purchased but also those acquired by own-account production or as social transfers in kind from government or nonprofit institutions. |
| Additivity | At current prices, the value of an aggregate is identical to the sum of the values 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 an aggregate and its components in some period are deflated using a set of interrelated price indices. |
| Aggregate | A set of transactions relating to a specified flow of goods and services, such as the total purchases made by resident households on consumer goods and services in some period. The term “aggregate” is also used to mean the value of the designated set of transactions. |
| Aggregation | The process of combining, or adding, different sets of transactions to obtain larger sets 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” is also used to mean the process of adding the values of the 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. |
| Axiomatic, or test 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. An index number may then be chosen based on the number of tests satisfied. Not all tests may be considered to be equally important and the failure to satisfy one or two key tests may be considered sufficient grounds for rejecting an index. |
| Average of price relatives | See Carli index. |
| Base period | The base period is usually understood to mean the period with which all the other periods are compared. The term, however, has different meanings in different contexts. Three types of base periods may be distinguished:
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| Basket | A specified set of goods and services and their quantities. In a CPI context, the set may comprise the actual quantities of consumption goods or services acquired or used by households in some period, or may be made up of hypothetical quantities. |
| Basket price index | A price index that measures the proportionate change between periods 0 and t in the total value of a specified basket of goods and services: that is, ∑ptq / ∑p0q, where the term q is the quantities of the specified goods and services. See Lowe index. |
| Bias | A systematic tendency for the calculated CPI to diverge from some ideal or preferred index, resulting from the method of data collection or processing, or the index formula used. See Cost of living bias and Representativity bias. |
| Bilateral indices | A type of index that measures the aggregate price change between two periods based on prices observed in these two periods only. Depending on the index formula, the underlying quantities purchased or expenditures can be from the price reference period (for example, Laspeyres), the current period (for example, Paasche), the price reference and the current periods (for example, Fisher, Walsh, Törnqvist), or any other past period (for example, Lowe, Young). |
| Bouncing | A situation in which the set of prices for the second period is simply a reordering of the set of prices for the first period, the price relatives thus being obtained by matching each price in the first period with another price from the same set of prices. |
| Carli price index | An elementary price index defined as a simple, or unweighted, arithmetic average of the sample price relatives. |
| Carryforward | A situation in which a missing price in some period is imputed as being equal to the last price observed for that item. |
| Central product classification | An internationally agreed-upon classification of goods and services based on the physical characteristics of goods or on the nature of the services rendered. |
| Chain index | An index number series for a long sequence of periods obtained by linking together index numbers spanning shorter sequences of periods. See Linking; see also equation 6 of Appendix 6 to the Manual. |
| Chaining/chain linking | The construction of a continuous price series by multiplying together price indices that have been constructed using different weight reference periods. The resulting index is referred to as a “chain index.” |
| Characteristics | The physical and economic attributes of a good or service that serve to identify it and enable it to be classified. Some characteristics will help determine price and are commonly referred to as price-determining characteristics. |
| Circularity (transitivity) | An index number property such that, if jIk denotes a particular kind of price index that measures the change between periods j and k, then jIl ≡ jIk.kIl where the indices jIl and kIl are of the same type. When an index is transitive, the index that compares periods j and l indirectly through period k is identical with the index that compares j and l directly. One test that might be required under the axiomatic approach is that the index number should be transitive. |
| COICOP | The Classification of Individual Consumption by Purpose. It is the internationally preferred classification for CPIs, household budget surveys, and the International Comparison Program. |
| Commensurability | See Invariance to changes in the units of measurement test. |
| Commodity reversal test | A test that might be used 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. |
| Component | A subset of the goods and services that make up some defined aggregate. |
| Conditional cost of living index | A conditional cost of living index measures the change in the cost of maintaining a given utility level, or standard of living, on the assumption that all the factors, except the prices covered by the index, that influence the consumer’s utility or welfare (for example, the state of the physical environment) remain constant. See Cost of living index. |
| 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 whether 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. |
| Consumer price index (CPI) | An official indicator constructed to measure the changes over time in the general level of prices for consumer goods and services that households acquire, use, or pay for consumption. Its exact definition may vary from country to country. |
| Consumption | Consumption of goods and services is the act of completely using up the goods and services in a process of production or for the direct satisfaction of human needs or wants. The activity of consumption consists of the use of goods and services for the satisfaction of individual or collective human needs or wants. Additionally,
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| Consumption of own production | Goods or services that are consumed by the same household that produces them. The housing services consumed by owner-occupiers fall within this category. If goods and services produced and consumed within the same household are to be included in CPIs, prices must be estimated for them. Their inclusion or exclusion depends on the intended scope of the CPI. It should be noted that activities undertaken by households that produce services for their own use are outside of the scope of the System of National Accounts (SNA) production boundary, except for services provided by owner-occupied dwellings and services produced by employing paid domestic staff. The own-account production of all goods that are retained by their producers for their own final consumption or gross capital formation is included in the SNA production boundary. |
| Continuity | The property whereby the price index is a continuous function of its price and quantity vectors. |
| Cost of living bias | An alternative term used to describe Substitution bias. |
| Cost of living index | An index that measures the change between two periods in the minimum expenditures that would be required to achieve a constant standard of living (that is level of utility or economic well-being). As consumers may be expected to change the quantities they consume in response to changes in relative prices (see Substitution effect), the cost of living index is not a basket index. The quantities and expenditures made in one or other, or possibly both, periods cannot usually be observed in a timely manner. Cost of living indices cannot be directly calculated but may be approximated by superlative indices. See Conditional cost of living index. |
| Coverage | The set of goods and services of which the prices are actually included in the index. For practical reasons, coverage may have to be less than the ideal scope of the index, that is, the set of goods and services that the compilers of the index would prefer to include if it were feasible. |
| Current period, or comparison period | In principle, the current period should refer to the most recent period for which the index has been compiled or is being compiled. The term is widely used, however, to mean the comparison period; that is, the period that is compared with the base period, usually the price reference or index reference period. It is also widely used simply to mean the later of the two periods being compared. The exact meaning is usually clear in the context. |
| Current prices | The actual prices prevailing in the period in question. |
| Current value | The actual value of some aggregate in the period in question: the quantities in the period multiplied by the prices of the same period. |
| 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 with regard to the size of some relevant variable, the largest sampling units being included and the rest given a zero chance of inclusion. |
| 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. |
| Democratic index Discount | A form of CPI in which the expenditure proportions of each household are given equal weight in the calculation of the index, irrespectively of the size of its expenditures. See Plutocratic index. A deduction from the list or advertised price of a good or a 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 index | A price or quantity index that treats both prices and quantities as continuous functions of time. By differentiating 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 the changes between consecutive periods are linked together. |
| Domain | An alternative term for the scope of an index. See Scope. |
| Domestic concept | The use of weights covering all consumption expenditure on the national territory, regardless of the nationality or normal residence of the consumer. See National concept. |
| 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 over the periods they cover. |
| Drobisch price index | The arithmetic average of the Laspeyres price index and the Paasche price index. |
| Durable consumer good | A consumer good that can be used repeatedly or continuously for purposes of consumption over a period of one year or more. |
| Dutot index | An elementary price index defined as the ratio of the unweighted arithmetic averages of the prices in the two periods compared. |
| Economic approach | The economic approach to index number theory assumes that the quantities are functions of the prices, the observed data being generated as solutions to various economic optimization problems. In the CPI context, the economic approach usually requires the CPI to be some kind of cost of living index. |
| Edgeworth price index | A basket price index in which the quantities in the basket are simple arithmetic averages of the quantities consumed in the two periods. |
| Editing | The process of scrutinizing and checking the prices reported by price collectors. Some checks may be carried out by computers using statistical programs written for the purpose. |
| Elasticity of substitution | A measure of the extent to which one product is substituted for another in response to relative price changes. A zero elasticity of substitution means that there is no substitution. |
| Elementary aggregate | The lowest level of groups of goods or services for which expenditure weights are assigned and held constant for a period of one year or more. An elementary aggregate should consist of relatively homogeneous set of goods or services, with similar end-uses and similar expected price movements. More detailed weights to reflect the relative importance of individual price observations within elementary aggregates may be applied and updated more frequently. The elementary aggregates are the building blocks for the calculation of the higher-level indices. |
| Elementary price index | In general, an elementary index is a price index for an elementary aggregate, but it can also refer to a price index for a more detailed level below the elementary aggregate. Expenditure weights cannot usually be assigned to the price relatives for the sampled products within an elementary aggregate, although other kinds of weighting may be explicitly or implicitly introduced into the calculation of elementary indices. For example, scanner data could be used to develop a more detailed weighting program within an elementary aggregate. Three examples of unweighted elementary index number formulae are the Carli, the Dutot, and the Jevons. |
| Expenditure weights | See Weights. |
| Explicit (or direct) quality adjustment | A direct estimate of the value of the quality difference between the old and new product used to adjust one of the prices accordingly. Pure price change is then estimated as the difference in the adjusted prices. See 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 to the proportionate change in the value of the aggregate in question. |
| Fisher price index | The geometric average of the Laspeyres price index and the Paasche price index. It is a symmetric index and a superlative index. |
| Fixed-basket indices | A time series of basket indices that all use the same basket; see equation 4 of Appendix 6 to the Manual. In a CPI context, the fixed basket usually consists of the total quantities of goods and services consumed by the designated set of households over a period of a year or more. |
| Fixed-weight indices | An abbreviated description for a series of weighted averages of price relatives that all use the same weights; see equation 13 of Appendix 6 to the Manual. The weights are usually either actual or hybrid expenditure shares. |
| Geometric Laspeyres index | A weighted geometric average of the price relatives using the expenditure shares of the price reference period as weights. Also called Logarithmic Laspeyres index. |
| Goods | Physical, produced objects for which a demand exists, over which ownership rights can be established and for which ownership can be transferred between institutional units by engaging in transactions on the market. |
| Hedonic method | A regression model in which the market prices of different products are expressed as a function of their characteristics. Nonnumerical characteristics are represented by dummy variables. Each regression coefficient is treated as an estimate of the marginal contribution of that characteristic to the total price. The estimates may be used to predict the price of a new product for which the 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 | An aggregate index as distinct from an elementary index. |
| Household budget surveys | Sample surveys of households in which the households are asked to provide data on, or estimates of, the value of the goods and services acquired, paid, and used for consumption as well as other purposes over a given period of time. Also referred to household income and expenditure surveys. |
| Household final consumption expenditure | It consists of the expenditure, including expenditure whose value must be estimated indirectly, incurred by resident households on individual consumption goods and services, including those sold at prices that are not economically significant and including consumption goods and services acquired abroad. They exclude expenditures incurred by governments or nonprofit institutions on goods or services provided to households as free social transfers in kind. |
| Households | A household is a group of persons who share the same living accommodation, who pool some, or all, of their income and wealth and who consume certain types of goods and services collectively, mainly housing and food. Most countries choose to exclude groups of persons living in large institutional households (barracks, retirement homes, and so on) from the scope of their CPIs. |
| Hybrid values or expenditures | Hypothetical values, or expenditures, in which the 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, such as b, are valued at the prices prevailing in a later period, such as 0. |
| Hybrid weights | Weights defined as hybrid value, or hybrid expenditure, shares. |
| Identity test | A test under the axiomatic approach that requires that, if each and every price remains unchanged between the two periods, the price index must equal unity. |
| Implicit (or indirect) quality adjustment | Estimating the pure price change component of the price difference between the old and new products based on the price changes observed for similar products. The difference between the estimate of pure price change and the observed price change is considered as change due to quality difference. See Explicit quality adjustment. |
| Imputed price1 | The price assigned to a variety for which the price is missing in a particular period. The term “imputed price” may also refer to the price assigned to an variety 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. |
| Indexation | The periodic adjustment of the money values of some regular scheduled payments based on the movement of the CPI or some other price index. The payments may be wages or salaries, social security or other pensions, other social security benefits, rents, interest payments, and so on. |
| Index reference period | The period for which the value of the index is set at 100. |
| Institutional unit | 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. Households are institutional units. Other kinds of units include enterprises and governments. |
| Institutional households | A group of individuals staying in an institution for long periods of time, such as retirement homes, military accommodation, and boarding schools, and sharing resources. Such people are treated as belonging to private “institutional” households. |
| 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. This test is also described 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 year prices test | A test that may be invoked under the axiomatic approach that requires that, if all the base period prices are multiplied by the positive scalar l, the new price index is 1/l times the old price index. |
| 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 outlet. 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. |
| Jevons price index Laspeyres price index | An elementary price index defined as the unweighted geometric average of the sample price relatives. A basket index in which the basket is composed of the actual quantities of goods and services in the earlier of the two periods compared, the price reference period; see equation 3 of Appendix 6 to the Manual. It can also be expressed as a weighted arithmetic average of the price relatives that uses the expenditure shares in the earlier period as weights; see equations 7–10 of Appendix 6 to the Manual. The earlier period serves as both the weight reference period and the price reference period. |
| Linking | Splicing together two consecutive sequences of price observations, or 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 the other sequence so that the value in the overlap period is the same in both sequences and the spliced sequences form one continuous series. See equation 6 of Appendix 6 to the Manual. |
| Lowe index | A price index that measures the proportionate change between periods 0 and t in the total value of a specified basket of goods and services; that is, ∑ptq / ∑p0q, where the term q is the specified quantities. The basket does not necessarily have to consist of the actual quantities in some period. See Appendix 6 to the Manual. This type of index is described in the Manual as a Lowe index after the index number pioneer who first proposed this general type of index. The class of indices covered by this definition is very broad and includes, by appropriate specification of the terms q, the Laspeyres, Paasche, Edgeworth, and Walsh indices. Lowe indices are widely used for CPI purposes, the quantities in the basket typically being those of some weight reference period b, which precedes the price reference period 0. |
| Lower-level index | An elementary index as distinct from an aggregate index. |
| Matched products or models | The practice of pricing exactly the same product in two or more consecutive periods. It is designed to ensure that the observed price changes are not affected by the quality change. The change in price between two perfectly matched products is described as a pure price change. |
| Model | A specific variety whose characteristics are regularly updated. See Variety. |
| Mean value test for prices | A test under the axiomatic approach, which requires that the price index should lie between the smallest price relative and the largest price relative. |
| Modified Lowe index | A version of the Lowe index that compiles the index based on short-term price changes rather than long-term changes. This approach makes it easier for national statistical offices to introduce replacement varieties in the sample when a sampled variety disappears. The short-term approach also facilitates quality adjustments because only the current and previous period prices are needed in order to introduce a new variety into the index. See Lowe index. |
| Modified Young index | A version of the Young index that compiles the index based on short-term price changes rather than long-term changes. This approach makes it easier for national statistical offices to introduce replacement varieties in the sample when a sample variety disappears. The short-term approach also facilitates quality adjustments because only the current and previous period prices are needed in order to introduce a new variety in the index. See Young index. |
| Multilateral indices | A type of index that measures the aggregate price change between two periods based on prices observed in multiple periods including the two comparison periods. Multilateral indices were developed for price comparisons across countries (purchasing power parities) and have been adapted to compare prices over time. For price comparisons over time, multilateral index formulas are mainly used with scanner data. In this context, their main advantage is to avoid chain drift. The most common multilateral index formulas in CPIs are the Gini–Eltetö–Köves–Szulc, the Geary–Khamis, and the time product dummy. See Chapter 10 for further details. |
| National concept | The use of weights covering the expenditure of residents of a country, regardless of whether the expenditure is made within or outside of the country. See Domestic concept. |
| Nonprobability sampling | The deliberate (that is, nonrandom) selection of a sample of outlets and products on the basis of the knowledge or judgment of the person responsible. Also known as purposive sampling and judgmental sampling. |
| Outlier | A term that is generally used to describe any extreme value in a set of survey data. In a CPI 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. |
| Owner-occupied housing | Dwellings owned by the households that live in them. The dwellings are fixed assets that their owners use to produce housing services for their own consumption, these services being usually included within the scope of the CPI. The value of the services provided may be imputed by the rents payable on the market for equivalent accommodation or by user costs. See Rental equivalence and User cost. In the System of National Accounts (SNA) framework, the production of housing services for their own final consumption by owner-occupiers has always been included within the production boundary in national accounts, although it constitutes an exception to the general exclusion of own-account service production. |
| Paasche price index | A basket index in which the basket is composed of the actual quantities of goods and services in the later of the two periods compared. The later period serves as the weight reference period and the earlier period as the price reference period. The Paasche index can also be expressed as a weighted harmonic average of the price relatives that uses the actual expenditure shares in the later period as weights. See equations 7–11 of Appendix 6 to the Manual. |
| Plutocratic index | A form of CPI in which the weights are based on total aggregated expenditure values rather than average household expenditure proportions. |
| Price reference period | The period of which the prices appear in the denominators of the price relatives. See Base period. |
| Price relative | The ratio of the price of a variety in one period to the price of that same variety in some other period. |
| Price updating | A procedure whereby the quantities in an earlier period are revalued at the prices of a later period. The resulting expenditures are hybrid. In practice, the price-updated expenditures may be obtained by multiplying the original expenditures by price relatives or price indices. |
| Probability proportional to size sampling | A sampling procedure whereby each unit in the universe has a probability of selection proportional to the size of some known variable, such as the value of the sales of an outlet. |
| Probability sampling | The random selection of a sample of units, such as outlets or products, in such a way that each unit in the universe has a known nonzero probability of selection. |
| 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. |
| Purchaser’s price | The purchaser’s price is the amount paid by the purchaser, excluding any value-added tax or similar tax deductible 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. The purchaser’s price of a good includes any transport charges paid separately by the purchaser to take delivery at the required time and place. |
| Pure price change | The change in the price of the same variety; or the change in the price after adjusting for any change in quality. |
| Quality adjustment | An adjustment to the price of a variety of which the characteristics have changed over time. Quality adjustments are designed to remove the part of the observed price that is due to differences in the price-determining characteristics. In a CPI context, the adjustment is needed when the price of a replacement variety must be compared with the price of the variety 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. |
| Quantity relative | The ratio of the quantity of a product in one period to the quantity of that same product in some other period. |
| Quantity weights | A term sometimes used to describe the quantities in the basket. However, expenditures rather than quantities act as weights for price relatives. See Weights. |
| Quota sampling | Sample selection using judgmental procedures with respect to known characteristics such as product group or outlet type. The sample is drawn so as to contain the same proportions as in the total population of products, items, or outlets. |
| Ratio of averages | See Dutot index. |
| Rebasing | It refers to changing the weight reference period, price reference period, or index reference period. The weight reference period, price reference period, and index reference period may be changed separately or at the same time. |
| Reference population | The set of households included within the scope of the index. |
| Rental equivalence | The estimation of the imputed rents payable by owner-occupiers on the basis of the rents payable on the market for accommodation of the same type. |
| Replacement variety | A variety chosen to replace a variety for which prices have been collected previously, either because the previous variety has disappeared altogether or because it accounts for a diminishing share of the sales of the outlet, or the expenditures within the elementary aggregate. |
| Representative variety | A variety, or category of varieties, that accounts for a significant proportion of the total expenditures within an elementary aggregate, and for which the average price change is expected to be close to the average for all varieties within the aggregate. |
| Representativity bias | Bias in a basket index that results from the use of quantities that are not representative of the two periods compared; that is, that systematically diverge from the average quantities consumed in the two periods. For example, representativity bias may result from the use of an old, out-of-date basket which deviates systematically from the baskets in both the periods compared. In practice, representativity bias tends to be similar to substitution bias, as it is attributable to the same economic factors. |
| Reweighting | Replacing the weights used in an index by a new set of weights. |
| Revision | Often refers to changing index weights and implementing new calculation or compilation methodologies. |
| Sample augmentation | Maintaining and adding to the sample of outlets, items, and varieties in the survey panel to ensure that they continue to be representative of the population of outlets. A fixed sample of outlets tends to be depleted over time, as outlets cease trading or stop responding. Including new outlets also tends to facilitate the inclusion of new products in the CPI. |
| Sampled price | The price collected for a sampled product in a specific outlet at a specific time, sometimes described as a price quote. |
| Sample rotation | Limiting the length of time that outlets and products are included in the 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 outlets and products. Rotation is designed to keep the sample up to date. |
| Sampling frame | A list of the units in the universe from which a sample of units can be selected. The list may contain information about the units, which may be used for probability proportional to size sampling. Examples of lists that may be used for retail outlets are business registers, telephone directories (“yellow pages”), local authority records, or trade directories. Such lists may not cover all the units in the designated universe and may also include units that do not form part of that universe. |
| Scanner data | Detailed data on sales of products obtained by scanning the bar codes for individual varieties at electronic points of sale in retail outlets. The data can provide detailed information about quantities, characteristics, and values of varieties sold, as well as their prices. Scanner data constitute a rapidly expanding source of data with considerable potential for CPI purposes. |
| Scope | The set of products for which the index is intended to measure the price changes. The scope of a CPI will generally be defined with regard to a designated set of consumption goods and services purchased by a designated set of households. In practice, certain goods and services or households may have to be excluded because it is too difficult, time-consuming, or costly to collect the relevant data on expenditures or prices: for example, illegal expenditures. The coverage of an index denotes the actual set of products included, as distinct from the intended scope of the index. |
| Seasonal products | They are products that either are not available on the market during certain seasons or periods of the year or are available throughout the year but with regular fluctuations in their quantities and prices that are linked to the season or time of the year. |
| Services | They are the result of a production activity that changes the conditions of the consuming units or facilitates the exchange of products or financial assets. |
| Specification | A description or list of the characteristics that can be used to identify an individual sampled variety to be priced. A tight specification is a fairly precise description of an item intended to narrow the range of varieties from which a price collector might choose, possibly reducing it to a unique variety, such as a particular brand of television set identified by a specific code number. A loose specification is a generic description of a range of items that allows the price collector some discretion as to which particular variety or model to select for pricing, such as color television sets of a particular size. |
| 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. |
| Substitute | A product of which the characteristics are similar to those of another product and that can be used to meet the same kinds of consumer needs or wants. |
| Substitution | The replacement of products by substitutes, typically in response to changes in relative prices. Rational utility-maximizing consumers, as price takers, typically react to changes in relative prices by reducing, at least marginally, their consumption of goods and services that have become relatively dearer and increasing their consumption of substitutes that have become relatively cheaper. Substitution results in a negative correlation between the quantity and price relatives. |
| Substitution bias | This is generally understood to be the bias that results when a basket index is used to estimate a cost of living index, because a basket index cannot take account of the effects on the cost of living of the substitutions made by consumers in response to changes in relative prices. In general, the earlier the period of which the basket is used, the greater the upward bias in the index; see Representativity bias. |
| Substitution effect | The effect of substitution on the value of an index. |
| Superlative index | A type of index formula that can be expected to approximate to the cost of living index. An index is said to be exact when it equals the true cost of living index for consumers whose preferences can be represented by a particular functional form. A superlative index is then defined as an index that is exact for a flexible functional form that can provide a second-order approximation to other twice-differentiable functions around the same point. The Fisher, the Törnqvist, and the Walsh price indices are examples of superlative indices. Superlative indices are generally symmetric indices. |
| Symmetric index | An index that treats both periods symmetrically by attaching equal importance to the price and expenditure data in both periods. The price and expenditure data for both periods enter into the index formula in a symmetric way. |
| System of National Accounts (SNA) | A coherent, consistent, and integrated set of macroeconomic accounts, balance sheets, and tables based on a set of internationally agreed-upon concepts, definitions, classifications, and accounting rules. Distribution and use of income accounts and household final consumption expenditure form part of the SNA. The expenditure data are some of the sources that are used to estimate expenditure weights for CPI purposes. |
| Time reversal | An index number property such that, if j Ik denotes a particular kind of price index formula that measures the change from period j to period k, then j Ik ≡ 1/kIj where k Ij measures the change from period k to period j. When an index has this property, the change is the same whether it is measured forward from the first to the second period or backward from the second to the first period. An index may be required to satisfy the time reversal test under the axiomatic approach. |
| Törnqvist price index | A symmetric index defined as the weighted geometric average of the price relatives in which the weights are simple arithmetic averages of the expenditure shares in the two periods. It is a superlative index. Also known as the Törnqvist–Theil price index. |
| Transitivity | See Circularity. |
| Unit value or average value | The unit value of a set of homogeneous products is the total value of the purchases/sales divided by the sum of the quantities. It is therefore a quantity-weighted average of the different prices at which the product is purchased/sold. Unit values may change over time as a result of a change in the mix of the products sold at different prices, even if the prices do not change. |
| Updating | Changing the index weights. See Revision and Rebasing. |
| User cost | The cost incurred over a period of time by the owner of a fixed asset or consumer durable as a consequence of using it to provide a flow of capital or consumption services. User cost consists mainly of the depreciation of the asset or durable (measured at current prices and not at historic cost) plus the capital, or interest, cost. |
| Uses approach | An approach to CPIs in which the consumption in some period is identified with the consumption goods and services actually used up by a household to satisfy their needs and wants (as distinct from the consumption goods and services acquired). In this approach, the consumption of consumer durables in a given period is measured by the values of the flows of services provided by the stocks of durables owned by households. These values may be estimated by the user costs. |
| Value | Price times quantity. The value of the expenditures on a set of homogeneous products can be factored uniquely into its price and quantity components. Similarly, the change over time in the value of a set of homogeneous products can be factored uniquely into the change in the unit value and the change in the total quantities. There are, however, many different ways of factoring the change over time in the value of a set of heterogeneous products into its price and quantity components, a phenomenon that gives rise to the index number problem. |
| Variety | The individual product for which prices are collected during the collection period. It includes the detailed specification of the product or item observed. |
| Walsh price index | A basket index in which the quantities are geometric averages of the quantities in the two periods; see Appendix 6 to the Manual. It is a symmetric index and a superlative index. |
| Weight reference period | The period of which the expenditure shares serve as the weights for a Young index, or of which the quantities make up the basket for a Lowe index. There may be no weight reference period when the expenditure shares for the two periods are averaged, as in the Törnqvist index, or when the quantities are averaged, as in the Walsh index. See Base period. |
| Weighted arithmetic average index | An index defined as a weighted arithmetic average of the price relatives: namely, Σw(pt / p0), where the weights w sum to unity. |
| Weights | A set of numbers summing to unity that are used to calculate averages. In a CPI context, the weights are generally actual or hybrid expenditure shares that sum to unity by definition. They are used to average price relatives or elementary price indices; see Appendix 6 to the Manual. Quantities of different kinds of products are not commensurate and not additive. They cannot be used to average elementary price indices. The quantities that make up a basket should therefore not be described as quantity weights. |
| Young index | A Young index is a weighted arithmetic average of the price relatives, Σw(pt / p0), in which the terms w refer to the actual expenditure shares of period b, the weight reference period; that is, w = sb = pbqb / Σpbqb. It is a weighted version of the Carli index. |
1
This definition differs from that used by the 2008 SNA.
