# Gross Domestic Product Estimates at Constant Prices

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Gross Domestic Product Estimates at Constant Prices
Notes on SNA_GDP Estimates at ConstantPrice 3/31/2017 Module-I: PP5 Gross Domestic Product Estimates at Constant Prices Welcome etc. Training Course Material for e-Library on System of National Accounts March 2009 UNSIAP_e-Learning Course_Module1

Outline Concepts and principles Value, price, quantity and volume
Estimate of GO at constant prices Index numbers for price and volume measures in a National Accounts System Techniques for obtaining estimates at constant prices Base, reference, and weighting periods of index Choice of base year in the national accounts and chaining II. Price and volume measures for Gross Value Added/ GDP

Value, Price and Quantity
Notes on SNA_GDP Estimates at ConstantPrice 3/31/2017 Value, Price and Quantity Value = Price multiplied by Quantity V = p * q Quantity: Unit for measuring amount of a good or service Price : Value per unit of quantity (of same quality) UNSIAP_e-Learning Course_Module1

Value, Price and Quantity (Contd.)
Notes on SNA_GDP Estimates at ConstantPrice 3/31/2017 Value, Price and Quantity (Contd.) Values are expressed in common unit (currency) and are additive across products Quantities are additive only at the narrowly defined single product level Value at a single product level vs at an aggregated (over several items, say, n ) level UNSIAP_e-Learning Course_Module1

Value, Price and Quantity (Contd.)
Notes on SNA_GDP Estimates at ConstantPrice 3/31/2017 Value, Price and Quantity (Contd.) For n items, denote, : price of item i in period t ; i= 1,2,......,n : quantity of item i in period t : value of item i at current prices in period t Thus at item level, : total value at current prices in period t for all items At aggregate level, UNSIAP_e-Learning Course_Module1

Notes on SNA_GDP Estimates at ConstantPrice
3/31/2017 Quantity, Quality and Volume Prices and values in 000’units of currency No change in prices Car production High priced model Low priced model Total Price per unit 20 15 Production in Year 1 10 30 Production in Year 2 Total value of production in Year 1 200 300 500 Total value of production in Year 2 400 150 550 UNSIAP_e-Learning Course_Module1

Quantity, Quality and Volume (Contd.)
Unit value in year 1 = 500/30 = Unit value in year 2 = 550/30 = Change in volume = 550/ percent Change in quantity = 30/ percent Change in prices = 0 percent; because prices remain unchanged Change in unit values = / percent

Quantity, Quality and Volume (Contd.)
Conclusions: Unit values are affected by the change in the product mix Change in product mix = change in average quality The term “VOLUME” is preferred to “QUANTITY” Change in “QUALITY” is regarded as change in “VOLUME”, not as change in “PRICE”

What Are the Ways to Value an Aggregate?
Aggregate at current price - the value of the items of the aggregate (e.g., goods and services) using prices of the period Aggregate constant price - the value of items of the aggregate using fixed prices of a fixed period (called base period)

How to distinguish the two aggregates?
Notes on SNA_GDP Estimates at ConstantPrice 3/31/2017 How to distinguish the two aggregates? For example Gross output (GO) at current price is represented as i Pit Qit Pit : price of ith item at the period t Qit : volume or quantity of ith item at period t t : reference period of the estimates UNSIAP_e-Learning Course_Module1

How to distinguish..? GO at constant price is represented as i Pi0Qit
Pi0 : price of ith item at the base period 0 Qit : volume or quantity of ith item at period t

How to estimate GO at constant prices?
GO at current price GOt = PtQt Qt : quantity or volume at time t Pt : price at time t GO of period t at constant price of period 0 GO0,t = P0Qt Qt : quantity or volume at time t P0 : price at time 0

How to Estimate GO at Constant Prices? (Contd.)
Revaluation : Multiply the quantity or volume at time t by price at time 0 Deflation : Divide the GO at current price by price relative or price index with base 0 Extrapolation : Multiply the value at time 0 with volume relative or volume index

How to Estimate GO at Constant Prices? (Contd.)
Revaluation : Multiply quantity at time t by price at time 0 GO0,t = QtP0

How to Estimate GO at Constant Prices (Contd.)
Price deflation : Divide current price estimate by price relative/price index GO0,t = QtPt / (Pt / P0 )

How to Estimate GO at Constant Prices (Contd.)
Volume extrapolation : Multiply base year value by volume relative or volume index GO0,t = Q0P0 * Qt/Q0

Index Numbers of Prices and Volume
Denoting: a (fixed-base) Laspeyres volume index with period 0 as the base period a (fixed-base) Laspeyres price index with period 0 as the base period wi0 the base period weight, that is, item i's share in the total value in the base period What follows is popular Price and Volume Index ,

The Laspeyres Volume Index
Arithmetic average of quantity relatives with base period weights

The Laspeyres Price Index
Arithmetic average of price relatives with base period weights

The Paasche Volume Index
Further denoting: a (fixed-base) Paasche volume index with period 0 as base period Harmonic average of quantity relatives with current period weights

The Paasche price index
Further denoting: a (fixed-base) Paasche price index with period 0 as base period Harmonic average of price relatives with current period weights

The Fisher Price Index The Fisher Volume Index Geometric average of Laspeyres and Paasche indices

What is Meant by Estimates at Constant Prices?
The value of a product or group of products, valued for the current period using its own prices from an earlier period (which are kept constant) At the micro level: At the aggregate level: the total value of a group of products in period t where each item is revaluated at its own prices of period 0 (period 0 is kept constant for a period of time) Where: is the price of item i in period 0 is the quantity of item i in period t is the total value in period t measured at the prices of period 0

What is Meant by Estimates at Constant Prices?
Changes over time in a constant price time series reflects only changes on quantities (and quality) Thus it is an aggregated volume measure expressed in money terms which thus is additive It is not value of a product or group of products adjusted for changes in the general price level

What is the relationship between measures at Constant prices and Volume Index formulas?
Denoting: Q0,t the total value in period t measured at the prices of period 0 a (fixed-base) Laspeyres volume index with period 0 as the base period wi0 the base period weight, that is, item i's share in the total value in the base period. The measure of change from the base year in the constant price time series is: the Laspeyres (fixed-base) Volume Index Which is one of the several volume index formulas

What is the relationship between measures at Constant prices and Volume Index formulas?
The Laspeyres (fixed-base) Volume Index Measures at constant prices, one of several alternative volume measures Alternative volume measures based on: the Fisher index formula the Tornqvist superlative index formula the Paasche index formula chain-linked indices

The Implicit Price “Deflator”
For an aggregate, the relationship between a measure at constant prices and a measure at current prices is an implicit price ‘deflator’ Price measures for the main national accounts aggregates are (always) derived implicitly a (fixed base) Paasche Price Index implicitly derived One of several alternative formulas for aggregated price measures in general The proper index formula for constructing deflators to derive constant price estimates for (detailed) national accounts items

Two main requirements for volume and price measures in an accounting system
Volume measures for multiplicity of goods and services within an accounting framework should for each period be additive Required for compilation reasons (Use of the accounting framework as an estimation tool + consistency in aggregation) Analytical convenience The aggregate price measure times the aggregate volume measure should be equal to the current price value- The (weak) Factor Reversal Criteria (test) Required for: Compilation reasons Integrated analysis of movements in current price values and the related price and volume components

Two main requirements for volume and price measures in an accounting system
Volume measures should for each period be additive The (weak) Factor Reversal Criteria (test) Constant price Laspeyres (fixed-base) Volume measures combined with Paasche Price indices fulfill these requirements But are not the only ones

How to Obtain Constant Price Estimates for Detailed National Accounts Items?
The three main techniques for deriving constant price estimates at the detailed compilation level Revaluation Volume extrapolation Deflation

Revaluation That is to revalue current quantities by multiplying with prices of base year Require complete count of quantities produced or used limited use, mainly in agriculture

Volume extrapolation That is to update the base year's value according to the movement in an appropriate volume index (volume indicator) difficult to incorporate new products properly when constructing volume indices directly difficult to properly adjust for changes in quality for many products it is difficult to define the unit of quantity in general not the preferred technique (except under hyper inflation)

Deflation That is to deflate by a suitable price indicator
easy to incorporate new products and new activities when collected current price data easier to properly adjust for changes in quality when constructing price indices prices for related products may show similar movements: the idea of representative prices in general the preferred technique

Base and Reference Periods
The period which is equal to 100 Base period: (1)The pricing year (the base year) for the constant price data in the national accounts (2) Price base period: The period (or data) whose prices are used as denominators in calculating the price relatives pt / p0 (3)Quantity base period: The period (or data) whose quantities are used as denominators in calculating the quantity relatives qt /q0

Weight Period The period (s) from which the weights are taken
Equal to the base period for a (fixed-base) Laspeyres index (w0) and to the current period for a (fixed-base) Paasche index (wt) Fisher, Tornqvist, and other (fixed-base) symmetric indices have weight from two periods. Chain-linked indices have as many weight periods as links The base period is equal to the weight period for a Laspeyres index and other base year weighted indices, but not for current weighted indices such as Paasche, symmetric indices such as Fisher and Tornqvist, or for chain-linked indices

Why change base year? Structural changes in production structure
Structural changes in consumption patterns Structural changes in relative prices Appearance of new products Disappearance of old products Larger quality changes Goods and services are not comparable between periods that are to far apart How to derive continuous time series by chain-linking? When to chain-link and when not to?

Choice of Base Periods in the National Accounts and Chaining
Main Recommendations Do frequent change of base year and chain-linking Do not change the base period more frequently than annually (Years - not quarters as base period) Do not chain link over periods with substantial price/ volume oscillation Base years should be as normal as possible

How to Obtain Price and Volume Measurements for GDP?
Through the price and volume measures for its components From the production approach for Value added by industry Plus for taxes less subsidies on products From the expenditure approach for Government final consumption expenditures Plus for Households final consumption expenditures Plus for NPISH’s final consumption expenditures Plus for capital formation (including changes in inventories) Plus for exports minus for imports Integrated current supply and use tables, the optimal framework for price and volume measurements in the national accounts

Gross Value Added A residual item
No observable flows of goods and services as counterpart Cannot be factored directly into its own quantity and price components Value added at constant prices can only be defined and measured indirectly using the accounting relation as: Where: xij,t is the “quantity” of output of product i produced by industry j in period t mij,t is the “quantity” of product i used as intermediate consumption by industry j in period t is the (average) basic price of product i in period t, produced by domestic producers is the (average) purchasers price of product i used by domestic producers (covers domestic produced and imported products, and includes trade and transport margins, subsidies, and non- deductible product taxes

Laspeyres "volume" index for value added Paasche "price" index for value added

Double Deflation The derivation of value added at constant prices as a difference between output at constant prices and intermediate consumption (IC) at constant prices is called “double deflation”, although output and IC at constant prices could be derived either by deflation or by extrapolation Double deflation requires reliable volume and price measurements of both output and intermediate consumption requires a breakdown of output and intermediate consumption by product  Double deflation is not recommended when value added accounts for only a small proportion of output

Volume Measures for Value Added Alternative Methods
Double deflation - double extrapolation Separate estimates for output and intermediate consumption at constant prices, value added as the difference Requires current information regarding: intermediate consumption shares the structure of intermediate consumption

Volume Measures for Value Added Alternative Methods (Contd.)
Single extrapolation of value added Extrapolation with output Assumes fixed input output coefficients Price measures for intermediate consumption implicitly given Extrapolation with employment data Adjustments for normal increases in labor productivity?

Volume Measures for Value Added Alternative Methods (Contd.)
Single deflation of value added Deflation with the output deflator Assumes parallel price movements for output and intermediate consumption Changes in input output coefficients implicitly given Deflation with a wage index Deflation with a general measure of inflation such as the total CPI Do not result in a volume measure Provides a measure of a different concept, real income

Work explicitly with all elements of the production account for each kind of activity Produce and publish price and volume measures for Gross output and intermediate consumption in addition to value added Gross value added is a complex concept. Some economists even questions the economic meaning of volume measures for net concepts like value added Jumping to value added, and not focusing on gross output and intermediate consumption with value added as a derived balancing item, may lead to use of inferior methods In particular to deflation with the output deflator, when alternative and better methods exist. e.g., single extrapolation of value added with output as extrapolator

Other Approximate Measures of Value Added at Constant Prices Intermediate inputs based estimates Employment based estimates Total inputs based estimates Estimation of output at constant prices: some specific activities (Unique products): Construction Financial intermediation services indirectly measured Trade margins Non-market services

Input based measures for output and Value Added at Constant Prices to be used when no direct price or volume information for output is available Volume indicators for output based on compound volume indices for total observable inputs Price deflators for output based on compound price indices for total observable inputs Adjustments for normal increases in total factor productivity Adjustments for observed changes in mark-ups

Price and Volume Measures for GDP by Expenditure Categories
GDP at constant prices from the expenditure approach is derived as the sum of expenditure components at constant prices The expenditure components of GDP are aggregates of transactions that can be compiled by observing and recording actual transactions The value of these transactions can be factored into their own prices and quantities Therefore, more accurate measure of price and volume for GDP conceptually could be obtained through expenditure approach Commonly, the deflation of current values is used to derive data at constant prices for most of expenditure items, although extrapolation by volume index could also be used

Data requirements and compilation issues
Common problems: Price indices usually are Laspeyres indices Base year for volume and price indices differ from the base year for national accounts Not all volume and price indices have similar base period Coverage of activity in the national accounts and in the volume and price indices might (or usually) differ Coverage of volume and price indices might also change over time For many activities, no volume and price indices are available Data on value and/or quantity and/or price are incomplete

Data requirements and compilation issues
Practical guidance Compile estimates at more disaggregate level Use all the possible methods, make comparative analysis of results, and choose the best Make thorough analysis of coverage and compilation methods for source statistics, and adjust them to yield estimates consistent with SNA coverage and definitions There is no single recommendation, much depends on compiler’s capability to tackle intelligently different situations

Steps Involved in Changing the Base Year
In principle: Price and volume measurement in an integrated accounting framework (particularly constant price measures) requires access to large amount of detailed Paasche price indices (deflators) and/or Laspeyres volume indices tailor made to the national accounts needs and covering all GDP by activity and expenditure items; all using the same price and quantity base Change of base year implies a change of the price and quantity base for all these indices

Steps Involved in Changing the Base Year (Contd.)
In practice: National accountants are forced to use whatever information available Compiles approximate implicit Paasche price deflators and approximate Laspeyres volume indices by deflating with Laspeyres price indices and extrapolating with whatever volume indicators available Compilations should be conducted at a sufficient detailed level Conduct the aggregation from this detailed level to the main national accounts aggregates in accordance with main principles

Steps Involved in Changing the Base Year (Contd.)
At the detailed compilation level: Changing the reference period for the individual price and volume indices used from being equal to the old base year to being equal to the new base year Conducting the aggregation from this detailed compilation level and up to the national accounts aggregates accordingly

Steps Involved in Changing the Base Year (Contd.)
Steps in Practice: When changing from 1990 to 2000 as base year: Revaluation: Replace With Deflation: A change of base year by Changing the reference period from 1990 to 2000 for the deflators used at the most detailed level Volume extrapolation: Changing the period from which the level are being extrapolated Replace Q90,t = V2000 * I90,t With Q2000,t = V2000 *(I90,t / I90,2000)

Chain linking means to construct a volume index series by multiplying together the indices with different base and reference periods. For example, let I2,3 be a Laspeyres volume index measuring the volume change from period 2 to period 3 with weights from period 2, then an annual chain-linked Laspeyres index series from period 0 to period t can be constructed as Furthermore, observe that if the index formulas constituting each link in the index series satisfy the factor reversal test (that V=P*Q), then the chain-linked index series will also satisfy the factor reversal test