Volume and Price measurement

Volume and Price measurement
Robin Lynch National Accounts in Practice – Advanced course Luxembourg, 2-11 October 2017 THE CONTRACTOR IS ACTING UNDER A FRAMEWORK CONTRACT CONCLUDED WITH THE COMMISSION

Volume and price measurement
All entries in the national accounts are values expressed in monetary units This the common measuring unit for economic transactions, flows and stock levels It enables exchanges to be valued identically for supplier and user

My monthly expenditure on chocolate bars is as follows Jan 14 euro May 10 euro Feb 12 euro June 9 euro March 14 euro July 9 euro April 11 euro Aug 10 euro What do these figures tell us?

Price of chocolate bars is as follows Jan 0.5 euro May euro Feb 1 euro June 1.5 euro March 1 euro July 1.5 euro April 1 euro Aug euro What do these figures tell us?

I buy (eat?) a number of chocolate bars as follows Jan 28 bars May 10 bars Feb 12 bars June 6 bars March 14 bars July 6 bars April 11 bars Aug 5 bars

Value over time

Users want to know the price change over time Users want to know the “real” change in an economic measure such as GDP So we must take out price change to reveal the volume change

For an individual product, the fundamental identity when an exchange takes place is Value= quantity x price: v = p * q So if we know value and price, we can calculate quantity as value / price q = v / p

Quantity

Series showing changes in value
Jan 14 euro May 10 euro Feb 12 euro June 9 euro March 14 euro July 9 euro April 11 euro Aug 6 euro Expenditure relative to January Jan 0 euro May -4 euro Feb -2 euro June -5 euro March +0 euro July -5 euro April -3 euro Aug -8 euro

Index form facilitates comparison of behaviour over time, with other growth measures Index form helps mathematics of analysis Expenditure relative to January Jan 14/ May 10/14 Feb 12/14 June 9/14 March 14/14 July 9/14 April 11/14 Aug 6/14

Index form of volume growth
Index form Jan = 100 Jan Feb March April May June July Aug

Index numbers are usually expressed relative to a base figure of 100 This gives users a sense of relative growth But for conceptual purposes, it is easier if the simple ratio is used

The complete chocolate story
Value Price Quantity Jan Feb Mar Apr May June July Aug

Index form Putting the series in index form does not alter the relation V = p * q Scaling to 1 rather than 100

Index form for chocolate
Value Price Quantity Jan Feb Mar Apr May June July Aug

Index form (Jan = 100) Value Price Quantity Jan Feb Mar Apr May June July Aug

Change of reference period
Changing the reference period does not affect the percentage growth measures in the series So a recent year is normally chosen for the reference year, to help users get the message in terms of recent experience

Growth forwards and backwards
For the quantity growth measure referenced to May, growth from January to February is given by Feb/Jan = 0.43 Growth looking backwards from Feb to Jan is given by Jan/Feb = 2.32 Growth backwards is the reciprocal of growth forwards

Aggregate measures Values are in money terms, and so if we spend money on chocolate and ice-cream, we can easily calculate the total expenditure as the sum of the values spent on each

But we cannot calculate aggregate measures of prices and quantities in this way Apple harvest is 30,000 kilos, at 2 euros per kilo Orange harvest is 20,000 kilos at 1 euro per kilo Value of fruit harvest is 60,000 euros worth of apples plus 20,000 euros worth of oranges = 80,000 euros for the total fruit harvest

We can calculate the total weight of fruit as 30, ,000 = 50,000 kilo We can calculate the average price of fruit as (2 + 1)/2 = 1.5 But we have lost the connection between value, price and quantity v = p * q 50,000 * 1.5 = 75,000 euros (not 80,000 euros)

In the next year, the total value of the harvest is measured at 95,000 euros The change can be due to A change in the price of apples A change in the price of oranges A change in the size of the apple harvest A change in the size of the orange harvest

How can we partition the change into price and volume factors? We must use a measure of the relative economic importance of components to derive useful aggregate measures

Suppose complete data are available for the fruit harvest in the next period Apples - price rises from 2 to 4 euros per kilo Oranges – price drops from 1 euro to 50 cents per kilo Weight of apples drops from 30,000 to 20,000 kilos Weight of oranges rises from 20,000 to 30,000 kilos

How should we measure the change in volume of the harvest – in real terms?

Apples q p v Year 1 30000 2 60000 Year 2 20000 4 80000 Oranges 1 0.5 15000 Fruit 50000 1.5 2.25 95000

How should we weight together the real growth of each fruit? What figure reflects the relative importance of apples and oranges in the economy?

One measure of relative importance is the value of the harvests in year 1 (the base year) Growth of the harvest into the second year is the individual growth of apples and oranges, weighted by the value of year 1 harvests

Apples quantity growth index is 20/30 = .67 Oranges quantity growth index is 30/20 = 1.5 Year 1 value of apples as component of fruit harvest is 60/80 = .75 Year 1 value of oranges as component of fruit harvest is 20/80 = .25 Weighted index = .75 * * 1.5 = = 0.875

So this base year weighted measure shows % decrease in real growth of the fruit harvest This index form is called the Laspeyres index Lq,t = sum ( w0 . ( qt / q0 ) ) (1) Where w0 = v0 / sum ( v0 ) and the sum is over the different products

Other forms of the Laspeyres index
We can rearrange the equation into different forms

Lq,t = sum ( w0 . ( qt / q0 ) ) (1) Sum of growths weighted by product values in base year = sum ( v0 / sum ( v0 ) . ( qt / q0 ) ) = sum ( v0 . ( qt / q0 )) / sum (p0 . q0) = sum ((p0 . q0) . ( qt / q0 ))/ sum (p0 . q0) = sum ( p0 . qt ) / sum ( p0 . q0 ) (2)

Lq,t = sum ( p0 . qt ) / sum ( p0 . q0 ) (2) If we transform from index form by not dividing by the base year value, base year prices value the quantities of later periods – constant prices = sum ( p0 . ( vt /pt ) ) / sum ( v0 ) = sum ( vt . ( p0 / pt ) )/ sum ( v0 ) = sum ( vt / ( pt/p0 ) ) / sum ( v0 ) (3)

Index forms sum ( vt / ( pt/p0 ) ) / sum ( v0 ) (3) This form shows the value at time t divided by the relative price of the price at t to the base year price

Lq,t = sum ( w0 . ( qt / q0 ) ) This form of the relation says that a Laspeyres index is created by weighting together, according to their relative base year values, indices of quantity growth of the individual products

Lq,t = sum ( p0 . qt ) / sum ( p0 . q0 ) (2) This form shows that the series of Laspeyres indices can be thought of as the quantities occurring in year t, valued at the prices of the base year, relative to the base year value, If the series is not expressed in index form by omitting division by v0, then the series is a set of quantities for year t valued at base year prices i.e. “constant prices”

Lq,t = sum ( vt / ( pt/p0 ) ) / sum ( v0 ) (3) The third form shows that a series of Laspeyres indices can be created by “deflating” the current values of year t by the appropriate price deflator (pt/p0) and then converting to index form by dividing the deflated values by the base year value. This process of stripping out the effect of inflation by dividing product values by the respective price indices is known as “deflation”

Index forms Lq,t = sum ( vt / ( pt/p0 ) ) / sum ( v0 ) (3) This is a very useful form of the index because . .

Index forms Lq,t = sum ( vt / ( pt/p0 ) ) / sum ( v0 ) (3)
It allows us to use a proxy for the true price relative, and assume that all quantity prices move in the same way as the proxy

Exercise Using the figures for chocolate and ice-cream given, demonstrate that the three different forms of the Laspeyres index series give the same figures.

Base-weighted growth Lq,t = sum ( w0
Base-weighted growth Lq,t = sum ( w0 . ( qt / q0 ) ) Constant prices sum ( p0 . qt ) / sum ( p0 . q0 ) Deflated values Lq,t = sum ( vt / ( pt/p0 ) ) / sum ( v0 )

Is there another equally valid choice of weights?

Why not choose the weights of year 2? Another index form is obtained by considering growth from the point of view of the current year. This index is known as the Paasche index

A Paasche index uses the weights of year t, and measures the growth backwards from t to the reference year 0. So the growth from the reference year to the current year is the reciprocal of this number So a Paasche index is a Laspeyres index on the move, looking backwards !

For volumes, Paasche = 1 / L where looking backward from t to the base period 0 Lq,0 = sum( vt . ( q0/qt) ) / sum ( vt ) For prices Pp,0 = sum(vt) / sum(vt.(p0/pt) ) = sum ( pt.qt ) / sum (pt. qt .p0/pt ) = sum ( pt.qt ) / sum ( p0.qt ) (4)

If we consider version (2) for the Laspeyres volume index Lq,t = sum ( p0 . qt ) / sum ( p0 . q0 ) and the Paasche index for prices in the form Pp,t = sum ( pt.qt ) / sum ( p0.qt ) Then Lq,t * Pp,t = Vt / V0 the index series of values

So the Laspeyres volume index and the Paasche price index form a useful pair in that at aggregate index level Value = Paasche price * Laspyres volume Laspyres volume = Value / Paasche price So deflating values at an aggregate level by Paasche price indices will give Laspeyres volume indices

The simple relationship between Paasche and Laspeyres indices, may seem that the choice is determined by which set of weights best reflects the importance of product groups (base year or current year weights). But there is a practical issue which makes Laspeyres the popular choice What?

17 Volume and Price measurement exercise solution handout.pdf

Laspeyres indices need weighting data from an earlier year (the base year) which is not prone to large revision. Paasche index numbers use current (or at least very recent year) data for base weights – this data is more prone to revision, and so this generates changes to previously published economic growth statistics.

Linking series We can link index series over different time spans together by choosing a common link, and the ratios of the series at the link as a factor to put them on the same reference

Five yearly rebasing to annual chain-linking
Five yearly rebasing means Weights to combine individual economic series such as value added by industry, become out of date Introducing a new base year after five years can mean large revisions to growth Assumptions such as turnover moves consistently with value added over time are less likely to hold

Annual chain-linking Weights are more up to date
Weights are applied to time periods for which they are relevant Less revisions due to continuing updating of structure assumptions and weights

Prices used in national accounts
Consumer Price Index (CPI) and its components – deflating final consumption expenditure Producer Price Indices are used to deflate business turnover, and this is used as a proxy for movements in real value added Wage rates are used to render government value added in real terms

Double deflation The ideal situation to estimate value added in volume terms is to measure outputs and inputs in volume terms as year to year Laspeyres index forms. Then this “double deflation” and the additivity of the Laspeyres index form enables value added to be calculated as the difference between the two

Double deflation The process of double deflation depends on up-to-date and reliable information on industry structures Experience shows that whereas industry can give robust estimates of sales and turnover, they are less reliable on costs and the pricing of costs. And this can generate results which are hard to explain

Double deflation But sticking to historic structures is effectively returning to single deflation methods, as the assumption of constant structure means that no new information on inputs is used A reasonable compromise can be struck by using the supply-use structure to generate a consistent set of industry GVA in volume terms, and updating the structure on a regular basis where industry structure is known to be changing.

Prices – unit values for international trade
Estimating prices for exports is best done through direct survey of business, in an expanded producer price inquiry which identifies goods intended for export But imports pose a larger problem – surveys on prices are difficult due to a variety of factors, including confidentiality and multinational transfer pricing practice

Unit value indices These are derived from customs information, where information on value of consignment and number of homogeneous units are both available. The derived unit value indices are an approximation to the price of the goods involved These price indicators are considered inaccurate in many cases, but use din the light of no readily available alternative

Handling price change for new products
1. Assume its price moves according to other “similar” products and splice it on 2. Use hedonic methods to model price for the range in terms of characteristics of old products, to estimate a historic price for new product

Hedonic methods - Handling new products and quality changes
Example A freezer has 40 litre capacity and costs 400 euros, another 30 litre capacity and costs 300 euros A new freezer is introduced of 50 litre capacity and costs 400 euros What is the change in price?

Hedonic methods History suggests that price is a linear function of cubic capacity Expected price is 50*10 = 500 euros Actual price is 400 euros So this is a price reduction of 20% (400 is 20% less than 500)

Hedonic methods The same principles can be applied to much more complicated cases Note that stratification of detail has the same effect as hedonic estimation of quality change “Quality is quantity hidden in the public specification of the product” E.g. Box of chocolates – change the mix to change the quality / quantity

Thank you for listening and participating End

Volume and Price measurement

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Volume and Price measurement

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