Volume and Price measurement

Volume and Price measurement
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 Feb 12 euro June 9 March 14 euro July 9 April 11 euro Aug 6 What do these figures tell us?

Price of chocolate bars is as follows Jan 1 euro May 1 Feb 1 euro June 1.5 March 1 euro July 1.5 April 1 euro Aug 2 What do these figures tell us?

I eat chocolate bars as follows Jan 14 euro May 10 Feb 12 euro June 6 March 14 euro July 6 April 11 euro Aug 4

Users wish 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 and 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

Simple index form Jan 14 euro May 10 Feb 12 euro June 9
March 14 euro July 9 April 11 euro Aug 6 Expenditure relative to January Jan 0 euro May -4 Feb -2 euro June -5 March +0 euro July -5 April -3 euro Aug -8

Index form facilitates comparison of behaviour over time Expenditure relative to January Jan 14/14 euro May 10/14 Feb 12/14 euro June 9/14 March 14/14 euro July 9/14 April 11/14 euro Aug 6/14

Index form Index form Jan = 100 Jan 1.00 100.0 Feb 0.86 85.7
March April May June July Aug

Index numbers are usually expressed relative to a base figure of 100 This gives users a sense of relatibe 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 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 absorb the growth change message

Growth forwards and backwards
For the quantity growth measure referenced to May, growth from January to February is given by Feb/Jan = 0.86 (-14%) Growth looking backwards from Feb to Jan is given by Jan/Feb = 1.17 (+17%) So growth backwards is the reciprocal of growth forwards

Aggregate measures Values are in money terms, and so if we also spend money on apples and oranges, 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 weight of the apple harvest A change in the weight of the orange harvest

How can we partition the change into price and volume factors? We cannot directly observe the aggregate price and aggregate volume change We must use a model of the relative economic utilities to customers in order to derive useful aggregate measures

Let us 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 is the value of each harvest 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

Lq,t = sum ( w0 . ( qt / q0 ) ) (1) = 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) = sum ( p0 . ( vt /pt ) ) / sum ( v0 ) = sum ( vt . ( p0 / pt ) )/ sum ( v0 ) = sum ( vt / ( pt/p0 ) ) / sum ( v0 ) (3)

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”

Exercise Using the figures for apples and oranges given, demonstrate that the three different forms of the Laspeyres index series give the same figures.

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

Paasche = 1 /L where L = sum( vt . ( q0/qt) ) / sum ( vt ) For prices Pt = sum(vt) / sum(vt.(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 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 So deflating values at an aggregate level by Paasche price indices will give Laspeyres volume indices

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

Volume and Price measurement

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Volume and Price measurement

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