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Introduction to the SNA, advanced
Lesson 1
Estimating volumes
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1
Background
• Values recorded in statistical surveys and in the national
accounts consist of a combination of prices and quantities
• Economic analysts are interested in abstracting from price
changes and so volume estimates are required
• When volumes are estimated it is necessary to select a year as
the “base year”
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2
Background (cont’d)
• Until the 1990s most national statistics offices produced
volume series based on a particular year and the base year
was changed once every five years or even less frequently
– rapid changes in weights and prices reduced the
effectiveness of this approach and so more frequent
rebasing became necessary
– computers were a particularly important factor in forcing
this change because their quantities increased rapidly
while their prices were also falling rapidly
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3
Basic concepts
• Interest in volumes lies in their change over time rather than
their level
• For an individual product, changes in the volume are identical
to changes in its quantity
– however, the quantity must measured at a constant quality
– it does not make sense to estimate volumes directly from
quantities for products such as cars and computers
because their quality differs so much
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Basic concepts (cont’d)
• Once more than one product is involved it becomes necessary
to aggregate quantities
– not possible directly because of different units or different
quality for each product
– need to have some equivalent to value
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Quantity revaluation
• Assume that the quantity of wheat is 7 in year 1 and 6 in
year 2 while with the corresponding prices being 11 and 12
– value = price times quantity
– i.e. V1 = P1 x Q1 and V2 = P2 x Q2
– the value of wheat would be 77 (i.e. 11 x 7) in year 1 and
72 (i.e. 12 x 6) in year 2
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Quantity revaluation (continued)
• Substituting the price in year 1 for the year 2 price results in a
value of the quantity of wheat in year 2 expressed at the
prices of year 1
– Vol2 = P1 x Q2
– 66 = 11 x 6
– referred to as “quantity revaluation”
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7
Quantity revaluation (continued)
• From previous slide Vol2 = 66 (expressed at year 1 prices)
• The volume in year 1 equals the value in that year
– Vol0 = P0 x Q0 (= V0)
– 77 = 11 x 7
• So the change in volume from year I to year 2 is –14.3% (77 to
66)
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Quantity revaluation (continued)
• It is equally possible for the volume in year 1 to be expressed
in terms of year 2 prices
– in this case, the volume in year 1 would be 84 (i.e. 12 x 7)
– its value (and also volume) in year 2 is 72 (expressed in
terms of year 2 prices)
– its % change is still –14.3% (84 to 72 in this case)
Copyright 2010, The World Bank Group. All Rights Reserved.
9
Quantity revaluation – multiple products
• So far we have looked at the trivial case of a single product
• Extending the example to 2 products will show the
implications of the choice of base year
• Any year can be chosen as the base year
• Unlike the case for a single product, where the % change is
the same no matter which year is the base year, the choice of
base year will affect the % change in volumes for the total of
the 2 products
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Quantity revaluation – multiple products
• The reason is that the prices in the base year act as weights to
combine the quantities of the products
• Price relativities between products change over time so the
weights used to combine the quantities differ, depending on
the base year chosen
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Quantity revaluation – multiple products
(continued)
Wheat
Barley
Total
year 1 year 2 year 1 year 2 year 1 year 2
(1) Price
11
12
6
5
(2) Quantity
7
6
14
16
(3) % change
-14.3%
14.3%
(4) Value
77
72
84
80
161
152
(5) Volume
(year 1 prices)
77
66
84
96
161
162
(6) % change
(7) Volume
(year 2 prices)
-14.3%
84
(8) % change
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72
-14.3%
14.3%
70
80
14.3%
0.6%
154
152
-1.3%
12
Quantity revaluation – multiple products
(continued)
Wheat
Barley
Total
year 1
year 2
year 1
year 2
(1) Price
11
12
6
5
(2) Quantity
7
6
14
16
(3) % change
-14.3%
year 1
year 2
14.3%
(4) Value
77
72
84
80
161
152
(5) Volume
(year 1 prices)
77
66
84
96
161
162
(6) % change
(7) Volume
(year 2 prices)
-14.3%
84
(8) % change
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72
-14.3%
14.3%
70
80
14.3%
0.6%
154
152
-1.3%
13
Quantity revaluation – multiple products
(continued)
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14
Price deflation
• Quantity revaluation is not always possible because such
detailed information is required on quantities
– it is also difficult to ensure the quantities are measured at
a consistent quality level
• The commonly-used alternative to quantity revaluation is
price deflation
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15
Price deflation (continued)
• A price deflator is a price index produced by weighting
together the prices for products that are relevant to a
particular national accounts value (e.g. food in household final
consumption expenditure)
– this price index is then divided into the current value to
estimate the volume
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16
Price deflation (continued)
Wheat
Barley
Total
year 1 year 2 year 1 year 2 year 1 year 2
(1) Price
11
12
6
5
11
12
(2) Quantity
7
6
14
16
7
6
(3) Value
77
72
84
80
161
152
100.0
114.3
100.0
83.3
100.0
95.7
161
159
(4) Price index
(5) Volume
(year 1 prices)
(6) % change
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-1.2%
17
Price deflation (continued)
• Price deflation has a number of advantages over quantity
revaluation so it is used more commonly
– it requires less detailed data
• sample of prices instead of comprehensive data on
quantities
– price competition causes prices to move in similar ways
• this is not true of quantities
– quality changes are easier to take into account in prices
than in quantities
– the price changes for similar products can be used as
substitute prices for products that are not directly priced
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Double deflation
• The production approach to estimating GDP is based on
measuring gross product for each industry as the difference
between gross output and intermediate consumption
– GDP is obtained as the sum of the gross product for each
industry
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Double deflation (continued)
• The standard method of estimating volumes of industry gross
product is to deflate both gross output and intermediate
consumption separately and the volume of gross product is
the difference between them
– this procedure is called “double deflation”
– as is the case in terms of current values, the volume of
GDP is the sum of the volumes of gross product for each
industry
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Changing the base year
• If a country has volumes that are rebased only once every 5 or
10 years then the impact of changing to a more recent base
year can be very significant
• The reason is that goods and services are subject to the
“substitution effect”
– associated with the tendency for relatively less expensive
goods and services to be substituted for relatively more
expensive goods and services that are similar
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Changing the base year (continued)
• Products with relatively weak price increases (or with price
falls) usually experience the strongest relative volume growth
• The outcome is that these products have lower price weights
in a more recent base year than they would in an earlier base
year
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22
Long time series of volumes
• The biases introduced by having a base year that is several
years out of date have become more pronounced over the
past 20 years or so
• Analysts like to have long time series for the national accounts
so they can examine the behaviour of an economy at different
stages of the business cycle
– particularly when a recession occurs, which is a relatively
infrequent event in many countries
– the ways in which an economy has emerged from past
recessions can provide an indication of what may be
expected in future (or current) recessions
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Long time series of volumes
• It does not make sense to estimate volumes for many years on
a single base year
– the relevance of the underlying weights decreases the
further the year being considered is from the base year
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Chain volumes
• A method of overcoming the biases in a fixed-base volume
series that is rebased every 5 or 10 years is to rebase the
volumes every year
– the volumes then have to be linked together to form a
long-term time series
• The process of producing such series is referred to as
“chaining” or “chain linking” the volumes
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Chain volumes (continued)
• The most common chain is based on estimating volumes for
each year expressed in the previous year’s prices and then
linking together the percentage changes for each component,
including all high-level aggregates
• The downside of producing chain volumes is that additivity is
lost for most years in the chained series
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Chain volumes (continued)
Wheat
Barley
Total
Yr 1
Yr 2
Yr 3
Yr 1
Yr 2
Yr 3
(1) Price
11
12
14
6
5
4
(2) Quantity
7
6
6
14
16
18
-14.3
0.0
(3) % change
Yr 1
Yr 2
Yr 3
+14.3 +12.5
(4) Value
77
72
84
84
80
72
161
152
156
(5) Volume
(yr 1 prices)
77
66
66
84
96
108
161
162
174
-14.3
0.0
+0.6
+7.4
72
72
152
162
-14.3
0.0
-1.3
+6.6
(6) % change
(7) Volume
(yr 2 prices)
(8) % change
84
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+14.3 +12.5
70
80
90
+14.3 +12.5
154
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Chain volumes (continued)
Total
(1) Volume
(year 1 prices)
Yr 1
Yr 2
Yr 3
161
162
174
+0.6
+7.4
152
162
-1.3
+6.6
162.0
172.7
+0.6
+6.6
(2) % change
(3) Volume
(year 2 prices)
154
(4) % change
(5) Chain volume
(year 1 prices)
(6) % change
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161.0
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Non-additivity
Volumes (year 1 reference year)
Yr 1
Yr 2
Yr 3
(1) Wheat
77.0
66.0
66.0
(2) Barley
84.0
96.0
108.0
(3) Total
161.0
162.0
174.0
+0.6
+7.4
162.0
172.7
+0.6
+6.6
(4) % change
(5) Chain volume
(year 1 prices)
(6) % change
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161.0
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Real estimates
• Even in cases for which it is not possible to observe a price
and a quantity for products that are being deflated it is
possible to consider that, in principle, they could be split into
price and quantity components
• However, some national accounts transactions cannot be
viewed as having price and quantity components
– gross operating surplus
– taxes
– saving
• Volumes cannot be calculated but “real estimates” can
– they measure the purchasing power of the value over the
goods and services included in the deflator
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Conclusions
• Volume estimates are a critical component of the national
accounts
– it would not be going too far to say that there is little point
in compiling national accounts unless volume estimates
are an integral part
• The traditional method of changing base years once every 5
or 10 years is no longer satisfactory because of the potential
biases that are introduced into the volume series
• Many uses of the national accounts require lengthy time
series
• Annually chained volumes are strongly recommended for all
countries because they minimise the extent of biases in the
series, which outweighs the disadvantages of non-additivity
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31
References
• Eurostat Handbook on Price and Volume Measures in National
Accounts
• System of National Accounts, 2008
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