Download Session 20: Social accounting matrices and

Module H5 Session 20
Session 20: Social accounting matrices and
international comparisons
Learning objectives
At the end of this session the students will be able to



say what a social accounting matrix looks like
extract information from a SAM
explain about purchasing power parities and international comparisons
Social accounting matrices (SAMs)
What is a SAM?
A social accounting matrix (SAM) is a means of presenting a comprehensive set of national
accounting statistics in a matrix format which elaborates all the linkages between the
various accounts as shown in the SNA diagram below.
SADC Course in Statistics
Module H5 Session 20 – Page 1
Module H5 Session 20
In the diagram, the boxes enclosed with solid lines represent elements included in a supplyuse table (SUT). A SAM is an extension of an SUT that includes the boxes enclosed with
dotted lines. It will cover the income and saving (“sector”) accounts in more detail, but
usually less of the detail of the SUT.
The typical focus of a SAM is the disaggregation of the household sector into subgroups
distinguished by such categories as income-group, employment status, urban/rural
location, etc. (The main source of such data will be a household income and expenditure
survey.) A SAM provides a comprehensive statistical basis for economic modelling in
which the likely effects of economic events or policy initiatives can be determined.
What does a SAM look like?
In mathematical terms, a SAM is a square matrix in which each row and corresponding
column constitutes an “account”. Incomings are shown in the row and outgoings in the
column. Each row total equals the corresponding column total and each transaction
appears just once.
0
0
1
2
3
4
T
3,604
133
499
4,236
Imports
1
1,883
1,721
GVA
3,604
2
1,399
Gross
saving
452
33
1,884
Income paid
abroad
Capital
formation
3
414
Income
from
abroad
38
452
Tota
ls
Rest
of
world the
Accu
mula
tio
n
Incom
e
its us and
e
Final
consumption
Intermediate
consumption
Output at
basic prices
Goods and services
Production
Income and its use Taxes on
products
Accumulation
Rest of the world
Totals
Prod
uctio
n
Good
s
servic and
es
The very simplest form of matrix looks like this, similar but not quite the same as the
diagrammatic overview of the accounts: (figures from the SNA)
Exports
4
540
30
570
T
4,236
3,604
1,884
452
570
10,746
Net lending
to row
Each box in this summary SAM represents a more detailed sub-matrix and a fully expanded
SAM may have a large number of rows and columns. The South African SAM (for the
year 2002) has more than 200 rows and columns, that of Tanzania (for 2001) over 100.
SADC Course in Statistics
Module H5 Session 20 – Page 2
Module H5 Session 20
The precise layout and sub-categories used in a SAM is not laid down in the SNA. It is a
matter of choice, depending on the characteristics of the economy, the main use to which
the SAM will be put, and the availability of data.
The advantage of the matrix format is that it can present a very large amount of data in a
concise way, useful for sophisticated economic analysis. The disadvantage is that it is not
at all suitable for presentation to the non-specialist. The nature of each transaction has to
be inferred from its position in the matrix, which is not an easy thing to do.
Exercise 1
Examine South Africa’s SAM for 2002. it is contain in the Excel file
Module H5 Session 20 SA SAM 2002.xls
Identify the rows in the production columns that show total output and intermediate
consumption for each activity. Extract this information and present it in a simple table in
columns as shown on the next page. You will need to copy and paste special, transpose.
Calculate the gross value added and the input/output ratios for each activity. The totals are
shown as a guide.
SADC Course in Statistics
Module H5 Session 20 – Page 3
Module H5 Session 20
South Africa: Production accounts, 2002 (Rand million)
Total
output
Intermediate
consumption
Gross
value
added
Input/
output
ratios
2,517,467
1,453,588
1,063,879
58%
Agriculture
Coal
Gold
Other mining
Food
Textiles
Footwear
Petroleum
Other non-metallic minerals
Basic iron/steel
Electrical machinery
Radio
Transport equipment
Other manufacturing
Electricity
Water
Construction
Trade
Hotels and restaurants
Transport services
Communications
Financial intermediation
Real estate
Business activities
General government
Health and social work
Other activities/services
Totals
SADC Course in Statistics
Module H5 Session 20 – Page 4
Module H5 Session 20
International comparisons
There is considerable interest internationally in comparing the levels of GDP (or GNI) per
capita. This can be done simply by converting the GDP per capita at current prices
(measured in national currencies) into a common currency, such as US dollars, using
official exchange rates. However, such “nominal” comparisons include the effect of price
levels as well as the volumes of GDP and its components.
“Real” comparisons may be made by converting the GDP per capita (or other aggregates)
into a common currency using special conversion factors called Purchasing Power Parities
(PPPs). PPPs reflect the purchasing power of national currencies.
Purchasing Power Parities
The PPP rate is defined as the number of units of a country’s currency that is required to
buy the same amount of goods and services in the country as one US$ would buy in the US.
PPP as a rate of conversion ensures that money exchanged for a dollar buys the same
volume of goods and services in every country. By equalizing prices, PPP rates deliver a
measure of relative GDP which is based on what constitutes "real" income, the volume of
goods and services embodied in GDP. The method of using PPP is analogous to
measuring GDP in different years at fixed base year prices.
PPP rates can be derived using several methods, each yielding different estimates. PPP
rates are estimated on the basis of data from special price surveys. Price ratios of
comparable items between countries are computed, and aggregated using corresponding
weights based on GDP expenditure data. Several methods of aggregation exist, and there is
no universal agreement as to which is superior - it depends on the purpose.
PPPs can be used either for binary comparisons, or for comparison of a group of countries.
Binary comparisons between pairs of countries are obtained by computing the “ideal”
index, the Fisher index. However, the Fisher index is not transitive, thus, other methods
are (should be) used for multilateral comparisons. (Transitivity means that comparing
country A with C directly should give the same result as comparing country A with B and C
with B -- making the comparison of A and C indirectly.)
The two most commonly used methods of aggregation in multilateral comparisons are (i)
the Geary-Khamis and (ii) the Elteto, Koves and Szulc, which both produce transitive and
base-country invariant results.
(i) The Geary-Khamis method involves using observed price and expenditure data to
obtain implicit quantity estimates, and evaluate these quantities at a single set of average
“international prices” denominated in a common currency, like the “international dollar”.
(An “international dollar” has the same purchasing power as an US$ for total GDP in the
US, but the purchasing power of the components are determined by the average
international price structure, not the US price relatives.)
(continued…)
SADC Course in Statistics
Module H5 Session 20 – Page 5
Module H5 Session 20
(ii) The Elteto, Koves and Szulc, involves a two-step process. First step is to get a set of
binary Fisher indexes for all pairs of countries, and step two is to make these comparisons
transitive by computing geometric means of all the direct and indirect indexes.
The results using the Geary-Khamis method will generally differ both in ranking and level
compared to the results using the Elteto, Koves and Szulc method. The Geary-Khamis
method has one advantage over the Elteto, Koves and Szulc method: it is additive. This
means that components can be added to reach a total, making it possible to add
expenditure at “international prices” to reach GDP at international prices. Thus, the use of
the Geary-Khamis method makes it possible to put up an internally consistent set of
national accounts data at “international prices”. However, the Geary-Khamis method tends
to result in inflated quantity estimates for poorer countries.
Source: World Bank: extract from http://go.worldbank.org/ZQ3H5W6IT0
At the time of writing, the latest round of world-wide comparisons, for 2005, was still in
progress. The exercise is known as the “International Comparison Program” (ICP).
ICP-Africa
First results for Africa, to be regarded as preliminary, were made available in March 2007
by the African Development Bank in a publication entitled Comparative consumption and price
levels in African countries. They are reproduced on the next page. A brief commentary on the
results are also given from the same publication.
The results are for the final consumption expenditure by households, excluding housing
services, and not for GDP. Furthermore, they are expressed in a common African unit of
currency (the AFRIC) and price levels, not in terms of a world-wide unit of currency and
price levels. A common unit of currency is known as a “numeraire” currency.
The aggregation procedure used by AfDB is a modification of the Greary-Khamis method,
called the Iklé index. See the publication for further details.
Exercise 2



Check the ranking of the countries in the table by using Excel to sort the rows of
the table on the appropriate column of data.
Construct a chart to show the real per capita consumption of households in order.
Re-calculate the real per capita expenditures using a world-wide numeraire on the
assumption that the price level in Africa is 50 per cent of the world price level.
SADC Course in Statistics
Module H5 Session 20 – Page 6
Module H5 Session 20
The First Results of the International Comparison Program for Africa (2005)
Note: these results are preliminary and subject to revision
Individual Consumption Expenditure By Households
…
22
5
28
…
12
…
18
6
29
…
12
…
0.64%
0.39%
0.86%
…
2.14%
14.30
7.53
1.70
12.80
7.80
17.53
88.60
527.47
5.11
527.47
1138.00
527.47
Cape Verde
Central African Republic
Chad
Comoros
Congo, Democratic Republic
Côte d'Ivoire
1.48
1.18
1.09
1.39
1.15
1.16
…
309
439
509
77
550
…
262
403
365
67
474
5
12
18
6
14
13
…
27
21
17
43
15
…
34
20
24
44
16
…
0.20%
0.69%
0.04%
0.80%
1.82%
0.42
3.80
8.52
0.61
59.52
19.10
88.67
527.47
527.47
393.38
473.91
527.47
Djibouti
Egypt, Arab Republic
Equatorial Guinea
Ethiopia
Gabon
Gambia, The
1.35
0.64
1.58
0.57
1.58
0.75
515
918
1216
113
1771
151
381
1441
772
197
1121
202
7
46
2
47
1
41
16
10
8
41
3
39
22
4
10
39
7
37
0.06%
20.27%
0.16%
2.85%
0.32%
0.06%
0.75
70.00
1.01
72.06
1.40
1.46
177.72
5.78
527.47
8.67
527.47
28.58
Ghana
Guinea
Guinea-Bissau
Kenya
Lesotho
Liberia
0.97
0.68
1.09
0.81
1.06
0.91
380
255
179
376
443
90
392
373
165
463
420
98
29
44
19
38
21
32
23
32
38
25
20
42
21
23
40
17
19
43
1.68%
0.70%
0.04%
3.28%
0.20%
0.06%
21.34
9.28
1.33
35.27
2.38
3.23
9073.80
3644.33
527.47
75.55
6.36
1.00
Madagascar
Malawi
Mali
Mauritania
Mauritius
Morocco
0.66
0.86
1.03
0.91
1.03
1.15
214
133
290
463
3222
981
326
154
282
506
3139
855
45
37
24
33
25
15
35
40
29
19
1
9
30
42
33
15
1
9
1.12%
0.38%
0.67%
0.30%
0.78%
5.19%
17.05
12.40
11.73
2.91
1.24
30.20
2003.03
118.42
527.47
264.80
29.50
8.87
Mozambique
Namibia
Niger
Nigeria
Republic of Congo
Rwanda
0.91
1.5
0.95
1.11
1.34
0.73
227
1297
189
581
485
183
250
866
198
523
361
251
34
4
31
16
9
42
34
7
36
13
18
37
36
8
38
14
26
35
0.98%
0.36%
0.50%
13.73%
0.24%
0.43%
19.42
2.04
12.63
130.70
3.32
8.60
23323.00
6.36
527.47
131.27
527.47
557.81
Sao Tome and Principe
Senegal
Sierra Leone
South Africa
Sudan
Swaziland
1.22
1.09
0.89
1.35
0.96
1.08
…
573
261
2946
740
1316
…
524
292
2189
771
1220
10
17
35
8
30
20
…
14
31
2
11
6
…
13
32
2
11
5
…
1.14%
0.30%
20.62%
5.48%
0.27%
0.19
10.82
5.10
46.89
35.40
1.11
9900.00
527.47
2899.20
6.36
243.61
6.36
Tanzania
0.8
Togo
1.04
Tunisia
0.98
Uganda
0.75
Zambia
1
Zimbabwe
…
Source: African Development Bank
280
379
1624
228
337
…
349
363
1664
305
338
156
39
23
28
40
26
…
30
24
4
33
26
…
27
25
3
31
28
41
2.47%
0.38%
3.35%
1.62%
0.78%
0.36%
35.30
5.21
10.03
26.49
11.44
11.53
1119.36
527.47
1.30
1780.67
4463.50
…
SADC Course in Statistics
Exchange Rate
to the US$
Per Capita
Real Expenditures
3
27
11
36
43
22
Population (Million)
Per Capita Nominal
Expenditures US$
…
425
1143
335
…
609
Real Expenditure
Shares
(Africa=100%)
Price Level Index
(Africa = 1)
…
419
1388
292
…
635
Per Capita
Real Expenditures
1.53
0.99
1.21
0.87
0.72
1.04
Price Level Index
(Africa = 1)
Angola
Benin
Botswana
Burkina Faso
Burundi
Cameroon
Country
Per Capita Nominal
Expenditures US$
Rankings (1=highest)
Module H5 Session 20 – Page 7
Module H5 Session 20
Brief interpretation of the results
The table “Individual Consumption Expenditure By Household” summarizes the main
results for the 48 countries that took part in ICP-Africa 2005 and for whom it was possible
to calculate real (PPP-adjusted) Household Final Consumption Expenditure (HFCE).
HFCE accounts for around 70% of GDP in most African countries so it can be taken as a
good indicator of GDP. Clearly, when the full GDP detail becomes available, rankings are
likely to change for per capita and total aggregates.
The Price Level Indices (PLIs) shown in the first column are ratios of US dollar exchange
rates to PPPs expressed in AFRICs. A PLI of 1.0 means that the country has a price level
equal to the average for Africa. The PLIs in the Table range from 0.6 (Egypt and Ethiopia)
indicating price levels that are very low relative to the average for Africa - to over 1.6 (Gabon
and Equatorial Guinea) indicating relatively high price levels. For countries with low price
levels, Household consumption expenditure is higher when computed using PPPs than
when exchange rates are used. The opposite holds for countries with high price levels.
Real per capita HFCE is shown in the third column of the table. This can be taken as a
"welfare" indicator although it is only an approximate indicator and will be improved later
when expenditure on housing services is included and when individual expenditures of
government are added to obtain Actual Household Consumption. Country rankings are
given in the 7th column and show that Mauritius, South Africa and Tunisia are at the top
with per capita HFCE of over 1500 AFRIC and that DRC (Democratic Republic of the
Congo) and Liberia are far below with per capita HFCE of 130 or less.
In 2005, the weighted average per capita household consumption expenditure was about
603 AFRIC for the 48 countries. Analysis of previous rounds of the ICP suggests that the
AFRIC will be equal to about two US Dollars. This suggests that there will be no more than
ten countries (including DRC, Ethiopia, Guinea- Bissau, Liberia, Malawi, and Zimbabwe)
with per capita HFCE of less than a dollar a day.
The seventh column presents the country shares in total household consumption
expenditure for countries for which data are available. The shares show clearly how the
African region is dominated by a few large economies. Over 75% of total HFCE is
accounted for by just 7 countries; South Africa, Nigeria, Egypt, Morocco, Sudan, Tunisia
and Kenya. At the other end of the scale, the group of smallest economies that includes
Guinea-Bissau, Comoros, Djibouti, The Gambia, Liberia, Equatorial Guinea, Central
African Republic and Lesotho together accounts for only about 1% of HFCE.
Source: Comparative consumption and price levels in African countries, African Development Bank 2007
SADC Course in Statistics
Module H5 Session 20 – Page 8
Module H5 Session 20
Conclusion
This session concludes this module on index numbers and economic statistics. If you have
managed to work through the material presented, you should have gained a good
appreciation of the some of the practical issues (as well as the basic concepts) involved in
compiling indices and national accounts.
Often the demand for economic data outstrips both our capacity to supply them and the
ability of users to analyse them fully. Some key points to bear in mind in producing
economic statistics to an acceptable standard are the following:




keep things simple,
exploit administrative records to the full,
identify data or processing errors and correct them, and
make the data available as quickly as possible according to a timetable published in
advance.
SADC Course in Statistics
Module H5 Session 20 – Page 9