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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