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A SIMPLE APPROACH TO THE CREATION AND MANAGEMENT OF STATISTICAL INDICATORS OF SUSTAINABLE DEVELOPMENT IN SOUTH AFRICA by Luthando Mayekiso, [email protected], Statistics South Africa ABSTRACT Statistical indicators are conceptualized as outputs of processes called statistical value chains. The statistical information sourced into the statistical value chain is seen as inputs. This proposed architecture of statistical indicator systems is identified in a sample of the major statistical indicator systems and used to develop an approach for the management and creation of statistical indicator systems. The approach involves managing a collection of statistical value chains, data inputs, data outputs, data quality assessments, information visualizations and decision evaluations. The objectives of the study are to illustrate this approach on a real life problem and to highlight its limitations. The problem uses environmentally adjusted economic indicators to evaluate progress toward sustainable development in South Africa. The study is conducted at a national level. The design uses a set of environmental indicators in the United Nations Driver-Pressure-State-Impact-Response framework of 1995 from the national South African Environmental Indicators database. These are complemented with indicators from two other frameworks. The first is a set of environmentally adjusted Leontief multipliers from the 2003 United Nations System of Environmental Accounting. The second is a set of financial stability indicators from the 2004 Basel Committee’s Basel II framework. The indicators are combined within a single framework according to the Bellagio Principles of 1996 using a Vector Autoregressive Moving Average time series model. The robustness of the indicators to assumptions is evaluated using sensitivity and uncertainty analysis. The optimality of the indicators for decision making is evaluated using decision theory. The study includes all statistical populations in the South African economy that influence sustainable development in South Africa. The approach provides a simple framework for constructing and managing statistical indicators in order to make optimal of decisions. Key words: Sustainable development, statistical indicators, statistical value chain, statistical factor models, decision theory. 1. INTRODUCTION The research aimed at exploring statistical indicators of sustainable development. A statistical indicator is defined in [4] as “a data element that represents statistical data for a specified time, place and other characteristics”. In turn data are defined in [1] as characteristics or information, usually 1 numerical, that are collected through observation”. Representation is defined in [2] as the combination of a value domain, data type and if necessary, a unit of measure or a character set. 2. THE STATISTICAL INDICATOR VALUE CHAIN Statistical indicators can be seen to be produced by a Statistical Indicator Value Chain (SIVC). In a SIVC framework there is statistical data that can be represented and data that will be used to represent it. Representation involves associating domain values, data types and units of measurement of statistical data and data using set theory. Once domain values, data types and units of measurement (which are sets) from data and statistical data have been associated, using set theory, then one has a statistical indicator. The association of domain values, data types and units of measurement (or character sets) can be further optimized using methods of decision theory. The optimization includes maximizing statistical quality in order to match outputs (statistical indicators) to desired outcomes. When modeling is involved in statistical indicator creation and management, the optimized association can be enhanced using the methods of sensitivity and uncertainty analysis. 3. DATA ANALYSIS All the source statistical data were assessed for statistical quality and the statistical quality of the fitted models were evaluated using a framework of methods in [4]. The indicator creation involved conducting a principal component analysis on the data matrix according to the statistical factor model theory outlined in [3]. 3.1. statistical quality assessment of the aggregates The input data were evaluated using the South African Statistical Quality Assessment Framework (SASQAF) first edition using judgmental methods for the evaluation. The source data from Statistics South Africa and the South African reserve Bank satisfied most of the requirements of the SASQAF first edition. The assessment also included consideration of the IMF DQAF assessment of the national accounts data and DWAF internal quality system for the DWAF data. The model data and results were evaluated using the methods outlined in [4]. 3.2. statistical factor model identification using principal component analysis The statistical data matrix contained quarterly observations. The banking tier one capital to total assets, banking return on assets, banking return on equity1, banking interest to gross income1, banking non-interest expenses to gross income1, banking liquid assets to total assets1, banking liquid assets to short-term liabilities1, banking net overdues as a percentage of net qualifying capital reserves, household income gearing, household mortage debt as a percentage of market value of housing, household debt as a percentage of disposable income and banking total loans and advances were obtained from the South African Reserve Bank. The physical production volume seasonally adjusted coal, petroleum and fuel, basic iron and steel, ferrous metal products, metal products and machinery, electricity available (Gigawatt hours) and building material for distribution in South Africa were obtained from the South 1 Own calculations using South African Reserve Bank source data 2 African Reserve Bank. The agriculture, fisheries and forestry gross value added, gold income resource rent, Platinum Group Metals income resource rent and coal income resource rent were obtained from Statistics South Africa. Average rainfall for South Africa was obtained from the Department of Water Affairs and Forestry. The eigenvalue analysis showed that the proportion of the variance explained by the first principal component is 37,23%, while the cumulative of the first six components is 82,94%. The first principal component has high positive factor loadings for the seasonally adjusted physical production of metals, electricity available for distribution is South Africa and the general government services-personal services proxy employment multiplier. The first principal component has high negative factor loading for banking total loans and advances. The second principal component has high positive factor loadings for manufacturing, electricity-gas-water, construction, wholesale-retail-motor trade and accommodation, transport-storage-communication and finance-real estate-business proxy employment multipliers. The third principal component has high positive factor loadings for income gearing, household debt as a percentage of disposable income and banking return on equity. The third principal component has high negative factor loadings for banking non-interest expenses to gross income, banking liquid assets to short-term liabilities and gold income resource rent. 3.3. vector autoregressive model fit The first six principal components were fitted to a VAR(1) model with the log return of the seasonally adjusted annualized gross domestic product. The model parameters are given by; 0,0004 0,0002 0,0003 0,0004 0,0003 0.0007 0,005 0,47 0,93 0,21 0,17 0,089 0,48 0,29 0,04 16,73 0,476 48,04 0,221 0,371 0,3205 0,08 0,77 0,33 X t 1,24 137,52 0,14 0,28 0,74 0,185 0,005 0,146 X t 1 Z t 0,80 89,80 0,09 0,03 0,124 0,543 0,61 0,47 0,43 44,73 0,01 0,036 0,015 0,225 0,386 0,584 0,154 0,1 0,15 0,21 0,31 0,613 71,82 0,05 for t=1 to 44. The Information Criteria diagnostic measures of the model were -11,6774 for the Corrected Akaike Information Criterion, -11,4269 for the Hannan-Quinn Criterion, -12,2727 for the Akaike Information Criterion, -9,97905 for the Schwarz Criterion and 4,823 *10-6 for the Final Prediction Error Criterion. 3.4. decision theory The decision theory analysis of the model using the change in seasonally adjusted annualized GDP variable shows that the model in its present value does add a small amount of value in predicting the seasonally adjusted annualized GDP. It however, has little predictive power, which would be caused by too few significant variables in sustainable development issues. Despite the model’s limitations when the forecasts of the six principal components were compared with the true realizations of the components they were found to be plausible. The 3 model thus allowed for a limited amount of analysis of the sustainable development issues in the economy in accordance with the Bellagio Principles. This includes the empirical linkage of the GDP to quarterly average rainfall, UN SEEA measures and the UN DPSR model indicators in the form of the Greenhouse Gas Emission Inventory and the proxy multiplier indicators. 3.5. sensitivity and uncertainty analysis The model form and parameters were tested for impact on the overall model results using sensitivity and uncertainty analysis. Initially, the resource rent assumption of 3% interest rate in the El Serafy formula for mineral resource rent calculations was tested against an interest rate of 11,7% and no significant differences in the principal components and the overall model fit were observed. The sensitivity of the results to the model form were tested by fitting a Bayesian VAR(1) with lambda equal to 0.9 and theta equal to 0.1 as the prior parameters. The model had different parameter estimates, especially for the third principal component. The interpretation of the principal component forecast from the BVAR(1), however, disagreed with the true realization of the component while that of the VAR(1) model was more plausible. This indicated that the model results are sensitive to the model form. 4. CONCLUSIONS The statistical indicators created provided very conservative insights about the progress towards achieving sustainable development in South Africa. The decision theory analysis is very useful in getting on idea of the limitations of the data when forecasting future patterns. The short time period was as a result of data constraints for fitting a multivariate time series. The model results would improve when implemented over a longer time period and the sustainable development indicators would provide stronger results for decision making purposes in policy. 5. REFERENCES [1] UN Statistical Commission, Economic Commission for Europe. (2000), Conference Of European Statisticians Statistical Standards And Studies – No. 53 on Terminology on Statistical Metadata, Geneva. [2] Oxford University Press. (2003), The Oxford Dictionary of Statistical Terms, edited by Yadolah Dodge, The International Statistical Institute. [3] Meadows, P. (2005), Toward developing regional sustainability, Fourteenth conference of commonwealth statisticians, Cape Town, South Africa. [4] Parssian, A., Sarkar, S., Jacob, V. (2004), Assessing data Quality for information products: Impact of selection, projection, and Cartesian product, Journal of Management Science, Vol.50, No7. [5] Tsay, R. (2005), Analysis of Financial Time Series Analysis (Second edition), John Wiley and Sons. 4