Download 2. the statistical indicator value chain

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
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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
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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
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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.
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