Automated Supply-Use Balancing in the United Kingdom: A New Approach
Joshua Abramsky[1] (), Craig McLaren1, Neil Parkin1 and Christopher Quickfall1
Keywords:Supply-use, optimisation, GDP
1.Introduction
1.1.Background
Supply-Use (SU) balancing is a data reconciliation exercise used by National Statistics Institutes (NSIs) to reach a single “best estimate” of GDP from the many data sources used to calculate the three initial GDP measures and their components. It consists of adjusting the estimates of GDP components derived from the data sources such that the adjusted estimates are consistent with the accounting identities set out in the National Accounts documentation ([1] and [2]). Such adjustments must be allocated among the different estimates according to the relative reliability of the underlying data sources.
Traditionally, this exercise is implemented manually by NSI staff. However, taking advantage of recent developments in available computing power, many NSIs are developing software solutions to automate it. These solutions rely on well-established algorithms for solving quadratic programmes for which software implementations have been developed and are available on a commercial basis.
1.2.Summary of Paper
This paper briefly examines published NSI work on automating the SU balancing problem, specifically their mathematical expressions of the problem and their common approach to incorporating relative reliability information into the automated solution. It then considers these aspects of previous work in relation to the specific situation of the UK; develops a model suited to the UK’s current position; presents the results of this model, focusing on a comparison with the results of manual balancing; concludes that the current model is capable of producing acceptable solutions to the SU balancing problem; and summarises the UK’s priorities for future developments.
2.Methods
2.1.Literature Review
The most detailed and authoritative published papers on NSI automated balancing solutions have been presented by the Bureau of Economic Affairs (United States) and Statistics Netherlands. In this paper we will refer to [3] and [4] respectively.
[3] summarises the problem using matrix algebra (p. 204). Briefly, if the initial estimates, true values, errors, known covariance between the initial estimates and true values, and accounting constraints are each presented as a matrix, then under certain assumptions it is possible to use generalised least squares (GLS) to derive an objective function to be minimised that results in a matrix containing a unique solution for the best estimates of the true value. In this model, the relative reliability information mentioned in the Introduction is represented by the covariance matrix.
The most important of these assumptions is that the initial estimates are an unbiased estimator of the true values. It will also be noted that the covariance matrix between the initial estimates and true values must be known for the model to be used. If the former condition does not hold, and the covariances are unknown (estimated), it is not possible to guarantee that the results are the best estimate.
From Section 4 (pp. 204-5), it is clear that a full covariance matrix is not available to the BEA. The BEA has addressed this using the standard approach set out in [5]. However, as acknowledged in [3], this approach makes assumptions regarding the derivation of the covariance matrix from published metadata. The BEA’s contribution clarifies the strict conditions necessary for a NSI to fully maximise the quality gains from automating the SU balancing problem.
[4] details Statistics Netherlands’s approach to a further development of the problem: estimation of quarterly SU tables given annual values (benchmarking). For the purposes of this paper, however, it can be considered as a treatment of the SU balancing problem with some additional parameters. [4] explicitly treats the problem as a quadratic programme (p. 7) where the minimisation (cost) function consists of the sum of the squared adjustments weighted by a parameter representing relative reliability. Developing this parameter involves the same assumptions as the BEA have cited in [3] involving the covariance matrix. Henceforth, this approach will be referred to as the “subjective variance” approach.
2.2.UK Model
Briefly, the metadata currently available to the UK cannot support the assumptions made in the papers cited above.
The UK has therefore approached the problem from a different perspective. The aim of SU balancing is to develop a view on the level of the GDP components, making sure that all components are consistent. Now, each GDP component should intuitively have an upper bound (e.g. UK output is less than £100 trillion) and a lower bound (e.g. UK output is greater than 0) with the bounds chosen relative to the magnitude of the component. This information is used to guide the current manual SU process. If this process can be replicated automatically an automated SU solution is viable. The metadata can then be developed towards the conditions we know are required for a truly optimal quadratic programming solution.
In mathematical terms, the problem is expressed as a quadratic programme as in the Statistics Netherlands paper. The difference is that the weights are removed from the objective function, and two new constraint matrices are introduced, one for the upper and one for the lower bounds. In addition, two further constraint matrices are introduced to place further constraints on the maximum and minimum annual growths of each cell.
It turns out that this model lends itself to simulation for testing purposes. Upper and lower bounds can be calculated by applying percentages to the initial estimates, and these percentages can be derived from past manually-derived balancing solutions simply by taking the absolute percentage adjustment matrix from those solutions. This should guarantee that the solution will not impose larger adjustments than manual balancing.
3.Results
Figure 1.Absolute Percentage Adjustments to the Four SU Aggregates, Reference Year 2011.
No universally-accepted quality measure for SU outputs exists. As the usual descriptive statistics such as variance are inapplicable, it is not possible to create confidence intervals or the like. The implication of SU practice, however, is that adjustments should be minimised, so the assessment focuses on simple comparisons of the total size of adjustments between automatic and manual solutions. Within these, the highest-profile variables are aggregates (GVA, total supply and total demand), rather than the detailed cells of the supply and use tables. Therefore, the assessment has focused on this aspect of the results.
It is clear from the above that the automatic model has resulted in smaller adjustments at the aggregate level than were applied manually (Fig. 1) for three out of four of the SU aggregates and for the four aggregates in total. Lower-level data shows that the contrary result for GVA(I) is because of a large number of manual positive and negative adjustments to the GVAI(I) components that happen to net off – which seems intuitively undesirable.
4.Conclusions
4.1.Results
The results above show that the automated solution, using the upper/lower bounds model, is at least viable compared to the existing manual process.
4.2.Further Work
The first priority for the UK is to develop a subjective variance model for the UK. It will then be possible to test the upper/lower bounds and subjective variance models against each other in a UK context.
In addition, it is necessary to test the upper/lower bounds model in a production environment with no bounds available from past manual balancing rounds. This will test the “workaround” that the UK has used to compare the relative reliability information in a situation where it is non-comprehensive.
In the long term, though, there can be no doubt that the top priority must be to develop the metadata to the point where a truly optimal solution is possible.
References
[1]United Nations, System of National Accounts 2008 (2009), New York.
[2]Eurostat, European System of Accounts 2010 (2012), Luxembourg.
[3]B. Chen, “A Balanced System of US Industry Accounts and Distribution of the Aggregate Statistical Discrepancy by Industry,” Journal of Business and Economic Statistics (April 2012), pp. 202-211.)
[4]R. Bikker, J. Daalmans, and N. Mushkudiani, “Benchmarking Large Accounting Frameworks: A Generalised Multivariate Model,” Economic Systems Research (2013), pp. 1-18, DOI:10.1080/09535314.2013.801010.
[5]Stone, R., Meade, J. E., and Champernowne, D. G. (1942), “The Precision of National Income Estimates,” Review of Economic Studies, 9(2), 111–125.
1
[1] Office for National Statistics