Automated Supply-Use Balancing in the United Kingdom: A New Approach

Introduction SU balancing is the reconciliation of data sources to provide a GDP estimate It should depend on the quality of each data source Traditionally, this has been done manually But better computers are helping NSIs automate this So how to specify the algorithm?

Quadratic Programming - A Model QP is a well-established algorithm with multiple easily-available software implementations But what constraints and objective to use? Usual model Weight the objective (squared adjustments) for relative quality Accounting constraints Optional soft constraints for economic ratios

Literature Review Chen (2012) presents this model in matrix algebra terms Key points: Covariance matrix between initial estimates and true values must be known; initial estimates must be unbiased estimators of true values; if so, model produces unique best solution Similar conclusions in Bikker et al (2013) and van Tongeren and Picavet (2016)

The UK Position We do not know the covariance matrix (Chen) Nor do we know the standard errors of the underlying dist. of the initial estimates – or even whether they are normally distributed (Bikker et al, van Tongeren and Picavet) So can we develop a model suited to these conditions?

An Alternative Model Consider the matrices and vectors underlying the SU system For each cell, we should be able to allocate upper and lower bounds (eg, the UK agriculture industry produces less than £100 trillion for each product, and more than £0 for the agriculture product) Real bounds are much narrower So we can apply these as additional constraints in a LP/QP model No weights on the objective

Comparison of Models This model does not guarantee a unique best solution (indeed, the solution may not be unique – but this is unlikely) And, if the constraints are not set correctly, the problem can be infeasible These are consequences of the unavailable information So we can’t guarantee the outcome will be as good as the other model – but we don’t have to make its assumptions

Testing Testing was done on past UK SU tables Upper and lower bounds based on manual adjustments – if a cell had been manually adjusted by + or – x%, the upper and lower bounds were set as +/- x% Some different treatment based on different manual procedures (eg trade in goods)

Results See tables in paper For the 4 main SU aggregates (GDP(P), GDP(I), total supply, and total demand) total adjustments were lower for all except GDP(I) At the lower level, the lower manual GDP(I) adjustments were the result of higher (in absolute terms) adjustments netting off So results are positive

Conclusions Automation of the SU process is viable ONS is still not able to deliver the more ambitious aims of the alternative model That requires more work to establish the needed metadata This work should be a top priority for ONS and the other NSIs working on automated balancing