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

2. 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?

3. 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

4. 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)

5. 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?

6. 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

7. 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

8. 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)

9. 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

10. 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