DCLG Problem – Business rates and pooling Business rates and pooling Cameron Hall, Ian Hewitt, Mark Holland, Owen Jones, Zoe Lawson, Neeraj Oak, Eddie Wilson ESGI 91, Bristol 19 April, 2013
DCLG Problem – Business rates and pooling Introduction Aims of the new business rates retention scheme Central government are introducing a new business rates scheme with the aim of providing more incentive for local authorities (LAs) to enforce collection of business rates, and encouraging LAs to work together by participating in pools. However, it is unclear whether forming pools is advantageous under the new system, and, if so, whether there are strategies for LAs to work out how best to arrange themselves into pools.
DCLG Problem – Business rates and pooling Introduction The business rates retention scheme Terminology The new business rates retention scheme calculates the funding received by each LA on the basis of three inputs: f : the baseline funding level ( i.e. what the LA is expected to need), r : the business rates baseline ( i.e. the business rates the LA is expected to collect), and x : the business rates income ( i.e. the business rates collected and, potentially, available for the LA). The variables f and r are known from the outset (and have been set for the coming years), but x is unknown and must be forecast from historic data.
DCLG Problem – Business rates and pooling Introduction The business rates retention scheme Tariff rate Another important variable is the tariff rate , v , which is a monotone decreasing function of f r : 1 r ≤ 1 0 < f 2 , 2 , � f � 1 − f 1 f v = r , 2 ≤ r ≤ 1 , r f 0 , r ≥ 1 . If an LA has a high funding requirement ( f ) but a low expected income ( r ), then it receives a favourably low tariff rate ( v ).
DCLG Problem – Business rates and pooling Introduction The business rates retention scheme Payoff function The payoff function , P , describes how much money the LA receives from the business rates retention scheme: x − r (1 − s ) f , ≤ − s , f − s ≤ x − r P ( f , r , x ) = f + x − r , ≤ 0 , f � f � �� x − r f + 1 − v ( x − r ) , ≥ 0 , r f where s = 0 . 075 is the safety net threshold. P is an increasing function of x (the funds collected), but this is discounted by the tariff rate if x > r .
DCLG Problem – Business rates and pooling Introduction Pooling LAs are being encouraged to form geographically contiguous pools in the hope of increasing the funds that they receive and reducing risk. In a pool, the f , x , and r values for the LAs are summed before the expressions for v and P are applied. For a pair of LAs (or, equivalently, for a pair of pools that might consider amalgamating into a larger pool), pool formation will theoretically be favourable if P ( f A + f B , r A + r B , x A + x B ) > P ( f A , r A , x A ) + P ( f B , r B , x B ) .
DCLG Problem – Business rates and pooling Introduction Questions Given the known values for f and r , and projecting from past data on x , where is it favourable to pool? How big will ‘optimal’ pools be? Are there simple tools that can enable LAs to determine whether pool formation is favourable in their case? How might changing the details of the tariff rate affect optimal pool formation?
DCLG Problem – Business rates and pooling Introduction Our approaches Analysis of the two LA/pool case We used analytic methods to explore the simple problem of determining when it’s favourable for two LAs (or, equivalently, two pools) to combine. Data processing We converted the available data into easily-usable forms, and we explored methods for predicting future values of x from past data. Simulations and pooling algorithms We used r , f and generated x data to develop possible pooling strategies across the entire country.
DCLG Problem – Business rates and pooling Introduction An interesting point If no LA is going to need the safety net, the maximum amount received from central government can be achieved (albeit non-uniquely) by minimising the total tariff. Moreover, we find that � � f > r , and hence the tariff for a pool made of every LA is zero! Hence, from a purely mathematical point of view, maximum overall return can be achieved if every LA combines to form one big pool. (!)
DCLG Problem – Business rates and pooling When should two individuals pool? Two LAs considering a pool Imagine two LAs ( A and B ) considering whether they’d receive a greater income if pooled together or if apart: We already know f and r (and hence v ) for both LAs. How does the change in return associated with pooling depend on x ? Because P is piecewise linear with its domains of definition determined by x − r f , we introduce q = x − r as a dimensionless ‘ x ’ f variable, and plod through all of the different cases...
DCLG Problem – Business rates and pooling When should two individuals pool? Seventeen different cases... Dashed lines showing critical values of q A , q B and q AB q B = x B − r B f B 0 − s − s 0 q A = x A − r A f A
DCLG Problem – Business rates and pooling When should two individuals pool? Is there an advantage to pooling? If v A < v B , what is the sign of P AB − P A − P B ? +ve − ve q B = x B − r B − ve f B 0 zero +ve − s zero − ve − s 0 q A = x A − r A f A
DCLG Problem – Business rates and pooling When should two individuals pool? Is there an advantage to pooling? If v A = v B > 0, what is the sign of P AB − P A − P B ? zero +ve q B = x B − r B − ve f B 0 zero +ve − s zero − ve − s 0 q A = x A − r A f A
DCLG Problem – Business rates and pooling When should two individuals pool? Is there an advantage to pooling? If v A = v B = 0, what is the sign of P AB − P A − P B ? zero q B = x B − r B − ve f B 0 − s zero − ve − s 0 q A = x A − r A f A
DCLG Problem – Business rates and pooling When should two individuals pool? Some observations from the two individual analysis Pooling can only be advantageous if at least one of the potential participants expects x > r ( i.e. business rates income exceeds baseline). Pooling has no advantages if both of the potential participants have a zero levy rate.
DCLG Problem – Business rates and pooling When should two individuals pool? Some observations from the two individual analysis Pooling can only be advantageous if at least one of the potential participants expects x > r ( i.e. business rates income exceeds baseline). Pooling has no advantages if both of the potential participants have a zero levy rate. If one participant has income over the baseline and the other participant has income between the safety net and the baseline, and v � = 0 for at least one participant, pooling is always advantageous if the business rates income for the pool is less than the baseline. (!)
DCLG Problem – Business rates and pooling Data processing Challenges in data preparation The heterogeneity of English local government The big challenge with data processing in this project was to bring everything into a consistent form. We needed to:
DCLG Problem – Business rates and pooling Data processing Challenges in data preparation The heterogeneity of English local government The big challenge with data processing in this project was to bring everything into a consistent form. We needed to: Build tables for r i , f i and (for the billing authorities only ) the historic x values.
DCLG Problem – Business rates and pooling Data processing Challenges in data preparation The heterogeneity of English local government The big challenge with data processing in this project was to bring everything into a consistent form. We needed to: Build tables for r i , f i and (for the billing authorities only ) the historic x values. Deal with inconsistent spelling in the data: e.g. & or ‘and’; the apostrophe (or lack thereof) in ‘King’s Lynn’; etc.
DCLG Problem – Business rates and pooling Data processing Challenges in data preparation The heterogeneity of English local government The big challenge with data processing in this project was to bring everything into a consistent form. We needed to: Build tables for r i , f i and (for the billing authorities only ) the historic x values. Deal with inconsistent spelling in the data: e.g. & or ‘and’; the apostrophe (or lack thereof) in ‘King’s Lynn’; etc. Understand and implement the funding differences between unitary authorities, shire counties, shire districts, London boroughs, fire authorities etc. : x i for billing authorities are the business rates collected multiplied by a conversion factor depending on type, x i for non-billing authorities ( e.g. counties) are the sum of the income of the constituent billing authorities multiplied by (different) factors.
DCLG Problem – Business rates and pooling Data processing Challenges in data preparation Which LAs are allowed to pool? In addition to cleaning up the financial data, it’s essential to know which LAs are allowed to pool together. To join a pool, LAs can be logically adjacent ( e.g. Stroud and Gloucestershire), or geographically adjacent ( e.g. Bristol and North Somerset). Working out logical adjacency required yet more data preparation... Moreover, no geographical adjacency matrix was easily available, so we constructed our own on the basis of publicly available geographical data (postcode centroids).
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