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Accurate Statutory Valuation

Accurate Statutory Valuation. JOHN MacFARLANE University of Western Sydney. Content. Motivation Methodology Examples. Motivation. Much of estimation theory is focussed on (obsessed with?) unbiasedness There are many situation where unbiased estimation is not relevant: Appointments;

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Accurate Statutory Valuation

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  1. Accurate Statutory Valuation JOHN MacFARLANE University of Western Sydney

  2. Content Motivation Methodology Examples

  3. Motivation • Much of estimation theory is focussed on (obsessed with?) unbiasedness • There are many situation where unbiased estimation is not relevant: • Appointments; • Consultation times; • Software development time and cost;

  4. Motivation (Property) • Property returns (%) • Excess returns and under-performance are not (or should not be) symmetric • Downside risk • Property Tax Assessment • MVP – Mean Value Price Ratio (85-100% or 90-100%)

  5. Methodology • Estimation • Least Squares; • Symmetric Loss Function. Lead to unbiased parameter (expected value) estimates. • Maximum Likelihood Estimation (MLE) • May be biased but are consistent.

  6. Alternative Methodologies • Asymmetric Approaches • Weighted (penalised) least squares; • Asymmetric loss function • Asymmetric Approaches

  7. 1. Weighted Least Squares Minimise: whereλi = 1 if xi < θ = λ if xi ≥ θ λ = 1 normal least squares, unbiased λ > 1 over-estimates λ < 1 under-estimates λ ≥ 0 Non-linear as λ is a function of θ.

  8. Example 1 Comparable land values (n=3): $280,000; $300,000; $320,000.

  9. 1. Weighted Least Squares

  10. Summary of ResultsExample 1 λ = 0.1 λ = 0.5 λ = 1 λ = 2 : 285 295 300 305

  11. Example 2 Comparable land values (n=3): $280,000; $280,000; $340,000.

  12. Summary of ResultsExample 2 λ = 0.1 λ = 0.5 λ = 1 λ = 2 : 282.9 292 300 310

  13. Example 3 Comparable land values (n=4): $280,000; $300,000; $320,000; $380,000

  14. 1. Weighted Least Squares

  15. Summary of ResultsExample 3 λ = 0.1λ = 0.5 λ = 1 λ = 2 : 292.3 310 320 332

  16. Reverse Problem What is the optimal choice of λ for a required level of under-estimation (as inferred by the MVP standard)?

  17. 2. Asymmetric Loss Function Loss Function (LINEX) Requires a prior distribution for parameters

  18. If we assume that the data is normally distributed with unknown mean (μ) and KNOWN standard deviation (σ), then it can be shown that the optimal estimate wrt the LINEX loss function is:

  19. Example 1 Comparable land values (n=3): $280,000; $300,000; $320,000.

  20. If we take the standard deviation to be σ=$20,000 then That is, for a = 1, we would underestimate the value by about $8,200 or a little under 3%.

  21. Example3 Comparable land values (n=4): $280,000; $300,000; $320,000; $380,000

  22. If we take the standard deviation to be σ=$40,000 then That is, for a = 1, we would underestimate the value by about $14,000 or about 4%.

  23. Conclusion We have considered two different approaches to systematically under- or over-estimating values. They represent different approaches both of which deserve further examination.

  24. Thank you!Questions?

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