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Results
Advanced analysis
Everything below this line is original, exploratory analysis — not part of the IAAO Standard on Ratio Studies.
Imagine two cases:
- A house sells for $100K in a poor neighborhood where identical homes sell for $100K, but is assessed for $1M.
Verdict: over-assessed by 10×. - A mansion sells for $100K in a rich neighborhood where identical homes sell for $1M, and is assessed for $1M.
Verdict: the assessment is correct; the sale price is an invalid, non-arm's-length transaction.
Problem: comparing price ratios across sale-price deciles cannot distinguish between these two cases. What we really care about is this hypothesis:
But comparing price ratios across sale-price deciles only tests this hypothesis:
These are not the same hypothesis, because sometimes expensive homes sell for low prices in non-arm's length transactions.
To know for sure, we must run two additional tests:
- Look at it on a map
- Group by neighborhood price level
If the vertical equity bias is real, we should see high ratios clustered in poor neighborhoods, and the same bad vertical equity in the neighborhood price level chart. If we see no spatial pattern to high sales ratios, and the neighborhood price level chart is flat, the results may simply be an artifact of invalid sales with artificially low prices.
Map view
Neighborhood price level stats
Help and method notes
- Ratio = valuation / sale_price
- COD = 100 * mean(|ratio − median_ratio|) / median_ratio
- PRD = mean(ratio) / (sum(valuation) / sum(sale_price))
- PRB: OLS of ratio ~ a + b*ln(sale_price); HC3 robust SE; p-value via normal approximation.
- VEI computed per spec group rules (2/4/10 groups by N), proxy = 0.5*sale + 0.5*(valuation/median_ratio).