Power Laws and Inequalities: The Case of British District House Price Dispersion
Abstract
:1. Introduction
2. Economic Systems and Power Laws
3. Finance and the Distribution of Local House Prices
4. Method
5. Data
6. Discussion
6.1. Median and Growth
6.2. Comment on Aggregation and Time Profiles
7. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Zipf-Pareto | Lavalette | ||
---|---|---|---|
Expression | |||
10th City by size compared with the 15th City | α = 1 q = 1 and N = 146 q = 1 and N = 224 | 1.5 | 1.557 1.536 |
10th City by size compared with the 15th City | α = 0.25 q = 0.25 and N = 146 q = 0.25 and N = 224 | 1.107 | 1.117 1.113 |
maximum ÷ minimum | Nα | N2q | |
maximum ÷ median | ([N + 1]÷2)α | Nq | |
Median | ([N + 1]÷2)−α | ||
Slope ratio | Quartile ratio would be assessed as ω = 75%; QR 80%; and DR at 90% | ||
α = 0.5 q = 0.25 | Quartile ratio = 1.732 QR= 2, DR = 3 | Quartile ratio = 1.732 QR= 2, DR = 3 | |
90:50 ratio | |||
Coefficient of Variation. If the data follows a t-distribution | CoV of 0.398 is associated with a DR of 3.1; a QR of 2.01; and a Quartile ratio of 1.73. |
1 | https://www.centreforcities.org/wp-content/uploads/2016/01/2016-PUA-Table.pdf (accessed on 3 March 2023). |
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EWS q | R2 q | CV q | K-S q p-Val. | EWS α | R2 α | CV α | K-S α p-Val. | PUA q | PUA α | Non-PUA q | Non-PUA α | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
2004 | 0.215 | 0.986 | 487,030 | 0.472 | 0.349 | 0.775 | 759,075 | <0.001 | 0.239 | 0.400 | 0.204 | 0.325 |
2005 | 0.196 | 0.991 | 458,939 | 0.774 | 0.321 | 0.798 | 700,390 | <0.001 | 0.218 | 0.371 | 0.184 | 0.297 |
2006 | 0.183 | 0.991 | 437,908 | 0.774 | 0.309 | 0.849 | 680,811 | <0.001 | 0.204 | 0.360 | 0.172 | 0.284 |
2007 | 0.183 | 0.984 | 460,314 | 0.53 | 0.316 | 0.880 | 739,517 | <0.001 | 0.210 | 0.378 | 0.167 | 0.279 |
2008 | 0.187 | 0.977 | 462,056 | 0.24 | 0.326 | 0.893 | 763,492 | <0.001 | 0.217 | 0.393 | 0.169 | 0.286 |
2009 | 0.185 | 0.979 | 412,394 | 0.53 | 0.325 | 0.909 | 686,198 | <0.001 | 0.217 | 0.398 | 0.164 | 0.280 |
2010 | 0.198 | 0.981 | 472,642 | 0.278 | 0.348 | 0.909 | 813,374 | <0.001 | 0.233 | 0.426 | 0.176 | 0.300 |
2011 | 0.208 | 0.977 | 492,685 | 0.418 | 0.367 | 0.913 | 877,254 | <0.001 | 0.246 | 0.450 | 0.184 | 0.314 |
2012 | 0.211 | 0.975 | 497,050 | 0.32 | 0.373 | 0.915 | 897,356 | <0.001 | 0.251 | 0.459 | 0.186 | 0.318 |
2013 | 0.218 | 0.971 | 520,783 | 0.278 | 0.390 | 0.926 | 974,644 | <0.001 | 0.263 | 0.487 | 0.189 | 0.323 |
2014 | 0.229 | 0.963 | 580,549 | 0.206 | 0.413 | 0.940 | 1,146,962 | <0.001 | 0.279 | 0.519 | 0.195 | 0.337 |
2015 | 0.242 | 0.964 | 664,024 | 0.206 | 0.435 | 0.933 | 1,349,860 | <0.001 | 0.294 | 0.543 | 0.206 | 0.355 |
2016 | 0.255 | 0.964 | 751,260 | 0.088 | 0.456 | 0.922 | 1,568,640 | <0.001 | 0.307 | 0.561 | 0.220 | 0.379 |
2017 | 0.261 | 0.967 | 806,241 | 0.105 | 0.463 | 0.912 | 1,685,219 | <0.001 | 0.312 | 0.569 | 0.226 | 0.386 |
2018 | 0.258 | 0.971 | 802,638 | 0.149 | 0.455 | 0.905 | 1,640,559 | <0.001 | 0.307 | 0.559 | 0.224 | 0.379 |
2019 | 0.252 | 0.973 | 775,617 | 0.24 | 0.443 | 0.900 | 1,547,266 | <0.001 | 0.301 | 0.544 | 0.219 | 0.369 |
K-S p-Val. | Coefficient | Quartile | QR | DR | Skew | Kurt | ||
---|---|---|---|---|---|---|---|---|
TTWA 2006 | CoV | 0.257 | 1.423 | 1.527 | 1.792 | 0.38 | −0.16 | |
Lavalette | 0.876 | Min | 0.13 | 1.331 | 1.434 | 1.771 | ||
Max | 0.139 | 1.357 | 1.470 | 1.842 | ||||
Z-P | 0.002 | Min | 0.198 | 1.243 | 1.316 | 1.545 | ||
Max | 0.26 | 1.331 | 1.434 | 1.771 | ||||
TTWA 2017 | CoV | 0.346 | 1.509 | 1.718 | 2.139 | 0.89 | 0.48 | |
Lavalette | 0.881 | Min | 0.166 | 1.440 | 1.584 | 2.074 | ||
Max | 0.181 | 1.488 | 1.652 | 2.215 | ||||
Z-P | 0.038 | Min | 0.285 | 1.368 | 1.485 | 1.871 | ||
Max | 0.338 | 1.450 | 1.598 | 2.102 | ||||
ITL3 2006 | CoV | 0.348 | 1.627 | 1.832 | 2.263 | 1.69 | 4.7 | |
Lavalette | 0.623 | Min | 0.171 | 1.456 | 1.607 | 2.120 | ||
Max | 0.186 | 1.505 | 1.675 | 2.265 | ||||
Z-P | 0.003 | Min | 0.28 | 1.360 | 1.474 | 1.850 | ||
Max | 0.352 | 1.472 | 1.629 | 2.167 | ||||
ITL3 2017 | CoV | 0.598 | 1.957 | 2.373 | 3.332 | 2.37 | 7.93 | |
Lavalette | 0.214 | Min | 0.246 | 1.717 | 1.978 | 2.948 | ||
Max | 0.288 | 1.883 | 2.222 | 3.545 | ||||
Z-P | 0.052 | Min | 0.463 | 1.663 | 1.900 | 2.766 | ||
Max | 0.531 | 1.792 | 2.088 | 3.211 | ||||
LAD 2006 | CoV | 0.328 | 1.534 | 1.758 | 2.129 | 1.35 | 3.97 | |
Lavalette | 0.66 | Min | 0.173 | 1.462 | 1.616 | 2.139 | ||
Max | 0.178 | 1.479 | 1.638 | 2.186 | ||||
Z-P | 0.000 | Min | 0.278 | 1.357 | 1.470 | 1.842 | ||
Max | 0.324 | 1.428 | 1.567 | 2.038 | ||||
LAD 2017 | CoV | 0.546 | 1.969 | 2.357 | 3.308 | 2.52 | 11.42 | |
Lavalette | 0.000 | Min | 0.249 | 1.728 | 1.994 | 2.987 | ||
Max | 0.267 | 1.798 | 2.097 | 3.233 | ||||
Z-P | <0.001 | Min | 0.43 | 1.604 | 1.815 | 2.572 | ||
Max | 0.491 | 1.715 | 1.975 | 2.941 |
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Gray, D.P. Power Laws and Inequalities: The Case of British District House Price Dispersion. Risks 2023, 11, 136. https://doi.org/10.3390/risks11070136
Gray DP. Power Laws and Inequalities: The Case of British District House Price Dispersion. Risks. 2023; 11(7):136. https://doi.org/10.3390/risks11070136
Chicago/Turabian StyleGray, David Paul. 2023. "Power Laws and Inequalities: The Case of British District House Price Dispersion" Risks 11, no. 7: 136. https://doi.org/10.3390/risks11070136
APA StyleGray, D. P. (2023). Power Laws and Inequalities: The Case of British District House Price Dispersion. Risks, 11(7), 136. https://doi.org/10.3390/risks11070136