Exploring Distributions of House Prices and House Price Indices
房价与房价指数的分布探索AI 解读 ↓
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房价与房价指数的分布探索
- 研究问题
- 房屋成交价格和不同期限房价指数的整体分布与上尾形态如何，广义贝塔分布能否刻画幂律尾部向有限上限衰减的特征？
- 方法与思路
- 作者分析俄亥俄州房屋成交价格与美国邮政编码层面的房价指数，用修正广义贝塔、GB2 和尾部线性拟合评估分布形态。
- 材料陈述的贡献
- 摘要称房价及多年房价指数呈现幂律尾部突然衰减的负龙王现象，修正广义贝塔拟合较好；单年指数尾部更符合幂律及 GB2。
- 阅读关注点
- 应核对指数期限与样本构造、有限上限的统计证据、尾部区间选择和拟合检验，以及将房价视为收入分布代理的依据。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审及接收状态未核验；摘要未提供拟合数值，房价与收入的导数类比不能据此视为已验证关系。
原文摘要
We use house prices (HP) and house price indices (HPI) as a proxy to income distribution. Specifically, we analyze sale prices in the 1970-2010 window of over 116,000 single-family homes in Hamilton County, Ohio, including Cincinnati metro area of about 2.2 million people. We also analyze HPI, published by Federal Housing Finance Agency (FHFA), for nearly 18,000 US ZIP codes that cover a period of over 40 years starting in 1980's. If HP can be viewed as a first derivative of income, HPI can be viewed as its second derivative. We use generalized beta (GB) family of functions to fit distributions of HP and HPI since GB naturally arises from the models of economic exchange described by stochastic differential equations. Our main finding is that HP and multi-year HPI exhibit a negative Dragon King (nDK) behavior, wherein power-law distribution tail gives way to an abrupt decay to a finite upper limit value, which is similar to our recent findings for realized volatility of S\&P500 index in the US stock market. This type of tail behavior is best fitted by a modified GB (mGB) distribution. Tails of single-year HPI appear to show more consistency with power-law behavior, which is better described by a GB Prime (GB2) distribution. We supplement full distribution fits by mGB and GB2 with direct linear fits (LF) of the tails. Our numerical procedure relies on evaluation of confidence intervals (CI) of the fits, as well as of p-values that give the likelihood that data come from the fitted distributions.