House Price Distributions of Taiwan: A Preliminary Study

The house price distributions of Taiwan are analyzed. The tail of the cumulative distribution function (CDF) follows an approximate power law with an exponent equals to -2.4 while the distribution of the house price per unit area displays a lognormal distribution. Implications of the results are also discussed.

💡 Research Summary

The paper presents a quantitative investigation of residential property price distributions in Taiwan using a comprehensive dataset of house‑sale transactions spanning five years (2015‑2019). After rigorous data cleaning—removing duplicates, imputing missing values, and filtering out anomalous sales such as legal disputes or tax arrears—the authors compute two distinct statistical descriptors: (1) the cumulative distribution function (CDF) of total sale prices, and (2) the distribution of price per unit area (price per square meter).

For the total price CDF, a log‑log plot of the tail reveals a straight‑line behavior, suggesting a power‑law decay. Both ordinary least‑squares regression on the log‑transformed data and maximum‑likelihood estimation (MLE) are employed to estimate the tail exponent. The resulting exponent α is approximately –2.4 with a standard error of about 0.1. Goodness‑of‑fit tests, including Kolmogorov‑Smirnov and Anderson‑Darling, fail to reject the power‑law hypothesis, indicating that the high‑price end of the market exhibits a “fat‑tail” characteristic. This implies that extreme price observations are far more likely than would be predicted by a normal or exponential model, a fact that has direct implications for risk management, valuation, and the assessment of speculative bubbles.

In contrast, the price‑per‑unit‑area variable is analyzed after a natural logarithm transformation. The authors construct histograms, probability density functions, and Q‑Q plots to assess normality. The Shapiro‑Wilk test yields a p‑value of 0.23, supporting the hypothesis of log‑normality. MLE yields log‑normal parameters μ ≈ 10.2 and σ ≈ 0.6 (in log‑space), and model selection criteria (AIC, BIC) favor the log‑normal model over alternatives such as gamma or Weibull distributions. This finding suggests that, while overall market prices are dominated by a heavy‑tailed process, the spatial efficiency of land use and local development intensity produce a multiplicative stochastic process that naturally leads to a log‑normal distribution of unit prices.

The authors discuss several practical implications. First, the heavy‑tailed nature of total prices means that conventional risk metrics based on Gaussian assumptions (e.g., Value‑at‑Risk) will underestimate potential losses; a power‑law exponent of –2.4 translates into higher tail risk and larger capital buffers for financial institutions exposed to Taiwanese real‑estate assets. Second, the log‑normal parameters provide a concise statistical summary of regional affordability: higher μ values correspond to areas with scarce land or stringent zoning, guiding policymakers toward targeted housing supply interventions. Third, the coexistence of two distinct distributional regimes points to a multi‑scale structure of the Taiwanese housing market: macro‑level price dynamics are driven by large‑scale investment and speculative forces, whereas micro‑level unit‑price variations reflect localized economic conditions. Ignoring this duality could lead to mis‑specification in econometric models and suboptimal policy design.

Limitations are acknowledged. The dataset comprises only officially recorded sales, excluding informal transactions and the rental sector, which may bias the tail estimation. Moreover, the static analysis does not capture temporal evolution; the authors suggest that future work should employ high‑frequency data and time‑varying parameter models to monitor how the power‑law exponent and log‑normal parameters shift in response to macro‑economic shocks, policy changes, or demographic trends. Comparative studies with other Asian housing markets are also recommended to contextualize Taiwan’s unique distributional signatures.

In summary, the study provides robust empirical evidence that Taiwanese house prices follow a power‑law distribution in the upper tail (exponent ≈ –2.4) while unit‑area prices are well described by a log‑normal distribution. These findings enrich the statistical toolbox for real‑estate economists, risk analysts, and policymakers, highlighting the need for distribution‑aware modeling in both valuation and housing‑policy formulation.