建立購屋負擔風險指數再檢視家戶住宅之購屋能力 —台北與高雄地區購屋家戶之比較Reexamining Housing Affordability by Using the Affordable Risk Index − Empirical Comparison of Home Buyers in Taipei and Kaohsiung

在探討有關住宅負擔能力的研究中，一般使用價格所得比(price to income ratio, PIR)作為指標。然而家戶的購屋能力不只是與住宅價格和家戶所得有關，而且也與當時之住宅融資乃至住宅補貼政策有關。本研究延伸Gan & Hill(2009)所提出購屋可負擔極限值之概念，推估台北及高雄各樣本家戶最高之購屋負擔能力的極值，並將所推估之購屋極值與實際購屋價格加以比較。再經由對價格之機率分配的設定，推估其價格差距之發生概率。本研究稱此概率為「購屋負擔風險指數」，其值域介於0%到100%之間。當風險指數趨近於0%，則購屋負擔風險小；反之，當趨近於100%，則購屋負擔風險大。本研究進而應用此一風險指數探討不同所得層級家戶之購屋負擔風險。以2008年高雄與台北地區首次購屋或換屋之家戶為實證對象，且依家戶所得高低分為三組家戶層級以進行比較分析。實證結果發現，高雄地區之購屋負擔風險隨家戶所得之增加而下降；但是，台北地區則以高所得之家戶具有最大之購屋風險，其次是低所得與中所得家戶。透過敏感度分析，本研究發現隨著貸款比例的增加，低所得家戶則相對快速提升其購屋風險。

關鍵詞：購屋負擔、負擔風險指數、住宅價格、家戶所得、購屋

In measuring housing affordability, the price-to-income ratio(PIR) is the index in the literature that is mostly used to measure the ‘pressure’ of the real housing price on household income. However, the application of the PIR index is limited. Gan & Hill(2009) provide a concept of estimating the housing affordable limit and compute the affordability of individual households. In this study, the housing affordable price for a given household income is empirically estimated based on the assumptions of the ratio of living expenses and mortgage parameters. The estimated affordable price is then compared with the real price for the current housing unit to calculate the price gap. The cumulative probability of the price gap for each household is estimated according to the probability distribution of all collected individual housing prices. The cumulative probability, referred to as the “affordability risk index”, has a percentage ranging from 0% to 100%. The household has less housing affordability risk when the index approaches 0% and, conversely, the risk is high when the index approaches 100%. We adopt empirical data for the cities of Taipei and Kaohsiung in 2008, and compute the affordable risk index for households based on different income levels. Our findings show that the household with the lowest-income level has the highest affordable risk as expected in both cities. Yet, in Taipei city, households at the highest-income level are found to have an affordable risk that is higher than that for the households at other income levels.

Key words: housing affordability, affordable risk index, housing price, household income, home buyer