Using Data and Algorithms to Reduce Public Housing Wait Times

Using the methods we propose, policymakers can make data-driven allocations to achieve more efficient distribution throughout the public housing system. This approach aligns housing options with individual needs, thereby reducing spatial mismatch and generating significant welfare gains for a substantial population segment.

Shing-Yi Wang (UPenn)  Maisy Wong (UPenn)  Michael B. Wong (HKU)

Public housing waiting times have soared from an average of two years in 2010 to an average of 5.6 years in September 2023. Because of this, large numbers of low-income families reside in cramped and often substandard subdivided units. In response, the Government has launched the Transitional Housing and Light Public Housing programs. These initiatives aim to swiftly construct affordable housing options for those waiting for public rental housing.

However, there are concerns about the underutilization of Transitional Housing, especially in the New Territories, and the Government’s ability to meet its target of eliminating subdivided units by 2049. These challenges call for a comprehensive and effective approach to tackle the housing crisis and improve the living conditions of the city’s vulnerable populations in Hong Kong. In this paper, we propose using data analytics and computer algorithms to increase the utilization of Transitional Housing and reduce public housing wait times.

Problem: Low Utilization in the Transitional Housing Program

The Government introduced Transitional Housing (TH) and Light Public Housing (LPH) in 2018 and 2022 to provide short-term housing relief to vulnerable households, primarily on the public rental housing (PRH) waitlist and residing in subdivided units.[1] 8,420 and 5,540 TH units are expected to be completed in 2023 and 2024, respectively.[2] 30,000 LPH units are expected in the coming five years, with 2,100 in 2024-25. A large fraction of TH and LPH sites will be in relatively remote areas in the New Territories, such as Yuen Long and Sheung Shui.[3]

However, observers and analysts are increasingly concerned that TH and LPH sites in the New Territories will have low utilization. According to the government, the average occupancy of projects in the New Territories was close to 70 percent, versus over 90 percent for projects in urban areas or near public transport hubs. For example, United Court in Yuen Long had 800 vacant flats (out of 1,800 total) in November 2022, according to SCMP. Utilization may deteriorate since upcoming TH sites have even fewer transportation linkages than existing TH projects in the New Territories.

The vacancies are financially costly. Government financial assistance for each transitional housing unit is: (a) up to $200,000 per unit in vacant residential buildings, and (b) up to $550,000 per unit for erecting temporary structures on vacant land and in non-residential buildings[4]. Failure to move people out of subdivided housing results in higher rents and lower living standards for the urban poor. In this paper, we identify difficulties in the implementation of the TH program and propose improvements to policy design. 

Why is Transitional Housing Utilization Low?

Reason 1: Spatial mismatch between residents and TH projects

Subdivided units are generally located in urban areas, where employment opportunities are abundant. Moving to the New Territories would require that households uproot themselves. The costs of moving include: (1) increased distance from employment opportunities;[5] (2) difficulties of children switching schools; (3) separation from existing social networks.

Reason 2: Inefficient application process

Following the TH model, LPH projects are operated, managed, and maintained by invited organizations. Each operator will allocate units according to criteria set by the Government, handle tenancy matters, implement exit plans for tenants, and provide social services based on the needs of tenants.[6] Applicants apply separately to different projects. Operators do not know which other projects an applicant has applied to, or their relative preferences. Applicants are free to reject unlimited offers and can wait to apply for better options. Each operator assigns TH units in a decentralized manner.

To address these issues, the Government has recently started to provide moving cost subsidies and establish a centralized application portal. While these efforts are commendable, it is important to acknowledge that the current matching process is not optimized: applicants may choose to wait for better housing options, even when applicants prefer the units in the New Territories over their existing subdivided units. We believe that further adjustments are necessary to address underutilization.

Market Design: A Nobel-Winning Idea

To improve TH allocation and utilization, we turn to Alvin Roth’s groundbreaking work in market design, which earned the Nobel Prize in Economics in 2012. The fundamental concept behind this work is to gather data about individuals’ preferences regarding a given set of options, and then use computer algorithms to create matches that optimize overall utility. To illustrate, let’s consider the case of TH applicants with varying preferences for different locations. These individuals would submit their preferences through a centralized portal, and the algorithm would then facilitate the matching process.

In recent years, computer algorithms have been successfully implemented to improve allocations across various domains. For instance, such algorithms have been used to match doctors with hospitals, students with schools, and kidneys to patients. An excellent example of this is the use of an optimized computer algorithm in New York City to assign students, which led to a significant improvement in the assignment process: from 31,000 unmatched students in 2003 prior to implementing the revised algorithm, to about 3,000 in 2004, according to the New York Times.[7] Since then, the algorithm has consistently assigned nearly half of all students to their first-choice schools. This is a testament to the effectiveness of computer algorithms in optimizing allocation processes and ensuring that individuals receive the best possible outcomes.

Illustrative Examples

Utilizing a centralized computer algorithm can significantly improve the allocation, utilization, and satisfaction of units when households have diverse preferences for housing options. To illustrate this, let us consider two simple examples where households have rank-order preferences for different locations.

Figure 1 demonstrates the problems associated with decentralized assignment. In the current decentralized process, each household is limited to submitting one application at a time. However, if households prefer the same unit, vacancies can arise. For instance, suppose that a unit in Yuen Long is completed first, but no one applies for it, resulting in a vacant unit. Instead, as demonstrated in Figure 1, multiple families wait to apply for Sham Shui Po, only to discover later that it is oversubscribed. These inefficiencies can be resolved by eliciting household preferences and implementing an optimized algorithm that eliminates vacancies and oversubscriptions.

Figure 1: Vacancies Can Arise due to Decentralized Assignment

However, even with a centralized approach, using a basic algorithm may still yield suboptimal outcomes. Figure 2 shows an example. In this scenario, there is still only one available unit per location, and applicants are sequentially assigned to their top choice among the remaining units. The sequential algorithm assigns Family A to Yuen Long, Family B to Sai Kung and Family C to Sha Tin. However, this is an efficient algorithm because only one household gets its top choice. There exists a more effective algorithm called “Top Trading Cycles” (Shapley and Scarf 1974) that allows for better assignment of units based on households’ preferences. In the example, if we assign Family C to Sai Kung, Family B to Yuen Long, and Family A to Sha Tin, two families get their top choice. Therefore, it is crucial to carefully study the properties of the assignment mechanism to ensure optimal results.

Figure 2: Optimized Algorithm Can Improve Satisfaction

Policy Recommendation

We recommend that the Housing Bureau leverage data analysis and market design theory to improve housing matches and increase TH utilization. In particular, we propose that:

  1. Applicants submit preference rankings for TH projects to a centralized portal.
  2. The central platform then uses an optimally designed computer algorithm, incorporating both applicants’ preferences and operators’ selection criteria and preferences, to allocate housing.
  3. Applicants receive a limited number of housing unit offers to accept or reject, like in the PRH system.
  4. Instead of a strict quota system reserving 80% of TH units to households with a ≥3-year wait in the PRH queue, such households are flexibly accounted for and prioritised in the assignment system, thereby minimizing vacancies.

These modifications can bring substantial benefits to TH applicants and residents. First, the proposed system’s computer algorithm incorporates relative preferences, increasing the chances that applicants are matched with units they prefer.

Second, because the better matches are more aligned with applicants’ needs, the proposed changes will increase offer acceptance rates. Meanwhile, limiting the number of offers to applicants will increase TH utilization in the New Territories by raising the incentives to accept an offer rather than waiting for an urban TH unit.

Implementation Requires Only Limited Investment

The proposed policy changes mentioned above would require only limited investment, making them a feasible solution. In particular, adding an assignment algorithm to the government’s planned centralized application portal would require minimal software development.

Moreover, there is plenty of readily available expertise that can help design the centralized assignment algorithm. Local and international academic researchers have extensively studied the local context, making them a valuable resource in the implementation process.

A centralized system would not restrict operator autonomy, as operators can still retain the right to screen applicants post-centralized assignment to avoid unsuitable or potentially problematic tenants. In cases where applicants are rejected, they can re-enter the assignment algorithm to be reassigned to suitable housing options. This approach also reduces administrative overhead for operators since they will no longer have to handle overlapping applications.

Overall, the proposed policy changes offer a practical and cost-effective way to enhance TH allocation and utilization, ensuring that individuals are matched with suitable housing options while simultaneously reducing administrative costs and improving the efficiency of the allocation process.

Broader Benefits in the Housing System

While our initial proposal focuses on enhancing the Transitional Housing program, Hong Kong can leverage data analytics and computer algorithms to improve public housing provision on a broader scale. Scholars, such as Lui and Suen (2011) among others, have extensively documented significantly more spatial mismatch among residents of both Public Rental Housing and Homeownership Scheme homes compared to those in the private market. By collecting detailed preferences of housing location and characteristics and using computer algorithms to find optimal matches, we can substantially improve these allocations. These data can also be used to gauge the effectiveness of alternative housing policy interventions, such as allowing public renter households to swap units.

Using the methods we propose, policymakers can make data-driven allocations to achieve more efficient distribution throughout the public housing system. This approach aligns housing options with individual needs, thereby reducing spatial mismatch and generating significant welfare gains for a substantial population segment.

References

Kwan, Shawna. 2021. “Hong Kong Homes Ranked Least Affordable for 11th Year.” Bloomberg. Accessed at https://www.bloomberg.com/news/articles/2021-02-23/hong-kong-homes-ranked-world-s-least-affordable-for-11th-year on October 11, 2021.

Lui, Hon Kwong, & Suen, Wing. (2011). The effects of public housing on internal mobility in Hong Kong. Journal of Housing Economics, 20(1), 15-29.


[1]There are roughly 133,700 general applicants waiting for PRH at the end of 2022. There are about 107,000 sub-divided units in Hong Kong and there are about 214,000 people living in sub-divided units. 

[2]6960 TH units were completed in 2020-21.

[3]For LPH, two announced sites are in Tuen Mun: one site is in Sheung Shui, and one site is in Yuen Long.

[4] https://www.info.gov.hk/gia/general/201904/18/P2019041800364.htm?fontSize=1

[5]In 2016, 42.2% of the low-income population who rented sub-divided flats worked in the same district where they lived. See: https://www.info.gov.hk/gia/general/201801/18/P2018011800590.htm?fontSize=1

[6]See: https://www.legco.gov.hk/yr2022/english/panels/hg/papers/hg20221205cb1-847-1-e.pdf

[7] See: https://www.nytimes.com/2014/12/07/nyregion/how-game-theory-helped-improve-new-york-city-high-school-application-process.html

Translation

利用數據和算法減低公屋輪候時間


王欣儀 (賓州大學) 黃美施 (賓州大學) 王柏林


 

平均公屋等候時間從2010年的兩年劇增到今年9月的5.6年。因此,很多低收入家庭入住分間樓宇單位(俗稱「劏房」),被迫忍受擁擠惡劣的居住環境。作為應對之法,特區政府推出過渡性房屋及簡約公屋的資助計劃,旨在從速為輪候租住公屋者構建可負擔的住屋選擇。

然而,在新界的過渡性房屋出現使用不足的情況;政府又能否在2049年之前取締劏房,同樣令人顧慮。應付此等挑戰必須制定全面而有效的方法,在化解房屋危機之餘,同時提升本港弱勢社群的居住條件。本文建議採用數據分析和電腦算法,通過提高過渡性房屋的使用率,來減低公屋輪候時間。

過渡性房屋計劃棘手問題:使用率低


過渡性房屋及簡約公屋分別在2018年和2022年推出,為弱勢家庭提供短期房屋援助,對象主要是公屋輪候名冊登記者及居於劏房者。.[1] 預期在2023年及2024年將分別有8,420個及5,540個過渡性房屋單位落成。[2] 未來5年內則將有30,000個簡約公屋單位落成,其中有2,100個在2024至2025年度落成。這兩類房屋選址大多位於新界較偏遠地區,例如元朗和上水。[3]

另一方面,觀察員和分析家卻日益關注選址新界的這兩類房屋,其使用率勢將偏低。政府則指出,位於新界的有關房屋項目平均入住率接近7成,至於市區或鄰近公共運輸交通樞紐的項目,平均入住率更超過9成。例如據《南華早報》報導,2022年11月,元朗同心村空置單位高達800個(單位總數為1,800個)。日後位於新界的過渡性房屋新項目,選址將比區內現有項目更偏離交通網絡,其入住率或會每況愈下。

空置單位財政成本高昂。特區政府對每個過渡性房屋單位的資助金額如下:一、每個位於空置住宅樓宇內的單位可達200,000元,二、在空置土地上及非住宅樓宇中搭建臨時建築物,每個單位可達550,000元。[4]若無法協助居民遷出劏房,將令市區貧困家庭所付租金上漲,而生活水平則下降。下文將探討過渡性房屋計劃在執行上的困難,並建議改善政策設計的措施。

過渡性房屋使用率為何偏低?


原因:居民與房屋之間的地域錯配

劏房一般位於市區,就業機會處處。遷居新界就會令舉家與原來的生活圈分割;搬遷代價包括:1) 距離職場較遠;[5]  2) 子女轉校困難;3) 脫離原有社交網絡。

原因二:申請手續繁複

參照過渡性房屋的模式,簡約公屋項目亦交由獲邀機構營運、管理和維修。每家營運機構根據政府所定準則編配單位、處理租務事宜、執行租戶遷出計劃、按個別租戶的需要提供社會服務支援。[6] 申請者就不同項目各自提出申請,營運機構無從得知申請者已申請的其他項目及其住屋選擇。申請者可拒絕接受所獲分配的單位,次數不限,亦可就日後較佳的項目提出申請。各營運機構以非統一方式編配過渡性房屋單位。

為應對上述問題,政府近期已開始提供搬遷費津貼,並著手建立統一申請系統。雖然有關舉措值得嘉許,但現行配對程序並未優化。即使寧選位於新界的項目單位而不願租住現有劏房,申請者或仍會選擇輪候較佳的公屋單位。筆者認為,必須針對使用率不足的情況,進一步調整有關資助計劃。

市場機制設計:諾獎得主高見


要改善過渡性房屋分配和使用,筆者參考Alvin Roth 的市場機制設計,其開創性研究在2012年為他贏得諾貝爾經濟學獎。箇中基本概念在於搜集每個人從一組既定選項所選擇的次序,然後運用電腦算法產生配對,從而優化整體效用。以選擇居住地區次序各異的過渡性房屋申請者為例,若把各自的優先次序遞交至統一系統,即可利用電腦算法推進配對程序。

近年來,通過採取電腦算法,不同領域的編配工作都能加以優化,例如醫生分派到不同醫院,學生編排在不同學校就讀,病人輪候腎臟移植等。一個極佳的實例就是美國紐約市運用經優化的電腦算法,令學生的派位程序大大改善。《紐約時報》曾經報導,未能獲派所選學校的學生,由2003年修訂有關電腦算法前的31,000名減至2004年修訂後約3,000名。[7] 自此之後,有關算法一直令該市接近半數學生得以編派到其首選學校;足證電腦算法有助於優化分配程序,並確保每人獲得最佳成果。

實例闡釋


申請家庭的房屋選擇各有不同,處理申請程序時運用統一電腦算法,就能顯著改善公屋單位的編配、使用和滿意程度。茲列舉以下兩個簡單示例加以說明,其中申請家庭均可按優先次序,選擇位於不同區域的項目單位。

從【圖1】可見非統一編配所衍生的種種問題。在現行非統一編配機制下,每一申請家庭每次只限遞交一份申請表。若有多個申請戶選擇同一單位,就會出現一些單位空置的現象。例如位於元朗的某項目單位率先落成,卻乏人問津,以致成為空置單位。從圖中可見,反而有多個申請戶選擇輪候深水埗的項目,而結果發現單位超額申請。要剔除如此低效的安排,應先取得申請戶的選擇次序,然後以優化算法處理申請,以徹底消除公屋單位空置及超額申請的弊病。

圖1     非統一編配可導致公屋單位空置



話說回來,即使採取統一編配方式,若只運用基本算法,成果大概仍然有欠理想。【圖2】示例顯示,每區依然只得一個項目單位可供選擇,將按申請戶的各自首選編配到餘下單位。順序算法把甲家庭編配往元朗,乙家庭編配往西貢,丙家庭則編配往沙田。如此算法無疑效率欠佳,因為只得一個家庭獲編配首選單位。較具效益的一種算法是「頂級交易周期」(Top Trading Cycles)(Shapley and Scarf 1974),可根據申請戶的選擇次序達致較佳編配效果。在此示例中,若把丙家庭編配往西貢,乙家庭編配往元朗,甲家庭則編配往沙田,就可讓兩個申請戶獲編配首選單位。因此,要確保取得最佳成果,就必須對編配機制的特性細加研究。

圖2     優化電腦算法可改善滿意程度



筆者建議特區政府房屋局善用數據分析和市場機制設計理論,改善公屋配對,並讓過渡性房屋充分使用。建議措施如下:

所有申請者將有關過渡性房屋項目的選擇次序,交由統一申請系統一併處理。

統一系統隨即透過優化設計的電腦算法,將申請者的選擇次序與營運機構的甄選準則和次序納入其中,以編配項目單位。

可供申請者接納或拒絕的單位編配次數有限,亦即類似出租公營房屋計劃的安排。

在目前嚴格的過渡性房屋配額制度下,8成單位須預留給已輪候公屋3年或以上的申請戶,但透過本文建議的編配系統,則可作出靈活排序處理,從而盡量減低單位空置率。

以上各項調整措施可同時惠及過渡性房屋申請者及住客。首先,建議制度的電腦算法已納入相對選擇次序,申請者獲編配所選單位的機會因而較大。

其次,由於較佳配對成果更符合申請戶所需,筆者建議的調整措施將有利於提升編配單位的接納比率。限制申請戶取捨單位編配的次數,將可成為申請戶接納新界項目單位而不再輪候市區單位的誘因,由此可擴大過渡性房屋新界項目的單位使用率。

調整措施成本有限


上述建議的政策調整措施只需有限投資,無疑是可行方案。在特區政府所籌備的統一申請系統中增添編配算法,軟件開發所費工夫亦微不足道。

此外,設計統一編配算法的專才不在少數。本地及國際學術研究人員對本港情況素有研究,不失為推行調整措施的寶貴資源。

營運機構仍有權在統一編配單位後作出篩選,把不合適申請者或有潛在問題的租戶剔除,統一系統不會對營運機構造成掣肘。不獲批核的申請者,可重新進入編配算法,以便配對合適的單位。如此安排亦可減輕營運機構的間接行政成本,因為毋須再處理重疊申請。

整體而言,本文建議的政策改動提供具成本效益的實際方法,可促進過渡性房屋的分配和使用,確保各申請者獲編配合適的房屋選擇;同時亦可減輕行政費用,並提升編配程序的效率。

擴大公營房屋制度的效益


筆者的初步建議著眼於改良過渡性房屋計劃,香港可運用數據分析和電腦算法,從更廣闊的層面改善公共房屋供應。公屋租戶和居者有其屋計劃住戶出現地域錯配,比私人住宅市場更為嚴重,Lui 與 Suen (2011) 等學者已對此現象進行大量研究。通過收集對於公屋位置和特色的詳細選擇次序,加上運用電腦算法找出最佳配對,就能在編配單位方面達致更理想成果。這些數據還可以用來衡量其他住房政策的效益,例如允許公屋住戶交換住房單位的有效性。

採納筆者倡議的辦法,決策者就能通過基於數據的單位編配,提升整個公營房屋制度中的分配效率。這種方式能令選擇公屋單位與個別住戶需要互相匹配,從而減少地域錯配問題,並帶來重要福利收益,惠及一大部分香港市民。

 

參考文獻


Kwan, Shawna. (2021). “Hong Kong Homes Ranked Least Affordable for 11th Year.” Bloomberg. Accessed at https://www.bloomberg.com/news/articles/2021-02-23/hong-kong-homes-ranked-world-s-least-affordable-for-11th-year on October 11, 2021.

Lui, Hon Kwong, & Suen, Wing. (2011). The effects of public housing on internal mobility in Hong Kong. Journal of Housing Economics, 20(1), 15-29.

[1]截至2022年底,輪候公屋的一般申請者共約133,700名;全港劏房單位共約107,000個,住客人數約為214,000。

[2]6,960個過渡性房屋單位在2020至21年度落成。

[3]已公布的簡約公屋項目選址兩個在屯門,一個在上水,一個在元朗。

[4] https://www.info.gov.hk/gia/general/201904/18/P2019041800364.htm?fontSize=1

[5]2016年,租住劏房的低收入人口中,在其居住地區就業者佔42.2%。參看:https://www.info.gov.hk/gia/general/201801/18/P2018011800590.htm?fontSize=1

[6]參看: https://www.legco.gov.hk/yr2022/english/panels/hg/papers/hg20221205cb1-847-1-e.pdf

[7] 參看:https://www.nytimes.com/2014/12/07/nyregion/how-game-theory-helped-improve-new-york-city-high-school-application-process.html