Throwing out the baby with the bathwater: Location over-controls and residential lease length in Singapore

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1 Throwing out the baby with the bathwater: Location over-controls and residential lease length in Singapore Eric Fesselmeyer, Haoming Liu, and Alberto Salvo April 2, 2018 Abstract Giglio et al. (2015a) use hedonic regression to estimate price differences on residential property of varying lease length in Singapore. To control for geographic heterogeneity, they specify five-digit zip code fixed effects that, in the city-state, are excessively tight. We show that in a cross-section of new condominium apartments sold between 1995 and 2015, over ninetenths of five-digit zip codes displayed no within variation in lease length. We show how this matters when inferring the value households attach to housing many centuries into the future. Keywords: Fixed effects, discounting, declining discount rates, policy evaluation, long time horizon, real estate JEL classification: C18, D61, H43, Q51, R32 Eric Fesselmeyer, Haoming Liu, and Alberto Salvo, Department of Economics, National University of Singapore, 1 Arts Link, Singapore ecsef@nus.edu.sg, ecsliuhm@nus.edu.sg, albertosalvo@nus.edu.sg, phone: This note grew out of the review process of our manuscript How do Households Discount over Centuries? Evidence from Singapore s Private Housing Market, presented at ASSA, the East Asian Association of Environmental and Resource Economics congress, the Economics of Low-Carbon Markets workshop, Hitotsubashi University, IZA, National ChengChi University, National University of Singapore, the China Meeting of the Econometric Society, the IAERE conference, and the Singapore Economic Review conference.

2 1 Introduction In Singapore, residential property ownership takes the form either of freeholds, in which the right to the property is held in perpetuity, or of leaseholds, in which the property right reverts to the freeholder, such as the government, following initial horizons of 50 to 999 years. (2015a) and Fesselmeyer et al. Giglio et al. (2018) use different samples of Singaporean residential market transactions, and specify hedonic controls that differ in important ways, to estimate the impact of lease length on prices, from which discount rates over very long horizons are inferred. 1 Giglio et al. (GMS hereafter) obtain significant price discounts on multi-decade leases relative to property held in perpetuity. Fesselmeyer et al. (FLS hereafter) find that multi-century leases trade at a non-zero discount relative to freeholds and, beyond hedonic regression, fit smooth parametric forms to the wide range of lease lengths to test for declining discount rate schedules. 2 In terms of sample, GMS use transactions of privately developed apartments (about 18% of Singapore s 1.3 million residential units) and detached and semi-detached houses (6% of all units), both new and used construction. 3 To control for unobserved heterogeneity and maintenance, FLS exclude houses and restrict the sample to new apartments, thus excluding used properties. Moreover, in densely urbanized high-rise Singapore, and where new construction is typically sold years ahead of delivery, FLS control for floor level and the time between sale and delivery, covariates that GMS do not control for. 4 Another key difference between the hedonic regressions proposed by GMS and FLS lies in the location controls, based on property zip code. GMS specify fixed effects based on five-digit zip codes (e.g., 12772x) whereas FLS specify fixed effects based on three-digit zip codes (127xxx). In the city-state, a six-digit zip code (127720) perfectly predicts a building, such as an apartment tower, within which there is no variation in lease contract, the object of interest. Controlling for Singapore s five-digit zip codes, as GMS do, removes much of the variation in initial lease length, 1 Exploiting price differences across residential assets of varying lease length to infer households discount rates dates back at least to Fry and Mak (1984). Wong et al. (2008), Gautier and van Vuuren (2014) and Bracke et al. (2017) are other more recent examples. 2 FLS began work independently prior to learning of GMS s work from Maureen Cropper in early GMS use their estimates for Singapore in a second manuscript (Giglio et al., 2015b), as well as estimates from the UK housing market. In 2016, FLS attempted to purchase UK data to further test their findings relative to that of GMS, but after several phone and exchanges with data source Rightmove were informed of restrictions around the use and distribution of this data outside of the EU. correspondence in 2014 and 2016 are available. 3 Apartments developed by Singapore s public housing development authority, the Housing and Development Board (HDB), comprise the majority of residential properties. Purchases of such properties are subsidized and restricted. 4 FLS report a mean floor level of 9 and 87% of sales before the year construction is completed. 1

3 for example, perpetual freeholds, 999-year leases or 99-year leases. Residual co-variation in price and tenure remains in the GMS sample, net of the five-digit controls, thanks to the inclusion of used construction, since age and tenure for used property co-vary mechanically: fixing the unit or building, one more year of age implies one year less of lease. Price variation due to ageing in a panel of new and used units, where the same property is resold over time and building depreciation co-varies with lease years remaining, is not identifying variation, but rather confounding variation to be controlled for. GMS choose a linear functional form for their building age control. The purpose of this note is to quantify how much variation in lease length is removed on controlling for five-digit zip code, when the researcher does not resort to mechanical co-variation in property age and tenure. Hedonic regressions have to overcome the challenge that properties might differ in characteristics other than lease length. In this context, one may think that tighter fixed effects, such as five-digit zip codes, are more suitable, but not when they remove variation of interest. Moreover, as FLS argue, three-digit zip codes in the city-state are already quite fine, comprising a residential area of about 1 square km. Urban planning has led to residential areas comprising only 100 square km in all, and there are as many as 187 three-digit controls. We also show how the choice of five-digit versus three-digit zip code controls matters. 2 Five-digit zip codes remove variation in lease length Apartment units in Singapore are typically housed in multi-tower development projects, sharing land parcels and facilities such as a street entrance and parking space. For example, the privately developed Botannia condominium on West Coast Park, completed in 2009, consists of 11 tower buildings, each tower identified by a unique six-digit zip code: (towers 1 to 8 in unit steps) to ; (towers 9 and 10) and ; and (tower 11) Within the Botannia, there is no variation in lease contract. All 493 apartments, distributed over the 11 towers, are multi-century leaseholds with original tenure of 956 years granted on May 27, There are no other condominium apartments (or even houses) with five-digit zip codes 12772x, 12764x and 12765x beyond those comprising the Botannia condominium and its unique lease contract. Thus, in a cross-section of apartments (or even apartments and houses), five-digit fixed effects would 5 states Botannia is a 956-years leasehold development located at West Coast Park in District 05. Completed in 2009, it comprises eleven towers each scaling 12-storeys high and totals 493 units. Entering either of street numbers 27, 27A, 27B, 29A, 29B, 31A, 31B, 33A, 29, 31, or 33, and street name West Coast Park in returns each tower s unique six-digit zip code. 2

4 perfectly predict the original tenure contract for all properties in the example, namely 956 Yrs From 27/05/1928 for the 493 properties with five-digit zip codes 12772x, 12764x or 12765x. That is, these cross-sectional observations could not be used to identify an effect of lease length on prices. Table 1, panel A reports just how prevalent in a Singapore apartment cross-section is the lack of variation, within five-digit zip code, in lease type. Here we separately group freeholds, multicentury ( 999-year ) leaseholds, and multi-decade ( 99-year ) leaseholds. We consider privately developed condominium apartments, which form the bulk of GMS s sample and the entirety of FLS s sample. In a sample of new apartments transacted between 1995 and 2015, as many as 1,456 out of 1,516 five-digit zip codes, or 96%, experience no variation in lease type. In the example, 12772x, 12764x and 12765x are home to only multi-century leases (the Botannia development). 6 Next, consider the remaining lease length on each new apartment purchased in the sample. For example, the purchase of a Botannia apartment in 2009 would have a remaining lease of 956 ( ) = 875 years. Similarly, the 2005 purchase of a new apartment on 99-year land granted in 2001 would have 99 ( ) = 95 lease years remaining. Now group each transaction into the tenure bins adopted by Giglio et al. (2015a, Table IV), namely: years, 70-84, 85-89, 90-94, 95-99, 800+, and freehold. Apartment sales in as many as 1,374 out of 1,516 five-digit zip codes, or 91%, display no variation in tenure bin, e.g., 12772x, 12764x and 12765x recording sales of only 800+ year leases, or five-digit zip codes with only year leases sold. 7 The above discussion implies that a hedonic regression specifying excessively tight five-digit controls would hope to identify the effect of lease length on prices using a small subsample of properties. Unsurprisingly, GMS find no price differences between leaseholds with maturities of more than 700 years and freeholds (p.3, Giglio et al. 2015b, emphasis added). By contrast, Table 1A indicates that 108 out of 187 three-digit zip codes in the apartment sample, or 58%, are home to properties of varying lease type (right-most column). This proportion is to be compared with a paltry 4% of five-digit zip codes with more than one lease type (left-most column). Figure 1 plots the distribution of bilateral distances for each pair of development projects with a common three-digit zip code, for example, the distance between the Botannia (the 999-year leasehold in the above example) and the adjacent Infiniti (an 8-tower, 315-unit freehold condominium on 39 West Coast Park), both developments sharing the three-digit control 127xxx. Specifically, 6 Table 1, panel B shows that whether we add houses to the sample, as GMS do, makes no difference to the point made here: that five-digit zip codes remove variation in lease length. And ageing is not identifying variation or 8% (resp., 14 or 1%) of five-digit zip codes host apartment sales in exactly two (three) tenure bins. 3

5 75% of these bilateral distances are shorter than 1 km and 95% of the distances are shorter than 1.8 km. In other words, 95% of project pairs with a common three-digit zip code are located in a small area with a 0.9 km radius. Since residences agglomerate in 100 square km, or 14% of Singapore s land area, each of the 187 three-digit zip codes corresponds, on average, to a square of side no greater than 1 km. 8 Together, Table 1 and Figure 1 illustrate why three-digit geographic controls offer a good compromise between controlling for potentially confounding spatial heterogeneity and allowing residual variation in tenure (again, variation other than that arising from building age, another determinant of prices). 3 Comparing GMS to FLS hedonic regressions for Singapore FLS obtain a robust and statistically significant premium for freeholds over 999-year leaseholds, where GMS find none. Here, we attempt to reproduce the GMS sample of new and used condominium apartments and houses, and replicate their results, specifying five-digit zip code fixed effects as location controls. We then gradually adjust the design to obtain the results of FLS, based on a sample of new condominium apartments and using three-digit zip code fixed effects. We extracted all private housing transactions from REALIS, 9 for new and used property, condominium apartments and houses, for the period of January 1995 to December 2013, totaling 413,750 observations. Variables include the transaction price, original tenure contract (e.g., 999 Yrs From 21/06/1877 ), whether the property is new or used, the year construction was completed, the sixdigit zip code that identifies the building, and the land title type (always strata for apartments, mostly land for houses). Where tenure or zip code are missing, we imputed the characteristic using non-missing values for transacted properties in the same building or development project. We dropped 1,879 observations for which tenure, tenure starting year, or zip code is missing on all transacted property for the same development project over the sample period. We further dropped 831 records associated with multi-unit transactions. We imputed any missing completion year for property sold ahead of delivery, still during construction, from the date of first transaction for new property in the same building, considering that construction (reliably) takes about 4 years for condominiums and 2 years for houses. We dropped 26,501 observations for which completion year 8 Land use in 2010 ( Notice that 100/187 = 0.53 km 2 per fixed effect, i.e., less than a unit square, of side 1 km. Housing in Singapore agglomerates in specific local neighborhoods around different axes emanating from the original downtown area. 9 REALIS is the Urban Redevelopment Authority s (URA) Real Estate Information System. 4

6 remained missing. Table 2 describes our reproduction of the GMS sample, numbering 384,539 transactions, to be compared to Giglio et al. s (2015a) Table IV, listing 378,768. While we judge the reproduced sample to track the GMS sample fairly well, there are some differences. These differences include 34,547 transactions for 2011 in our reproduced sample versus 25,221 transactions in GMS that same year. In our reproduced sample, 17% of purchased properties have a remaining lease of years compared to only 7% in the GMS sample. There may be a difference in that we count remaining lease length at the time the keys are handed over, when utility from housing services begins to flow, not at the time the property is purchased, which if new could precede delivery by several years. 10 There may be a difference in how we adjust nominal transaction prices, including prepayments for property purchased still during construction, to January 2014 S$. Our use of complementary sources likely allowed us to complete more observations that are missing construction completion year in the original REALIS data. 11 Whereas GMS interpret the dummy variable HDB in the REALIS database to mean that the buyer is the Housing and Development Board, what this variable means is that the buyer currently lives in an apartment developed by the HDB. Table 2, bottom panel reports that over 99% of buyers are identified as households. 12 GMS sample corresponds to the purchase of used property (Table 2, middle panel). About 40% of the Table 3 reports our estimates using our reproduction of the GMS sample (384,539 transactions), to be compared to Giglio et al. s (2015a) Table VI. Following the GMS specification, on controlling for five-digit zip code fixed effects, 13 the price discount for new and used condominium apartments and houses with 813 to 994 years of lease remaining is not significantly different than zero relative to freeholds, the reference bin. Specifically, estimates on the year dummy of (s.e ) and (s.e ) in columns (1) and (2) of Table 3 are comparable to (s.e ) and (s.e ) in columns (1) and (2) of Giglio et al. (2015a) s Table VI. We use somewhat coarser bins than GMS for the original 99-year leaseholds, and estimates are statistically comparable, e.g., column (1) estimates range between ( year, s.e ) and What GMS do here is not clear from our reading of their article. 11 See Fesselmeyer et al. (2018) and their dataset and code, to be made available for replication. 12 Table VI, column (4) of Giglio et al. (2015a) focus(es) on properties that were bought by private individuals (and not the HDB) (p.26). 13 GMS interact zip code with transaction time (year-quarter or year-month), building type, and title type. GMS take units inside developments on land parcels classified as large by URA to be a distinct building type. In columns (1) to (7) we follow suit and specify interactions. Thus the number of regressors in these columns is two orders of magnitude larger than in columns (8) and (9), e.g., 22,416 regressors in column (7) versus 228 in column (8). In column (2), the ratio of the number of observations to number of regressors is only 3. 5

7 (56-63 year, s.e ), compared to a somewhat wide range between (95-99 year, s.e ) and (50-69 year, s.e ) in GMS. 14 In column (3), we continue specifying the GMS five-digit zip code fixed effects and, as in column (3) of Giglio et al. (2015a) Table VI, restrict the sample to properties that were built within 3 years of the transaction date. Compared to column (2), the point estimate on the year lease dummy falls by to , though it remains insignificantly different from zero (s.e ). Importantly, when controlling for five-digit zip code, the price difference between freeholds and or year leaseholds cannot be identified, and the estimated discount on year leaseholds is smaller than on year leaseholds and insignificant. 15 As explained, specifying five-digit zip code intercepts often accounts for i.e., perfectly predicts the development project, within which the original tenure contract is invariant. The coefficients on the tenure bins are then estimated off of within-property variation in remaining tenure as properties age. These two variables are highly correlated: with the passing of every year, a property depreciates on account of the ageing of the building as well as a shorter lease. GMS state that their specification includes 94,700 fixed effects (p.25), for a sample that includes about twice as many new property purchases. In the transaction sample of new condominium apartments, 1,672 projects would be divided into 1,516 five-digit zip codes (Table 1A). In columns (4) and (5) of Table 3, we repeat the same GMS specifications in columns (2) and (3) except that we now specify three-digit zip code fixed effects. These detailed controls strike a balance between controlling for geographic heterogeneity (Figure 1) and allowing for residual lease variation that is orthogonal to property age (Table 1). We are now able to estimate a significant price discount, of about 7 log points, for 813 to 994-year leaseholds relative to freeholds, whether we use our replication of the full GMS sample, or restrict this to properties aged 3 years or less. In column (6), we begin to control for the unit s floor, and the estimate on the year dummy is now log points and more precisely estimated, with a s.e. of versus in column (5). Floor levels in Singapore are informed by the leading digits of unit number contained 14 Table 3 aims to bridge differences in what GMS and FLS report in hedonic regressions for Singapore. Thus, column (9), discussed below, is comparable to FLS Table 2, column (3), based on a slightly longer sample period. A strength of the structural approach FLS propose is that one need not settle on bins that are somewhat arbitrary in the first place. We note that the lowest and highest lease lengths remaining among original 99-year leaseholds differ between what GMS report and our attempted reproduction of their sample, though this concerns few observations. 15 We note that the number of observations in column (3) relative to column (2) drops by about 30,000 less in Table 3 (from 384,539 to 259,011) than the corresponding drop GMS report (from 378,768 to 223,810). Further, GMS report estimates on the dummies for the shorter leases, while in our replication attempt these price effects are subsumed into the very tight fixed effects. 6

8 in the address, for example, #22-12 is informative of a 22nd-floor unit. GMS do not control for floor despite most properties in their Singapore sample (unlike UK property) being in high-rise buildings. In column (7), we drop purchases of houses (and of HDB executive condominiums, per the note to Table 3), and the 813 to 994-year leasehold discount becomes even more precisely estimated, with a s.e. of Finally, in columns (8) and (9), we further drop resales of used units aged up to 3 years from construction, however lightly used they might be, thus restricting the sample to new condominium apartments, i.e., the first purchase of each unit. To complete the bridge between GMS and FLS, we also allow prices to shift flexibly with the time difference between apartment purchase and construction completion, since this period averages three years. We further replace the interactions of three-digit zip code, year, month and larger land parcel fixed effects (as in GMS) by separate fixed effects. The number of regressors falls from 22,416 in column (7) to 228 in columns (8) and (9). Column (9) differs from column (8) in that the effect of apartment size and project size is non-linear, rather than linear (as in GMS). Compared to column (7), the estimate on the 813 to 994-year leasehold discount reported in column (9) is smaller, at , and the s.e. also shrinks, to 0.018, with a p-value of Despite the shorter sample ending December 2013 rather than January 2015 as in FLS, column (9) estimates are similar to those of FLS Table 2, column (3). 4 Concluding remarks Following an earlier literature, Giglio et al. (2015a) use hedonic regression to estimate price differences on residential property of varying lease length, in Singapore. To control for geographic heterogeneity, they specify five-digit zip code fixed effects that, in the city-state, are excessively tight. We show that in a cross-section of new condominium apartments sold between 1995 and 2015, over nine-tenths of five-digit zip codes displayed zero within variation in lease length. This is an example of a fixed-effects specification that, in an attempt to kill some of the omitted-variables-bias bathwater,...also remove(s) much of the useful information in the baby - the variable of interest (Angrist and Pischke, 2009, p.168). The authors may not be aware of this: by utilizing repeated sales of the same property over time, they introduce bad variation, since building depreciation and remaining lease length, both key determinants of used property prices, co-vary mechanically. We also show how this matters. Specifying still granular three-digit geographic controls that 7

9 do not remove the good variation, introducing controls such as floor that are key in a high-rise market, and choosing a more homogeneous sample that excludes used property as well as houses (a small share of the market), we show that multi-century leases trade at a non-zero discount relative to perpetual leases. The implication, both novel and policy relevant, is that households value housing many centuries into the future. 8

10 Table 1: Variation in lease length within zip code, by zip code granularity. Granularity of location control Five-digit Four-digit Three-digit zip code, zip code, zip code, e.g., 12772x e.g., 1277xx e.g., 127xxx Panel A: Condominiums Total no. of zip codes with residences No. of zip codes with only one lease type Fraction of total 96% 82% 42% No. of zip codes with exactly two lease types Fraction of total 4% 17% 51% No. of zip codes with all three lease types Fraction of total 0% 1% 7% Panel B: Condominiums and houses Total no. of zip codes with residences No. of zip codes with only one lease type Fraction of total 95% 72% 28% No. of zip codes with exactly two lease types Fraction of total 5% 24% 43% No. of zip codes with all three lease types Fraction of total 0% 4% 29% Notes: Residential property transactions across Singapore from the Urban Redevelopment Authority s (URA) Real Estate Information System (REALIS). Panel A considers transactions of new privately developed apartments ( condominiums ) between January 1995 and January 2015, as in Fesselmeyer et al. s sample. Panel B considers transactions of new and used condominiums and houses between January 1995 and December 2013, as in Giglio et al. s sample. Lease types are perpetual freeholds, original 999-year leaseholds, and original 99-year leaseholds. 999-year leaseholds span 825 to 986 years of remaining lease in the Fesselmeyer et al. sample and 813 to 994 years in the Giglio et al. sample. 99-year leaseholds span 56 to 99 years of remaining lease in the Fesselmeyer et al. sample and 21 to 103 years in the Giglio et al. sample. 9

11 Table 2: Reproduction of the Giglio et al. Singapore sample (January 1995 to December 2013). Share of transactions by remaining lease length (years) Purchase year N 21-69y 70-84y 85-89y 90-94y y y Freehold , , , , , , , , , , , , , , , , , , , Total 384, State of the purchased unit: New or used properties Building of unit being purchased New Used Total Condominium apartment 199, , ,214 Executive condominium 20,048 6,155 26,203 House (detached/semi) 12,093 26,029 38,122 Total 231, , ,539 Characteristics of the buyer according to his/her address at the time of purchase The buyer currently lives in: Building of unit HDB Condominium Not being purchased apartment apartm./house available Total Condominium apartment 130, ,101 1, ,214 Executive condominium 20,698 5, ,203 House (detached/semi) 12,278 25, ,122 Total 163, ,681 2, ,539 Notes: Residential property transactions between January 1995 and December 2013 from REALIS. Despite its local name, an executive condominium is a higher-quality apartment whose purchase faces similar restrictions and subsidies as a regular HDB apartment (and is sometimes referred to as an HDB executive condominium). 10

12 Table 3: Bridging the difference between what Giglio et al. and Fesselmeyer et al. find for Singapore. 5-digit zip code (almost project level) 3-digit zip code (area with a 0.9 km radius) Condominiums & houses Condominiums & houses Only condominiums The dependent variable New & New & Age New & Age Age Age New New is the transaction price Used Used 3y Used 3y 3y 3y units units in log (1) (2) (3) (4) (5) (6) (7) (8) (9) 813 to 994 years (1=yes) *** ** ** *** * * (0.020) (0.022) (0.024) (0.018) (0.033) (0.027) (0.026) (0.017) (0.018) 87 to 103 years (1=yes) *** *** *** *** *** *** *** *** *** (0.025) (0.026) (0.026) (0.013) (0.015) (0.014) (0.013) (0.012) (0.012) 64 to 86 years (1=yes) *** *** *** *** *** *** No New No New (0.038) (0.041) (0.091) (0.022) (0.044) (0.040) (0.048) units units 56 to 63 years (1=yes) ** digit *** 3-digit 3-digit 3-digit 3-digit 3-digit (0.151) (0.159) explains (0.049) explains explains explains explains explains 21 to 55 years (1=yes) *** *** 5-digit *** 3-digit 3-digit No Age No New No New (0.056) (0.059) explains (0.286) explains explains 3y units units units Floor (log) 0.063*** 0.063*** 0.073*** 0.068*** (0.003) (0.004) (0.006) (0.006) First floor of building (1=yes) 0.025*** 0.015** 0.029** (0.006) (0.007) (0.013) (0.010) Top floor of building (1=yes) *** *** *** *** (0.010) (0.015) (0.017) (0.012) Unit size Linear Linear Linear Linear Linear Linear Linear Linear Log Project size Linear Linear Linear Linear Linear Linear Linear Linear Log Age Linear Linear Linear Linear Linear Linear Linear - - Purchase-completion year bins No No No No No No No Yes Yes 5-digit zip-yr-mo-building type Yes (qtr) Yes Yes digit zip-yr-mo-building type Yes Yes Yes Yes digit zip, yr, mo, large parcel Yes Yes R Observations 384, , , , , , , , ,787 Number of regressors 83, ,534 52,793 61,351 29,812 29,696 22, Dependent variable mean Notes: *** p<0.01, ** p<0.05, * p<0.1. The dependent variable is the logarithm of the property s transaction price. We adjust nominal prices, including prepayments, to January 2014 S$. Lease length remaining is at the time the keys are handed over. Project size is the number of units transacted within the development. Following GMS, neither unit size nor project size (set to 1 for houses) is interacted with building type. Age is the time difference between purchase and construction completion for units purchased after completion, and 0 otherwise. Purchase-completion year bins are dummies that indicate the time difference (negative or positive) between purchase and completion. OLS regressions. Standard errors in parentheses are clustered by five-digit zip code and purchase year. Following GMS, columns (1) to (6) consider purchases of condominiums, houses, and executive condominiums (see notes to Table 3). Columns (7) to (9) consider purchases of condominiums. Columns (8) and (9) consider the first purchase of each unit, i.e., resales of used units aged up to 3 years from construction are also excluded. Columns (8) and (9) include three-digit zip code, purchase year, purchase month, and larger land parcel fixed effects, rather than interactions of them. Larger land parcel is a project-specific dummy according to URA s classification (columns (1) to (7) follow GMS and treat this as a building type distinct to apartment). In all columns the dummy for freeholds is omitted. 11

13 Figure 1: Bilateral distance between development project pairs (each project with invariant lease contract) within the same three-digit zip code. The sample includes 1,672 development projects with sales of apartment units recorded between 1995 and

14 References Angrist, J. D. and Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist s Companion. Princeton University Press. Bracke, P., Pinchbeck, E. W., and Wyatt, J. (2017). The time value of housing: Historical evidence on discount rates. Economic Journal, DOI /ecoj Fry, M. J. and Mak, J. (1984). Is land leasing a solution to unaffordable housing? Inquiry, XXII: pp Economic Gautier, P. A. and van Vuuren, A. (2014). The estimation of present bias and time preferences using land-lease contracts. Mimeo, VU University of Amsterdam. Giglio, S., Maggiori, M., and Stroebel, J. (2015a). Very long-run discount rates. Quarterly Journal of Economics, 130(1): pp Giglio, S., Maggiori, M., Stroebel, J., and Weber, A. (2015b). Climate change and long-run discount rates: Evidence from real estate. Mimeo, University of Chicago. Fesselmeyer, E., Liu, H., and Salvo, A. (2018). How do households discount over centuries? Evidence from Singapore s private housing market. Mimeo, National University of Singapore. Wong, S. K., Chau, K. W., Yiu, C. Y., and Yu, M. K. W. (2008). Intergenerational discounting: A case from Hong Kong. Habitat International, 32: pp