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The Time Value of Housing:
Historical Evidence on Discount Rates∗
Philippe Bracke†Edward W. Pinchbeck‡James Wyatt§
December 2016
Abstract Most London housing transactions involve trading long leases of varying lengths.
We exploit this to estimate the time value of housing—the relationship between the price
of a property and the term of ownership—over a hundred years and derive implied dis-
count rates. For our empirical analysis, we compile a unique historical dataset (1987 to
1992) to abstract from the right to extend leases currently enjoyed by tenants. Across a
variety of specifications and samples we find that leasehold prices are consistent with a
time declining schedule and low long-term discount rates in housing markets.
Keywords housing, leasehold, discount rates
JEL codes G10, R30
∗We thank seminar participants at the LSE/Spatial Economics Research Centre, American Real
Estate and Urban Economics Association conference in Reading, Helsinki Government Institute for
Economic Research, North American Meetings of the Regional Science Association, as well as Pat Bayer,
Dean Buckner, Tom Davidoff, Piet Eichholtz, Hua Kiefer, Colin Lizieri, Sean Holly, Geoff Meen, John
Muellbauer, Henry Overman, Olmo Silva, Silvana Tenreyro, and Garry Young for useful comments.
Any views expressed are solely those of the authors and cannot be taken to represent those of the Bank
of England, its Monetary and Financial Policy Committees or the Prudential Regulation Authority.
†Bank of England, email: philippe.bracke@bankofengland.co.uk. Corresponding author.
‡London School of Economics and Spatial Economics Research Centre, email: e.w.pinchbeck@lse.
ac.uk
§Parthenia Research and Fellow of the Royal Institution of Chartered Surveyors, email: jwyatt@
parthenia.co.uk
1 Introduction
The shape of discount rate functions — or the term structure of discount rates — pro-
vokes considerable research interest across a number of fields. In this paper we use sales
of leasehold dwellings to investigate discount rates in housing markets, complementing
a recent literature that exploits features of property tenure to estimate market discount
rates over long horizons (Wong et al., 2008; Gautier and van Vuuren, 2014; Giglio et al.,
2015a; Giglio et al., 2015b; Fesselmeyer et al., 2016). Under a leasehold arrangement a
property is owned only for a fixed term so the intuition for why leasehold prices may con-
tain information on discount rates is straightforward. Consider two identical properties,
one sold with a fixed term 99-year lease and the other with a 999-year lease.1Absent any
other contractual differences, the gap between the two sale prices must reflect the value
of an ownership claim for 900 years, discounted 99 years from now.
As with Giglio et al. (2015a) (henceforth GMS), our empirical analysis centres on the
English housing market.2Our contribution can be distinguished by two main differences
relative to that paper. First, we compile and refine a unique historical dataset of property
sales from 1987-1992 (before the start of the GMS sample), taking advantage of a geo-
graphical setting—Prime Central London, the highly urbanised core of London covering
Mayfair, Chelsea and Kensington—in which leaseholds account for four-fifths of sales.
In England and Wales, reforms in 1993 gave many leaseholders rights to extend their
leases or purchase them outright, at a premium agreed with the landlord or decided by
a tribunal (if the two parties fail to reach agreement). This option is regarded as valu-
able, especially for short lease properties, and is exercised for most leases well before the
term runs down.3The historical dataset allows us to abstract from these rights. Second,
we concentrate on the shorter end of the term structure and estimate discount rates for
leases in the 1-to-99 year range. (With no extension rights before 1993, we find a greater
proportion of short leases in the historical data.) This range is likely to be important for
public policies that have medium- to long-term consequences — for example infrastruc-
ture investments, pension savings, mortgages and related financial products — and given
the similarities between very short leases and rentals, our findings also relate to research
on rent-price ratios (Smith and Smith, 2006; Gallin, 2008; Campbell et al., 2009; Bracke,
1Terms of these lengths are commonly granted on new leases in England and Wales.
2GMS also analyse the housing market in Singapore.
3A further complication arises in this setting because following the 1993 legislation, a number of
real estate companies began to publish and promote graphs purporting to show the relationship between
lease length and sales price. These graphs have subsequently become the received wisdom for valuers
(and tribunals) in determining the premium for lease extension. Surveyors and agents have used this
estimated premium to value and price leasehold properties.
1
2015).
The principal finding from analysis of our historical sales dataset is that the housing
market discount rate schedule over 100 years is declining, with rates net of rental growth
around 3% at 100 years. To bridge our paper directly with the GMS study, we next
replicate our historical analysis using a sample of sales from the same period (2004-
2013). Crucially, we continue to find a declining term structure of discount rates in this
later setting. In terms of discount rate levels, our estimate of 2% at 100 years from this
exercise sits comfortably with the GMS finding of 1.9% for the same sample period. By
comparing between the two samples (1987-1992 and 2004-2013) we can also shed new
light on whether the housing market term structure changes over time. We find that on
average housing market discount rates are 1.6 percentage points lower in the later setting,
showing for the first time that decisions about the long-run may be context specific.
Our regressions use street fixed effects and a large number of property characteristics
extracted from sales brochures to disentangle lease length from other neighbourhood and
property features. We control for the condition of the property to reflect that a rental
externality (Henderson and Ioannides, 1983) may reduce incentives to maintain properties
held on short leases. By only comparing leaseholds with other leaseholds we rule out
unobserved differences between (and selection into) leasehold and freehold properties,
and in restricting attention to hard-to-redevelop flats we control for potential differences
in the value of a redevelopment option (Capozza and Sick, 1991). We also take account
of residual contractual differences between leases, carefully separating out those sold with
a share in the freehold and controlling for rents paid to the freeholder (so-called ground
rents) where these are significant. Our setting is one in which very few buyers require
mortgage finance so this is also unlikely to be driving results. Additionally, we undertake
a number of auxiliary regressions that demonstrate that: (a) conditional on our controls
there is no relationship between rental value and lease length for properties in our sample
and (b) that our findings are largely insensitive to changes in sample and specifications,
including those that (i) use minimal controls, (ii) use within building variation, (iii) use
different time periods or geographies, or (iv) rely on different estimation methods. These
results lead us to conclude that omitted variables, for example omitted structural building
characteristics or contractual features, are unlikely to be behind our main results.
Our results are directly relevant in a number of housing settings, including to individu-
als in England and Wales who own or are contemplating buying a lease.4In addition,
4As we explain elsewhere in the paper, under UK legislation the relationship between lease length
and sales price net of the value of the option to extend is a component of the statutory premium to
extend a lease. Later in this paper, we show how our findings contrast with conventional practitioner
2
housing market discount rates may be useful in situations that require estimates of real
estate values in the far-off future, for example long duration mortgages or housing equity
release products (reverse mortgages). In some policy settings outside of housing, such as
pension financing, infrastructure investments, and environmental regulation, benefits also
accrue only in the far-off future. Debates following the Stern review (Stern et al., 2006;
Weitzman, 2007; Nordhaus, 2007) demonstrate that in such cases assumptions about dis-
count rates can be paramount in deciding the optimal policy response. Some authorities,
notably the Office of Budgetary Management in the United States, guide policy-makers
to use a constant discount rate across all time horizons, while others including in the
UK, France, Norway and Denmark have adopted time-declining policy rates (Cropper
et al., 2014). Whether our findings can be usefully deployed to these questions depends
on the risk characteristics of residential real estate as compared to the ones of the policy
application. For instance, infrastructure investments share with real estate some impor-
tant features such as indivisibility, low liquidity and location specificity; the discount
rates patterns uncovered in this paper may therefore provide some additional guidance
in cases where housing and infrastructure values are closely related.
The paper proceeds as follows. In the next section we describe the institutional setting of
the leasehold market in the UK. The following section sets out the data sources that we use
for our empirical analysis. We explain our approach in Section 4 before reporting results
in Section 5. In Section 6 we discuss threats to identification, paying close attention to
findings in the recent literature and outlining techniques and several auxiliary regressions
we undertake to resolve them. Section 7 concludes.
2 Institutional framework
2.1 Residential leasehold in England and Wales
In England and Wales as many as 1 million houses and 2 million flats are owned under
long leases, 40% of recent new build properties are leased, and leaseholds account for
around a quarter of residential sales.5Leaseholds proliferate where populations are most
wisdom in this area and lead us to believe that leaseholders commonly overpay for extensions. In a
related contribution, Badarinza and Ramadorai (2014) examine some 450 decisions by the UK First-
Tier Tribunal—previously known as the Leasehold Valuation Tribunal (LVT)— to settle disputes over
the valuation of lease extensions and enfranchisements. Interestingly, these authors contend that the
discount rates implicitly adopted by tribunals are high and actually increasing with lease length.
5Department of Communities and Local Government Table FA1221 (S108): Household type by
tenure, 2011-12; housing stock estimates from https://www.gov.uk/government/policies/helping-people-
3
Figure 1: Fraction of leasehold and freehold sales, Land Registry 2013
Notes: The Land Registry contains all residential property sales in England and Wales since 1995. The
dataset is available at http://www.landregistry.gov.uk/market-trend-data/public-data. The
public version of the dataset only contains an indicator variable which labels properties as freeholds
or leaseholds. For the main analysis of this paper, we use proprietary data from real estate agencies in
Central London.
0
.2
.4
.6
.8
1
England and Wales London Prime Central London
Freehold Leasehold
concentrated—they account for around half of the sales in London and over four fifths of
sales in Prime Central London (Figure 1).
Leasehold ownership is an alternative way to hold residential property outside the more
widely studied home-ownership and rental forms of tenure.6Conceptualising tenure forms
as distinct bundles of use, transfer, and contracting rights and obligations (Besley and
Ghatak, 2009), the fundamental characteristic of leasehold ownership is that it grants the
purchaser of the lease– the lessee or leaseholder – use rights for a long but finite period,
commonly 99 or 125 years at origination, known as the term of the lease. As such it
lies between freehold home ownership (indefinite use rights) and renting (use rights for
a short fixed period). As with freehold owners, leaseholders can gift or sell the asset
(transfer rights) and mortgage or rent the property (contract rights).7Existing leasehold
to-buy-a-home.
6A full account of the history of residential leasehold and its evolution lies outside the scope of this
work. Interested readers are referred to McDonald (1969) who describes the origins of residential leasehold
ownership in the granting of land, or ground, leases in feudal England. Under such arrangements, tenants
would develop leased land, often to agreed parameters, and use it for the term of the lease with the land
and buildings reverting to the land owner thereafter. McDonald (1969) suggests several reasons why this
arrangement may have evolved, for example to enable management of the large fixed costs of providing
services such as drainage, sea-defences, street lighting, and road construction.
7Although technically the leaseholder cannot assign or sublet without the freeholder’s approval.
4
interests can then be bought and sold on the open market. When such a trade takes
place, the buyer inherits the existing lease agreement in full, including the duration of
the remaining use rights of the contract. This is known as the unexpired term of the lease
and is simply the original term reduced by the elapsed time since the lease was granted.
In contrast to freehold ownership, leasehold ownership implies multiple interests in the
same real estate asset since the seller of the leasehold – the lessor or freeholder – retains
an interest in the asset beyond the initial sale.8Land rents, known as ground rents, are
typically paid annually in accordance with a payment schedule agreed at the start of the
lease and represent an income to lessors rather than a payment for services.9Lessors
also commonly retain the right to veto redevelopment or alteration to the property by
the leaseholder during the term of the lease. If a leaseholder does wish to redevelop, the
freeholder will demand a premium which is subject to negotiation between the parties.
Nearly all flats in England and Wales are owned with leasehold contracts.10 This own-
ership structure provides a way to share costs for public goods (for example a shared
staircase, garden, or lift) when a single building contains more than one dwelling. In
some cases the individual leaseholders collectively own the freehold interest while in other
cases it is owned by a third party. The former is known as owning a leasehold with a
share in the freehold. It effectively allows owners to extend their leases indefinitely and is
therefore analogous to freehold ownership of houses in terms of the use rights it grants.11
The institutional framework around the right to extend or purchase a lease outright is an
important consideration in our analysis. Prior to 1993, most leaseholders in England and
Wales had no rights over leased property assets at the end of the lease term such that the
land and all buildings would revert to the lessor. The only option open to leaseholders
that wished to retain ownership was to negotiate a new lease with the lessor, either before
8This interest – usually thought of as corresponding to the ownership of the ground beneath the
real estate asset which has been leased – is known as the freehold interest, and can also be traded in
secondary markets. Note the distinction between a freehold interest in a real estate asset and freehold
ownership of an asset. The former implies that there is a lease over the property and there being two
interests. The latter implies a single interest.
9In some cases ground rents are of a nominal amount, known as a peppercorn ground rent, or a
fixed rent with no review. More often, ground rent payments are subject to review in intervals of 20,
25, 30 or 33 years. The lease sets out how the ground rent is reviewed at the review date but according
to Savills (2012) it is common for ground rents to either double, to increase by a fixed amount, to be
rebased against the retail price index (RPI), or to be rebased against a percentage of the capital value
of the underlying property at such times.
10A few flats are in fact held freehold, rather than share of freehold. These freehold flats will usually
be the flat where the freeholder lives. They could have the right to receive ground rents from other leases
in the building and, as described below, a stake in the residual interest as with other freehold interests.
11The owner of the freehold interest for flats usually provides management and maintenance services
to the building on behalf of the leaseholder(s), recovering costs through a fee known as a service charge.
This applies regardless of whether the block is owned leasehold or share of freehold.
5
an existing lease expired or at the end of the lease term. Major institutional changes in
1993 - described in detail in the Appendix - granted widespread rights for leaseholds to
extend their leases or to purchase them outright, at a price agreed with the landlord or
decided by a tribunal. For the reasons set out in the introduction, leasehold sales after
1993 could be less informative about discount rates. Compiling the historical dataset we
describe in the next section permits us to sidestep issues relating to enfranchisement that
could confound discount rate interpretations based on later sales.
3 Data
3.1 Context and data sources
To undertake the empirical analysis we first create a dataset of transactions in the Prime
Central London (PCL) area for the period 1987 to 1992.12 We use a definition of PCL
provided by real estate agents operating in the London market, including properties that
belong to the following postcode districts: SW1, SW3, SW5, SW7, SW10, W1, W2,
W8, W11, W14.13 A large proportion of the PCL housing stock has for 300 years been
owned by a small number of private land-owners – including the Grosvenor, Cadogan, de
Walden, Portman, Crown, Ilchester, and Phillimore Estates. These estates historically
made extensive use of the leasehold tenure system to develop land in this area, maintaining
some degree of control over the built environment.
Our primary source of data is Lonres.com, a subscription service for real estate agents and
surveyors working in the PCL area. Sales information in the Lonres sample is provided
by individual agents connected to the Lonres network and collated into a database. Many
of the major agencies operating in the PCL market are in the Lonres database, including
Savills, Knight Frank, and John D Wood & Co. Because the database provides only a
limited number of data fields, we extract and merge in additional property attributes
from the original PDF sales brochures. In addition to the Lonres.com historical archives,
we obtained access to the internal records of John D Wood & Co. (JDW), a real estate
agency operating in the PCL area. Sale prices in the JDW sample, which also starts
in 1987, have been verified by agents.14 To obtain a clean dataset we drop suspected
12Individual sale data before 1987 are extremely sparse in our data and therefore of little use for
econometric analysis.
13Postcode districts correspond to the first half of British postcodes and, in London, they typically
include 10,000–20,000 separate addresses.
14These prices are likely to be correctly measured because they are used to calculate agents’ commis-
sions.
6
duplicate sales where the address is the same and a second sales occurs within 90 days,
and data points where street or leasehold information is missing. Because we use a street-
fixed effect strategy, all transactions on streets with just one property in the dataset are
also dropped.
We abstract from the right to extend leases by excluding sales that occurred after the
Leasehold Reform Act of 1993, and those occurring in 1992 since this was an election
year and both main parties were proposing leasehold reform. By doing so, we minimise
concerns that leasehold prices in our data are influenced by the expectation of a reform.15
Following the earlier 1967 Act, some low-value leasehold houses had already become
enfranchisable, i.e. the leaseholder had the right to purchase the freehold of the property
in exchange for a premium. Whether a house was enfranchisable or not depended on
its rateable value. This is unobserved in our data so we obtained this information from
the relevant local authorities, identifying a list of houses which were enfranchisable at
the time and further exclude them from our sample.16 Taken together these restrictions
give us confidence we can avoid potentially confounding effects of rights to extend on the
leasehold prices in our data.
In the last part of the Results section, we compare our findings with a similar sample
of properties sold in PCL between 2004 and 2013. The information on these property
transactions is again taken from Lonres.com. While the next subsection describes the
1987-1991 sample, statistics on the 2004-2013 sample are presented in Appendix C.
3.2 Descriptive statistics
Table 1 describes the complete dataset of 8,184 records, splitting the data into categories
based on the type of dwelling (flats and houses) and data source (Lonres and JDW
records). More than half the data points are leaseholds with less than 100 years unexpired
term. Figure 2 shows the distribution of lease lengths in the sample: there are many
data points for leases with 55–65 years left, for 85–100 years left, and between 120 and
125 years; there is a group of sales with unexpired leases between 950 and 999 years.
The third column of Table 1 includes freehold houses and share of freehold flats, which
are displayed for illustrative purposes since they are not part of the empirical analysis.
Although share of freehold flats have a lease term, it is critical to put them together
15As a robustness check, we also ran the analysis including 1992 sales. Results were materially
unchanged.
16Rather than dropping enfranchisable houses, as a robustness check we also run the analysis including
them but assigning them a dummy. This had no material effect on results.
7
Table 1: Data points
Notes: Lonres.com is our main data source. Real estate agency John D Wood & Co. provided additional
data for this paper. The table shows the number of sales in our dataset which belong to the following
categories: leaseholds with unexpired term below 100 years, leaseholds with unexpired term above 100
years, and freeholds (including flats sold with a share of freehold). Our empirical analysis is restricted
to leasehold properties; we only include freehold properties in this table for illustrative purposes. The
average unexpired term for leasehold flats with more than 100 years to expiry is 307, whereas the median
unexpired term is 124.
Number of Number of Number of Total
leaseholds leaseholds freeholds or data points
<100 years ≥100 years share of F/H in sample
Lonres.com records
Houses 525 9 1,109 1,643
Flats 3,353 906 236 4,495
John D Wood & Co. records
Houses 116 2 888 1,006
Flats 605 428 7 1,040
Total 4,599 1,345 2,240 8,184
with freehold properties since their purchase includes a share of the freehold value of the
building and, with it, the right to extend one’s lease indefinitely.17 Figure 3 shows the
location of sales in the dataset and Figure C2 in the Appendix shows how observations
in the dataset are spread across the different quarters between 1987 and 1991.
All sale prices reported in the John D Wood & Co. archive are verified exchange prices.
By contrast, only around 15% of Lonres data points have been verified against other data
sources. When the price is non-verified, the figure may coincide with the original asking
price. Non-verified properties are equally found, in roughly the same proportion, across
leasehold of different lengths and our hedonic regression contains a variable that flags
non-verified properties.18
Table 2 refers to the estimation sample (leasehold properties) and contains the descriptive
statistics for all variables. Those that were immediately available from the original data
tables include: House (whether the property is a house, as opposed to a flat), Bedrooms
17Leasehold term for these properties tend to be long. In our dataset, more than a third of share of
freehold flats have a lease term longer than 945 years. A failure to account for these shares of freehold
properties could result in spurious conclusions about the implied value of lease term. This is even more
critical for recent data: Table C1 in the Appendix shows that more than one third of PCL flats were
sold as share of freehold in 2004-2013.
18Among verified sales in Lonres.com, the average difference between the asking price and the verified
price is 4.48%. We also ran our analysis only on verified properties and got similar estimates from the
ones presented in this paper, albeit with a much smaller number of observations.
8
Table 2: Estimation sample: Descriptive statistics
Notes: The table does not contain information on sale dates (described in Figure C2), sale locations
(mapped in Figure 3), and lease length (see Figure 2). Price and floor area are the only continuous
variables in the analysis; all other property attributes are dummy variables. The John D Wood & Co.
dataset groups together all floors from the third upwards. The Lonres dataset always specifies the exact
floor but all floors above the fourth are grouped together. Floor area is only available for approximately
2,000 data points (We have not found any systematic correlation between the presence of the floor area
variable and other attributes such as location or number of bedrooms).
count mean sd min max
Price 5,944 327,281 337,192 25,000 7,000,000
Lease 5,944 1 0 1 1
FH-Flat 5,944 0 0 0 0
House 5,944 .11 .31 0 1
Studio 5,944 .042 .2 0 1
2-Bedroom 5,944 .36 .48 0 1
3-Bedroom 5,944 .22 .41 0 1
4-Bedroom 5,944 .092 .29 0 1
5-Bedroom 5,944 .05 .22 0 1
6-Bedroom 5,944 .026 .16 0 1
7-Bedroom 5,944 .0064 .08 0 1
8-Bedroom 5,944 .003 .055 0 1
9-Bedroom 5,944 .001 .032 0 1
10-Bedroom 5,944 .0005 .022 0 1
11-Bedroom 5,944 .00017 .013 0 1
PurposeBuilt 5,944 .25 .43 0 1
Verified 5,944 .29 .45 0 1
OnerousGrRent 5,944 .14 .35 0 1
LwGr-Floor 5,938 .14 .34 0 1
Gr-Floor 5,938 .12 .33 0 1
2nd-Floor 5,938 .13 .34 0 1
3rd-Floor (Lnr) 5,938 .087 .28 0 1
3rdOrMore Floor (JDW) 5,938 .043 .2 0 1
4th-Floor (Lnr) 5,938 .056 .23 0 1
5thOrMore-Floor (lnr) 5,938 .051 .22 0 1
Maisonette 5,938 .12 .33 0 1
Mews 5,570 .014 .12 0 1
Detached 5,570 .0016 .04 0 1
TwoOrMore-Bathroom 5,570 .4 .49 0 1
Garden 5,570 .13 .34 0 1
Balcony 5,570 .21 .41 0 1
Terrace 5,570 .14 .35 0 1
Patio 5,570 .11 .32 0 1
CommunalGarden 5,570 .15 .35 0 1
Refurbished 5,570 .25 .43 0 1
InNeed 5,570 .068 .25 0 1
Sqft 1,996 1,286 971 157 13,747
9
Figure 2: Leasehold observations by years remaining
Notes: The histogram includes all leasehold observations in the sample, counted by length of the unex-
pired term. Freehold and share of freehold properties are not included. Bins are 5 years wide. There
are 43 properties spread between 150 and 980 years of remaining term—they are not visualised in the
histogram.
0
200
400
600
Observations
0 25 50 75 100 125 150
Leasehold unexpired term (years) 975 1000
(entered as a categorical variable), Sale Quarter,Street (entered as fixed effect),
Floor level,Verified (for sales in the Lonres dataset, this variable indicates whether
the sale price has been verified), Maisonette (indicates multi-level apartments), and
Onerous Ground Rent (we define the ground rent as onerous when it is above 0.1%
of the sale price).19 All other variables shown were extracted from pdf brochures. Most
are self-explanatory; InNeed indicates the presence, in the property advert, of the key
phrase “in need”, which is often followed by expressions such as “of improvements”, “of
refurbishment”, and so on.
4 Methodology
This section develops a simple approach to estimate discount rates from sales prices,
relying on the intuition that the gap between the sale prices of the property held forever
and a property leased only for tyears reflects the value of full ownership discounted t
years from now. We call this the present value of use rights, i.e. the present value of
19This threshold (0.1% of the sale value) is commonly used by market practitioners to identify ground
rents that are high enough to impact the transaction price. We experimented with other thresholds and
did not find notable differences in results.
10
Figure 3: Location of sales
Notes: Addresses in the sample have been geocoded using Google Maps (https://developers.google.
com/maps/documentation/geocoding/) and then mapped with R and the ggmap package.
Figure 4: Number of transactions per quarter
Notes: The pattern in sales well reflects the experience of market practitioners in that period and is
consistent with national and local price indices. 1988 was a boom year, with real estate agents enjoying
“high volumes, high prices, and high commissions”. After that came a fall in the market in 1989, and
the number of sales stabilised in 1990-1991.
0
500
1,000
1987 1988 1989 1990 1991
Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4
11
consumption and/or investment returns that flow from the asset. We proceed in two
steps: first estimating the discounts associated with leaseholds of a given length, then
retrieving the implied discount rates.
Our identifying assumption is that conditional on controls the only source of discounts
are differences in the present value of use rights. Potential confounders include any
unobserved factors which drive price differences between properties that are related to
the term of the lease but do not arise because of discounting.
4.1 Measuring leasehold discounts
We model the logarithm of the price of a leasehold property, held for tyears, as:
p(t) = p(∞) + ln f(t),(1)
where p(∞) is the log price of a property held on an infinite lease. The function f(t)
represents the discount associated with a given lease length as opposed to a property held
forever (but still on a leasehold arrangement to avoid potential biases deriving from price
differences between leaseholds and freeholds that do not depend on lease length).
To model the price of a property held forever we follow the literature on hedonic regres-
sions (Hill, 2013):
p(∞) = αj+Xβ +λs,(2)
where αjare street fixed effects, Xare property attributes, and λsare quarterly dum-
mies denoting the time of the sale (s).20 Our baseline specifications include the full set
of property attributes listed in Table 2, with the exception of square footage which is
available for a subset of data points.
To estimate ln f(t), we employ three methods: (1) leasehold buckets, (2) leasehold dum-
mies, and (3) a semiparametric approach based on Yatchew (1997). The bucket method
divides leasehold properties into several large groups according to their lease length so
that price effects can be estimated for each bucket. The dummy method pushes this
further such that each integer value of lease length up to 999 years (the highest in our
20Repeat sales regressions are an alternative to hedonic models but they require a sample with a
sufficient number of properties which have been sold twice. Since the main sample includes only the
years from 1987 to 1991, the repeat sales regression would only include properties that sold twice within
5 years. The resulting sample would be small and potentially affected by selection bias, as property that
sold often could have particular (observed or unobserved) characteristics.
12
data) takes a categorical variable:21
ln f(t) =
999
X
t=1
γt·d(t).
The semiparametric estimation approach described in Yatchew (1997) is reported in the
Appendix as a robustness check. By sorting all the observations in ascending order with
respect to tand differencing them, we take advantage of the fact that ln f(t0)−ln f(t)
tends towards zero. We can then use simple OLS to estimate a version of equation 1
that does not contain f(t). In a second step, we can apply common non-parametric
estimation techniques to retrieve lnf(t) from ˜p(t) = pt−ˆp(∞), where the predicted price
of a property held forever (ˆp(∞)) is derived from the first step described above.
4.2 Estimating discount rates
Taking Gordon (1959)’s simple constant discount rate model to equation 1 implies that:22
ln f(t) = ln(1 −e−RtT).(3)
Our aim is to explore whether Rtis constant, i.e. Rt1=Rt2=R, or varies over the time
horizon in question.
Prior expectations are that f(t) should satisfy f(0) = 0, f0(t)>0, and limx→∞ f(t)=1
indicating that a zero year lease should have no market value, that all else equal more
years on a lease should make the property more valuable, and that at some point very
long but finite leases should be equivalent to infinite leases. In practice, since we estimate
21To retrieve the true price discounts in each category the γcoefficients must be exponentiated.
Jensen’s inequality could cause the estimated discount to be larger than the actual discount, because
an average of logarithms is not the same as the logarithm of an average. In practice, the consequences
of Jensen’s inequality are likely to be limited. We confirmed this by running our baseline regression on
simulated data. The impact of Jensen’s inequality on estimates was apparent only at the third or fourth
decimal point.
22If the price of owning the property for one period is P(1), then the price of owning the property
forever is:
P(∞) = P(1)
R∞
,
where R∞is the net discount rate applied with an infinite horizon. In turn, R∞=r∞−g∞, where r∞
represents the gross discount rate and g∞the growth rate of P(1) over time. For a property held for t
years, we have that
P(t) = P(∞) (1 −e−Rtt
| {z }
f(t)
).
13
the γt’s in an unconstrained way, these conditions do not always hold and in Figure 5 the
points are scattered and some estimates lie above the long-lease line. Before attempting
inferences about discount rates we therefore fit a local polynomial through the estimated
points, fine tuning the bandwidth of the polynomial within reasonable limits. We then
use the predicted values of the polynomial curves to compute the discount rates at each
point in the term range by solving for each Rtthat corresponds to a pair {Rt, t}in
equation 3.
5 Results
5.1 Leasehold discounts
Our first results focus on leasehold discounts in the historical setting (1987-1991). Table
3 shows the output of the hedonic regressions. The first specification uses the bucket
approach and includes both leasehold houses and leasehold flats. The second specification
is the baseline specification which focuses only on leasehold flats and adopts the more
granular dummy approach where each lease term integer has its own categorical variable.
Appendix Table B1 contains the first stage of the semiparametric approach alongside
other robustness regressions.
Coefficients across the two models are generally in line with intuition. Houses command a
premium of 20% over flats controlling for other attributes such as bedrooms and street.23
The coefficient on InNeed of 15-20% implies a discount for properties advertised as “in
need of improvement”, an important control if poor maintenance is correlated with lease
term. The (unreported) coefficients on SaleQuarter together imply a mix-adjusted
index of house prices in Prime Central London. This is increasing in 1987–1989 and
decreasing thereafter, a pattern consistent with other historical indices such as the Na-
tionwide regional house price index for London (see Figure B1 in the Appendix). The
R-squared indicates that these models are able to explain approximately 78-82% of the
variation in house prices.
The first model of the Table, which excludes freehold properties, is designed to test for
price differences between long leasehold properties of different lease lengths. We group
leaseholds into four buckets: below 80 years, between 80 and 99 years, between 100 and
23Coefficients on floor dummies are generally negative and significant, with first floor being the omitted
category. In Prime Central London most houses have a Victorian architectural style; in these buildings
(usually two or three-floor tall) the ground and first floors have the highest ceilings and are considered
superior to the other floors.
14
Table 3: Hedonic regressions: Leasehold buckets and model with dummies
Notes: The baseline categories are flats, 1-bedroom properties, 1st floor. Both regressions include
leasehold properties only. The second model is run on leasehold flats. All models have street and quarter
fixed effects.
(1) (2)
log(Price) log(Price)
Baseline: Lease ≥900 Lease Flats
House 0.193∗∗∗ (0.061)
Studio -0.409∗∗∗ (0.030) -0.424∗∗∗ (0.033)
2-Bedroom 0.337∗∗∗ (0.015) 0.331∗∗∗ (0.013)
3-Bedroom 0.620∗∗∗ (0.022) 0.615∗∗∗ (0.022)
4-Bedroom 0.878∗∗∗ (0.033) 0.875∗∗∗ (0.032)
5-Bedroom 1.079∗∗∗ (0.060) 1.125∗∗∗ (0.067)
6-Bedroom 1.168∗∗∗ (0.076) 1.143∗∗∗ (0.104)
7-Bedroom 1.175∗∗∗ (0.126) 1.446∗∗∗ (0.194)
8-Bedroom 1.013∗∗∗ (0.264) 0.862 (0.550)
9-Bedroom 0.987∗∗∗ (0.195)
11-Bedroom 1.471∗∗∗ (0.074)
PurposeBuilt -0.015 (0.026) -0.027 (0.021)
Verified -0.087∗∗∗ (0.016) -0.102∗∗∗ (0.016)
OnerousGrRent -0.146∗∗∗ (0.027) -0.115∗∗∗ (0.018)
LwGr-Floor -0.126∗∗∗ (0.024) -0.127∗∗∗ (0.022)
Gr-Floor -0.035∗(0.020) -0.020 (0.018)
2nd-Floor -0.080∗∗∗ (0.016) -0.060∗∗∗ (0.015)
3rd-Floor (Lnr) -0.107∗∗∗ (0.021) -0.105∗∗∗ (0.020)
3rdOrMore Floor (JDW) -0.111∗∗∗ (0.027) -0.091∗∗∗ (0.027)
4th-Floor (Lnr) -0.088∗∗∗ (0.031) -0.086∗∗∗ (0.026)
5thOrMore-Floor (lnr) 0.022 (0.041) -0.004 (0.032)
Maisonette -0.027 (0.022) -0.019 (0.024)
Mews 0.157∗(0.086)
Detached 0.533∗∗ (0.229)
TwoOrMore-Bathroom 0.140∗∗∗ (0.016) 0.130∗∗∗ (0.015)
Garden 0.056∗∗∗ (0.019) 0.086∗∗∗ (0.019)
Balcony 0.056∗∗∗ (0.013) 0.083∗∗∗ (0.011)
Terrace 0.084∗∗∗ (0.016) 0.080∗∗∗ (0.015)
Patio -0.016 (0.021) -0.012 (0.020)
CommunalGarden 0.010 (0.020) 0.005 (0.017)
Refurbished 0.029∗∗∗ (0.011) 0.017 (0.011)
InNeed -0.189∗∗∗ (0.021) -0.153∗∗∗ (0.018)
Lease <80 -0.104∗(0.058)
Lease [80,100) -0.023 (0.049)
Lease [100,125) -0.013 (0.049)
Lease [125, 900) 0.025 (0.062)
Quarter (sale date) X X
Street X X
Observations 5570 5164
R squared 0.784 0.815
Standard errors in parentheses
clustered at the street level
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
15
Figure 5: Dummy estimates
Notes: The chart represents the lease length dummy estimates for the model shown in the second column
of Table 3. The chart also plot the 95% confidence bands associated with each coefficient. The dashed
horizontal line represents the value of long leases and in this case represents the value of a 999-year lease.
0
50
100
150
200
0 50 100 150
Leasehold unexpired term (years) 980 1000
124 years, between 125 and 900 years, and above 900 years (the baseline group).24 The
coefficients for other leasehold categories are not significant except for the coefficient on
leaseholds with less than 80 years, which is significant at the 10% level. These results
suggest that in this historical setting, very long maturity leaseholds cannot be easily
statistically distinguished from other very long maturity leaseholds of a different length.
The second model of Table 3 is our baseline specification in which we drop houses to
focus purely on leasehold flats and adopt the leasehold dummy estimation approach. Our
main object of interest, the dummy coefficients, are not tabulated but are displayed—
exponentiated—in Figure 5. These estimates indicate the discount associated with all
leasehold flats of a specific lease length with respect to leasehold flats with 999 years
remaining. The point estimates are shown as dots with the 95% confidence intervals
represented by the bars appearing to vary in line with the histogram of Figure 2, with
the smallest errors corresponding to leases groups computed from more observations.
24Choices over the boundaries for each group are inevitably arbitrary to some extent. Grouping
leaseholds with less than 80 years together follows UK legislation which requires a different computation
for the premium to be paid to enfranchise a lease when the lease reaches 80 years, presumably because
the value of the lease is expected to decline rapidly after that.
16
Figure 6: Smooth f(t) function
Notes: The chart shows the second-degree local polynomial with a 15-year bandwidth on both sides
fitted through the dots displayed in Figure 5. The chart focuses on the 1-99 year range. The dummy
estimates are plotted as circles where the size of the circle is proportional to the number of observations
for that specific lease length. The grey bands around them represent 95% confidence bands, computed
using boostrapping with 1,000 iterations.
0
50
100
0 50 100
Leasehold unexpired term (years)
5.2 Discount rates
The exponentiated γtcoefficients in Figure 5 define the shape of f(t) in equation (3)
above.25 As expected the estimates are slightly scattered so in Figure 6 we fit a local
polynomial to these points, weighting by the number of sales at that specific lease length.
The curve is a second-degree local polynomial with a bandwidth of 15 years on both
sides and an Epanechnikov weighting scheme. Confidence bands are represented by the
grey areas around the curve. Since we implement a two-step procedure, we compute
the confidence bands using bootstrapping, reshuffling the original dataset one thousand
times. Although the curve is fitted across the whole lease range, we focus on leases of
1-to-99 years given our findings in the previous section.
The polynomial fulfills the conditions described above: it is increasing and remains below
the line representing the value of 999-year leases (the horizontal line at 100). We next use
the predicted values of the polynomial curve to compute the discount rate at each point
in the term range by solving for each Rtthat corresponds to a pair {Rt, t}in equation 3.
25The choice of the baseline in the estimation of f(t) could have an impact on coefficients. Because
999-year leases (our baseline leasehold category) could be randomly more expensive or cheaper than other
properties, as a robustness check, we also ran the analysis by using the average price of all leases between
100 and 999 years as the reference price of long leases (p(∞)). Results were substantially unchanged.
17
Figure 7: Implied discount rates
Notes: The chart shows the discount rates implied by the curve fitted in Figure 6. The discount rates
implied by the corresponding individual dummy estimates are also plotted. As in Figure 6, the circle
size is proportional to the number of observations for that specific lease length.
This Figure represents a leasehold flat v.s. leasehold flat analysis, significantly departing from the con-
ventional basis for establishing relativity used by market practitioners.
0
.02
.04
.06
.08
.1
0 50 100
Leasehold unexpired term (years)
The result is shown by the line in Figure 7, with circles representing the discounts derived
from the original dummy estimates. Overall, these results indicate that leasehold prices
in our setting appear to be consistent with a declining discount rate schedule. Very short
leases imply discount rates of around 5-6%, whereas long leases, close to 100 years left,
imply discount rates close to 3%.
These net discount rates can be used to estimate the gross discount rates prevailing at the
time of our analysis (1987-1992). One way of doing so is to add the long-run rate of real
rent growth, as in GMS who take a real rent growth of 0.62% using the CPI component
“actual rents for housing” (series D7CE) from the UK Office of National Statistics for
the period 1996-2012 . This would imply a 0.62% upward shift of the dots in Figure 7.
5.3 Comparison to existing estimates and changes over time
In this subsection, we first compare our findings to existing estimates of the effect of
leasehold term on sales prices. The most natural starting place is to compare our estimates
to heuristics commonly followed by leasehold valuers and Tribunals in the UK markets
because, like us, these mostly focus on the 1-to-99 year range and also purport to abstract
18
from leaseholder rights.26 Such a comparison highlights that the shape of the curve we
fit diverges substantially from the curves in common use by practitioners—as we show in
Figure B7 in the Appendix.
Although our central focus is not on very long-run discount rates implied by leases of
maturities longer than 100 years, we can also demonstrate that our results sit comfortably
with the recent academic findings in GMS. To illustrate, in the first column of Table 4
we show results from GMS Table III. In the second column, we present results from a
similar specification but using our 2004-2013 PCL sample. To be consistent with GMS
main results, in this regression we use freehold properties as the baseline. There are no
major differences in coefficients derived from the two studies except for the shortest-lease
bucket.27 Following the calibration method adopted by GMS, our results for this sample
are consistent with very long-term discount rates of around 2% in 2004-2013, very close
to GMS’s main finding that very long term net discount rates in housing markets are
close to 1.9% in this period for England as a whole.
At the other end of the spectrum, the discount rate on very short leases can be compared
to the average rent-price ratio in the area, given some degree of substitutability between
renting for a few years and buying a short lease. Bracke (2015) measures rent-price ratios
in 2006-2012 in the same PCL area and finds a median rent-price ratio of 5%, consistent
with discount rates of 4-7% seen for very short leases in the 2004-2013 sample.
To investigate changes over time in more depth, we next contrast estimates of discount
rates across the 1-to-99 year range in our two sample periods. In Figure 8 we show that
discount rates in the 2004-2013 sample of sales are consistently lower than in the 1987-
1991 data across the whole range. Both lines decline slowly with regressions confirming
that the slope of both lines is non-zero. Importantly, the average level of the two lines is
materially different with the average 1987-1991 rate (4.1%) being significantly higher than
the average rate in 2004-2013 (2.5%). There could be many explanations behind these
findings, for instance changes in the risk-free rate, the riskiness of housing, and changes
to the institutional setting (including the influence of the existing relativity graphs).
Although unable to fully distinguish between them at this time, we do demonstrate in
Appendix Figure B4 that implied discount rates were stable either side of the 4.5% drop in
26We are sceptical about the validity of these heuristics due to lack of a rigorous statistical approach
and the impossibility of replication. See Appendix A for more details.
27This likely derives from differences in the spatial scope of the two studies. In a robustness check
Giglio et al., 2015a report findings for London graphically (with standard errors unreported). These show
coefficients that are similar to GMS’s baseline results above but with a 13% discount for the shortest-
lease bucket. Interestingly the GMS London analysis also finds a positive coefficient on the 700+ year
group.
19
Table 4: Comparison with Giglio et al
Notes: The first column of the Table reports the results from GMS Table III, column (1). The second
column reports results from an analogous regression run on PCL properties advertised for sale between
2004 and 2013 (the same sample period used by GMS) and recorded by the portal Lonres. In these
regressions the baseline category is freehold properties.
Giglio et al (2015) This Paper
England + Wales PC London 2004-2013
80-99 years -0.176∗∗∗ -0.105∗∗∗
(0.007) (0.016)
100-124 years -0.110∗∗∗ -0.080∗∗∗
(0.008) (0.016)
125-149 years -0.089∗∗∗ -0.043∗∗
(0.008) (0.021)
150-300 years -0.033∗∗∗ -0.037
(0.01) (0.056)
700+ years -0.003 0.035
(0.007) (0.021)
Observations 1,373,383 15,807
the Bank of England base rate between October 2008 and March 2009. At the same time,
Clark (1988)’s findings that long-term interest rates in land markets fell from around 10%
in Medieval England to around 4% by the start of the 19th Century place our results
within a much longer historical perspective.
6 Threats to identification and robustness checks
The baseline specification in column 2 of Table 3 incorporates a number of strategies
to isolate the present value of use rights from other sources of variation. The street
fixed effects partial out granular location-specific effects and help us control for some
unobserved housing attributes, for example where properties on the same street share
the same style and layout.28 This regression uses the most complete set of structural
dwelling attributes that our historical dataset allows. We control for the condition of the
property to reflect that a rental externality (Henderson and Ioannides, 1983) may reduce
incentives to maintain properties held on short leases.29
By only comparing leaseholds with other leaseholds we rule out potentially unobserved
differences between leasehold and freehold properties and related concerns, for example
endogenous selection of properties into freehold and leasehold tenure, buyer preferences
for freeholds, or other factors that drive systematic value differences between the property
28We also ran our analysis using postcode fixed effects instead of street fixed effects and obtained
nearly identical estimates.
29It should also be noted that UK leaseholders have an obligation to maintain a property in good
state and that failure to do so might trigger a dilapidation claim from the freeholder.
20
Figure 8: Implied discount rates: 1987-1991 and 2004-2013 samples
Notes: The chart shows implied discount rates for the two samples with the 1987-1991 curve replicating
that shown in Figure 7 and the 2004-2013 curve derived from the associated dataset.
0
.02
.04
.06
.08
.1
0 50 100
Leasehold unexpired term (years)
1987−1991 2004−2013
groups. Remaining observable contractual differences between leases are accounted for by
carefully separating out and excluding those leases sold with a share in the freehold and
by controlling for rents paid to the freeholder (so-called ground rents) where these are
significant. Auxiliary analysis in Giglio et al. (2015a) Appendix A.1.7 gives us confidence
that additional contract features — such as restrictive covenants — are unlikely to vary
systematically with remaining lease term. Similarly by comparing flats only with other
flats we avoid unobserved differences between flats and houses, including corresponding
concerns around market segmentation and endogenous dwelling structure. Since flats
cannot usually be redeveloped to a higher density, restricting attention to these dwellings
has the additional benefit of controlling for potential differences in the value of a redevel-
opment option which could be correlated with the term of the lease (Capozza and Sick,
1991).30
We aim to further mitigate omitted variable concerns in two supplementary regressions.
In the first, we test whether lease length has an effect rental value conditional on our set of
controls. To do so we match properties in our main specification to a dataset of property
30The value of a redevelopment option is likely a function of the up-front costs of redevelopment and
the increased rents that will result. With a short lease, the value of the option is low because there are
few periods over which to recover capital costs. Our argument is that if flats cannot be redeveloped to
a higher density then redevelopment gains will be hard to achieve whatever the term of the lease.
21
Figure 9: Rents and leasehold term
Notes: The chart shows the effect of unexpired lease term on rents, where rental values are matched
from later data. The underlying regression mirrors our baseline specification column 3 of Table 3 but
adds the quarter of the rental. As previously, the dots are the point estimates and the whiskers the 95%
confidence interval.
50
100
150
200
250
0 20 40 60 80 100
Leasehold unexpired term (years)
rentals in the period 2004-2014 which restricts the sample to around 1,000 properties.
Figure 9 shows that there is no clear relationship between lease length and rental price.
We conclude that if rental values are strongly correlated over time, omitted property
characteristics that drive both rents and prices are unlikely to be biasing our results. For
the second auxiliary regression, we repeat our baseline analysis but additionally including
a building fixed effect for all properties that share the same street name and number.
Results, displayed in Figure 10, demonstrate that our main finding of a declining discount
rate is robust to this demanding specification which controls for all unobserved variation
at the level of the building, including for example age of the structure.31
A number of additional regressions reported in the Appendix demonstrate that our main
results are robust to specification and sample changes. These include models where (i)
the dependent variable is price per square foot32;(ii) we interact street and quarter dum-
mies to allow for street-quarter intercepts, which amounts to comparing only properties
31In unreported results we also confirm our main findings our insensitive to two additional variations
on our baseline specification. In the first of these we use postcodes instead of streets as our geographical
fixed effects. In the second, we include the dwelling’s Council Tax band, which is based on the assessed
value of the property used for taxation purposes, as an additional control. In both cases our sample size
is reduced so we prefer the baseline specification above.
32Square footage is available for around half of our data points. Examining the dataset reveals no
clear pattern to omission, i.e. expensive and less expensive properties, or big or small properties, are
equally likely to have square footage recorded.
22
Figure 10: Building fixed effects
Notes: The chart shows discount rates implied by a local polynomial fitted through leasehold estimates
derived from a model that mirrors column 3 of Table 3 but additionally includes building fixed effects.
Discount rates implied by individual dummies are also plotted, with circle size proportional to the number
of observations.
0
.03
.06
.09
.12
.15
0 50 100
Leasehold unexpired term (years)
Implied discount rates
within the same street and sold in the same quarter;33 (iii) we split the sample into the
submarkets of Kensington vs Chelsea; and (iv) we split the sample into the boom period
(1987-1988) vs the bust period (1990-1991). Finally, in the spirit of Altonji et al. (2005)
and Oster (2016), we show in Appendix Figure B8 that a regression specification with
only street fixed effects and no other control variable is able to replicate the shape of
leasehold prices shown in Figure 6 (delivering a declining schedule of discount rates).
Moreover, since the R-squared of our full specification is 81%, there is relatively little
scope for omitted variables to have a large impact on results.
A more general concern may be that our results lack external validity to policy settings
if the discount rates we uncover are driven by time preferences as well as horizon-specific
features of housing markets, such as the riskiness of housing or financing frictions in
mortgage markets specific to some parts of the term range. In this context we note that
a high proportion of buyers in this area were not dependent on mortgage financing.34
33In practice, this reduces the effective sample size by a third but results remain the same.
34Census data from the website Neighbourhood Statistics (https://neighbourhood.statistics.
gov.uk/dissemination/) shows that in the Prime Central London area in 2001, 66% of homes were
owned outright (without a mortgage), and in 2011, this fraction went up to 70%.
23
7 Conclusion
This paper describes the association between lease length and sales prices of flats in
the London market, using data from two distinct periods: 1987-1991 when leaseholders
had no rights over leased assets on lease expiry and 2004-2013 when they did. We
compute housing market discount rates through the application of the simple Gordon
model. Results are suggestive of declining discount rates over the 1-to-99 year range in
both samples. To the extent that discount rates in housing markets are a useful indicator
for social discount rates, these findings could support the use of a declining discount rate
function for policy-making, as have already been adopted in the UK and in France.
We investigate whether the average level of housing market discount rates stays constant
between two samples of sales: in 1987-1991 and 2004-2013. We find rates in the later
period are significantly lower (by 1.6 percentage points on average) than rates in the
earlier setting, albeit slightly converging at very long horizons to between 2 and 3%. To
the best of our knowledge, this is the first demonstration that long-run housing market
discount rates implied by leaseholds may change over time.
Our findings are also relevant to current and potential leaseholders in England and Wales
where the relationship between lease length and property value, assuming no rights to
extend a lease, is an important factor in determining the price required to purchase a
lease extension or to enfranchise a leasehold property. The results stand in direct contrast
to rule-of-thumb approaches to valuing lease term used by market practitioners. These
differences suggest that lease extensions could result in transfers between leaseholders and
freeholders that are out of kilter with market values (Badarinza and Ramadorai, 2014).
24
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26
Appendices
27
A Rights to extend and enfranchise a lease
Prior to 1967, leaseholders in England and Wales had no rights over leased property
assets at the end of the lease term such that the land and all buildings would revert to
the lessor. The only option open to leaseholders that wished to retain ownership was to
negotiate a new lease with the lessor, either before an existing lease expired or at the end
of the lease term. A statutory right for leaseholders to extend their leases or to purchase
the freehold, a process known as enfranchisement, was first introduced in legislation in
1967, granting rights to owners of leases on low value houses, defined on the basis of the
property’s rateable value, an assessment of the value of the property made for taxation
purposes. In 1993 a subsequent Act widened the scope of rights to cover the vast majority
of houses and flats.
The legislation sets out a method to decide how much a leaseholder needs to pay to
extend the lease or purchase the freehold but leaves the precise parameters to determine
the premium unspecified. In practice premiums are usually negotiated bilaterally between
the leaseholder and the freeholder, often with the benefit of professional advice. If the
leaseholder and freeholder cannot reach an agreement, the leaseholder can ‘hold over’ and
remain in the property paying a market rent. They also have the option of bringing a
dispute to a statutory tribunal, where a panel of independent experts hear evidence and
decide the premium payable following the statutory guidelines. 35
One component of the statutory valuation is the ratio of the value of the lease at its
current unexpired term to the value of the property if it were held on a freehold. The
legislation dictates that this ratio—known as relativity—should be calculated assuming
that the lease interest does not benefit from the right to extend or enfranchise, and
to disregard any improvements the tenant has made to the property. Outside of these
assumptions, the legislation offers no guidance on what relativity looks like,how it should
be calculated, and under what circumstances it should vary. As a result, relativity has
been subject to intense debate since rights to enfranchise were introduced and a number
of graphs of relativity have been complied and promoted by market practitioners. Some
of the leading graphs currently in circulation for the Prime Central London (PCL) area
are shown in Figure A1. Such graphs rely on small and non-randomly selected data
samples and enshrine ad hoc adjustments to individual property values based on expert
35Although direct data on the size of the market for lease extensions is difficult to come by, the
activity of the Leasehold Advisory Service (LAS), a free advice service for leaseholders, provides an
indirect measure. In 2012/13 LAS received more than 800,000 website visits and fielded more than
40,000 telephone or written queries with the second most common line of inquiry being lease extension
(Leasehold Advisory Service Performance Statistics 2012/13 and Annual Report and Accounts 2012/13).
28
Figure A1: Practitioner graphs of relativity for Prime Central London
Source : Royal Institution of Chartered Surveyors (2009)
opinion in an attempt to ensure that properties are comparable. Moreover, decisions
taken about the construction of sample, adjustments adopted, and line fitting methods
to draw the graphs are not disclosed, and no information is provided to evaluate their
statistical properties.
29
B Additional analysis and robustness checks
70
80
90
100
110
1987q1 1988q1 1989q1 1990q1 1991q1 1992q1
Hedonic model Nationwide index (London)
Figure B1: Price index implied by hedonic regression (1990q1 = 100)
Notes: The chart plots the coefficients on quarterly dummies in the first model of Table 3, compared
with the Nationwide price index for London. The period that goes from 1987 to 1989 was characterised
by a boom and then the market stabilised. The price pattern is consistent with the quantity trend shown
in Figure C2. The behavior of our index after the boom differs slightly from the one of the Natiowide
index. This may be due to the different coverage of the two indices—Natiowide covers the whole London
area whereas our observations only come from Prime Central London.
30
Figure B2: Smoothed f(t) function, Kensington vs Chelsea
Notes: Most of the property sales in our dataset are located in an administrative area known as the
Royal Borough of Kensington and Chelsea (this is the area populated by dots in Figure 3). The charts
below replicate Figure 6 but only include the sales which have occurred in the Kensington neighborhood
(the first two charts) and the Chelsea neighborhood (the last two charts). The number of observations
per chart clearly diminishes, which makes the fitting curve (especially the local polynomial) less smooth.
However, the general shape of the curve is preserved even at a smaller spatial scale.
0
50
100
0 50 100
Leasehold unexpired term (years)
Kensington
0
50
100
0 50 100
Leasehold unexpired term (years)
Chelsea
31
Figure B3: Smoothed f(t) function, boom period (1987-1988) vs bust period (1990-1991)
Notes: As the previous figure in this appendix, this figure replicates Figure 6, this time comparing sales
which occur in the first two years, 1987–1988 (in the first two charts), with sales which occur in the last
two years of the sample, 1990–1991 (in the last two charts). The 1987–1988 was characterised by high
sale volumes and growing prices, whereas the 1990–1991 saw flat volumes and prices (see Figures C2 and
B1). As in the previous figure, the analysis of subsamples does not produce significantly different results
from those shown in the main part of the text and in Figure 6.
0
50
100
0 50 100
Leasehold unexpired term (years)
1987−1988
0
50
100
0 50 100
Leasehold unexpired term (years)
1990−1991
32
Figure B4: Discount rates before and after Bank of England rate cut
Notes: Discount rates computed as in Figure 7 for both samples. Base rates were between 4% and 5.75%
in the earlier period and were stable at 0.5% in the later one.
.02
.04
.06
.08
.1
0 20 40 60 80 100
Leasehold unexpired term (years)
2004−2008q3 2009q2−2013
33
Table B1: Additional hedonic regressions
Notes: The baseline categories are flats, 1-bedroom properties, 1st floor. The first column displays
the results of a regression including quarter-street interactions as fixed effects to allow for specific local
conditions in a given quarter. Since this specification automatically excludes quarter-street combinations
where there are less than two sales, the reported number of observations drops by approximately 3,000.
The second column refers to a regression run on price per square foot. The number of observations drops
substantially because few properties have information on floor area. Interestingly, when including floor
area the premium on houses (as opposed to flats) disappears. The third model represents the first stage
of the Yatchew (1997) approach. The sample for this model includes only leasehold flats.
(1) (2) (3)
log(Price) log(Price/Sqft) log(Price)
Semiparametric,
Baseline: Lease ≥900 Baseline: Lease ≥900 Lease Flats
House 0.150 (0.093) 0.101 (0.189)
Studio -0.431∗∗∗ (0.049) -0.146∗∗∗ (0.055) -0.376∗∗∗ (0.041)
2-Bedroom 0.344∗∗∗ (0.017) 0.081∗∗∗ (0.021) 0.378∗∗∗ (0.036)
3-Bedroom 0.630∗∗∗ (0.033) 0.156∗∗∗ (0.030) 0.650∗∗∗ (0.039)
4-Bedroom 0.866∗∗∗ (0.044) 0.216∗∗∗ (0.046) 0.848∗∗∗ (0.039)
5-Bedroom 1.170∗∗∗ (0.092) 0.297∗∗∗ (0.082) 1.048∗∗∗ (0.049)
6-Bedroom 1.208∗∗∗ (0.110) 0.329∗∗∗ (0.122) 1.040∗∗∗ (0.098)
7-Bedroom 1.253∗∗∗ (0.131) 0.199 (0.227) 1.318∗∗∗ (0.196)
8-Bedroom 1.556∗∗∗ (0.198) 0.411∗∗∗ (0.137) 0.907∗∗∗ (0.242)
PurposeBuilt -0.004 (0.030) -0.047 (0.029) -0.035∗(0.020)
Verified -0.087∗∗∗ (0.022) -0.060∗∗∗ (0.021) -0.100∗∗∗ (0.017)
OnerousGrRent -0.111∗∗∗ (0.023) -0.073∗∗∗ (0.023) -0.130∗∗∗ (0.018)
LwGr-Floor -0.135∗∗∗ (0.034) -0.197∗∗∗ (0.029) -0.135∗∗∗ (0.022)
Gr-Floor -0.031 (0.025) -0.040 (0.025) -0.019 (0.021)
2nd-Floor -0.066∗∗∗ (0.023) -0.024 (0.025) -0.060∗∗∗ (0.019)
3rd-Floor (Lnr) -0.123∗∗∗ (0.029) -0.068∗∗∗ (0.022) -0.086∗∗∗ (0.022)
3rdOrMore Floor (JDW) -0.112∗∗ (0.046) -0.065∗∗ (0.030)
4th-Floor (Lnr) -0.089∗∗∗ (0.034) -0.062∗∗ (0.031) -0.066∗∗∗ (0.024)
5thOrMore-Floor (lnr) -0.020 (0.044) -0.025 (0.034) -0.020 (0.027)
Maisonette -0.012 (0.034) -0.108∗∗∗ (0.032) -0.015 (0.021)
Mews 0.358 (0.224) 0.171 (0.266)
Detached 0.454 (0.283)
TwoOrMore-Bathroom 0.113∗∗∗ (0.018) 0.043∗∗∗ (0.012) 0.128∗∗∗ (0.012)
Garden 0.095∗∗∗ (0.023) 0.033 (0.032) 0.094∗∗∗ (0.017)
Balcony 0.069∗∗∗ (0.017) 0.066∗∗∗ (0.020) 0.077∗∗∗ (0.013)
Terrace 0.088∗∗∗ (0.020) 0.068∗∗∗ (0.020) 0.091∗∗∗ (0.015)
Patio -0.000 (0.027) -0.044 (0.029) -0.012 (0.018)
CommunalGarden 0.009 (0.022) 0.028∗(0.015) -0.003 (0.016)
Refurbished 0.023 (0.014) 0.020 (0.015) 0.020∗(0.011)
InNeed -0.151∗∗∗ (0.026) -0.142∗∗∗ (0.023) -0.164∗∗∗ (0.019)
log(Sqft) -0.312∗∗∗ (0.035)
Leasehold term X X
Quarter (sale date) X X X
Street X X
Street*Quarter X
Observations 4112 1905 5163
R squared 0.872 0.718 0.650
Standard errors in parentheses
clustered at the street level
∗p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01
34
Figure B5: Results of the semiparametric estimation
Notes: The left-hand side of the Figure represents the curve fitted through the quality adjusted sale
prices obtained in the first stage. (Table B1 shows the coefficients from the first stage of the semipara-
metric method, which are similar to the coefficients shown in Table 3.) The curve is a second-degree
local polynomial with a bandwidth of 15 years on both sides and an Epanechnikov weighting scheme.
Confidence bands are represented by the gray areas around the curve. The right-hand side of the figure
charts the discount rates implied by the curve. Results are similar to those depicted in Figure 7, which
is derived from a standard regression with dummies.
0
50
100
150
200
0 50 100
Leasehold unexpired term (years)
Short vs long lease prices (%)
0
.02
.04
.06
.08
.1
0 50 100
Leasehold unexpired term (years)
Implied discount rates
35
Figure B6: Distribution of residuals
Notes: The left-hand side chart shows the distribution of residuals, which look normal around zero. The
right-hand side chart plots the individual residuals against leasehold unexpired terms. Residuals and
lease length do not appear to be correlated; we do not see systematically larger residuals for some lease
lengths and smaller residuals for others.
0
500
1000
1500
# data points
−3 −2 −1 0 1 2 3
Residuals
−2
−1
0
1
2
Residuals
0 20 40 60 80 100
Leasehold unexpired term (years)
36
Figure B7: Paper’s findings vs existing practice
Notes: The main text reported that the shape of the curves we fit diverges substantially from the curves
in common use by practitioners. To visually illustrate these differences, we run a new specification
designed to mirror the approach underlying most relativity curves, including houses as well as flats and
freeholds as well as leaseholds. We then fit a curve to leasehold dummies as in earlier results, plotting
in Figure B7 the results alongside another ‘relativity curve’, derived from a set of 601 Tribunal decisions
in the London region, compiled by real estate agency John D Wood & Co. (The analysis was run by
James Wyatt and the aggregate data is available at http://www.johndwood.co.uk/r/surveyors/pdfs/
publications/The_Pure_Tribunal_Graph.pdf.) The figure highlights the two differences with existing
practice mentioned in the text: first, we find a larger difference between a long leasehold and a freehold;
second, our curve is higher in the middle range of leasehold terms, between 30 and 70 years.
40%
80%
Freehold value
0 50 100
Leasehold unexpired term (years)
Local polynomial Tribunals
37
Figure B8: The relation between price and leasehold term controlling for different groups
of variables
Notes: The charts replicate Figure 6 but starting from regressions with limited control variables. The
upper left chart plots the unconditional average prices (rebased so that the price of a 999-year lease is
100) as a function of the lease term. The r-squared reported in the title refers to a regression of log
prices on lease-term dummies. The upper right chart refers to a regression with all the controls showed
in Table 3, whereas the chart in the lower left corner refers to the same regression as the one in the upper
left chart with the addition of street fixed effects. The lower right chart replicates Figure 6.
0
50
100
150
0 50 100
Leasehold unexpired term (years)
No controls (R2: 11%)
0
50
100
150
0 50 100
Leasehold unexpired term (years)
Controls, no street FE (R2: 67%)
0
50
100
150
0 50 100
Leasehold unexpired term (years)
Street FE, no controls (R2: 50%)
0
50
100
150
0 50 100
Leasehold unexpired term (years)
Controls and street FE (R2: 81%)
38
C Information on the 2004-2013 sample
The 2004-2013 sample is extracted from Lonres.com. Table C1 shows that there are
26,776 sales in the sample, 19,940 of which refer to flats. The recent sample contains
more share of freehold flats than the 1987-1991 sample.
Table C1: Data points for 2004-2013 sample
Notes: The data come from Lonres.com. The table shows the number of sales in our dataset which belong
to the following categories: leaseholds with unexpired term below 100 years, leaseholds with unexpired
term above 100 years, and freeholds (including flats sold with a share of freehold).
Number of Number of Number of Total
leaseholds leaseholds freeholds or data points
<100 years ≥100 years share of F/H in sample
Houses 362 169 6,305 6,836
Flats 5,957 6,189 7,794 19,940
Total 6,319 6,358 14,099 26,776
0
200
400
600
800
1000
Observations
0 25 50 75 100 125 150
Leasehold unexpired term (years) 975 1000
Figure C1: Leasehold observations by years remaining (2004-2013 sample)
Notes: The histogram include all leasehold observations in the 2004-2013 sample, counted by length of
the unexpired term. Freehold and share of freehold properties are not included. Bins are 5 years wide.
39
Table C2: Descriptive statistics for the 2004-2013 sample
Notes: The table does not contain information on sale dates (described in Figure C2) and lease length
(see Figure C1). Price and floor area are the only continuous variables in the analysis; all other property
attributes are dummy variables.
count mean sd min max
Price 26,776 1,605,720 2,113,652 50,000 56,000,000
Lease 26,776 .47 .5 0 1
House 26,776 .26 .44 0 1
Studio 26,776 .034 .18 0 1
1-Bedroom 26,776 .18 .38 0 1
2-Bedroom 26,776 .36 .48 0 1
3-Bedroom 26,776 .23 .42 0 1
4-Bedroom 26,776 .11 .31 0 1
5-Bedroom 26,776 .054 .23 0 1
6-Bedroom 26,776 .023 .15 0 1
7-Bedroom 26,776 .0079 .089 0 1
8-Bedroom 26,776 .0031 .056 0 1
9-Bedroom 26,776 .001 .032 0 1
10-Bedroom 26,776 .00075 .027 0 1
11-Bedroom 26,776 .00034 .018 0 1
Verified 26,776 .89 .32 0 1
Maisonette 26,776 .084 .28 0 1
LwGr-Floor 26,776 .11 .31 0 1
1st-Floor 26,776 .12 .32 0 1
2nd-Floor 26,776 .11 .31 0 1
3rd-Floor (Lnr) 26,776 .092 .29 0 1
4th-Floor (Lnr) 26,776 .064 .24 0 1
5thOrMore-Floor (lnr) 26,776 .072 .26 0 1
Gr-Floor 26,776 .099 .3 0 1
FH-Flat 26,776 .0038 .062 0 1
Sqft 25,673 1,438 1,171 64 23,231
0
200
400
600
800
1,000
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4 Q1Q2Q3Q4
Figure C2: Number of transactions per quarter (2004-2013 sample)
40
