The Value of Status:
Exploring the Price of Relative Positioning

Danny Ben-Shahar∗, Yongheng Deng†, Tsur Somerville‡
Eyal Sulganik§, and Hongjia Zhu¶
This version: April 2, 2024∗

Coller School of Management, Tel Aviv University, bdanny@tauex.tau.ac.il
Wisconsin School of Business, University of Wisconsin-Madison, yongheng.deng@wisc.edu‡
Sauder School of Business, University of British Columbia, tsur.somerville@sauder.ubc.ca§
Reichman University, sulganik@runi.ac.il¶
Jinan University, zhuhjecon@hotmail.com†

1Abstract
In the standard economics model, individual utility is a function of one’s own consumption. Yet, the pursuit of status, which depends on the recognition of others andone’s standing relative to them, is an important driver of human behavior. Motivated by literature in linguistics and psychology that correlates between one’s vertical
positioning and well-being, we explore the value of vertical status – one’s physical vertical positioning relative to others. Using transactions in high-rise residential buildings
in Vancouver (Canada), we find an economically significant price premium for being
higher than other units in both one’s own building and surrounding buildings, conditional on a unit’s absolute height, view, and other unit and building characteristics.
Our findings further suggest that people weigh more heavily the disutility from having
others positioned above them than the utility from having others below them. Finally,
we find that the marginal value of vertical status increases with height.

Keywords: Status, Vertical Hierarchy, Tall Buildings, House Prices
JEL Classification: D12, D91, R21

1Introduction

Status is a fundamental characteristic and metric of hierarchy and power within societies andorganizations (Weber 1922). Works as early as Smith (1759) and Marshall (1890) address
status as one of the motivating factors for consumer behavior. Veblen (1899) and Duensberry(1949) place status respectively in implicit and explicit utility functions. Heffetz and Frank(2010) delineate distinct attributes of status: “desirability”, the resources that status brings
along; “visibility”, being observable to others; and “positionality”, the position (or rank)
relative to others. In this paper, we specifically explore the latter attribute – status originatedfrom relative vertical positioning.
In their seminal work on metaphors in language and the mind, Lakoff and Johnson(1980) show that the use of metaphors that utilize the vertical dimension explicitly ties “up”
to positive associations and “down” to negative ones. For example, “happy” is up whereas“sad” is down, as in “I am feeling up” versus “He is low these days,” respectively.1 In Dr.
Suess’s Yertle the Turtle (Geisel 1950), Yertle the King is not only concerned about being
high per se, but rather seeks to be positioned higher than all he can see – being furious whenthe moon “dares to be higher than Yertle the King.” In line with Yertle’s aspiration andfollowing Heffetz and Frank (2010), we empirically explore the value vertical status – i.e.,the value of the relative positioning within the vertical space.2
To study vertical status (relative vertical positioning), we use the height of condominium
apartments relative to the height of both the other units in the same building and relative
to the height of nearby buildings. By exploiting the variation in individual condominiumtransaction prices attributable to relative vertical differentiation, we estimate the shadow
price of the characteristic of status that is expressed in this vertical up-down paradigm.
Specifically, we estimate the shadow price of vertical status using prices from more than
55,000 transactions in nearly 320 condominium towers in the Vancouver (Canada) downtown
peninsula over the period 1992–2016, using controls for absolute floor level, view, unit’s
1

Among the other numerous examples in Lakoff and Johnson (1980) are “control” is up, whereas “lackof control” is down, as in “I am on top of the situation” versus “he is under my control and “virtue” is up
and “lack of virtue” is down, e.g. “she is an upstanding citizen” versus “that was a low-down thing to do.”2
The Oxford Dictionary defines vertical status as “the status of a person in relation to others at adifferent hierarchical level” Oxford University Press https://www.oxfordreference.com.

1physical characteristics, as well as building and temporal fixed effects.
We find a significant value for vertical status. Ceteris paribus, we estimate the average
vertical status price premium for a unit on the top floor relative to that on the bottom floorof the same building at about 6–7 percent of the average transaction price (equal to about
73K CAD or 56K USD – deflated to July 2018 condo values). Additionally, our evidenceshows that the marginal value of vertical status rises convexly, so that the marginal valueof moving up is greater, the higher the floor is in a given building. Furthermore, we findevidence that people weigh more heavily the dis-utility from having others positioned above
them than the utility of being above others. Finally, we find that vertical status further holds
in comparing unit’s relative height with neighbouring buildings. Accordingly, the verticalstatus price premium of a unit that is higher than the tops of all other nearby buildings – ascompared to an otherwise identical unit that is lower than the tops of all nearby buildings– is equal to 3–4 percent of the average transaction price. The results are robust to a seriesof sampling and test design specifications.
Our study contributes to the literature in several ways. First, we believe that our workis the first to rigorously and richly explore the vertical status paradigm.3 Second, unlike
previous empirical studies in this area, our assessment of the benefit from status is not basedon surveys of subjective happiness and well-being related to income and job satisfaction nor
on experimental evidence, but rather on actual observed transaction prices. This allows us
to directly and explicitly estimate the shadow price of the vertical status. Third, we showthat the status paradigm stems mainly from the negative effect (dis-utility) that is derived
from being below the joneses rather than the positive effect (utility) of being above them.
Finally, we find that the marginal price effect of relative status is non-constant, rather it
increases with relative vertical position.
The remainder of the paper proceeds as follows. Section 2 reviews the relevant status
literature and work on vertical features of buildings. Section 3 presents the methodology formeasuring vertical status and the estimating equation. Section 4 describes the data. Section
5 presents the results, including an analysis of non-linearity in the vertical status function, an
3

As we discuss more fully in Section 2, Nase, van Assendelft, and Remoy (2019) and Nase and Barr
(2022) include a relative status measure as a control in their estimation of office rents and apartment unit
values.

2

assessment of asymmetry in one’s utility and dis-utility from having others below and above
her, respectively, status related to neighbouring buildings, and a series of robustness tests.
Section 6 provides a summary and concluding remarks. Finally, the Appendix provides
details on data construction (Appendix A), distribution of the measures of neighborhood
vertical status (Appendix B), and a detailed description of our methodology for constructing
view measures (Appendix C).

2

Literature Review

An extensive literature across the social sciences explores the role of status in individual
well-being. In economics, following the seminal analysis by Duensberry (1949), more recent
theoretical work that addresses social comparison and status in the utility function includes,
among others, Becker (1974), Gilboa and Schmeidler (2001), Samuelson (2004), Rayo andBcker (2007), and Rablen (2008). Empirically, Easterlin (1995) showed the role of positioningin happiness: relative (and not absolute) income drives the variation in happiness over time.4
Other studies that examine relative positioning and status are often either experimental
or utilize income ordering within a workplace as the position indicator of well-being. For
example, Brown et al. (2008) find that satisfaction and well-being depend on individual wage
ordinal rank within the comparison group; Boyce, Brown, and Moore (2010), using moregeneral British survey data, present evidence that rank-income overpowers both referenceincome and absolute-income in predicting life satisfaction; and Blanchflower and Oswald(2004) and Groot and Van den Brink (1999) find that happiness and satisfaction from wage
income is associated with relative rather than absolute wages.5
Recently, Bursztyn et al. (2018) used a quasi-field experiment to document the preference
for status, separating it from other features that both increase utility and may be correlated
4

See also, the Easterlin (1974) paradox, by which happiness varies positively with income within andacross countries, but does not rise within a country as income rises over time.
5
While these studies indicate the imperative effect of (non-vertical) status on individual utility as one’s
relative position in the context of workplace and wages, they do not fully control for other factors – suchas future income growth, non-wage benefits, work environment, and professional opportunities – that may
determine job satisfaction and are likely correlated with current income and wage structure. In addition,
see Heffetz and Frank (2010) for a survey of the extant empirical and experimental work on preference forstatus.

3

with status. Employing a credit card market setting in Indonesia, they show that adding thepremium label to a credit card almost doubles its uptake, as compared to the control card,
despite no change in fees or benefits. Their experiment design allows them to separate consumption benefits from status signals. 6 They also find that holders of the ”status” premium
card are more likely to use it in social situations, where it serves as a status signaling mechanism. In contrast to Bursztyn et al. (2018) who assess the visibility characteristic of status
by credit card uptake and use, we focus on the relative vertical positionality characteristicof status and estimate its shadow price.
Our use of building height as a mechanism to express vertical status is not unique. In
psychology, based on a series of behavioral experiments, Dorfman, Ben-Shahar, and Heller(2018) find a bi-directional causality between a subject’s social power and her/his presumed
apartment’s floor in a fictional building.7 In urban economics, Helsley and Strange (2008)
explain the evolution of skyscrapers in a game-theoretic setting model, where developers
compete for status by constructing the tallest building. Their model finds empirical support
in works by Barr (2012) on height competition among developers in New York City andAhlerldt and McMillen (2018) on land values and development in Chicago.
In our framework, we posit that vertical status is an element, along with view, sunlight,
absolute height, and noise that are included in the bundle of height amenities. In the pricingof height, these amenities are offset by vertical transportation costs, time, and inconvenience,
in determining the net height premium or vertical gradient. Estimates of height premium
are not new; see, for example, Wong et al. (2011) for a detailed list of studies that include
floor in hedonic estimations of property value. More recently, Danton and Himbert (2018),
Liu, Rosenthal, and Strange (2018), Nase, van Assendelft, and Remoy (2019), and Naseand Barr (2022) estimate vertical rent and price gradients for commercial and residentialbuildings with varying degrees of control for the other amenities in the height bundle. The
latter two also include a height-based measure of status, which they compute by the ratio of
the floor on which the transacted unit is located to the total number of floors in the building.
6

For example, while generating high status, a Lamborghini, is also fast, handles well, and may offer an
excellent sound system.
7
Tower-Richardi et al. (2014) show that people associate a subject’s “social status” with living in a higher
residential location (hilltop).

4

Nase, van Assendelft, and Remoy (2019) find no effect of a status measure on the rent priceof commercial real estate leases; whereas Nase and Barr (2022) find small positive values
for vertical status in residential data from Rotterdam but not from Manhattan. Our study
substantially differs from these studies, as we use data and a framework that allows us to
explore heterogeneity in the value of vertical status, the extent of preference for being above(below) others, and status effects associated with surrounding buildings.
Finally, in order to cleanly estimate vertical status, we must control for the effect of viewon the transaction price. Pricing views has long been part of the real estate literature—e.g.,
see Bourassa, Hoesli, and Sun (2004) for a review of early empirical estimates of the valueof view. Continuous measures of view—such as those in Hamilton and Morgan (2010),
Hindsley, Hamilton, and Morgan (2013), Nase, van Assendelft, and Remoy (2019), Naseand Barr (2022), and Dai, Felsenstein, and Grinberger (2021)—are based on GIS softwareand developed databases of topographic features and urban forms. We follow and refine theapproach of Dai, Felsenstein, and Grinberger (2021), estimating unit-specific view based on
the information on building alignments and units per floor.

3

Method3.1

Specification of Vertical Status

In this paper, we characterize vertical status as a specific physical form of hierarchy: positionality along the vertical dimension, as represented by an apartment unit’s relative height
within a building. Specifically, we adopt the functional form presented in Brown et al. (2008)
and Boyce, Brown, and Moore (2010), mapping their characterization of utility from one’s
place in the hierarchy of income to a physical vertical ordering by discrete building floor.
We express vertical status V S from locating on floor i in an N -story building by:

V SiN = 0.5 +(i − 1) − η(N − i)2[(i − 1) + η(N − i)]

5

(1)

.
The first and second terms in both the numerator and denominator of the right-handside fraction in (1) are, respectively, the number of floors below i (i.e., i − 1) and the numberof floors above i (i.e., N − i), where the latter is multiplied by the parameter η, 0 ≤ η < ∞(see the discussion that follows below). Equation (1) can be reduced to:

V SiN =(i − 1)(i − 1) + η(N − i)(2).
The parameter η in (1) and (2) captures the degree of upward\downward comparison.
That is, the extent to which vertical status is driven by i’s dis-utility from being below otherunits vis-à-vis the utility gained from being above other units. As η increases, it increases(decreases) the relative weighting on the number of floors above (below) the reference unit,
N − i (i-1). Mapping into preferences, η > 1 (η < 1) indicates a greater weight on the loss
(benefit) that is associated with the presence of those above (below) i.
In our initial estimation of the value of vertical status, we set η = 1 in equation (2).
This imposes the assumption that vertical status is symmetrical in preferences, so that theutility of being above someone is equal to the dis-utility of being below her. We will relax
this assumption later in the paper to assess the value of η, which will shed more light on the
structure of preference for status. Note that when η = 1, equation (2) reduces to:

V SiN =(i − 1)(N − 1)(3).
Equation (2), and by extension equation (3), generate a vertical status measure that iscomparable across buildings, as its value lies within [0, 1], where the vertical status of thefirst (top) floor is equal to 0 (1).

6

3.2

Estimating Equation

Following equation (3), we estimate a standard semi-log hedonic model of condominium
apartment transaction prices:lnPjimt = β0 + β1 Xj + β2 V Sim + β3 Vimt + β4 Fi + β5 Zm + β6 Yt + ϵit(4).
The dependent variable in equation (4), lnPjimt , is the log transaction price per squarefoot of unit j located on floor i in (an N -story) building m and sold at time period (monthyear) t. The independent variables in (4) include Xj , a vector of unit’s structural characteristics (floor area, age, number of bedrooms, number of bathrooms, and a dummy forwhether the unit has been renovated); Vimt , a vector of view variables, which provide abuilding-floor-year specific view measure for each compass quadrant (see the description below); Fi , a vector of floor fixed-effects; Zm , a vector of building fixed-effects; and Yt , a vectorof month-year time fixed-effects. In addition, β0 and β2 are parameters, β1 , β3 , β4 , β5 , andβ6 are vectors of parameters, and ϵjimt is a random disturbance term. In estimating equation(4), our primary parameter of interest is the coefficient on vertical status β2 , so we leave
the coefficient vectors β3 and β4 for view and the vertical price gradient simply as controls,
rather than investigate their forms.

4

Data

Our data include the universe of condominium apartment transactions that occurred in
downtown Vancouver, British Columbia (Canada) over the period Jan 1992 – July 2016.8
Vancouver provides a natural framework for our analysis, as owner-occupied mid- and highrise condominium apartment units are a significant share of the housing stock.9 While8

The end date of July 2016 avoids a series of taxes and restrictions placed thereafter on short-term
rentals, foreign buyers, and vacant properties.
9
According to the 2016 Canadian census, about 24.6 percent of owner-occupied units in the City of
Vancouver were in buildings of 5 stories or more. In comparison, according to the 2015 American Housing
Survey, in the New York-Newark-Jersey City, Miami, and Seattle MSAs this estimated share was only 16.3,
8.0, and 2.8 percent, respectively.

7

Figure 1: Building Locations
multi-family rental and condominium buildings are present in many different areas of thecity and the metropolitan area, they are especially concentrated in the city’s downtown
peninsula. Figure 1 shows the location of the 318 condominium buildings in our dataset
within the approximately 2x3 kilometer downtown peninsula. Our transaction information
and building and unit characteristics data are drawn from British Columbia (BC) Assessment, the Province’s assessment authority, and the City of Vancouver.10 From the universeof about 76K observations, our final dataset includes 55,195 observations across 318 residential buildings, all of which are five floors or higher. Appendix A includes an accounting of
the derivation of our sample from the universe of sales.11
Figures 2 and 3 present the distribution of the data by building height. As shown, there
is considerable representation by building height across the distribution through buildings
with 35 stories in height, both in individual buildings and by transactions. Above 37 floors,
the sample turns somewhat sparse. Results on the vertical status effect, however, are robust
to the omission of buildings above either 35 floors or 45 floors.12
10

BC Assessment data include information on property characteristics and transaction prices. The Cityof Vancouver data provide information on property tax reports, GIS building footprint and shape, and parcel
map.
11
Nearly all of the reduction in the count from the universe is from units in buildings with four or fewer
floors, pre-sales transactions, and transactions that are flagged as not suitable for data analysis by BC
Assessment.
12
The distribution of transactions by floor is approximately log-normal with a peak at floor 3, as there

8Figure 2: Building Count by Height

Figure 3: Transactions by Height

Estimating the effect of vertical status requires that we control for other amenities thatare associated with floor level. For shared building attributes such as building height, status,
location, quality, and shared amenities, we include a vector of building fixed-effects in theestimation. For individual unit height and view, we include floor fixed-effects and a set ofview measures, respectively.13 For the latter, we follow Dai, Felsenstein, and Grinberger(2021) and use geographic information system (GIS) software and files of building massing
adjusted for year of construction to derive a continuous measure of view based on the total
area of a plane of unobstructed lines of sight up to one kilometer. Our view measure isfloor-building-year-compass quadrant specific.14
As we do not directly observe the orientation of apartment units on each floor, we use
two alternative approaches to assess the unit-specific view measure. In the first, we assign
all units on a floor of a given building in a given year the same value for view in eachcompass-quadrant. Assuming that all units on a floor have an equal probability of selling,
the coefficients for the values of these views are unbiased estimates of the mean individual
unit view effect on a given floor. We refer to this measure as an average floor view. In
another approach, we impose the assumption that units with high positive residuals in aare buildings with commercial units and/or amenity and service space on bottom floors.
13
Noise levels are concave in height (see Wu et al. 2019) and are captured by floor fixed-effects.
14
We have distinct values for the view quadrant: 1-90 degrees (NE), 91-180 degrees (SE), 181-270 (SW),and 271-360 (NW). These are unique for each floor-building-year, where the latter controls for the timingof new construction over our study period. In addition to view, the quadrant-specific measures capture
exposure to natural light by compass direction.

9

first-stage hedonic price regression that excludes view and status are those with the best
views. We refer to this measure as an individual specific view, which may be an upwardly
biased estimate of the view value. Detailed descriptions of the derivations of the average
floor view and individual specific view measures are presented in Appendix C. 15
Figure 4 presents the distribution of average floor view values by quadrant. As shown,many units have a limited view because they face an adjacent building. Given our lack ofpriors on the shape of the view valuation function, in the estimation we treat view nonlinearly, converting the view values by quadrant into deciles so that we gave forty distinct
view dummies (four quadrants by nine dummies for declines 2-10 per quadrant).
Table 1 presents descriptive statistics of the variables in estimated equation (4). As indicated in the table, the typical unit is a 1- to 2-bathroom, 880-square-foot condominium
apartment located on the 12th floor of an 8-year-old structure. For convenience, we show
price variables in nominal terms as well as indexed to July 2018 Vancouver Census Metropolitan Area (CMA) condo prices—both total price and per sqft.16 Notably, the mean indexed
price is $C 1.15M (where $C 1.00 = $US 0.76 in July 2018), reflecting the high cost of realestate in Vancouver.

15

As described below, our estimated value of vertical status is robust to the choice of the view measure.
Also, while we report the view measures computed with a 1-kilometer radius, results are robust to increasing
the view radius to 5 kilometers.
16
To deflate to July 2018 condominium prices, we use a repeat-sales index for condominium transactionsin the Vancouver CMA, excluding those in the downtown peninsula. These data are sourced from BC
Assessment, using the assessment roll and their database of registered transactions deemed suitable forvaluation. We windsorize using these deflated prices.

10((a)) NE Quadrant((b)) SE Quadrant((c)) SW Quadrant((d)) NW Quadrant

Figure 4: Distribution of Average Floor View Values by Quadrant

11Transaction priceprice per sq ft
ln sales price per sq ft
Real price - condo price index 7/18=100
Real price per sf - condo price index 7/18=100.
Floor area
# of Bedrooms# of baths (full+part)
Unit effective age
Dummy = unit renovated/updated(i−1)
Vertical Status, (N−1)
Unit’s floor - calculated
Highest residential floor in building
Dummy - unit is a penthouse
Dummy, - unit is on top floor
Floor avg. view (sq km), NE quadrant
Floor avg. view (sq km), SE quadrant
Floor avg. view (sq km), SW quadrant
Floor avg. view (sq km), NW quadrant
Estm unit specific view in NE quadrant
Estm unit specific view in SE quadrant
Estm unit specific view in SW quadrant
Estm unit specific view in NW quadrant

count
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274
55274

mean
434947468.177
6.024822
1146964
1243.514.8795179
1.548667
1.495875
7.895896.0703767.5044494
12.07012
22.83327.0069291.0341028.1502232.1995143.1807022.1047762.0812138.1055159.0868737.0615936

Table 1: Summary Statistics

12

sd432351.4
249.8523.495412880629.1
349.9701.3890218.7564196.6161746
8.245227.2557831.2762962
8.240589
9.389515.0829532.181495.2210233.261329.2335436.1579714.1658972.1961742.1671448.120923min
65000
93.56538
4.538661
304142339.18
.305
0
1
0
0
0
1
5
0
0
.000071.000103.000512.000107
0
0
0
0

max
1.50e+07
13691.64
9.524541
2.75e+07
27653
4.469
4
4
88
1
1
60
60
1
1
.780326.780502.78065.780636.780326.780502.78065.780636

5

Results

5.1

Base Specification

Table 2 presents the results from the baseline estimation of equation (4), where η = 1.17
Columns 1– 3 present the outcomes for the full sample and differ by choice of the view
measure: no view, floor average view, and unit-specific view controls in columns 1, 2, and3, respectively. We also repeat the estimation for the sub-sample of buildings with up to
40 stories in height, using average view and unit-specific view controls in columns 4 and
5, respectively. As indicated in columns 1–5, the estimated coefficient on vertical status isstatistically and economically significant under all specifications. Specifically, ceteris paribus,
a unit on the top floor of a building sells for an average price premium of about 9.0–9.4
percent, as compared to the same unit on the bottom floor of the building (equal to about$C 103K–107K or $US 78K—82K).18 In all subsequent estimations, we use the full set ofcontrols employed in Table 2, including the unit average view measure. All Results, however,are robust to using unit-specific measure (not reported and available upon request).
Table 2 presents the results from the baseline estimation of equation (4), where η = 1.19
Columns 1– 3 present the outcomes for the full sample and differ by choice of the view
measure: no view, floor average view, and unit-specific view controls in columns 1, 2, and3, respectively. We also repeat the estimation for the sub-sample of buildings with up to
40 stories in height, using average view and unit-specific view controls in columns 4 and
5, respectively. As indicated in columns 1–5, the estimated coefficient on vertical status isstatistically and economically significant under all specifications. Specifically, ceteris paribus,
a unit on the top floor of a building sells for an average price premium of about 9.0–9.4
percent, as compared to the same unit on the bottom floor of the building (equal to about
17Standard errors are clustered at the building level. In addition, we use fixed-effects for the number ofbedrooms and the total number of full and partial bathrooms. Results are robust to using the latter in acontinuous form.
18
While we do not show the height gradient constructed from these fixed effects nor view premia outcomesin the table, the marginal price effects in rising in both. Appendix C provides more detail on the view effects.
19Standard errors are clustered at the building level. In addition, we use fixed-effects for the number ofbedrooms and the total number of full and partial bathrooms. Results are robust to using the latter in acontinuous form.

13

$C 103K–107K or $US 78K—82K).20 In all subsequent estimations, we use the full set ofcontrols employed in Table 2, including the unit average view measure. All Results, however,are robust to using unit-specific measure (not reported and available upon request).

(1)All
0.089∗∗∗(0.017)(2)
All
0.094∗∗∗(0.017)(3)All
0.090∗∗∗(0.017)(4)<40 Flrs
0.099∗∗∗(0.016)(5)<40 Flrs
0.094∗∗∗(0.016)

Floor area

-1.34∗∗∗(0.14)-1.34∗∗∗(0.14)-1.28∗∗∗(0.13)-1.40∗∗∗(0.15)-1.36∗∗∗(0.13)

Floor area - sq

1.13∗∗∗(0.14)

1.13∗∗∗(0.14)

1.06∗∗∗(0.13)

1.20∗∗∗(0.14)

1.15∗∗∗(0.13)

Floor area - cubed-0.35∗∗∗(0.053)-0.35∗∗∗(0.052)-0.33∗∗∗(0.049)-0.39∗∗∗(0.054)-0.37∗∗∗(0.047)

Floor area - 4th

0.038∗∗∗(0.0066)

0.038∗∗∗(0.0066)

0.035∗∗∗(0.0063)

0.043∗∗∗(0.0068)

0.041∗∗∗(0.0060)

Unit effective age-0.026∗∗∗(0.00081)-0.026∗∗∗(0.00079)-0.026∗∗∗(0.00080)-0.026∗∗∗(0.00082)-0.026∗∗∗(0.00083)

Unit effective age - sq

0.000057∗(0.000024)

0.000047∗(0.000023)

0.000041(0.000023)

0.000049∗(0.000023)

0.000044(0.000023)

Dummy, unit renovated

0.028(0.015)0.028(0.015)0.027(0.014)0.028(0.015)0.028(0.014)

No

Yes

No

Yes

No

(i−1)
Vertical Status, (N−1)

Floor Avg View

Unit Specific View
No
No
Yes
No
Yes
N
55274
55274
55274
53616
53616
adj. R2
0.943
0.944
0.947
0.942
0.945
∗
∗∗
∗∗∗
Standard errors in parentheses. p < 0.05,
p < 0.01,
p < 0.001
The dependent variable is log price per square foot. All regressions include fixed
effects for # of bedrooms, # of bathrooms, floor, building, and month-year. The
sample for regressions (4)-(5) is restricted to buildings with fewer than 40 floors.
Vertical status is for η = 1. Standard errors are clustered at the building level.

Table 2: Vertical Status – Baseline Regressions

20
While we do not show the height gradient nor view premia outcomes in the table, Appendix ?? and C,
respectively explore these results in detail.

14

The above empirical specifications control for, inter alia, unit height, up to a fourth-degree
polynomial of unit size, and average building effect. To address potential unique unobserved
features of units on top floors, Table 3 presents outcomes from re-estimating equation (4),specifically controlling for these units. We include a dummy variable for whether a unit isidentified as a penthouse (columns 1 and 3) or on the top floor (columns 2 and 3). Further,in columns 4 and 5 we exclude the top 10 and 15 percent, respectively, of vertical statusvalues—which always include the top floor units whose vertical status equals 1.

(i−1)
Vertical Status, (N−1)

Dummy, unit is a penthouse(1)All
0.081∗∗∗(0.017)(2)
All
0.042∗(0.016)

0.094∗∗∗(0.014)(3)
All
0.043∗∗(0.016)(4)
Status < 0.9
0.048∗∗(0.017)(5)
Status < 0.8
0.038∗(0.019)0.061∗∗∗(0.017)0.059∗∗∗ 0.048∗∗∗(0.0085) (0.0092)
Observations
55274
55274
55274
50578
44871
Adjusted R2
0.944
0.944
0.944
0.946
0.948
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
The dependent variable is log price per square foot. All regressions include the unitcharacteristic controls from Table 2, specification (2), along with the set of fixed effects
for # of bedrooms, # of bathrooms, floor, building, and month-year and the building
specific average floor view measures. Regressions (4)-(5) restrict the sample toobservations with status values below the indicated threshold. Vertical status is forη = 1. Standard errors are clustered at the building level.
Dummy, unit is on top floor

Table 3: Vertical Status Effect of Top Floors
The results from the specifications in Table 3 show that after controlling for penthouse
and/or top floor (columns 1-3) or excluding the top 10-15 percent of vertical status values(columns 4-5), the effect of vertical status remains positive (significant at 1 to 5 percent
depending on specification) with a range of magnitude between 3.8 to 8.1 percent. Theselower estimates (as compared to 9.0–9.4 percent shown in Table 2) are consistent with theconvexity of price in relation to vertical status, i.e., that top floor units are also those withthe highest marginal status effect. Hence, controlling for those units or excluding themfrom the sample decreases the estimated average vertical status price effect.21 Discussions
21

Convexity of price with regard to vertical status would suggest that those with stronger (weaker)

15with developers confirm that, other than for penthouses, unit features are essentially consistent throughout all floors of a building. In all further estimations, we therefore include apenthouse dummy.
To allow for varying vertical status preferences across floors, we re-estimate equation (4),stratifying the sample by units: (a) below/above the sample median floor (columns 1 and 2,
respectively); and (b) short/tall buildings, i.e. buildings that are below/above the medianbuilding height floor count (columns 3 and 4, respectively), where the median is based ontransaction count.22 Results from these specifications are presented in Table 4.

(1)
(2)
(3)
(4)
Low
High
Short
Tall
(i−1)
Vertical Status, (N0.094∗∗∗ 0.27∗∗∗ 0.087∗∗∗0.11−1)(0.018) (0.070) (0.021) (0.076)
Observations
28233
27041
27096
28178
Adjusted R2
0.944
0.945
0.946
0.944
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
The dependent variable is log price per square foot. All regressions
include the unit characteristic controls from Table 2 specification(2), along with fixed effects for # of bedrooms, # of bathrooms,
floor, building, and month-year; the building specific average floor
view measures; and the penthouse dummy from Table 3. “Low”
are units on or below the 10th (median) floor. “High” are thoseabove that floor. “Short” are units in buildings at or below themedian building height of 23 stories. “Tall” are units in buildings
above thisheight. Medians are for the total number of transactions.
Vertical statusis for η = 1. Standard errors are clustered at thebuilding level.

Table 4: Vertical Status – Lower vs Higher Floors and Short vs. Tall Buildings
As shown, outcomes indicate differences in preference for vertical status. The point
estimate for the marginal effect of vertical status is approximately three times as high forunits that are above the median floor (column 2), as compared to those below the medianfloor (column 1). The difference between units in shorter and taller buildings (columns 3
and 4, respectively) is smaller in magnitude and not statistically different from zero, though
preferences for vertical status sort into higher (lower) floors. While we do not formally show separation in
equilibrium, intuitively, the single-crossing property required for separation maintains, as the net cost ofoccupying higher floors (i.e., the cost net of the benefit associated with vertical status) is lower, the greater
is the preference for the vertical status.
22
The median unit floor in the data is 10. The median number of floors in a building by transactions is23.

16

the point estimates suggest that marginal vertical status may be higher in taller buildings.
In summary, results suggest heterogeneity in the preference for vertical status that manifests
in non-homogeneous marginal prices of vertical status across different floor levels. Below we
explore the convexity in the price effect of status by allowing for both more nonlinearity inthe relative floor effect and different η parameter for different floors.

5.2

Vertical Status Functional FormIn the analysis above, we assume that η = 1 on the right-hand side of equation (2). This
imposes that the vertical status effect is symmetric in individual preferences; i.e., that the disutility from being below some and the benefit from being above others are equally weighted
in the utility function. We now relax this assumption and use the fuller expression of V S
found in equation (2), using different values of η. In equation (2), note that as η approaches
infinity, V S approaches a dichotomous variable with the value of 1 for top-floor units and 0
for all other units. In other words, all that one is concerned with is that there are no units
above her. Similarly, when η approaches 0, then V S approaches a dichotomous variablewith the value of 0 for the bottom floor unit and 1 for all other units; that is, all that one
considers is that there are some units below her.
Figure 5 presents the sample distribution of vertical status for different levels of η (η =0.5, 1, 2, and 3) based on equation (2). As shown, while the distribution is roughly uniformfor η = 1, the mass of the distribution shifts towards 0, as the value of η increases, except for
the top floor units that remain at 1. In contrast, when η < 1, the mass of the distribution
shifts toward 1, except for the bottom floor units that remain at 0.
Next, we examine how varying η changes the estimated marginal price effect of verticalstatus. To do so, we re-estimate equation (4) using different values of η. Following equation(2), we compute V S for η to varying from 0.5 to 5.0. Results from these estimations arepresented in Table 5. As shown, the coefficient on the vertical status variable is positiveand significant for all values of η. The estimated coefficient on vertical status declines inmagnitude as η increases, though at a decreasing rate, stabilizing at η = 3.

To assess the appropriate value of η, Figure 6 presents the coefficient on V S obtained17

((a)) η = 0.5((b)) η = 1((c)) η = 2((d)) η = 3

Figure 5: Distribution of Vertical Status by η

18

Vertical status, η = 0.5

Vertical status, η = 0.75

(1)0.089∗∗∗(0.025)

(2)

(3)

(4)

(5)

(6)

0.080∗∗∗(0.019)0.074∗∗∗(0.017)

Vertical status, η = 1.0

0.065∗∗∗(0.013)

Vertical status, η = 2.0

0.064∗∗∗(0.012)

Vertical status, η = 3.0

0.064∗∗∗(0.011)
55274
0.944

Vertical status, η = 5.0

Observations
55274
55274
55274
55274
55274
Adjusted R2
0.944
0.944
0.944
0.944
0.944
Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
The dependent variable is log price per square foot. All regressions include the unitcharacteristic controls from Table 2, specification (2), along with the set of fixed
effects for # of bedrooms, # of bathrooms, floor, building, and month-year; thebuilding specific average floor view measures; and the penthouse dummy from
Table 3. Standard errors are clustered at the building level. regressions vary by
the value of η used to calculate V S for each unit.

Table 5: Vertical Status – Allowing for Variation in η19

from estimating equation (4) for η = [0.5, 25]. As shown, the level of the coefficient flattens
beginning with η = 3. Also, Figure 7 plots the change in the estimated vertical status
coefficient in units of standard deviation against the same set of η values and highlights
the same pattern in stability of the estimated coefficient around η = 3. Finally, Figure 8
presents , regression adjusted-R2 for the same set of η, demonstrating that a maximum levelof adjusted-R2 is reached at about η = 3. Taken together, these results suggest that theappropriate value for η is greater than 1, implying that the preference for vertical status is
more heavily weighted towards the loss from being below some than the benefit from being
above others.23 This conclusion is also consistent with a higher marginal value of verticalstatus for units above the median floor, shown earlier in Tables 4 and 3.

23
Our evidence according to which η > 1 for vertical status is also consistent with Boyce, Brown, andMoore (2010) who find that η = 1.75 for rank-income.

20

Figure 6: Status Coefficient by η

Figure 7: Std. Dev. Change in Est. Coeff.

Figure 8: Adjusted R-Sq by η
Recall that Tables 4 and 3 indicate that the marginal effect of vertical status varies
between lower and upper floors for η = 1. Correspondingly, we now vary η in the range of
0.5–25 and re-estimate equation (4), stratifying the sample by units on floors below/above themedian floor within each building (i.e., own building lower versus upper floors). Results fromthese estimations are presented in Figure 9. As shown, consistent with previous outcomes,
the marginal price effect of vertical status is greater for upper floor units, as compared tolower ones for all values of η. Also, as discussed above, the coefficient point estimates stabilize
at η > 1.
Finally, we allow the marginal price effect of vertical status to vary non-parametrically,

21

Figure 9: Upper vs Lower: Status Coefficient by η
relying on the above results to evaluate this relaxation of the parametric form for η = 3.
Specifically, we allocate the vertical status measure (for η = 3) into 10 bins of equal numberof observations by value, creating V S decile fixed-effects. We then re-estimate equation (4),replacing the continuous measure of vertical status with the V S decile fixed-effects. Figure
10 plots the point estimates and their 95 percent confidence intervals. As shown, verticalstatus is lower in magnitude for lower deciles of vertical status value, higher and at a plateau
for the mid-range deciles, and increasing convexly for the top three deciles. These findings
reinforce the separation pattern in vertical status preferences indicated earlier in Tables 4
and 3.

22

Figure 10: Non-Linear Status, η=3

23

5.3

Vertical Status and Neighboring Buildings

We complete the exploration of relative status by estimating the price effect generated fromthe vertical position of one’s own unit relative to the heights of the collection of neighboringbuildings. For apartment j on floor i in building m, let Rm be the total number of buildingsin the ring of a defined radius around the reference unit’s building and kim be the number ofbuildings (among Rm ) whose maximum elevation is below that of the reference apartment
unit j, as defined by its floor i, i.e., kim = [0, Rm ]. We then define the area vertical status,
AV Si m, as:AV Sim =kim
kim + η(Rm − kim )(5)Equation (5) is analogous to equation (2), where kim and Rm in (5) respectively replacei − 1 and N in (2). Similar to the distribution of V S in equation (2), in equation (5)AV S = [0, 1]. Specifically, when unit j on floor i is above all neighboring buildings, thenkim = Rm , yielding AV Sim = 1 for all η. When all buildings in the neighboring ring are
higher than i, then kim = 0 and AV Sim = 0 for all η. The values for k and R for any
unit typically fall and rise, respectively, with the size of the ring radius used in defining
neighbouring buildings. In Appendix B, we show the distribution of AV S and its descriptive
statistics for different values of η and different ring radii.
We re-estimate equation (4) adding AV S on the right-hand side of the equation. Resultsfrom this estimation are presented in Table 6, where columns 1–3 (4–6) are based on an AV S
computation under a 100- (250-) meter ring and within each triplet we vary the value of η
used in computing the vertical status (area vertical status) measure (η equals either 1, 3, or
5). As show, both vertical status and area vertical status are generally positive and significant(with the exception of the area vertical status for η = 1 and 250-meter ring). Specifically,
estimated coefficients on the area vertical status measure suggest a price premium of 2.2–4.7
percent for a unit that is higher than all surrounding buildings, as compared with one thatis lower than all surrounding buildings. For η = 3, the range of this price premium is 2.6–3.7

24percent. The outcomes for the (within-building) vertical status coefficient are robust to theinclusion of the area vertical status measure, ranging from 6.0–7.2 percent with all coefficientestimates statistically different from zero at the 1 percent level.

Vertical Status, η=1
Area Vertical Status, η=1
Vertical Status, η=3Area Vertical Status, η=3(1)
100m Ring
0.068∗∗∗(0.017)0.022∗(0.011)(2)
100m Ring

0.060∗∗∗(0.012)0.026∗(0.011)(3)100m Ring(4)
250m Ring
0.072∗∗∗(0.016)0.018(0.017)(5)250m Ring(6)
250m Ring

0.061∗∗∗(0.012)0.037∗(0.017)0.060∗∗∗
0.060∗∗∗(0.011)(0.011)
Area Vertical Status, η=50.028∗
0.047∗∗(0.011)(0.017)
Observations
55195
55195
55195
55195
55195
55195
Adjusted R2
0.944
0.944
0.944
0.944
0.944
0.944
∗
∗∗
∗∗∗
Standard errors in parentheses. p < 0.05,
p < 0.01,
p < 0.001. The dependent variable islog price per square foot. All regressions include the unit characteristic controls from Table 2,
specification (2),along with the set of fixed effects for # of bedrooms, # of bathrooms, floor, building,and month-year; the building specific average floor view measures; and the penthouse dummy from
Table 3.Standard errors are clustered at the building level. Regressions vary with the value of ηand the radius of the ring used to define the set of neighbouring buildings for the “Area Vertical
Status” AV S measure, which like V S is [0,1].
Vertical Status, η=5

Table 6: Vertical Status Relative to Neighbouring Buildings
To further gauge the price effect of area vertical status, we re-estimate equation (4),considering AV S non-parametrically. Specifically, for η = 3 and a ring radius of 250 meters,
we allocate the computed AV S into 10 bins (of equal number of observations) based on value,
creating AV S decile fixed-effects (lowest decile as the base group). Figure 11 presents theestimated coefficients and their 95 percent confidence interval. As shown, while AV S decile
coefficients are all positive and generally increase with deciles, only the two highest deciles
are statistically different from zero with 95 percent confidence – implying that being taller
than all of the surrounding, ceteris paribus, generates about 5 percent price premium.24
24
We see these outcomes as confirming Dr. Suess’ insights on status: King Yertle (the turtle) revels inbeing the king of the pond but additionally so for being king “as far as he could see,” (if his eyesight is goodenough to see up to 250m).

25

Figure 11: Area Status Coefficient by Deciles

5.4

Additional Robustness Tests

We present a series of additional tests that assess the robustness of our findings to samplingrelated issues. Specifically, we test whether our results are driven by: (a) the inclusion offoreign buyers/investors in the sample; (b) data period and building vintage; (c) unobserved
unit quality; and (d) higher priced neighbourhoods who might have greater preference forstatus. In these tests, we re-estimate equation (4) for η = 3 with various sample specifications
in order to validate robustness.
Miyakawa, Shimizu, and Uesugi (2022) and Devaney and Scofield (2017) report that
foreign buyers pay more for commercial properties. While we do not observe the residency
status of the buyers in our data, the Canadian Housing Statistics Program reports that
condominium apartments built in 2015/2016 in the Vancouver CMA exhibit higher foreign
ownership (15.7 percent) than for all condominium apartments (8.4 percent).25 To test
whether foreign buyers drive the vertical status effect in our data, we thus stratify the
sample by structure age: 75th percentile and higher (12 years or more); 50th percentile andhigher (6 years or more); 50th percentile and lower (5 years or less); and 25th percentile andlower (2 years or less). Results from re-estimating equation (4) for the stratified sample with25

See Statistics Canada, Cansim database Table 46100018.

26

η = 3 are presented in Table 7. The results are robust to these specifications. The estimatedcoefficients on the vertical status variable for all sub-samples are not statistically different
from one another and are generally similar to the those obtained for η = 3 in Table 5.

Relative Status,= 3.0
Observations
Adjusted R2(1)
All
0.069∗∗∗(0.012)
55274
0.944

(2)
Older
0.078∗∗∗(0.012)
28074
0.951

(3)
Old
0.081∗∗∗(0.014)
14841
0.948

(4)
Newer
0.072∗∗∗(0.017)
27200
0.944

(5)
New
0.071∗∗∗(0.020)
15489
0.935

Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
The dependent variable is log price per square foot. All regressions include the unitcharacteristic controls from Table 2, specification (2), along with the set of fixed
effects for # of bedrooms, # of bathrooms, floor, building, and month-year; thebuilding specific average floor view measures; and the penthouse dummy from
Table 3. Standard errors are clustered at the building level. Regression (1) includes
observations; in Regression (2) (“older”) the sample is limited to transactions of
all units above median age (≥6 years); in Regression (3) (“Old”) the sample is fortransactions of units in the top 25th percentile of age (≥12 years); “Newer”; and“New” in Regression (4) and (5), limit the sample to units below the median unitage (≤5 years) and to the newest 25 pct (≤2 years) of units, respectively.

Table 7: Robustness - Newer vs Older Buildings
Existing evidence suggests that the share of foreign investment in the real estate markets
has increased during our sample period.26 To further test for the possible effect of foreign
buyers on the vertical status coefficient, we stratify the sample by transaction year withperiods before 2005, before 2011, after 2009, and after 2012. Results from the estimation ofequation (4) for these specifications are presented in Table ??. As indicated in the table,
outcomes on the vertical status effect are robust to these specifications, as all vertical status
coefficients are once again of similar magnitude and statistically different from zero.
Above we controlled for or excluded top floors. Here we segment the data by age andexclude renovated units to address age-related unobservables. The underlying rationale isthat the market value of higher-grade finishings relative to baseline features may decline
26

Data on foreign investment in residential real estate in Australia, for example, shows a significant
increase in the volume of investment beginning in the 2013–2014 reporting period. Most of the increase isfrom Chinese registered companies and citizens. See Australia Foreign Investment Review Board, Annual
Reports, https://firb.gov.au/about/publication/.

27

with property age (e.g., a fashionable kitchen countertop may matter substantively when
the unit is new but less so for older units, where that counter top has become dated). Also,
by omitting renovated units, we exclude units that have been upgraded.27 Table 9 presents
the outcomes for the following sub-samples of our transactions data: column 1 excludes units
built prior to 1970; column 2 further excludes units that had a building permit for renovation;column 3 includes units older than median age (transactions of units at least 6 years old);and column 4 includes the oldest quartile (transactions of units at least 12 years old). As
indicted in the table, the point estimates for status are robust to these specifications, as
all coefficients on vertical status are significant and within one standard deviation of one
another.

Relative Status,= 3.0
Observations
Adjusted R2(1)
Post 1970
0.064∗∗∗(0.012)
53562
0.944

(2)
No Reno0.064∗∗∗(0.012)
52516
0.944

(3)
Older
0.074∗∗∗(0.013)
25943
0.951

(4)
Old
0.074∗∗∗(0.014)
13902
0.948

Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001
The dependent variable is log price per square foot. All regressions
include the unit characteristic controls from Table 2 specification(2), along with fixed effects for # of bedrooms, # of bathrooms,
floor, building, and month-year; the building specific average floor
view measures; and the penthouse dummy from Table 3. Regression(1) is for all units built after 1970 to exclude those most likely tohave been renovated. In regressions (2)-(4) the sample excludes
all units that can be identified as having been renovated or updated.
Regression (3) further limits the sample to units above medianage (≥6 years). And in regression (4) the sample is constrained
to units in the top 25th percentile of age (≥12 years). Standard
errors are clustered at the building level.

Table 9: Robustness – Older without Renovation

Finally, we test whether the vertical status price effect is driven by a greater preference forstatus in more expensive neighborhoods. To do so, we estimate a first-stage regression thatis a variation of equation (4), replacing building fixed-effects with census tract fixed-effects.
27

Renovation is measured by the presence of a building permit having been drawn. Strata (condominium)
board rules generally require permits for substantive renovations because of risk to common property.

28

We then stratify the sample by census tract value based on the distribution of the census
tract fixed-effect point estimates: up to the 25th percentile; up to the 50th percentile; above
the 50th percentile; and above the 75th percentile. Results from re-estimating equation (4)for the stratified sample are presented in Table 10. As indicated in the table, outcomes arerobust to these specifications, as all vertical status coefficients are significant and roughly of
the same magnitude.28

Relative Status,= 3.0
Observations
Adjusted R2(1)
All
0.069∗∗∗(0.012)
55274
0.944

(2)
25th Pct
0.077∗∗∗(0.021)
16427
0.959

(3)
50th Pct
0.076∗∗∗(0.016)
28874
0.954

(4)
75th Pct
0.071∗∗∗ .
(0.013)
45263
0.950

.
.

Standard errors in parentheses. ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001. The

variable is log price per square foot. All regressions include the unitcharacteristic controls from Table 2 specification (2), along with fixed
effects for # of bedrooms, # of bathrooms, floor, building, and month-year;
the building specific average floor view measures; and the penthousedummy from Table 3. Percentiles for each regression (1)-(4) are is basedon a unit’scensus tract fixed effect CDF from a 1st stage hedonic regression
to identify census tract fixed effects. The samples are the units at or below
these percentile values. Standard errors are clustered at the building level.

Table 10: Robustness - Higher vs Lower Price Neighbourhoods

6

Summary

The economics, psychology, and sociology literatures have long recognized and substantiated the fundamental role of status in individual choices and behaviour. In this paper,
we contribute to this literature by establishing, exploring, and pricing the relative vertical
positionality aspect of status; namely the desire to (not to) be vertically positioned above(below) others. We refer to this as vertical status, designating hierarchy in the physical28

Census tracts do not have equal numbers of transactions among our buildings so that the distribution
by census tracts is different than the distribution of transactions.

29

vertical space.
To estimate the value of vertical status, we use an extensive dataset of condominium
apartment transactions from Vancouver (Canada). We show that, ceteris paribus, verticalstatus composes an average premium of 6–7 of the average unit price for the highest verticalstatus housing unit relative to the lowest one within the same building. In addition, we
find that vertical status is convex in floor level, implying that those with greater (lesser)
preference for vertical status tend to sort into higher (lower) floors. We also find evidence
that people weigh more heavily the dis-utility from having some positioned above themthan the utility from having others below them. Finally, results indicate that the preference
for vertical status persists not only in relation to other floors in one’s own building, but
further extends in relation to other buildings in one’s neighborhood. Overall, our outcomesare consistent with Dr. Suess’ allegory on Yertle the Turtle (Geisel 1950) regarding humanpreferences and behavior: it is not only that we desire to be above others in the verticaldimension, but also it is particularly our strong distaste for seeing others above us.

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Appendix

A

Data Set Construction

BC Assessment reports 76,799 individual unit transactions with a reported price that occurred in 1992–2016 and are registered in the Land Title Office. We limit the data to one
price per transaction per day such that if multiple prices are recorded on the same day, we
use the highest among them. Of these reported transactions, 3,950 are in buildings that are
four stories or lower and are dropped from the sample. We also remove sales that are notfee-simple or that BC Assessment internally deems invalid for statistical appraisal, removing
another 5,515 observations. We further drop transactions that likely reflect the price of apre-sale contract, i.e., transactions that occur on the first three days of occupancy – thus
removing 5,197 additional transactions. Due to missing data for control variables, we further drop 6,804 observations of which 5,521 are due to unobservable bedroom count. We
also windsorize by price (using real house prices), dropping the top and bottom 0.05 percentof the sample (prices under $C30,412 and over $C10,800,000). Finally, we remove outliers,
including units with more than four bedrooms or more than four bathrooms, a total of 50
transactions, as well as 79 transactions that occur in buildings without neighbouring buildings over three stories in the 100m radius. This leaves a sample of 55,274 transactions, outof which 55,195 are with neighbouring buildings.

B

Vertical Status and Area Vertical Status Measures

Figure B-1 depicts the distribution of AV S by η and ring radius. Table B-1 further presentssummary statistics of V S and AV S for different levels of η and ring radius. As indicated in
the table, V S and AV S do not exhibit substantial difference in the first and second moments
for the 100-meter radius. For the 250-meter ring, there are some differences in the meanvalue, however, the standard deviations remain similar in magnitude.

34

((a)) η = 1, 100m ring((b)) η = 3. 100m ring((c)) η = 1, 250m ring((d)) η = 3, 250m ring

Figure B-1: Distribution of Area Relative Status by η and Ring Radius

35

count

mean

sd

min

max

100m Ring
Relative status, η= 0.5
Relative Status, η= 1.0
Relative Status, η= 2.0
Relative Status, η= 3.0
Area relative status, η=.5
Area relative status, η=1
Area relative status, η=2
Area relative status, η=3# of buildings in ring
# of buildings in ring above unit

55195
55195
55195
55195
55195
55195
55195
55195
55195
55195

.623045.5044542.3865195.322631.6203229.5198933.4145633.3556963
18.12729
7.701513.2632138.2762869.2709012.2605718.3143381.3144282.305706.2971714
11.82937.491203

0
0
0
0
0
0
0
0
2
0

1
1
1
1
1
1
1
1
57
52

250m Ring
Relative status, η= 0.5
Relative Status, η= 1.0
Relative Status, η= 2.0
Relative Status, η= 3.0
Area relative status, η=.5
Area relative status, η=1
Area relative status, η=2
Area relative status, η=3# of buildings in ring
# of buildings in ring above unit

55195
55195
55195
55195
55195
55195
55195
55195
55195
55195

.623045.5044542.3865195.322631.7133793.6099331.493679.4240944
96.26222
35.05127.2632138.2762869.2709012.2605718.2608983.2782066.2792871.2722462
50.98937
33.39329

0
0
0
0
0
0
0
0
6
0

1
1
1
1
1
1
1
1
264
259

Table B-1: Summary Statistics - Relative Status Measures

C

View Estimation

C.1

Floor Average View Measure

For the GIS 3-D modelling, floors in each building are identified in meters of elevation. The
City of Vancouver property footprint database includes the elevation of a building’s base, its
massing, and the height of the tallest point of the structure. Heights are allocated to floors
with an assumption of a lobby height of 4.7 meters, a mechanical floor every 30 floors with aheight of 4.65 meters, and a roof and equipment height of 6.2 meters. The remaining heightis allocated evenly by floor. On each floor, the view level is assumed to be 1.7 meters above36

the floor height.29
The same database allows us to construct the massing of all other buildings in a given
year based on the year of completion. We make the following assumptions for the temporalvariation in the city’s built form: (a) prior to construction of the current building, the lot
was occupied by a three-story building, as we have no data on earlier urban built forms
and it is reasonable to assume low density development; (b) tower podium form is 3-storytall base, where we use the building tower footprint for tower and podiums; (c) a building’s
massing is completed one year prior to the year of completion; and (d) within the completion
year, date of completion is July 1.
This approach should yield an unbiased estimate of the view effect on price but withhigher standard errors, as all units on a floor in a given building in a specific year are assigned
the same view for each quadrant. We relax the latter assumption by further estimating aunit-specific view measure, as described next.

C.2

Unit-Specific View Measure

To generate an estimate of unit-specific views based on average floor views, we assume thatthe rank ordering of unobserved differences in prices among units on a given floor in agiven building is a one to one mapping of the rank ordering of the view value. Based onbuilding alignment, the number of units per floor, and view values for each quadrant, werank estimated views for units on a floor from highest to lowest and then assign these tounits in the same ordinal ranking based on residuals from a first-stage regression. The view
values are generated in a first-stage regression as per column 4 in Table 2, however, withcensus tract replacing building fixed-effects. For each unit, we thus estimate the amountof view in each quadrant that a unit might exhibit, depending on (a) building’s alignment
relative to 0 degrees due north; (b) number of units on a floor; (c) how the view is allocatedamong the units on a floor; and (d) an estimation of the arc of view that the unit exhibits.
• Building’s alignment. If the building alignment is due north (0 degrees) and a unit
facing that direction has a 180-degree arc of view, then it would have a view equal to 100
29

These are taken from the ”CTBUH Tall Building Height Calculator” (Council on Tall Buildings and
Urban Habitat https://www.ctbuh.org/) and then using the eye height of an average individual.

37percent of the N.W. and N.E. quadrant view values for its floor. If the alignment is 45
degrees, then said unit would have 50 percent of the N.W., 100 percent of the N.E., and50 percent of the S.E. view quadrants. The building alignment is 0-89 degrees under theassumption that a building has four 90-degree corners. For simplicity, we restrict the possible
unit alignments to 0, 25, 45, and 70 degrees. These reflect the orientation of the street gridon Vancouver’s downtown peninsula, which runs roughly on a N.W. to S.E. axis: 82 percent
of units are within 3 degrees of one of these alignments, with 72 percent of units aligned
between 42 and 48 degrees.
• Number of units on a floor. The number of units on a floor summarizes their potential
view arc. For example, one unit on a floor would get 100 percent of the views in all directions.
For 2 units, we assume that each gets get half of the floor view and that the floor is divided
into N-S and E-W. Translating these shares into degrees of view depends on the numberof units per floor and whether the unit is a corner unit or not. Roughly: i) a unit thatoccupies the entire floor receives 360 degrees of view; ii) a unit on a corner – 250 degrees;
and iii) a unit that faces only a single direction – 160 degrees. In the sample, 78 percentof the transactions are on a floor with six or more other units (with a mode of eight units
per floor). With eight units on a floor there are four corner units and four units that face asingle direction• View arc. Discussions with an architect suggest that one loses 10 degrees of angle ofview when looking out a window, as one cannot see along the building’s edge. Hence, facing
one direction implies a 180-degree arc of view net of 10 degrees on each side. Therefore, if
facing due east (90 degree orientation), the view is 10-170 degrees. For a corner unit, thisgenerates 250 degrees (170 + 80). A unit that occupies half a floor includes two corners andwould be 180 (not 170 because of the second corner) + 80 + 80 = 340 degrees. We assume
that it is the midpoint between a corner unit (250) and a whole floor (360) rounded to 300.
This yields the following view arcs based on the number of units per floor: i) 1 unit per floor– 360 degrees for the unit; ii) 2 units per floor – half floor each – 300 degrees each; iii) 3
units – a half floor unit (300 degrees), and two corner units of 250 degrees each;, iv) 4 units
per floor– 4 corner units (250 degrees each); and v) 5+ units per floor – 4 corner units (250degrees each), and then 160 degrees for each of the units above the count of 4.
38

Combining the building’s angle with the number of units on a floor we can generate theset of possible views for each unit on a floor. We further assume that for floors with 2, 3,
and 5+ units, the division in the building is aligned either N-S or E-W. We test for both N-S
and E-W, and find no meaningful quantitative difference in results. We thus report basedon the estimation of the E-W alignment.
The first-stage estimation of equation (4) generates view coefficients for the value of viewin each quadrant. Following this first-stage estimation, we use coefficients for the maximum
view value in a particular direction, i.e., the estimated coefficient for the top decile of view
quantity, typically an unobstructed view in a direction. Multiplying these shadow prices by
the estimated view arc from above (based on building alignment, number of units per floor,
and estimated view arcs) and the actual view amount in a quadrant for the floor from the
GIS analysis, yields estimated view values for each unit on a floor. We then create theirordinal ranking and, thus, for each floor in each building, based on the number of units per
floor, we have an ordinal ranking of the view value for each unit, though we do not know
which unit has which view value.30 . From the same first-stage estimation of equation (4), we
also get a residual for each transaction. Using the mean residual by unit (most units transact
multiple times over the sample period), we create an ordinal ranking of mean residual value
by building and floor.
The final stage is matching ordinal rankings by building by floor. For a floor on a building,the unit with the largest mean residual is assigned the first ranked view for that floor, theunit with the second highest mean residual is allocated the second highest estimated view,and so on. If there are six units on a floor, the unit with the lowest residual gets the lowest
estimated view value. The lowest possible view type is the sixth highest as we only havesix-unit types for views in a building with six or more units. Hence, if there are more thansix units on a floor, all units from the sixth down in residual value receive the same view
value. In aggregate, under this approach with building fixed-effects, a unit with the top view
decile in every direction has a 21 percent higher value than one with the lowest view decile.
Figure C-1 shows the difference in view values between the average floor view (panel a)30

While we generate different estimates based on whether the first stage uses census tract or building
fixed-effects, we also test for the outcomes with and without the four buildings over 44 stories and with both
1- and 5-kilometer rings. The final results in the hedonic regressions are robust across these different criteria

39

((a)) Avg Floor View((b)) Est unit-specific View

Figure C-1: Comparing View Coefficientsand the estimated unit-specific view (panel b). For presentation, the view effects in a decile
are summed across all four quadrants so that we present the estimated effect of view onvalue for a unit with 2nd decile view values across all quadrants. Estimated view effects aresubstantially larger with the unit-specific estimates. Using the floor average view, a unit with
top decile views in each direction would have an 11 percent higher value than a unit withthe lowest decile view. In contrast, using the estimated unit-specific view, this difference isapproximately 25 percent. Importantly, as noted above, the estimated relative status priceeffect is robust to the approach used for estimating unit view.

40