Urban Transit Infrastructure and Inequality: The Role of Access to Non-Tradable Goods and Services - Kwok ...
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1 Urban Transit Infrastructure and Inequality: The Role
2 of Access to Non-Tradable Goods and Services∗
3 Brandon Joel Tan† Kwok Hao Lee‡
4 January 2022
5 Abstract
6 Since low-income workers are overwhelmingly employed in non-tradable sectors, in
7 response to transit expansion, changes in consumption travel patterns induce a spa-
8 tial re-organization of low-income jobs in the city, with important implications for
9 inequality. We develop an urban spatial model with heterogeneous worker groups,
10 incorporating travel to consume non-tradable goods and services. The model is es-
11 timated using detailed farecard and administrative data from Singapore. After the
12 Downtown Line was built, we find large welfare gains for high-income workers, but
13 near zero for low-income workers. All workers benefit from improved access to con-
14 sumption opportunities, but jobs in the low-income non-tradable sector move to less
15 attractive workplaces. If we abstract away from consumption travel, we underestimate
16 the line’s effect on inequality by a factor of five. Furthermore, the resulting model fails
17 to capture the spatial re-organization of low-income jobs in the city.
∗
We thank Pol Antras, Nick Buchholz, Antonio Ciccone, Edward Glaeser, Nathan Hendren, Kate Ho,
Adam Kapor, Matthew Kahn, Jakub Kastl, Gabriel Kreindler, Jeffrey Lin, Marc Melitz, David Nagy, Christo-
pher Neilson, Stephen Redding, participants of the NBER Summer Institute: Urban Economics 2021, 15th
North American Meeting of the Urban Economics Association, and the 10th European Meeting of the Urban
Economics Association, and a number of other colleagues, conference and seminar participants for helpful
comments and suggestions. We thank the Singapore Land Transport Authority for providing data to Kwok
Hao Lee. Finally, we thank the Princeton Institute for International and Regional Studies, as well as the
Department of Economics at Princeton University, for financial support. Responsibility for results, opinions
and errors is the authors’ alone.
†
Corresponding Author; Department of Economics, Harvard University, btan@g.harvard.edu
‡
Princeton University, khl@princeton.edu
1 1 Introduction
2 Across the world, public transit networks are growing faster than ever before. Each year,
3 more than a trillion dollars is invested in building and expanding transportation infrastruc-
4 ture (Lefevre, Leipziger, and Raifman 2014). In particular, as their cities densify, countries
5 have rapidly built urban mass transit systems to alleviate congestion and combat climate
6 change.1
7 With 68% of the world population projected to live in urban areas by 2050, governments
8 will continue to spend vast sums on mass transit (United Nations 2018). Yet how are
9 the economic gains from transit expansion shared between low- and high-income workers?
10 This question is important because inequality is increasingly becoming a major issue across
11 cities around the world.2 Existing research focuses on differential access to employment
12 opportunities across worker groups emphasizing the cost of travel to work (Tsivanidis 2019;
13 Balboni et al. 2020). However, a large share of urban trips are unrelated to work and are made
14 for the consumption of non-tradable goods and services such as restaurants, coffee shops,
15 retail stores, salons, and cinemas. According to the National Household Travel Survey, 31%
16 of travel miles are made for work purposes, while 33% of travel miles are made for shopping
17 or meals and another 26% for social or recreational purposes.3 Additionally, non-tradable
18 consumption makes up over 50% of total household expenditure (Department of Statistics
19 2018).4
20 Thus, to evaluate how transit expansion affects inequality, we need to account for travel
21 related to the consumption of non-tradable goods. First of all, low- and high-income workers
22 face differential reductions in travel costs from consumption trips and differential changes
23 in access to consumption opportunities. Second, in general equilibrium, workers trade off
24 paying higher rents with improved access to both employment and consumption. Since each
25 type of worker has a different budget set, their different choices shape their residential pat-
1
Worldwide, mass transit carried 53 billion passengers in 2017 with nearly 650 transit lines covering
14,000 kilometers (UITP 2018). See Figure A1 for an illustration of this fact. Just between 2015 and 2017,
roughly 1,900 kilometers of new track was put into service, and the International Association of Public
Transport projects that more than 200 new transit lines will open across the world between 2018 and 2023
(UITP 2018).
2
In particular, there is concern that low income workers face much larger commuting costs than high
income workers. See: “Long Commutes Are Awful, Especially for the Poor”, The Atlantic; “Public Transit
Cuts Felt Deepest in Low-Income Areas”, NYTimes; “How long commutes worsen inequality”, CBS News.
3
See Appendix Figure A2 (Department of Transportation 2017).
4
See Appendix Figure A3.
1
1 terns across the city. Third, where workers choose to consume non-tradables determines
2 the spatial distribution of non-tradable sector jobs. These urban non-tradable sectors over-
3 whelmingly employ low-income workers - such as waiters, dishwashers, manicurists and so
4 on.5 In response to changes in transit access, jobs may move to locations which are less
5 (or more) productive, that pay lower (or higher) wages, or that require longer (or shorter)
6 commutes by worker group. This re-organization of commercial activity across space dif-
7 ferentially changes each worker group’s expected access to employment, or expected income
8 net of commuting.
9 In this paper, we develop an urban spatial model with heterogeneous worker groups by
10 income (low/high). In our model, workers travel to work and to consume non-tradable
11 goods and services. The city in which they reside is modeled as a set of neighborhoods,
12 with a transportation network characterized by the bilateral travel times between locations.
13 Worker groups differ in their preferences over residential and consumption locations, produc-
14 tivities over workplaces and sectors, consumption patterns, and travel costs and elasticities.
15 First of all, workers choose where to live. Each type of worker trades off rents against res-
16 idential amenities, as well as access to employment and consumption opportunities. Next,
17 they choose where to work, based on type-specific wages, match-specific productivities and
18 commute distances. Then, they choose where to consume non-tradables based on prices,
19 type-specific idiosyncratic consumption amenities, and travel distances. Non-tradable and
20 tradable sectors have different input requirements over commercial floor space and labor
21 provided by each worker group, with the non-traded sector being much more intensive in
22 low-income labor. Market clearing in the non-traded sector implies that, in each location,
23 consumption travel patterns drive the demand for non-traded production, and hence also the
24 demand for low-income workers. Finally, the model also accommodates agglomeration forces,
25 and allows for type-specific spillovers in endogenous residential amenities. These spillovers
26 thus drive segregation in the city.
27 With the model in hand, we study the equilibrium effects of the Downtown Line (DTL)
28 opening in Singapore. To distinguish travel patterns across worker groups and locations,
29 we exploit government farecard data on the universe of public transportation trips linked
30 to individuals over a three year period before and after the line opening. Moreover, we use
5
According to Autor and Dorn (2013), low income jobs have been rapidly moving into non-tradable
services since the 1980s, and the trend is only expected to intensify with the decline of low-skill intensive
manufacturing. See Appendix Figure A4.
2
1 detailed administrative spatial data on land use, rents, expenditures and employment in our
2 structural estimation. As the then-longest underground and automated rapid mass transit
3 line in Singapore the DTL was designed to connect the northwest and east to the center of
4 the city. To ground our structural analysis, we first utilize a spatial differences-in-differences
5 procedure, finding that the DTL increased nearby housing prices by 5% over a four year
6 period. Event study estimates show that neighborhoods with a DTL station experienced a
7 20% in increase in trips after the line opening. However, there were large differences, across
8 locations, in how low- and high-income workers adjusted their travel patterns in response to
9 the DTL.
10 Motivated by our reduced-form analysis, we estimate our model using data from before
11 the DTL opening. We find that each worker type likes different places in which to live, work
12 and consume non-tradables. These measures of location attractiveness are theory-consistent
13 and validated against external data on associated amenities. Model-implied average wages by
14 worker type and residence are also highly correlated with those observed in administrative
15 data. Low-income workers have larger travel elasticities than high-income workers, and
16 elasticities are larger than for consumption than for work travel across both types. Spillovers
17 in residential amenities are larger for low-income workers, and residential elasticities are
18 slightly larger for high-income workers. In the pre-DTL equilibrium, low-income workers
19 commute shorter distances than high-income workers do, but travel as far as the latter to
20 consume non-tradables. High-income workers live near the center of the cit and the DTL
21 directly serves many of these neighborhoods. Meanwhile, low-income workers live away from
22 the city center. Finally, high-income workers spend more of their overall expenditures on
23 non-tradables than low-income workers.
24 To quantify the welfare and inequality effects of the DTL, we compute counterfactuals
25 using exact-hat methods (Dekle, Eaton, and Kortum 2008). Using changes in travel times
26 as observed in the farecard data before and after the opening of the line, we find that the
27 model predicts well post-DTL travel flows, residential patterns and the entry of firms in
28 the non-tradable sector. Moreover, we find that the DTL improves welfare for high income
29 workers by 3.15%. However, low income workers experience near zero net benefits. Although
30 both groups can better access consumption opportunities, low-income workers see their jobs
31 (in non-tradable production) moving to places they deem less attractive, offsetting their
32 gains from the consumption channel. This disparity between the rich and the poor is driven
3
1 by two mechanisms. First, the DTL disproportionately improves access for the many high-
2 income areas served directly by the line. Second, more consumers consume non-tradables
3 near the city center because the DTL has made it easier for them to go downtown. Thus,
4 non-tradable low-income jobs move to the center of the city, yet low income workers still live
5 away from the center. Average commute times increased 1.5% for low income workers, while
6 high income workers saw a 1% reduction. Abstracting away from travel to consume non-
7 tradables, we find a five-fold underestimation of the inequality effects of the DTL. Absent
8 non-tradable consumption, we see that both worker groups benefit but a slightly larger share
9 of the gains go to high-income workers. Thus it is quantitatively important to capture the
10 spatial re-organization of low-income non-tradable sector jobs. Aggregate welfare gains are
11 also underestimated by about 40%, stemming from ignoring improved consumption access.
12 Finally, we conduct a model decomposition exercise. We find that low-income workers
13 spend less on non-tradables; thus they gain less from better consumption opportunities.
14 They also have lower travel costs and higher travel elasticities; so they can better substitute
15 to more attractive work and consumption locations, therefore benefiting less from shorter
16 trips. Yet these low-income workers have relatively more dispersed residential preferences,
17 so they are less able to move house to capitalize on improved access elsewhere.6
18 This paper speaks directly to the literature studying the impact of transportation infras-
19 tructure within cities (McDonald et al. 1995; Gibbons and Machin 2005; Baum-Snow and
20 Kahn 2005; Glaeser, Kahn, and Rappaport 2008; Billings 2011; Donaldson and Hornbeck
21 2016; Severen 2018; Donaldson 2018; Brooks and Lutz 2019; Gupta, Van Nieuwerburgh, and
22 Kontokosta 2020; Heblich, Redding, and D. Sturm 2020). The most closely related papers
23 to ours are Tsivanidis (2019) and Balboni et al. (2020), who study the Bus Rapid Transit
24 (BRT) systems focusing on inequality in Colombia and Tanzania respectively. Both papers
25 estimate quantitative spatial models restricted to workplace commuting, finding small in-
26 equality effects. We innovate on the literature by incorporating the role of travel to access
27 non-tradable goods and services. These travel costs are crucial to evaluate the distributional
28 welfare effects of transit expansions. Consistent with prior work, when we abstract from
29 consumption trips, we find the DTL barely affects inequality. However, in our setting, the
6
In Online Appendix F, we also evaluate the cost effectiveness of the DTL via the Marginal Value of
Public Funds measure (Hendren and Sprung-Keyser 2020). Combining construction and operating cost data
with estimates of willingness to pay from our quantitative model, we find that the DTL provides 8.65 dollars
of benefits per dollar of government spending. The social benefit-cost ratio is 5.28. Although these benefits
largely accrue to high-income workers, the DTL remains highly cost effective.
4
1 consumption trip channel appears to be economically important in assessing inequality.
2 Our paper also contributes to several other strands of literature. The first is the growing
3 body of work on quantitative spatial models more generally (Redding and D. M. Sturm 2008;
4 Allen and Arkolakis 2014; Ahlfeldt et al. 2015; Redding 2016; Allen, Arkolakis, and Li 2016;
5 Caliendo et al. 2018; Desmet, Nagy, and Rossi-Hansberg 2018; Monte, Redding, and Rossi-
6 Hansberg 2018; Adao, Arkolakis, and Esposito 2019; Allen and Arkolakis 2019).7 We are the
7 first paper to consider a quantitative spatial model with heterogeneous workers incorporating
8 both travel for work and consumption. This paper also speaks to quantifying the value of
9 urban amenities (Roback 1982; Blomquist et al. 1988; Glaeser, Kolko, et al. 2001; Albouy
10 et al. 2016; Cragg and Kahn 1997; Bayer et al. 2009, Fan, Guthrie, and Levinson 2016;
11 Diamond 2016; Almagro and Domı́nguez-Iino 2020). We demonstrate the important role of
12 non-tradable retail amenities in shaping inequality and the spatial distribution of economic
13 activity in the city. Moreover, we are also able to quantify differences in preferences over
14 amenities across worker groups. Finally, our paper is related to the literature on inequality
15 in cities (Brueckner et al. 1999, Glaeser, Resseger, and Tobio 2009; Su et al. 2018; Fogli and
16 Guerrieri 2019; Couture et al. 2019). We show that changes in travel access can have large
17 implications for urban inequality.
18 The rest of the paper proceeds as follows. Section 2 discusses the context of Singapore
19 and the Downtown Line, as well as the data. Section 3 presents reduced form results and
20 facts which motivate our structural model. Section 4 develops the model, while Section 5
21 estimates it. Section 6 quantifies the impact of the Downtown Line. We conclude in Section
22 7.
23 2 Background and Data
24 2.1 Context: Singapore and the Downtown Line
25 Singapore is an island city-state in Southeast Asia. With a population of about 6 million
26 inhabitants, Singapore is the third densest country in the world, and is among the densest
7
Our paper is closely related to and builds on methods from Miyauchi, Nakajima, and Redding (2020)
who explore the role of consumption access and agglomeration in the Greater Tokyo metropolitan area.
5
1 cities (World Bank 2019).89 Inequality in the city-state is high; with a Gini coefficient of
2 46.4, Singapore ranks only behind Hong Kong and the United States among high-income
3 countries.
4 The population in Singapore is heavily reliant on public transportation, comprising buses,
5 light-rail and mass-rail networks. The Singapore government heavily restricts the supply of
6 cars with a Vehicle Quota System.10 As a result, only 10% of households in Singapore own
7 a car, and far fewer drive to work. With the public transit system carrying over 4 million
8 passengers per day, public transportation is the primary means of travel for the population.11
9 Approximately 60% of trips are made on buses, as opposed to rail lines.
10 The Downtown Line is the longest underground and mass rapid transit line in Singapore.
11 At 41.9 kilometres (26.0 miles) and with 34 operation stations, the line runs from Bukit
12 Panjang station in the north-west to Expo station in the east via the Central Area.12 The
13 line was first announced on 23 October 2001, and was built in three phases. The first phase
14 opened in December 2013, and was composed of 6 stations from Bugis to Chinatown station
15 within the Downtown area. The second phase from Bukit Panjang to Rochor station, which
16 linked the north-west to the center of the city, opened in December 2015. The third and final
17 phase from Fort Canning to Expo station, connecting the east to the city of the city, opened
18 in October 2017. The line, at a cost of 15.5 billion USD, is considered the government’s most
19 ambitious public transit project to date (The Straits Times 2017). The purpose of the line
20 was to provide the north-west and eastern areas a direct link to the center of the city, and
21 to alleviate congestion on various other rail and bus routes.
8
There are highly restrictive immigration policies with strict foreign worker quotas, and limited out- and
in- migration (Ministry of Manpower 2020).
9
The spatial distribution of non-tradables across Singapore is similar to that of other major cities (see
Figure A5).
10
According to the 2019 Worldwide Cost of Living Survey carried out by the Economist Intelligence Unit,
Singapore “remains the most expensive place in the world to buy and run a car.” As of 2018, the price of
a Volkswagen Golf 1.4 is US $110,479.80, 5 times more expensive than in the United States (US$21,845).
Additionally, the city’s Electronic Road Pricing System imposes large tolls for driving to encourage the use
of public transportation. Tolls are highest during commuting hours – a car trip from the northwest to the
center of the city 8am and 9am on a weekday is tolled up to 15 dollars.
11
Appendix Table A1 provides a summary of the mass-rail lines in Singapore.
12
See Figure A6.
61 2.2 Data
2 Our primary source of data is public transit fare card data (EZ-Link) from the Land Trans-
3 port Authority of Singapore.13 We observe all trips made by public transit (mass rail, light
4 rail or bus) linked to a individual’s fare card.14 Our data set covers one week every quarter
5 between June 2015 and June 2018, and three full months between Dec 2015 and February
6 2016. The longer quarterly data set allows us to observe changes in transit patterns from
7 before the opening of Phase 2 of the Downtown Line to after the opening of Phase 3. The
8 full three months of data captures the period directly before and after the opening of Phase
9 2 of the Downtown Line. In total, we observe over a billion trips. For each trip, we observe
10 the origin, destination, and start and end time of the trip. Each individual in our data set
11 is categorized into eight groups: Adult, Low-Income Worker, Primary Student, Secondary
12 Student, Tertiary Student, Senior Citizen, Military, and Person with Disabilities. In our
13 analysis, we focus the Adult and Low-Income Worker categories. Low-Income Workers are
14 those who earn a monthly salary below the 25th percentile ($2000 SGD prior to 2020).15 We
15 link all bus and train stops to subzones as delineated by the Urban Redevelopment Author-
16 ity which is the smallest geographic unit across our datasets. Singapore is divided into 323
17 subzones with a median size of 1,229,894 square meters. These are contained within larger
18 spatial units including 55 planning areas and 5 planning regions.
19 We use our fare card data to generate work and consumption travel probabilities condi-
20 tional on residential subzone. We restrict our data set to 3 million fare cards with at least 20
21 trips over our panel.16 We include only Adult and Low-Income fare cards in order to capture
22 the working population, dropping students, people with disabilities, those in the military,
23 and the elderly. First we identify each individual’s residence as the modal first origin and
24 last destination of the day, where each person typically starts or ends the day. Next, we
25 identify each individual’s workplace as the modal destination during the morning rush hour
26 (5am to 11 am) and origin during evening rush hour (3pm to 11pm). Finally, we classify all
27 remaining trips as consumption trips.
13
We present a heat map visualization of the data in Appendix Figure A7.
14
These fare cards are called EZ-Link cards.
15
Low Income Workers receive up to a 25% subsidy on their fare costs. The Central Provident Fund
automatically determines eligibility based on tax filings and sends an individual application package informing
workers of their eligibility, details of the scheme, and how to apply for the subsidized card (Ministry of
Transport 2014).
16
We get similar probabilities with different trip thresholds for inclusion in our data set.
71 We also use data from several other administrative sources. The General Household
2 Survey (GHS) 2015 from the Department of Statistics provides detailed information on pop-
3 ulation, employment, income, and demographics at the subzone level. The GHS is conducted
4 in between the Population Censuses which are conducted once in ten years covering a wider
5 range of topics. Most data is compiled from administrative records across multiple sources,
6 and additional information not available from administrative sources is collected from a
7 sample survey of over 30,000 households. The Labor Force Survey 2018 provides data on
8 employment and wages by industry. The Household Expenditure Survey 2018 provides de-
9 tailed data on household and worker expenditures by income bracket. We classify itemized
10 expenditures on goods and services into tradables and non-tradables. The REALIS dataset
11 from the Urban Redevelopment Authority provides data at the subzone level on residential
12 and commercial land use (broken down by sector) as well as average rent per square meter
13 by commercial and residential land. Housing and Development Board (HDB) transaction
14 data provides the universe of HDB flat sales with information on price, address, flat size,
15 and number of rooms between 1999 and 2019.
16 Finally, we also collect spatial data on amenities from the government data portal.17
17 First of all, we have two cross-sectional data sets, dating to 2015 and 2018, covering the
18 universe of licensed food establishments in Singapore from the Singapore Food Authority.
19 Second, data on all supermarkets and hawker centers in Singapore are from the National
20 Environment Agency.18 Third, the Ministry of Education provides data on the location of all
21 schools. Fourth, the Singapore Land Authority provides data on all parks and community
22 clubs. Fifth, the Singapore Ministry of Health provides data on the location of all clinics.
23 We geocode all data and link each address or coordinates to the subzones in which they are
24 contained.
25 3 Reduced Form Results
26 In this section, we present reduced form results on the impact of the Downtown Line and
27 motivating facts which guide our structural model. In all our analysis, we define low-income
28 workers as those earning below the 25-percentile ($2000 SGD or $1500 USD per month, less
17
https://data.gov.sg
18
We present a map of the data in Appendix Figure A8.
81 than half of median earnings)19 and high-income workers as those earning above, consistent
2 with our fare card data set. Our unit of analysis is the subzone, which we will henceforth
3 call a neighborhood.
4 3.1 Residential patterns
5 Low and high income groups have different residential patterns across the city. Figure 1
6 plots the share of high-income workers that live in each neighborhood in 2015. High income
7 workers primarily cluster near the center of the city (eg. Bukit Timah, Tanglin) with only
8 some concentration in certain neighborhoods near the coasts of the island (eg. East Coast
9 Park). On the other hand, low income workers live farther from the city center, with many
10 living closer to the north. Figure 1 also shows that the Downtown Line runs through some
11 of the neighborhoods with the highest concentration of high-income workers in Singapore,
12 clustered in or just west of the city center. The many low income residents in the north
13 are not directly served by the Downtown Line. This suggests that high-income workers may
14 disproportionately benefit from the DTL, since the line serves them directly.
15 3.2 Employment patterns
16 We find that neighborhoods which employ many low income workers are intensive in non-
17 tradable sector production. Figure 2 plots the relationship between the share of commercial
18 land used by non-tradable sectors and the share of workers that are low-income. We find a
19 strong positive correlation as expected. Labor Force Survey data shows that 51% of workers
20 in the non-tradables sector are low income, while making up only 25% of the labor force, as
21 shown in Table A2.20 Only 14% of workers in the tradables sector are low income. Appendix
22 Figure A9 plots the share of high-income workers that work in each neighborhood. This
23 suggests that the spatial distribution of non-tradable jobs is highly important for low-income
24 workers.
19
Singapore’s median income in 2019 was $4,563.
20
Specifically, 61% of employees in the food and accommodation, 49% in retail, and 41% in personal
services are low-income.
91 3.3 Consumption patterns
2 Using itemized Household Expenditure Survey data broken down by income group, we find
3 that high-income consumers spend more on non-tradables than low-income consumers. Fig-
4 ure A10 shows that high-income workers spend 67% of their income on non-tradable goods
5 and services, 14% on tradables and the remaining on housing. In contrast, low-income work-
6 ers spend just 57% of their income on non-tradable goods and services and 20% on tradables.
7 This suggests that improving access to consumption opportunities will raise welfare more for
8 high-income than low-income workers.
9 3.4 Travel patterns
10 We find that low income workers make shorter commutes, at a median of 25 minutes, relative
11 to 30 minutes for high income workers. However, consumption trips are more similar in times
12 across income groups and are shorter than workplace trips at around 23 minutes for high-
13 income workers and 22 minutes for low-income workers respectively. Figure 3 plots the travel
14 time distributions by worker group and type of travel. Low-income workers make 5% more
15 trips on average than high-income workers. Consumers also make more trips on the weekend
16 than weekdays. Figure A11 presents the average number of daily trips by worker group and
17 weekday vs weekend travel.
18 3.5 Impact of the DTL on Housing Prices
19 We find that the Downtown Line (DTL) had a large impact on residential prices. Using a
20 spatial difference-in-differences framework, we exploit the announcement of precise station
21 locations on the DTL on July 15, 2008. We estimate that over 4 years, residential prices
22 increase by 4.84% for apartments within one kilometer (km) of a DTL station, relative to
23 those between 1 and 5km. See Figure 4a. Additionally, we also estimate the relationship,
24 over time, between housing prices and distance from the DTL. The estimated regression
25 coefficients are plotted in Figure 4b. Post-announcement, the closer the flats are to the
26 DTL, the higher their prices, all else equal.21
27 Increased property prices indicate that residents highly value improvements in access
28 from the DTL. These price increases reflects a combination of both improved access to work
21
For details on the precise specification and analysis, see Online Appendix B.1.
101 and consumption locations. We find that the price effects increase over time, suggesting
2 a longer-run re-organization of economic activity. These dynamics motivate our general
3 equilibrium structural model.
4 3.6 Impact of the DTL on Travel
5 We find a sharp uptick in travel to DTL subzones in response to the line opening. Figure 5
6 plots the daily volume of trips to or from subzones with and without a DTL station between
7 December 2015 and February 2016 by low- and high-income workers, with Phase 2 of the
8 DTL opening on December 27th 2015. We observe about a 20% increase in trips after the
9 opening. Over all sub-zones, the volume of low-income trips increases by a smaller percentage
10 than high-income trips. This suggests that high-income workers are taking greater advantage
11 of the new DTL than low-income workers. We also find that low- and high-income workers
12 adjust their travel patterns differently across neighborhoods. In Figure 6a and 6b, we plot the
13 travel patterns by income group for two of the major locations on the DTL line separately,
14 Bukit Panjang and Upper Bukit Timah. High-income workers increase their travel to and
15 from Bukit Panjang by about 40% on average, while low-income workers increase their travel
16 volume by about 20%. On the other hand, both worker groups increase their travel to and
17 from Upper Bukit Timah by the same amount. This suggests that it is important for a
18 model to account for differential travel response in evaluating welfare across worker groups.
19 Lastly, we plot changes in travel patterns over a longer time horizon in Figure 7. We find
20 that the responses in travel flow are dynamic, growing over time. Again, this suggests that
21 accounting for long-run responses with the re-organization of economic activity is important,
22 motivating our general equilibrium structural model.
23 3.7 DTL and Non-Tradable Production
24 Using two cross-sections of food establishment license data between 2015 (before the opening
25 of Phase 2 and 3 of the DTL) and 2018 (after the opening), we find that, in subzones with
26 a DTL station, relatively more food establishments entered between 2015 and 2018. The
27 number of food establishments in DTL locations increased by about 15% relative to non-DTL
28 locations. See Appendix Table A3.
111 4 Quantitative Model
2 This section presents a model of the internal structure of a closed city with heterogenous
3 workers and travel choice over workplace and consumption locations.
4 4.1 Setup
5 Our closed city has n ∈ N neighborhoods.22 Neighborhoods differ in their exogenous ameni-
6 ties, productivities, residential and commercial floor space, as well as bilateral commute
7 times. High- and low-income workers decide where to live, where to consume non-tradable
8 goods and services, and where and in which sector to work.23 Each worker type has different
9 preferences, productivities, wages, travel costs, and consumption shares. Utility is derived
10 from the consumption of a tradable good, a non-tradable good, and residential floor space.
11 On the production side, there are two sectors G ∈ {T, N }, the tradable and non-tradable
12 sectors. Firms are located across the city and produce using labor and commercial floorspace.
13 Sectors differ in their demand for different worker types, with the non-tradable sector relying
14 more on low-income workers and the tradable sector relying more on the high-income workers.
15 Demand for goods in the non-tradable sector depends on where consumers choose to travel to
16 consume non-tradables, while tradable goods are costlessly traded across the city. Demand
17 for labor by worker type varies across the city based on the productivity of each sector in each
18 location, commercial rents and demand for production. A competitive land sector supplies
19 floor space using land and capital with constant returns to scale technology. In equilibrium,
20 the price of floor space, wages, and prices of goods adjust to clear the goods, land and labor
21 markets.
22 4.2 Workers
23 The city is populated by different worker groups indexed by θ ∈ {+, −}, denoting high- and
24 low-income workers respectively. Each type of worker has a fixed population Rθ . A worker ω
25 in group θ chooses a location n in which to live, a location i and sector G in which to work,
22
The population of each worker group is determined exogenously. Singapore is a small city-state with
tightly regulated in- and out-migration.
23
In additional analyses, we allow each worker to make many consumption trips to different locations.
We find that this extension collapses to the same estimating equations as in the main model. This material
is available in a supplement provided upon request by the authors.
121 and a location j in which to consume non-tradable goods and services. We assume indirect
2 utility is Cobb-Douglas and takes the form:
Bnθ bθn (ω) θ θ
wiG aiG (ω) sθj (ω)
uθniGj (ω) = αT θ
× × , (1)
QαnHθ PnT exp(κθ τni ) P N αN θ exp(κθ τnj )
j
3 where 0 < αT,θ , αH,θ , αN,θ < 1 and αT,θ + αH,θ + αN,θ = 1. To ease exposition in this
4 subsection, fix a residential neighborhood n, work neighborhood i, sector G, consumption
5 neighborhood j and worker type θ.
6 Individuals consume residential floorspace, a tradable good, and a non-tradable good.
7 We accommodate different preferences, productivities, wages, travel costs and consumption
8 shares by type. The first term in the product in Equation 1 covers the utility factors specific
9 to the worker’s residence. She receives Bnθ in common residential amenities in neighborhood
10 n. Differences in residential preferences across groups will drive worker types to live in
11 different neighborhoods. However, this worker dislikes more expensive residential floor space
12 Qn and tradable goods PnT . We assume that the tradable good is traded without cost in the
13 city and assume it is our numeraire: PnT = P T = 1.
14 The second and third terms in the product in Equation 1 correspond to the utility terms
15 specific to the worker’s workplace and consumption neighborhood respectively. She earns a
θ
16 wage wiG per efficiency unit in neighborhood i. Meanwhile, she dislikes a more expensive
17 price PjN of the non-tradable good in neighborhood j. To work in neighborhood i and
18 consume non-tradables in neighborhood j, the worker pays iceberg travel costs exp(κθ τni )
19 and exp(κθ τnj ) respectively. These travel costs increase with the time τ it takes to travel
20 between neighborhoods. The parameter κθ controls the size of these travel costs by worker
21 group. We expect differences in travel costs since low-income workers receive subsidies on
22 travel. Higher travel costs imply larger gains from reductions in travel time.
23 Next, high- and low-income workers have different consumption shares over housing, αH,θ ,
24 tradables, αT,θ , and non-tradables, αN,θ . These shares measure the relative importance of
25 housing, tradable and non-tradable consumption for utility for people of type θ. Larger con-
26 sumption shares on housing imply larger implications of changes in rents for welfare. Larger
27 consumption shares on non-tradables imply larger implications of access to consumption
28 opportunities for welfare.
Finally, worker ω has idiosyncratic draws for residential amenities in neighborhood n,
13bθn (ω), efficiency units of labor (productivity) in neighborhood i and sector G, aθiG (ω), and
consumption amenities in neighborhood j, sθj (ω)). We assume that these idiosyncratic shocks
are drawn from the following independent Frechet distributions:
Rθ
FnRθ (b) = exp(−TnRθ b−ϵ )
Lθ
Lθ
FiG (a) = exp(−TiLI θ TGLG θ a−ϵ ) (2)
Sθ
FjSθ (s) = exp(−TjSθ s−ϵ )
1 where all the shape parameters, ϵ, are greater than 1 and all the scale parameters, T ,
2 are greater than zero. The scale parameters, TnRθ , TiLI θ , TGLG θ , and TjSθ , control the overall
3 level of the draws for residential preferences, work location productivity, sector productivity,
4 and consumption preferences respectively. We allow scale parameters to vary across worker
5 groups, to capture differences in preferences and productivities over locations across types.
6 We also allow shape parameters, ϵRθ , ϵLθ , ϵSθ , which control the dispersion of the distributions
7 to differ across groups. A higher ϵ corresponds to a smaller dispersion of idiosyncratic taste
8 shocks. The sensitivity of choices to other variables such as travel costs is governed by the
9 dispersion of preferences or productivity. When workers have similar matches in different
10 locations (high ϵ), their choices are more sensitive to these other variables. Differences in
11 heterogeneity across groups will be important in determining the incidence of travel costs,
12 since these differences control the extent to which individuals are willing to bear high travel
13 costs to work or consume in a location.
14 Timing. Workers first choose where to live; then, in a second step, they choose where
15 to work and where to consume non-tradables. First, individuals observe their idiosyncratic
16 residential amenities draws for all neighborhoods and choose to live in some neighborhood n.
17 Second, individuals observe their idiosyncratic productivities for all workplaces and idiosyn-
18 cratic consumption preferences in all neighborhoods, then choose to work in some neighbor-
19 hood i and sector G, and to consume non-tradables in some neighborhood j. We solve the
20 worker problem by backward induction.
21 4.2.1 Employment Location Decision
22 Having chosen a neighborhood n in which to live, individuals draw a vector of match-
23 productivities with firms across the city as in Equation 2. With these draws in hand, workers
24 choose to work in the neighborhood that offers the highest income net of their type-specific
141 commuting costs:
θ θ
wiG aiG (ω)
max . (3)
i,G exp(κθ τni )
2 Fix a worker type θ who has made the choice to live in neighborhood n. Since idiosyncratic
3 productivities are distributed according to a Frechet distribution, the probability she decides
4 to work in neighborhood i and sector G is given by the following gravity equation:
Lθ
T LI θ TGLG θ [wiG
θ
exp(−κθ τni )]ϵ
λLθ
niG|n = P Pi LI θ LG θ
(4)
l H Tl TH [wlH θ
exp(−κθ τnl )]ϵLθ
5 Individuals are more likely to travel to work in a neighborhood that pays a high wage
6 net of travel costs, as in the numerator, relative to those in all other locations, as in the
7 denominator. The sensitivity of employment decisions to commute costs is governed by the
8 dispersion of productivities across neighborhoods. Similar matches across workplaces in dif-
9 ferent locations and sectors (high ϵ) imply that choices are more sensitive to commute costs.
10 Differences in productivity heterogeneity across worker types is important in determining
11 the incidence of travel costs, controlling the extent to which workers are willing to bear high
12 commute costs to work in a neighborhood. Differences in productivity across neighborhoods
13 and commute costs by type drive differences in work travel patterns across worker groups.
14 Expected income prior to drawing the vector of match productivities is directly related
15 to the denominator in Equation 4 through
"X X #1/ϵLθ
ϵLθ − 1
ϵLθ
Wθn ≜ ELθ
n [v] = Γ TlLI θ THLG θ [wlH
θ
exp(−κθ τnl )] (5)
ϵLθ l H
16 where Γ(.) is the Gamma function. Intuitively, in locations with better access to em-
17 ployment Wθn , or access to locations with high expected income by type, workers are better
18 off.
19 4.2.2 Consumption Location Decision
20 Having chosen where to live n, individuals draw a vector of idiosyncratic preference shocks
21 with consumption locations across the city as in Equation 2. With these draws in hand,
22 workers choose to consume non-tradables in the neighborhood with the best consumption
151 amenities, accounting for travel costs and the price of non-tradables.
sθj (ω)
max αN
(6)
j
PjN exp(κτnj )
2 Again, fix a worker type θ and residence location n. Since idiosyncratic consumption tastes
3 sθj (ω) are distributed according to a Frechet distribution, the probability this worker decides
4 to consume non-tradables in j is given by the following gravity equation:
αN Sθ
TjSθ [PjN exp(κτnj )]−ϵ
λSθ
nj|n =P N (7)
Sθ N α exp(κθ τ −ϵSθ
m Tm [Pm nm )]
5 Individuals are more likely to travel to consume in neighborhoods with high consumption
6 amenities net of the price of non-tradables and travel costs, as in the numerator, relative to
7 those in all other locations, as in the denominator. The sensitivity of consumption decisions
8 to travel costs is governed by the dispersion of preferences across neighborhoods. Similar
9 amenities across consumption locations (high ϵ) imply that choices are more sensitive to
10 travel costs. Differences in preference heterogeneity across worker types is important in de-
11 termining the incidence of travel costs, controlling the extent to which workers are willing
12 to bear high travel costs to consume non-tradables in a neighborhood. Differences in prefer-
13 ences across neighborhoods and travel costs by type drive differences in consumption travel
14 patterns across worker groups.
15 Expected utility from non-tradable consumption prior to drawing the vector of idiosyn-
16 cratic preferences is directly related to the denominator in Equation 7 through
"X #αN θ /ϵSθ
ϵSθ − 1
αN Sθ
Sθn ≜ ESθ
n [γ] = Γ TmSθ [PmN exp(κθ τnm )]−ϵ (8)
ϵSθ m
17 where Γ(.) is the Gamma function. Intuitively, in locations with better access to con-
18 sumption Sθn , or access to locations with low prices and high amenities by type, workers are
19 better off.
20 4.2.3 Residential Location Decision
21 In the first stage, individuals choose where to live to maximize their expected indirect util-
22 ity after observing their idiosyncratic residential amenity draws across all neighborhoods.
161 Workers of type θ solve the following problem:
Bnθ bθn (ω) θ θ
max Unθ (ω) = Wn Sn (9)
n QαnH
2 Workers are attracted to locations with high residential amenities, low housing prices,
3 high net incomes, and high utility from consumption of non-tradables.
4 Since idiosyncratic residence amenity draws are Frechet distributed, the share of type-θ
5 workers who live in neighborhood n is
−αT H Rθ
T Rθ [PnT Q−α Bnθ Wnθ Snθ ]ϵ
λRθ
n = Pn T
n
(10)
T −α H
Rθ
k Tk [Pk Q−α
k Bkθ Wkθ Skθ ]ϵRθ
6 Similar residential amenities across neighborhoods (high ϵ) imply that choices are more
7 sensitive to changes in access to employment, access to consumption, and rents. Differences
8 in preferences across neighborhoods by type drive differences in residential patterns in the
9 city across worker groups.
10 4.2.4 Expected Utility
11 Since we consider a “closed city”, expected utility from living in the city prior to drawing
12 the vector of idiosyncratic preferences is directly related to the denominator in Equation 10
13 through
"X #1/ϵRθ
ϵRθ − 1
−αT −αH Rθ
Ū θ = Γ TkRθ [PkT Qk Bkθ Wkθ Skθ ]ϵ . (11)
ϵRθ k
14 4.3 Firms
15 4.3.1 Technology
16 There is a representative firm for the non-tradable and non-tradable sectors, G ∈ {N, T },
17 in each neighborhood i ∈ N. Firms produce under perfect competition and with a constant
18 returns to scale technology. Firms production is Cobb-Douglas over labor and commercial
19 floor space. Output is specified as
G G
YiG = AiG LβiG HiG
1−β
(12)
171 where β G ∈ [0, 1] and HiG is commercial floor space. Meanwhile, labor input LiG is a
2 Cobb-Douglas aggregate over each worker group’s effective units of labor, ÑiGθ :
Y β Gθ
LiG = ÑiGθ (13)
θ
β Gθ = 1. Each sector and neighborhood has different productivities AiG . Sec-
P
3 where θ
4 tors differ in the intensity in which they use different types of workers β Gθ . The tradable
5 sector requires a higher share of high-income workers, while the non-tradable sector heavily
6 relies on low-income workers. Thus, the spatial distribution of non-tradable versus tradable
7 production is strongly related to that of low-income versus high-income jobs. As a result,
8 different worker types living in the same neighborhood may have different levels of access to
9 employment opportunities.
10 4.3.2 Factor Demand
11 Under perfect competition and free entry, firms make zero profits in equilibrium. Further-
12 more, the price of each variety is equal to its marginal cost:
β G G
PiG = AiG −1 WiG qi1−β (14)
13 where qi is the price of commercial floor space in workplace i and
β β G+ G−
WiG = wiG+ wiG− (15)
14 is the cost of labor for sector G in location i. In this definition, wiGθ is the wage per efficiency
15 unit for a worker of type θ. Wages are different across both sectors and locations, with each
16 sector and location pair facing an upward-sloping supply function for effective units of labor
17 for each worker type. Solving the firm’s profit maximization problem, we find that the
18 demand for labor and commercial floorspace can be written as
LiG = β G PiG YiG /WiG (16)
19
HiG = (1 − β G )PiG YiG /qiG (17)
20
ÑiGθ = β Lθ,G LiG WiG /wiGθ (18)
181 4.4 Land Market
2 Following Ahlfeldt et al. (2015), after factoring in the tax equivalent of land use regulations,
3 the land market equilibrium requires no arbitrage between the commercial and residential
4 use of floor space. The commercial price of floor space for both the tradable and non-tradable
5 sector is
qi = ξi Qi , (19)
6 where ξi equals one plus the tax equivalent of land use regulations that restrict commercial
7 land use relative to residential land use. We allow this wedge between commercial and
8 residential floor prices to vary across neighborhoods.
9 Floor space is supplied by perfectly competitive developers using land Ki and capital Mi ,
10 with constant returns to scale technology:
Hi = MiµH Ki1−µH (20)
11 where Hi is total floor space and µH is the share of land in floor space production. Therefore,
12 the corresponding dual cost function for floor space is Qi = µ−µ
H
H
(1 − µH )−(1−µH ) PµH R1−µ
i
H
,
13 where P is the common price for capital across all neighborhoods, and Ri is the price for
14 land in neighborhood i. Cost minimization implies that
µH −1 1−µH
µ−1
µH µH
Qi = PKi Hi H (21)
15 As the production of non-tradable goods and the demand for floor space rise in response
16 to increased consumption travel, increased rents may drive out tradable production and
17 residents, shifting commercial and residential spatial patterns across the city.
18 4.5 Market Clearing
19 Land. The expression for demand for residential floor space in neighborhood n is
P H,θ θ R
R α R λn W n
Hn = θ (22)
Qn
20 where we sum over the housing expenditures for all the residents in neighborhood n across
21 worker groups, using the fact that expenditures on residential floor space is a constant share
22 of income (since workers have Cobb-Douglas utility).
191 Market clearing for floor space requires that the total supply of floor space equals the
2 total floor space demanded from both residents and firms in each neighborhood j:
X
Hj = HjR + HjG . (23)
G∈{N,T }
3 Labor. Using the commuting probabilities from Equation 4, the supply of workers to
4 any location is the sum over the number of commuters by origin that travel to that work
5 location:
X
NiGθ = λLθ R θ
niG|n λn R (24)
n
6 Labor supply in the model takes a log-linear form that depends on two forces. Firstly, more
7 workers commute to destinations paying higher wages. Second, firms attract workers when
8 they have better access to them through the commuting network. Ultimately, workers care
9 about wages net of commute costs. Meanwhile, total effective labor supply to location i is
10 given by
X
ÑiGθ = Rn λLθ Lθ θ
ni|n λniG|ni āniG (25)
n
where āθniG is the average productivity of type-θ workers who live in n and decide to work in
i. Using the properties of the Frechet distribution, we have24
Lθ
āθniG = Γ(ϵLθ )(TiLI θ TGLG θ /λLθ
niG|n )
1/ϵ (26)
11 In each neighborhood i and sector G, market clearing requires that the supply of effective
12 labor, as in Equation 25, equals the demand for effective labor, as in Equation 16. Wages
13 by worker type are endogenously determined by market clearing.
14 Non-tradables. In each neighborhood j, total receipts for non-tradables must equal
15 total expenditures on non-tradables:
N N XX
PjN AiN LβiN HiN
1−β
= αN,θ λSθ R θ
nj|n λn R Wnθ . (27)
n∈N θ
16 Prices of non-tradables are endogenously determined to clear the market. We sum over
17 expenditures of non-tradables for all the workers who travel from some neighborhood n to
18 consume in neighborhood j across worker groups, using the fact that expenditures on non-
19 tradables is a constant share of income (since worker utility is Cobb-Douglas). This market
Lθ Lθ
24 θ
āniG = E[aθinG |TiLI θ TGLG θ (wiG
θ
exp(−κτni ))ϵ > TlLI θ TH
LG θ θ
(wlH exp(−κτnl ))ϵ , ∀l, H]
201 clearing condition implies that where workers decide to consume non-tradables is closely
2 linked to where non-tradables are produced.
3 4.6 Externalities
4 4.6.1 Productivities
5 A location’s productivity depends on both an exogenous component A¯iG that reflects fea-
6 tures independent of economic activity (e.g. access to roads, slope of land) as well as the
7 endogenous density of employment in that location:
X
AiG = ĀiG ( Niθ /H̄i )µA (28)
θ
8 where H̄i is the total units of land in location i. The strength of agglomeration externalities
9 is governed by the parameter µA .
10 4.6.2 Amenities
11 Amenities in a neighborhood are a function of an exogenous component B̄n and a residential
12 externality. In turn, this externality depends on the endogenous ratio of high-skilled and
13 low-skilled residents:
Bnθ = B̄nθ (Rnθ /Rn−θ )µU θ (29)
14 In our model, instead of being a function of the total density of residents, endogenous
15 amenities depend on the demographic composition of workers across income groups, similar
16 to Tsivanidis (2019). Workers are more willing to pay to live in neighborhoods that are high
17 in amenities of their type. As workers locate in these neighborhoods, they increase these
18 type-specific endogenous amenities even more, strengthening the segregation effect. We let
19 the strength of residential externalities differ across worker groups and estimate the relative
20 strength of these forces.
21 4.7 Equilibrium
22 We now define the general equilibrium of our model.
23 Definition Given vectors of exogenous location characteristics {B̄nθ , ĀiG , τij , H̄j , ψi , ξi },
24 city group-wise populations {Rθ }, and model parameters {α, β, κθ , TnRθ , TiLI θ , TGLG θ , TjSθ , ϵRθ ,
211 ϵLθ , ϵSθ , µH , µA , µU θ }, an equilibrium is defined as a vector of endogenous objects {qi , wiG
θ
, HiG ,
2 ÑiGθ , λRθ Lθ Sθ θ
n , λniG|n , λnj|n , Ū } such that:
3 1. Labor Market Clearing: The supply of labor by individuals in Equation 25 is
4 consistent with demand for labor by firms in Equation 16.
5 2. Floorspace Market Clearing: The market for floorspace clears as in Equation 23,
6 its price is consistent with residential populations 22 and commercial floorspace use
7 17, and total floor space is consistent with land developer optimality 21.
8 3. Goods Market Clearing: Non-tradable consumption matches non-tradable produc-
9 tion in each neighborhood, as in Equation 27.
10 4. Closed City: Populations add up to the city total.
11 4.8 Model Discussion
12 First of all, our model captures the direct distributional implications of changing access
13 to consumption, in addition to changing employment access. Transit improvements affect
14 how easily different worker types access consumption opportunities, and these effects also
15 depend on where they (want to) live, work and consume. Suppose travel costs fell between
16 low-income neighborhoods and locations in which non-tradable goods are cheap and high
17 in (type-specific) quality. Then low-income workers would become better off. Access to
18 consumption is more important to welfare for worker types with 1) larger expenditures on
19 non-tradables, 2) larger dispersion of preferences over consumption locations (more inelastic
20 demand), and 3) higher travel costs.
21 Next, consumption travel shapes the residential patterns of the city in a type-specific
22 manner. Workers now trade off access to non-tradables, along with access to employment
23 and higher rents in their residential decisions. Worker types with less dispersion in residential
24 amenities are better able to take advantage of both improved access to consumption and
25 employment in other locations.
26 Lastly, incorporating travel to consume non-tradables also has distributional implications
27 for access to employment across worker groups. Responding to changes in transit access,
28 consumers change where they consume non-tradables, trading off travel costs and type-
29 specific amenities and prices. Thus relative factor demand changes across locations. Since
221 firms selling non-tradables hire more low-income workers, low-income jobs move to where
2 residents are traveling more for consumption (thus demanding more non-tradable production
3 in those locations). High-income jobs in tradables may also move away from locations with
4 greater consumption travel, since commercial rents will rise in response to greater production
5 of non-tradables. Therefore, low (high) income jobs could move to locations closer or further
6 from where low (high) income workers live, locations with higher or lower wages for low
7 (high) income workers, or locations which are more or less productive for low (high) income
8 workers. Since commercial activity between tradable and non-tradable sectors reorganizes
9 across space, each worker group faces differential changes in expected access to employment or
10 expected income net of commuting. Therefore, it is an empirical question whether inequality
11 rises or falls.
12 5 Estimation
13 This section estimates the model from Section 4. First, using gravity specifications from the
14 model, we estimate workplace and consumption preferences and access across neighborhoods
15 and across worker groups. Second, we estimate type-specific work and consumption travel
16 costs, as well as associated elasticities. Third, we estimate parameters that govern the
17 dispersion of idiosyncratic residential amenities and residential spillovers by type. Fourth,
18 we estimate residential amenities across neighborhoods and across high- and low-income
19 workers. Fifth, we show how the model can be inverted to obtain unobservable endogenous
20 variables that rationalize the observed data as an equilibrium of the model. Finally, we
21 describe the calibration of remaining parameters to the data or the existing literature.
22 5.1 Estimating Consumption Preferences and Access
23 First, we estimate workplace and consumption preferences and access. For each worker type
24 θ ∈ {+, −}, we combine the consumption travel flow Equation 7 with the specification of
25 travel costs ϕSθ = ϵSθ κθ . The resulting gravity equation relates the variation in work travel
26 flows to the variation in travel times:
ln λSθ Sθ Sθ Sθ Sθ
nj|n = ηj − µn − ϕ τnj + unj . (30)
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