Population Density across the City: The Case of 1900 ManhattanJason BarrRutgers University, NewarkNovember 6, 2013

Motivation• Little work in economics has explored how population bursts

determined land use patterns within the city during period of rapid urbanization.

• Land use today is a direct product of decisions made over a century ago.• Buildings are durable by nature and expensive to tear down.• Zoning regulations have tended to “lock-in” uses that were in

place circa 1916.• Landmark preservation also serves similar purpose.

• Aim to test theories of determinants of urban spatial structure before land use controls.

Current Residential Buildings Built before 1917*

*Includes conversions to resid.

Landmark Districts in Manhattan Today

Urban Density in the 19th C.• Average densities within cities remained

around 125-150 people per acre, despite rapid urbanization.• Land annexations kept pace with

population growth.• However, within cities, very unequal

distribution of populations.

Urban Density in the 19th C

NYC Density Today (2010)Borough 2010 Pop Density

Bronx 1,385,108 51.5

Brooklyn 2,504,700 55.9

Manhattan 1,585,873 112.6Queens 2,230,722 32.0Staten Island 468,730 12.4Pelham, NY 12,396 8.8

NYC 8,175133 42.3

Note: All densities are people per acre

Research Questions

• What role did the pre-European ecology and topography play? • How did local amenities, including access to

public transportation, and parks affect density?• How did location to Broadway, downtown and

rivers affect density?• Why the Lower East Side?• Building scale and the problem of tenement

reform.

Basic Theory: Density

(demand) Density Housing(supply) Density Structuralsize Fam

Familyper HousingPer Acre HousingFam size

FamHouse

AcreHouse

FamPop

AcrePopDensity

#/

#

Basic Theory: Density• Positively related to amount of housing per acre (e.g.,

more floors per acre, means more people per acre.)• A higher price for housing will increase structural density.

• Negatively related to housing per person. The greater the demand for larger houses per family, the lower the density at a location.• A higher price for housing will reduce H/Family, and thus increase

density.

• The greater the price of housing per square foot, the more density, cet. par.

Theory: Demand• Agents choose housing quantity subject to budge constraint:

Y=Z+P*H+TX.• TX= cost of commuting distance X• Assume there is a quantity of neighborhood amenity, A, that

will affect price of housing (e.g. parks, access to transportation).

• Assume A is negatively related to distance• Given spatial equilibrium condition:• Price of housing falls from center to compensate for commuting

costs.• Price of housing falls from center to compensate for loss of

amenity.• Density falls from center

Theory: Income & Density

• Income can affect density in negative or positive way depending on how higher income people value amenity.• If rich have high valuation for amenity, then they will

outbid poor to live closer to the center.• This will bid up price of housing, increasing structural

density, but rich will also use their income to buy more housing.• ”Central Park Effect”: High Structural Density but Low

Housing Density.• Standard relationship between income and distance to

center can be inverted (similar to Paris or Madrid).

Theory: Supply

• Housing reformers decried the fixed plot sizes of 25’ x 100’ as being bad for health and promoting excess density.• They argued that building tenements on larger

plots would reduce building density.• This would not be true if there were constant

returns to scale with building.

Theory: Supply

• Building housing with capital (K)--# floors, and Land (L):

• If we assume L is exogenously determined, then structural density—floors per acre (FAR):

• if CRS,

LrKLPK

1

11

LrPK

11

iP

LKFAR

Manhattan• Amenities (hypothesized affect on density):• Access to public transportation (the Els). (+)• Access to parks (+)• Access to high ground (+)• Closeness to “paisanos” (+)

• Disamenities:• Poor drainage (+ or -)

• Location-based (for jobs, retail or recreation):• Distance to downtown (+)• Distance to Broadway (+)• Distance the rivers (+ or -).

• Supply: Block size (-)

Mannahatta• Pre-European ecology could affect later settlement patterns in a

few ways.

• Early lock-in: If early development creates local economies of scale and fixed-cost “lock-in”, then attractive locations in the 17th century are likely to predict density in the early 20th century.• Locations on Manhattan favorable to early agriculture might be a predictor of

later density.• Location of Oak Tulip trees is important because they grow on land good for

agriculture (on slopes, not too wet, not too dry).

• Health and disease: • low-lying wetlands were breeding grounds for disease; higher elevations were

more salubrious.• Sewage removal was more likely to be worse in low lying areas.

Mannahatta

Sanderson (2009)

Mannahatta

Mannahatta

Els Map

Density at the Block Level

Immigration Patterns

MA of density vs distance from City Hall

Results w/o Demographics

The Lower East Side

The Lower East Side

foreign

Extreme Density and Enthicity

- 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 800

900

1000

1100

1200

1300

Russian/Pol Aus. Hung.

Density vs Ethnicity in LES

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1800

900

1000

1100

1200

1300

Density vs HHI

Extreme Density and Family Size

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85800

900

1000

1100

1200

1300

Density vs Fraction of Pop. With 6 or more people per Household on Block

Economies of Scale Results