Discussion of

“Highly DisaggregatedTopological Land Unavailability”by Chandler Lutz and Ben Sand

Chris Foote

Research DepartmentFederal Reserve Bank of Boston

November 29, 2017

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 1 / 10

Disclaimer: I do not speak for:

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 2 / 10

Disclaimer: I do not speak for:

Eric Rosengren, President of Boston Fed

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 2 / 10

Disclaimer: I do not speak for:

Eric Rosengren, President of Boston Fed Janet Yellen, Chair of Federal Reserve

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 2 / 10

Overview of Paper

Saiz elasticities often used to generate exogenous variation inhousing prices

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 3 / 10

Overview of Paper

Saiz elasticities often used to generate exogenous variation inhousing prices

No discussion of regulations in Lutz-Sand (LS) paper, onlyland unavailability.

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 3 / 10

Overview of Paper

Saiz elasticities often used to generate exogenous variation inhousing prices

No discussion of regulations in Lutz-Sand (LS) paper, onlyland unavailability.

Some differences between LS measure of land unavailability andthat of Saiz...

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 3 / 10

Overview of Paper

Saiz elasticities often used to generate exogenous variation inhousing prices

No discussion of regulations in Lutz-Sand (LS) paper, onlyland unavailability.

Some differences between LS measure of land unavailability andthat of Saiz...

... but many similarities, too.

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 3 / 10

Overview of Paper

Saiz elasticities often used to generate exogenous variation inhousing prices

No discussion of regulations in Lutz-Sand (LS) paper, onlyland unavailability.

Some differences between LS measure of land unavailability andthat of Saiz...

... but many similarities, too.

Remark: Paper could do a better job of spelling out similaritiesand differences, both for point estimates and standard errors ofsecond-stage regressions.

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 3 / 10

My remarks

I am going to focus primarily on the “circles vs. polygons” aspectof the paper

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 4 / 10

My remarks

I am going to focus primarily on the “circles vs. polygons” aspectof the paper

There are good reasons why Saiz uses 50km radii

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 4 / 10

My remarks

I am going to focus primarily on the “circles vs. polygons” aspectof the paper

There are good reasons why Saiz uses 50km radiiAuthors could think harder about model in Saiz (2010). Could thismodel be

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 4 / 10

My remarks

I am going to focus primarily on the “circles vs. polygons” aspectof the paper

There are good reasons why Saiz uses 50km radiiAuthors could think harder about model in Saiz (2010). Could thismodel be

. . . improved theoretically?

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 4 / 10

My remarks

I am going to focus primarily on the “circles vs. polygons” aspectof the paper

There are good reasons why Saiz uses 50km radiiAuthors could think harder about model in Saiz (2010). Could thismodel be

. . . improved theoretically?

. . . better implemented empirically?

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 4 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:Cities are circles with endogenously determined radii

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:Cities are circles with endogenously determined radiiCities have different amenities and productivities

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:Cities are circles with endogenously determined radiiCities have different amenities and productivitiesHouses are the same size across and within cities

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:Cities are circles with endogenously determined radiiCities have different amenities and productivitiesHouses are the same size across and within citiesPopulation/city area/city radii are all endogenous w.r.t amenitiesand productivities

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:Cities are circles with endogenously determined radiiCities have different amenities and productivitiesHouses are the same size across and within citiesPopulation/city area/city radii are all endogenous w.r.t amenitiesand productivitiesAmenities/productivity → Pop. → No. of houses → city area

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:Cities are circles with endogenously determined radiiCities have different amenities and productivitiesHouses are the same size across and within citiesPopulation/city area/city radii are all endogenous w.r.t amenitiesand productivitiesAmenities/productivity → Pop. → No. of houses → city areaSpatial equilibrium exists both within and across cities

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:Cities are circles with endogenously determined radiiCities have different amenities and productivitiesHouses are the same size across and within citiesPopulation/city area/city radii are all endogenous w.r.t amenitiesand productivitiesAmenities/productivity → Pop. → No. of houses → city areaSpatial equilibrium exists both within and across citiesJobs are all located in each city’s central business district (CBD)

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:Cities are circles with endogenously determined radiiCities have different amenities and productivitiesHouses are the same size across and within citiesPopulation/city area/city radii are all endogenous w.r.t amenitiesand productivitiesAmenities/productivity → Pop. → No. of houses → city areaSpatial equilibrium exists both within and across citiesJobs are all located in each city’s central business district (CBD)Per-mile (linear) commuting costs are the same across cities

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:Cities are circles with endogenously determined radiiCities have different amenities and productivitiesHouses are the same size across and within citiesPopulation/city area/city radii are all endogenous w.r.t amenitiesand productivitiesAmenities/productivity → Pop. → No. of houses → city areaSpatial equilibrium exists both within and across citiesJobs are all located in each city’s central business district (CBD)Per-mile (linear) commuting costs are the same across citiesRents at the edges of all cities are pinned down by constructioncosts (zero cost of marginal land)

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz (2010) Model

Saiz adapts the “urban model” to encompass land unavailability:Cities are circles with endogenously determined radiiCities have different amenities and productivitiesHouses are the same size across and within citiesPopulation/city area/city radii are all endogenous w.r.t amenitiesand productivitiesAmenities/productivity → Pop. → No. of houses → city areaSpatial equilibrium exists both within and across citiesJobs are all located in each city’s central business district (CBD)Per-mile (linear) commuting costs are the same across citiesRents at the edges of all cities are pinned down by constructioncosts (zero cost of marginal land)Higher rents at the CBD equalize utility there with utility at edge ofcity

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 5 / 10

Saiz Picture

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 6 / 10

City Area in Model

Φk : Radius of city k

Λk · πΦ2k = γHk

Φ2k =

γHkΛkπ

Φk =

√

γHkΛkπ

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 7 / 10

City Area in Model

Φk : Radius of city k

Λk : Fraction of developable land within city k ’s radius

Λk · πΦ2k = γHk

Φ2k =

γHkΛkπ

Φk =

√

γHkΛkπ

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 7 / 10

City Area in Model

Φk : Radius of city k

Λk : Fraction of developable land within city k ’s radius

γ: Size of each house in all cities

Λk · πΦ2k = γHk

Φ2k =

γHkΛkπ

Φk =

√

γHkΛkπ

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 7 / 10

City Area in Model

Φk : Radius of city k

Λk : Fraction of developable land within city k ’s radius

γ: Size of each house in all cities

Hk : Number of houses in city k

Λk · πΦ2k = γHk

Φ2k =

γHkΛkπ

Φk =

√

γHkΛkπ

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 7 / 10

Why is the model so important?Saiz Prop. 1: Amenity/productivity shocks raise house prices bymore in cities with less land

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 8 / 10

Why is the model so important?Saiz Prop. 1: Amenity/productivity shocks raise house prices bymore in cities with less land

Radius Φk has to increase by more in SF vs. required expansion inWichita

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 8 / 10

Why is the model so important?Saiz Prop. 1: Amenity/productivity shocks raise house prices bymore in cities with less land

Radius Φk has to increase by more in SF vs. required expansion inWichita

Undevelopable land within a city matters for that city’s houseprices, even though people are free to move across cities

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 8 / 10

Why is the model so important?Saiz Prop. 1: Amenity/productivity shocks raise house prices bymore in cities with less land

Radius Φk has to increase by more in SF vs. required expansion inWichita

Undevelopable land within a city matters for that city’s houseprices, even though people are free to move across citiesSaiz Prop. 2: Cities with low land availability tend to be moreproductive or have higher amenities

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 8 / 10

Why is the model so important?Saiz Prop. 1: Amenity/productivity shocks raise house prices bymore in cities with less land

Radius Φk has to increase by more in SF vs. required expansion inWichita

Undevelopable land within a city matters for that city’s houseprices, even though people are free to move across citiesSaiz Prop. 2: Cities with low land availability tend to be moreproductive or have higher amenities

High productivity/amentities in San Francisco make people want tolive there ...

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 8 / 10

Why is the model so important?Saiz Prop. 1: Amenity/productivity shocks raise house prices bymore in cities with less land

Radius Φk has to increase by more in SF vs. required expansion inWichita

Undevelopable land within a city matters for that city’s houseprices, even though people are free to move across citiesSaiz Prop. 2: Cities with low land availability tend to be moreproductive or have higher amenities

High productivity/amentities in San Francisco make people want tolive there ...... even though SF’s low land availability makes houses much moreexpensive than those in Wichita

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 8 / 10

Why is the model so important?Saiz Prop. 1: Amenity/productivity shocks raise house prices bymore in cities with less land

Radius Φk has to increase by more in SF vs. required expansion inWichita

Undevelopable land within a city matters for that city’s houseprices, even though people are free to move across citiesSaiz Prop. 2: Cities with low land availability tend to be moreproductive or have higher amenities

High productivity/amentities in San Francisco make people want tolive there ...... even though SF’s low land availability makes houses much moreexpensive than those in Wichita

Saiz Proposition 3: Population in the existing distribution of citiesshould be independent of the degree of land availability

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 8 / 10

Why is the model so important?Saiz Prop. 1: Amenity/productivity shocks raise house prices bymore in cities with less land

Radius Φk has to increase by more in SF vs. required expansion inWichita

Undevelopable land within a city matters for that city’s houseprices, even though people are free to move across citiesSaiz Prop. 2: Cities with low land availability tend to be moreproductive or have higher amenities

High productivity/amentities in San Francisco make people want tolive there ...... even though SF’s low land availability makes houses much moreexpensive than those in Wichita

Saiz Proposition 3: Population in the existing distribution of citiesshould be independent of the degree of land availability

Two cities with low land availability: San Francisco (big) vs. BentonHarbor, MI (small)

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 8 / 10

Why is the model so important?Saiz Prop. 1: Amenity/productivity shocks raise house prices bymore in cities with less land

Radius Φk has to increase by more in SF vs. required expansion inWichita

Undevelopable land within a city matters for that city’s houseprices, even though people are free to move across citiesSaiz Prop. 2: Cities with low land availability tend to be moreproductive or have higher amenities

High productivity/amentities in San Francisco make people want tolive there ...... even though SF’s low land availability makes houses much moreexpensive than those in Wichita

Saiz Proposition 3: Population in the existing distribution of citiesshould be independent of the degree of land availability

Two cities with low land availability: San Francisco (big) vs. BentonHarbor, MI (small)

Holding Λk constant, elasticities are lower in more populated areas

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 8 / 10

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 9 / 10

Two potential routes for the authors

1 Show that Saiz’s theoretical model can be improved usingzip-code level data

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 10 / 10

Two potential routes for the authors

1 Show that Saiz’s theoretical model can be improved usingzip-code level data

Are commuting costs linear?

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 10 / 10

Two potential routes for the authors

1 Show that Saiz’s theoretical model can be improved usingzip-code level data

Are commuting costs linear?Are all jobs located in the CBD?

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 10 / 10

Two potential routes for the authors

1 Show that Saiz’s theoretical model can be improved usingzip-code level data

Are commuting costs linear?Are all jobs located in the CBD?

2 Show that the empirical implementation of the Saiz model can beimproved with the use of zip code-level data.

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 10 / 10

Two potential routes for the authors

1 Show that Saiz’s theoretical model can be improved usingzip-code level data

Are commuting costs linear?Are all jobs located in the CBD?

2 Show that the empirical implementation of the Saiz model can beimproved with the use of zip code-level data.

Are cities really circular?

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 10 / 10

Two potential routes for the authors

1 Show that Saiz’s theoretical model can be improved usingzip-code level data

Are commuting costs linear?Are all jobs located in the CBD?

2 Show that the empirical implementation of the Saiz model can beimproved with the use of zip code-level data.

Are cities really circular?Saiz model has endogenous Φk , but regressions use 50km radiithat can overlap

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 10 / 10

Two potential routes for the authors

1 Show that Saiz’s theoretical model can be improved usingzip-code level data

Are commuting costs linear?Are all jobs located in the CBD?

2 Show that the empirical implementation of the Saiz model can beimproved with the use of zip code-level data.

Are cities really circular?Saiz model has endogenous Φk , but regressions use 50km radiithat can overlapHow does endogenous population matter in the regressions?(Serially correlated growth?)

Foote (Boston Fed) Lutz-Sand Discussion November 29, 2017 10 / 10