Why are Skyscrapers so Tall? Land Use and the Spatial Location of Buildings in New York Jason Barr, Rutgers U., Newark Jeffrey Cohen, Hartford U. AEA Meetings 2011

Skyscrapers Most recognizable form of urban land use. Determinants of their height not well-studied. If skyscrapers contribute to agglomeration effects, then factors that drive height can determine urban growth.

Variables of Interest Focus here is on the locational or land based aspects of height—i.e., those elements of height that are spatially based. Likely that effects of location based variables vary across space. Variables of interest: ◦ Plot size ◦ Bedrock depths ◦ Distance to cores (Wall St & Grand Central)

Variation in Building Height (all types of uses, )

Avg. Elevation and Bedrock Depth Relative to Sea Level, meters

Related Lit.: Skyscrapers Barr (2010): time series of height. Barr (forthcoming): building level of height; OLS and spatial to test for competitive effect. Barr et al. (2010): bedrock depths had little influence on location of business districts.

General OLS findings of this work Plot size is positively related to height (no statistical evidence of endogeneity). Plot elasticity about Height “gradient” about 10% per mile from the core. Bedrock depths do not affect height, on average. Cost of digging to bedrock are relatively modest.

Geographically Weighted Regressions Cohen and Coughlin (2010) McMillen and Redfearn (2010) McMillen and McDonald (2004) Conclusion of work: GWR shows evidence of varied effects across space: ◦ Airport noise on housing prices in Atlanta. ◦ Chicago housing prices near Els. ◦ Zoning regulations across space.

Geographically Weighted Regression Model β i = (∑ w ij X j X’ j ) -1 (∑ w ij X j Y j ), X j =explanatory vars. for all obs. except i ; Y j is a vector heights for all observations except i ; w ij is the weight that building j is given for building i ; and the summations given by ∑ are taken over all buildings, j.

Weight Matrix Gaussian weights: d = Cartesian distance between two buildings. b = bandwidth parameter (here b=0.026). Note: w ij =0 if d=0 (i.e. building not connected to self).

OLS Results for NYC: ln(height) Ln(Plot)0.131FIRE/Emp. t (8.6)**(5.0)** Rental dummy-0.08Population t (2.4)*(1.4) Depth to bedrock Materials Costs t (0.8)(4.3)** Distance to core-0.095Interest Rate t (3.6)**(2.3) * Zoning Dummy-0.452Constant3.7 (4.1)** (23.0)** Multiple, (3.5)** Observations458 FAR, R-squared0.35 (4.8)** * Sig. at 95%, ** Sig. at 99%. Robust t-stats below coeffs.

GWR Model Results 4 nonparametric vars: Distance, Ln(Plot), Bedrock Depth, Year Other parametric controls (given above) Descriptive Stats for GWR vars: distanceLn(plot)depthyearconstant Mean Median St. Dev Min Max Coeff. of Var

Significance Tests for Non- Stationarity VariableSiP-Value Constant Dist Core (miles) * Ln(Plot) * Depth to bedrock year

Bedrock depth coefficients

Distance to core coefficients

Plot size coefficients

Concluding Remarks Evidence of spatial variation in effects on height. Distance: ◦ Downtown largest effect ◦ Midtown: east-west effect Plot size: ◦ Downtown largest effect ◦ Midtown: north-south effect Bedrock: ◦ Slight effect overall ◦ Positive effects downtown

Concluding Remarks Next steps: ◦ Hypothesis tests ◦ Robustness checks ◦ Further explorations on implications for theories of urban growth.