NYC-WTC_000187725

NYC 9/11 Public Portal Document

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represent the JK submarkets in which the housing stock is positive.According to the CATLAS procedure for large scale problems, the Jacobian matrix of (9) was obtained and set equal to zero on the off-diagonal elements. Then, using the diagonal elements, a Newton-Raphson procedure was applied to adjust the rent vector iteratively until converge occurred, on the equilibrium. Various starting points are used for the housing rent vector. As long as rents are within 30% of the correct equilibrium values, the solution is obtained in seven or fewer iterations for housing market equilibrium. Policy runs are faster than Base Runs because the starting point for convergence is the pre-policy equilibrium point and most reasonable policies do not deviate greatly from such an equilibrium. The convergence tolerance used in all runs was that the maximum absolute value percent deviation in rents be within 0.1% of the rent of the previous iteration and that demanded and occupied stocks in each (j.k) be within 0.1% of each other. The estimated model's calibrated results are shown in Table 2.3. Predicted results for housing rents fit fairly well with rents computed from observed values by means of Rjj^ = aj^CWjj^)^. For single family housing, the average percentage error in average rent by zone (APE) is 16%, for condominiums it is 20.4%, and for rental apartments it is 14.6%. The model predicts, on average, that households spend 15.7% of potential income on commuting, 19.2% on housing rent, and 65.1% on shopping expenditures. The average percentage error in occupancy rates prior to the adjustment of the fixed effects is 4.8%. The average percentage error in shopping trips prior to the adjustment of the Kj^'s is 38.9%. The travel time elasticity of housing demand is -0.367 on average, and the rent elasticity of housing demand is -0.363 on average.Table 2.4 shows how these elasticities vary by income levels and with respect to commuting mode. Both elasticities are higher for the lowest income groups.

The total number of possible equations is 598 for Manhattan (2 housing types by 299 zones), 120 for Queens (3 housing types by 40 zones), 201 for Brooklyn (3 housing types by 67 zones), 126 for the Bronx (3 housing types by 42 zones) and ten for the suburban counties (2 housing types by 5 counties). Although this gives 1,055 possible zones, some zones have no housing of one or more types. Most such zones having only one housing type are in Manhattan. T9 These elasticities are computed by changing the travel time or rent of a residential choice (j,k,m) by one percent, keeping all else constant, and then taking the weighted average of such elasticities across all the (j,k,m).

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