NoPricesInversionModel: Function to invert model, so amenities, wages, productivities, and development density are chosen to match model to data. This function requires data on the amount of floorspace.

Description

Function to invert model, so amenities, wages, productivities, and development density are chosen to match model to data. This function requires data on the amount of floorspace.

Usage

NoPricesInversionModel(
  N,
  L_i,
  L_j,
  K,
  t_ij,
  alpha = 0.7,
  beta = 0.7,
  theta = 7,
  delta = 0.3585,
  rho = 0.9094,
  lambda = 0.01,
  epsilon = 0.01,
  mu = 0.3,
  eta = 0.15,
  nu_init = 0.05,
  tol = 10^-10,
  maxiter = 1000,
  FS
)

Value

A list containing the equilibrium values for the variables of the model. The reported variables are population (Li), employment (Lj), normalized rents (Q_norm), endogenous amenities (A), exogenous amenities (a), endogenous productivities (B), exogenous productivities (b), wages (w), density of development (varphi), aggregate welfare (U), share of commercial floorspace (ttheta), floorspace (FS), residential floorspace (FS_r) and commercial floorspace (FS_f)

Arguments

N: Integer - Number of locations.
L_i: Nx1 matrix - Number of residents in each location.
L_j: Nx1 matrix - Number of workers in each location.
K: Nx1 matrix - Land area
t_ij: NxN matrix - Travel times across all possible locations.
alpha: Float - Utility parameter that determines preferences for consumption.
beta: Float - Output elasticity wrt labor
theta: Float - Commuting elasticity and migration elasticity.
delta: Float - Decay parameter agglomeration
rho: Float - Decay parameter congestion
lambda: Float - Agglomeration force
epsilon: Float - Parameter that transforms travel times to commuting costs
mu: Float - Floorspace prod function: output elasticity wrt capital, 1-mu wrt land.
eta: Float - Congestion force
nu_init: Float - Convergence parameter to update wages. Default nu=0.01.
tol: Int - tolerance factor
maxiter: Integer - Maximum number of iterations for convergence. Default maxiter=1000.
FS: Nx1 array - Total floorspace in the location