inversionModel {IGCities}

Function to invert model, so amenities, wages, productivities, and development density are chosen to match model to data.

Description

Function to invert model, so amenities, wages, productivities, and development density are chosen to match model to data.

Usage

inversionModel(
  N,
  L_i,
  L_j,
  Q,
  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 = 0.1548,
  nu_init = 0.005,
  tol = 10^-10,
  maxiter = 1000
)

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.

Q

Nx1 matrix - Floorspace prices

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 elast 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.

Value

Equilibrium values.

Examples

N=5
L_i = c(63, 261, 213, 182, 113)
L_j = c(86, 278, 189, 180, 99)
Q = c(2123, 1576, 1371, 1931, 1637)
K = c(0.44, 1.45, 1.15, 0.87, 0.58)
t_ij = rbind(c(0.0, 6.6, 5.5, 5.6, 6.4),
             c(6.7, 0.0, 3.9, 4.6, 4.4),
             c(5.5, 3.9, 0.0, 2.8, 3.0),
             c(5.6, 4.6, 2.8, 0.0, 2.7),
             c(6.4, 4.4, 3.0, 2.7, 0.0))

inversionModel(N=N,
               L_i=L_i,
               L_j=L_j,
               Q=Q,
               K=K,
               t_ij=t_ij)