inversionModel: Function to invert model, so amenities, wages,...

In davidzarruk/IGCities: Simulate Impact of Different Urban Policies Through a General Equilibrium Model

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)
               

davidzarruk/IGCities documentation built on Sept. 28, 2024, 11:36 a.m.