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Created September 28, 2022 13:56
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bianchi.ipynb
{
"cells": [
{
"cell_type": "markdown",
"id": "0f3336e1",
"metadata": {},
"source": [
"# Bianchi Overborrowing Model.\n",
"\n",
"Python implementation of \n",
"\n",
"* Overborrowing and Systemic Externalities (AER 2011) by Javier Bianchi\n",
"\n",
"Author: John Stachurski."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "cad1e184",
"metadata": {
"lines_to_next_cell": 1
},
"outputs": [],
"source": [
"import numpy as np\n",
"from numba import njit\n",
"from scipy.io import loadmat\n",
"from scipy.interpolate import interp1d\n",
"from scipy.optimize import root, newton\n",
"from collections import namedtuple\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"id": "9990f4f1",
"metadata": {},
"source": [
"from scipy.interpolate import interp1d\n",
"from quantecon.optimize.root_finding import brentq "
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "5c76f927",
"metadata": {
"lines_to_next_cell": 1
},
"outputs": [],
"source": [
"def d_infty(x, y):\n",
" return np.max(np.abs(x - y))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "3a2ac16e",
"metadata": {
"lines_to_next_cell": 1
},
"outputs": [],
"source": [
"# Define a namedtuple to store parameters and arrays\n",
"Model = namedtuple(\n",
" 'Model', ('σ', 'η', 'β', 'ω', 'κ', 'R', 'b_grid', 'yN', 'yT', 'P')\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "5818b7cc",
"metadata": {},
"outputs": [],
"source": [
"def create_overborrowing_model(σ=2, # CRRA utility parameter\n",
" η=(1/0.83)-1, # elasticity (elasticity = 0.83)\n",
" β=0.906, # discount factor\n",
" ω=0.3070, # share for tradables\n",
" κ=0.3235, # constraint parameter\n",
" r=0.04, # interest rate\n",
" n_B=100, # bond grid size\n",
" b_grid_min=-1.02, # grid min\n",
" b_grid_max=-0.2000): # grid max\n",
" \"\"\"\n",
" Creates an instance of the overborrowing model using default parameter\n",
" values from Bianchi AER 2011.\n",
"\n",
" \"\"\"\n",
"\n",
" # Read in Markov transitions and y grids from Bianchi's Matlab file\n",
" markov_data = loadmat('matlab/proc_shock.mat')\n",
" yT, yN, P = markov_data['yT'], markov_data['yN'], markov_data['Prob']\n",
" n_y = len(yT)\n",
"\n",
" # Shift P from column to row major\n",
" P = np.ascontiguousarray(P)\n",
"\n",
" # Set up grid for bond holdings\n",
" b_grid = np.linspace(b_grid_min, b_grid_max, n_B)\n",
"\n",
" return Model(σ=σ, η=η, β=β, ω=ω, κ=κ, R=(1 + r), \n",
" b_grid=b_grid, yN=yN, yT=yT, P=P)"
]
},
{
"cell_type": "markdown",
"id": "ae08f86f",
"metadata": {},
"source": [
"## Decentralized Equilibrium"
]
},
{
"cell_type": "markdown",
"id": "48625ab1",
"metadata": {},
"source": [
"Here's my effort to compute the decentralized equilibrium. "
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "07d2705e",
"metadata": {},
"outputs": [],
"source": [
"def initialize_decentralized_eq_search(model):\n",
"\n",
" # Unpack\n",
" σ, η, β, ω, κ, R, b_grid, yN, yT, P = model\n",
" n_B = len(b_grid)\n",
" n_y = len(yN)\n",
"\n",
" # Reshape\n",
" b = np.reshape(b_grid, (n_B, 1))\n",
" YT = np.reshape(yT, (1, n_y))\n",
" YN = np.reshape(yN, (1, n_y))\n",
"\n",
" bp = np.tile(b, (1, n_y)) # initial guess for bp\n",
"\n",
" c = b * R + YT - b # corresponding consumption \n",
" price = ((1 - ω) / ω) * c**(1+η)\n",
" b_bind = -κ * (price * YN + YT)\n",
" c_bind = b * R + YT - b_bind\n",
"\n",
" return c, c_bind, bp"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "b35a60a0",
"metadata": {},
"outputs": [],
"source": [
"@njit\n",
"def compute_marginal_utility(c, model):\n",
"\n",
" # Unpack and set up\n",
" σ, η, β, ω, κ, R, b_grid, yN, yT, P = model\n",
" n_y = len(yN)\n",
"\n",
" YN = np.reshape(yN, (1, n_y))\n",
"\n",
" # Compute an aggregated consumption good assuming c_N = y_N\n",
" totalc = ω * c**(-η) + (1-ω) * YN**(-η)\n",
"\n",
" # Compute marginal utility \n",
" mup = ω * totalc**(σ/η-1/η-1) * (c**(-η-1)) \n",
"\n",
" return mup"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "b6d5ba91",
"metadata": {},
"outputs": [],
"source": [
"def compute_exp_marginal_utility(mu, bp, model):\n",
"\n",
" # Unpack and set up\n",
" σ, η, β, ω, κ, R, b_grid, yN, yT, P = model\n",
" n_B, n_y = len(b_grid), len(yN)\n",
"\n",
" # Allocate memory\n",
" exp_mu = np.empty((n_B, n_y)) \n",
" mu_vals = np.empty(n_y)\n",
"\n",
" f = interp1d(b_grid, mu, axis=0, bounds_error=False, fill_value='extrapolate')\n",
"\n",
" # Compute expected marginal utility in today's grid\n",
" for i in range(n_B):\n",
" for j in range(n_y):\n",
" exp_mu[i, j] = β * R * f(bp[i, j]) @ P[j, :]\n",
" return exp_mu"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "95c61365",
"metadata": {},
"outputs": [],
"source": [
"def compute_binding_indicies(exp_mu, # Expected marginal utility\n",
" c_bind, # Current guess of c_bind\n",
" model, tol=1e-7): \n",
"\n",
" # Calculate utility differential when consumption is constrained\n",
" mu_constrained = compute_marginal_utility(c_bind, model)\n",
" constrained_euler_diff = mu_constrained - exp_mu\n",
"\n",
" # Indices where the constraints bind\n",
" return np.where(constrained_euler_diff > tol, 1, 0)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "5c397037",
"metadata": {},
"outputs": [],
"source": [
"def compute_consumption_at_constraint(c, model):\n",
"\n",
" # Unpack and set up\n",
" σ, η, β, ω, κ, R, b_grid, yN, yT, P = model\n",
" n_B, n_y = len(b_grid), len(yN)\n",
" b_grid_min, b_grid_max = b_grid[0], b_grid[-1]\n",
"\n",
" # Reshape\n",
" b = np.reshape(b_grid, (n_B, 1))\n",
" YT = np.reshape(yT, (1, n_y))\n",
" YN = np.reshape(yN, (1, n_y))\n",
"\n",
" # Get current price\n",
" price = (1 - ω) / ω * (c / YN)**(1 * η)\n",
"\n",
" # Obtain bond purchases at the constraint\n",
" b_bind = - κ * (price * YN + YT)\n",
" b_bind[b_bind > b_grid_max] = b_grid_max\n",
" b_bind[b_bind < b_grid_min] = b_grid_min\n",
" \n",
" # Update c_bind\n",
" c_bind = R * b + YT - b_bind\n",
" c_bind[c_bind < 0] = np.inf\n",
"\n",
" return c_bind"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "ff588a55",
"metadata": {},
"outputs": [],
"source": [
"def decentralized_update(c, # Current consumption policy\n",
" c_bind, # Consumption at constraint\n",
" bp, # Current bond purchase policy\n",
" model): # Instance of Model\n",
"\n",
" # Unpack and set up\n",
" σ, η, β, ω, κ, R, b_grid, yN, yT, P = model\n",
" b_grid_min, b_grid_max = b_grid[0], b_grid[-1]\n",
" n_B = len(b_grid)\n",
" n_y = len(yN)\n",
"\n",
" # Reshape\n",
" b = np.reshape(b_grid, (n_B, 1))\n",
" YT = np.reshape(yT, (1, n_y))\n",
" YN = np.reshape(yN, (1, n_y))\n",
"\n",
" # Make c a new array so it won't be modified in place\n",
" old_c = c\n",
" c = np.empty_like(old_c)\n",
"\n",
" # Compute expected marginal utility given current guess of c, bp\n",
" mu = compute_marginal_utility(old_c, model)\n",
" exp_mu = compute_exp_marginal_utility(mu, bp, model)\n",
"\n",
" # Indices where the constraints bind\n",
" idx_bind = compute_binding_indicies(exp_mu, c_bind, model)\n",
"\n",
" # Update consumption \n",
" for i in range(n_B):\n",
" for j in range(n_y):\n",
"\n",
" if idx_bind[i, j]: # Use borrowing constraint to set c\n",
" c[i, j] = c_bind[i, j]\n",
" else: # Use Euler equation to find c\n",
" def euler_diff(cc):\n",
" return (ω*cc**(-η) + (1-ω)*yN[j]**(-η))**(σ/η -1/η -1) \\\n",
" * ω*cc**(-η-1) - exp_mu[i, j]\n",
" c0 = old_c[i, j]\n",
" c[i, j] = newton(euler_diff, c0) \n",
"\n",
" # Update bp \n",
" bp = R * b + YT - c\n",
" bp[bp > b_grid_max] = b_grid_max\n",
" bp[bp < b_grid_min] = b_grid_min\n",
"\n",
" price = (1 - ω) / ω * (c / YN)**(1 * η)\n",
" c = R * b + YT - np.maximum(bp, -κ * (price * YN + YT))\n",
"\n",
" # Update c_bind based on the new c\n",
" c_bind = compute_consumption_at_constraint(c, model)\n",
"\n",
" return c, c_bind, bp, idx_bind"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "18143802",
"metadata": {},
"outputs": [],
"source": [
"def solve_decentralized_equilibrium(model, # Instance of Model\n",
" α=0.2, # Damping parameter\n",
" print_step=10, # Display frequency\n",
" iter_max=50_000, # Iteration tolerance\n",
" tol=1.0e-5): # Numerical tolerance\n",
"\n",
" \n",
" # Initialize \n",
" c, c_bind, bp = initialize_decentralized_eq_search(model)\n",
" current_iter = 0\n",
" error = tol + 1\n",
"\n",
" while error > tol and current_iter < iter_max:\n",
" \n",
" # Store current values and update\n",
" old_c = c\n",
" old_bp = bp\n",
" updates = decentralized_update(c, c_bind, bp, model)\n",
" c, c_bind, bp, idx_bind = updates\n",
"\n",
" # Compute error and update iteration\n",
" error = max(d_infty(c, old_c), d_infty(bp, old_bp))\n",
" current_iter += 1\n",
" if current_iter % print_step == 0:\n",
" print(f\"Current error = {error} at iteration {current_iter}.\")\n",
" \n",
" # Add smoothing \n",
" bp = α*bp + (1-α)*old_bp\n",
" c = α*c + (1-α)*old_c\n",
"\n",
" print(f\"DE converged at iteration {current_iter}.\")\n",
" return c, bp"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "3260d254",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Starting solver\n",
"\n",
"Current error = 0.07906818040072672 at iteration 10.\n",
"Current error = 0.03942241359330756 at iteration 20.\n",
"Current error = 0.021038530890898244 at iteration 30.\n",
"Current error = 0.006616254425749035 at iteration 40.\n",
"Current error = 0.0013697438352179847 at iteration 50.\n",
"Current error = 0.0002415452677952401 at iteration 60.\n",
"Current error = 3.938847455542405e-05 at iteration 70.\n",
"DE converged at iteration 78.\n",
"Solver done\n",
"\n"
]
}
],
"source": [
"# Solve the model\n",
"model = create_overborrowing_model()\n",
"print(\"Starting solver\\n\")\n",
"c, bp = solve_decentralized_equilibrium(model)\n",
"print(\"Solver done\\n\")\n",
"b_grid = model.b_grid"
]
},
{
"cell_type": "markdown",
"id": "80b737f2",
"metadata": {},
"source": [
"Here's a plot but this doesn't quite line up with the first figure created by main.m"
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "e580d8ff",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Plot\n",
"fig, ax = plt.subplots()\n",
"ax.plot(b_grid, b_grid, 'k--')\n",
"for i in range(16):\n",
" ax.plot(b_grid, bp[:, i])\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "198a82e5",
"metadata": {},
"source": [
"## Planner's Problem"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "17cda715",
"metadata": {},
"outputs": [],
"source": [
"# Create model and unpack \n",
"model = create_overborrowing_model()\n",
"σ, η, β, ω, κ, R, b_grid, yN, yT, P = model\n",
"n_B, n_y = len(b_grid), len(yN)\n",
"b_grid_min, b_grid_max = b_grid[0], b_grid[-1]"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "c4cffbdc",
"metadata": {},
"outputs": [],
"source": [
"# Reshape\n",
"b = np.reshape(b_grid, (n_B, 1))\n",
"YT = np.reshape(yT, (1, n_y))\n",
"YN = np.reshape(yN, (1, n_y))"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "f6f62bee",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Current error = 0.07906818040072672 at iteration 10.\n",
"Current error = 0.03942241359330756 at iteration 20.\n",
"Current error = 0.021038530890898244 at iteration 30.\n",
"Current error = 0.006616254425749035 at iteration 40.\n",
"Current error = 0.0013697438352179847 at iteration 50.\n",
"Current error = 0.0002415452677952401 at iteration 60.\n",
"Current error = 3.938847455542405e-05 at iteration 70.\n",
"DE converged at iteration 78.\n"
]
}
],
"source": [
"# Solve decentralized to get initial conditions\n",
"c_de, bp_de = solve_decentralized_equilibrium(model)\n",
"c_bind_de = compute_consumption_at_constraint(c_de, model)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "491d2d4f",
"metadata": {},
"outputs": [],
"source": [
"# Calculate utility differential when consumption is constrained\n",
"exp_mu_de = compute_exp_marginal_utility(c_de, bp_de, model)\n",
"mu_constrained_de = compute_marginal_utility(c_bind_de, model)\n",
"constrained_euler_diff_de = mu_constrained_de - exp_mu_de"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "f367ce5c",
"metadata": {},
"outputs": [],
"source": [
"# Get binding indices\n",
"idx_bind_de = compute_binding_indicies(exp_mu_de, c_bind_de, model)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "3b86d325",
"metadata": {
"lines_to_next_cell": 1
},
"outputs": [],
"source": [
"euler_diff_de = np.where(idx_bind_de, constrained_euler_diff_de, 0.0)\n",
"lagrange_de = euler_diff_de"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "718d5da8",
"metadata": {
"lines_to_next_cell": 1
},
"outputs": [],
"source": [
"def psi(c):\n",
" return ((1 - ω) / ω) * (η + 1) * κ * (c / YN)**η"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "febd59c9",
"metadata": {},
"outputs": [],
"source": [
"# Set some initial conditions\n",
"lagrange_sp = lagrange_de / (1 - psi(c_de)) \n",
"idx_bind_sp = idx_bind_de\n",
"c_bind = c_bind_de # Added by JS"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "adb84369",
"metadata": {},
"outputs": [],
"source": [
"c = np.copy(c_de)\n",
"bp = np.copy(bp_de)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "f8eb8017",
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [],
"source": [
"α = 0.02\n",
"tol = 1e-5\n",
"euler_tol = 1e-7\n",
"error = tol + 1\n",
"current_iter = 0\n",
"iter_max = 100_000\n",
"print_step = 10"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "21a9fcd0",
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Current error = 0.10060453106394263 at iteration 10.\n",
"Current error = 0.08220122658202111 at iteration 20.\n",
"Current error = 0.06716438693297122 at iteration 30.\n",
"Current error = 0.05487819415420414 at iteration 40.\n",
"Current error = 0.044839480134495235 at iteration 50.\n",
"Current error = 0.03663711989287033 at iteration 60.\n",
"Current error = 0.029935194387143316 at iteration 70.\n",
"Current error = 0.02445923330262767 at iteration 80.\n",
"Current error = 0.01998497440889546 at iteration 90.\n",
"Current error = 0.01632917913585208 at iteration 100.\n",
"Current error = 0.013342128230700245 at iteration 110.\n",
"Current error = 0.010901490163311878 at iteration 120.\n",
"Current error = 0.00890731116699428 at iteration 130.\n",
"Current error = 0.0072779217370366744 at iteration 140.\n",
"Current error = 0.005946591941988433 at iteration 150.\n",
"Current error = 0.004858798569455369 at iteration 160.\n",
"Current error = 0.003969992185246074 at iteration 170.\n",
"Current error = 0.0032437726581204807 at iteration 180.\n",
"Current error = 0.0026503984306756045 at iteration 190.\n",
"Current error = 0.0021655684851226153 at iteration 200.\n",
"Current error = 0.0017694271206463164 at iteration 210.\n",
"Current error = 0.0014457507840496264 at iteration 220.\n",
"Current error = 0.001181283651183196 at iteration 230.\n",
"Current error = 0.0009651947486027934 at iteration 240.\n",
"Current error = 0.0008273589918097457 at iteration 250.\n",
"Current error = 0.0007797870562655795 at iteration 260.\n",
"Current error = 0.0007399847196214449 at iteration 270.\n",
"Current error = 0.0007018606101993896 at iteration 280.\n",
"Current error = 0.0006631998029427155 at iteration 290.\n",
"Current error = 0.0006241703354015193 at iteration 300.\n",
"Current error = 0.000585533033624408 at iteration 310.\n",
"Current error = 0.0005480290069526106 at iteration 320.\n",
"Current error = 0.0005106261903811138 at iteration 330.\n",
"Current error = 0.0004758041732191298 at iteration 340.\n",
"Current error = 0.00044305635959096534 at iteration 350.\n",
"Current error = 0.0004109408790120561 at iteration 360.\n",
"Current error = 0.00037973947407854425 at iteration 370.\n",
"Current error = 0.00034967710992961365 at iteration 380.\n",
"Current error = 0.0003209268563302281 at iteration 390.\n",
"Current error = 0.00029361521590676176 at iteration 400.\n",
"Current error = 0.0002678276139052027 at iteration 410.\n",
"Current error = 0.00024361389924831833 at iteration 420.\n",
"Current error = 0.00022099360856286943 at iteration 430.\n",
"Current error = 0.00019996091486906842 at iteration 440.\n",
"Current error = 0.00018048919922741824 at iteration 450.\n",
"Current error = 0.00016253519988862486 at iteration 460.\n",
"Current error = 0.00014604271668416935 at iteration 470.\n",
"Current error = 0.00013094586793482854 at iteration 480.\n",
"Current error = 0.0001171719060515386 at iteration 490.\n",
"Current error = 0.00010464363509399277 at iteration 500.\n",
"Current error = 9.328144611409073e-05 at iteration 510.\n",
"Current error = 8.300499371682868e-05 at iteration 520.\n",
"Current error = 7.373455097559045e-05 at iteration 530.\n",
"Current error = 6.539209641132082e-05 at iteration 540.\n",
"Current error = 5.7902152060806955e-05 at iteration 550.\n",
"Current error = 5.119241440221245e-05 at iteration 560.\n",
"Current error = 4.5194205104959195e-05 at iteration 570.\n",
"Current error = 3.984277045643303e-05 at iteration 580.\n",
"Current error = 3.50774553976585e-05 at iteration 590.\n",
"Current error = 3.0841774955714385e-05 at iteration 600.\n",
"Current error = 2.708340314327984e-05 at iteration 610.\n",
"Current error = 2.3754096841077654e-05 at iteration 620.\n",
"Current error = 2.0809569769575376e-05 at iteration 630.\n",
"Current error = 1.8209329270657548e-05 at iteration 640.\n",
"Current error = 1.5916486628020365e-05 at iteration 650.\n",
"Current error = 1.3897549876240589e-05 at iteration 660.\n",
"Current error = 1.2122206447084949e-05 at iteration 670.\n",
"Current error = 1.056310156100082e-05 at iteration 680.\n"
]
}
],
"source": [
"while error > tol and current_iter < iter_max:\n",
" \n",
" old_c = np.copy(c)\n",
" old_bp = np.copy(bp)\n",
"\n",
" mup = compute_marginal_utility(c, model)\n",
"\n",
" lfh_sp = mup + lagrange_sp * psi(c)\n",
"\n",
" rhs_sp = compute_exp_marginal_utility(lfh_sp, bp, model)\n",
"\n",
" # This is equation u_T +mu*psi= β*R E [(u_T(t+1)+mu_t+1 ]+mu_t\n",
" lagrange_sp = lfh_sp - β * R * rhs_sp \n",
" lagrange_sp[idx_bind_sp == 0] = 0\n",
"\n",
" for i in range(n_B):\n",
" for j in range(n_y):\n",
" \n",
" if lagrange_sp[i, j] >= euler_tol: # Borrowing constraint binds\n",
" c[i, j] = c_bind[i, j]\n",
" idx_bind_sp[i, j] = 1\n",
"\n",
" else: # Use the Euler equation \n",
" def euler_diff(cc):\n",
" return (ω*cc**(-η) + (1-ω)*yN[j]**(-η))**(σ/η-1/η-1) \\\n",
" * ω * cc**(-η-1) - rhs_sp[i, j]\n",
" c0 = c[i, j]\n",
" c[i, j] = root(euler_diff, c0).x\n",
" idx_bind_sp[i, j] = 0\n",
" \n",
" bp = R * b + YT - c\n",
" bp[bp > b_grid_max] = b_grid_max\n",
" bp[bp < b_grid_min] = b_grid_min\n",
"\n",
" price = ((1 - ω) / ω) * (c / YN)**(1+η)\n",
"\n",
" # Check collateral constraint\n",
" c = R * b + YT - np.maximum(bp, -κ * (price * YN + YT))\n",
" price = ((1 - ω) / ω) * (c / YN)**(1+η)\n",
" bp = R * b + YT - c\n",
"\n",
" error = d_infty(c, old_c)\n",
"\n",
" # Add smoothing\n",
" bp = α*bp + (1-α)*old_bp\n",
" c = α*c + (1-α)*old_c\n",
"\n",
" # Compute c_bind\n",
" bmax_collat = -κ * (price * YN + YT)\n",
" c_bind = R * b + YT - bmax_collat\n",
"\n",
" # Compute error and update iteration\n",
" current_iter += 1\n",
" if current_iter % print_step == 0:\n",
" print(f\"Current error = {error} at iteration {current_iter}.\")"
]
},
{
"cell_type": "markdown",
"id": "585b1f50",
"metadata": {},
"source": [
"Here's my current output. You can see it doesn't quite correspond to Fig 1 in the paper."
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "acefd347",
"metadata": {
"lines_to_next_cell": 2
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"y_point = 0\n",
"ax.plot(b_grid, b_grid, 'k--')\n",
"ax.plot(b_grid, bp_de[:, y_point], label='decentralized')\n",
"ax.plot(b_grid, bp[:, y_point], label='planner')\n",
"ax.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dba1a120",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"jupytext": {
"cell_metadata_filter": "-all",
"main_language": "python",
"notebook_metadata_filter": "-all"
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.12"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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