{
"cells": [
{
"cell_type": "markdown",
"id": "f5e7b1d0",
"metadata": {
"id": "f5e7b1d0"
},
"source": [
"![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\")
"
]
},
{
"cell_type": "markdown",
"id": "7735eea6",
"metadata": {},
"source": [
"# Uncertain Expansion Example Notebook"
]
},
{
"cell_type": "markdown",
"id": "75201d8b",
"metadata": {},
"source": [
"# 1 Preliminaries \n",
"\n",
"## 1.1 Model Setup\n",
"$$\n",
"\\begin{align}\n",
"X_{t+1} \\left( \\mathsf{q} \\right) = & \\hspace{.2cm} \\psi^x \\left[D_t \\left( \\mathsf{q} \\right), X_{t} \\left( \\mathsf{q} \\right), {\\sf q} W_{t+1}, {\\sf q} \\right], \\cr\n",
"\\log G_{t+1} \\left( \\mathsf{q} \\right) - \\log G_t \\left( \\mathsf{q} \\right) = & \\hspace{.2cm} \\psi^g \\left[ D_t \\left( \\mathsf{q} \\right), X_{t} \\left( \\mathsf{q},\n",
" \\right), {\\sf q} W_{t+1}, {\\sf q} \\right], \\cr\n",
"{\\widehat C}_t \\left( \\mathsf{q} \\right) = & \\hspace{.2cm} \\kappa \\left[D_t \\left( \\mathsf{q} \\right), X_{t} \\left( \\mathsf{q} \\right) \\right] + {\\widehat G}_t \\left( \\mathsf{q} \\right).\n",
"\\end{align}\n",
"$$\n",
"\n",
"In addition, there are a set of first-order conditions and co-state equations detailed in Chapter 8 of the book. These are compiled automatically by the code.\n",
"\n",
"\n",
"## 1.2 Inputs\n",
"\n",
"The `Expansion Suite` uses the function `uncertain_expansion` to approximate a solution to the above system locally. The user must specify several sets of inputs. Define the relevant variables:\n",
"\n",
"```{list-table}\n",
"* - Input\n",
" - Description\n",
" - Notation in text\n",
"* - `control_variables`\n",
" - Variables chosen by the decision-maker at time $t$\n",
" - $D_t$\n",
"* - `state_variables`\n",
" - Variables that describe the current state of the system\n",
" - $X_t$\n",
"* - `shock_variables`\n",
" - Variables representing different entries of the Brownian motion variable\n",
" - $W_t$\n",
"```\n",
"\n",
"The $t+1$ variables will be automatically created from this. For example, if a state variable is inputted as `Z_t`, an additional state variable `Z_tp1` will be automatically generated. \n",
"We also need to define the equilibrium conditions:\n",
"\n",
"```{list-table}\n",
"* - Input\n",
" - Description\n",
" - Notation in text\n",
"* - `kappa`\n",
" - Log share of capital not allocated to consumption\n",
" - $\\kappa(X_t(q),D_t(q))$\n",
"* - `growth`\n",
" - Law of motion for $\\hat{G}_{t+1}-\\hat{G}_t$\n",
" - $\\psi^g(D_t(q),X_t(q),qW_{t+1},q)$\n",
"* - `state_equations`\n",
" - Law of motion for state variables\n",
" - $\\psi^x(D_t(q),X_t(q),qW_{t+1},q)$\n",
"```\n",
"\n",
"The remaining equilibrium conditions will be automatically computed by the code. The user must also define a list of parameters and their corresponding values. This can be done by specifying pairs of inputs such as `beta = 0.99` or `gamma = 1.01` within the body of the function `create_args`. \n",
"\n",
"Note that the user must define the variables and parameters *before* defining the equations. Make sure that the **equations use the same expressions for variables and parameters** as previously defined by the user. \n",
"\n",
"The output is of class `ModelSolution`, which stores the coefficients for the linear-quadratic approximation for the jump and state variables; continuation values; consumption growth; and log change of measure, as well as the steady-state values of each variables. \n",
"\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"id": "f92a0d85",
"metadata": {},
"source": [
"# 2 Example\n",
"We will now walk through the computation using the example above. Begin by installing the following libraries and downloading `RiskUncertaintyValue`, which contains the functions required to solve the model:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "f0d30383",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import os\n",
"import sys\n",
"import sympy as sp\n",
"workdir = os.getcwd()\n",
"# !git clone https://github.com/lphansen/RiskUncertaintyValue \n",
"workdir = os.getcwd() + '/RiskUncertaintyValue' \n",
"sys.path.insert(0, workdir+'/src') \n",
"import numpy as np\n",
"import seaborn as sns\n",
"import autograd.numpy as anp\n",
"from scipy import optimize\n",
"np.set_printoptions(suppress=True)\n",
"np.set_printoptions(linewidth=200)\n",
"from IPython.display import display, HTML\n",
"from BY_example_sol import disp\n",
"display(HTML(\"\"))\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import norm\n",
"\n",
"from lin_quad import LinQuadVar\n",
"from lin_quad_util import E, concat, next_period, cal_E_ww, lq_sum, N_tilde_measure, E_N_tp1, log_E_exp, kron_prod, distance\n",
"from utilities import mat, vec, sym\n",
"from uncertain_expansion import uncertain_expansion, generate_symbols_and_args, compile_equations, get_parameter_value, \\\n",
" generate_ss_function, automate_step_1, change_parameter_value\n",
"from elasticity import exposure_elasticity, price_elasticity\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"np.set_printoptions(suppress=True)\n",
"import pickle\n",
"import pandas as pd\n",
"from scipy.optimize import fsolve\n",
"# import sympy as sp"
]
},
{
"cell_type": "markdown",
"id": "bd7ccfd2",
"metadata": {},
"source": [
"## 2.1 Parameters\n",
"Use the following function to define and set the values for your parameters."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d0589f27",
"metadata": {},
"outputs": [],
"source": [
"def create_args():\n",
" # Define parameters here\n",
" sigma_k1 = 0.92 * anp.sqrt(3)\n",
" sigma_k2 = 0.4 * anp.sqrt(3)\n",
" sigma_k3 = 0.0\n",
" sigma_z1 = 0.0\n",
" sigma_z2 = 5.7 * anp.sqrt(3)\n",
" sigma_z3 = 0.0\n",
" sigma_y1 = 0.0\n",
" sigma_y2 = 0.0\n",
" sigma_y3 = 0.00031 * anp.sqrt(3)\n",
" \n",
" # Base parameters\n",
" delta = 0.01/4\n",
" a = 0.0922\n",
" epsilon = 1.0\n",
" gamma = 1.001 #Do not change this name\n",
" rho = 1.001 #Do not change this name\n",
" beta = anp.exp(-epsilon * delta) #Do not change this name\n",
" \n",
" # Capital evolution parameters\n",
" phi_1 = 1 / 8 /4\n",
" phi_2 = 8.0\n",
" beta_k = 0.04 /4\n",
" alpha_k = 0.04 /4\n",
" \n",
" # Other states\n",
" beta_z = 0.056 /4\n",
" beta_2 = 0.194 /4\n",
" mu_2 = 6.3 * (10**(-6))\n",
" \n",
" # Return as a dictionary\n",
" return locals()\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "34fc3cb5",
"metadata": {},
"source": [
"## 2.2 Variables\n",
"Define your variables as below. You may only have one growth variable and one perturbation variable. Apart from this, you may add more variables to the list as you wish."
]
},
{
"cell_type": "markdown",
"id": "34b7a11b",
"metadata": {},
"source": [
"Control variable : $i = \\frac{I_{k,t}}{K_t}$\n",
"\n",
"State variable: $X = [Z_1, Z_2]$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "7615f2d0",
"metadata": {},
"outputs": [],
"source": [
"# Define variable names\n",
"control_variables = [\"imk_t\"]\n",
"state_variables = [\"Z_t\", \"Y_t\"]\n",
"growth_variables = [\"log_gk_t\"]\n",
"perturbation_variable = [\"q_t\"]\n",
"shock_variables = [\"W1_t\", \"W2_t\", \"W3_t\"]"
]
},
{
"cell_type": "markdown",
"id": "2b4da5f2",
"metadata": {},
"source": [
"The user does not need to change the following code, which creates symbols for the defined parameters and variables. "
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "152ab471",
"metadata": {},
"outputs": [],
"source": [
"parameter_names, args = generate_symbols_and_args(create_args)\n",
"globals().update(parameter_names)\n",
"variables = control_variables + state_variables + growth_variables + perturbation_variable + shock_variables\n",
"variables_tp1 = [var + \"p1\" for var in variables]\n",
"symbols = {var: sp.Symbol(var) for var in variables + variables_tp1}\n",
"globals().update(symbols) "
]
},
{
"cell_type": "markdown",
"id": "a701f77b",
"metadata": {},
"source": [
"## 2.3 Define Equilibrium Conditions\n",
"Ensure that you use the same names for your variables and parameters from before. You must have one output constraint and one capital growth equation, but you may add as many state equations as you wish. The first-order conditions and co-state equations will be automatically handled and do not need to be specified."
]
},
{
"cell_type": "markdown",
"id": "8a129614",
"metadata": {},
"source": [
"State variables, growth variable and consumption-capital ratio:\n",
"\n",
"$$\n",
"X_t = [Z_1, Z_2]\\\\\n",
"\\hat G = \\log K\\\\\n",
"\\hat C_t - \\hat G_t = \\kappa(D_t, X_t)\n",
"$$\n",
"\n",
"The evolution equations:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"X_{t+1} =& \\psi^x (D_t(q), X_t(q), qW_{t+1}, q) \\\\\n",
"\\hat G_{t+1} - \\hat G_{t} =& \\psi^g (D_t(q), X_t(q), qW_{t+1}, q)\\\\\n",
"\\kappa(D_t, X_t) =& \\log{\\alpha-D_t}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b4433e3b",
"metadata": {},
"outputs": [],
"source": [
"# Output constraint\n",
"kappa = sp.log(a - imk_t)\n",
"\n",
"# Capital growth equation\n",
"growth = epsilon * (phi_1 * sp.log(1. + phi_2 * imk_t) - alpha_k + beta_k * Z_t \\\n",
" - q_t**2 * 0.5 * (sigma_k1**2 + sigma_k2**2 + sigma_k3**2) * sp.exp(Y_t)) \\\n",
" + sp.sqrt(epsilon) * sp.exp(0.5 * Y_t) * (sigma_k1 * W1_tp1 + sigma_k2 * W2_tp1 + sigma_k3 * W3_tp1) \n",
"\n",
"# Technology growth equation\n",
"technology_growth = Z_t - epsilon * beta_z * Z_t \\\n",
" + sp.sqrt(epsilon) * sp.exp(0.5 * Y_t) * (sigma_z1 * W1_tp1 + sigma_z2 * W2_tp1 + sigma_z3 * W3_tp1)\n",
"\n",
"# Volatility growth equation\n",
"volatility_growth = Y_t - epsilon * beta_2 * (1 - mu_2 * sp.exp(-Y_t)) \\\n",
" - q_t**2 * 0.5 * (sigma_y1**2 + sigma_y2**2 + sigma_y3**2) * sp.exp(-Y_t) * epsilon \\\n",
" + sp.exp(-0.5 * Y_t) * (sigma_y1 * W1_tp1 + sigma_y2 * W2_tp1 + sigma_y3 * W3_tp1) * sp.sqrt(epsilon)\n",
"\n",
"# State equations\n",
"state_equations = [technology_growth, volatility_growth]\n"
]
},
{
"cell_type": "markdown",
"id": "bd416d24",
"metadata": {},
"source": [
"## 2.4 Code Settings\n",
"You may additionally set the following:\n",
"* **Initial guess** for steady-state variables. This must have the same length as the number of variables\n",
"* **Recursive terms initialization**. These are initializations for terms like $\\log N_t^*$ and $\\hat{R}_t-\\hat{V}_t$, which may be loaded from a previous solution.\n",
"* **Convergence tolerance**. How small the maximum error across the approximated terms must be before the algorithm is considered to have converged.\n",
"* **Maximum iterations**. The maximum number of iterations for the algorithm can take.\n",
"* **Save location**. Save the model solution to this location so that it can be accessed later."
]
},
{
"cell_type": "markdown",
"id": "bfb1a135",
"metadata": {},
"source": [
"The order of the initial guess is as follows:\n",
"$$\n",
"\\left[\n",
" {\\widehat V_t} - {\\widehat C_t}, \\widehat C_t - \\widehat K_t, D_t, MX_t, MG_t, \\widehat G_{t+1} - \\widehat G_t, X_t \n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "c98abc6e",
"metadata": {},
"outputs": [],
"source": [
"# Initial guess for the solution: the order is:\n",
"\n",
"initial_guess = np.concatenate([np.array([-2.1968994 , -4.123193 , anp.exp(-2.57692626)]),np.ones(3),np.array([0.01937842, 0. , -11.97496092])])\n",
"\n",
"savepath = None\n",
"init_util = None\n",
"iter_tol = 1e-5\n",
"max_iter = 50\n",
"\n",
"#Code for loading pre-solution\n",
"# with open(savepath,'rb') as f:\n",
"# preload = pickle.load(f)\n",
"# init_util = preload['util_sol']"
]
},
{
"cell_type": "markdown",
"id": "d24a71a4",
"metadata": {},
"source": [
"## 2.5 Run Code\n",
"You are now ready to run the function `uncertain_expansion`. You do not need to change anything in the following code."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "160c739d",
"metadata": {
"tags": [
"hide-output"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[Z_tp1, Y_tp1, log_gk_tp1]\n",
"[-sqrt(epsilon)*(W1_tp1*sigma_k1 + W2_tp1*sigma_k2 + W3_tp1*sigma_k3)*exp(0.5*Y_t) - epsilon*(Z_t*beta_k - alpha_k + phi_1*log(imk_t*phi_2 + 1.0) - 0.5*q_t**2*(sigma_k1**2 + sigma_k2**2 + sigma_k3**2)*exp(Y_t)) + log_gk_tp1, Z_t*beta_z*epsilon - Z_t + Z_tp1 - sqrt(epsilon)*(W1_tp1*sigma_z1 + W2_tp1*sigma_z2 + W3_tp1*sigma_z3)*exp(0.5*Y_t), -Y_t + Y_tp1 + beta_2*epsilon*(-mu_2*exp(-Y_t) + 1) - sqrt(epsilon)*(W1_tp1*sigma_y1 + W2_tp1*sigma_y2 + W3_tp1*sigma_y3)*exp(-0.5*Y_t) + 0.5*epsilon*q_t**2*(sigma_y1**2 + sigma_y2**2 + sigma_y3**2)*exp(-Y_t)]\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968993672636477\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154922961948\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045179079975\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154922961948\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123192938559636\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154925317954\n",
" Equation 2: 8.34543252281605E-8\n",
" Equation 3: 0.000581045193629781\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154925317954\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727306135664\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 9.19587321845938E-8\n",
" Equation 3: 0.000581033504244238\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151722814\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0000000149011612\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614286549239\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0000000149011612\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941719258452\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0000000149011612\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581047494947445\n",
" Equation 4: -0.00650614247126997\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145155298725040\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842028876096\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154926661940\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184092771\n",
" Equation 4: -0.00650614262019363\n",
" Equation 5: -0.0508941711677371\n",
" Equation 6: -0.0000145154926661940\n",
" Equation 7: 0.0145338156371238\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 1.4901161193880158e-08\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151993512\n",
" Equation 8: 2.08616256714322E-10\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.974960741559176\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941625348600\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 8.87586832504228E-9\n",
"Variable Dictionary:\n",
" vmk_t: -2.190969671823048\n",
" log_cmk_t: -4.126677382067626\n",
" imk_t: 0.07606369322178491\n",
" m0_t: 0.6061091869275164\n",
" m1_t: 0.00027091309285176557\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853376275452266\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 3.34013856026841E-9\n",
" Equation 2: 0.00000608440719052084\n",
" Equation 3: -0.00000187658854466921\n",
" Equation 4: -0.00000563217594579807\n",
" Equation 5: -0.0000137841625971271\n",
" Equation 6: -3.34013856026841E-9\n",
" Equation 7: 1.20480242449261E-9\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896408239047855\n",
" log_cmk_t: -4.126671003857404\n",
" imk_t: 0.07606349139493146\n",
" m0_t: 0.605767370898716\n",
" m1_t: 1.0526260585288875e-08\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343692950123\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -8.07718909118238E-13\n",
" Equation 2: -4.49280905812088E-8\n",
" Equation 3: 1.31242751666427E-8\n",
" Equation 4: -3.57598943685755E-9\n",
" Equation 5: -5.35580195965482E-10\n",
" Equation 6: 8.07718909118238E-13\n",
" Equation 7: -9.07102951780425E-12\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410969301474\n",
" log_cmk_t: -4.126671037648796\n",
" imk_t: 0.07606349266754037\n",
" m0_t: 0.6057671544702979\n",
" m1_t: -1.3428522154266637e-11\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343899843996\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -2.72091377206962E-15\n",
" Equation 2: 1.45716327892842E-10\n",
" Equation 3: -4.67853811247920E-11\n",
" Equation 4: -1.22541490843453E-11\n",
" Equation 5: 6.83248383285139E-13\n",
" Equation 6: 2.72091377206962E-15\n",
" Equation 7: 2.94608087925141E-14\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968993672636477\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154922961948\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045179079975\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154922961948\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123192938559636\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154925317954\n",
" Equation 2: 8.34543252281605E-8\n",
" Equation 3: 0.000581045193629781\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154925317954\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727306135664\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 9.19587321845938E-8\n",
" Equation 3: 0.000581033504244238\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151722814\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0000000149011612\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614286549239\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0000000149011612\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941719258452\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0000000149011612\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581047494947445\n",
" Equation 4: -0.00650614247126997\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145155298725040\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842028876096\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154926661940\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184092771\n",
" Equation 4: -0.00650614262019363\n",
" Equation 5: -0.0508941711677371\n",
" Equation 6: -0.0000145154926661940\n",
" Equation 7: 0.0145338156371238\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 1.4901161193880158e-08\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151993512\n",
" Equation 8: 2.08616256714322E-10\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.974960741559176\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941625348600\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 8.87586832504228E-9\n",
"Variable Dictionary:\n",
" vmk_t: -2.190969671823048\n",
" log_cmk_t: -4.126677382067626\n",
" imk_t: 0.07606369322178491\n",
" m0_t: 0.6061091869275164\n",
" m1_t: 0.00027091309285176557\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853376275452266\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 3.34013856026841E-9\n",
" Equation 2: 0.00000608440719052084\n",
" Equation 3: -0.00000187658854466921\n",
" Equation 4: -0.00000563217594579807\n",
" Equation 5: -0.0000137841625971271\n",
" Equation 6: -3.34013856026841E-9\n",
" Equation 7: 1.20480242449261E-9\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896408239047855\n",
" log_cmk_t: -4.126671003857404\n",
" imk_t: 0.07606349139493146\n",
" m0_t: 0.605767370898716\n",
" m1_t: 1.0526260585288875e-08\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343692950123\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -8.07718909118238E-13\n",
" Equation 2: -4.49280905812088E-8\n",
" Equation 3: 1.31242751666427E-8\n",
" Equation 4: -3.57598943685755E-9\n",
" Equation 5: -5.35580195965482E-10\n",
" Equation 6: 8.07718909118238E-13\n",
" Equation 7: -9.07102951780425E-12\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410969301474\n",
" log_cmk_t: -4.126671037648796\n",
" imk_t: 0.07606349266754037\n",
" m0_t: 0.6057671544702979\n",
" m1_t: -1.3428522154266637e-11\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343899843996\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -2.72091377206962E-15\n",
" Equation 2: 1.45716327892842E-10\n",
" Equation 3: -4.67853811247920E-11\n",
" Equation 4: -1.22541490843453E-11\n",
" Equation 5: 6.83248383285139E-13\n",
" Equation 6: 2.72091377206962E-15\n",
" Equation 7: 2.94608087925141E-14\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Iteration 1: mu_0 error = 5.75982404e-20\n",
"Iteration 1: J1 error = 0.000561672114\n",
"Iteration 1: J2 error = 0.000554623791\n",
"Iteration 1: error = 0.000561672114\n",
"Iteration 2: mu_0 error = 7.79270311e-20\n",
"Iteration 2: J1 error = 8.52838789e-08\n",
"Iteration 2: J2 error = 7.83537071e-08\n",
"Iteration 2: error = 8.52838789e-08\n"
]
}
],
"source": [
"ModelSol = uncertain_expansion(control_variables, state_variables, shock_variables, variables, variables_tp1,\n",
" kappa, growth, state_equations, initial_guess, parameter_names,\n",
" args, approach = '1', init_util = init_util, iter_tol = iter_tol, max_iter = max_iter,\n",
" savepath=savepath)"
]
},
{
"cell_type": "markdown",
"id": "6ead42d5",
"metadata": {},
"source": [
"You can also run the model solution for different parameters using code like the one displayed below, which loops over values of $\\gamma$ and $\\lambda$ and saves them to appropriately named outputs:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "696cb7ad",
"metadata": {
"tags": [
"hide-output"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[Z_tp1, Y_tp1, log_gk_tp1]\n",
"[-sqrt(epsilon)*(W1_tp1*sigma_k1 + W2_tp1*sigma_k2 + W3_tp1*sigma_k3)*exp(0.5*Y_t) - epsilon*(Z_t*beta_k - alpha_k + phi_1*log(imk_t*phi_2 + 1.0) - 0.5*q_t**2*(sigma_k1**2 + sigma_k2**2 + sigma_k3**2)*exp(Y_t)) + log_gk_tp1, Z_t*beta_z*epsilon - Z_t + Z_tp1 - sqrt(epsilon)*(W1_tp1*sigma_z1 + W2_tp1*sigma_z2 + W3_tp1*sigma_z3)*exp(0.5*Y_t), -Y_t + Y_tp1 + beta_2*epsilon*(-mu_2*exp(-Y_t) + 1) - sqrt(epsilon)*(W1_tp1*sigma_y1 + W2_tp1*sigma_y2 + W3_tp1*sigma_y3)*exp(-0.5*Y_t) + 0.5*epsilon*q_t**2*(sigma_y1**2 + sigma_y2**2 + sigma_y3**2)*exp(-Y_t)]\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968993672636477\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154922961948\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045179079975\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154922961948\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123192938559636\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154925317954\n",
" Equation 2: 8.34543252281605E-8\n",
" Equation 3: 0.000581045193629781\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154925317954\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727306135664\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 9.19587321845938E-8\n",
" Equation 3: 0.000581033504244238\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151722814\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0000000149011612\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614286549239\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0000000149011612\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941719258452\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0000000149011612\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581047494947445\n",
" Equation 4: -0.00650614247126997\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145155298725040\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842028876096\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154926661940\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184092771\n",
" Equation 4: -0.00650614262019363\n",
" Equation 5: -0.0508941711677371\n",
" Equation 6: -0.0000145154926661940\n",
" Equation 7: 0.0145338156371238\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 1.4901161193880158e-08\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151993512\n",
" Equation 8: 2.08616256714322E-10\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.974960741559176\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941625348600\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 8.87586832504228E-9\n",
"Variable Dictionary:\n",
" vmk_t: -2.190969671823048\n",
" log_cmk_t: -4.126677382067626\n",
" imk_t: 0.07606369322178491\n",
" m0_t: 0.6061091869275164\n",
" m1_t: 0.00027091309285176557\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853376275452266\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 3.34013856026841E-9\n",
" Equation 2: 0.00000608440719052084\n",
" Equation 3: -0.00000187658854466921\n",
" Equation 4: -0.00000563217594579807\n",
" Equation 5: -0.0000137841625971271\n",
" Equation 6: -3.34013856026841E-9\n",
" Equation 7: 1.20480242449261E-9\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896408239047855\n",
" log_cmk_t: -4.126671003857404\n",
" imk_t: 0.07606349139493146\n",
" m0_t: 0.605767370898716\n",
" m1_t: 1.0526260585288875e-08\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343692950123\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -8.07718909118238E-13\n",
" Equation 2: -4.49280905812088E-8\n",
" Equation 3: 1.31242751666427E-8\n",
" Equation 4: -3.57598943685755E-9\n",
" Equation 5: -5.35580195965482E-10\n",
" Equation 6: 8.07718909118238E-13\n",
" Equation 7: -9.07102951780425E-12\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410969301474\n",
" log_cmk_t: -4.126671037648796\n",
" imk_t: 0.07606349266754037\n",
" m0_t: 0.6057671544702979\n",
" m1_t: -1.3428522154266637e-11\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343899843996\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -2.72091377206962E-15\n",
" Equation 2: 1.45716327892842E-10\n",
" Equation 3: -4.67853811247920E-11\n",
" Equation 4: -1.22541490843453E-11\n",
" Equation 5: 6.83248383285139E-13\n",
" Equation 6: 2.72091377206962E-15\n",
" Equation 7: 2.94608087925141E-14\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968993672636477\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154922961948\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045179079975\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154922961948\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123192938559636\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154925317954\n",
" Equation 2: 8.34543252281605E-8\n",
" Equation 3: 0.000581045193629781\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154925317954\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727306135664\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 9.19587321845938E-8\n",
" Equation 3: 0.000581033504244238\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151722814\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0000000149011612\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614286549239\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0000000149011612\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941719258452\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0000000149011612\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581047494947445\n",
" Equation 4: -0.00650614247126997\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145155298725040\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842028876096\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154926661940\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184092771\n",
" Equation 4: -0.00650614262019363\n",
" Equation 5: -0.0508941711677371\n",
" Equation 6: -0.0000145154926661940\n",
" Equation 7: 0.0145338156371238\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 1.4901161193880158e-08\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151993512\n",
" Equation 8: 2.08616256714322E-10\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.974960741559176\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941625348600\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 8.87586832504228E-9\n",
"Variable Dictionary:\n",
" vmk_t: -2.190969671823048\n",
" log_cmk_t: -4.126677382067626\n",
" imk_t: 0.07606369322178491\n",
" m0_t: 0.6061091869275164\n",
" m1_t: 0.00027091309285176557\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853376275452266\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 3.34013856026841E-9\n",
" Equation 2: 0.00000608440719052084\n",
" Equation 3: -0.00000187658854466921\n",
" Equation 4: -0.00000563217594579807\n",
" Equation 5: -0.0000137841625971271\n",
" Equation 6: -3.34013856026841E-9\n",
" Equation 7: 1.20480242449261E-9\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896408239047855\n",
" log_cmk_t: -4.126671003857404\n",
" imk_t: 0.07606349139493146\n",
" m0_t: 0.605767370898716\n",
" m1_t: 1.0526260585288875e-08\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343692950123\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -8.07718909118238E-13\n",
" Equation 2: -4.49280905812088E-8\n",
" Equation 3: 1.31242751666427E-8\n",
" Equation 4: -3.57598943685755E-9\n",
" Equation 5: -5.35580195965482E-10\n",
" Equation 6: 8.07718909118238E-13\n",
" Equation 7: -9.07102951780425E-12\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410969301474\n",
" log_cmk_t: -4.126671037648796\n",
" imk_t: 0.07606349266754037\n",
" m0_t: 0.6057671544702979\n",
" m1_t: -1.3428522154266637e-11\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343899843996\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -2.72091377206962E-15\n",
" Equation 2: 1.45716327892842E-10\n",
" Equation 3: -4.67853811247920E-11\n",
" Equation 4: -1.22541490843453E-11\n",
" Equation 5: 6.83248383285139E-13\n",
" Equation 6: 2.72091377206962E-15\n",
" Equation 7: 2.94608087925141E-14\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Iteration 1: mu_0 error = 5.75982404e-20\n",
"Iteration 1: J1 error = 0.000561672114\n",
"Iteration 1: J2 error = 0.000554623791\n",
"Iteration 1: error = 0.000561672114\n",
"Iteration 2: mu_0 error = 7.79270311e-20\n",
"Iteration 2: J1 error = 8.52838789e-08\n",
"Iteration 2: J2 error = 7.83537071e-08\n",
"Iteration 2: error = 8.52838789e-08\n",
"[Z_tp1, Y_tp1, log_gk_tp1]\n",
"[-sqrt(epsilon)*(W1_tp1*sigma_k1 + W2_tp1*sigma_k2 + W3_tp1*sigma_k3)*exp(0.5*Y_t) - epsilon*(Z_t*beta_k - alpha_k + phi_1*log(imk_t*phi_2 + 1.0) - 0.5*q_t**2*(sigma_k1**2 + sigma_k2**2 + sigma_k3**2)*exp(Y_t)) + log_gk_tp1, Z_t*beta_z*epsilon - Z_t + Z_tp1 - sqrt(epsilon)*(W1_tp1*sigma_z1 + W2_tp1*sigma_z2 + W3_tp1*sigma_z3)*exp(0.5*Y_t), -Y_t + Y_tp1 + beta_2*epsilon*(-mu_2*exp(-Y_t) + 1) - sqrt(epsilon)*(W1_tp1*sigma_y1 + W2_tp1*sigma_y2 + W3_tp1*sigma_y3)*exp(-0.5*Y_t) + 0.5*epsilon*q_t**2*(sigma_y1**2 + sigma_y2**2 + sigma_y3**2)*exp(-Y_t)]\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968993672636477\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358308937536\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402750360566\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358308937536\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123192938559636\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358339741041\n",
" Equation 2: 8.34543252281605E-8\n",
" Equation 3: -0.250402731337517\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358339741041\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727306135664\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 9.19587321845938E-8\n",
" Equation 3: -0.250402772870156\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338151722814\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0000000149011612\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667619978970\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0000000149011612\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276348856458\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402741459475\n",
" Equation 4: -0.0160667614640710\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358337698094\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358333908130\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743770222\n",
" Equation 4: -0.0160667617533380\n",
" Equation 5: -0.0600276341268781\n",
" Equation 6: -0.00557358333908130\n",
" Equation 7: 0.0145338156371238\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338151993512\n",
" Equation 8: 2.08616256714322E-10\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276254416350\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 8.87586832504228E-9\n",
"Variable Dictionary:\n",
" vmk_t: -2.4990412620769447\n",
" log_cmk_t: -3.8188399396908546\n",
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"\n",
"Substituted Equations:\n",
" Equation 1: -0.000301532242793315\n",
" Equation 2: 0.0386458943704886\n",
" Equation 3: -0.0700506740870134\n",
" Equation 4: -0.00243311177293890\n",
" Equation 5: -0.00632609272245618\n",
" Equation 6: 0.000301532242793311\n",
" Equation 7: 0.00000954912477009462\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.5931567574112755\n",
" log_cmk_t: -3.7289026398205487\n",
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"\n",
"Substituted Equations:\n",
" Equation 1: -0.0000631230706961651\n",
" Equation 2: 0.0242757003594813\n",
" Equation 3: -0.0273500781652956\n",
" Equation 4: -0.0000658967204150204\n",
" Equation 5: 0.00121462877264170\n",
" Equation 6: 0.0000631230706961668\n",
" Equation 7: 0.00000762066205286290\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.638449426639722\n",
" log_cmk_t: -3.6719560781959393\n",
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"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000116178985622405\n",
" Equation 2: 0.00844161572937896\n",
" Equation 3: -0.00394579816985263\n",
" Equation 4: 0.000455193416019484\n",
" Equation 5: 0.000762942441250680\n",
" Equation 6: -0.0000116178985622370\n",
" Equation 7: 0.00000349570250840351\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6434607937665993\n",
" log_cmk_t: -3.6648097637088544\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00000621795361824447\n",
" Equation 2: 0.00136260774340347\n",
" Equation 3: -0.000298049568510650\n",
" Equation 4: 0.000160809857545657\n",
" Equation 5: 0.0000690675012368642\n",
" Equation 6: -0.00000621795361824187\n",
" Equation 7: 5.49742981579334E-7\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6427858769844788\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00000184305788123503\n",
" Equation 2: 0.0000594400760061120\n",
" Equation 3: 0.000144296664201377\n",
" Equation 4: 0.0000342938686621053\n",
" Equation 5: -0.00000585695644572449\n",
" Equation 6: -0.00000184305788123330\n",
" Equation 7: 2.31843045443193E-8\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.642293766679322\n",
" log_cmk_t: -3.6640636968089506\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 7.46372257013662E-7\n",
" Equation 2: 0.0000277636445140672\n",
" Equation 3: 0.0000518888867312994\n",
" Equation 4: 0.0000136351400746582\n",
" Equation 5: -4.01170693472762E-7\n",
" Equation 6: -7.46372257011928E-7\n",
" Equation 7: 8.74118862188855E-9\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6420121515313357\n",
" log_cmk_t: -3.6641583544202163\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 1.03154115142085E-7\n",
" Equation 2: 0.00000220689972829646\n",
" Equation 3: 0.00000858569987771673\n",
" Equation 4: 0.00000151851223440837\n",
" Equation 5: 1.64163410802474E-7\n",
" Equation 6: -1.03154115141217E-7\n",
" Equation 7: 6.98362936490254E-10\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.641954245079993\n",
" log_cmk_t: -3.664181927080247\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -2.37681131477763E-8\n",
" Equation 2: -6.53054561983168E-7\n",
" Equation 3: -0.00000185359081250613\n",
" Equation 4: -5.11343997488395E-7\n",
" Equation 5: 5.83304151165340E-8\n",
" Equation 6: 2.37681131477763E-8\n",
" Equation 7: -2.06777919439793E-10\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.641964570247612\n",
" log_cmk_t: -3.664177927424757\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -8.68045460164502E-10\n",
" Equation 2: -2.32881025574727E-8\n",
" Equation 3: -6.83356736475016E-8\n",
" Equation 4: -5.12985432448571E-8\n",
" Equation 5: 1.01894310930291E-8\n",
" Equation 6: 8.68045460164502E-10\n",
" Equation 7: -7.42287698321520E-12\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649683024446\n",
" log_cmk_t: -3.6641777715933546\n",
" imk_t: 0.06657476759180911\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 1.34565882742299E-11\n",
" Equation 2: 3.83401310699583E-10\n",
" Equation 3: 1.03601990875113E-9\n",
" Equation 4: -9.98819836908749E-9\n",
" Equation 5: 1.03558297045201E-9\n",
" Equation 6: -1.34565882742299E-11\n",
" Equation 7: 1.21114056284011E-13\n",
" Equation 8: -7.17289651426266E-43\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649633748024\n",
" log_cmk_t: -3.664177773441421\n",
" imk_t: 0.06657476763076715\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 2.46759730704316E-12\n",
" Equation 2: 5.56350521208060E-11\n",
" Equation 3: 2.05184508272893E-10\n",
" Equation 4: -3.08540203108887E-9\n",
" Equation 5: 1.36583756896872E-10\n",
" Equation 6: -2.46759730704316E-12\n",
" Equation 7: 1.88174129056584E-14\n",
" Equation 8: 2.22415843880715E-41\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649633748024\n",
" log_cmk_t: -3.664177773441421\n",
" imk_t: 0.06657476763076715\n",
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" m1_t: -2.6035421405655454e-09\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 2.46759730704316E-12\n",
" Equation 2: 5.56350521208060E-11\n",
" Equation 3: 2.05184508272893E-10\n",
" Equation 4: -3.08540203108887E-9\n",
" Equation 5: 1.36583756896872E-10\n",
" Equation 6: -2.46759730704316E-12\n",
" Equation 7: 1.88174129056584E-14\n",
" Equation 8: 2.22415843880715E-41\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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" log_gk_t: 0.01937842\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968993672636477\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358308937536\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402750360566\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358308937536\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123192938559636\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358339741041\n",
" Equation 2: 8.34543252281605E-8\n",
" Equation 3: -0.250402731337517\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358339741041\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727306135664\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 9.19587321845938E-8\n",
" Equation 3: -0.250402772870156\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338151722814\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0000000149011612\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667619978970\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0000000149011612\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276348856458\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0000000149011612\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402741459475\n",
" Equation 4: -0.0160667614640710\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358337698094\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842028876096\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358333908130\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743770222\n",
" Equation 4: -0.0160667617533380\n",
" Equation 5: -0.0600276341268781\n",
" Equation 6: -0.00557358333908130\n",
" Equation 7: 0.0145338156371238\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 1.4901161193880158e-08\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338151993512\n",
" Equation 8: 2.08616256714322E-10\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.974960741559176\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276254416350\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 8.87586832504228E-9\n",
"Variable Dictionary:\n",
" vmk_t: -2.4990412620769447\n",
" log_cmk_t: -3.8188399396908546\n",
" imk_t: 0.07107896538859211\n",
" m0_t: 0.6708625092622533\n",
" m1_t: 0.11979133410667753\n",
" mg_t: 1.0000000000000009\n",
" log_gk_t: 0.004078415544384683\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -0.000301532242793315\n",
" Equation 2: 0.0386458943704886\n",
" Equation 3: -0.0700506740870134\n",
" Equation 4: -0.00243311177293890\n",
" Equation 5: -0.00632609272245618\n",
" Equation 6: 0.000301532242793311\n",
" Equation 7: 0.00000954912477009462\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.5931567574112755\n",
" log_cmk_t: -3.7289026398205487\n",
" imk_t: 0.06875688288000965\n",
" m0_t: 0.548219847461722\n",
" m1_t: -0.02307775158220332\n",
" mg_t: 0.9999999999999996\n",
" log_gk_t: 0.003704197375870328\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -0.0000631230706961651\n",
" Equation 2: 0.0242757003594813\n",
" Equation 3: -0.0273500781652956\n",
" Equation 4: -0.0000658967204150204\n",
" Equation 5: 0.00121462877264170\n",
" Equation 6: 0.0000631230706961668\n",
" Equation 7: 0.00000762066205286290\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.638449426639722\n",
" log_cmk_t: -3.6719560781959393\n",
" imk_t: 0.06698705419426898\n",
" m0_t: 0.5238878109405951\n",
" m1_t: -0.014533835038480864\n",
" mg_t: 0.9999999999999991\n",
" log_gk_t: 0.003413314651906058\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000116178985622405\n",
" Equation 2: 0.00844161572937896\n",
" Equation 3: -0.00394579816985263\n",
" Equation 4: 0.000455193416019484\n",
" Equation 5: 0.000762942441250680\n",
" Equation 6: -0.0000116178985622370\n",
" Equation 7: 0.00000349570250840351\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6434607937665993\n",
" log_cmk_t: -3.6648097637088544\n",
" imk_t: 0.06662582872674504\n",
" m0_t: 0.541038981121622\n",
" m1_t: -0.0013164503468426191\n",
" mg_t: 0.9999999999999993\n",
" log_gk_t: 0.0033515161371127622\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00000621795361824447\n",
" Equation 2: 0.00136260774340347\n",
" Equation 3: -0.000298049568510650\n",
" Equation 4: 0.000160809857545657\n",
" Equation 5: 0.0000690675012368642\n",
" Equation 6: -0.00000621795361824187\n",
" Equation 7: 5.49742981579334E-7\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6427858769844788\n",
" log_cmk_t: -3.663844175070631\n",
" imk_t: 0.06656774129621157\n",
" m0_t: 0.5481768298579396\n",
" m1_t: 0.00011164568845901794\n",
" mg_t: 0.9999999999999996\n",
" log_gk_t: 0.00334151534734168\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00000184305788123503\n",
" Equation 2: 0.0000594400760061120\n",
" Equation 3: 0.000144296664201377\n",
" Equation 4: 0.0000342938686621053\n",
" Equation 5: -0.00000585695644572449\n",
" Equation 6: -0.00000184305788123330\n",
" Equation 7: 2.31843045443193E-8\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.642293766679322\n",
" log_cmk_t: -3.6640636968089506\n",
" imk_t: 0.06657255574351265\n",
" m0_t: 0.5493062604246624\n",
" m1_t: 7.64708886791394e-06\n",
" mg_t: 0.9999999999999997\n",
" log_gk_t: 0.0033422862639455736\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 7.46372257013662E-7\n",
" Equation 2: 0.0000277636445140672\n",
" Equation 3: 0.0000518888867312994\n",
" Equation 4: 0.0000136351400746582\n",
" Equation 5: -4.01170693472762E-7\n",
" Equation 6: -7.46372257011928E-7\n",
" Equation 7: 8.74118862188855E-9\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6420121515313357\n",
" log_cmk_t: -3.6641583544202163\n",
" imk_t: 0.06657432656093322\n",
" m0_t: 0.5499712673821173\n",
" m1_t: -3.1292639966093615e-06\n",
" mg_t: 0.9999999999999999\n",
" log_gk_t: 0.003342567081851625\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 1.03154115142085E-7\n",
" Equation 2: 0.00000220689972829646\n",
" Equation 3: 0.00000858569987771673\n",
" Equation 4: 0.00000151851223440837\n",
" Equation 5: 1.64163410802474E-7\n",
" Equation 6: -1.03154115141217E-7\n",
" Equation 7: 6.98362936490254E-10\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.641954245079993\n",
" log_cmk_t: -3.664181927080247\n",
" imk_t: 0.06657485733246968\n",
" m0_t: 0.5500820857994922\n",
" m1_t: -1.111886782868601e-06\n",
" mg_t: 1.0\n",
" log_gk_t: 0.0033426527571405983\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -2.37681131477763E-8\n",
" Equation 2: -6.53054561983168E-7\n",
" Equation 3: -0.00000185359081250613\n",
" Equation 4: -5.11343997488395E-7\n",
" Equation 5: 5.83304151165340E-8\n",
" Equation 6: 2.37681131477763E-8\n",
" Equation 7: -2.06777919439793E-10\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.641964570247612\n",
" log_cmk_t: -3.664177927424757\n",
" imk_t: 0.066574770978437\n",
" m0_t: 0.5500568860059079\n",
" m1_t: -1.9422963398257696e-07\n",
" mg_t: 1.0\n",
" log_gk_t: 0.003342638870283248\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -8.68045460164502E-10\n",
" Equation 2: -2.32881025574727E-8\n",
" Equation 3: -6.83356736475016E-8\n",
" Equation 4: -5.12985432448571E-8\n",
" Equation 5: 1.01894310930291E-8\n",
" Equation 6: 8.68045460164502E-10\n",
" Equation 7: -7.42287698321520E-12\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649683024446\n",
" log_cmk_t: -3.6641777715933546\n",
" imk_t: 0.06657476759180911\n",
" m0_t: 0.5500546124929157\n",
" m1_t: -1.9740150403183506e-08\n",
" mg_t: 1.0\n",
" log_gk_t: 0.0033426383253947764\n",
" Z_t: -5.123497510187612e-41\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 1.34565882742299E-11\n",
" Equation 2: 3.83401310699583E-10\n",
" Equation 3: 1.03601990875113E-9\n",
" Equation 4: -9.98819836908749E-9\n",
" Equation 5: 1.03558297045201E-9\n",
" Equation 6: -1.34565882742299E-11\n",
" Equation 7: 1.21114056284011E-13\n",
" Equation 8: -7.17289651426266E-43\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649633748024\n",
" log_cmk_t: -3.664177773441421\n",
" imk_t: 0.06657476763076715\n",
" m0_t: 0.5500542311196926\n",
" m1_t: -2.6035421405655454e-09\n",
" mg_t: 1.0\n",
" log_gk_t: 0.003342638331647379\n",
" Z_t: 1.5886845991479667e-39\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 2.46759730704316E-12\n",
" Equation 2: 5.56350521208060E-11\n",
" Equation 3: 2.05184508272893E-10\n",
" Equation 4: -3.08540203108887E-9\n",
" Equation 5: 1.36583756896872E-10\n",
" Equation 6: -2.46759730704316E-12\n",
" Equation 7: 1.88174129056584E-14\n",
" Equation 8: 2.22415843880715E-41\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649633748024\n",
" log_cmk_t: -3.664177773441421\n",
" imk_t: 0.06657476763076715\n",
" m0_t: 0.5500542311196926\n",
" m1_t: -2.6035421405655454e-09\n",
" mg_t: 1.0\n",
" log_gk_t: 0.003342638331647379\n",
" Z_t: 1.5886845991479667e-39\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 2.46759730704316E-12\n",
" Equation 2: 5.56350521208060E-11\n",
" Equation 3: 2.05184508272893E-10\n",
" Equation 4: -3.08540203108887E-9\n",
" Equation 5: 1.36583756896872E-10\n",
" Equation 6: -2.46759730704316E-12\n",
" Equation 7: 1.88174129056584E-14\n",
" Equation 8: 2.22415843880715E-41\n",
" Equation 9: 1.38777878078145E-17\n",
"Iteration 1: mu_0 error = 6.93747089e-16\n",
"Iteration 1: J1 error = 0.181631325\n",
"Iteration 1: J2 error = 0.172195867\n",
"Iteration 1: error = 0.181631325\n",
"Iteration 2: mu_0 error = 5.26549561e-17\n",
"Iteration 2: J1 error = 0.0224542295\n",
"Iteration 2: J2 error = 0.0248510469\n",
"Iteration 2: error = 0.0248510469\n",
"Iteration 3: mu_0 error = 3.94039727e-18\n",
"Iteration 3: J1 error = 0.00169963076\n",
"Iteration 3: J2 error = 0.00125459299\n",
"Iteration 3: error = 0.00169963076\n",
"Iteration 4: mu_0 error = 2.77826807e-19\n",
"Iteration 4: J1 error = 0.000126707777\n",
"Iteration 4: J2 error = 0.000167554585\n",
"Iteration 4: error = 0.000167554585\n",
"Iteration 5: mu_0 error = 1.01643954e-19\n",
"Iteration 5: J1 error = 8.58312988e-06\n",
"Iteration 5: J2 error = 0.000133254362\n",
"Iteration 5: error = 0.000133254362\n",
"Iteration 6: mu_0 error = 1.01643954e-20\n",
"Iteration 6: J1 error = 1.92186795e-07\n",
"Iteration 6: J2 error = 6.36410481e-05\n",
"Iteration 6: error = 6.36410481e-05\n",
"Iteration 7: mu_0 error = 0\n",
"Iteration 7: J1 error = 1.88907326e-07\n",
"Iteration 7: J2 error = 2.85413492e-05\n",
"Iteration 7: error = 2.85413492e-05\n",
"Iteration 8: mu_0 error = 8.47032947e-20\n",
"Iteration 8: J1 error = 1.04464107e-07\n",
"Iteration 8: J2 error = 1.26670543e-05\n",
"Iteration 8: error = 1.26670543e-05\n",
"Iteration 9: mu_0 error = 6.77626358e-20\n",
"Iteration 9: J1 error = 4.78420567e-08\n",
"Iteration 9: J2 error = 5.61174198e-06\n",
"Iteration 9: error = 5.61174198e-06\n",
"[Z_tp1, Y_tp1, log_gk_tp1]\n",
"[-sqrt(epsilon)*(W1_tp1*sigma_k1 + W2_tp1*sigma_k2 + W3_tp1*sigma_k3)*exp(0.5*Y_t) - epsilon*(Z_t*beta_k - alpha_k + phi_1*log(imk_t*phi_2 + 1.0) - 0.5*q_t**2*(sigma_k1**2 + sigma_k2**2 + sigma_k3**2)*exp(Y_t)) + log_gk_tp1, Z_t*beta_z*epsilon - Z_t + Z_tp1 - sqrt(epsilon)*(W1_tp1*sigma_z1 + W2_tp1*sigma_z2 + W3_tp1*sigma_z3)*exp(0.5*Y_t), -Y_t + Y_tp1 + beta_2*epsilon*(-mu_2*exp(-Y_t) + 1) - sqrt(epsilon)*(W1_tp1*sigma_y1 + W2_tp1*sigma_y2 + W3_tp1*sigma_y3)*exp(-0.5*Y_t) + 0.5*epsilon*q_t**2*(sigma_y1**2 + sigma_y2**2 + sigma_y3**2)*exp(-Y_t)]\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968993672636477\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154922961948\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045179079975\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154922961948\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123192938559636\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154925317954\n",
" Equation 2: 8.34543252281605E-8\n",
" Equation 3: 0.000581045193629781\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154925317954\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727306135664\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 9.19587321845938E-8\n",
" Equation 3: 0.000581033504244238\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151722814\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0000000149011612\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614286549239\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0000000149011612\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941719258452\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0000000149011612\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581047494947445\n",
" Equation 4: -0.00650614247126997\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145155298725040\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842028876096\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154926661940\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184092771\n",
" Equation 4: -0.00650614262019363\n",
" Equation 5: -0.0508941711677371\n",
" Equation 6: -0.0000145154926661940\n",
" Equation 7: 0.0145338156371238\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 1.4901161193880158e-08\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151993512\n",
" Equation 8: 2.08616256714322E-10\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.974960741559176\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941625348600\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 8.87586832504228E-9\n",
"Variable Dictionary:\n",
" vmk_t: -2.190969671823048\n",
" log_cmk_t: -4.126677382067626\n",
" imk_t: 0.07606369322178491\n",
" m0_t: 0.6061091869275164\n",
" m1_t: 0.00027091309285176557\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853376275452266\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 3.34013856026841E-9\n",
" Equation 2: 0.00000608440719052084\n",
" Equation 3: -0.00000187658854466921\n",
" Equation 4: -0.00000563217594579807\n",
" Equation 5: -0.0000137841625971271\n",
" Equation 6: -3.34013856026841E-9\n",
" Equation 7: 1.20480242449261E-9\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896408239047855\n",
" log_cmk_t: -4.126671003857404\n",
" imk_t: 0.07606349139493146\n",
" m0_t: 0.605767370898716\n",
" m1_t: 1.0526260585288875e-08\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343692950123\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -8.07718909118238E-13\n",
" Equation 2: -4.49280905812088E-8\n",
" Equation 3: 1.31242751666427E-8\n",
" Equation 4: -3.57598943685755E-9\n",
" Equation 5: -5.35580195965482E-10\n",
" Equation 6: 8.07718909118238E-13\n",
" Equation 7: -9.07102951780425E-12\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410969301474\n",
" log_cmk_t: -4.126671037648796\n",
" imk_t: 0.07606349266754037\n",
" m0_t: 0.6057671544702979\n",
" m1_t: -1.3428522154266637e-11\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343899843996\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -2.72091377206962E-15\n",
" Equation 2: 1.45716327892842E-10\n",
" Equation 3: -4.67853811247920E-11\n",
" Equation 4: -1.22541490843453E-11\n",
" Equation 5: 6.83248383285139E-13\n",
" Equation 6: 2.72091377206962E-15\n",
" Equation 7: 2.94608087925141E-14\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968993672636477\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154922961948\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045179079975\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154922961948\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123192938559636\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154925317954\n",
" Equation 2: 8.34543252281605E-8\n",
" Equation 3: 0.000581045193629781\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154925317954\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727306135664\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 9.19587321845938E-8\n",
" Equation 3: 0.000581033504244238\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151722814\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0000000149011612\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614286549239\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0000000149011612\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941719258452\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0000000149011612\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581047494947445\n",
" Equation 4: -0.00650614247126997\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145155298725040\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842028876096\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154926661940\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184092771\n",
" Equation 4: -0.00650614262019363\n",
" Equation 5: -0.0508941711677371\n",
" Equation 6: -0.0000145154926661940\n",
" Equation 7: 0.0145338156371238\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 1.4901161193880158e-08\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941711674630\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338151993512\n",
" Equation 8: 2.08616256714322E-10\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.974960741559176\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000145154923780911\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: 0.000581045184137569\n",
" Equation 4: -0.00650614261990664\n",
" Equation 5: -0.0508941625348600\n",
" Equation 6: -0.0000145154923780911\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 8.87586832504228E-9\n",
"Variable Dictionary:\n",
" vmk_t: -2.190969671823048\n",
" log_cmk_t: -4.126677382067626\n",
" imk_t: 0.07606369322178491\n",
" m0_t: 0.6061091869275164\n",
" m1_t: 0.00027091309285176557\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853376275452266\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 3.34013856026841E-9\n",
" Equation 2: 0.00000608440719052084\n",
" Equation 3: -0.00000187658854466921\n",
" Equation 4: -0.00000563217594579807\n",
" Equation 5: -0.0000137841625971271\n",
" Equation 6: -3.34013856026841E-9\n",
" Equation 7: 1.20480242449261E-9\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896408239047855\n",
" log_cmk_t: -4.126671003857404\n",
" imk_t: 0.07606349139493146\n",
" m0_t: 0.605767370898716\n",
" m1_t: 1.0526260585288875e-08\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343692950123\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -8.07718909118238E-13\n",
" Equation 2: -4.49280905812088E-8\n",
" Equation 3: 1.31242751666427E-8\n",
" Equation 4: -3.57598943685755E-9\n",
" Equation 5: -5.35580195965482E-10\n",
" Equation 6: 8.07718909118238E-13\n",
" Equation 7: -9.07102951780425E-12\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410969301474\n",
" log_cmk_t: -4.126671037648796\n",
" imk_t: 0.07606349266754037\n",
" m0_t: 0.6057671544702979\n",
" m1_t: -1.3428522154266637e-11\n",
" mg_t: 1.0\n",
" log_gk_t: 0.004853343899843996\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -2.72091377206962E-15\n",
" Equation 2: 1.45716327892842E-10\n",
" Equation 3: -4.67853811247920E-11\n",
" Equation 4: -1.22541490843453E-11\n",
" Equation 5: 6.83248383285139E-13\n",
" Equation 6: 2.72091377206962E-15\n",
" Equation 7: 2.94608087925141E-14\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1896410981754433\n",
" log_cmk_t: -4.126671037516452\n",
" imk_t: 0.07606349266305397\n",
" m0_t: 0.6057671537273439\n",
" m1_t: -1.7210410799997146e-14\n",
" mg_t: 1.0\n",
" log_gk_t: 0.00485334389911725\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -5.11743425413158E-17\n",
" Equation 2: 3.28626015289046E-14\n",
" Equation 3: -8.35442826030430E-15\n",
" Equation 4: -1.96734989410530E-14\n",
" Equation 5: 8.75672335323573E-16\n",
" Equation 6: 5.11743425413158E-17\n",
" Equation 7: 7.80625564189563E-18\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Iteration 1: mu_0 error = 4.16333634e-17\n",
"Iteration 1: J1 error = 0.0203519049\n",
"Iteration 1: J2 error = 0.0416920021\n",
"Iteration 1: error = 0.0416920021\n",
"Iteration 2: mu_0 error = 5.55111512e-17\n",
"Iteration 2: J1 error = 3.98211977e-07\n",
"Iteration 2: J2 error = 6.64200954e-08\n",
"Iteration 2: error = 3.98211977e-07\n",
"[Z_tp1, Y_tp1, log_gk_tp1]\n",
"[-sqrt(epsilon)*(W1_tp1*sigma_k1 + W2_tp1*sigma_k2 + W3_tp1*sigma_k3)*exp(0.5*Y_t) - epsilon*(Z_t*beta_k - alpha_k + phi_1*log(imk_t*phi_2 + 1.0) - 0.5*q_t**2*(sigma_k1**2 + sigma_k2**2 + sigma_k3**2)*exp(Y_t)) + log_gk_tp1, Z_t*beta_z*epsilon - Z_t + Z_tp1 - sqrt(epsilon)*(W1_tp1*sigma_z1 + W2_tp1*sigma_z2 + W3_tp1*sigma_z3)*exp(0.5*Y_t), -Y_t + Y_tp1 + beta_2*epsilon*(-mu_2*exp(-Y_t) + 1) - sqrt(epsilon)*(W1_tp1*sigma_y1 + W2_tp1*sigma_y2 + W3_tp1*sigma_y3)*exp(-0.5*Y_t) + 0.5*epsilon*q_t**2*(sigma_y1**2 + sigma_y2**2 + sigma_y3**2)*exp(-Y_t)]\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968993672636477\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358308937536\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402750360566\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358308937536\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123192938559636\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358339741041\n",
" Equation 2: 8.34543252281605E-8\n",
" Equation 3: -0.250402731337517\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358339741041\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727306135664\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 9.19587321845938E-8\n",
" Equation 3: -0.250402772870156\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338151722814\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0000000149011612\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667619978970\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0000000149011612\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276348856458\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0000000149011612\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402741459475\n",
" Equation 4: -0.0160667614640710\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358337698094\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842028876096\n",
" Z_t: 0.0\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358333908130\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743770222\n",
" Equation 4: -0.0160667617533380\n",
" Equation 5: -0.0600276341268781\n",
" Equation 6: -0.00557358333908130\n",
" Equation 7: 0.0145338156371238\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 1.4901161193880158e-08\n",
" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338151993512\n",
" Equation 8: 2.08616256714322E-10\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
" m1_t: 1.0\n",
" mg_t: 1.0\n",
" log_gk_t: 0.01937842\n",
" Z_t: 0.0\n",
" Y_t: -11.974960741559176\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276254416350\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 8.87586832504228E-9\n",
"Variable Dictionary:\n",
" vmk_t: -2.4990412620769447\n",
" log_cmk_t: -3.8188399396908546\n",
" imk_t: 0.07107896538859211\n",
" m0_t: 0.6708625092622533\n",
" m1_t: 0.11979133410667753\n",
" mg_t: 1.0000000000000009\n",
" log_gk_t: 0.004078415544384683\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -0.000301532242793315\n",
" Equation 2: 0.0386458943704886\n",
" Equation 3: -0.0700506740870134\n",
" Equation 4: -0.00243311177293890\n",
" Equation 5: -0.00632609272245618\n",
" Equation 6: 0.000301532242793311\n",
" Equation 7: 0.00000954912477009462\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.5931567574112755\n",
" log_cmk_t: -3.7289026398205487\n",
" imk_t: 0.06875688288000965\n",
" m0_t: 0.548219847461722\n",
" m1_t: -0.02307775158220332\n",
" mg_t: 0.9999999999999996\n",
" log_gk_t: 0.003704197375870328\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -0.0000631230706961651\n",
" Equation 2: 0.0242757003594813\n",
" Equation 3: -0.0273500781652956\n",
" Equation 4: -0.0000658967204150204\n",
" Equation 5: 0.00121462877264170\n",
" Equation 6: 0.0000631230706961668\n",
" Equation 7: 0.00000762066205286290\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.638449426639722\n",
" log_cmk_t: -3.6719560781959393\n",
" imk_t: 0.06698705419426898\n",
" m0_t: 0.5238878109405951\n",
" m1_t: -0.014533835038480864\n",
" mg_t: 0.9999999999999991\n",
" log_gk_t: 0.003413314651906058\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000116178985622405\n",
" Equation 2: 0.00844161572937896\n",
" Equation 3: -0.00394579816985263\n",
" Equation 4: 0.000455193416019484\n",
" Equation 5: 0.000762942441250680\n",
" Equation 6: -0.0000116178985622370\n",
" Equation 7: 0.00000349570250840351\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6434607937665993\n",
" log_cmk_t: -3.6648097637088544\n",
" imk_t: 0.06662582872674504\n",
" m0_t: 0.541038981121622\n",
" m1_t: -0.0013164503468426191\n",
" mg_t: 0.9999999999999993\n",
" log_gk_t: 0.0033515161371127622\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00000621795361824447\n",
" Equation 2: 0.00136260774340347\n",
" Equation 3: -0.000298049568510650\n",
" Equation 4: 0.000160809857545657\n",
" Equation 5: 0.0000690675012368642\n",
" Equation 6: -0.00000621795361824187\n",
" Equation 7: 5.49742981579334E-7\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6427858769844788\n",
" log_cmk_t: -3.663844175070631\n",
" imk_t: 0.06656774129621157\n",
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" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00000184305788123503\n",
" Equation 2: 0.0000594400760061120\n",
" Equation 3: 0.000144296664201377\n",
" Equation 4: 0.0000342938686621053\n",
" Equation 5: -0.00000585695644572449\n",
" Equation 6: -0.00000184305788123330\n",
" Equation 7: 2.31843045443193E-8\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.642293766679322\n",
" log_cmk_t: -3.6640636968089506\n",
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" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 7.46372257013662E-7\n",
" Equation 2: 0.0000277636445140672\n",
" Equation 3: 0.0000518888867312994\n",
" Equation 4: 0.0000136351400746582\n",
" Equation 5: -4.01170693472762E-7\n",
" Equation 6: -7.46372257011928E-7\n",
" Equation 7: 8.74118862188855E-9\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6420121515313357\n",
" log_cmk_t: -3.6641583544202163\n",
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" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 1.03154115142085E-7\n",
" Equation 2: 0.00000220689972829646\n",
" Equation 3: 0.00000858569987771673\n",
" Equation 4: 0.00000151851223440837\n",
" Equation 5: 1.64163410802474E-7\n",
" Equation 6: -1.03154115141217E-7\n",
" Equation 7: 6.98362936490254E-10\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.641954245079993\n",
" log_cmk_t: -3.664181927080247\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -2.37681131477763E-8\n",
" Equation 2: -6.53054561983168E-7\n",
" Equation 3: -0.00000185359081250613\n",
" Equation 4: -5.11343997488395E-7\n",
" Equation 5: 5.83304151165340E-8\n",
" Equation 6: 2.37681131477763E-8\n",
" Equation 7: -2.06777919439793E-10\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.641964570247612\n",
" log_cmk_t: -3.664177927424757\n",
" imk_t: 0.066574770978437\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -8.68045460164502E-10\n",
" Equation 2: -2.32881025574727E-8\n",
" Equation 3: -6.83356736475016E-8\n",
" Equation 4: -5.12985432448571E-8\n",
" Equation 5: 1.01894310930291E-8\n",
" Equation 6: 8.68045460164502E-10\n",
" Equation 7: -7.42287698321520E-12\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649683024446\n",
" log_cmk_t: -3.6641777715933546\n",
" imk_t: 0.06657476759180911\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 1.34565882742299E-11\n",
" Equation 2: 3.83401310699583E-10\n",
" Equation 3: 1.03601990875113E-9\n",
" Equation 4: -9.98819836908749E-9\n",
" Equation 5: 1.03558297045201E-9\n",
" Equation 6: -1.34565882742299E-11\n",
" Equation 7: 1.21114056284011E-13\n",
" Equation 8: -7.17289651426266E-43\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649633748024\n",
" log_cmk_t: -3.664177773441421\n",
" imk_t: 0.06657476763076715\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 2.46759730704316E-12\n",
" Equation 2: 5.56350521208060E-11\n",
" Equation 3: 2.05184508272893E-10\n",
" Equation 4: -3.08540203108887E-9\n",
" Equation 5: 1.36583756896872E-10\n",
" Equation 6: -2.46759730704316E-12\n",
" Equation 7: 1.88174129056584E-14\n",
" Equation 8: 2.22415843880715E-41\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649633748024\n",
" log_cmk_t: -3.664177773441421\n",
" imk_t: 0.06657476763076715\n",
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" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 2.46759730704316E-12\n",
" Equation 2: 5.56350521208060E-11\n",
" Equation 3: 2.05184508272893E-10\n",
" Equation 4: -3.08540203108887E-9\n",
" Equation 5: 1.36583756896872E-10\n",
" Equation 6: -2.46759730704316E-12\n",
" Equation 7: 1.88174129056584E-14\n",
" Equation 8: 2.22415843880715E-41\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968993672636477\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358308937536\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402750360566\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358308937536\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123192938559636\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358339741041\n",
" Equation 2: 8.34543252281605E-8\n",
" Equation 3: -0.250402731337517\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358339741041\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727306135664\n",
" m0_t: 1.0\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 9.19587321845938E-8\n",
" Equation 3: -0.250402772870156\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338151722814\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0000000149011612\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667619978970\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276348856458\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402741459475\n",
" Equation 4: -0.0160667614640710\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358337698094\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358333908130\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743770222\n",
" Equation 4: -0.0160667617533380\n",
" Equation 5: -0.0600276341268781\n",
" Equation 6: -0.00557358333908130\n",
" Equation 7: 0.0145338156371238\n",
" Equation 8: 0\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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" mg_t: 1.0\n",
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" Y_t: -11.97496092\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276339911644\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338151993512\n",
" Equation 8: 2.08616256714322E-10\n",
" Equation 9: 2.21489222795856E-10\n",
"Variable Dictionary:\n",
" vmk_t: -2.1968994\n",
" log_cmk_t: -4.123193\n",
" imk_t: 0.07600727192876003\n",
" m0_t: 1.0\n",
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" mg_t: 1.0\n",
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" Y_t: -11.974960741559176\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00557358319645006\n",
" Equation 2: 2.20139613205106E-8\n",
" Equation 3: -0.250402743748048\n",
" Equation 4: -0.0160667616112773\n",
" Equation 5: -0.0600276254416350\n",
" Equation 6: -0.00557358319645006\n",
" Equation 7: 0.0145338153483628\n",
" Equation 8: 0\n",
" Equation 9: 8.87586832504228E-9\n",
"Variable Dictionary:\n",
" vmk_t: -2.4990412620769447\n",
" log_cmk_t: -3.8188399396908546\n",
" imk_t: 0.07107896538859211\n",
" m0_t: 0.6708625092622533\n",
" m1_t: 0.11979133410667753\n",
" mg_t: 1.0000000000000009\n",
" log_gk_t: 0.004078415544384683\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -0.000301532242793315\n",
" Equation 2: 0.0386458943704886\n",
" Equation 3: -0.0700506740870134\n",
" Equation 4: -0.00243311177293890\n",
" Equation 5: -0.00632609272245618\n",
" Equation 6: 0.000301532242793311\n",
" Equation 7: 0.00000954912477009462\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.5931567574112755\n",
" log_cmk_t: -3.7289026398205487\n",
" imk_t: 0.06875688288000965\n",
" m0_t: 0.548219847461722\n",
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" mg_t: 0.9999999999999996\n",
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" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -0.0000631230706961651\n",
" Equation 2: 0.0242757003594813\n",
" Equation 3: -0.0273500781652956\n",
" Equation 4: -0.0000658967204150204\n",
" Equation 5: 0.00121462877264170\n",
" Equation 6: 0.0000631230706961668\n",
" Equation 7: 0.00000762066205286290\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.638449426639722\n",
" log_cmk_t: -3.6719560781959393\n",
" imk_t: 0.06698705419426898\n",
" m0_t: 0.5238878109405951\n",
" m1_t: -0.014533835038480864\n",
" mg_t: 0.9999999999999991\n",
" log_gk_t: 0.003413314651906058\n",
" Z_t: 0.0\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.0000116178985622405\n",
" Equation 2: 0.00844161572937896\n",
" Equation 3: -0.00394579816985263\n",
" Equation 4: 0.000455193416019484\n",
" Equation 5: 0.000762942441250680\n",
" Equation 6: -0.0000116178985622370\n",
" Equation 7: 0.00000349570250840351\n",
" Equation 8: 0\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6434607937665993\n",
" log_cmk_t: -3.6648097637088544\n",
" imk_t: 0.06662582872674504\n",
" m0_t: 0.541038981121622\n",
" m1_t: -0.0013164503468426191\n",
" mg_t: 0.9999999999999993\n",
" log_gk_t: 0.0033515161371127622\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00000621795361824447\n",
" Equation 2: 0.00136260774340347\n",
" Equation 3: -0.000298049568510650\n",
" Equation 4: 0.000160809857545657\n",
" Equation 5: 0.0000690675012368642\n",
" Equation 6: -0.00000621795361824187\n",
" Equation 7: 5.49742981579334E-7\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6427858769844788\n",
" log_cmk_t: -3.663844175070631\n",
" imk_t: 0.06656774129621157\n",
" m0_t: 0.5481768298579396\n",
" m1_t: 0.00011164568845901794\n",
" mg_t: 0.9999999999999996\n",
" log_gk_t: 0.00334151534734168\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 0.00000184305788123503\n",
" Equation 2: 0.0000594400760061120\n",
" Equation 3: 0.000144296664201377\n",
" Equation 4: 0.0000342938686621053\n",
" Equation 5: -0.00000585695644572449\n",
" Equation 6: -0.00000184305788123330\n",
" Equation 7: 2.31843045443193E-8\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.642293766679322\n",
" log_cmk_t: -3.6640636968089506\n",
" imk_t: 0.06657255574351265\n",
" m0_t: 0.5493062604246624\n",
" m1_t: 7.64708886791394e-06\n",
" mg_t: 0.9999999999999997\n",
" log_gk_t: 0.0033422862639455736\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 7.46372257013662E-7\n",
" Equation 2: 0.0000277636445140672\n",
" Equation 3: 0.0000518888867312994\n",
" Equation 4: 0.0000136351400746582\n",
" Equation 5: -4.01170693472762E-7\n",
" Equation 6: -7.46372257011928E-7\n",
" Equation 7: 8.74118862188855E-9\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6420121515313357\n",
" log_cmk_t: -3.6641583544202163\n",
" imk_t: 0.06657432656093322\n",
" m0_t: 0.5499712673821173\n",
" m1_t: -3.1292639966093615e-06\n",
" mg_t: 0.9999999999999999\n",
" log_gk_t: 0.003342567081851625\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 1.03154115142085E-7\n",
" Equation 2: 0.00000220689972829646\n",
" Equation 3: 0.00000858569987771673\n",
" Equation 4: 0.00000151851223440837\n",
" Equation 5: 1.64163410802474E-7\n",
" Equation 6: -1.03154115141217E-7\n",
" Equation 7: 6.98362936490254E-10\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.641954245079993\n",
" log_cmk_t: -3.664181927080247\n",
" imk_t: 0.06657485733246968\n",
" m0_t: 0.5500820857994922\n",
" m1_t: -1.111886782868601e-06\n",
" mg_t: 1.0\n",
" log_gk_t: 0.0033426527571405983\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -2.37681131477763E-8\n",
" Equation 2: -6.53054561983168E-7\n",
" Equation 3: -0.00000185359081250613\n",
" Equation 4: -5.11343997488395E-7\n",
" Equation 5: 5.83304151165340E-8\n",
" Equation 6: 2.37681131477763E-8\n",
" Equation 7: -2.06777919439793E-10\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.641964570247612\n",
" log_cmk_t: -3.664177927424757\n",
" imk_t: 0.066574770978437\n",
" m0_t: 0.5500568860059079\n",
" m1_t: -1.9422963398257696e-07\n",
" mg_t: 1.0\n",
" log_gk_t: 0.003342638870283248\n",
" Z_t: 1.2511593431471581e-44\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: -8.68045460164502E-10\n",
" Equation 2: -2.32881025574727E-8\n",
" Equation 3: -6.83356736475016E-8\n",
" Equation 4: -5.12985432448571E-8\n",
" Equation 5: 1.01894310930291E-8\n",
" Equation 6: 8.68045460164502E-10\n",
" Equation 7: -7.42287698321520E-12\n",
" Equation 8: 1.75162308040602E-46\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649683024446\n",
" log_cmk_t: -3.6641777715933546\n",
" imk_t: 0.06657476759180911\n",
" m0_t: 0.5500546124929157\n",
" m1_t: -1.9740150403183506e-08\n",
" mg_t: 1.0\n",
" log_gk_t: 0.0033426383253947764\n",
" Z_t: -5.123497510187612e-41\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 1.34565882742299E-11\n",
" Equation 2: 3.83401310699583E-10\n",
" Equation 3: 1.03601990875113E-9\n",
" Equation 4: -9.98819836908749E-9\n",
" Equation 5: 1.03558297045201E-9\n",
" Equation 6: -1.34565882742299E-11\n",
" Equation 7: 1.21114056284011E-13\n",
" Equation 8: -7.17289651426266E-43\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649633748024\n",
" log_cmk_t: -3.664177773441421\n",
" imk_t: 0.06657476763076715\n",
" m0_t: 0.5500542311196926\n",
" m1_t: -2.6035421405655454e-09\n",
" mg_t: 1.0\n",
" log_gk_t: 0.003342638331647379\n",
" Z_t: 1.5886845991479667e-39\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 2.46759730704316E-12\n",
" Equation 2: 5.56350521208060E-11\n",
" Equation 3: 2.05184508272893E-10\n",
" Equation 4: -3.08540203108887E-9\n",
" Equation 5: 1.36583756896872E-10\n",
" Equation 6: -2.46759730704316E-12\n",
" Equation 7: 1.88174129056584E-14\n",
" Equation 8: 2.22415843880715E-41\n",
" Equation 9: 1.38777878078145E-17\n",
"Variable Dictionary:\n",
" vmk_t: -2.6419649633748024\n",
" log_cmk_t: -3.664177773441421\n",
" imk_t: 0.06657476763076715\n",
" m0_t: 0.5500542311196926\n",
" m1_t: -2.6035421405655454e-09\n",
" mg_t: 1.0\n",
" log_gk_t: 0.003342638331647379\n",
" Z_t: 1.5886845991479667e-39\n",
" Y_t: -11.974960924566787\n",
"\n",
"Substituted Equations:\n",
" Equation 1: 2.46759730704316E-12\n",
" Equation 2: 5.56350521208060E-11\n",
" Equation 3: 2.05184508272893E-10\n",
" Equation 4: -3.08540203108887E-9\n",
" Equation 5: 1.36583756896872E-10\n",
" Equation 6: -2.46759730704316E-12\n",
" Equation 7: 1.88174129056584E-14\n",
" Equation 8: 2.22415843880715E-41\n",
" Equation 9: 1.38777878078145E-17\n",
"Iteration 1: mu_0 error = 4.85671225e-12\n",
"Iteration 1: J1 error = 0.0763109039\n",
"Iteration 1: J2 error = 0.149825263\n",
"Iteration 1: error = 0.149825263\n",
"Iteration 2: mu_0 error = 3.69260178e-13\n",
"Iteration 2: J1 error = 0.0742028963\n",
"Iteration 2: J2 error = 0.00377263883\n",
"Iteration 2: error = 0.0742028963\n",
"Iteration 3: mu_0 error = 2.83523205e-14\n",
"Iteration 3: J1 error = 0.0426752296\n",
"Iteration 3: J2 error = 0.0115643531\n",
"Iteration 3: error = 0.0426752296\n",
"Iteration 4: mu_0 error = 2.1649349e-15\n",
"Iteration 4: J1 error = 0.0196440557\n",
"Iteration 4: J2 error = 0.00631105131\n",
"Iteration 4: error = 0.0196440557\n",
"Iteration 5: mu_0 error = 1.66533454e-16\n",
"Iteration 5: J1 error = 0.00875601935\n",
"Iteration 5: J2 error = 0.00304739801\n",
"Iteration 5: error = 0.00875601935\n",
"Iteration 6: mu_0 error = 2.49800181e-16\n",
"Iteration 6: J1 error = 0.00388192984\n",
"Iteration 6: J2 error = 0.00145136446\n",
"Iteration 6: error = 0.00388192984\n",
"Iteration 7: mu_0 error = 6.9388939e-17\n",
"Iteration 7: J1 error = 0.00171945238\n",
"Iteration 7: J2 error = 0.000685601145\n",
"Iteration 7: error = 0.00171945238\n",
"Iteration 8: mu_0 error = 6.10622664e-16\n",
"Iteration 8: J1 error = 0.000761490256\n",
"Iteration 8: J2 error = 0.00032275865\n",
"Iteration 8: error = 0.000761490256\n",
"Iteration 9: mu_0 error = 6.80011603e-16\n",
"Iteration 9: J1 error = 0.000337230499\n",
"Iteration 9: J2 error = 0.000151362525\n",
"Iteration 9: error = 0.000337230499\n",
"Iteration 10: mu_0 error = 3.33066907e-16\n",
"Iteration 10: J1 error = 0.000149343847\n",
"Iteration 10: J2 error = 7.07720679e-05\n",
"Iteration 10: error = 0.000149343847\n",
"Iteration 11: mu_0 error = 1.11022302e-16\n",
"Iteration 11: J1 error = 6.61374547e-05\n",
"Iteration 11: J2 error = 3.2996527e-05\n",
"Iteration 11: error = 6.61374547e-05\n",
"Iteration 12: mu_0 error = 2.49800181e-16\n",
"Iteration 12: J1 error = 2.92892035e-05\n",
"Iteration 12: J2 error = 1.53458221e-05\n",
"Iteration 12: error = 2.92892035e-05\n",
"Iteration 13: mu_0 error = 4.02455846e-16\n",
"Iteration 13: J1 error = 1.29708261e-05\n",
"Iteration 13: J2 error = 7.12058416e-06\n",
"Iteration 13: error = 1.29708261e-05\n",
"Iteration 14: mu_0 error = 1.94289029e-16\n",
"Iteration 14: J1 error = 5.74417563e-06\n",
"Iteration 14: J2 error = 3.29715323e-06\n",
"Iteration 14: error = 5.74417563e-06\n"
]
}
],
"source": [
"gamma_values = [1.001, 8.001]\n",
"rho_values = [1.001, 1.5]\n",
"\n",
"for gamma_i in gamma_values:\n",
" for llambda_i in rho_values:\n",
" args = change_parameter_value('gamma', parameter_names, args, gamma_i)\n",
" args = change_parameter_value('rho', parameter_names, args, llambda_i)\n",
" output_folder = 'output'\n",
" if not os.path.exists(output_folder):\n",
" os.makedirs(output_folder)\n",
" print(f\"Created output folder at: {output_folder}\")\n",
" savepath = output_folder+'/single_capital_gamma_{}_rho_{}.pkl'.format(gamma_i, llambda_i)\n",
" uncertain_expansion(control_variables, state_variables, shock_variables, variables, variables_tp1,\n",
" kappa, growth, state_equations, initial_guess, parameter_names,\n",
" args, approach = '1', init_util = init_util, iter_tol = iter_tol, max_iter = max_iter,\n",
" savepath=savepath)\n",
" "
]
},
{
"cell_type": "markdown",
"id": "9690979c",
"metadata": {},
"source": [
"Note that the order of the variables listed in the solution is the same as before, except with ${\\widehat V_t} - {\\widehat C_t}$ removed:"
]
},
{
"cell_type": "markdown",
"id": "45006bef",
"metadata": {},
"source": [
"$$\n",
"\\left[\n",
" \\widehat C_t - \\widehat K_t, D_t, MX_t, MG_t, \\widehat G_{t+1} - \\widehat G_t, X_t \n",
"\\right]\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "a9c651a6",
"metadata": {},
"source": [
"## 2.6 Plot Elasticities"
]
},
{
"cell_type": "markdown",
"id": "4ae75fe6",
"metadata": {},
"source": [
"First, if you did not run the code above, you can load a pre-solved solution by specifying `save_path` as follows:"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9424b51e",
"metadata": {},
"outputs": [],
"source": [
"save_path = 'output/res.pkl'\n",
"with open(save_path, 'rb') as f:\n",
" ModelSol = pickle.load(f)"
]
},
{
"cell_type": "markdown",
"id": "a6e609d3",
"metadata": {},
"source": [
"If you used the loop above, you can also use the following code to load all your solutions dynamically:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "f790bb90",
"metadata": {},
"outputs": [],
"source": [
"models = {}\n",
"for gamma_i in gamma_values:\n",
" for rho_i in rho_values:\n",
" save_path = 'output/single_capital_gamma_{}_rho_{}.pkl'.format(gamma_i, rho_i)\n",
" try:\n",
" with open(save_path, 'rb') as f:\n",
" model_key = f\"gamma_{gamma_i}_rho_{rho_i}\"\n",
" models[model_key] = pickle.load(f)\n",
" except FileNotFoundError:\n",
" print(f\"File not found: {save_path}\")"
]
},
{
"cell_type": "markdown",
"id": "c07fdccb",
"metadata": {},
"source": [
"We can use `plot_exposure_elasticity_quantiles` to plot exposure elasticities for different shocks.\n",
"* `model_list` is a list of solutions you want to use to compute elasticities\n",
"* `quantile` specifies the quantiles to be plotted\n",
"* `T` specifies the number of periods (using the time-unit that you specified the parameters in)\n",
"\n",
"Additional optional parameters are included for aesthetics."
]
},
{
"cell_type": "markdown",
"id": "e8f2b0b3",
"metadata": {},
"source": [
"Here is an example:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "4a9cd9ef",
"metadata": {},
"outputs": [],
"source": [
"def plot_exposure_quantiles(\n",
" model_list, \n",
" quantile, \n",
" Mtgrowth_list,\n",
" T, \n",
" num_shocks, \n",
" time_unit='quarters', \n",
" ylimits=None, \n",
" titles=None, \n",
" title=None, \n",
" shock_names=None, \n",
" colors=None, \n",
" save_path=None\n",
"):\n",
" \"\"\"\n",
" Plot exposure elasticity quantiles for multiple models across subplots,\n",
" with special handling for num_shocks = 1 (plots second shock only).\n",
" \n",
" Parameters:\n",
" - model_list: List of model results to plot.\n",
" - quantile: List of quantiles to calculate.\n",
" - T: Integer, time horizon.\n",
" - num_shocks: Integer, number of shocks to include.\n",
" - time_unit: String, label for x-axis time units (e.g., \"quarters\").\n",
" - ylimits: List, optional y-axis limits for the subplots.\n",
" - titles: List of titles for individual subplots.\n",
" - title: String, optional title for the overall figure.\n",
" - shock_names: List of strings, names for the shocks (optional).\n",
" - colors: List of strings, colors for the quantiles.\n",
" - save_path: String, optional path to save the plot.\n",
" \"\"\"\n",
" sns.set_style(\"darkgrid\")\n",
" num_models = len(model_list)\n",
"\n",
" # Default settings\n",
" if titles is None:\n",
" titles = [f'Model {i + 1}' for i in range(num_models)]\n",
" if shock_names is None:\n",
" shock_names = [f'Shock {i + 1}' for i in range(num_shocks)]\n",
" if colors is None:\n",
" colors = ['green', 'red', 'blue']\n",
"\n",
" # Adjust num_shocks and shock_names if num_shocks = 1\n",
" if num_shocks == 1:\n",
" num_shocks = 1\n",
" shock_names = [shock_names[1] if len(shock_names) > 1 else \"Shock 2\"]\n",
"\n",
" # Initialize figure and axes\n",
" fig, axes = plt.subplots(\n",
" num_shocks, num_models, figsize=(8 * num_models, 6 * num_shocks), squeeze=False\n",
" )\n",
"\n",
" # Main plotting loop\n",
" for model_idx, res in enumerate(model_list):\n",
" Mtgrowth = Mtgrowth_list[model_idx]\n",
" X1_tp1 = res['X1_tp1']\n",
" X2_tp1 = res['X2_tp1']\n",
" \n",
" # Calculate exposure elasticity for each shock\n",
" expo_elas_shocks = [\n",
" [exposure_elasticity(Mtgrowth, X1_tp1, X2_tp1, T, shock=i, percentile=p) for p in quantile]\n",
" for i in range(num_shocks if num_shocks > 1 else 2) # Include shock 2 when num_shocks = 1\n",
" ]\n",
"\n",
" # Select only the second shock if num_shocks = 1\n",
" if num_shocks == 1:\n",
" expo_elas_shocks = [expo_elas_shocks[1]]\n",
"\n",
" # Prepare data for plotting\n",
" index = ['T'] + [f'{q} quantile' for q in quantile]\n",
" shock_data = [\n",
" pd.DataFrame([np.arange(T), *[e.flatten() for e in expo_elas_shocks[i]]], index=index).T\n",
" for i in range(len(expo_elas_shocks))\n",
" ]\n",
"\n",
" # Plot each shock in a separate subplot\n",
" for shock_idx in range(len(expo_elas_shocks)):\n",
" ax = axes[shock_idx, model_idx]\n",
" for quantile_idx, quantile_label in enumerate(index[1:]):\n",
" sns.lineplot(data=shock_data[shock_idx], x='T', y=quantile_label, ax=ax, \n",
" color=colors[quantile_idx], label=quantile_label)\n",
"\n",
" # Customize the subplot\n",
" ax.set_xlabel('')\n",
" ax.set_ylabel('Exposure elasticity', fontsize=14)\n",
" if shock_names:\n",
" ax.set_title(f'{titles[model_idx]} - {shock_names[shock_idx]}', fontsize=16)\n",
" else:\n",
" ax.set_title(f'{titles[model_idx]} - Shock {shock_idx + 1}', fontsize=16)\n",
" ax.tick_params(axis='y', labelsize=12)\n",
" ax.tick_params(axis='x', labelsize=12)\n",
" ax.legend(fontsize=12, loc='lower right')\n",
"\n",
" # Set y-axis limits if provided\n",
" if ylimits:\n",
" ax.set_ylim(ylimits)\n",
"\n",
" # Set x-axis label for all subplots\n",
" for ax_row in axes:\n",
" for ax in ax_row:\n",
" ax.set_xlabel(f'{time_unit}', fontsize=14)\n",
"\n",
" # Set the main figure title, if provided\n",
" if title:\n",
" fig.suptitle(title, fontsize=18)\n",
"\n",
" plt.tight_layout()\n",
"\n",
" # Save and/or display the plot\n",
" if save_path:\n",
" plt.savefig(save_path, dpi=300)\n",
" plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "6f1800f1",
"metadata": {},
"source": [
"Here is an example: first we define a function for computing the approximation of the log growth of $M_t$. As an example, we compute the log growth of $C^t$, where we know from the ordering above that this has index `[0]` in the output array. We subtract the first difference of this from $\\hat{G}_{t+1}-\\hat{G}_t$, which is has index `[0]` in the array of state variables."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "a07ec9e3",
"metadata": {},
"outputs": [],
"source": [
"def compute_logMtM0(model):\n",
" return model['JX1_tp1'][0] + 0.5 * model['JX2_tp1'][0] - (\n",
" model['J1_t'][0] + 0.5 * model['J2_t'][0]) \\\n",
" + (model['X0_t'][0] + model['X1_tp1'][0] + 0.5 * model['X2_tp1'][0])\n"
]
},
{
"cell_type": "markdown",
"id": "bbc641da",
"metadata": {},
"source": [
"You can use the following code to plot the results for a selection of models."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "b672281f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"model_list=[\n",
" models['gamma_1.001_rho_1.5']\n",
" ]\n",
"\n",
"plot_exposure_quantiles(\n",
" model_list,\n",
" quantile=[0.1, 0.5, 0.9],\n",
" Mtgrowth_list = [compute_logMtM0(model) for model in model_list],\n",
" T=160,\n",
" num_shocks=1,\n",
" time_unit='quarters',\n",
" titles=None,\n",
" title=None,\n",
" save_path=None\n",
")\n"
]
},
{
"cell_type": "markdown",
"id": "6ec9ccfd",
"metadata": {},
"source": [
"It is also possible to compute price elasticities similarly:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "48ca0837",
"metadata": {},
"outputs": [],
"source": [
"def plot_price_elasticity(models, T, quantile, time_unit, title=None, ylimits=None, save_path=None):\n",
" \"\"\"\n",
" Calculate and plot price elasticity for different models across subplots.\n",
" \n",
" Parameters:\n",
" - models: List of result dictionaries to plot.\n",
" - T: Integer, time horizon.\n",
" - quantile: List of quantiles to calculate.\n",
" - time_unit: String, label for x-axis time units (e.g., \"quarters\").\n",
" - ylimits: Optional, list of y-axis limits for each subplot.\n",
" - save_path: Optional, path to save the figure.\n",
" \"\"\"\n",
" sns.set_style(\"darkgrid\")\n",
" num_models = len(models)\n",
"\n",
" # Initialize figure and axes for subplots\n",
" fig, axes = plt.subplots(1, num_models, figsize=(8 * num_models, 8), squeeze=False)\n",
" axes = axes.flatten() # Ensure axes are flattened for easy iteration\n",
" titles = [r'$\\gamma=1$',r'$\\gamma=4$',r'$\\gamma=8$']\n",
"\n",
" for idx, res in enumerate(models):\n",
" # Extract data from the current model\n",
" X1_tp1 = res['X1_tp1']\n",
" X2_tp1 = res['X2_tp1']\n",
" gc_tp1 = res['gc_tp1']\n",
" vmr_tp1 = res['vmr1_tp1'] + 0.5 * res['vmr2_tp1']\n",
" logNtilde = res['log_N_tilde']\n",
"\n",
" # Calculate log_SDF\n",
" β = get_parameter_value('beta', res['parameter_names'], res['args'])\n",
" ρ = get_parameter_value('rho', res['parameter_names'], res['args'])\n",
" log_SDF = np.log(β) - ρ * gc_tp1 + (ρ - 1) * vmr_tp1 + logNtilde\n",
"\n",
" # Calculate price elasticity for each shock\n",
" price_elas_shock = [\n",
" price_elasticity(gc_tp1, log_SDF, X1_tp1, X2_tp1, T, shock=1, percentile=p) for p in quantile\n",
" ]\n",
"\n",
" # Prepare data for plotting\n",
" index = ['T'] + [f'{q} quantile' for q in quantile]\n",
" shock_data = pd.DataFrame(\n",
" [np.arange(T), *[e.flatten() for e in price_elas_shock]],\n",
" index=index\n",
" ).T\n",
"\n",
" # Plot on the respective subplot\n",
" ax = axes[idx]\n",
" qt = [f'{q} quantile' for q in quantile]\n",
" colors = ['green', 'red', 'blue']\n",
"\n",
" for j in range(len(quantile)):\n",
" sns.lineplot(data=shock_data, x='T', y=qt[j], ax=ax, color=colors[j], label=qt[j])\n",
" \n",
" # Customize the subplot\n",
" ax.set_xlabel(time_unit, fontsize=30)\n",
" ax.set_ylabel('Price elasticity', fontsize=30)\n",
" ax.set_title(titles[idx], fontsize=30)\n",
" ax.tick_params(axis='y', labelsize=30)\n",
" ax.tick_params(axis='x', labelsize=30)\n",
" if idx == 0:\n",
" ax.legend(fontsize=25)\n",
" else:\n",
" ax.legend().set_visible(False)\n",
"\n",
" # Set y-axis limits if provided\n",
" # if ylimits and idx < len(ylimits):\n",
" # ax.set_ylim(ylimits[idx])\n",
" if ylimits:\n",
" ax.set_ylim(ylimits)\n",
" plt.tight_layout()\n",
"\n",
" # Save and/or display the plot\n",
" if save_path:\n",
" plt.savefig(save_path, dpi=500)\n",
" plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "bb0c8e83",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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XDv0ZOHTo0EHXXXedRowYocjIyOruIiqIYAHwDOMYtR1jGP6gro3j2pZ0KIo4wn8RRwCeqa3jODtbLkmEI0dMSklxJhGcSQVn2ZMljmJj7WrUyKFGjVyTCYWJhMJkQmQkyxr5mto6joGi6to49umkQ1F79uzRDz/8oC+++MLlyaXCoCEoKEjDhg3TrbfeylNLtQDBAuAZxjFqO8Yw/EFdG8e1OelQFHGEfyGOADzja+O4cHZCcnKADh826fDhACUnO78fPnwmoeDJMkeRkQ41aeJMKDRu7FDjxnY1buz4s25XkybOWQpBQVX4xlClfG0cAxVR18axu7GEpRr6Uqpt27Zp2bJlWrZsmQ4fPuyyMV5hLiQvL0/z5s3TvHnzNGjQIP3rX/9iwzgAAACgDiOOAIDqdfq0M6GQnOxc3siZUDiTVEhODlBWlnsJhdBQZxKhpISCM6ngPB4aWsVvCgBQZao96bB582YtXLhQy5YtU0pKSrHXHQ6HTCaT+vTpo8OHDys5OdkIHH744QetW7dOM2fOVO/evau76wAAAABqCHEEAFSN/HwpOdmkpKQAJSU5EwhHjphcZi24O0MhOtqhpk3tatrU+b1ZM2dyoWnTM8mF8HCWOQIAf1ctSYcDBw5o4cKFWrhwobH2amEAYDKZjHKLFi00cuRIjR49Wk2bNpUkrVu3Tl988YW+++472Ww2ZWZm6h//+Ifmzp2r+Pj46ug+AAAAgBpAHAEAlZeVJSOhcOjQme+F5aNHTXI4ys8CREYWTygU1ps1c85UCAurhjcEAPB5VbanQ2pqqr799lstXLhQW7dulVRygBAaGqrBgwfrmmuuKfOpo8TERN111106ceKETCaTrr/+ek2ePLkquo5KYC1WwDOMY9R2jGH4g7o2jn19TwfiiLqJOALwTOE4TkvL0okTdiUlBbgkFIp+T0sr/3d+vXoONW9uV/PmzgRCYSKhSROHMVshPLwa3hjqFH4fwx/UtXFcI3s6ZGdna+nSpVq4cKF+/fVX2Ww2SWemOhcNEvr06aNrrrlGgwcPVr169cq9dseOHTVhwgSNHz9ekvTLL794s+sAAAAAaghxBACULjtbOngwQAcOmP78HqCDBwOUlCTt3x+q06fLn6UQEeFMKrRo4UwsNG9uV3z8me8NGjhY8ggA4DVeSTqsWLFCCxcu1PLly5WbmyvJ9WmkwnqzZs00evRojRo1Ss2bN/f4PgMGDDCudezYMW90HQAAAEANIY4AAMlul44eNenAgQDt3+/8fubLpGPHynqi1Pm7Mjb2TBKheXPHn8kFZzk+3q6IiOp5LwAASF5KOowZM8bl6SNTkfR4SEiIBg8erNGjR6tv376Vuk/hk0wmk0n169ev1LUAAAAA1CziCAB1xenTckkkFJYPHnTOXsjLK3uaQf36DrVqZVfLlna1bOlQmzYOdekSrKiobDVubFNoaDW9EQAA3ODV5ZUKAwaHw6HevXtr9OjRGjp0qEK99K9fcnKyJOcTSj169PDKNQEAAADULOIIAP7g9Glp374A7d3r+rVvn0knTpS9/rXZ7FDz5o4/kwrOxEKrVs7lkFq2tCsqSi7LHznXEA9WerpDVmvVvi8AADzltaSDw+FQ06ZNNXLkSF199dWKj4/31qUNERERmj17tlq0aKGoqCivXx8AAABA9SKOAFCbZGU5EwuuyQWT9u0LKGcZJCk6umhSwZlYKCw3a+aQxauPhQIAUHO88k/aiBEjdPXVV6tfv34uU6K9LSYmRjExMVV2fQAAAADVhzgCgC/KyZH273edqVBYTkkpO7HQoIFdrVs71KaNXW3a2NW6tfN7q1Z2RUZW0xsAAKCGeSXp8OKLL3rjMi5OnTrFeqsAAACAHyOOAFBTHA4pJcWkXbsCtGtXgHbvdn7fsydAycllJxaiohwuCYWiXyQWAADwUtLhySeflORci3XatGkVvs7Jkyc1duxY7dy5U82aNdPcuXO90T0AAAAAPog4AkBVy8uT9u51JhUKEwuF37OySp9hFRFRfLZCYZmJUwAAlM0rSYevv/7amA5dmWChXr16WrdunTe6BAAAAMDHEUcA8JbUVJNLQqHw+8GDJtntJScXzGaHWrVyqH17m9q2PfO9bVu7GjRwqApXfQMAwK95dSPpyq7DmpOTY5SzsrIq2yUAAAAAPo44AoAnUlNN2rkzQDt2BCgx8czXiROlL4lUv75DHTrY1batXe3b29WunfN7q1Z2BQVVY+cBAKgjvJZ0qKz09HS99NJLRj0iIqIGewMAAACgNiCOAPxTWpqUmGjWjh0B2rnTmVjYsaPs5EKLFsUTC+3a2RUXx6wFAACqk1tJh02bNumGG26Qw+Eos53D4VDnzp0r3SmTyaSWLVtW+joAAAAAag5xBIDypKefSS4Unblw/HjZyYWOHe3q2NH253dngiEsrBo7DgAASuVW0qF79+4aPXq0vvrqq3LblhdQlMVkMhlTq0eNGlXh6wAAAACoecQRAAoVFEi7dwcoISFA27cHKCHBrISEAB0+XHpyIT7ebiQVOna0qVMn58yF8PBq7DgAAPCY28srPfLII1q2bJkyMzOrrDOFgcZVV12l66+/vsruAwAAAKB6EEcAdYvDIR07ZlJCQsCfX87kwq5dAcrPL3mNo+bNzyQXOnWyGTMXSC4AAFA7uZ10iI6O1rPPPqvly5cXe+3rr7+W5HzCqCJPFlksFoWGhqphw4bq0aOHevfu7fE1AAAAAPge4gjAf+XmSjt3OpML27aZjVkMpe27EBbm0Dnn2HXOObY/v9vVubNNbMUCAIB/MTkqM4/5T506dTKmM2/fvr3SnULtZbPZlZaWVS33slgCFB0dpvT0LFmt9mq5J+BtjGPUdoxh+IO6No5jYsJkNpe+nEl1Io5AIeII35eRIW3datbmzQHassWsrVudsxfs9uKzF0wmh9q2tatzZ7uRXDjnHJvi4x0K8I1fP7Ue4xj+gHEMf1DXxrG7sYTbMx3K43A4jIABAAAAANxBHAH4FodDOnrUpC1bnMmFzZsDtHWrWQcPlvwBQ3S0Q1262FxmMHToYFdoaDV3HAAA+AyvJB2mT5/ujcsAAAAAqEOII4Ca5XBI+/ebXGYwbNkSoOPHS04wtGhhV9euNp17rl3dutnUtatdjRs7RN4QAAAU5ZWkw+jRo71xGQAAAAB1CHEEUH3sdmnvXpM2bjRr8+YzMxhOnSqeMQgIcKh9e7u6dnUmF84915lsiIqq/n4DAIDax2vLKwEAAAAAgJrncEjJyc4Ewx9/BOiPP8zatMmskyeLJxiCghzq3Nmuc8+1GUmGc85heSQAAFBxJB0AAAAAAKjFjh836Y8/ArRxozO5sHFjgE6cKL5EUkiIQ1272tWjh03nnmtTt27O/RcCA2ug0wAAwG+5lXTo3LmzUTaZTEpISCj1dW8p6T4AAAAAag/iCMD7Tp7Un4mFM7MYkpKKJxgsFucMhh49bOrZ067u3W3q1IkEAwAAqHpuJR0cDodMJpMcDkeprwMAAABAUcQRQOXYbNL27QHasMGs9evN2rAhQLt3m4u1M5mcezB0725Xz5429ehhU5cudtWrVwOdBgAAdZ7XllcqK5gAAAAAgJIQRwBnpKaatGFDwJ8JBrN+/92srKzi+zC0aOGcwVA4i+Hcc22qX78GOgwAAFACt5IOo0ePrtTrAAAAAOoe4gigdFarcxbD+vVmI8mwd2/xZZLCwx3q1cum3r2dXz162BUbS6IOAAD4LpODx4rgRTabXWlpWdVyL4slQNHRYUpPz5LVaq+WewLexjhGbccYhj+oa+M4JiZMZnPxDzaBmlQX4ogTJ87MYli/3rknQ3Z28VkM7dvb1Lu3Xb172/SXv9jUsaNd5uIrKqGOq2v/dsE/MY7hD+raOHY3lvDa8koAAAAAAEByOKS9e0369VeL1q41a+1as/btKx6g169/ZhZDnz429expU3R0DXQYAADAi2o06ZCenq5o/qICAAAA4AHiCPgaq1XasiXASDCsXWvWiRPFkwwdOhQuk+ScydChg10BTDwCAAB+pkqSDkeOHNGcOXOUmZmpp556qtR2N998s06dOqWhQ4fq5ptvVnx8fFV0BwAAAEAtQByB2uL0aen3353JhV9/de7HcPZSScHBDvXsaVO/fjb17etcKikqqmb6CwAAUJ28uqdDQUGBXnnlFX3yySey2Wxq2LChVq5cWWr7nj17Kjc3V5IUGBio+++/X/fcc4+3uoMaUBfWYgW8iXGM2o4xDH9Q18axL+7pQBwBX48jMjKkX38165dfLPrtN7M2bw6QzeaaZIiMdKhvX5vOO8+mfv2s6t7druDgKngDgOrev13wT4xj+IO6No6rfU+H/Px8/eMf/9Dq1atVmMc4fvy4cnJyVK9evWLt09LSlJOTI5PJZJz/6quvKikpSVOmTPFWtwAAAAD4MOII+KKiSYbVq83aujVADodrkqF5c/ufCQbnTIaOHVkqCQAAQPJi0uGVV17RL7/8IpPJJJPJJIfDoaioKKWnp5cYLAQEBOi2227TqlWrtGfPHuOcL7/8Uh07dtRNN93kra4BAAAA8FHEEfAF7iQZ2re36fzznV99+9rUvLnXFg0AAADwK15ZXunQoUMaMmSI7HbnFJKIiAg98cQTuuqqq2Q2m8s9f8WKFXrqqaeUmpoqh8Oh0NBQrVixQhEREZXtGqqZr0+LBnwN4xi1HWMY/qCujWNfWl6JOAKFqjuOkMK0eHGuVq4MKDPJcMEFNvXv70w0NGpEkgG+o6792wX/xDiGP6hr47hal1eaO3eubDabJCk8PFz/+9//1K5dO7fPv/jii/XJJ5/o2muvVXZ2tnJycjR37lzdfvvt3ugeAAAAAB9EHIGaMHu2WffdJ9ntIS7HSTIAAAB4h1cecVq3bp0kyWQyacyYMR4FCoVat26tO++801jH9eeff/ZG1wAAAAD4KOII1ISMDJMcDql9e7tuuy1f776boy1bTuuXX7L14ot5GjXKSsIBAACgErySdNi7d69RHjJkSIWvM3ToUKO8c+fOSvUJAAAAgG8jjkBNuOceq/LypLVrc0gyAAAAVAGvJB1OnjxplJs0aVLh68THx0uSHA6HMjIyKtstAAAAAD6MOAI1JTCwpnsAAADgv7ySdAgs8hfbqVOnKnydvLw8oxwSElJGSwAAAAC1HXEEAAAA4H+8knSIi4szylu2bKnwdRITEyU513SNiYmpdL8AAAAA+C7iCAAAAMD/eCXp0LVrV6P85ZdfVvg6c+bMMcpdunSpVJ8AAAAA+DbiCAAAAMD/eCXpMGjQIEnONVSXLl2qRYsWeXyNlStXav78+Ub9oosu8kbXAAAAAPgo4ggAAADA/3gl6XD55ZcrLi5OJpNJDodDjz/+uD788EPZ7Xa3zv/888/10EMPyeFwSHJOsx42bJg3ugYAAADARxFHAAAAAP7H4o2LBAYG6tFHH9Wjjz4qk8mkgoICvfjii/roo480bNgwnXvuuYqPj1dYWJgkKSsrS0lJSdq6dau+++47HTlyxAgUTCaTHn74YQUFBXmjayU6ePCgZs+erbVr1+rAgQPKzs5WTEyMmjZtqoEDB2rkyJFq2rRpld2/LG+99ZbefPNNSdIPP/yg5s2bu33uyZMn1adPnwrdt0WLFlq6dGmFzgUAAAAqorbFERKxREmIJQAAAFCUV5IOkjRixAht2LBBn3/+ufGk0vHjx/Xxxx+XeV7RIMHhcOj222/XVVdd5a1uubBarXr99df1wQcfyGazubx29OhRHT16VBs3btTMmTP14IMP6u6771ZAgFcmg7hlx44devfddyt8/vbt273YGwAAAKDq1YY4QiKWAAAAANzltaSDJE2ePFkNGzbUv//9b1mtVplMJklnAoKzmUwmI0gwm80aN26c7rrrLm92yWCz2TRu3DgtWbKk3LYFBQV6+eWXtWPHDr3yyitV0p+zHT9+XPfdd5/y8vIqfA0CBQAAANRGvhxHSMQSAAAAgCe8mnSQpLFjx+rKK6/Uu+++q++++07Z2dmltnU4HAoKCtLw4cN11113qW3btt7ujuGNN95wCRKioqL0wAMP6NJLL1WDBg2UkpKib775Ru+9955ycnIkSd9++63atWun++67r8r6JUnHjh3THXfcoeTk5EpdJzEx0Si3bNnSraAIAAAA8AW+GkdIxBIAAACAJ0yO0h4f8oKCggJt2rRJO3bsUHJysrKysiRJkZGRatCggbp27apu3bopODi4qrogSdq9e7euuuoqYxp0kyZN9Nlnn6lJkybF2u7atUu33HKL0tPTJTnXmf3uu+88Wg/VExs3btS4ceN05MiRYq95ug7rqFGjjCeUBg8erDfeeMNr/XSXzWZXWlpWtdzLYglQdHSY0tOzZLW6t9kg4GsYx6jtGMPwB3VtHMfEhMlsrr5lfyrCV+IIiViiuhBHAJ5hHMMfMI7hD+raOHY3lvD6TIeiAgMD1bt3b/Xu3bsqb1OumTNnGkGCyWTSq6++WmKQIEnt27fXm2++qVtuuUUOh0MFBQWaOXOmpk+f7tU+ORwOffzxx3rxxRdVUFBQ6esVFBRo9+7dRr1jx46VviYAAABQE3wljpCIJQAAAABP+fYjTl6QlpampUuXGvX+/furZ8+eZZ7Tp08fDRo0yKgvWrSozOndntqwYYOuv/56TZs2zSVIiImJqfA19+zZ43KtTp06VaqPAAAAQF1HLAEAAAB4zu+TDitXrnT5A3rEiBFunTd8+HCjnJubqxUrVnilP5MmTdKNN96oTZs2GcfMZrMeffRR3XjjjRW+7o4dO1zqBAoAAABA5RBLAAAAAJ7z+6TDmjVrXOr9+vVz67y+ffu61H/66Sev9OePP/5wqXfo0EGff/657r777kpdt3D9VUmKiIhQs2bNKnU9AAAAoK4jlgAAAAA859aeDkWnB5tMJi1btqzU172lpPtURGJiolGOiYlR48aN3TovJiZGjRo10tGjRyVJW7ZsqXRfioqKitKYMWN00003KSgoqNLXK/p0Ek8mAQAAwBfU5jhCIpYAAAAAKsKtpENycrJMJpMcDodMJlOZr3tLSfepiL179xrlli1benRuixYtjEDh0KFDpb5/TzRu3FhDhgzRTTfdpIiIiEpdq6iigULHjh2Vn5+vH374QUuXLtWmTZt04sQJBQQEqGHDhurevbuuuOIKXXbZZV77OQMAAABnq81xhEQsQSwBAACAinAr6VBbZWRkKC8vz6g3atTIo/MbNmxolPPz85WamqrY2NhK9WnWrFmVOr8kR44cUUZGhkt9yJAhSk5OLtb2wIEDOnDggBYsWKBzzjlHU6dOVdeuXb3eJwAAAKA2I5YglgAAAEDFuJV06NOnT6Verympqaku9cjISI/Or1+/vks9MzOz0oFCVSi6Bqskt6eTJyQk6Oabb9ZLL72kyy67rCq6BgAAgDqstsYRErFEeYglAAAAUBq3kg6ffPJJpV6vKdnZ2S71sLAwj84/u31WVlal+1QVik6HLlS/fn1dd911uvLKK9WyZUuZzWYlJSVpxYoV+uijj5SWliZJysnJ0fjx4/W///1P3bp1q+6uAwAAwI/V1jhCIpYglgAAAEBF+fXySvn5+S71wMBAj863WFx/PAUFBZXuU1U4O1Do0qWL3njjDTVv3tzleIcOHdShQwf99a9/1f33369169ZJkvLy8jR+/HgtXry42HuuCIsloNLXcIfZHODyHaiNGMeo7RjD8AeMY5SEWKL6YwniCMB9jGP4A8Yx/AHjuGQ+m3Q4depUsSnJnrLb7S51Tzc6CwhwHSze3ODOm7p27ar8/HwlJSXJbrfr/fffV0xMTKnto6Ki9M4772jUqFE6dOiQJOngwYP6+uuvdd1111WqLwEBJkVHe/YUWGVFRNSr1vsBVYFxjNqOMQx/wDj2D96IIyRiidJUVSxBHAFUDOMY/oBxDH/AOHbllaTDk08+Kcn5h/i0adMqfJ2TJ09q7Nix2rlzp5o1a6a5c+dWql9ms9mlfnbgUB6r1epSDwoKqlR/qso999zj8Tnh4eEaP368xo0bZxxbsGBBpZMOdrtDJ09ml9/QC8zmAEVE1NPJkzmy2Tz7bwv4CsYxajvGMPxBXRvHERH1fOZJLF+NIyRiibJURSxBHAF4hnEMf8A4hj+oa+PY3VjCK0mHr7/+2njypzLBQr169Yxput5Qr55rhikvL8+j889u76uBQkVdccUVCg0NNdar3bhxo3JzcxUSElKp61qt1fs/mM1mr/Z7At7GOEZtxxiGP2AcVz9fjSMKr1kUsYSrqogliCMAzzGO4Q8Yx/AHjGNXXnvEyRvThXNycoyyNzZai4yMdKmfPn3ao/PP7kNUVFRlu+RTLBaLunbtatQLCgp09OjRGuwRAAAA6hpfjCMkYonyEEsAAACgNL4xr1pSenq6nn/+eaMeERFR6WvGxsa6rL2alpbm0fknTpxwqZe1tmlt1aBBA5d6enp6DfUEAAAA8FxVxBESsYQ7iCUAAABQEreWV9q0aZNuuOGGcp9Ccjgc6ty5c6U7ZTKZ1LJly0pfJygoSHFxccYTN0eOHPHo/JSUFKMcFxfnd1OipeJPlvnjewQAAEDNqK1xhEQs4Q5iCQAAAJTErZkO3bt31+jRo+VwOEr8Kqq0Nu58STKeJho1apRX3mD79u2N8oEDB2Sz2dw6z2q16sCBA0a9Q4cOXumPtzkcDmVkZGjPnj1au3atx8HQ2U9sRUdHe7N7AAAAqMNqcxwhEUuUh1gCAAAAJXF7eaVHHnmk2Lqm3lYYNIwYMULXX3+9V67ZvXt3o5yTk6Ndu3a5dd6OHTtcNn8reh1f8sknn6hv374aNmyYbr31Vs2ZM8ftc+12uxISEox6dHS0GjduXBXdBAAAQB1VW+MIiViiLMQSAAAAKI1byytJzj8in332WS1fvrzYa19//bUk59NFFXmyyGKxKDQ0VA0bNlSPHj3Uu3dvj69RmgEDBmjmzJlG/ccff1SnTp3KPe/HH390qffv399rffKmjh07utR//vlnPfDAA26d+/PPP7tsiNe3b1+XdWsBAACAyqqtcYRELFEWYgkAAACUxu2kgyRdfvnluvzyy4sd//rrr40/MKdPn+6dnnlJjx491KxZMyUnJ0uSZs+erTvvvFPBwcGlnpOTk6PZs2cb9fj4ePXq1avK+1oRPXv2VFRUlDIyMiQ5183dvHmzzj333DLPs9lsLgGUJP3tb3+rqm4CAACgDquNcYRELFEaYgkAAACUxe3llcpT3uZwNSUgIEA33nijUT98+LCmTp1a5jmTJ0/WsWPHjPott9zis0/tBAUFFXsq7Omnn1Z2dnaZ57344ovatGmTUe/Zs6fOP//8qugiAAAAUCpfjSMkYonSEEsAAACgLB7NdCiNLz6VVNRNN92kTz/91HhC6csvv5TD4dDEiRMVGhpqtMvOztbUqVM1b94841irVq10ww03lHjdpKQkDRo0yOVYYmKi999AOe677z4tWLDA2Mhtx44duvXWW/XCCy+oTZs2Lm3T0tI0ffp0LViwwDgWEhKiadOmVWufAQAAAF+PIyRiiaKIJQAAAOAOryQdRo8e7Y3LVJl69erp5Zdf1h133KGcnBxJ0pw5c7RkyRJdcsklatSokVJSUrRixQqdPHnS5bzXXntNQUFBNdV1t0RGRurNN9/UnXfeaWxYt2XLFg0fPlx9+/Y11p3dv3+/Vq9erdzcXOPcoKAgvfXWW8UCCgAAAKCq+XocIRFLEEsAAADAU15JOlSEw+FQcnKyUlNT1bhxYzVq1KhK79ezZ0/NmjVLY8eO1alTpyRJJ0+e1Pz580tsHxERobfffludO3eu0n55S+/evfX+++/r4YcfNqZz22w2rV69WqtXry7xnIYNG2rGjBkaMGBAdXYVAAAAqLDqjiMkYomSEEsAAACgNF7b06Go06dP68cffyz19c8++0wDBw7U5Zdfrr/97W+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egYK93BnvUFe8a9QuFZQJA0q9pSr1lSrotZeD3qBKfWUKeoMq85Wl12W2CToH/TPhQXegEFTQW6ISTzAnBPCYnlH5PAAAAAAAABg+QgfAZbt3G1q2zNSyZXbI8MYbfd+HYebMVPrsBTtkOPjg5NCuMtTVJc976+VZ/27u84b1MjdvkpEa+FfpqZoaJadOV2ra9NxAIR0wcOmjXMlUUl3xTnXEOtQR71BHrF0dsY7udel2JhjojHWoK2GHAqEeYUFnrFOxVGzExuo1vSr3lavUW6YyX5kTEGRCgewwoDQrKCj1lnWHCOmgoNRbpqAvqLKs1zgjAAAAAAAAAD2NyyNGGzdu1JIlS7R06VJt2LBBoVBItbW1ampq0jHHHKPTTjtNTU1NIzoGy7L04osv6pFHHtGKFSu0e/duSVJjY6NmzpypU089VSeccIICgcCQ+l+2bJn+9Kc/afny5dq+fbsSiYQaGxs1ffp0nXjiifrEJz6h8vJyNz/SuJRISKtWdZ/FsGxZ32cxVFZaOuywpN7/fvtx2GFJVVfn+SaWJaO1pc9gwXxvvTw7dwy8e2mpktP3s89WmJYJF6Y74YJVUTn4Dz4GxZKx7lAg3qHOrIAgEyB0ZS1n1ndmtkmv64p3jsj4/KZfZb4ylfnK08/pZX+5yrx9rPeVqdxf3vd6n73e7xnOaTIAAKAv1BLUEgAAABiYYVmWta8HMVoSiYR+8pOf6Fe/+pWSyWS/2/l8Pl122WU6//zzZY7Ateg3bdqkr33ta1q+fPmA202dOlU/+tGPtGDBgrz7bmlp0be+9S0999xzA25XW1ur66+/Xscee2zefecjmUyppaXL1T774/WaqqkpU2trlxKJ0bnG/O7dhl57rfsshuXL+z6LYc6cTMCQ0vvfn9ScOXu5D4Nlydi9W95178jz7jo7TMgEDO+tl9m2Z8BxpWpqlJyxn5L7zbSfZ8y0H/vNlNXYKBm9xziWJFIJtcfa1BZtU3u0Te2xdns51tZ7fcxezgQMnemwwO1LDnlNryr9lSr3V6rCV6EKf/ej3FfZZyhQ7qvoFRBUBSs0pXGCutrjozaPATfti3+LAbeNt3lcW1smj4f7LQ0WtUS3kaglir2OANzGPEYxYB6jGIy3eZxvLTFuQodkMqn/+I//0FNPPZX3PieffLJuuukmV8exbt06ffGLX9SuXbvy2t7r9ep///d/ddxxx+112127dmnx4sVav3593uP5zne+ozPPPDPv7femmIoFy5Lee8/Q0qUe/eMfHi1d6tW6db3/UlVUWHrf+/I8i6GrS95318qzLvvxjjzr1slsbxtwPMmJk5xQIZUTMOwnq7pm+B94BEUSEScMaIvuUXus3V5OBwYdsfb0+ja1R7uDg0y4EEq4N6dKvWW5AUE6NCj3l9vrfJUq92eHCN2hQnm6Xe4rV8ATkOFCmDPe/ueE4sMcRjEYb/OY0GHwqCX65mYtUUx1BDAamMcoBsxjFIPxNo/zrSXGzeWVbrnllpwiobq6WpdeeqmOP/541dXVafv27Xr00Ud1xx13KBwOS5Iee+wxzZo1SxdddJErY+jq6tLFF1+cUyQcfvjhuuCCC3TooYfK4/Fo1apVuuuuu/TMM89Isn9RdeWVV2rJkiWaNWtWv30nk0ldfvnlOUXC3LlzddFFF+nwww9XSUmJ1q1bp/vuu09//OMfnW2+//3va7/99tORRx7pymccy5JJ+4bPdsBgP3bs6P2XaK9nMSQS8rz7XneosHatPJmgYdvWft/fMgylpk6zw4T9us9USM7YT8npM/b5vRWSqaTaYnu0J9KqPdE92hNtVWvW8p6o/VpbdI9ao+nndDuSjLgyhjJfuSr9laoKVKnSX6VKf6UqA1Xd7UCVqpz1lSr3VeYEDGW+cu5DAAAABo1agloCAAAA+RsXZzqsXbtWn/zkJ53ToCdNmqT77rtPkyZN6rXtO++8o8WLF6u1tVWSfXr0k08+qSlTpgx7HDfeeKNuv/12p33GGWfo+9//fp+nXd9xxx360Y9+5LSPOuoo3Xnnnf32/fvf/17/8z//47SPPvpo/exnP5Pf3/ua7o899piuuuoqpdI3GN5///31yCOPyOPxDOlzZRtLv1AKh6Xlyz3OmQyvvupRZ2fuL9d9PksLFqR05JEJHXFEUosWJVWTPqnAaG+T55235XnnbXnXrJZn7dt2sPDeehmJRL/vm6qrU3LmLCVmzVZy/1lKzpxlP+83UyopGfTnGAzLshRKhNQaaekOCyLpACHaqrZIVmCQfs6EDO2xgc/E2BvTMO0wICscqAhUqsqfHRpUqspfrcpAVW64ELD3K8bAYLwl4ig+zGEUg/E2jznTYXCoJXKNVC0xluoIoBAwj1EMmMcoBuNtHnN5pSyXX365Hn/8cUmSYRi67777tHDhwn63f/XVV7V48WJl/mg+/elP6/rrrx/WGNra2vThD39YkYj9i+85c+bowQcflM/n63efb33rWzm/JPrtb3+rRYsW9doukUjo+OOP144d9g2F6+vr9eSTT6qioqLfvm+99VbdcsstTvuGG27Q6aefPtiP1UshFwudndIrr3j097979PLLXr3xhql4PDdkqKiwtGhRUkcemdQRRyS14NCESjt2yvvOGnneXpN+flued9bIs31bv+9lBYNK7rd/OljYvztY2H+WrJraYX92yQ4QuhJdao20qCXcrOZIs70cyVoO2+2W9PrWSMuwzzoo91WoOlCt6pIa1QRqVBWoVk2J/VwdqFF1VjvzenWgWuX+CpkGBzh6Gm//c0LxYQ6jGIy3eUzoMDjUEr2NRC1RyHUEUIiYxygGzGMUg/E2j7m8UlpLS4uefvppp33UUUcNWCRI0qJFi3TCCSc4pyU//vjj+q//+i+VDuPyNg8//LBTJEjSV7/61QGLBEm68sor9ec//1nxeFySdP/99/dZKLzwwgtOkSBJX/ziFwcsEiTpggsu0L333qvm5manbzdCh0LS2Sm9+qodMvz1r16tWGEqkcgNGSZMSNkBw6KEPjBjsw7RCvnX2qGC96nV8rzz9oA3cU5OmKjknLlKzp6jxOy5Ss6areSs2UpNatLAd47OlQkQWsLNOSFBS7hZLdGW9PoWtUZacsKFod4c2Wf6VB2o6RUO1JTUOMFBdUn6OZBeV1KjKn+VfJ6B5y0AAECxoJbo23ioJQAAADB0RR86vPjii84XbUk69dRT89rvlFNOcQqFSCSi559/XieddNKQx5HpS5KCwaBOOOGEve5TV1enD37wg3rhhRckSX/5y18Ui8V6neac3Xdm7Hvj9/v18Y9/XL/73e8kSa+//rp27typxsbGve5bqLq6us9k+Nvf7DMZeoYM06amdNSCdh3d9I6O9i7V7B1/k3fNKnmfeltG+vq7PVmGodT0GUrMmavk7Lnp5zlKzp4jq6q6//HEu9Qc3q3d4V3px+4ez93LLeFmxVKxIX3ugCeg2pK69KNWtSV1qimpUW2wTnUldapJr3OWg3Uq85a5chNkAACAYkYt0bdirCUAAADgnqIPHV5++eWcdr43OTviiCNy2i+88MKQC4VYLKbXX3/daS9YsEAleV67/4gjjnAKhY6ODr3++uu9PsM//vEPZ3natGlqamrKu+9MoZBKpfTSSy/pjDPOyGvfQhAKScuWSU8+6dNLL3m0fHnvkGFqQ0gfnrpOx5Qs1bEdj2r/9X+R+UhHn/1Zfr+S+8+yz1iYYz8Ss+cquf8sqaREsWQsK0TYrd3bn9Tu9d0BQnOPUCGUCA36M5V4StKhQW06NKjtHRpkwoWgHTSUeksJEAAAAEYAtcTAfY/lWgIAAAAjp+hDhzVr1jjLtbW1mjhxYl771dbWasKECc6pxm+++eaQx/Duu+/m/ELqgAMOyHvf+fPn57TffPPNnEKho6NDW7duda3vsVIoRKPSBz4Q1ObNktT9a62p5c06tvQVHRt6XMd3PqIZuzZIu3L3tbxe+3JI8+YrPneemvdr0tap1dpQbWpHrFk7Qzu0M7xDO0MPa+fbO7R7hR0ktEX3DHqcAU9ADcFG1QfrVR9sUH1pg+pK0svBejWk23XBejtA8A39tHsAAAC4i1picH2PlVoCAAAAI6voQ4d3333XWZ4+ffqg9p02bZpTKGzatEmWZQ3pF+Xr1q3Lac+YMSPvfadOnZrT3rhxo2t9T548WaZpKpVK9dl3IbNSlhrDG2V6vDo2+ayO03M6Vs9rRucGqTO9jWGoc8ok7ZoxUZumVmttU4neapT+WRnS1thu7Qq/oObwg7K2WVL/94TO4TE8qgvW28FBaYMaMmFCzsMOERqCDSrzlXMWAgAAwBhFLdG/sVxLAAAAYGQVdeiwZ88eRaPdN9qdMGHCoPZvaGhwlmOxmJqbm1VfXz/ocezcuTOnPZhxZI9BkrZtyz063rPvwVxH1ev1qra2Vrt37+6z70IWTHTolY458iTtX33tqi3R2xP9erKhQq/WhvRGQ1Kr6i2F/duUkyiE0o8spmGqIdioxtIJaizNPHcv22cqNKi+tF7VgRqZRv43iAYAAMDYRC0xsLFcSwAAAGBkFXXo0NzcnNOuqqoa1P4VFRU57ba2tiEVCsMZR0lJifx+v2KxmDOGgfqurq4e1NgqKiqcQqFn34WsPSB96IK46kLSW41SWzAiKZKzTVWgWlOyw4SyifZyMDtYmKDaklp5TM+++SAAAAAoSNQSezdWawkAAACMrKIOHUKh3J+0l5WVDWr/ntt3dXXtk3GUlpY6hULPMbjRd8ZQP1820zRUWzu4MQxFrcr09x+2KJlKyjRMeQyPTNMjj5F+mB4Z4rJGKHyZqyxUVQVlWft2LMBQMIdRDMbbPDZNviPlg1oiv74zhltLjFYdIY2/v/MoTsxjFAPmMYrBeJvH+dYSRR06ZL5cZ/h8vkHt7/Xm/vFk38BtOOPo2e/eZI87kUiMWt9DYRiGPJ7RKWRrgjWj8j7AaDBNLtuFsY05jGLAPEY2aonh9T1Yo1lHZPB3HsWAeYxiwDxGMWAe5yrqP43MTc0yBnvjtp6TxRpiXJVMJgfsd2+yx93zM41k3wAAAMB4RS0xvL4BAAAwfhV16ODx5F6nf7BfhHv+Wsfv9w9pHD1/MdTzy/3eZG/fcwwj2TcAAAAwXlFLDK9vAAAAjF9FHToEg8GcdjQaHdT+Pbcf6hfpkpKSnHbP05j3JhLpvkFyzzH07Huwn3GgvgEAAIDxilpieH0DAABg/Crq0KGqqiqn3dnZOaj9e94Mrbq6etTHYVmWwuFwv2Po2R7OZxzq5wMAAACKDbXE3lFLAAAAoC9FHTrU19fnXGe0paVlUPvv3r07p11bWzukcTQ0NOS0m5ub8963paUl51Tuurq6nNfr6+t7bT8Y2dv37BsAAAAYr6gl8uu/v74BAAAwfhV16OD3+9XY2Oi0t23bNqj9t2/f7iw3NjYO+ZThqVOn5rQHM46e206ZMsW1vltbW3N++TR58uS89wUAAACKGbXEwKglAAAA0J+iDh0kafbs2c7yhg0b8r45WiKR0IYNG5z2nDlzhjyGnvu+++67ee/bc9vszyPZhUNpaakrfQ/nMwIAAADFhloi/76pJQAAAJBR9KHDoYce6iyHw2G98847ee23evXqnBupZfczWPX19WpqanLa//znP/Ped8WKFTntnuPweDw68MADnfZbb72Vcwr1cPoGAAAAxjNqiaH3DQAAgPGr6EOHo48+Oqf93HPP5bVfz+2OOuoo18axevXqnNOt+2NZlp5//nmnPX369F6nQPfse8+ePVq+fHleY8r+jKWlpTrssMPy2g8AAAAYD6gl+kctAQAAgP4UfeiwYMGCnOuLLlmyJOdXR30Jh8NasmSJ0546deqwv0SfdNJJzrJlWbrnnnv2us+zzz6rzZs3O+1PfvKTfW73iU98Iucmd/n0vXLlSr3yyitO+8QTTxzydWYBAACAYkQt0TdqCQAAAAyk6EMH0zR11llnOe2tW7fqmmuuGXCf73znO9q5c6fTXrx4cc4X8aE48sgjc65zevfdd+sf//hHv9tv375d3/3ud512MBjU5z73uT63nT59uj784Q877SeeeEIPP/xwv313dnbqG9/4htM2DEPnnHNOXp8DAAAAGC+oJXqjlgAAAMDeFH3oIElnn312zi+U7r//fl199dUKhUI524VCIX3zm9/UQw895KybMWOGzjzzzD773bx5s+bOnZvz6I9hGLrqqqucdjwe18UXX6wnnnii17arVq3SF7/4xZxi5fzzz1djY2O//V9xxRXy+XxO++qrr9a9994ry7Jyttu0aZPOPfdcvf322866T33qU5o/f36/fQMAAADjFbVEN2oJAAAA5MOwen6TLFLLly/Xeeedp3A47KyrrKzUcccdpwkTJmj79u16/vnn1d7e7rweDAZ133339fslevPmzTrhhBNy1q1Zs2bAcVx//fW66667ctbNnTtXixYtkt/v1+rVq/Xyyy/nfMFftGiR7rrrLnm93gH7/s1vfqNrr702Z920adP0wQ9+UOXl5Vq3bp1eeuklJRIJ5/X99ttPDzzwgMrLywfsGwAAABivqCWoJQAAAJC/cRM6SNLSpUt18cUXq6OjY6/bVlZW6rbbbtOiRYv63WYohYIkXXvttfrNb36z9wFLOvzww/Wzn/0s7y/yd955p374wx8qlUrtdds5c+bol7/8pSZMmJBX34Vg48aNWrJkiZYuXaoNGzYoFAqptrZWTU1NOuaYY3TaaaepqalpXw8T48Rpp52m1atXD2nfF154QRMnThxwm507d+r+++/X3//+d61bt06dnZ2qrq7WhAkT9MEPflCnn3669t9//yG9P8anDRs26OSTT1Y8Htcll1yiSy+9dNB9jOS8bGtr04MPPqgXX3xRb7/9ttra2lReXq6JEyfq/e9/v04//XQddNBBQ+obxWM48/iiiy7Ss88+O6T3vffee/X+979/r9sxj4sXtUQuaglgeKglMNZQS6AYUEuMnnEVOkjSrl27dNNNN+nxxx9XJBLp9brP59NJJ52kK6+8cq9foIdaKEjS3//+d91444166623+nx94sSJOu+887R48WJ5PJ68+sz417/+pRtuuEGvvvpqnwVDdXW1zj77bF144YUKBAKD6ntfSSQS+slPfqJf/epXSiaT/W7n8/l02WWX6fzzz5dpjourh2EficfjWrhwoeLx+JD231uhcNddd+nmm2/u89+pjMw1lK+66ipu3oi9SiaTOuecc7Rs2TJJGlKhMJLz8pFHHtE111yjtra2Abc75ZRT9J3vfEcVFRV5943iMdx5fPzxx2vLli1Deu98CgXmcfGjlqCWANxALYGxhloCxYBaYnSNu9AhIxQK6dVXX9WWLVvU1tam0tJSzZgxQwsXLlRlZeWojWPz5s164403tGvXLsViMdXU1GjevHk68MADB10g9LRr1y4tW7ZMO3fuVDgcVmVlpebMmaNDDjlkTH2pSCaT+o//+A899dRTee9z8skn66abbhrBUWG8W7VqlU4//fQh7z9QoTCYXzBK8bEFYwAAJghJREFU9mUT7rzzzjH19xqj73/+53/0+9//3mkP9gvWSM7Lu+66S9dff33efc+cOVN/+MMfRvX/1ygMw5nH7e3tA/7qfG/2Vigwj8cXaomx852DWgKFiFoCYw21BIoBtcToGvjCnkWstLRUxxxzzL4ehqZMmaIpU6aMSN8NDQ36xCc+MSJ9j6Zbbrklp0iorq7WpZdequOPP151dXXavn27Hn30Ud1xxx3OdXYfe+wxzZo1SxdddNG+GjaKXM9ToV988UVXLi+wZMmSnC9jwWBQF154oU466SRNmjRJu3fv1jPPPKPbbrtNra2tkqRXX31V3/3ud3tdhxnIuP7663O+XA3WSM7Lv/71r/rBD37gtL1er8455xx9+tOf1rRp09TW1qYXX3xRt912m/OrknfffVf/8R//oV/96lcyDGPInwtjy3Dncc9/t3/3u9/pfe9733CHJYl5PB5RS4wd1BIoRNQSGEuoJVAMqCVG37g90wFjw9q1a/XJT37SOQ160qRJuu+++zRp0qRe277zzjtavHix8z8pn8+nJ598csQKMYxv1113ne6++25JdvG6dOnSYffZ0tKij370o+rs7JQkVVRU6Le//a3mzZvXa9sdO3Zo8eLF2rBhg7Puvvvu02GHHTbscaB4dHZ26lvf+pb+7//+r9dr+f6qYyTnZSwW04knnuh8cfL5fPrFL36ho446qte27e3t+spXvqLly5c76370ox/p1FNP3etnwNjmxjyWpLvvvlvXXXedJPvU/WXLlrly81vmMVC4qCVQqKglMBZQS6AYUEvsO1yoEgXt1ltvdYoEwzB0880391kkSNLs2bP105/+1En44vG4br311lEbK8aXVatWOct9fWEaijvvvNP5MiZJ3/3ud/vte8KECfrFL36hkpISZ92Pf/xjV8aB4rBq1Sp9+tOf7vPL1WCM5Lz84x//mHNNzMsuu6zPL1dS901Z6+vrnXU//elPB7w2N8Y+t+axlPvrpClTprhSJEjMY6CQUUugUFFLoNBRS6AYUEvsW4QOKFgtLS16+umnnfZRRx2lhQsXDrjPokWLcm7I9/jjjysUCo3YGDF+vf32286yG4VCIpHQgw8+6LRnzpypk046acB99ttvP33+85932kuXLtXGjRuHPRaMbS0tLfre976nz3zmMzm/EqqtrR10XyM9L5csWeIsV1VVafHixQP2XVtbq6985StOe8OGDXrllVcG3Adjk5vzOCO7UHDrAI/EPAYKFbUEChm1BAoVtQSKAbVEYSB0QMF68cUXFY/HnXa+pwudcsopznIkEtHzzz/v9tAwzm3dulV79uxx2m78D2f58uVqbm522ieffHJe1+XLnu+S9OSTTw57LBi7/va3v+ljH/uY7r33XiUSCWf94YcfrjvuuGPQ/Y3kvNy6datWrlzptE844QQFg8G99t1zDMz54uP2PJbsonft2rVO261CgXkMFC5qCRQqagkUKmoJFANqicJB6ICC9fLLL+e0jzzyyLz2O+KII3LaL7zwgmtjAqTc06Eld/6HM9T5ftBBB+Wc1vfiiy8OeywYu9555x11dHQ47WAwqP/8z//U3Xffrerq6kH3N5Lzcqh919fXa9asWQP2jbHN7Xks2dd1j8ViTtutQoF5DBQuagkUKmoJFCpqCRQDaonCQeiAgrVmzRpnuba2VhMnTsxrv9raWk2YMMFpv/nmm66PDeNb9ml1Pp9P+++//7D7zJ7vhmFo/vz5ee1nmqbmzJnjtP/1r3/Jsqxhjwdjm2EYOuWUU/Too4/qvPPOk2kO7X/3Izkvs/uWpAMPPDDvcWV/ydu6dWvOL6hQPNyax1Luv9uSe4UC8xgoXNQSKFTUEih01BIoBtQS+553Xw8A6M+7777rLE+fPn1Q+06bNk07duyQJG3atEmWZeV1Gh+Qj+z/4cycOVN+v1/Lli3To48+qtdee01bt25VLBZTXV2d5syZo2OPPVann366SktL++1z3bp1znJDQ4PKysryHs+0adP0+uuvS5JCoZB27tyZUyxj/PD5fDr11FP1pS99SQcccMCw+xvJeZndt2EYmjZt2qD6zrZhwwbV1dXlvT8Km9vzWMr9d7u8vFxTpkzR6tWr9dBDD+mVV17Rpk2bFA6HVVtbqxkzZujYY4/Vpz71KdXU1AzYL/MYKFzUEihU1BIoVNQSKAbUEoWD0AEFac+ePYpGo057sF96GhoanOVYLKbm5uacu7sDw5F9SrTP59OZZ57pfCHKtm3bNm3btk0vvPCCbrvtNn3jG9/o93rCO3fudJaHM98lafv27RQK49TZZ5+ts88+27X+RnJeZvddU1Mjv98/rL5RPNyex1Luv9s1NTX66le/queee67Xdjt27NCOHTu0dOlS3Xbbbbrkkkt07rnn9tsv8xgoTNQSKGTUEihU1BIoBtQ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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"model_list = [models['gamma_1.001_rho_1.5'],models['gamma_8.001_rho_1.5']]\n",
"T = 160\n",
"plot_price_elasticity(model_list,T,[0.1,0.5,0.9],'quarters','0',[0,0.25],None)"
]
},
{
"cell_type": "markdown",
"id": "2e77d327",
"metadata": {},
"source": [
"
\n",
"
\n",
"
\n",
"\n",
"# 3 Outputs\n",
"\n",
"## 3.1 List of Outputs \n",
"\n",
"We now examine the contents of `ModelSol`, which contains the attributes listed below. Each approximation is stored in a class `LinQuadVar`, which contains the coefficients for $X_{1,t}, X_{2,t}, X_{1,t}'X_{1,t}, W_{t+\\epsilon}, W_{t+\\epsilon}'W_{t+\\epsilon}, X_{1,t}'W_{t+\\epsilon}$ and the constant.\n",
"\n",
"\n",
"```{list-table}\n",
"* - Input\n",
" - Type\n",
" - Description\n",
"* - `JXn_t`\n",
" - *LinQuadVar*\n",
" - Approximation of jump and state variables at time $t$. Replace `n` with `0,1,2` to get the zeroth, first and second-order contribution. Omit `n` to get the full approximation. The variables are indexed in the order specified in Section 2. \n",
"* - `Jn_t`\n",
" - *LinQuadVar*\n",
" - Same as `JXn_t` but limited to jump variables.\n",
"* - `Xn_tp1`\n",
" - *LinQuadVar*\n",
" - Same as `JXn_t` but limited to state variables.\n",
"* - `JXn_t_tilde`\n",
" - *LinQuadVar*\n",
" - Same as `JXn_t` but using distorted measure. This variation is also available for `Jn_t` and `Xn_tp1`.\n",
"* - `util_sol`\n",
" - *dict*\n",
" - Dictionary containing solutions of the continuation values, including $\\mu^0, \\Upsilon_0^2, \\Upsilon_1^2,$ and $\\Upsilon_2^2$ etc.\n",
"* - `vmrn_tp1`\n",
" - *LinQuadVar*\n",
" - Approximation of continuation values $\\widehat{V}^1_{t+\\epsilon}-\\widehat{R}^1_t$ . Replace `n` with `0,1,2` to get the zeroth, first and second-order contribution. Omit `n` to get the full approximation. \n",
"* - `gcn_tp1`\n",
" - *LinQuadVar*\n",
" - Approximation of consumption growth $\\widehat{C}_{t+\\epsilon}-\\widehat{C}_t$ . Replace `n` with `0,1,2` to get the zeroth, first and second-order contribution. Omit `n` to get the full approximation. \n",
"* - `ss`\n",
" - *dict*\n",
" - Steady states for state and jump variables\n",
"* - `log_N_tilde`\n",
" - *LinQuadVar*\n",
" - Approximation for the log change of measure\n",
"```\n",
"For example, we can obtain the coefficients for the first-order contribution of $\\log{C_t/K_t}$ in the following way, noting that `cmk_t` was listed as the first jump variable when we specified the equilibrum conditions.\n"
]
},
{
"cell_type": "code",
"execution_count": 64,
"id": "9ab60024",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'c': array([[-0.00000005]]),\n",
" 'x': array([[ 0. , 0.00056165, -0. ]])}"
]
},
"execution_count": 64,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"## Log consumption over capital approximation results, shown in the LinQuadVar coefficients form\n",
"ModelSol['JX1_t'][0].coeffs"
]
},
{
"cell_type": "markdown",
"id": "4c7156db",
"metadata": {},
"source": [
"We can also display the full second-order approximation of $\\log{C_t/K_t}$ using the `disp` function, which renders a `LinQuadVar` object in LATEX form."
]
},
{
"cell_type": "code",
"execution_count": 65,
"id": "68ad25a4",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\log\\frac{C_t}{K_t}=-4.127+\\begin{bmatrix}2.116e-16&0.0005616\\end{bmatrix}X_t^1+\\begin{bmatrix}1.058e-16&0.0002808\\end{bmatrix}X_t^2+X^{1T}_{t}\\begin{bmatrix}7.68e-33&3.191e-20\\\\3.032e-76&-4.388e-20\\end{bmatrix}X^1_{t}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Log consumption over capital approximation results, shown in the Latex analytical form\n",
"disp(ModelSol['JX_t'][0],'\\\\log\\\\frac{C_t}{K_t}') "
]
},
{
"cell_type": "markdown",
"id": "a952413c",
"metadata": {},
"source": [
"Another example:"
]
},
{
"cell_type": "code",
"execution_count": 66,
"id": "0a28d287",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\log\\frac{K_{t+\\epsilon}^2}{K_t^2}=-1.9e-05+\\begin{bmatrix}3.427e-26&1.26e-13\\end{bmatrix}X_t^1+\\begin{bmatrix}-3.388e-19&0.009999\\end{bmatrix}X_t^2+X^{1T}_{t}\\begin{bmatrix}-8.797e-35&-3.656e-22\\\\-1.521e-78&1.454e-23\\end{bmatrix}X^1_{t}+X^{1T}_{t}\\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}W_{t+1}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Log capital growth process second order approximation results\n",
"disp(ModelSol['X2_tp1'][0],'\\\\log\\\\frac{K_{t+\\epsilon}^2}{K_t^2}') "
]
},
{
"cell_type": "markdown",
"id": "09047922",
"metadata": {},
"source": [
"
\n",
"\n",
"## 3.2 Simulate Variables \n",
"Given a series of shock processes, we can simulate the path of our state and jump variables using the `ModelSolution.simulate` method. Here, we simulate 400 periods of i.i.d standard multivariate normal shocks."
]
},
{
"cell_type": "code",
"execution_count": 67,
"id": "db492e54",
"metadata": {},
"outputs": [],
"source": [
"n_J, n_X, n_W = ModelSol['var_shape']\n",
"Ws = np.random.multivariate_normal(np.zeros(n_W),np.eye(n_W),size = 400)\n",
"JX_sim = ModelSol.simulate(Ws)"
]
},
{
"cell_type": "markdown",
"id": "54b619f8",
"metadata": {},
"source": [
"
\n",
"
\n",
"\n",
"# 4 Using `LinQuadVar` in Computation \n",
"\n",
"In the previous section, we saw how to use `uncertain_expansion` to approximate variables and store their coefficients as `LinQuadVar` objects. In this section, we explore how to manipulate `LinQuadVar` objects for different uses.\n",
"\n",
"To aid our examples, we first extract the steady states for the state evolution processes from the previous model solution:\n",
"\n",
"See [src/lin_quad.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/lin_quad.py) for source code of `LinQuadVar` definition."
]
},
{
"cell_type": "code",
"execution_count": 68,
"id": "6c904c8c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-4.12667104, 0.07606349, 0.60576715])"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ModelSol['ss'][[0,1,2]]"
]
},
{
"cell_type": "code",
"execution_count": 71,
"id": "d7f9aeac",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5 3 3\n"
]
}
],
"source": [
"n_J, n_X, n_W = ModelSol['var_shape']\n",
"print(n_J, n_X, n_W)\n",
"X0_tp1 = LinQuadVar({'c':np.array([[ModelSol['ss'][0]],[ModelSol['ss'][1]],[ModelSol['ss'][2]]])}, shape = (n_X, n_X, n_W))"
]
},
{
"cell_type": "markdown",
"id": "4f7a05ea",
"metadata": {},
"source": [
"## 4.1 `LinQuadVar` Operations \n",
"We can sum multiple LinQuads together in two different ways. Here we demonstrate this with an example by summing the zeroth, first and second order contributions of our approximation for capital growth. "
]
},
{
"cell_type": "code",
"execution_count": 72,
"id": "6f22ab40",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\log\\frac{K_{t+\\epsilon}}{K_t}=-4.127+\\begin{bmatrix}-3.388e-19&0.009999\\end{bmatrix}X_t^1+\\begin{bmatrix}0.004&0.001739\\end{bmatrix}W_{t+1}+\\begin{bmatrix}-1.694e-19&0.004999\\end{bmatrix}X_t^2+X^{1T}_{t}\\begin{bmatrix}-4.399e-35&-1.828e-22\\\\-7.605e-79&7.268e-24\\end{bmatrix}X^1_{t}+X^{1T}_{t}\\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}W_{t+1}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gk_tp1 = X0_tp1[0] + ModelSol['X1_tp1'][0] + 0.5 * ModelSol['X2_tp1'][0] \n",
"disp(gk_tp1,'\\\\log\\\\frac{K_{t+\\epsilon}}{K_t}') "
]
},
{
"cell_type": "markdown",
"id": "bb5e6d0c",
"metadata": {},
"source": [
"In the next example, we sum together the contributions for both capital growth and technology:"
]
},
{
"cell_type": "code",
"execution_count": 73,
"id": "79982125",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'c': array([[-4.12668054],\n",
" [ 0.07606349],\n",
" [ 0.5828862 ]]),\n",
" 'x': array([[-0. , 0.00999859, 0. ],\n",
" [ 0. , 0.986 , 0. ],\n",
" [ 0. , 0. , 0.9515 ]]),\n",
" 'xw': array([[ 0. , 0. , 0. , 0. , 0. , 0. , 0.00199981, 0.00086948, 0. ],\n",
" [ 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.01239013, 0. ],\n",
" [ 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , -0.10696016]]),\n",
" 'x2': array([[-0. , 0.0049993, 0. ],\n",
" [ 0. , 0.493 , 0. ],\n",
" [ 0. , 0. , 0.47575 ]]),\n",
" 'xx': array([[-0. , -0. , -0. , 0. , -0. , -0. , 0. , 0. , 0. ],\n",
" [ 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ],\n",
" [ 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.02425]]),\n",
" 'w': array([[0.00399962, 0.00173897, 0. ],\n",
" [0. , 0.02478025, 0. ],\n",
" [0. , 0. , 0.21392032]])}"
]
},
"execution_count": 73,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lq_sum([X0_tp1, ModelSol['X1_tp1'], 0.5 * ModelSol['X2_tp1']]).coeffs"
]
},
{
"cell_type": "markdown",
"id": "1eb2e7e3",
"metadata": {},
"source": [
"## 4.2 `LinQuadVar` Split and Concat \n",
"`split` breaks multiple dimensional LinQuad into one-dimensional LinQuads, while `concat` does the inverse."
]
},
{
"cell_type": "code",
"execution_count": 75,
"id": "625e6e2f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 75,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"gk_tp1, Z_tp1, Y_tp1 = ModelSol['X1_tp1'].split()\n",
"concat([gk_tp1, Z_tp1, Y_tp1])"
]
},
{
"cell_type": "markdown",
"id": "1e00f7f9",
"metadata": {},
"source": [
"## 4.3 Evaluate a `LinQuadVar` \n",
"We can evaluate a LinQuad at specific state $(X_{t},W_{t+\\epsilon})$ in time. As an example, we evaluate all 5 variables under steady state with a multivariate random normal shock."
]
},
{
"cell_type": "code",
"execution_count": 76,
"id": "f7d0893c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ -4.12667002],\n",
" [ 0.07606348],\n",
" [ 0.60576726],\n",
" [ -0.00018954],\n",
" [ 1. ],\n",
" [ 0.00223285],\n",
" [ 0.00817758],\n",
" [-11.99963929]])"
]
},
"execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x1 = np.zeros([n_X ,1])\n",
"x2 = np.zeros([n_X ,1])\n",
"x3 = np.zeros([n_X, 1])\n",
"w = np.random.multivariate_normal(np.zeros(n_W),np.eye(n_W),size = 1).T\n",
"ModelSol['JX_tp1'](*(x1,x2,w))"
]
},
{
"cell_type": "markdown",
"id": "72f12124",
"metadata": {},
"source": [
"## 4.4 Next period expression for `LinQuadVar` \n",
"`ModelSol` allows us to express a jump variable $J_t$ as a function of $t$ state and shock variables. Suppose we would like to compute its next period expression $J_{t+\\epsilon}$ with shocks. The function `next_period` expresses $J_{t+\\epsilon}$ in terms of $t$ state variables and $t+\\epsilon$ shock variables. For example, we can express the $t+\\epsilon$ expression for the first-order contribution to consumption over capital as:"
]
},
{
"cell_type": "code",
"execution_count": 48,
"id": "e50060c4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'x': array([[-0. , 0.03710412, -0. , 0.00006824],\n",
" [-0. , 0.944 , -0. , -0. ],\n",
" [-0. , -0. , 0.806 , -0. ],\n",
" [ 0. , -0.0366626 , 0. , -0.10516689]]),\n",
" 'w': array([[ 0.00799924, 0.00347793, -0. ],\n",
" [-0. , 0.04956051, -0. ],\n",
" [-0. , -0. , 0.42784065],\n",
" [-0.00799924, -0.00347793, -0. ]]),\n",
" 'c': array([[ 0.00111162],\n",
" [ 0. ],\n",
" [ 0. ],\n",
" [-0.0012811 ]])}"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ModelSol[\"X1_tp1\"].coeffs"
]
},
{
"cell_type": "code",
"execution_count": 77,
"id": "30a0718d",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\log\\frac{C_{t+\\epsilon}^1}{K_{t+\\epsilon}^1}=-5.482e-08+\\begin{bmatrix}-7.17e-35&0.0005538\\end{bmatrix}X_t^1+\\begin{bmatrix}8.464e-19&1.392e-05\\end{bmatrix}W_{t+1}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cmk1_tp1 = next_period(ModelSol['J1_t'][0], ModelSol['X1_tp1'])\n",
"disp(cmk1_tp1, '\\\\log\\\\frac{C_{t+\\epsilon}^1}{K_{t+\\epsilon}^1}') "
]
},
{
"cell_type": "code",
"execution_count": 78,
"id": "094dcae3",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\log\\frac{C_{t+\\epsilon}^2}{K_{t+\\epsilon}^2}=-7.039e-06+\\begin{bmatrix}6.46e-42&1.605e-11\\end{bmatrix}X_t^1+\\begin{bmatrix}9.347e-27&4.033e-13\\end{bmatrix}W_{t+1}+\\begin{bmatrix}-7.17e-35&0.0005538\\end{bmatrix}X_t^2+X^{1T}_{t}\\begin{bmatrix}-1.862e-50&-9.87e-38\\\\-5.174e-94&3.24e-38\\end{bmatrix}X^1_{t}+X^{1T}_{t}\\begin{bmatrix}-4.163e-53&2.01e-40\\\\-4.396e-95&-9.443e-23\\end{bmatrix}W_{t+1}+W_{t+1}^{T}\\begin{bmatrix}2.457e-37&6.325e-24\\\\5.189e-79&-8.698e-24\\end{bmatrix}W_{t+1}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cmk2_tp1 = next_period(ModelSol['J2_t'][0], ModelSol['X1_tp1'], ModelSol['X2_tp1'])\n",
"disp(cmk2_tp1, '\\\\log\\\\frac{C_{t+\\epsilon}^2}{K_{t+\\epsilon}^2}') "
]
},
{
"cell_type": "markdown",
"id": "17a90814",
"metadata": {},
"source": [
"## 4.6 Compute the Expectation of time $t+\\epsilon$ `LinQuadVar` \n",
"\n",
"Suppose the distribution of shocks has a constant mean and variance (not state dependent). Then, we can use the `E` function to compute the expectation of a time $t+\\epsilon$ `LinQuadVar` as follows:\n"
]
},
{
"cell_type": "code",
"execution_count": 79,
"id": "ec4a6591",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\mathbb{E}[\\log\\frac{C_{t+\\epsilon}^2}{K_{t+\\epsilon}^2}|\\mathfrak{F_t}]=-7.039e-06+\\begin{bmatrix}6.456e-42&1.609e-11\\end{bmatrix}X_t^1+\\begin{bmatrix}-7.17e-35&0.0005538\\end{bmatrix}X_t^2+X^{1T}_{t}\\begin{bmatrix}-1.862e-50&-9.87e-38\\\\-5.174e-94&3.24e-38\\end{bmatrix}X^1_{t}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"E_w = ModelSol['util_sol']['μ_0']\n",
"cov_w = np.eye(n_W)\n",
"E_ww = cal_E_ww(E_w, cov_w)\n",
"E_cmk2_tp1 = E(cmk2_tp1, E_w, E_ww)\n",
"disp(E_cmk2_tp1, '\\mathbb{E}[\\\\log\\\\frac{C_{t+\\epsilon}^2}{K_{t+\\epsilon}^2}|\\mathfrak{F_t}]')"
]
},
{
"cell_type": "markdown",
"id": "ae74e865",
"metadata": {},
"source": [
"Suppose the distribution of shock has a state-dependent mean and variance (implied by $\\tilde{N}_{t+\\epsilon}$ shown in the notes), we can use `E_N_tp1` and `N_tilde_measure` to compute the expectation of time $t+\\epsilon$ `LinQuadVar`."
]
},
{
"cell_type": "code",
"execution_count": 80,
"id": "be1c3394",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\mathbb{\\tilde{E}}[\\log\\frac{C_{t+\\epsilon}^2}{K_{t+\\epsilon}^2}|\\mathfrak{F_t}]=-7.039e-06+\\begin{bmatrix}6.456e-42&1.609e-11\\end{bmatrix}X_t^1+\\begin{bmatrix}-7.17e-35&0.0005538\\end{bmatrix}X_t^2+X^{1T}_{t}\\begin{bmatrix}-1.862e-50&-9.87e-38\\\\1.354e-50&3.24e-38\\end{bmatrix}X^1_{t}$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N_cm = N_tilde_measure(ModelSol['util_sol']['log_N_tilde'],(1,n_X,n_W))\n",
"E_cmk2_tp1_tilde = E_N_tp1(cmk2_tp1, N_cm)\n",
"disp(E_cmk2_tp1_tilde, '\\mathbb{\\\\tilde{E}}[\\\\log\\\\frac{C_{t+\\epsilon}^2}{K_{t+\\epsilon}^2}|\\mathfrak{F_t}]')"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d6d38d56",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"colab": {
"provenance": []
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"kernelspec": {
"display_name": "base",
"language": "python",
"name": "python3"
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"language_info": {
"codemirror_mode": {
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"file_extension": ".py",
"mimetype": "text/x-python",
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