Mexico Macroeconomic analysis.ipynb

{
 "nbformat": 4,
 "nbformat_minor": 0,
 "metadata": {
  "colab": {
   "name": " Final exam_Bertrand.ipynb",
   "provenance": [],
   "collapsed_sections": []
  },
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3"
  },
  "language_info": {
   "name": "python"
  }
 },
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_G9WYIyIW9RR"
   },
   "source": [
    "# Country choice: Mexico    , mi pais favorito\n",
    "\n",
    "![mexcio.jpeg](data:image/jpeg;base64,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)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "FsCpT1CpU-WJ",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1642808019313,
     "user_tz": -330,
     "elapsed": 1975,
     "user": {
      "displayName": "Bertrand Kwibuka",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GhRvCbz_WuDbIMDrPTEKSNqTbtcDv2w8bsCkexQdfs=s64",
      "userId": "03353322417714764277"
     }
    }
   },
   "source": [
    "#@title Default title text\n",
    "#installing all necessary dependencies \n",
    "\n",
    "import numpy as np\n",
    "import scipy.optimize as opt\n",
    "from scipy.optimize import fsolve\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.linalg as la\n",
    "import numpy as np\n",
    "from numpy.linalg import matrix_rank\n",
    "\n",
    "import sympy as sym\n",
    "from sympy import *\n",
    "from sympy import symbols, Matrix, Transpose\n",
    "from sympy import lambdify\n",
    "\n",
    "import math\n",
    "import cmath\n",
    "from math import *\n",
    "\n",
    "import mpmath as mp\n",
    "from math import sqrt\n",
    "from matplotlib import rcParams\n"
   ],
   "execution_count": 2,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mDCwx19SEQRo"
   },
   "source": [
    "# Inputing data for savings rate, capital output ratio and labor hours for Mexico to plot data plots\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "G5z8BKK_fFys",
    "executionInfo": {
     "status": "error",
     "timestamp": 1642807989332,
     "user_tz": -330,
     "elapsed": 8,
     "user": {
      "displayName": "Bertrand Kwibuka",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GhRvCbz_WuDbIMDrPTEKSNqTbtcDv2w8bsCkexQdfs=s64",
      "userId": "03353322417714764277"
     }
    },
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 272
    },
    "outputId": "407be632-64f9-4848-c721-9debfa9ac30c"
   },
   "source": [
    "\n",
    "#timing \n",
    "time=[t for t in range(1970,2100)]\n",
    "\n",
    "#Pop_growth: \n",
    "\n",
    "s_data = [0.194,0.177,0.181,0.191,0.196,0.192,0.189,0.208,0.208,0.223,0.223,0.217,0.225,0.258,0.233,0.225,0.177,0.216,0.208,0.199,0.194,0.182,0.16,0.191,0.2,0.185,0.175,0.179,0.173,0.175,0.161,0.142,0.144,0.193,0.211,0.202,0.215,0.214,0.208,0.199,0.203]\n",
    "\n",
    "#K/Y: \n",
    "\n",
    "ky_data = np.array([1.3,1.413,1.449,1.452,1.52,1.61,1.582,1.677,1.676,1.674,1.679,1.676,1.508,1.851,1.943,1.828,1.803,1.786,2.186,2.183,2.134,2.101,2.098,2.151,1.986,2.213,2.243,2.165,2.183,2.196,2.263,2.437,2.494,2.57,2.544,2.562,2.517,2.519,2.588,2.898,2.802])\n",
    "\n",
    "#labor hours: \n",
    "\n",
    "l_data = np.array([20.355,20.778,21.208,21.627,22.035,22.685,22.889,23.076,23.406,24.057,24.719,24.785,24.878,24.24,24.474,24.847,24.792,24.813,24.859,24.995,25.127,24.447,24.5,24.79,25.398,24.75,25.529,26.979,26.208,26.836,26.065,25.3,26.028,25.164,25.35,25.777,25.551,25.234,25.816,23.924,25.908])\n",
    "\n"
   ],
   "execution_count": 1,
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "ignored",
     "traceback": [
      "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m",
      "\u001B[0;31mNameError\u001B[0m                                 Traceback (most recent call last)",
      "\u001B[0;32m<ipython-input-1-4c1fa48d8063>\u001B[0m in \u001B[0;36m<module>\u001B[0;34m()\u001B[0m\n\u001B[1;32m      9\u001B[0m \u001B[0;31m#K/Y:\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0m\n\u001B[1;32m     10\u001B[0m \u001B[0;34m\u001B[0m\u001B[0m\n\u001B[0;32m---> 11\u001B[0;31m \u001B[0mky_data\u001B[0m \u001B[0;34m=\u001B[0m \u001B[0mnp\u001B[0m\u001B[0;34m.\u001B[0m\u001B[0marray\u001B[0m\u001B[0;34m(\u001B[0m\u001B[0;34m[\u001B[0m\u001B[0;36m1.3\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.413\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.449\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.452\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.52\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.61\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.582\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.677\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.676\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.674\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.679\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.676\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.508\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.851\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.943\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.828\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.803\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.786\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.186\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.183\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.134\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.101\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.098\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.151\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m1.986\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.213\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.243\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.165\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.183\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.196\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.263\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.437\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.494\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.57\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.544\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.562\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.517\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.519\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.588\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.898\u001B[0m\u001B[0;34m,\u001B[0m\u001B[0;36m2.802\u001B[0m\u001B[0;34m]\u001B[0m\u001B[0;34m)\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0m\n\u001B[0m\u001B[1;32m     12\u001B[0m \u001B[0;34m\u001B[0m\u001B[0m\n\u001B[1;32m     13\u001B[0m \u001B[0;31m#labor hours:\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0;34m\u001B[0m\u001B[0m\n",
      "\u001B[0;31mNameError\u001B[0m: name 'np' is not defined"
     ]
    }
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "j5dlR5mfBdgN"
   },
   "source": [
    "# **Working on the model ** "
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "iR6XRNjfSN2H"
   },
   "source": [
    "# Set parameter values\n",
    "\n",
    "# Iteration parameters\n",
    "S = 100 # number of periods in the shooting\n",
    "niter=200 # number of possible trials of the intial value\n",
    "epsilon=.00005 #convergence criterion\n",
    "\n",
    "# Model Parameters\n",
    "theta = 0.3 # Share of capital in output rents\n",
    "delta = 0.035 # Capital depreciation rate\n",
    "alpha = 3.1 # disutility from labor parameter\n",
    "beta = 0.946 # Discount factor\n",
    "T = 3.9*24 # Total number of hours owned in a week"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "r4W6OynaBYuQ"
   },
   "source": [
    "# In the guess of the initial consumption, we will feed in the actual time series of the exogenous variables \n",
    "# Population and TFP grow at exogenous rate\n",
    "# Capital taxes are 0.2 in the first 20 years and then 0.12 forever\n",
    "# Government spending share fluctuates around 0.13 (where error is normally distribution with mean 0 and sd 0.0005) for the first 20 years\n",
    "# In the long run, government spending share is constant\n",
    "\n",
    "\n",
    "gamma = 1.001 # TFP to the power 1/(1-theta) growth rate. Long run growth rate of per capita income \n",
    "gA_ast = gamma**(1-theta) # = (1+g) in our model. TFP growth rate\n",
    "n_ast = 1.020 # population growth rate. n_ast = (1+n) in our model\n",
    "\n",
    "chi_ast = 0.107 # long-run government share\n",
    "tau_ast = 0.084 # long-run capital tax\n",
    "\n",
    "##\n",
    "\n",
    "##Check the sources of the following parameters and how they calculated them: \n",
    "\n",
    "##\n",
    "\n",
    "H0 = 22127*1000000/52\n",
    "N0 = 25654920\n",
    "k0 = 1.95**(1/(1-theta))*(H0/N0)\n",
    "A0 = 1**(1-theta)"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "nwQ-sQ0-BYxB",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1628888320223,
     "user_tz": -330,
     "elapsed": 9,
     "user": {
      "displayName": "Bertrand Kwibuka",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjTN0MNu3HMdyI-k1Xwr3e4pF521hd01Rv-Qhh-wg=s64",
      "userId": "14120959365019312055"
     }
    },
    "outputId": "41ab2c37-cf7b-4f0d-b889-0b6356acb796"
   },
   "source": [
    "# SS- Steady State\n",
    "c1 = theta*(1/(1-tau_ast)*(gA_ast**(1/(1-theta))/beta - 1)+ delta)**(-1) # steady state (k/h)**(1-theta)\n",
    "c2 = 1 - chi_ast - c1*(gA_ast**(1/(1-theta))*n_ast - 1 + delta)  # steady state c/y ratio\n",
    "c3 = c2*alpha/(1-theta) # steady state (barh - h)/h\n",
    "h_ast = 1/(1+c3)*T\n",
    "k_ast = c1**(1/(1-theta))*h_ast\n",
    "y_ast = k_ast**theta*h_ast**(1-theta)\n",
    "c_ast = c2*y_ast\n",
    "\n",
    "print(\"[k_ast, c_ast, h_ast] = \", k_ast, c_ast, h_ast)"
   ],
   "execution_count": null,
   "outputs": [
    {
     "output_type": "stream",
     "text": [
      "[k_ast, c_ast, h_ast] =  109.4716511015576 25.95525388038508 22.29159035940587\n"
     ],
     "name": "stdout"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "0z6eEWYvBY1b",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1628888321700,
     "user_tz": -330,
     "elapsed": 12,
     "user": {
      "displayName": "Bertrand Kwibuka",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjTN0MNu3HMdyI-k1Xwr3e4pF521hd01Rv-Qhh-wg=s64",
      "userId": "14120959365019312055"
     }
    },
    "outputId": "e9e6eb79-fc50-4f9a-fde9-910f1c41570a"
   },
   "source": [
    "# Inputting series of exogenous variables \n",
    "\n",
    "#timing \n",
    "\n",
    "time = 100\n",
    "\n",
    "# defining variables over time \n",
    "\n",
    "chi =[1]*time \n",
    "tau =[1]*time\n",
    "gt  =[1]*time\n",
    "nt  =[1]*time\n",
    "\n",
    "\n",
    "\n",
    "#chi_tt =np.array([0.05128205128,0.1136363636,0.05376344086,0,0.1226415094,0.06194690265,-0.01801801802,0.008928571429,0,-0.07692307692,0.07142857143,0.008849557522,-0.2021276596,0.04081632653,-0.01030927835,0,-0.05434782609,-0.04545454545,-0.02325581395,0.01149425287,0.06451612903,0.08823529412,0.2330827068,-0.0390625,0.06569343066,-0.06201550388,-0.06611570248,-0.01680672269,-0.01709401709,-0.01739130435,0.008620689655,0.008547008547,-0.01739130435,-0.06481481481,0.009174311927,-0.009259259259,0,0.02702702703,0.09016393443,-0.03389830508]),\n",
    "#tau_ast  = np.array([0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-3.059405941,0,0,0,0,0,-0.05208333333,-0.2631578947,-0.08571428571,0.1025641026,0.03703703704,0.05813953488,0.01149425287,0.06451612903,-0.1204819277,-0.1216216216,-0.1384615385,0.01515151515,0.04347826087,0.06756756757,0.03896103896,0.0253164557,0.0125])\n",
    "#gA_ast   = np.array([-0.04775657236,0.01870605515,0.02767060001,-0.01228658208,-0.02944335504,0.008092279059,-0.03257884483,0.03264937749,0.02927819843,0.01777221813,0.04772793558,0.00621966604,-0.1367506783,-0.02954874869,-0.0008371470768,-0.05926115541,-0.01379724119,-0.1151531636,0.004046760459,0.006944048896,0.02952848157,0.0006797218319,-0.001796032284,0.06658728305,-0.06645780551,0.01314596532,0.02735068795,0.01180369654,-0.01875648437,0.01723391664,-0.02258941881,0.006763970741,-0.01936418702,0.00879879299,0.01002316835,0.01921003344,0.0003104206106,-0.01792552347,-0.08240297309,0.04720472149,])\n",
    "#s_data = [0.194,0.177,0.181,0.191,0.196,0.192,0.189,0.208,0.208,0.223,0.223,0.217,0.225,0.258,0.233,0.225,0.177,0.216,0.208,0.199,0.194,0.182,0.16,0.191,0.2,0.185,0.175,0.179,0.173,0.175,0.161,0.142,0.144,0.193,0.211,0.202,0.215,0.214,0.208,0.199,0.203]\n",
    "#gA_ast = np.array([1.0000,  0.9544 ,  0.9726 ,  1.0003 ,  0.9882 ,  0.9599 ,  0.9677 ,  0.9372 ,  0.9688 ,  0.9980 ,  1.0161 ,  1.0670 ,  1.0737 ,  0.9445 ,  0.9174 ,  0.9167 ,  0.8654 ,  0.8536 ,  0.7655 ,  0.7686 ,  0.7739 ,  0.7975 ,  0.7980 ,  0.7966 ,  0.8534 ,  0.8002 ,  0.8109 ,  0.8337 ,  0.8437 ,  0.8281 ,  0.8427 ,  0.8240 ,  0.8297 ,  0.8139 ,  0.8211 ,  0.8294 ,  0.8457 ,  0.8459 ,  0.8310 ,  0.7678 ,  0.8058 ])\n",
    "\n",
    "\n",
    "\n",
    "# Trajectory of Exogenous Variables\n",
    "\n",
    "\n",
    "chi_ast  = np.array([0.074,0.078,0.088,0.093,0.093,0.106,0.113,0.111,0.112,0.112,0.104,0.112,0.113,0.094,0.098,0.097,0.097,0.092,0.088,0.086,0.087,0.093,0.102,0.133,0.128,0.137,0.129,0.121,0.119,0.117,0.115,0.116,0.117,0.115,0.108,0.109,0.108,0.108,0.111,0.122,0.118])\n",
    "\n",
    "tau_ast  = np.array([0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.41,0.101,0.101,0.101,0.101,0.101,0.101,0.096,0.076,0.07,0.078,0.081,0.086,0.087,0.093,0.083,0.074,0.065,0.066,0.069,0.074,0.077,0.079,0.08])\n",
    "\n",
    "n_ast    = np.array([1.032,1.032,1.033,1.034,1.03,1.032,1.033,1.033,1.031,1.034,1.032,1.031,1.031,1.033,1.034,1.035,1.035,1.034,1.032,1.03,1.03,1.029,1.028,1.026,1.025,1.024,1.023,1.022,1.022,1.02,1.019,1.018,1.017,1.018,1.02,1.021,1.022,1.022,1.022,1.022,1.021])\n",
    "\n",
    "gA_ast   = np.array([1,0.9678715503,1.013306006,1.019836632,0.9914882317,0.9798921573,1.005703845,0.977808355,1.023508041,1.021018595,1.012631541,1.03482585,1.004376913,0.9141855336,0.979821939,0.9994144137,0.9605011021,0.9904538089,0.9265435465,1.002842512,1.004889705,1.021202911,1.00047608,0.9987446936,1.049417738,0.9559593514,1.009306233,1.019601818,1.008346378,0.987076312,1.012243247,0.9844849781,1.004762168,0.9866643574,1.006205587,1.007076538,1.013670458,1.000217352,0.9876402875,0.9460796837,1.034428036])\n",
    "\n",
    "\n",
    "#taking care of steady states/ long term values: \n",
    "\n",
    "# 1. chi[t]:\n",
    "for i in range(0, time):\n",
    "    \n",
    "    if i < len(chi_ast):\n",
    "        chi[i] = chi_ast[i]\n",
    "    else:\n",
    "        chi[i] = chi_ast[len(chi_ast)-1]\n",
    "# 2.tau[t]:\n",
    "for i in range(0, time):\n",
    "    \n",
    "    if i < len(tau_ast):\n",
    "        tau[i] = tau_ast[i]\n",
    "    else:\n",
    "        tau[i] = tau_ast[len(tau_ast)-1]\n",
    "\n",
    "# 3. gt[t]:\n",
    "for i in range(0, time):\n",
    "    \n",
    "    if i < len(gA_ast):\n",
    "        gt[i] = gA_ast[i]\n",
    "    else:\n",
    "        gt[i] = gA_ast[len(gA_ast)-1]\n",
    "\n",
    "# 4. nt[t]:\n",
    "for i in range(0, time):\n",
    "    \n",
    "    if i < len(n_ast):\n",
    "        nt[i] = n_ast[i]\n",
    "    else:\n",
    "        nt[i] = n_ast[len(n_ast)-1]\n",
    "\n",
    "#verifying if they fit time value: \n",
    "\n",
    "print(len(chi))\n",
    "print(chi)\n",
    "\n",
    "print(len(tau))\n",
    "print(tau)\n",
    "\n",
    "print(len(gt))\n",
    "print(gt)\n",
    "\n",
    "print(len(nt))\n",
    "print(nt)\n",
    "\n",
    "# Plot of Exogenous Variables\n",
    "#Check plots on the last graph "
   ],
   "execution_count": null,
   "outputs": [
    {
     "output_type": "stream",
     "text": [
      "100\n",
      "[0.074, 0.078, 0.088, 0.093, 0.093, 0.106, 0.113, 0.111, 0.112, 0.112, 0.104, 0.112, 0.113, 0.094, 0.098, 0.097, 0.097, 0.092, 0.088, 0.086, 0.087, 0.093, 0.102, 0.133, 0.128, 0.137, 0.129, 0.121, 0.119, 0.117, 0.115, 0.116, 0.117, 0.115, 0.108, 0.109, 0.108, 0.108, 0.111, 0.122, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118, 0.118]\n",
      "100\n",
      "[0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.41, 0.101, 0.101, 0.101, 0.101, 0.101, 0.101, 0.096, 0.076, 0.07, 0.078, 0.081, 0.086, 0.087, 0.093, 0.083, 0.074, 0.065, 0.066, 0.069, 0.074, 0.077, 0.079, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08, 0.08]\n",
      "100\n",
      "[1.0, 0.9678715503, 1.013306006, 1.019836632, 0.9914882317, 0.9798921573, 1.005703845, 0.977808355, 1.023508041, 1.021018595, 1.012631541, 1.03482585, 1.004376913, 0.9141855336, 0.979821939, 0.9994144137, 0.9605011021, 0.9904538089, 0.9265435465, 1.002842512, 1.004889705, 1.021202911, 1.00047608, 0.9987446936, 1.049417738, 0.9559593514, 1.009306233, 1.019601818, 1.008346378, 0.987076312, 1.012243247, 0.9844849781, 1.004762168, 0.9866643574, 1.006205587, 1.007076538, 1.013670458, 1.000217352, 0.9876402875, 0.9460796837, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036, 1.034428036]\n",
      "100\n",
      "[1.032, 1.032, 1.033, 1.034, 1.03, 1.032, 1.033, 1.033, 1.031, 1.034, 1.032, 1.031, 1.031, 1.033, 1.034, 1.035, 1.035, 1.034, 1.032, 1.03, 1.03, 1.029, 1.028, 1.026, 1.025, 1.024, 1.023, 1.022, 1.022, 1.02, 1.019, 1.018, 1.017, 1.018, 1.02, 1.021, 1.022, 1.022, 1.022, 1.022, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021, 1.021]\n"
     ],
     "name": "stdout"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "tGAEraGwBwku",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1628888324229,
     "user_tz": -330,
     "elapsed": 714,
     "user": {
      "displayName": "Bertrand Kwibuka",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjTN0MNu3HMdyI-k1Xwr3e4pF521hd01Rv-Qhh-wg=s64",
      "userId": "14120959365019312055"
     }
    },
    "outputId": "0a147adc-a316-4c0c-d69a-40554d125ec7"
   },
   "source": [
    "#  \n",
    "\n",
    "# THE SHOOTING ALGORITHM \n",
    "\n",
    "#\n",
    "\n",
    "#T = 5*24 # Total number of hours owned in a week\n",
    "\n",
    "# Initial Conditions for capital\n",
    "\n",
    "k = [k0]*(S)\n",
    "c = [1]*(S)\n",
    "h = [1]*(S)\n",
    "\n",
    "#Initial condition for consumption\n",
    "c_0_L = .12 *c_ast\n",
    "c_0_H = 15 *c_ast\n",
    "\n",
    "\n",
    "#Solve for k_t+1 and c_t+1 and h_t+1 until convergence along the saddle path\n",
    "\n",
    "niter = 500\n",
    "S = 100\n",
    "\n",
    "flag  = 0\n",
    "\n",
    "# k_t+1*(1+g)^(1/1-theta)*(1+n)=(1-chi_t)*(k_t^theta*h_t^(1-theta))-c_t+(1-delta)*k_t\n",
    "#Start iteration\n",
    "for j in range(0,niter):\n",
    "    c[0] = (c_0_L+c_0_H)/2 #Initial guess for c_o\n",
    "    #print(c_0_L , c_0_H, c[0])\n",
    "    def func(x): \n",
    "        return T - alpha*c[0]/((1-theta))*(k[0]/x)**(-(theta)) - x #Consumption-Leisure choice\n",
    "\n",
    "    root = fsolve(func, 15)   #check if I can increase from 15 to 20 \n",
    "    h[0] = root[0]\n",
    "    #print(k[0], c[0], h[0])\n",
    "    \n",
    "    #Generate paths for c and k given intitial guess for c_0\n",
    "    for t in range(0,S-1):\n",
    "        k[t+1] = (k[t]**theta*h[t]**(1-theta)*(1- chi[t]) +(1-delta)*k[t]-c[t])/(gt[t]**(1/(1-theta))*nt[t])\n",
    "        #print(k[t+1])\n",
    "        \n",
    "        \n",
    "        if k[t+1] < 0:\n",
    "            flag = 1\n",
    "            #print(flag)\n",
    "            break\n",
    "        if k[t+1]>2*k_ast:\n",
    "            flag =2\n",
    "            #print(flag)\n",
    "            break\n",
    "            \n",
    "        def cfunc(z):\n",
    "            # Solves for c_t+1 and h_t+1 simultaneously\n",
    "            fc = z[0]\n",
    "            fh = z[1]\n",
    "            f1 = T - alpha*fc/((1-theta))*(k[t+1]/fh)**(-(theta)) - fh \n",
    "            f2 = fc/c[t] - beta/(gt[t]**(1/(1-theta)))*(1 + (1-tau[t+1])*(theta*(k[t+1]/fh)**(-(1-theta))-delta)) \n",
    "            return [f1, f2]\n",
    "        \n",
    "        sol = fsolve(cfunc, [15, 15])\n",
    "        #print(\"anuradha\", sol)\n",
    "        c[t+1] = sol[0]\n",
    "        h[t+1] = sol[1]\n",
    "        \n",
    "        # Check for convergence\n",
    "        # Update the intitial value if not convergence\n",
    "        if t== S-2:\n",
    "            #print(\"anuradha\",k[t+1], c[t+1], h[t+1])\n",
    "            if (abs(k[S-1]-k_ast)/k_ast < epsilon) and abs((c[S-1] -c_ast)/c_ast < epsilon):\n",
    "                flag = 10\n",
    "                print( \"Converged in iteration \", j)\n",
    "                break\n",
    "            # Update initial guess for c\n",
    "            elif (k[S-1]-k_ast)/k_ast <=epsilon:\n",
    "                flag =1\n",
    "            elif (k[S-1] - k_ast)/k_ast >= epsilon:\n",
    "                flag =2\n",
    "        \n",
    "        \n",
    "    if flag == 1:\n",
    "        c_0_H = c[0]\n",
    "        #print(\"anuradha\")\n",
    "    elif flag == 2:\n",
    "        c_0_L = c[0]\n",
    "        #print(\"anuradha2\")\n",
    "    elif flag == 10:\n",
    "        break\n",
    "        \n",
    "\n",
    "\n",
    "        #Ends iteration loop\n",
    "        #End shooting algorithm if reached max number of iterations\n",
    "    \n",
    "if j == niter-1:\n",
    "    print('Failure in Convergence!')\n",
    "  \n"
   ],
   "execution_count": null,
   "outputs": [
    {
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:33: RuntimeWarning: invalid value encountered in power\n",
      "/usr/local/lib/python3.7/dist-packages/scipy/optimize/minpack.py:162: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n",
      "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:58: RuntimeWarning: invalid value encountered in double_scalars\n",
      "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:59: RuntimeWarning: invalid value encountered in double_scalars\n"
     ],
     "name": "stderr"
    },
    {
     "output_type": "stream",
     "text": [
      "Converged in iteration  47\n"
     ],
     "name": "stdout"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "N1cZmCL9BwoM",
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1628888326053,
     "user_tz": -330,
     "elapsed": 7,
     "user": {
      "displayName": "Bertrand Kwibuka",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjTN0MNu3HMdyI-k1Xwr3e4pF521hd01Rv-Qhh-wg=s64",
      "userId": "14120959365019312055"
     }
    },
    "outputId": "0337ee27-362b-4f4f-a5f7-19692f5ccf7f"
   },
   "source": [
    "##\n",
    "\n",
    "## Checking steady states and long term values equivalence: looks good \n",
    "\n",
    "##\n",
    "\n",
    "t = S-2\n",
    "print(k[t+1], c[t+1], h[t+1])\n",
    "print([k_ast, c_ast, h_ast])\n",
    "print(c[0])\n",
    "print(h)\n",
    "\n",
    "\n",
    "print(epsilon)\n",
    "print((k[S-1]-k_ast)/k_ast <epsilon)\n",
    "print((c[S-1]-c_ast)/c_ast <epsilon)\n",
    "print((h[S-1]-h_ast)/h_ast)"
   ],
   "execution_count": null,
   "outputs": [
    {
     "output_type": "stream",
     "text": [
      "109.46894590726568 19.085219200048517 34.05657463155685\n",
      "[109.4716511015576, 25.95525388038508, 22.29159035940587]\n",
      "18.939424965625754\n",
      "[23.584572973054453, 23.55028833801707, 22.589921069942577, 22.887071046629117, 23.424185026357733, 23.263421768656496, 22.683306640437763, 22.831797078272533, 22.159105730391058, 22.86675758739466, 23.557650840441955, 24.168149067053513, 25.56466923781911, 26.231208947124617, 24.07265349899465, 23.994377125600444, 24.59233467424538, 23.98002466567967, 23.703942644855005, 21.43581890131839, 21.596767216309164, 21.797926748207402, 22.466466933143312, 22.486506543280157, 22.34492660224433, 23.673038251914228, 22.121483138146157, 22.258565867081426, 22.72372241324377, 22.863118332751437, 22.389773608968163, 22.709365966366374, 22.17944618804327, 22.253597479431527, 21.75385366715855, 21.833242325647017, 21.91007704348078, 22.164620132237214, 22.008759969691653, 21.449991948358925, 19.559120475288058, 20.229569001581915, 20.799932899733324, 21.280253949020672, 21.68132162791712, 22.013859635831775, 22.287984234942076, 22.512890040731662, 22.696707388884498, 22.846477926076883, 22.968204378964334, 23.0669415482187, 23.146905725541927, 23.211587857001117, 23.26386173974698, 23.30608263889657, 23.340174373463363, 23.36770455068707, 23.389948557000427, 23.40794338702945, 23.422532582419546, 23.43440357658337, 23.44411867567795, 23.45214079821362, 23.458854974969064, 23.464586494597707, 23.469616478213744, 23.474195583625345, 23.47855647953383, 23.482925693553568, 23.487535426579836, 23.492635941274226, 23.498509176188126, 23.505484311935046, 23.51395612521544, 23.524407114362646, 23.53743457061785, 23.553784006202623, 23.574390635105903, 23.600430932525114, 23.633386662681783, 23.675124135604772, 23.727991779186034, 23.79493930011915, 23.87966159987587, 23.98676996081249, 24.121991446124063, 24.292394427132884, 24.50663294775198, 24.775194412680914, 25.110623036406828, 25.527675247403444, 26.0433436190331, 26.67666600792292, 27.448223112088613, 28.379231566427425, 29.490174805381958, 30.798991716960394, 32.31896307063503, 34.05657463155685]\n",
      "5e-05\n",
      "True\n",
      "True\n",
      "0.5277768020345296\n"
     ],
     "name": "stdout"
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "eMfm5RyiJYLh"
   },
   "source": [
    "#Savings rate and K/Y\n",
    "\n",
    "S= 41\n",
    "\n",
    "\n",
    "A=[A0]*S\n",
    "N=[N0]*S\n",
    "C=[0]*S\n",
    "K=[0]*S\n",
    "Y=[0]*S\n",
    "G=[0]*S\n",
    "s=[0]*S\n",
    "ky_ratio=[0]*S\n",
    "\n",
    "#redefining 'n_ast' as a scalar so that N0 can be calculated:\n",
    "n_ast = 1.020\n",
    "\n",
    "for t in range(1,S):\n",
    "  A[t]=A0*gamma**t\n",
    "  N[t]=(N0*n_ast)**t\n",
    "\n",
    "for t in range(S):\n",
    "  C[t]=c[t]*A[t]*N[t]\n",
    "  K[t]=k[t]*A[t]*N[t]\n",
    "  Y[t]=(A[t]**(1-theta))*(K[t]**theta)*((h[t]*N[t])**(1-theta))\n",
    "  G[t]=chi_t[t]*Y[t]\n",
    "  s[t]=(Y[t]-G[t]-C[t])/Y[t]\n",
    "  ky_ratio[t]=K[t]/Y[t]"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bqSgzy0U_mak"
   },
   "source": [
    "# Plotting data and model plots "
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "9c7k8F2wBY7O",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 846
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1628888330593,
     "user_tz": -330,
     "elapsed": 1206,
     "user": {
      "displayName": "Bertrand Kwibuka",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjTN0MNu3HMdyI-k1Xwr3e4pF521hd01Rv-Qhh-wg=s64",
      "userId": "14120959365019312055"
     }
    },
    "outputId": "4e7034ef-f289-410e-9bcb-aa30fbbf5633"
   },
   "source": [
    "# Plots\n",
    "\n",
    "# Periods for the time-path in the graph\n",
    "time=[t for t in range(1970,2070)]\n",
    "ll = len(time)\n",
    "\n",
    "#Re-introducing h[t] here for plotting: \n",
    "print(h)\n",
    "\n",
    "#savings rate\n",
    "plt.figure()\n",
    "plt.plot(time[:41], s, 'r-',linestyle='dashed', label='model')\n",
    "plt.plot(time[:41], s_data, 'b-', label='data')\n",
    "\n",
    "plt.xlim(1970,2010)\n",
    "plt.ylim(0, 0.35)\n",
    "plt.title(\"Savings rate: Mexico\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "#savings rate\n",
    "plt.figure()\n",
    "plt.plot(time[:41], ky_ratio, 'r-',linestyle='dashed', label='model')\n",
    "plt.plot(time[:41], ky_data, 'b-', label='data')\n",
    "plt.xlim(1970,2010)\n",
    "plt.ylim(0, 4.5)\n",
    "plt.title(\"Mexico; K/Y\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "#labour hours plot \n",
    "\n",
    "plt.figure()\n",
    "plt.plot(time[:41], l_data, 'b-', label='data')\n",
    "plt.plot(time[:41], h[0:41], 'r-', linestyle='dashed', label='model')\n",
    "plt.xlim(1970,2010)\n",
    "plt.ylim(18, 30)\n",
    "plt.title(\"Mexico: labour\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n"
   ],
   "execution_count": null,
   "outputs": [
    {
     "output_type": "stream",
     "text": [
      "[23.584572973054453, 23.55028833801707, 22.589921069942577, 22.887071046629117, 23.424185026357733, 23.263421768656496, 22.683306640437763, 22.831797078272533, 22.159105730391058, 22.86675758739466, 23.557650840441955, 24.168149067053513, 25.56466923781911, 26.231208947124617, 24.07265349899465, 23.994377125600444, 24.59233467424538, 23.98002466567967, 23.703942644855005, 21.43581890131839, 21.596767216309164, 21.797926748207402, 22.466466933143312, 22.486506543280157, 22.34492660224433, 23.673038251914228, 22.121483138146157, 22.258565867081426, 22.72372241324377, 22.863118332751437, 22.389773608968163, 22.709365966366374, 22.17944618804327, 22.253597479431527, 21.75385366715855, 21.833242325647017, 21.91007704348078, 22.164620132237214, 22.008759969691653, 21.449991948358925, 19.559120475288058, 20.229569001581915, 20.799932899733324, 21.280253949020672, 21.68132162791712, 22.013859635831775, 22.287984234942076, 22.512890040731662, 22.696707388884498, 22.846477926076883, 22.968204378964334, 23.0669415482187, 23.146905725541927, 23.211587857001117, 23.26386173974698, 23.30608263889657, 23.340174373463363, 23.36770455068707, 23.389948557000427, 23.40794338702945, 23.422532582419546, 23.43440357658337, 23.44411867567795, 23.45214079821362, 23.458854974969064, 23.464586494597707, 23.469616478213744, 23.474195583625345, 23.47855647953383, 23.482925693553568, 23.487535426579836, 23.492635941274226, 23.498509176188126, 23.505484311935046, 23.51395612521544, 23.524407114362646, 23.53743457061785, 23.553784006202623, 23.574390635105903, 23.600430932525114, 23.633386662681783, 23.675124135604772, 23.727991779186034, 23.79493930011915, 23.87966159987587, 23.98676996081249, 24.121991446124063, 24.292394427132884, 24.50663294775198, 24.775194412680914, 25.110623036406828, 25.527675247403444, 26.0433436190331, 26.67666600792292, 27.448223112088613, 28.379231566427425, 29.490174805381958, 30.798991716960394, 32.31896307063503, 34.05657463155685]\n"
     ],
     "name": "stdout"
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": [],
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": [],
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": [],
      "needs_background": "light"
     }
    }
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UWqG96sVRwUn"
   },
   "source": [
    "# The model for labor is highly dependent on the value of T which is unknown for Mexico! I kept it at T=3.9 to have this plot\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qbOglbFRUJTd"
   },
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1Tz1QriJmf8i"
   },
   "source": [
    "# Question 2: Plotting counterfactuals for Mexico\n",
    "\n",
    "# Savings rate in  Mexico and analyzing TFP"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 281
    },
    "id": "Nc4PexYkqBEM",
    "executionInfo": {
     "status": "ok",
     "timestamp": 1628888702592,
     "user_tz": -330,
     "elapsed": 658,
     "user": {
      "displayName": "Bertrand Kwibuka",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjTN0MNu3HMdyI-k1Xwr3e4pF521hd01Rv-Qhh-wg=s64",
      "userId": "14120959365019312055"
     }
    },
    "outputId": "b84bccd6-7a9c-46d4-94d9-fe0a4605a3de"
   },
   "source": [
    "#Re-introduction of TFP factor data: normalized just for plotting \n",
    "\n",
    "\n",
    "A_data = np.array([1.0000,  0.9544 ,  0.9726 ,  1.0003 ,  0.9882 ,  0.9599 ,  0.9677 ,  0.9372 ,  0.9688 ,  0.9980 ,  1.0161 ,  1.0670 ,  1.0737 ,  0.9445 ,  0.9174 ,  0.9167 ,  0.8654 ,  0.8536 ,  0.7655 ,  0.7686 ,  0.7739 ,  0.7975 ,  0.7980 ,  0.7966 ,  0.8534 ,  0.8002 ,  0.8109 ,  0.8337 ,  0.8437 ,  0.8281 ,  0.8427 ,  0.8240 ,  0.8297 ,  0.8139 ,  0.8211 ,  0.8294 ,  0.8457 ,  0.8459 ,  0.8310 ,  0.7678 ,  0.8058 ])\n",
    "A = [1]*(len(time)) # Model A\n",
    "\n",
    "for i in range(0, len(time)):\n",
    "   \n",
    "    if i < len(A_data):\n",
    "        A[i] = A_data[i]\n",
    "    else:\n",
    "        A[i] = A_data[len(A_data)-1]\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(time, A, 'g-', label='Mexico')\n",
    "plt.plot(time[:41], A_data[0:41])\n",
    "plt.xlim(1970,2030)\n",
    "plt.ylim(0,3)\n",
    "plt.title(\"TFP factor\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ],
   "execution_count": null,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": [],
      "needs_background": "light"
     }
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "kxQ5o1kMA5j6",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 281
    },
    "executionInfo": {
     "status": "ok",
     "timestamp": 1628888790863,
     "user_tz": -330,
     "elapsed": 509,
     "user": {
      "displayName": "Bertrand Kwibuka",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GjTN0MNu3HMdyI-k1Xwr3e4pF521hd01Rv-Qhh-wg=s64",
      "userId": "14120959365019312055"
     }
    },
    "outputId": "bbbe4087-77d2-4d9a-963b-d15f104bd824"
   },
   "source": [
    "# Plot dynamics of normalized c, h, k and savings rate\n",
    "\n",
    "# Periods for the time-path in the graph\n",
    "time=[t for t in range(1970,2100)]\n",
    "\n",
    "#plotting \n",
    "plt.plot(time[:41], A_data, '-r', label='TFP only')   #TFP growth from series \n",
    "plt.plot(time[:41], s, 'r-', label='Benchmark', linestyle='dashed')  #Savings rate from the model \n",
    "plt.plot(time[:41], s_data, 'b-', label='Data')   #Savings rate from series \n",
    "\n",
    "plt.xlim(1970,2010)\n",
    "plt.ylim(0,1.5)\n",
    "plt.title(\"Mexico: TFP only\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n"
   ],
   "execution_count": null,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": [],
      "needs_background": "light"
     }
    }
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "RgGKN-0qrFbe"
   },
   "source": [],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QtVG_TnoV0MW"
   },
   "source": [
    "# Bear with the scaling of this graph. All individual graphs are correct, but it may look off because savings rate and TFP for Mexico have really distant values. There was no model to refer to as a counterfactual plot."
   ]
  }
 ]
}