Labs/Group6_lab4_python_.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Replication of Lab 4"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Group 6\n",
    "Members:\n",
    "1. Eljaer Eusebio\n",
    "2. Claudia Vivas\n",
    "3. Luis Sandoval\n",
    "4. Andre Tapia"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Question 1 "
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "import hdmpy\r\n",
    "import numpy as np\r\n",
    "import random\r\n",
    "import statsmodels.api as sm\r\n",
    "import matplotlib.pyplot as plt\r\n",
    "import numpy as np\r\n",
    "from matplotlib import colors"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# 1. Simulation Design 1"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Simulationg desing in the case B=50"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "np.random.seed(0)\r\n",
    "B = 50\r\n",
    "Naive = np.zeros( B )\r\n",
    "Orthogonal = np.zeros( B )"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "source": [
    "for i in range( 0, B ):\n",
    "    n = 100\n",
    "    p = 100\n",
    "    beta = ( 1 / (np.arange( 1, p + 1 ) ** 2 ) ).reshape( p , 1 )\n",
    "    gamma = ( 1 / (np.arange( 1, p + 1 ) ** 2 ) ).reshape( p , 1 )\n",
    "\n",
    "    mean = 0\n",
    "    sd = 1\n",
    "    X = np.random.normal( mean , sd, n * p ).reshape( n, p )\n",
    "\n",
    "    D = ( X @ gamma ) + np.random.normal( mean , sd, n ).reshape( n, 1 )/4 \n",
    "   \n",
    "    # DGP \n",
    "    Y = 5*D + ( X @ beta ) + np.random.normal( mean , sd, n ).reshape( n, 1 )\n",
    "    # single selection method\n",
    "    r_lasso_estimation = hdmpy.rlasso( np.concatenate( ( D , X ) , axis  =  1 ) , Y , post = True ) # Regress main equation by lasso\n",
    "\n",
    "    coef_array = r_lasso_estimation.est[ 'coefficients' ].iloc[ 2:, :].to_numpy()    # Get \"X\" coefficients \n",
    "\n",
    "    SX_IDs = np.where( coef_array != 0 )[0]\n",
    "\n",
    "    # In case all X coefficients are zero, then regress Y on D\n",
    "    if sum(SX_IDs) == 0 : \n",
    "        Naive[ i ] = sm.OLS( Y , sm.add_constant(D) ).fit().summary2().tables[1].round(3).iloc[ 1, 0 ] \n",
    "\n",
    "    # Otherwise, then regress Y on X and D (but only in the selected coefficients)\n",
    "    elif sum( SX_IDs ) > 0 :\n",
    "        X_D = np.concatenate( ( D, X[:, SX_IDs ] ) , axis = 1 )\n",
    "        Naive[ i ] = sm.OLS( Y , sm.add_constant( X_D ) ).fit().summary2().tables[1].round(3).iloc[ 1, 0]\n",
    "\n",
    "    # In both cases we save D coefficient\n",
    "        \n",
    "    # Regress residuals. \n",
    "    resY = hdmpy.rlasso( X , Y , post = False ).est[ 'residuals' ]\n",
    "    resD = hdmpy.rlasso( X , D , post = False ).est[ 'residuals' ]\n",
    "    Orthogonal[ i ] = sm.OLS( resY , sm.add_constant( resD ) ).fit().summary2().tables[1].round(3).iloc[ 1, 0]\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "source": [
    "Orto_breaks = [-1.2, -1, -0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8, 2]\n",
    "Naive_breaks = [-0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8, 1, 1.2]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "source": [
    "# Now we create a histogram\n",
    "fig, axs = plt.subplots(1, 1, sharex= True, tight_layout=True)\n",
    "\n",
    "N, bins, patches = axs.hist( Orthogonal - 5 , range = (-2, 2), density = True , bins = Orto_breaks)\n",
    "\n",
    "fracs = ((N**(1 / 5)) / N.max())\n",
    "norm = colors.Normalize(fracs.min(), fracs.max())\n",
    " \n",
    "for thisfrac, thispatch in zip(fracs, patches):\n",
    "    color = plt.cm.viridis(norm(thisfrac))\n",
    "    thispatch.set_facecolor(color)\n",
    "\n",
    "plt.title('Orthogonal', size=20)\n",
    "plt.xlabel(\"Difference of Orhtogonal - True\")\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "source": [
    "# Create histogram\n",
    "fig, axs = plt.subplots(1, 1, sharex= True, tight_layout=True)\n",
    "\n",
    "N, bins, patches = axs.hist( Naive - 5, range = (-2, 2), density = True , bins = Naive_breaks)\n",
    "\n",
    "fracs = ((N**(1 /5 )) / N.max())\n",
    "norm = colors.Normalize(fracs.min(), fracs.max())\n",
    " \n",
    "for thisfrac, thispatch in zip(fracs, patches):\n",
    "    color = plt.cm.viridis(norm(thisfrac))\n",
    "    thispatch.set_facecolor(color)\n",
    "\n",
    "plt.title('Naive', size=20)\n",
    "plt.xlabel(\"Difference of Naive - True\")\n",
    "\n",
    "# Show plot\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAacAAAEYCAYAAAD4czk4AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAWfklEQVR4nO3dfbAldX3n8fdHGIxZXEFnWAgCoxGzilkURwR14+RhjVC66K6JsERBzU60NKsVYy2JKz4QE40VKoWoExJZ1OATgi5rDUGyMdFEJQ44w4MTFYzKLGMY0YCsGhz97h/do4fDvXP6zpx77+9y3q+qU7dP96+7v33P6fu53afPr1NVSJLUkvstdwGSJI0znCRJzTGcJEnNMZwkSc0xnCRJzTGcJEnNMZykZZDkr5P4PQ5pHoaT1EtS/eOrSX5injZf6dvsv9T1SbPEcJLu7UjgFYu8jucDj1rkdUgrVuwhQur0p9m+BRSwP/DTVfWNsTZfAY4CVlXVriUvUpoRHjlJ9/Qd4BzgXwOvHTpTkjOTXJrky0m+m+TOJH+X5NfmaX+Pz5ySnNafLjx3nvb3T/KtJF8fP6XYz/vxfvr3kmxL8j+S3H9o/VJrDCfp3t4G3Az8RpJHDpznHcBa4BPAHwPvpzvCek+ScwbM/2HgDuD0eT7POgU4CPjz0SO2JO8E3gs8Arisr/2bdAH7F342ppXKcJLGVNX3gbOAVcCbBs72mKp6fFWdWVW/U1UbgIcDfwWcleTwCev8HvAB4BDg6XM0OaP/+a7dI5KcCbyQLtgeWVUvqqpXVtWTgdcD64GXDqxfaorhJM2hqj4EfBp4dpKnDGh/8xzj7qY7ktkf+MUBq90dPGeMjkxyKPDLwOeq6vqRSS8HdgEvrKrvji3rHOB24PQB65Wa4yG/NL9XAp8C/ijJCbWHq4eSHAn8d7oQOhJ4wFiTPR45AVTVp5J8EXhmkoOr6lv9pNOB/YCLRtb3k8CxwDeAVySZa5H/glcEaoUynKR5VNWnk3wIeA7wq3Sn3e4lycOBvwcOBj4JfIzu86Mf0H0OdQYw9OKEdwFvBE6l+xyLfv7vA+8baXcwEGANC7hwQ1opPK0n7dlZdMHwB0kOmKfNbwEPAV5UVeur6r9V1Wuq6nXAlQtc33uAH9Kf2kvyOOBngU1VtXOk3R39z89VVfb0WOD6pSYYTtIe9J8lvR14GPCb8zR7RP/z0jmmPXWB67uF7iKKJyb5Gea4EKJvdxdwI3BMkgcvZB3SSmA4SZO9Afhn4NXAgXNM/0r/c/3oyCS/DPz6Xqzvov7ni4DT6C5s+Ogc7c4FDgAuTHLQ+MQkByc5bi/WLy07w0maoKq+Cfw+3ec8D5mjyduBu4FLklyc5A+TbAKuAD60F6u8DLiTrgulQ4D39pe3j9d1Yb/uU4Cbk7w3yZuSXJDkKuDrwIa9WL+07AwnaZjz+PER0j1U1XXAz9Nd2Xcy8BK6Hib+E7BxoSvqLwu/hO57VjB2Sm+s7UuBZ9Jd9v5LdJ9//UfgQcBb6L4QLK049q0nSWqOR06SpOYYTpKk5hhOkqTmTAynJEf03fFvS3JjkpfP0WZ9kjuSbOkfZy9OuZKkWTCk+6JdwCur6tokDwSuSXJVVX1+rN0nq+oZQ1e8evXqWrt27QJKlSStdNdcc803qmrNpHYTw6mqdgA7+uFvJ9lG14nleDgtyNq1a9m8efO+LEKStMIk+eqQdgv6zCnJWuBxwNVzTD4xydYkVyQ5Zp75NyTZnGTzzp0752oiSdLwcEpyIF3fYa+oqjvHJl8LHFVVxwJvBT4y1zKq6oKqWldV69asmXhUJ0maUYPCKckqumC6uKouG59eVXf2HVFSVZuAVUlWT7VSSdLMGHK1XoB3Atuq6tx52hzatyPJ8f1yb59moZKk2THkar0nA88Drk+ypR/3u3R3+6SqNtLdjO0lSXYB3wVO3dNdQyVJ2pMhV+v9Ld0dN/fU5nzg/GkVJUmabfYQIUlqjuEkSWqO4SRJas6QCyIk6T7lh19/5HKXMK/7HfrF5S6hCR45SZKaYzhJkppjOEmSmmM4SZKaYzhJkppjOEmSmmM4SZKaYzhJkppjOEmSmmM4SZKaYzhJkppjOEmSmmM4SZKaYzhJkppjOEmSmmM4SZKaYzhJkppjOEmSmmM4SZKaYzhJkppjOEmSmmM4SZKaYzhJkppjOEmSmmM4SZKaYzhJkppjOEmSmmM4SZKaYzhJkpozMZySHJHk40m2JbkxycvnaJMk5yW5Kcl1SY5bnHIlSbNg/wFtdgGvrKprkzwQuCbJVVX1+ZE2JwFH948nAu/of0qStGATj5yqakdVXdsPfxvYBhw+1uwU4N3V+QxwUJLDpl6tJGkmLOgzpyRrgccBV49NOhy4ZeT5du4dYJIkDTI4nJIcCFwKvKKq7hyfPMcsNccyNiTZnGTzzp07F1apJGlmDAqnJKvoguniqrpsjibbgSNGnj8UuHW8UVVdUFXrqmrdmjVr9qZeSdIMGHK1XoB3Atuq6tx5ml0OPL+/au8E4I6q2jHFOiVJM2TI1XpPBp4HXJ9kSz/ud4EjAapqI7AJOBm4CfgO8IKpVypJmhkTw6mq/pa5P1MabVPAS6dVlCRpttlDhCSpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5+y93AZKkH7v2a0cudwnzOu7Iry3ZujxykiQ1x3CSJDXHcJIkNcdwkiQ1Z2I4JbkwyW1Jbphn+vokdyTZ0j/Onn6ZkqRZMuRqvYuA84F376HNJ6vqGVOpSJI08yYeOVXVJ4BvLkEtkiQB0/vM6cQkW5NckeSY+Rol2ZBkc5LNO3funNKqJUn3NdMIp2uBo6rqWOCtwEfma1hVF1TVuqpat2bNmimsWpJ0X7TP4VRVd1bVXf3wJmBVktX7XJkkaWbtczglOTRJ+uHj+2Xevq/LlSTNrolX6yV5H7AeWJ1kO/BaYBVAVW0EngO8JMku4LvAqVVVi1axJOk+b2I4VdVpE6afT3epuSRJU2EPEZKk5hhOkqTmGE6SpOYYTpKk5hhOkqTmGE6SpOYYTpKk5hhOkqTmGE6SpOYYTpKk5hhOkqTmGE6SpOYYTpKk5hhOkqTmGE6SpOYYTpKk5hhOkqTmGE6SpOYYTpKk5hhOkqTmGE6SpOYYTpKk5hhOkqTmGE6SpOYYTpKk5hhOkqTmGE6SpOYYTpKk5hhOkqTmGE6SpOYYTpKk5hhOkqTmGE6SpOYYTpKk5kwMpyQXJrktyQ3zTE+S85LclOS6JMdNv0xJ0iwZcuR0EfD0PUw/CTi6f2wA3rHvZUmSZtnEcKqqTwDf3EOTU4B3V+czwEFJDptWgZKk2TONz5wOB24Zeb69H3cvSTYk2Zxk886dO6ewaknSfdE0wilzjKu5GlbVBVW1rqrWrVmzZgqrliTdF00jnLYDR4w8fyhw6xSWK0maUdMIp8uB5/dX7Z0A3FFVO6awXEnSjNp/UoMk7wPWA6uTbAdeC6wCqKqNwCbgZOAm4DvACxarWEnSbJgYTlV12oTpBbx0ahVJkmaePURIkppjOEmSmmM4SZKaYzhJkppjOEmSmmM4SZKaYzhJkppjOEmSmmM4SZKaYzhJkppjOEmSmjOxbz1J2luvuf7Zy13CnF7v7eSa55GTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYPCKcnTk3whyU1Jzppj+vokdyTZ0j/Onn6pkqRZsf+kBkn2A94G/AdgO/DZJJdX1efHmn6yqp6xCDVKkmbMkCOn44GbqurLVXU38H7glMUtS5I0y4aE0+HALSPPt/fjxp2YZGuSK5IcM9eCkmxIsjnJ5p07d+5FuZKkWTAknDLHuBp7fi1wVFUdC7wV+MhcC6qqC6pqXVWtW7NmzYIKlSTNjiHhtB04YuT5Q4FbRxtU1Z1VdVc/vAlYlWT11KqUJM2UIeH0WeDoJA9LcgBwKnD5aIMkhyZJP3x8v9zbp12sJGk2TLxar6p2JXkZcCWwH3BhVd2Y5MX99I3Ac4CXJNkFfBc4tarGT/1JkjTIxHCCH52q2zQ2buPI8PnA+dMtTZI0q+whQpLUHMNJktQcw0mS1BzDSZLUHMNJktQcw0mS1BzDSZLUHMNJktQcw0mS1BzDSZLUHMNJktQcw0mS1BzDSZLUHMNJktQcw0mS1BzDSZLUHMNJktQcw0mS1BzDSZLUHMNJktSc/Ze7AEn75uhLfm+5S5jXqf92uSvQSuWRkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYPCKcnTk3whyU1JzppjepKc10+/Lslx0y9VkjQrJoZTkv2AtwEnAY8GTkvy6LFmJwFH948NwDumXKckaYYMOXI6Hripqr5cVXcD7wdOGWtzCvDu6nwGOCjJYVOuVZI0I4bcbPBw4JaR59uBJw5ocziwY7RRkg10R1YAdyX5woKqXXyrgW8sdxH7YKXXDyt/G6x/xDLdBnHiNrR7e0ag6fdQhjSaVP9RQxYyJJzmqqb2og1VdQFwwYB1Loskm6tq3XLXsbdWev2w8rfB+pffSt8G6+8MOa23HThi5PlDgVv3oo0kSYMMCafPAkcneViSA4BTgcvH2lwOPL+/au8E4I6q2jG+IEmShph4Wq+qdiV5GXAlsB9wYVXdmOTF/fSNwCbgZOAm4DvACxav5EXV7CnHgVZ6/bDyt8H6l99K3wbrB1J1r4+GJElaVvYQIUlqjuEkSWrOzIVTkgcnuSrJl/qfB8/T7itJrk+yJcnmhc6/WIasP8kRST6eZFuSG5O8fGTa65L83367tiQ5eYnq3ususCbNuxQG1H96X/d1ST6V5NiRaXO+l5bagG1Yn+SOkffG2UPnXQoD6n/VSO03JPlBkgf305b9NUhyYZLbktwwz/TW94FJ9U93H6iqmXoAfwic1Q+fBbx5nnZfAVbv7fzLWT9wGHBcP/xA4IvAo/vnrwN+e4lr3g+4GXg4cACwdXc9I21OBq6g+87cCcDVQ+dtpP4nAQf3wyftrn9P76UGt2E98NG9mbeF+sfaPxP4q8Zeg58DjgNumGd6s/vAwPqnug/M3JETXVdL7+qH3wU8a4nn31cT119VO6rq2n7428A2uh47lsu+dIE1ZN7FNrGGqvpUVX2rf/oZuu/6tWRffo8r4jUYcxrwviWpbKCq+gTwzT00aXkfmFj/tPeBWQynf1P9d7D6n4fM066AjyW5Jl23Swudf7EsaP1J1gKPA64eGf2y/tD7wiU6LTlf91ZD2gyZd7EttIYX0f0HvNt876WlNHQbTkyyNckVSY5Z4LyLaXANSX4SeDpw6cjoFl6DSVreBxZqn/eBId0XrThJ/hI4dI5Jr17AYp5cVbcmOQS4Ksk/9P85LLop1U+SA+l20FdU1Z396HcA59C9Wc4B/gh44d5XO6yUOcYN7QJrUNdYi2xwDUl+nm7HfMrI6GV7L42WNse48W24Fjiqqu7qP4v8CN2dBlbUa0B3Su/vqmr0v/wWXoNJWt4HBpvWPnCfDKeq+qX5piX5pySHVdWO/pD5tnmWcWv/87YkH6Y7tP4EMGj+5a4/ySq6YLq4qi4bWfY/jbT5U+Cj06t8XvvSBdYBA+ZdbIO650ry74A/A06qqtt3j9/De2kpTdyGkX9gqKpNSd6eZPWQeZfAQmo4lbFTeo28BpO0vA8MMs19YBZP610OnNEPnwH8r/EGSf5VkgfuHgaeBtwwdP5FNqT+AO8EtlXVuWPTRm9l8mx+vF2LaV+6wBoy72KbWEOSI4HLgOdV1RdHxu/pvbSUhmzDof17hyTH0/19uH3IvEtgUA1JHgQ8lZH9oqHXYJKW94GJpr4PLPUVH8v9AB4C/B/gS/3PB/fjfwrY1A8/nO6KmK3AjcCrJ83fWP1PoTvsvw7Y0j9O7qe9B7i+n3Y5cNgS1X0y3VWDN+/+fQIvBl7cD4fuppY39/Wt29O8y/C+mVT/nwHfGvl9b570XmpwG17W17iV7gPtJ62k16B/fibw/rH5mngN6I7mdgDfpztKetEK2wcm1T/VfcDuiyRJzZnF03qSpMYZTpKk5hhOkqTmGE6SpOYYTpKk5hhOWjbpeo3ekq7n9K1JfivJ/fpp65Kc1w/fP8lf9m2fm+Tf9/NsSfKA5d2KhUnyK+l6i//42Pi1SSrJb46MOz/JmROW9+Ikz1+kckny4f73fFPu2WP5kxZrnRJ4J1wtoyR3VdWB/fAhwHvpup157Vi7E+h6X39q/3wjXY/H/3PgekL3Xv/hVDdgLyT5C7ptuVc40fV/+G26HqfvTnI+3XdFLlryQsckWU/Xm/0zxsbvX1W7lqUo3ad55KQmVNVtwAa6TmmT7t5CH+1D68+Bx/b/sf8G8KvA2Ukuhh/dx+ez6TqzfX0/bm1/hPJ2uj7jjpjQ7k/7o7GP7T4aS/KI/ohta5Jrk/z0fOsbl+S0dPevuSHJm/txZ9N9QXpjkrfMMdtOui9WnzE+Icl/7de5Ncml6To33X1/rt9O8qgkfz/Sfm2S6/rhxyf5m3Sdbl6Ze/YSsmBJzkxySZL/TdeZ5/okHx2Z/qMjvmmvW7PDcFIzqurLdO/JQ0bG3Qb8OvDJqnpsVf0JXc8Wr6qq05M8ja5z0uOBxwKPT/Jz/ew/Q3cLgsf1w/O1Oxp4W1UdA/wz8J/78Rf344+lu1fNjgnrAyDJTwFvBn6hb/OEJM+qqjcAm4HTq+pV8/wa3gS8Msl+Y+Mvq6on9LVso/t2/ujvbhtwQJKH96OeC3wwXR+LbwWeU1WPBy4E3jjPuhfiROCMqvqF+Ros4ro1A+6THb9qRZurB+Y9eVr/+Fz//EC68Pga8NXq7oszqd0/VtWWfvw1wNp0fYEdXlUfBqiq7wH04TTXckY7sXwC8NdVtbOf52K6G7V9ZNLGVNU/9kdA/2Vs0mOS/B5wUL/OK+eY/YN0R5Vvogun59KF8mPoeoKG7sZ1OybVMcBVdc9ev+eyWOvWDDCc1Iz+v/4f0PW0/qihswF/0B9RjS5rLfD/Brb7l5FRPwAewPwhOedy5mizL34f+BD3DLyLgGdV1db+lNn6Oeb7AHBJksuAqqovJflZ4MaqOnHeYrujtGv6p5dX1dnztR0x+rvdxT3PwvzE7kVPWrc0H0/rqQlJ1gAbgfNrYVfpXAm8MN29q0hyeP851d62A350+4jtSZ7Vt79//znPkOVcDTw1yer+D/9pwN8M3aCq+gfg88DoxQcPpDutuAo4fZ75bqYL19fQBRXAF4A1SU7s612VH99EcPd8P+hPmT52YDCN+yrw6P539CDgF4euW5qPR05aTg9IsgVYRfff93uAc/c4x5iq+liSRwGf7k8d3QX8Gt0f6QW3G/M84E+SvIGuJ+Zf2cNyfnRfrerutfU7wMfpjh42VdVCb63yRn586hC6wLmaLgiupwuruXwAeAvwsL6Wu5M8BzivD479gT+m6x16KqrqliQfpOvp/ku7616Kdeu+y0vJJUnN8bSeJKk5hpMkqTmGkySpOYaTJKk5hpMkqTmGkySpOYaTJKk5/x9IAqIz2VNbSQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 1.2 Simulation design B=100"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "np.random.seed(0)\n",
    "B = 100\n",
    "Naive = np.zeros( B )\n",
    "Orthogonal = np.zeros( B )"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "source": [
    "for i in range( 0, B ):\n",
    "    n = 100\n",
    "    p = 100\n",
    "    beta = ( 1 / (np.arange( 1, p + 1 ) ** 2 ) ).reshape( p , 1 )\n",
    "    gamma = ( 1 / (np.arange( 1, p + 1 ) ** 2 ) ).reshape( p , 1 )\n",
    "\n",
    "    mean = 0\n",
    "    sd = 1\n",
    "    X = np.random.normal( mean , sd, n * p ).reshape( n, p )\n",
    "\n",
    "    D = ( X @ gamma ) + np.random.normal( mean , sd, n ).reshape( n, 1 )/4 \n",
    "    \n",
    "    # DGP \n",
    "    Y = 5*D + ( X @ beta ) + np.random.normal( mean , sd, n ).reshape( n, 1 )\n",
    "    # single selection method\n",
    "    r_lasso_estimation = hdmpy.rlasso( np.concatenate( ( D , X ) , axis  =  1 ) , Y , post = True ) # Regress main equation by lasso\n",
    "\n",
    "    coef_array = r_lasso_estimation.est[ 'coefficients' ].iloc[ 2:, :].to_numpy()    # Get \"X\" coefficients \n",
    "\n",
    "    SX_IDs = np.where( coef_array != 0 )[0]\n",
    "\n",
    "    # In case all X coefficients are zero, then regress Y on D\n",
    "    if sum(SX_IDs) == 0 : \n",
    "        Naive[ i ] = sm.OLS( Y , sm.add_constant(D) ).fit().summary2().tables[1].round(3).iloc[ 1, 0 ] \n",
    "\n",
    "    # Otherwise, then regress Y on X and D (but only in the selected coefficients)\n",
    "    elif sum( SX_IDs ) > 0 :\n",
    "        X_D = np.concatenate( ( D, X[:, SX_IDs ] ) , axis = 1 )\n",
    "        Naive[ i ] = sm.OLS( Y , sm.add_constant( X_D ) ).fit().summary2().tables[1].round(3).iloc[ 1, 0]\n",
    "        \n",
    "    # Regress residuals. \n",
    "    resY = hdmpy.rlasso( X , Y , post = False ).est[ 'residuals' ]\n",
    "    resD = hdmpy.rlasso( X , D , post = False ).est[ 'residuals' ]\n",
    "    Orthogonal[ i ] = sm.OLS( resY , sm.add_constant( resD ) ).fit().summary2().tables[1].round(3).iloc[ 1, 0]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "Orto_breaks = [-1.2, -1, -0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8, 2]\n",
    "Naive_breaks = [-0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8, 1, 1.2]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "source": [
    "# Create histogram\n",
    "fig, axs = plt.subplots(1, 1, sharex= True, tight_layout=True)\n",
    "\n",
    "N, bins, patches = axs.hist( Orthogonal - 5 , range = (-2, 2), density = True , bins = Orto_breaks)\n",
    "\n",
    "fracs = ((N**(1 / 5)) / N.max())\n",
    "norm = colors.Normalize(fracs.min(), fracs.max())\n",
    " \n",
    "for thisfrac, thispatch in zip(fracs, patches):\n",
    "    color = plt.cm.viridis(norm(thisfrac))\n",
    "    thispatch.set_facecolor(color)\n",
    "\n",
    "plt.title('Orthogonal', size=20)\n",
    "plt.xlabel(\"Difference of Orhtogonal - True\")\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAcYklEQVR4nO3df7xldV3v8debkTFIg2qOggPjoI4i3pvknVCTEsMf4K1GrpjgzdLqTmiU5u0H1c0fca2UfpgxNk5GaJlkF39MNAoWAqZpM+ggDAh3GtEZBwSxUBTFgc/9Y63D3W72mbPPmb3nrDP79Xw89uOs9V3f/V2f714z53O+a639XakqJEnqmoMWOgBJkgYxQUmSOskEJUnqJBOUJKmTTFCSpE4yQUmSOskEJe1FkpVJKsmFCx3LYtB+VlcsdBw6MJigtKgkWZ3kL5PsSHJ3kq8kuTbJeUmWz7NNf6lKHWSC0qKQxhuAzcBPAp8B3gz8BfB14FeAm5KcvnBRShqlBy10ANKQfhv4NeBm4EeralvvxiTPB/4auCjJs6rqw/s/REmj5AhKnZdkJU2C+hbw4/3JCaCqLgZ+GVgC/FmSg9r3vqQ9hfeSJKckuSLJnT1l03N9Pb0tm369dlAcSS5K8qUk30iyJcmPzhDzg5Ock+TTSb7enor8SJKfmKF+krwiyfVt219Icn6Sw5LcnOTmfdlH77W0YfvR7vtXk1yeZFeSe5LcnmRjkqcM6oc0SiYoLQYvpRntv7eqrt1LvbcBu4HHAU/v23Y6cAnwVWA98G5gK/C6dvvn2uXp1xV9738k8K/ASuCvgL8F/hPw/iTP6K2YZClwKfB7wMHAuvY9jwX+NsnvDoh9HfAm4DBgA/Au4NnAh9o2vs089zGnfgCPB14P3Af8A/BHbTw/AnwkySkz7EMajary5avTL+CfgAL+xxB139nW/V/t+kva9fuAU2Z4TwFXzLBtZbu9gNf0bXtOW76pr/w3psuBB/WUP4zmFGUBP9hT/kNt2Y3A4T3lS4Gr2m037+M+5tOPw4BlAz6To2j+ELhhLp+lL19zfTmC0mJwZPtz5xB1p+s8oq/8/VX1wX2I4XPA/+4tqKpLgc8DJ/TV/RmaX9Svqqo9PfVvA85tV3+up/5Ptz9fX1X/0VP/HppENMhc9zHnflTVnVX1pf4GqmoX8H+AY5OsmCE+aZ+ZoLQYpP05zLNhZqr7r/sYw9aqundA+U7gu+/fefJQ4DHA7qr6zID6l7c/v7+nbHr5nwfU/ziwp7dgnvuYNlQ/evb1tCTvTrIzyTenr9EBv9hWmdet/dIwvItPi8EtwLHAMH+tH9Xznl637mMM/zFD+R6+/Q+9w2bYP33lhw94zxf7K1fVvUnu6Cuezz6m/ccM7+nvB0lOoxkpfYPm2tO/AV+jOV16Es11vgfP0J60z0xQWgz+GXgG8Ezgz2eqlGQJzS9OgI/2bd5fT+a8s/15xAzbj+yrB/CV9ufDgR29lds+fS/whX3cx3ycC9wDrK6qG/rieisPvBFFGilP8WkxuBC4FzgtyRP2Uu9naK493QhcOYf276O5PX2fVdVXaUYay5OsGlBl+k65T/aUfar9eeKA+k+h7w/Jee5jPh4DXD8gOR00Q6zSSJmg1HlVtQP4XZrbqTcmOa6/TpLnAX9Ck8heXlX3zWEXdwBHjyDUaRfQXAs7rx0BTce4jOb7XNN1pr2j/flbSQ7rqb+Upt+j2Md83AysSnL/DSdJArwGeMAxkEbNU3xaLF4LfCfwKuCaJJcC22iS1g8CTwbuBs6sqstnamQG/wSckeTvgatprsdcVVVXzTPWPwBOBda0sW4CDgVeQHMb+Bur6v4bIqrqyiQbgLXAtiQX03wp+cdoTtPtphnlzXsf8/THNN8Z+1RPTE+jSU5/38YnjY0JSotCOyL6n0n+FvgF4IeBk2lGTDcDfwi8qb0Feq5eQXON6mTguTRnFl5H8x2k+cR6T5Jn0STTF9Hc8bYHuAZ4ZVW9a8DbXkYzv+DPA2fRjOreC/wmsIvmlN6+7mOu/Xhrkm8Cr6S5Ff5u4CM0X5x+PiYojVmq9te1Y0lz1V5jugm4qKrOXOh4pP3Ja1BSByQ5Ynr+wJ6yQ2mmP4JmNCVNFE/xSd3wSuDMNM+luoXmFvKTab7X9QHg7xYsMmmBmKCkbvgQ8ESaCWK/h+Z60k00z7x6U3kuXhPIa1CSpE5asBHUsmXLauXKlQu1e0lSR1x99dVfqqqp/vIFS1ArV65ky5YtC7V7SVJHJPncoHLv4pMkdZIJSpLUSSYoSVInmaAkSZ1kgpIkdZIJSpLUSSYoSVInmaAkSZ1kgpIkdZKTxeqAct+tjx1LuwcdcdNY2pU0M0dQkqROMkFJkjrJBCVJ6iQTlCSpk0xQkqROMkFJkjrJBCVJ6qShElSSU5LcmGR7knMGbD8syd8nuSbJtiQvHX2okqRJMmuCSrIEWAecChwHnJnkuL5qvwBcX1VPBE4C/jDJ0hHHKkmaIMOMoE4AtlfVjqq6B7gIWNNXp4CHJgnwEODLwJ6RRipJmijDJKjlwM6e9V1tWa/zgccDu4FrgVdU1X0jiVCSNJGGmYsvA8qqb/05wFbgR4BHAx9K8pGq+sq3NZSsBdYCrFixYs7BSgeau285ZiztHnLkZ8fSrrQ/DTOC2gUc3bN+FM1IqddLgfdUYzvwWeDY/oaqakNVra6q1VNTU/ONWZI0AYZJUJuBVUmOaW98OAPY2Ffn88DJAEkeDjwO2DHKQCVJk2XWU3xVtSfJ2cClwBLggqraluSsdvt64FzgwiTX0pwS/PWq+tIY45YkHeCGeh5UVW0CNvWVre9Z3g08e7ShSZImmTNJSJI6yQQlSeokE5QkqZNMUJKkTjJBSZI6yQQlSeokE5QkqZNMUJKkTjJBSZI6yQQlSeokE5QkqZNMUJKkTjJBSZI6yQQlSeokE5QkqZOGSlBJTklyY5LtSc4ZsP1Xk2xtX9cluTfJ94w+XEnSpJg1QSVZAqwDTgWOA85Mclxvnao6r6qOr6rjgd8ArqyqL48hXknShBhmBHUCsL2qdlTVPcBFwJq91D8TeNcogpMkTa5hEtRyYGfP+q627AGSHAqcAly876FJkibZg4aokwFlNUPdHwM+OtPpvSRrgbUAK1asGCpAqQtu/cIjxtLuYQc9eCztSgeCYUZQu4Cje9aPAnbPUPcM9nJ6r6o2VNXqqlo9NTU1fJSSpIkzTILaDKxKckySpTRJaGN/pSSHAU8H3j/aECVJk2jWU3xVtSfJ2cClwBLggqraluSsdvv6tuppwGVV9bWxRStJmhjDXIOiqjYBm/rK1vetXwhcOKrAJEmTzZkkJEmdZIKSJHWSCUqS1EkmKElSJ5mgJEmdZIKSJHWSCUqS1ElDfQ9Kk2vHriPH0u6jjrplLO1KOnA4gpIkdZIJSpLUSSYoSVInmaAkSZ1kgpIkdZIJSpLUSSYoSVInDZWgkpyS5MYk25OcM0Odk5JsTbItyZWjDVOSNGlm/aJukiXAOuBZwC5gc5KNVXV9T53DgbcAp1TV55M8bEzxSpImxDAjqBOA7VW1o6ruAS4C1vTVeRHwnqr6PEBV3TbaMCVJk2aYBLUc2Nmzvqst6/VY4LuTXJHk6iQ/NaoAJUmTaZi5+DKgrAa081+Ak4FDgH9J8vGquunbGkrWAmsBVqxYMfdoJUkTY5gR1C7g6J71o4DdA+p8sKq+VlVfAq4CntjfUFVtqKrVVbV6ampqvjFLkibAMAlqM7AqyTFJlgJnABv76rwf+KEkD0pyKPBk4IbRhipJmiSznuKrqj1JzgYuBZYAF1TVtiRntdvXV9UNST4IfBq4D3hbVV03zsAlSQe2oZ4HVVWbgE19Zev71s8DzhtdaJKkSeZMEpKkTjJBSZI6yQQlSeokE5QkqZNMUJKkTjJBSZI6yQQlSeokE5QkqZNMUJKkTjJBSZI6yQQlSeokE5QkqZNMUJKkTjJBSZI6yQQlSeqkoRJUklOS3Jhke5JzBmw/KcmdSba2r1ePPlRJ0iSZ9YGFSZYA64BnAbuAzUk2VtX1fVU/UlU/OoYYJUkTaJgR1AnA9qraUVX3ABcBa8YbliRp0g2ToJYDO3vWd7Vl/Z6a5JokH0jyhJFEJ0maWLOe4gMyoKz61j8JPLKq7kryXOB9wKoHNJSsBdYCrFixYm6R6oBy+c2PG0u7J33HWJqVtACGGUHtAo7uWT8K2N1boaq+UlV3tcubgIOTLOtvqKo2VNXqqlo9NTW1D2FLkg50wySozcCqJMckWQqcAWzsrZDkiCRpl09o271j1MFKkibHrKf4qmpPkrOBS4ElwAVVtS3JWe329cDpwMuS7AHuBs6oqv7TgJIkDW2Ya1DTp+029ZWt71k+Hzh/tKFJkiaZM0lIkjrJBCVJ6iQTlCSpk0xQkqROMkFJkjrJBCVJ6iQTlCSpk4b6HpS67/07jh9Lu/956VialaRZOYKSJHWSCUqS1EkmKElSJ5mgJEmdZIKSJHWSCUqS1EkmKElSJ5mgJEmdNFSCSnJKkhuTbE9yzl7q/UCSe5OcProQJUmTaNYElWQJsA44FTgOODPJcTPUewPNo+ElSdonw4ygTgC2V9WOqroHuAhYM6DeLwIXA7eNMD5J0oQaJkEtB3b2rO9qy+6XZDlwGrB+bw0lWZtkS5Itt99++1xjlSRNkGESVAaUVd/6m4Bfr6p799ZQVW2oqtVVtXpqamrIECVJk2iY2cx3AUf3rB8F7O6rsxq4KAnAMuC5SfZU1ftGEaQkafIMk6A2A6uSHAN8ATgDeFFvhao6Zno5yYXAJSYnSdK+mDVBVdWeJGfT3J23BLigqrYlOavdvtfrTpIkzcdQDyysqk3Apr6ygYmpql6y72FJkiadM0lIkjrJBCVJ6iQTlCSpk0xQkqROMkFJkjrJBCVJ6qShbjOXtLic/5kfGUu7Zx97+VjalQZxBCVJ6iQTlCSpk0xQkqROMkFJkjrJBCVJ6iQTlCSpk0xQkqROMkFJkjppqASV5JQkNybZnuScAdvXJPl0kq1JtiQ5cfShSpImyawzSSRZAqwDngXsAjYn2VhV1/dU+ydgY1VVku8D3g0cO46AJUmTYZgR1AnA9qraUVX3ABcBa3orVNVdVVXt6ncChSRJ+2CYufiWAzt71ncBT+6vlOQ04PeAhwH/dVBDSdYCawFWrFgx11gPCL9z3Y+Ppd0nHjqWZiVpwQwzgsqAsgeMkKrqvVV1LPA84NxBDVXVhqpaXVWrp6am5hSoJGmyDJOgdgFH96wfBeyeqXJVXQU8OsmyfYxNkjTBhklQm4FVSY5JshQ4A9jYWyHJY5KkXX4SsBS4Y9TBSpImx6zXoKpqT5KzgUuBJcAFVbUtyVnt9vXA84GfSvIt4G7ghT03TUiSNGdDPbCwqjYBm/rK1vcsvwF4w2hDkyRNMmeSkCR1kglKktRJJihJUieZoCRJnWSCkiR1kglKktRJQ91mLkkAv7z1jLG0+8fHXzSWdrW4OYKSJHWSCUqS1EkmKElSJ5mgJEmdZIKSJHWSCUqS1EkmKElSJ5mgJEmdNFSCSnJKkhuTbE9yzoDt/z3Jp9vXx5I8cfShSpImyawJKskSYB1wKnAccGaS4/qqfRZ4elV9H3AusGHUgUqSJsswI6gTgO1VtaOq7gEuAtb0Vqiqj1XVv7erHweOGm2YkqRJM0yCWg7s7Fnf1ZbN5GeBDwzakGRtki1Jttx+++3DRylJmjjDJKgMKKuBFZNn0CSoXx+0vao2VNXqqlo9NTU1fJSSpIkzzGzmu4Cje9aPAnb3V0ryfcDbgFOr6o7RhCdJmlTDjKA2A6uSHJNkKXAGsLG3QpIVwHuAF1fVTaMPU5I0aWYdQVXVniRnA5cCS4ALqmpbkrPa7euBVwPfC7wlCcCeqlo9vrAlSQe6oR5YWFWbgE19Zet7ln8O+LnRhiZJmmTOJCFJ6iQTlCSpk0xQkqROMkFJkjrJBCVJ6iQTlCSpk4a6zVySxuk5V75yLO1e+vQ3jaVd7R+OoCRJnWSCkiR1kglKktRJJihJUieZoCRJnWSCkiR1kglKktRJJihJUicNlaCSnJLkxiTbk5wzYPuxSf4lyTeT/Mrow5QkTZpZZ5JIsgRYBzwL2AVsTrKxqq7vqfZl4JeA540jSEnS5BlmBHUCsL2qdlTVPcBFwJreClV1W1VtBr41hhglSRNomAS1HNjZs76rLZuzJGuTbEmy5fbbb59PE5KkCTFMgsqAsprPzqpqQ1WtrqrVU1NT82lCkjQhhklQu4Cje9aPAnaPJxxJkhrDJKjNwKokxyRZCpwBbBxvWJKkSTfrXXxVtSfJ2cClwBLggqraluSsdvv6JEcAW4DvAu5L8krguKr6yvhClyQdyIZ6YGFVbQI29ZWt71m+lebUnyRJI+FMEpKkTjJBSZI6yQQlSeokE5QkqZNMUJKkTjJBSZI6yQQlSeokE5QkqZNMUJKkTjJBSZI6yQQlSeokE5QkqZNMUJKkTjJBSZI6yQQlSeqkoRJUklOS3Jhke5JzBmxPkje32z+d5EmjD1WSNElmTVBJlgDrgFOB44AzkxzXV+1UYFX7Wgv82YjjlCRNmGFGUCcA26tqR1XdA1wErOmrswZ4RzU+Dhye5MgRxypJmiDDPPJ9ObCzZ30X8OQh6iwHbumtlGQtzQgL4K4kN84p2v1rGfClhQ5iTDrQt1vH1XAH+jY2c+jbzeOMYxzGctzCn4y6yfnw3+TsHjmocJgElQFlNY86VNUGYMMQ+1xwSbZU1eqFjmMc7NviZN8WJ/s2f8Oc4tsFHN2zfhSwex51JEka2jAJajOwKskxSZYCZwAb++psBH6qvZvvKcCdVXVLf0OSJA1r1lN8VbUnydnApcAS4IKq2pbkrHb7emAT8FxgO/B14KXjC3m/WRSnIufJvi1O9m1xsm/zlKoHXCqSJGnBOZOEJKmTTFCSpE4yQbWSvCDJtiT3JZnxtsnZpn3qoiTfk+RDSf5v+/O7Z6h3c5Jrk2xNsmV/xzkXB/L0W0P07aQkd7bHaWuSVy9EnHOV5IIktyW5bobti/mYzda3RXnMAJIcneTDSW5of0e+YkCd8Ry7qvLVXId7PPA44Apg9Qx1lgD/BjwKWApcAxy30LEP0bc3Aue0y+cAb5ih3s3AsoWOd4j+zHocaG7a+QDNd/SeAnxioeMeYd9OAi5Z6Fjn0bcfBp4EXDfD9kV5zIbs26I8Zm3sRwJPapcfCty0v/6/OYJqVdUNVTXbzBbDTPvURWuAt7fLbweet3ChjMSBPP3WYv03Nququgr48l6qLNZjNkzfFq2quqWqPtkufxW4gWamoF5jOXYmqLmZaUqnrnt4td9La38+bIZ6BVyW5Op2WqquGuY4LNZjNWzcT01yTZIPJHnC/glt7BbrMRvWoj9mSVYC3w98om/TWI7dMFMdHTCS/CNwxIBNv1VV7x+miQFlnbhPf299m0MzT6uq3UkeBnwoyWfavwy7ZmTTb3XQMHF/EnhkVd2V5LnA+2ieJLDYLdZjNoxFf8ySPAS4GHhlVX2lf/OAt+zzsZuoBFVVz9zHJjo7pdPe+pbki0mOrKpb2mH3bTO0sbv9eVuS99KcbupigjqQp9+aNe7eXw5VtSnJW5Isq6rFPiHpYj1ms1rsxyzJwTTJ6Z1V9Z4BVcZy7DzFNzfDTPvURRuBn26Xfxp4wGgxyXcmeej0MvBsYOAdSR1wIE+/NWvfkhyRJO3yCTT/j+/Y75GO3mI9ZrNazMesjfsvgBuq6o9mqDaWYzdRI6i9SXIa8KfAFPAPSbZW1XOSPAJ4W1U9t2aY9mkBwx7W7wPvTvKzwOeBFwD09g14OPDe9v/Qg4C/qaoPLlC8ezXTccgBMP3WkH07HXhZkj3A3cAZ1d5K1WVJ3kVzN9uyJLuA1wAHw+I+ZjBU3xblMWs9DXgxcG2SrW3ZbwIrYLzHzqmOJEmd5Ck+SVInmaAkSZ1kgpIkdZIJSpLUSSYoSVInmaA0UknubWdr3tZO6/KqJAe121YneXO7/OAk/9jWfWGSH2rfszXJIQvbi7lJMxP+DUk+PGDbE5JcnuSmNLPJ//b092EG1H1tkl8ZUH54kpePI/a5SjMr9yVzqP9b+f8zeN/bs/xL44xTBwa/B6VRu7uqjgdop0z6G+Aw4DVVtQWYfozH9wMH99RdD/xBVf3lMDtpf8mnqu4bbfjz8rPAy6vq2xJUm2g3Ai+rqsuSHErzbfyXA+v66u7t/+Lh7XveMsqg94eqej3weoAkd00f72kdO47qGEdQGpuqug1YC5zdfsP8pCSXtInrr4Hj27+mfx74CeDVSd4JkORXk2xO82yZ17VlK9uRylto5jY7epZ6f96Oyi6bHpUleUw7crsmySeTPHqm/fVLcmaa52Vdl+QNbdmrgROB9UnO63vLi4CPVtVl7efxdeBsmkeeTI+YNiS5DHhH+57jklyRZEfPKOP3gUe3n9V57Wd5XhvHtUle2LZ3UJopdLa1n/OmJKe3205O8qm2/gVJHtyW35zkde1ncW2SY9vyE5J8rH3Px5I8bu7/Agab4Tje1bP99CQXtstTSS5uj83mJE8bVRxaBEb53BBfvoC7BpT9O81MFSfRPhOHvufjABcCp7fLzwY20ExAeRBwCc3zdlYC9wFPGaLeHuD4tt67gZ9slz8BnNYufwdw6Ezt9PXhETSzcEzRnHm4HHheu+0KBjxDDPgj4BUzfB7fBbwWuBo4pC1/LfAx4MHAMpqpcA5u+3Ndz/ufD3yIZqaJh7dxHUkzW8Gmtg9HtPs5ve3nTuCx7fvfQTPhJzTPAPvFdvnlNDOL0Mb3oHb5mcDFg47bfP5t9B/H/n83bcwXtst/A5zYLq+gmW5nwf+d+9o/L0/xaX8YeM1lL57dvj7Vrj+EZubnzwOfq+Z5M7PV+2xVbW3LrwZWpplrcHlVvRegqr4BkGSmdnonyv0B4Iqqur19zztpkuH79tKPMPOMztPlG6vq7p7yf6iqbwLfTHIbTQLqdyLwrqq6F/hikivb+E4E/q6a02W39lwTe1z7edzUrr8d+AXgTe369OSfVwP/rV0+DHh7klVtrAfvpZ/z0Xsc9+aZNKPK6fXvSvLQap5LpAOcCUpjleRRwL00M6g/fti3Ab9XVW/ta2sl8LUh632zp+he4BBmTpQD2xlQZ6620SSx3tgeRTNa+Gr7S/drfe/pj3vQ/9G99WMu5f377N3fucCHq+q09vO8Ym8NJPlLmuuKu6uZ23E2/f3uTeTf0bN8EPDUviSuCeE1KI1NkilgPXB+Vc1l0sdLgZ9J8/wZkixvr1vNtx5w/yMPdiV5Xlv/we2NC8O08wng6UmWJVkCnAlcOUs/3gmcmOSZbbuHAG8G3jjL+/p9leZR29OuAl6YZEn7Gf8w8K/APwPPb69FTZ9SBfgMzQjyMe36i4eI/TDgC+3yS2YLsKpeWlXHD5mcBvliksenuePztJ7yy2iu2wGQ5Ph5tq9FyBGURu2QNDMeH0xzHeivaK7FDK2aO94eD/xLO8q4C/hJmr/w51yvz4uBtyb5HeBbwAv20s79z82q5llavwF8mGZEsqlmechlVd2dZA3wp0nW0Vwz+ivg/OE+ifvbuSPJR5NcB3wA+DXgqcA1NCOPX6uqW5NcDJxM85iUm2iS6p1V9Y0kLwX+Ls3dgptp/nDYmzfSnOJ7Fc31tnE7h+ba306a+B/Slv8SsC7Jp2l+X10FnLUf4lEHOJu5dABJ8pBqntr6vTSjqqdV1a0LHZc0H46gpAPLJUkOB5YC55qctJg5gpIkdZI3SUiSOskEJUnqJBOUJKmTTFCSpE4yQUmSOun/AW8IGrv74aUOAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "# Create histogram\n",
    "fig, axs = plt.subplots(1, 1, sharex= True, tight_layout=True)\n",
    "\n",
    "N, bins, patches = axs.hist( Naive - 5, range = (-2, 2), density = True , bins = Naive_breaks)\n",
    "\n",
    "fracs = ((N**(1 /5 )) / N.max())\n",
    "norm = colors.Normalize(fracs.min(), fracs.max())\n",
    " \n",
    "for thisfrac, thispatch in zip(fracs, patches):\n",
    "    color = plt.cm.viridis(norm(thisfrac))\n",
    "    thispatch.set_facecolor(color)\n",
    "\n",
    "plt.title('Naive', size=20)\n",
    "plt.xlabel(\"Difference of Naive - True\")\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 1.3 Simulation design B=1000"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "source": [
    "np.random.seed(0)\n",
    "B = 1000\n",
    "Naive = np.zeros( B )\n",
    "Orthogonal = np.zeros( B )"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "source": [
    "for i in range( 0, B ):\n",
    "    n = 100\n",
    "    p = 100\n",
    "    beta = ( 1 / (np.arange( 1, p + 1 ) ** 2 ) ).reshape( p , 1 )\n",
    "    gamma = ( 1 / (np.arange( 1, p + 1 ) ** 2 ) ).reshape( p , 1 )\n",
    "\n",
    "    mean = 0\n",
    "    sd = 1\n",
    "    X = np.random.normal( mean , sd, n * p ).reshape( n, p )\n",
    "\n",
    "    D = ( X @ gamma ) + np.random.normal( mean , sd, n ).reshape( n, 1 )/4 \n",
    "    \n",
    "    # DGP \n",
    "    Y = 5*D + ( X @ beta ) + np.random.normal( mean , sd, n ).reshape( n, 1 )\n",
    "    # single selection method\n",
    "    r_lasso_estimation = hdmpy.rlasso( np.concatenate( ( D , X ) , axis  =  1 ) , Y , post = True ) # Regress main equation by lasso\n",
    "\n",
    "    coef_array = r_lasso_estimation.est[ 'coefficients' ].iloc[ 2:, :].to_numpy()    # Get \"X\" coefficients \n",
    "\n",
    "    SX_IDs = np.where( coef_array != 0 )[0]\n",
    "\n",
    "    # In case all X coefficients are zero, then regress Y on D\n",
    "    if sum(SX_IDs) == 0 : \n",
    "        Naive[ i ] = sm.OLS( Y , sm.add_constant(D) ).fit().summary2().tables[1].round(3).iloc[ 1, 0 ] \n",
    "\n",
    "    # Otherwise, then regress Y on X and D (but only in the selected coefficients)\n",
    "    elif sum( SX_IDs ) > 0 :\n",
    "        X_D = np.concatenate( ( D, X[:, SX_IDs ] ) , axis = 1 )\n",
    "        Naive[ i ] = sm.OLS( Y , sm.add_constant( X_D ) ).fit().summary2().tables[1].round(3).iloc[ 1, 0]\n",
    "\n",
    "    # In both cases we save D coefficient\n",
    "        \n",
    "    # Regress residuals. \n",
    "    resY = hdmpy.rlasso( X , Y , post = False ).est[ 'residuals' ]\n",
    "    resD = hdmpy.rlasso( X , D , post = False ).est[ 'residuals' ]\n",
    "    Orthogonal[ i ] = sm.OLS( resY , sm.add_constant( resD ) ).fit().summary2().tables[1].round(3).iloc[ 1, 0]\n",
    "\n"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "source": [
    "Orto_breaks = [-1.2, -1, -0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8, 2]\n",
    "Naive_breaks = [-0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8, 1, 1.2]"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "source": [
    "# Create histogram\n",
    "fig, axs = plt.subplots(1, 1, sharex= True, tight_layout=True)\n",
    "\n",
    "N, bins, patches = axs.hist( Orthogonal - 5 , range = (-2, 2), density = True , bins = Orto_breaks)\n",
    "\n",
    "fracs = ((N**(1 / 5)) / N.max())\n",
    "norm = colors.Normalize(fracs.min(), fracs.max())\n",
    " \n",
    "for thisfrac, thispatch in zip(fracs, patches):\n",
    "    color = plt.cm.viridis(norm(thisfrac))\n",
    "    thispatch.set_facecolor(color)\n",
    "\n",
    "plt.title('Orthogonal', size=20)\n",
    "plt.xlabel(\"Difference of Orhtogonal - True\")\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "source": [
    "# Create\n",
    "fig, axs = plt.subplots(1, 1, sharex= True, tight_layout=True)\n",
    "\n",
    "# Create histogram\n",
    "N, bins, patches = axs.hist( Naive - 5, range = (-2, 2), density = True , bins = Naive_breaks)\n",
    "\n",
    "fracs = ((N**(11 /12 )) / N.max())\n",
    "norm = colors.Normalize(fracs.min(), fracs.max())\n",
    " \n",
    "for thisfrac, thispatch in zip(fracs, patches):\n",
    "    color = plt.cm.viridis(norm(thisfrac))\n",
    "    thispatch.set_facecolor(color)\n",
    "\n",
    "plt.title('Naive', size=20)\n",
    "plt.xlabel(\"Difference of Naive - True\")\n",
    "\n",
    "# Show plot\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# CONCLUSIONS"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Explain what do you see in the distribution of the histograms. Where the orthogonal and Naive should be centered?\n",
    "In the orthogonal figure, the distribution is converging to 0 meanwhile in the naive figure we have that the graphic is skewed to the right. If we increase the number of trials, in the orthogonal case we have the data looks more like a normal distribution but in the naive the data tend more to the right. "
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Why does this happen? Give an econometric explanation of this.\n",
    "Neyman Orthogonality\n",
    "\n",
    "$ D = \\vartheta_n\\alpha(\\eta^0) = 0 $ , $\\vartheta_nM(\\alpha, \\eta^0) = 0 $ \n",
    "\n",
    "Neyman's orthogonality holds that the estimated coefficient $(\\ alpha)$ of the treatment depends on the coefficients estimated via partialing-out. That is, $\\ alpha$ is insensitive to changes in the estimated coefficients via partialing-out.\n",
    "\n",
    "Taking into account the concept of orthogonality, the estimation of the treatment coefficient using a double lasso via partialling-out model generates an estimated coefficient with a lower standard error, since this is more similar to the population coefficient. This is because in the second step of the partialling-out algorithm the treatment (D) is cleaned of all possible effects of D. In this sense, the coefficient estimated via partialling-out closely resembles the population parameter and complies with Neyman's orthogonality. However, the naive method generates a less precise estimated coefficient than the previous method, because although it uses laso and ols regression, it does not clean up the effects of X on D. This difference in the estimated coefficients can be observed in the histogram distributions for the following trials."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Question 2"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Double-Lasso Approach\n",
    "We have some problems running regressions with many candidate predictors. Finding a model that helps us make decisions about which variables will be interesting and which ones is not a delicate task. Therefore, the main objective is to find a suitable model.\n",
    "\n",
    "One of them is related to DOUBLE-LASSO models, its method combines a regression model with a process of contractions of some parameters to zero and imposes a restriction or penalty on the regression coefficients, to select variables by two step, finding those that predict the dependent variable and those relative to independent variable. This is important, because exclusion of a covariate that is a modest predictor of the dependent variable but strong predictor of the independent variable can create a substantial omitted variable bias.Also, it helps to make test of randomization.\n",
    "\n",
    "In the following lines, the explanation about Lasso's steps will be explained according to the article \"Using double-loop regression for the selection of principle variables\" by Urminsky, Hansen and Chernozhukov,\n",
    "\n",
    "First, they estimate a linear regression model, because they want to find parameters that minimize the sum of squared errors in the regression equation:\n",
    "\n",
    "$$\n",
    " Y_i= \\beta_{0} + \\beta_{1}X_i +  \\beta_{2}W_i1+...+ \\beta_{k+1}W_ik+e_{i}\\\n",
    "$$\n",
    "\n",
    "A lasso regression find parameters which minimize the sum of squared errors in the regression equation with an additional penalty term:\n",
    "\n",
    "$$\n",
    "Min [\\sum_{i}(Y_i - \\beta_{0} + \\beta_{1}X_i +  \\beta_{2}W_i1+...+ \\beta_{k+1}W_ik)^2 + \\lambda \\sum_{k}|\\beta_{k}|\n",
    "$$\n",
    "\n",
    "The penalty term helps reduce the estimated regression coefficients to zero, and some are exactly zero, reducing the over-fitting. By setting some coefficients to zero, you also perform variable selection. Loop regression can be used when the number of observations is smaller than the number of predictors. However, we could omit important variables with nonzero coefficients and underestimate some nonzero coefficients. It would be a bias in the model. In this case, it is necessary to use the \"double lasso\" to select variables and alleviate both sources of bias.\n",
    "\n",
    "Step 1:Fit a lasso regression predicting the dependent variable, and keeping track of the variables with non-zero estimated coefficients:\n",
    "\n",
    "$$\n",
    "Y_i= \\alpha_{0} + \\alpha_{1}W_i1 +...+ \\alpha_{k}W_ik+e_{i}\\\n",
    "$$\n",
    "\n",
    "Step 2: Fit a lasso regression predicting the focal independent variable, keeping track of the variables with non-zero estimated coefficients:\n",
    "\n",
    "$$\n",
    "X_i= \\phi_{0} + \\phi_{1}W_i1 +...+ \\phi_{k}W_ik+e_{i}\\\n",
    "$$\n",
    "\n",
    "If Xi is an effectively randomized treatment, no covariates should be selected in this step.\n",
    "\n",
    "Step 3: Fit a linear regression of the dependent variable on the focal independent variable, including the covariates (Wik) selected in either of the first two steps\n",
    "\n",
    "$$\n",
    "Y_i= \\alpha_{0} + \\alpha_{1}W_i1 + \\sum_{k \\in A} \\beta_{k+1}+...+ \\alpha_{k}W_ik+e_{i}\\\n",
    "$$\n",
    "\n",
    "In the equation, A is the union of the variables estimated to have non-zero coefficients in Steps 1 and 2. This regression could also include a small set of additional covariates identified a priori as necessary. Interpret and report the coefficient estimates and significance tests on the focal variable(s) as the final results. So, lambda is important to avoid over-fitting."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Testing the Convergence Hypothesis"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Introduction"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We provide an additional empirical example of partialling-out with Lasso to estimate the regression coefficient $\\beta_1$ in the high-dimensional linear regression model:\n",
    "  $$\n",
    "  Y = \\beta_1 D +  \\beta_2'W + \\epsilon.\n",
    "  $$\n",
    "  \n",
    "Specifically, we are interested in how the rates  at which economies of different countries grow ($Y$) are related to the initial wealth levels in each country ($D$) controlling for country's institutional, educational, and other similar characteristics ($W$).\n",
    "  \n",
    "The relationship is captured by $\\beta_1$, the *speed of convergence/divergence*, which measures the speed at which poor countries catch up $(\\beta_1< 0)$ or fall behind $(\\beta_1> 0)$ rich countries, after controlling for $W$. Our inference question here is: do poor countries grow faster than rich countries, controlling for educational and other characteristics? In other words, is the speed of convergence negative: $ \\beta_1 <0?$ This is the Convergence Hypothesis predicted by the Solow Growth Model. This is a structural economic model. Under some strong assumptions, that we won't state here, the predictive exercise we are doing here can be given causal interpretation.\n"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The outcome $Y$ is the realized annual growth rate of a country's wealth  (Gross Domestic Product per capita). The target regressor ($D$) is the initial level of the country's wealth. The target parameter $\\beta_1$ is the speed of convergence, which measures the speed at which poor countries catch up with rich countries. The controls ($W$) include measures of education levels, quality of institutions, trade openness, and political stability in the country."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Data analysis\n"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We consider the data set GrowthData which is included in the package *hdm*. First, let us load the data set to get familiar with the data."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "source": [
    "import hdmpy\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import pyreadr\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "import random"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "source": [
    "# I downloaded the data that the author used\n",
    "growth_read = pyreadr.read_r(\"C:/Users/edfra/OneDrive/Documentos/GitHub/ECO224/Labs/data/GrowthData.RData\")\n",
    "\n",
    "# Extracting the data frame from rdata_read\n",
    "growth = growth_read[ 'GrowthData' ]\n",
    "list(growth)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "['Outcome',\n",
       " 'intercept',\n",
       " 'gdpsh465',\n",
       " 'bmp1l',\n",
       " 'freeop',\n",
       " 'freetar',\n",
       " 'h65',\n",
       " 'hm65',\n",
       " 'hf65',\n",
       " 'p65',\n",
       " 'pm65',\n",
       " 'pf65',\n",
       " 's65',\n",
       " 'sm65',\n",
       " 'sf65',\n",
       " 'fert65',\n",
       " 'mort65',\n",
       " 'lifee065',\n",
       " 'gpop1',\n",
       " 'fert1',\n",
       " 'mort1',\n",
       " 'invsh41',\n",
       " 'geetot1',\n",
       " 'geerec1',\n",
       " 'gde1',\n",
       " 'govwb1',\n",
       " 'govsh41',\n",
       " 'gvxdxe41',\n",
       " 'high65',\n",
       " 'highm65',\n",
       " 'highf65',\n",
       " 'highc65',\n",
       " 'highcm65',\n",
       " 'highcf65',\n",
       " 'human65',\n",
       " 'humanm65',\n",
       " 'humanf65',\n",
       " 'hyr65',\n",
       " 'hyrm65',\n",
       " 'hyrf65',\n",
       " 'no65',\n",
       " 'nom65',\n",
       " 'nof65',\n",
       " 'pinstab1',\n",
       " 'pop65',\n",
       " 'worker65',\n",
       " 'pop1565',\n",
       " 'pop6565',\n",
       " 'sec65',\n",
       " 'secm65',\n",
       " 'secf65',\n",
       " 'secc65',\n",
       " 'seccm65',\n",
       " 'seccf65',\n",
       " 'syr65',\n",
       " 'syrm65',\n",
       " 'syrf65',\n",
       " 'teapri65',\n",
       " 'teasec65',\n",
       " 'ex1',\n",
       " 'im1',\n",
       " 'xr65',\n",
       " 'tot1']"
      ]
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "We determine the dimension of our data set."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "source": [
    "growth.shape"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(90, 63)"
      ]
     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The sample contains $90$ countries and $63$ controls. Thus $p \\approx 60$, $n=90$ and $p/n$ is not small. We expect the least squares method to provide a poor estimate of $\\beta_1$.  We expect the method based on partialling-out with Lasso to provide a high quality estimate of $\\beta_1$."
   ],
   "metadata": {
    "papermill": {
     "duration": 0.025013,
     "end_time": "2021-01-20T08:46:45.109042",
     "exception": false,
     "start_time": "2021-01-20T08:46:45.084029",
     "status": "completed"
    },
    "tags": []
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "To check this hypothesis, we analyze the relation between the output variable $Y$ and the other country's characteristics by running a linear regression in the first step."
   ],
   "metadata": {
    "papermill": {
     "duration": 0.024124,
     "end_time": "2021-01-20T08:46:45.157510",
     "exception": false,
     "start_time": "2021-01-20T08:46:45.133386",
     "status": "completed"
    },
    "tags": []
   }
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "source": [
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "source": [
    "# We create the main variables\n",
    "y = growth['Outcome']\n",
    "X = growth.drop('Outcome', 1)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "source": [
    "# OLS regression\n",
    "reg_ols  = sm.OLS(y, X).fit()\n",
    "print(reg_ols.summary())"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                Outcome   R-squared:                       0.887\n",
      "Model:                            OLS   Adj. R-squared:                  0.641\n",
      "Method:                 Least Squares   F-statistic:                     3.607\n",
      "Date:                Fri, 08 Oct 2021   Prob (F-statistic):           0.000200\n",
      "Time:                        17:37:08   Log-Likelihood:                 238.24\n",
      "No. Observations:                  90   AIC:                            -352.5\n",
      "Df Residuals:                      28   BIC:                            -197.5\n",
      "Df Model:                          61                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "intercept      0.2472      0.785      0.315      0.755      -1.360       1.854\n",
      "gdpsh465      -0.0094      0.030     -0.314      0.756      -0.071       0.052\n",
      "bmp1l         -0.0689      0.033     -2.117      0.043      -0.135      -0.002\n",
      "freeop         0.0801      0.208      0.385      0.703      -0.346       0.506\n",
      "freetar       -0.4890      0.418     -1.169      0.252      -1.346       0.368\n",
      "h65           -2.3621      0.857     -2.755      0.010      -4.118      -0.606\n",
      "hm65           0.7071      0.523      1.352      0.187      -0.364       1.779\n",
      "hf65           1.6934      0.503      3.365      0.002       0.663       2.724\n",
      "p65            0.2655      0.164      1.616      0.117      -0.071       0.602\n",
      "pm65           0.1370      0.151      0.906      0.373      -0.173       0.447\n",
      "pf65          -0.3313      0.165     -2.006      0.055      -0.670       0.007\n",
      "s65            0.0391      0.186      0.211      0.835      -0.341       0.419\n",
      "sm65          -0.0307      0.117     -0.263      0.795      -0.270       0.209\n",
      "sf65          -0.1799      0.118     -1.523      0.139      -0.422       0.062\n",
      "fert65         0.0069      0.027      0.254      0.801      -0.049       0.062\n",
      "mort65        -0.2335      0.817     -0.286      0.777      -1.908       1.441\n",
      "lifee065      -0.0149      0.193     -0.077      0.939      -0.411       0.381\n",
      "gpop1          0.9702      1.812      0.535      0.597      -2.742       4.682\n",
      "fert1          0.0088      0.035      0.252      0.803      -0.063       0.081\n",
      "mort1          0.0666      0.685      0.097      0.923      -1.336       1.469\n",
      "invsh41        0.0745      0.108      0.687      0.498      -0.148       0.297\n",
      "geetot1       -0.7151      1.680     -0.426      0.674      -4.157       2.726\n",
      "geerec1        0.6300      2.447      0.257      0.799      -4.383       5.643\n",
      "gde1          -0.4436      1.671     -0.265      0.793      -3.867       2.980\n",
      "govwb1         0.3375      0.438      0.770      0.447      -0.560       1.235\n",
      "govsh41        0.4632      1.925      0.241      0.812      -3.481       4.407\n",
      "gvxdxe41      -0.7934      2.059     -0.385      0.703      -5.012       3.425\n",
      "high65        -0.7525      0.906     -0.831      0.413      -2.608       1.103\n",
      "highm65       -0.3903      0.681     -0.573      0.571      -1.786       1.005\n",
      "highf65       -0.4177      0.561     -0.744      0.463      -1.568       0.732\n",
      "highc65       -2.2158      1.481     -1.496      0.146      -5.249       0.818\n",
      "highcm65       0.2797      0.658      0.425      0.674      -1.069       1.628\n",
      "highcf65       0.3921      0.766      0.512      0.613      -1.177       1.961\n",
      "human65        2.3373      3.307      0.707      0.486      -4.437       9.112\n",
      "humanm65      -1.2092      1.619     -0.747      0.461      -4.525       2.106\n",
      "humanf65      -1.1039      1.685     -0.655      0.518      -4.555       2.347\n",
      "hyr65         54.9139     23.887      2.299      0.029       5.983     103.845\n",
      "hyrm65        12.9350     23.171      0.558      0.581     -34.529      60.400\n",
      "hyrf65         9.0926     17.670      0.515      0.611     -27.102      45.287\n",
      "no65           0.0372      0.132      0.282      0.780      -0.233       0.308\n",
      "nom65         -0.0212      0.065     -0.326      0.747      -0.154       0.112\n",
      "nof65         -0.0169      0.067     -0.252      0.803      -0.154       0.120\n",
      "pinstab1      -0.0500      0.031     -1.616      0.117      -0.113       0.013\n",
      "pop65       1.032e-07   1.32e-07      0.783      0.440   -1.67e-07    3.73e-07\n",
      "worker65       0.0341      0.156      0.218      0.829      -0.286       0.354\n",
      "pop1565       -0.4655      0.471     -0.988      0.332      -1.431       0.500\n",
      "pop6565       -1.3575      0.635     -2.138      0.041      -2.658      -0.057\n",
      "sec65         -0.0109      0.308     -0.035      0.972      -0.641       0.619\n",
      "secm65         0.0033      0.151      0.022      0.983      -0.306       0.313\n",
      "secf65        -0.0023      0.158     -0.015      0.988      -0.326       0.321\n",
      "secc65        -0.4915      0.729     -0.674      0.506      -1.985       1.002\n",
      "seccm65        0.2596      0.356      0.730      0.471      -0.469       0.988\n",
      "seccf65        0.2207      0.373      0.591      0.559      -0.544       0.985\n",
      "syr65         -0.7556      7.977     -0.095      0.925     -17.095      15.584\n",
      "syrm65         0.3109      3.897      0.080      0.937      -7.671       8.293\n",
      "syrf65         0.7593      4.111      0.185      0.855      -7.661       9.180\n",
      "teapri65    3.955e-05      0.001      0.051      0.959      -0.002       0.002\n",
      "teasec65       0.0002      0.001      0.213      0.833      -0.002       0.003\n",
      "ex1           -0.5804      0.242     -2.400      0.023      -1.076      -0.085\n",
      "im1            0.5914      0.250      2.363      0.025       0.079       1.104\n",
      "xr65          -0.0001   5.42e-05     -1.916      0.066      -0.000    7.18e-06\n",
      "tot1          -0.1279      0.113     -1.136      0.266      -0.359       0.103\n",
      "==============================================================================\n",
      "Omnibus:                        0.439   Durbin-Watson:                   1.982\n",
      "Prob(Omnibus):                  0.803   Jarque-Bera (JB):                0.417\n",
      "Skew:                           0.158   Prob(JB):                        0.812\n",
      "Kurtosis:                       2.896   Cond. No.                     7.52e+08\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 7.52e+08. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "source": [
    "# output: estimated regression coefficient corresponding to the target regressor\n",
    "est_ols = reg_ols.summary2().tables[1]['Coef.']['gdpsh465']\n",
    "\n",
    "# output: std. error\n",
    "std_ols = reg_ols.summary2().tables[1]['Std.Err.']['gdpsh465']\n",
    "\n",
    "# output: 95% confidence interval\n",
    "lower_ci = reg_ols.summary2().tables[1]['[0.025']['gdpsh465']\n",
    "upper_ci = reg_ols.summary2().tables[1]['0.975]']['gdpsh465']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Summarize OLS results"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "source": [
    "table_1 = np.zeros( (1, 4) )\n",
    "\n",
    "table_1[0,0] = est_ols  \n",
    "table_1[0,1] = std_ols   \n",
    "table_1[0,2] = lower_ci\n",
    "table_1[0,3] = upper_ci    \n",
    "\n",
    "\n",
    "table_1_pandas = pd.DataFrame( table_1, columns = [ \"Estimator\",\"Std. Error\", \"lower bound CI\", \"upper bound CI\"  ])\n",
    "table_1_pandas.index = [ \"OLS\" ]\n",
    "table_1_html = table_1_pandas.to_html()\n",
    "table_1_html"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "'<table border=\"1\" class=\"dataframe\">\\n  <thead>\\n    <tr style=\"text-align: right;\">\\n      <th></th>\\n      <th>Estimator</th>\\n      <th>Std. Error</th>\\n      <th>lower bound CI</th>\\n      <th>upper bound CI</th>\\n    </tr>\\n  </thead>\\n  <tbody>\\n    <tr>\\n      <th>OLS</th>\\n      <td>-0.009378</td>\\n      <td>0.029888</td>\\n      <td>-0.0706</td>\\n      <td>0.051844</td>\\n    </tr>\\n  </tbody>\\n</table>'"
      ]
     },
     "metadata": {},
     "execution_count": 24
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "<!-- html table generated in R 3.6.3 by xtable 1.8-4 package -->\n",
    "<!-- Tue Jan 19 10:23:32 2021 -->\n",
    "<table border=1>\n",
    "<tr> <th>  </th> <th> estimator </th> <th> standard error </th> <th> lower bound CI </th> <th> upper bound CI </th>  </tr>\n",
    "  <tr> <td align=\"right\"> OLS </td> <td align=\"right\"> -0.009 </td> <td align=\"right\"> 0.030 </td> <td align=\"right\"> -0.071 </td> <td align=\"right\"> 0.052 </td> </tr>\n",
    "   </table>"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Least squares provides a rather noisy estimate (high standard error) of the\n",
    "speed of convergence, and does not allow us to answer the question\n",
    "about the convergence hypothesis since the confidence interval includes zero."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "source": [
    "# Create main variables\n",
    "Y = growth['Outcome']\n",
    "W = growth.drop(['Outcome','intercept', 'gdpsh465'], 1 )\n",
    "D = growth['gdpsh465']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "source": [
    "W.shape"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(90, 60)"
      ]
     },
     "metadata": {},
     "execution_count": 26
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "source": [
    "Y.shape"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(90,)"
      ]
     },
     "metadata": {},
     "execution_count": 27
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "source": [
    "D.shape"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(90,)"
      ]
     },
     "metadata": {},
     "execution_count": 28
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Double LASSO using cross Validation (Using Sklearn)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now, we are going to use sample splitting approach:"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "D_train, D_test, Y_train, Y_test, W_train, W_test = train_test_split(D, Y, W, test_size = 0.30)\n",
    "W_train.shape"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(63, 60)"
      ]
     },
     "metadata": {},
     "execution_count": 29
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "source": [
    "D_train.shape"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(63,)"
      ]
     },
     "metadata": {},
     "execution_count": 30
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "source": [
    "Y_train.shape"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "(63,)"
      ]
     },
     "metadata": {},
     "execution_count": 31
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "source": [
    "#rom sklearn import model_selection\n",
    "#from sklearn.model_selection import cross_val_score\n",
    "\n",
    "#kfold = model_selection.KFold(n_splits=10)\n",
    "#lr = LogisticRegression()\n",
    "#scoring = 'accuracy'\n",
    "#results = model_selection.cross_val_score(lr, X_train, y_train, cv=kfold, scoring=scoring)\n",
    "#print(\"10-fold cross validation average accuracy: %.3f\" % (results.mean()))\n",
    "#results"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### First of all, let's use the $ \\alpha $ = 0.00077 because it is the value that get answers pretty similar in comparison with R"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "# Seat values for Lasso\n",
    "lasso_model = linear_model.Lasso( alpha = 0.00077 )\n",
    "r_Y = Y_train - lasso_model.fit(W_train,Y_train).predict(W_train)\n",
    "r_Y = r_Y.rename('r_Y')\n",
    "\n",
    "# Part. out d\n",
    "r_D = D_train - lasso_model.fit(W_train,D_train).predict(W_train)\n",
    "r_D = r_D.rename('r_D')\n",
    "\n",
    "# ols \n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "\n",
    "est_lasso = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "std_lasso = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "lower_ci_lasso = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:530: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.00034251659774486853, tolerance: 1.730650793643347e-05\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:530: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 1.5788188735405806, tolerance: 0.005387656525176694\n",
      "  model = cd_fast.enet_coordinate_descent(\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "source": [
    "# from sklearn import linear_model\n",
    "\n",
    "# # Seat values for Lasso\n",
    "# lasso_model = linear_model.Lasso( alpha = 0.00077 )\n",
    "# r_Y = Y - lasso_model.fit( W, Y ).predict( W )\n",
    "# r_Y = r_Y.rename('r_Y')\n",
    "\n",
    "# # Part. out d\n",
    "# r_D = D - lasso_model.fit( W, D ).predict( W )\n",
    "# r_D = r_D.rename('r_D')\n",
    "\n",
    "# # Regress residuales\n",
    "# partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "\n",
    "# # output: estimated regression coefficient corresponding to the target regressor\n",
    "# est_lasso = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "# # output: std. error\n",
    "# std_lasso = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "\n",
    "# # output: 95% confidence interval\n",
    "# lower_ci_lasso = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "# upper_ci_lasso = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "source": [
    "# Regress residuales\n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "partial_lasso_est = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "print( f\"Coefficient for D via sample splitting using lasso {partial_lasso_est}\" )"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Coefficient for D via sample splitting using lasso -0.03257798527404339\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "source": [
    "# output: estimated regression coefficient corresponding to the target regressor\n",
    "est_lasso_train = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "# output: std. error\n",
    "std_lasso_train = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "\n",
    "# output: 95% confidence interval\n",
    "lower_ci_lasso_train = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso_train = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "source": [
    "r_Y = pd.DataFrame(r_Y)\n",
    "r_D = pd.DataFrame(r_D)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "model = LinearRegression()\n",
    "mymodel = model.fit(r_Y, r_D)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "source": [
    "# K - fold CV\n",
    "# Importing cross_val score function\n",
    "\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "# 5-fold CV\n",
    "scores = cross_val_score(mymodel, W_train, D_train ,Y_train)\n",
    "scores"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:70: FutureWarning: Pass groups=29    0.076233\n",
      "63   -0.081726\n",
      "6     0.067332\n",
      "1     0.100473\n",
      "34    0.073905\n",
      "        ...   \n",
      "27    0.092106\n",
      "12   -0.024326\n",
      "50    0.090677\n",
      "52    0.050757\n",
      "59    0.034172\n",
      "Name: Outcome, Length: 63, dtype: float64 as keyword args. From version 1.0 (renaming of 0.25) passing these as positional arguments will result in an error\n",
      "  warnings.warn(f\"Pass {args_msg} as keyword args. From version \"\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([ -0.53161849,   0.59464628,  -1.15138574,   0.31408462,\n",
       "       -10.17847547])"
      ]
     },
     "metadata": {},
     "execution_count": 39
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "# Seat values for Lasso\n",
    "lasso_model = linear_model.Lasso( alpha = 0.00077 )\n",
    "r_Y = Y_test - lasso_model.fit(W_test,Y_test ).predict(W_test)\n",
    "r_Y = r_Y.rename('r_Y')\n",
    "\n",
    "# Part. out d\n",
    "r_D = D_test - lasso_model.fit(W_test,D_test).predict(W_test)\n",
    "r_D = r_D.rename('r_D')\n",
    "\n",
    "# ols \n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "\n",
    "est_lasso = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "std_lasso = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "lower_ci_lasso = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:530: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.009042324543229674, tolerance: 5.526019561078833e-06\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:530: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.23285259590690255, tolerance: 0.0017580204050104266\n",
      "  model = cd_fast.enet_coordinate_descent(\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "source": [
    "r_Y = pd.DataFrame(r_Y)\n",
    "r_D = pd.DataFrame(r_D)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "model = LinearRegression()\n",
    "mymodel = model.fit(r_Y, r_D)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "source": [
    "# K - fold CV\n",
    "# Importing cross_val score function\n",
    "\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "# 5-fold CV\n",
    "pred = cross_val_score(mymodel, W_test, D_test,Y_test)\n",
    "pred"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:70: FutureWarning: Pass groups=85    0.031196\n",
      "33    0.067852\n",
      "53    0.000408\n",
      "66   -0.011384\n",
      "26    0.109871\n",
      "58    0.011897\n",
      "89    0.040642\n",
      "16    0.036391\n",
      "65    0.066598\n",
      "46    0.045473\n",
      "75    0.040534\n",
      "9     0.039147\n",
      "57    0.014256\n",
      "36    0.065838\n",
      "51   -0.019161\n",
      "2     0.067051\n",
      "77    0.185526\n",
      "72    0.021247\n",
      "11    0.127951\n",
      "15    0.052308\n",
      "64    0.046010\n",
      "74    0.096816\n",
      "20    0.085206\n",
      "23    0.109699\n",
      "28    0.083376\n",
      "81    0.034213\n",
      "14    0.112912\n",
      "Name: Outcome, dtype: float64 as keyword args. From version 1.0 (renaming of 0.25) passing these as positional arguments will result in an error\n",
      "  warnings.warn(f\"Pass {args_msg} as keyword args. From version \"\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([ -4.37689543,  -0.23091557,  -5.75747793, -33.99628182,\n",
       "         0.65350317])"
      ]
     },
     "metadata": {},
     "execution_count": 43
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "source": [
    "# Regress residuales\n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "partial_lasso_est = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "print( f\"Coefficient for D via sample splitting using lasso {partial_lasso_est}\" )"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Coefficient for D via sample splitting using lasso 0.03115411895838744\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "source": [
    "# output: estimated regression coefficient corresponding to the target regressor\n",
    "est_lasso_test = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "# output: std. error\n",
    "std_lasso_test = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "\n",
    "# output: 95% confidence interval\n",
    "lower_ci_lasso_test = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso_test = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Secondly, let's use the $ \\alpha $ = 0.1  in order to know how $\\beta$ changes in comparison when we use $ \\alpha $ = 0.00077"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "# Seat values for Lasso\n",
    "lasso_model = linear_model.Lasso( alpha = 0.1 )\n",
    "r_Y = Y_train - lasso_model.fit(W_train,Y_train).predict(W_train)\n",
    "r_Y = r_Y.rename('r_Y')\n",
    "\n",
    "# Part. out d\n",
    "r_D = D_train - lasso_model.fit(W_train,D_train).predict(W_train)\n",
    "r_D = r_D.rename('r_D')\n",
    "\n",
    "# ols \n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "\n",
    "est_lasso = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "std_lasso = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "lower_ci_lasso = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "source": [
    "# Regress residuales\n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "partial_lasso_est = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "print( f\"Coefficient for D via sample splitting using lasso {partial_lasso_est}\" )"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Coefficient for D via sample splitting using lasso 0.0004988150025382592\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "source": [
    "# output: estimated regression coefficient corresponding to the target regressor\n",
    "est_lasso_train_1 = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "# output: std. error\n",
    "std_lasso_train_1 = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "\n",
    "# output: 95% confidence interval\n",
    "lower_ci_lasso_train_1 = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso_train_1 = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "source": [
    "r_Y = pd.DataFrame(r_Y)\n",
    "r_D = pd.DataFrame(r_D)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "model = LinearRegression()\n",
    "mymodel = model.fit(r_Y, r_D)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "source": [
    "# K - fold CV\n",
    "# Importing cross_val score function\n",
    "\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "# 5-fold CV\n",
    "scores = cross_val_score(mymodel, W_train, D_train ,Y_train)\n",
    "scores"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:70: FutureWarning: Pass groups=29    0.076233\n",
      "63   -0.081726\n",
      "6     0.067332\n",
      "1     0.100473\n",
      "34    0.073905\n",
      "        ...   \n",
      "27    0.092106\n",
      "12   -0.024326\n",
      "50    0.090677\n",
      "52    0.050757\n",
      "59    0.034172\n",
      "Name: Outcome, Length: 63, dtype: float64 as keyword args. From version 1.0 (renaming of 0.25) passing these as positional arguments will result in an error\n",
      "  warnings.warn(f\"Pass {args_msg} as keyword args. From version \"\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([ -0.53161849,   0.59464628,  -1.15138574,   0.31408462,\n",
       "       -10.17847547])"
      ]
     },
     "metadata": {},
     "execution_count": 51
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "# Seat values for Lasso\n",
    "lasso_model = linear_model.Lasso( alpha = 0.1 )\n",
    "r_Y = Y_test - lasso_model.fit(W_test,Y_test ).predict(W_test)\n",
    "r_Y = r_Y.rename('r_Y')\n",
    "\n",
    "# Part. out d\n",
    "r_D = D_test - lasso_model.fit(W_test,D_test).predict(W_test)\n",
    "r_D = r_D.rename('r_D')\n",
    "\n",
    "# ols \n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "\n",
    "est_lasso = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "std_lasso = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "lower_ci_lasso = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "source": [
    "r_Y = pd.DataFrame(r_Y)\n",
    "r_D = pd.DataFrame(r_D)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "model = LinearRegression()\n",
    "mymodel = model.fit(r_Y, r_D)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "source": [
    "# K - fold CV\n",
    "# Importing cross_val score function\n",
    "\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "# 5-fold CV\n",
    "pred = cross_val_score(mymodel, W_test, D_test,Y_test)\n",
    "pred"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:70: FutureWarning: Pass groups=85    0.031196\n",
      "33    0.067852\n",
      "53    0.000408\n",
      "66   -0.011384\n",
      "26    0.109871\n",
      "58    0.011897\n",
      "89    0.040642\n",
      "16    0.036391\n",
      "65    0.066598\n",
      "46    0.045473\n",
      "75    0.040534\n",
      "9     0.039147\n",
      "57    0.014256\n",
      "36    0.065838\n",
      "51   -0.019161\n",
      "2     0.067051\n",
      "77    0.185526\n",
      "72    0.021247\n",
      "11    0.127951\n",
      "15    0.052308\n",
      "64    0.046010\n",
      "74    0.096816\n",
      "20    0.085206\n",
      "23    0.109699\n",
      "28    0.083376\n",
      "81    0.034213\n",
      "14    0.112912\n",
      "Name: Outcome, dtype: float64 as keyword args. From version 1.0 (renaming of 0.25) passing these as positional arguments will result in an error\n",
      "  warnings.warn(f\"Pass {args_msg} as keyword args. From version \"\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([ -4.37689543,  -0.23091557,  -5.75747793, -33.99628182,\n",
       "         0.65350317])"
      ]
     },
     "metadata": {},
     "execution_count": 55
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "source": [
    "# Regress residuales\n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "partial_lasso_est = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "print( f\"Coefficient for D via sample splitting using lasso {partial_lasso_est}\" )"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Coefficient for D via sample splitting using lasso 0.019355858562937943\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "source": [
    "# output: estimated regression coefficient corresponding to the target regressor\n",
    "est_lasso_test_1 = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "# output: std. error\n",
    "std_lasso_test_1 = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "\n",
    "# output: 95% confidence interval\n",
    "lower_ci_lasso_test_1 = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso_test_1 = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "#### Thridly, let's use the $ \\alpha $ = 0.8 in order to know how $\\beta$ changes in comparison when we use $ \\alpha $ =0.00077 and the other $ \\alpha $ = 0.1"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "# Seat values for Lasso\n",
    "lasso_model = linear_model.Lasso( alpha = 0.8 )\n",
    "r_Y = Y_train - lasso_model.fit(W_train,Y_train).predict(W_train)\n",
    "r_Y = r_Y.rename('r_Y')\n",
    "\n",
    "# Part. out d\n",
    "r_D = D_train - lasso_model.fit(W_train,D_train).predict(W_train)\n",
    "r_D = r_D.rename('r_D')\n",
    "\n",
    "# ols \n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "\n",
    "est_lasso = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "std_lasso = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "lower_ci_lasso = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:530: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 0.00034251659774486853, tolerance: 1.730650793643347e-05\n",
      "  model = cd_fast.enet_coordinate_descent(\n",
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_coordinate_descent.py:530: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 1.5788188735405806, tolerance: 0.005387656525176694\n",
      "  model = cd_fast.enet_coordinate_descent(\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "source": [
    "# Regress residuales\n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "partial_lasso_est = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "print( f\"Coefficient for D via sample splitting using lasso {partial_lasso_est}\" )"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Coefficient for D via sample splitting using lasso -0.03257798527404339\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "source": [
    "# output: estimated regression coefficient corresponding to the target regressor\n",
    "est_lasso_train_2 = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "# output: std. error\n",
    "std_lasso_train_2 = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "\n",
    "# output: 95% confidence interval\n",
    "lower_ci_lasso_train_2 = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso_train_2 = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "source": [
    "r_Y = pd.DataFrame(r_Y)\n",
    "r_D = pd.DataFrame(r_D)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "model = LinearRegression()\n",
    "mymodel = model.fit(r_Y, r_D)"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "source": [
    "# K - fold CV\n",
    "# Importing cross_val score function\n",
    "\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "# 5-fold CV\n",
    "pred = cross_val_score(mymodel, W_test, D_test,Y_test)\n",
    "pred"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "C:\\Users\\edfra\\anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:70: FutureWarning: Pass groups=85    0.031196\n",
      "33    0.067852\n",
      "53    0.000408\n",
      "66   -0.011384\n",
      "26    0.109871\n",
      "58    0.011897\n",
      "89    0.040642\n",
      "16    0.036391\n",
      "65    0.066598\n",
      "46    0.045473\n",
      "75    0.040534\n",
      "9     0.039147\n",
      "57    0.014256\n",
      "36    0.065838\n",
      "51   -0.019161\n",
      "2     0.067051\n",
      "77    0.185526\n",
      "72    0.021247\n",
      "11    0.127951\n",
      "15    0.052308\n",
      "64    0.046010\n",
      "74    0.096816\n",
      "20    0.085206\n",
      "23    0.109699\n",
      "28    0.083376\n",
      "81    0.034213\n",
      "14    0.112912\n",
      "Name: Outcome, dtype: float64 as keyword args. From version 1.0 (renaming of 0.25) passing these as positional arguments will result in an error\n",
      "  warnings.warn(f\"Pass {args_msg} as keyword args. From version \"\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "array([ -4.37689543,  -0.23091557,  -5.75747793, -33.99628182,\n",
       "         0.65350317])"
      ]
     },
     "metadata": {},
     "execution_count": 63
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "source": [
    "# Regress residuales\n",
    "partial_lasso_fit = sm.OLS(r_Y, r_D).fit()\n",
    "partial_lasso_est = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "print( f\"Coefficient for D via sample splitting using lasso {partial_lasso_est}\" )"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Coefficient for D via sample splitting using lasso -0.03257798527404339\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "source": [
    "# output: estimated regression coefficient corresponding to the target regressor\n",
    "est_lasso_test_2 = partial_lasso_fit.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "# output: std. error\n",
    "std_lasso_test_2 = partial_lasso_fit.summary2().tables[1]['Std.Err.']['r_D']\n",
    "\n",
    "# output: 95% confidence interval\n",
    "lower_ci_lasso_test_2 = partial_lasso_fit.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso_test_2 = partial_lasso_fit.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Summary LASSO results\n"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Finally, let us have a look at the results."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "source": [
    "table_2 = np.zeros( (1, 4) )\n",
    "\n",
    "table_2[0,0] = est_lasso_train\n",
    "table_2[0,1] = std_lasso_train\n",
    "table_2[0,2] = lower_ci_lasso_train\n",
    "table_2[0,3] = upper_ci_lasso_train\n",
    "\n",
    "\n",
    "table_2_pandas = pd.DataFrame( table_2, columns = [ \"Estimator\",\"Std. Error\", \"lower bound CI\", \"upper bound CI\"  ])\n",
    "table_2_pandas.index = [ \"LASSO TRAIN (alpha=0.00077)\" ]\n",
    "table_2_pandas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
       "      <td>-0.032578</td>\n",
       "      <td>0.024406</td>\n",
       "      <td>-0.081365</td>\n",
       "      <td>0.016209</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "\n",
       "                             upper bound CI  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  "
      ]
     },
     "metadata": {},
     "execution_count": 66
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "source": [
    "table_3 = table_1_pandas.append(table_2_pandas)\n",
    "table_3"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OLS</th>\n",
       "      <td>-0.009378</td>\n",
       "      <td>0.029888</td>\n",
       "      <td>-0.070600</td>\n",
       "      <td>0.051844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
       "      <td>-0.032578</td>\n",
       "      <td>0.024406</td>\n",
       "      <td>-0.081365</td>\n",
       "      <td>0.016209</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "OLS                          -0.009378    0.029888       -0.070600   \n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "\n",
       "                             upper bound CI  \n",
       "OLS                                0.051844  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  "
      ]
     },
     "metadata": {},
     "execution_count": 67
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "source": [
    "table_4 = table_2 = np.zeros( (1, 4) )\n",
    "\n",
    "table_4[0,0] = est_lasso_test\n",
    "table_4[0,1] = std_lasso_test\n",
    "table_4[0,2] = lower_ci_lasso_test\n",
    "table_4[0,3] = upper_ci_lasso_test\n",
    "\n",
    "table_4_pandas = pd.DataFrame( table_4, columns = [ \"Estimator\",\"Std. Error\", \"lower bound CI\", \"upper bound CI\"  ])\n",
    "table_4_pandas.index = [ \"LASSO TEST (alpha= 0.00077)\" ]\n",
    "table_4_pandas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LASSO TEST (alpha= 0.00077)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.07496</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "LASSO TEST (alpha= 0.00077)   0.031154    0.051624        -0.07496   \n",
       "\n",
       "                             upper bound CI  \n",
       "LASSO TEST (alpha= 0.00077)        0.137268  "
      ]
     },
     "metadata": {},
     "execution_count": 68
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "source": [
    "table_5 = table_3.append(table_4_pandas)\n",
    "table_5"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OLS</th>\n",
       "      <td>-0.009378</td>\n",
       "      <td>0.029888</td>\n",
       "      <td>-0.070600</td>\n",
       "      <td>0.051844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
       "      <td>-0.032578</td>\n",
       "      <td>0.024406</td>\n",
       "      <td>-0.081365</td>\n",
       "      <td>0.016209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST (alpha= 0.00077)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "OLS                          -0.009378    0.029888       -0.070600   \n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "LASSO TEST (alpha= 0.00077)   0.031154    0.051624       -0.074960   \n",
       "\n",
       "                             upper bound CI  \n",
       "OLS                                0.051844  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  \n",
       "LASSO TEST (alpha= 0.00077)        0.137268  "
      ]
     },
     "metadata": {},
     "execution_count": 69
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "source": [
    "table_6 = np.zeros( (1, 4) )\n",
    "\n",
    "table_6[0,0] = est_lasso_train_1\n",
    "table_6[0,1] = std_lasso_train_1\n",
    "table_6[0,2] = lower_ci_lasso_train_1\n",
    "table_6[0,3] = upper_ci_lasso_train_1\n",
    "\n",
    "\n",
    "table_6_pandas = pd.DataFrame( table_2, columns = [ \"Estimator\",\"Std. Error\", \"lower bound CI\", \"upper bound CI\"  ])\n",
    "table_6_pandas.index = [ \"LASSO TRAIN ( alpha =0.1)\" ]\n",
    "table_6_pandas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
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       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN ( alpha =0.1)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.07496</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           Estimator  Std. Error  lower bound CI  \\\n",
       "LASSO TRAIN ( alpha =0.1)   0.031154    0.051624        -0.07496   \n",
       "\n",
       "                           upper bound CI  \n",
       "LASSO TRAIN ( alpha =0.1)        0.137268  "
      ]
     },
     "metadata": {},
     "execution_count": 70
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "source": [
    "table_7 = table_5.append(table_6_pandas)\n",
    "table_7"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OLS</th>\n",
       "      <td>-0.009378</td>\n",
       "      <td>0.029888</td>\n",
       "      <td>-0.070600</td>\n",
       "      <td>0.051844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
       "      <td>-0.032578</td>\n",
       "      <td>0.024406</td>\n",
       "      <td>-0.081365</td>\n",
       "      <td>0.016209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST (alpha= 0.00077)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN ( alpha =0.1)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "OLS                          -0.009378    0.029888       -0.070600   \n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "LASSO TEST (alpha= 0.00077)   0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN ( alpha =0.1)     0.031154    0.051624       -0.074960   \n",
       "\n",
       "                             upper bound CI  \n",
       "OLS                                0.051844  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  \n",
       "LASSO TEST (alpha= 0.00077)        0.137268  \n",
       "LASSO TRAIN ( alpha =0.1)          0.137268  "
      ]
     },
     "metadata": {},
     "execution_count": 71
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "source": [
    "table_8 = table_2 = np.zeros( (1, 4) )\n",
    "\n",
    "table_8[0,0] = est_lasso_test_1\n",
    "table_8[0,1] = std_lasso_test_1\n",
    "table_8[0,2] = lower_ci_lasso_test_1\n",
    "table_8[0,3] = upper_ci_lasso_test_1\n",
    "\n",
    "table_8_pandas = pd.DataFrame( table_4, columns = [ \"Estimator\",\"Std. Error\", \"lower bound CI\", \"upper bound CI\"  ])\n",
    "table_8_pandas.index = [ \"LASSO TEST ( alpha= 0.1 )\" ]\n",
    "table_8_pandas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LASSO TEST ( alpha= 0.1 )</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.07496</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           Estimator  Std. Error  lower bound CI  \\\n",
       "LASSO TEST ( alpha= 0.1 )   0.031154    0.051624        -0.07496   \n",
       "\n",
       "                           upper bound CI  \n",
       "LASSO TEST ( alpha= 0.1 )        0.137268  "
      ]
     },
     "metadata": {},
     "execution_count": 72
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "source": [
    "table_9 = table_7.append(table_8_pandas)\n",
    "table_9"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OLS</th>\n",
       "      <td>-0.009378</td>\n",
       "      <td>0.029888</td>\n",
       "      <td>-0.070600</td>\n",
       "      <td>0.051844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
       "      <td>-0.032578</td>\n",
       "      <td>0.024406</td>\n",
       "      <td>-0.081365</td>\n",
       "      <td>0.016209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST (alpha= 0.00077)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN ( alpha =0.1)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST ( alpha= 0.1 )</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "OLS                          -0.009378    0.029888       -0.070600   \n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "LASSO TEST (alpha= 0.00077)   0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN ( alpha =0.1)     0.031154    0.051624       -0.074960   \n",
       "LASSO TEST ( alpha= 0.1 )     0.031154    0.051624       -0.074960   \n",
       "\n",
       "                             upper bound CI  \n",
       "OLS                                0.051844  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  \n",
       "LASSO TEST (alpha= 0.00077)        0.137268  \n",
       "LASSO TRAIN ( alpha =0.1)          0.137268  \n",
       "LASSO TEST ( alpha= 0.1 )          0.137268  "
      ]
     },
     "metadata": {},
     "execution_count": 73
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "source": [
    "table_10 = np.zeros( (1, 4) )\n",
    "\n",
    "table_10[0,0] = est_lasso_train_2\n",
    "table_10[0,1] = std_lasso_train_2\n",
    "table_10[0,2] = lower_ci_lasso_train_2\n",
    "table_10[0,3] = upper_ci_lasso_train_2\n",
    "\n",
    "\n",
    "table_10_pandas = pd.DataFrame( table_2, columns = [ \"Estimator\",\"Std. Error\", \"lower bound CI\", \"upper bound CI\"  ])\n",
    "table_10_pandas.index = [ \"LASSO TRAIN (alpha=0.8)\" ]\n",
    "table_10_pandas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
       "      <td>0.024739</td>\n",
       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         Estimator  Std. Error  lower bound CI  upper bound CI\n",
       "LASSO TRAIN (alpha=0.8)   0.019356    0.024739       -0.031495        0.070207"
      ]
     },
     "metadata": {},
     "execution_count": 74
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "source": [
    "table_11 = table_9.append(table_10_pandas)\n",
    "table_11"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OLS</th>\n",
       "      <td>-0.009378</td>\n",
       "      <td>0.029888</td>\n",
       "      <td>-0.070600</td>\n",
       "      <td>0.051844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
       "      <td>-0.032578</td>\n",
       "      <td>0.024406</td>\n",
       "      <td>-0.081365</td>\n",
       "      <td>0.016209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST (alpha= 0.00077)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN ( alpha =0.1)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST ( alpha= 0.1 )</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
       "      <td>0.024739</td>\n",
       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "OLS                          -0.009378    0.029888       -0.070600   \n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "LASSO TEST (alpha= 0.00077)   0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN ( alpha =0.1)     0.031154    0.051624       -0.074960   \n",
       "LASSO TEST ( alpha= 0.1 )     0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN (alpha=0.8)       0.019356    0.024739       -0.031495   \n",
       "\n",
       "                             upper bound CI  \n",
       "OLS                                0.051844  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  \n",
       "LASSO TEST (alpha= 0.00077)        0.137268  \n",
       "LASSO TRAIN ( alpha =0.1)          0.137268  \n",
       "LASSO TEST ( alpha= 0.1 )          0.137268  \n",
       "LASSO TRAIN (alpha=0.8)            0.070207  "
      ]
     },
     "metadata": {},
     "execution_count": 75
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "source": [
    "table_12 = np.zeros( (1, 4) )\n",
    "\n",
    "table_12[0,0] = est_lasso_test_2\n",
    "table_12[0,1] = std_lasso_test_2\n",
    "table_12[0,2] = lower_ci_lasso_test_2\n",
    "table_12[0,3] = upper_ci_lasso_test_2\n",
    "\n",
    "\n",
    "table_12_pandas = pd.DataFrame( table_2, columns = [ \"Estimator\",\"Std. Error\", \"lower bound CI\", \"upper bound CI\"  ])\n",
    "table_12_pandas.index = [ \"LASSO TEST (alpha=0.8)\" ]\n",
    "table_12_pandas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LASSO TEST (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
       "      <td>0.024739</td>\n",
       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        Estimator  Std. Error  lower bound CI  upper bound CI\n",
       "LASSO TEST (alpha=0.8)   0.019356    0.024739       -0.031495        0.070207"
      ]
     },
     "metadata": {},
     "execution_count": 76
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "source": [
    "table_13 = table_11.append(table_12_pandas)\n",
    "table_13"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OLS</th>\n",
       "      <td>-0.009378</td>\n",
       "      <td>0.029888</td>\n",
       "      <td>-0.070600</td>\n",
       "      <td>0.051844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
       "      <td>-0.032578</td>\n",
       "      <td>0.024406</td>\n",
       "      <td>-0.081365</td>\n",
       "      <td>0.016209</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST (alpha= 0.00077)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN ( alpha =0.1)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST ( alpha= 0.1 )</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
       "      <td>0.024739</td>\n",
       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
       "      <td>0.024739</td>\n",
       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "OLS                          -0.009378    0.029888       -0.070600   \n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "LASSO TEST (alpha= 0.00077)   0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN ( alpha =0.1)     0.031154    0.051624       -0.074960   \n",
       "LASSO TEST ( alpha= 0.1 )     0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN (alpha=0.8)       0.019356    0.024739       -0.031495   \n",
       "LASSO TEST (alpha=0.8)        0.019356    0.024739       -0.031495   \n",
       "\n",
       "                             upper bound CI  \n",
       "OLS                                0.051844  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  \n",
       "LASSO TEST (alpha= 0.00077)        0.137268  \n",
       "LASSO TRAIN ( alpha =0.1)          0.137268  \n",
       "LASSO TEST ( alpha= 0.1 )          0.137268  \n",
       "LASSO TRAIN (alpha=0.8)            0.070207  \n",
       "LASSO TEST (alpha=0.8)             0.070207  "
      ]
     },
     "metadata": {},
     "execution_count": 77
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "source": [
    "table_13_html = table_13.to_html()\n",
    "print(table_13_html)"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "<table border=\"1\" class=\"dataframe\">\n",
      "  <thead>\n",
      "    <tr style=\"text-align: right;\">\n",
      "      <th></th>\n",
      "      <th>Estimator</th>\n",
      "      <th>Std. Error</th>\n",
      "      <th>lower bound CI</th>\n",
      "      <th>upper bound CI</th>\n",
      "    </tr>\n",
      "  </thead>\n",
      "  <tbody>\n",
      "    <tr>\n",
      "      <th>OLS</th>\n",
      "      <td>-0.009378</td>\n",
      "      <td>0.029888</td>\n",
      "      <td>-0.070600</td>\n",
      "      <td>0.051844</td>\n",
      "    </tr>\n",
      "    <tr>\n",
      "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
      "      <td>-0.032578</td>\n",
      "      <td>0.024406</td>\n",
      "      <td>-0.081365</td>\n",
      "      <td>0.016209</td>\n",
      "    </tr>\n",
      "    <tr>\n",
      "      <th>LASSO TEST (alpha= 0.00077)</th>\n",
      "      <td>0.031154</td>\n",
      "      <td>0.051624</td>\n",
      "      <td>-0.074960</td>\n",
      "      <td>0.137268</td>\n",
      "    </tr>\n",
      "    <tr>\n",
      "      <th>LASSO TRAIN ( alpha =0.1)</th>\n",
      "      <td>0.031154</td>\n",
      "      <td>0.051624</td>\n",
      "      <td>-0.074960</td>\n",
      "      <td>0.137268</td>\n",
      "    </tr>\n",
      "    <tr>\n",
      "      <th>LASSO TEST ( alpha= 0.1 )</th>\n",
      "      <td>0.031154</td>\n",
      "      <td>0.051624</td>\n",
      "      <td>-0.074960</td>\n",
      "      <td>0.137268</td>\n",
      "    </tr>\n",
      "    <tr>\n",
      "      <th>LASSO TRAIN (alpha=0.8)</th>\n",
      "      <td>0.019356</td>\n",
      "      <td>0.024739</td>\n",
      "      <td>-0.031495</td>\n",
      "      <td>0.070207</td>\n",
      "    </tr>\n",
      "    <tr>\n",
      "      <th>LASSO TEST (alpha=0.8)</th>\n",
      "      <td>0.019356</td>\n",
      "      <td>0.024739</td>\n",
      "      <td>-0.031495</td>\n",
      "      <td>0.070207</td>\n",
      "    </tr>\n",
      "  </tbody>\n",
      "</table>\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The least square method provides a rather noisy estimate of the speed of convergence. We can not answer the question if poor countries grow faster than rich countries. The least square method does not work when the ratio $p/n$ is large.\n",
    "\n",
    "First of all, these are the $\\beta$'s for Lasso when $\\alpha$ = 0.00077.\n",
    "\n",
    "On the one hand, for  sample splitting via Lasso provides a more precise estimate. \n",
    "The Lasso (Train sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-8.14\\%,1.03\\%]$ only includes negative numbers. This empirical evidence does NOT support the convergence hypothesis.\n",
    "\n",
    "On the other hand, The Lasso (Test sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-17.38\\%,-0.87\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "Secondly, these are the $\\beta$'s for Lasso when $\\alpha$ = 0.1.\n",
    "\n",
    "On the one hand, for  sample splitting via Lasso provides a more precise estimate. \n",
    "The Lasso (Train sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-17.38\\%,-0.87\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "On the other hand, The Lasso (Test sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-17.38\\%,-0.87\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "First of all, these are the $\\beta$'s for Lasso when $\\alpha$ = 0.8\n",
    "\n",
    "On the one hand, for  sample splitting via Lasso provides a more precise estimate. \n",
    "The Lasso (Train sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-8.06\\%,-0.12\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "On the other hand, The Lasso (Test sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-8.06\\%,-0.12\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "<table border=\"1\" class=\"dataframe\">\n",
    "  <thead>\n",
    "    <tr style=\"text-align: right;\">\n",
    "      <th></th>\n",
    "      <th>Estimator</th>\n",
    "      <th>Std. Error</th>\n",
    "      <th>lower bound CI</th>\n",
    "      <th>upper bound CI</th>\n",
    "    </tr>\n",
    "  </thead>\n",
    "  <tbody>\n",
    "    <tr>\n",
    "      <th>OLS</th>\n",
    "      <td>-0.009378</td>\n",
    "      <td>0.029888</td>\n",
    "      <td>-0.070600</td>\n",
    "      <td>0.051844</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
    "      <td>-0.035543</td>\n",
    "      <td>0.022953</td>\n",
    "      <td>-0.081426</td>\n",
    "      <td>0.010340</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "      <th>LASSO TEST (alpha= 0.00077)</th>\n",
    "      <td>-0.091273</td>\n",
    "      <td>0.040154</td>\n",
    "      <td>-0.173811</td>\n",
    "      <td>-0.008736</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "      <th>LASSO TRAIN ( alpha =0.1)</th>\n",
    "      <td>-0.091273</td>\n",
    "      <td>0.040154</td>\n",
    "      <td>-0.173811</td>\n",
    "      <td>-0.008736</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "      <th>LASSO TEST ( alpha= 0.1 )</th>\n",
    "      <td>-0.091273</td>\n",
    "      <td>0.040154</td>\n",
    "      <td>-0.173811</td>\n",
    "      <td>-0.008736</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "      <th>LASSO TRAIN (alpha=0.8)</th>\n",
    "      <td>-0.040951</td>\n",
    "      <td>0.019292</td>\n",
    "      <td>-0.080605</td>\n",
    "      <td>-0.001296</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "      <th>LASSO TEST (alpha=0.8)</th>\n",
    "      <td>-0.040951</td>\n",
    "      <td>0.019292</td>\n",
    "      <td>-0.080605</td>\n",
    "      <td>-0.001296</td>\n",
    "    </tr>\n",
    "  </tbody>\n",
    "</table>"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Double LASSO using theoretical Lambda (HDM package)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "source": [
    "res_Y = hdmpy.rlasso( W, Y, post=True ).est['residuals']\n",
    "res_D = hdmpy.rlasso( W, D, post=True ).est['residuals']\n",
    "\n",
    "r_Y = pd.DataFrame(res_Y, columns=['r_Y'])\n",
    "r_D = pd.DataFrame(res_D, columns=['r_D'])"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "source": [
    "# OLS regression\n",
    "reg_ols  = sm.OLS(r_Y, r_D).fit()\n",
    "print(reg_ols.summary())"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "                                 OLS Regression Results                                \n",
      "=======================================================================================\n",
      "Dep. Variable:                    r_Y   R-squared (uncentered):                   0.127\n",
      "Model:                            OLS   Adj. R-squared (uncentered):              0.117\n",
      "Method:                 Least Squares   F-statistic:                              12.92\n",
      "Date:                Fri, 08 Oct 2021   Prob (F-statistic):                    0.000533\n",
      "Time:                        17:37:10   Log-Likelihood:                          152.68\n",
      "No. Observations:                  90   AIC:                                     -303.4\n",
      "Df Residuals:                      89   BIC:                                     -300.9\n",
      "Df Model:                           1                                                  \n",
      "Covariance Type:            nonrobust                                                  \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "r_D           -0.0498      0.014     -3.594      0.001      -0.077      -0.022\n",
      "==============================================================================\n",
      "Omnibus:                        4.622   Durbin-Watson:                   1.510\n",
      "Prob(Omnibus):                  0.099   Jarque-Bera (JB):                5.807\n",
      "Skew:                           0.120   Prob(JB):                       0.0548\n",
      "Kurtosis:                       4.221   Cond. No.                         1.00\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
      "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "source": [
    "# output: estimated regression coefficient corresponding to the target regressor\n",
    "est_lasso_HDM = reg_ols.summary2().tables[1]['Coef.']['r_D']\n",
    "\n",
    "# output: std. error\n",
    "std_lasso_HDM = reg_ols.summary2().tables[1]['Std.Err.']['r_D']\n",
    "\n",
    "# output: 95% confidence interval\n",
    "lower_ci_lasso_HDM = reg_ols.summary2().tables[1]['[0.025']['r_D']\n",
    "upper_ci_lasso_HDM = reg_ols.summary2().tables[1]['0.975]']['r_D']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "source": [
    "table_3 = np.zeros( (1, 4) )\n",
    "\n",
    "table_3[0,0] = est_lasso_HDM\n",
    "table_3[0,1] = std_lasso_HDM\n",
    "table_3[0,2] = lower_ci_lasso_HDM \n",
    "table_3[0,3] = upper_ci_lasso_HDM\n",
    "\n",
    "\n",
    "table_3_pandas = pd.DataFrame( table_3, columns = [ \"Estimator\",\"Std. Error\", \"lower bound CI\", \"upper bound CI\"  ]) \n",
    "table_3_pandas.index = [ \"LASSO_HDM\" ]\n",
    "table_3_pandas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LASSO_HDM</th>\n",
       "      <td>-0.049811</td>\n",
       "      <td>0.013858</td>\n",
       "      <td>-0.077347</td>\n",
       "      <td>-0.022276</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Estimator  Std. Error  lower bound CI  upper bound CI\n",
       "LASSO_HDM  -0.049811    0.013858       -0.077347       -0.022276"
      ]
     },
     "metadata": {},
     "execution_count": 82
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Using HDM package via lasso provides estimation with $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-7.73\\%,-2.22\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Double LASSO using method = \"partialling out\""
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "source": [
    "lasso_direct = hdmpy.rlassoEffect(x=W, y=Y, d=D, method=\"partialling out\")\n",
    "lasso_direct"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "{'alpha': -0.04981144483733834,\n",
       " 'se': array([0.01539133]),\n",
       " 't': array([-3.23633167]),\n",
       " 'pval': array([0.00121077]),\n",
       " 'coefficients': -0.04981144483733834,\n",
       " 'coefficient': -0.04981144483733834,\n",
       " 'coefficients_reg':                     0\n",
       " (Intercept)  0.058101\n",
       " x0          -0.075565\n",
       " x1           0.000000\n",
       " x2           0.000000\n",
       " x3           0.000000\n",
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       " x57          0.000000\n",
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       " x59          0.000000\n",
       " \n",
       " [61 rows x 1 columns],\n",
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       "        [ True],\n",
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       "        [False],\n",
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       "        [False],\n",
       "        [False]]),\n",
       " 'residuals': {'epsilon': array([[-3.49848290e-02],\n",
       "         [ 9.52657707e-02],\n",
       "         [ 1.25530270e-02],\n",
       "         [ 1.45051157e-02],\n",
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       "         [ 6.10442897e-03],\n",
       "         [ 2.38808615e-02],\n",
       "         [ 2.35925129e-02],\n",
       "         [-2.51882039e-02],\n",
       "         [-3.28317379e-03],\n",
       "         [ 3.26116159e-02],\n",
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       "         [ 3.30063634e-02],\n",
       "         [ 8.17543261e-03],\n",
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       "         [-1.67216885e-02],\n",
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       "         [ 1.59537137e-02],\n",
       "         [ 3.11297929e-02],\n",
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       "         [ 5.24599190e-02],\n",
       "         [-3.68484872e-02],\n",
       "         [ 1.13668751e-03],\n",
       "         [-4.48824215e-02],\n",
       "         [-6.64123390e-02],\n",
       "         [-6.81015576e-02],\n",
       "         [-7.44072496e-02],\n",
       "         [-2.98153308e-02],\n",
       "         [-8.19576069e-03],\n",
       "         [-3.66941527e-02],\n",
       "         [-6.98023480e-02],\n",
       "         [-5.31157210e-02],\n",
       "         [ 2.87182891e-02],\n",
       "         [-1.93314850e-02],\n",
       "         [ 5.00891034e-03],\n",
       "         [ 4.85815925e-03],\n",
       "         [-1.24003980e-02],\n",
       "         [-1.34087606e-01],\n",
       "         [ 4.70689433e-02],\n",
       "         [ 3.83224267e-02],\n",
       "         [ 6.37296176e-03],\n",
       "         [ 4.03832896e-03],\n",
       "         [-3.39895257e-02],\n",
       "         [ 7.51715850e-02],\n",
       "         [ 3.80763871e-02],\n",
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       "         [-1.31492060e-02]]),\n",
       "  'v': array([[ 0.52224775],\n",
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       "         [-0.25627972],\n",
       "         [-0.03672719],\n",
       "         [ 0.30348206],\n",
       "         [ 0.1539853 ],\n",
       "         [-0.06556942],\n",
       "         [ 0.13924958],\n",
       "         [-0.20928515],\n",
       "         [ 0.40570607],\n",
       "         [ 0.50044004],\n",
       "         [-0.13422303],\n",
       "         [ 0.03624017],\n",
       "         [-0.16286397],\n",
       "         [-0.06729083],\n",
       "         [-0.02076426],\n",
       "         [-0.32382142],\n",
       "         [-0.02041192],\n",
       "         [ 0.04473323],\n",
       "         [-0.43936259],\n",
       "         [ 0.1996553 ],\n",
       "         [ 0.39777497],\n",
       "         [-0.21166601],\n",
       "         [ 0.32571938],\n",
       "         [ 0.18176374],\n",
       "         [-0.37870359],\n",
       "         [-0.30497948],\n",
       "         [-0.11113707],\n",
       "         [ 0.11492087],\n",
       "         [-0.08623875],\n",
       "         [-0.01314347],\n",
       "         [ 0.08676469],\n",
       "         [ 0.08652982]])},\n",
       " 'samplesize': 90}"
      ]
     },
     "metadata": {},
     "execution_count": 83
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "source": [
    "est_lasso_part_out = lasso_direct[\"coefficients\"]\n",
    "std_lasso_part_out = lasso_direct[\"se\"]\n",
    "lower_ci_lasso_part_out = est_lasso - 1.96*std_lasso\n",
    "upper_ci_lasso_part_out = est_lasso + 1.96*std_lasso"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "source": [
    "table_4 = np.zeros( (1, 4) )\n",
    "\n",
    "table_4[0,0] = est_lasso_part_out\n",
    "table_4[0,1] = std_lasso_part_out\n",
    "table_4[0,2] = lower_ci_lasso_part_out\n",
    "table_4[0,3] = upper_ci_lasso_part_out\n",
    "\n",
    "\n",
    "table_4_pandas = pd.DataFrame( table_4, columns = [ \"Estimator\",\"Std. Error\", \"lower bound CI\", \"upper bound CI\"  ]) \n",
    "table_4_pandas.index = [ \"LASSO_partialling_out\" ]\n",
    "table_4_pandas"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
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       "      <th>upper bound CI</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>LASSO_partialling_out</th>\n",
       "      <td>-0.049811</td>\n",
       "      <td>0.015391</td>\n",
       "      <td>-0.080414</td>\n",
       "      <td>0.015258</td>\n",
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      "text/plain": [
       "                       Estimator  Std. Error  lower bound CI  upper bound CI\n",
       "LASSO_partialling_out  -0.049811    0.015391       -0.080414        0.015258"
      ]
     },
     "metadata": {},
     "execution_count": 85
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The partialling-out approach via lasso does not allow us to answer the question about the convergence hypothesis since the confidence interval includes zero."
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "source": [
    "table_14 = table_13.append(table_3_pandas)\n",
    "table_14"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
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       "      <th>upper bound CI</th>\n",
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       "      <th>OLS</th>\n",
       "      <td>-0.009378</td>\n",
       "      <td>0.029888</td>\n",
       "      <td>-0.070600</td>\n",
       "      <td>0.051844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
       "      <td>-0.032578</td>\n",
       "      <td>0.024406</td>\n",
       "      <td>-0.081365</td>\n",
       "      <td>0.016209</td>\n",
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       "    <tr>\n",
       "      <th>LASSO TEST (alpha= 0.00077)</th>\n",
       "      <td>0.031154</td>\n",
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       "      <td>-0.074960</td>\n",
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       "      <th>LASSO TRAIN ( alpha =0.1)</th>\n",
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       "    <tr>\n",
       "      <th>LASSO TEST ( alpha= 0.1 )</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
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       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
       "      <td>0.024739</td>\n",
       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
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       "    <tr>\n",
       "      <th>LASSO TEST (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
       "      <td>0.024739</td>\n",
       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO_HDM</th>\n",
       "      <td>-0.049811</td>\n",
       "      <td>0.013858</td>\n",
       "      <td>-0.077347</td>\n",
       "      <td>-0.022276</td>\n",
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      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "OLS                          -0.009378    0.029888       -0.070600   \n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "LASSO TEST (alpha= 0.00077)   0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN ( alpha =0.1)     0.031154    0.051624       -0.074960   \n",
       "LASSO TEST ( alpha= 0.1 )     0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN (alpha=0.8)       0.019356    0.024739       -0.031495   \n",
       "LASSO TEST (alpha=0.8)        0.019356    0.024739       -0.031495   \n",
       "LASSO_HDM                    -0.049811    0.013858       -0.077347   \n",
       "\n",
       "                             upper bound CI  \n",
       "OLS                                0.051844  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  \n",
       "LASSO TEST (alpha= 0.00077)        0.137268  \n",
       "LASSO TRAIN ( alpha =0.1)          0.137268  \n",
       "LASSO TEST ( alpha= 0.1 )          0.137268  \n",
       "LASSO TRAIN (alpha=0.8)            0.070207  \n",
       "LASSO TEST (alpha=0.8)             0.070207  \n",
       "LASSO_HDM                         -0.022276  "
      ]
     },
     "metadata": {},
     "execution_count": 86
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "source": [
    "table_15 = table_14.append(table_4_pandas)\n",
    "table_15"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
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       "      <th>LASSO_HDM</th>\n",
       "      <td>-0.049811</td>\n",
       "      <td>0.013858</td>\n",
       "      <td>-0.077347</td>\n",
       "      <td>-0.022276</td>\n",
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       "    <tr>\n",
       "      <th>LASSO_partialling_out</th>\n",
       "      <td>-0.049811</td>\n",
       "      <td>0.015391</td>\n",
       "      <td>-0.080414</td>\n",
       "      <td>0.015258</td>\n",
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      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "OLS                          -0.009378    0.029888       -0.070600   \n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "LASSO TEST (alpha= 0.00077)   0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN ( alpha =0.1)     0.031154    0.051624       -0.074960   \n",
       "LASSO TEST ( alpha= 0.1 )     0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN (alpha=0.8)       0.019356    0.024739       -0.031495   \n",
       "LASSO TEST (alpha=0.8)        0.019356    0.024739       -0.031495   \n",
       "LASSO_HDM                    -0.049811    0.013858       -0.077347   \n",
       "LASSO_partialling_out        -0.049811    0.015391       -0.080414   \n",
       "\n",
       "                             upper bound CI  \n",
       "OLS                                0.051844  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  \n",
       "LASSO TEST (alpha= 0.00077)        0.137268  \n",
       "LASSO TRAIN ( alpha =0.1)          0.137268  \n",
       "LASSO TEST ( alpha= 0.1 )          0.137268  \n",
       "LASSO TRAIN (alpha=0.8)            0.070207  \n",
       "LASSO TEST (alpha=0.8)             0.070207  \n",
       "LASSO_HDM                         -0.022276  \n",
       "LASSO_partialling_out              0.015258  "
      ]
     },
     "metadata": {},
     "execution_count": 87
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "source": [
    "coef_df = pd.DataFrame(table_15) \n",
    "coef_df"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
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       "      <th>LASSO TEST ( alpha= 0.1 )</th>\n",
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       "      <td>0.137268</td>\n",
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       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
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       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
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       "    <tr>\n",
       "      <th>LASSO TEST (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
       "      <td>0.024739</td>\n",
       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO_HDM</th>\n",
       "      <td>-0.049811</td>\n",
       "      <td>0.013858</td>\n",
       "      <td>-0.077347</td>\n",
       "      <td>-0.022276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO_partialling_out</th>\n",
       "      <td>-0.049811</td>\n",
       "      <td>0.015391</td>\n",
       "      <td>-0.080414</td>\n",
       "      <td>0.015258</td>\n",
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      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "OLS                          -0.009378    0.029888       -0.070600   \n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "LASSO TEST (alpha= 0.00077)   0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN ( alpha =0.1)     0.031154    0.051624       -0.074960   \n",
       "LASSO TEST ( alpha= 0.1 )     0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN (alpha=0.8)       0.019356    0.024739       -0.031495   \n",
       "LASSO TEST (alpha=0.8)        0.019356    0.024739       -0.031495   \n",
       "LASSO_HDM                    -0.049811    0.013858       -0.077347   \n",
       "LASSO_partialling_out        -0.049811    0.015391       -0.080414   \n",
       "\n",
       "                             upper bound CI  \n",
       "OLS                                0.051844  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  \n",
       "LASSO TEST (alpha= 0.00077)        0.137268  \n",
       "LASSO TRAIN ( alpha =0.1)          0.137268  \n",
       "LASSO TEST ( alpha= 0.1 )          0.137268  \n",
       "LASSO TRAIN (alpha=0.8)            0.070207  \n",
       "LASSO TEST (alpha=0.8)             0.070207  \n",
       "LASSO_HDM                         -0.022276  \n",
       "LASSO_partialling_out              0.015258  "
      ]
     },
     "metadata": {},
     "execution_count": 88
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "source": [
    "variables = list(coef_df.index.values)\n",
    "variables"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "['OLS',\n",
       " 'LASSO TRAIN (alpha=0.00077)',\n",
       " 'LASSO TEST (alpha= 0.00077)',\n",
       " 'LASSO TRAIN ( alpha =0.1)',\n",
       " 'LASSO TEST ( alpha= 0.1 )',\n",
       " 'LASSO TRAIN (alpha=0.8)',\n",
       " 'LASSO TEST (alpha=0.8)',\n",
       " 'LASSO_HDM',\n",
       " 'LASSO_partialling_out']"
      ]
     },
     "metadata": {},
     "execution_count": 89
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "source": [
    "coef_df['variables'] = variables\n",
    "coef_df"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimator</th>\n",
       "      <th>Std. Error</th>\n",
       "      <th>lower bound CI</th>\n",
       "      <th>upper bound CI</th>\n",
       "      <th>variables</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>OLS</th>\n",
       "      <td>-0.009378</td>\n",
       "      <td>0.029888</td>\n",
       "      <td>-0.070600</td>\n",
       "      <td>0.051844</td>\n",
       "      <td>OLS</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.00077)</th>\n",
       "      <td>-0.032578</td>\n",
       "      <td>0.024406</td>\n",
       "      <td>-0.081365</td>\n",
       "      <td>0.016209</td>\n",
       "      <td>LASSO TRAIN (alpha=0.00077)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST (alpha= 0.00077)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "      <td>LASSO TEST (alpha= 0.00077)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN ( alpha =0.1)</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "      <td>LASSO TRAIN ( alpha =0.1)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST ( alpha= 0.1 )</th>\n",
       "      <td>0.031154</td>\n",
       "      <td>0.051624</td>\n",
       "      <td>-0.074960</td>\n",
       "      <td>0.137268</td>\n",
       "      <td>LASSO TEST ( alpha= 0.1 )</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TRAIN (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
       "      <td>0.024739</td>\n",
       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
       "      <td>LASSO TRAIN (alpha=0.8)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO TEST (alpha=0.8)</th>\n",
       "      <td>0.019356</td>\n",
       "      <td>0.024739</td>\n",
       "      <td>-0.031495</td>\n",
       "      <td>0.070207</td>\n",
       "      <td>LASSO TEST (alpha=0.8)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO_HDM</th>\n",
       "      <td>-0.049811</td>\n",
       "      <td>0.013858</td>\n",
       "      <td>-0.077347</td>\n",
       "      <td>-0.022276</td>\n",
       "      <td>LASSO_HDM</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LASSO_partialling_out</th>\n",
       "      <td>-0.049811</td>\n",
       "      <td>0.015391</td>\n",
       "      <td>-0.080414</td>\n",
       "      <td>0.015258</td>\n",
       "      <td>LASSO_partialling_out</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Estimator  Std. Error  lower bound CI  \\\n",
       "OLS                          -0.009378    0.029888       -0.070600   \n",
       "LASSO TRAIN (alpha=0.00077)  -0.032578    0.024406       -0.081365   \n",
       "LASSO TEST (alpha= 0.00077)   0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN ( alpha =0.1)     0.031154    0.051624       -0.074960   \n",
       "LASSO TEST ( alpha= 0.1 )     0.031154    0.051624       -0.074960   \n",
       "LASSO TRAIN (alpha=0.8)       0.019356    0.024739       -0.031495   \n",
       "LASSO TEST (alpha=0.8)        0.019356    0.024739       -0.031495   \n",
       "LASSO_HDM                    -0.049811    0.013858       -0.077347   \n",
       "LASSO_partialling_out        -0.049811    0.015391       -0.080414   \n",
       "\n",
       "                             upper bound CI                    variables  \n",
       "OLS                                0.051844                          OLS  \n",
       "LASSO TRAIN (alpha=0.00077)        0.016209  LASSO TRAIN (alpha=0.00077)  \n",
       "LASSO TEST (alpha= 0.00077)        0.137268  LASSO TEST (alpha= 0.00077)  \n",
       "LASSO TRAIN ( alpha =0.1)          0.137268    LASSO TRAIN ( alpha =0.1)  \n",
       "LASSO TEST ( alpha= 0.1 )          0.137268    LASSO TEST ( alpha= 0.1 )  \n",
       "LASSO TRAIN (alpha=0.8)            0.070207      LASSO TRAIN (alpha=0.8)  \n",
       "LASSO TEST (alpha=0.8)             0.070207       LASSO TEST (alpha=0.8)  \n",
       "LASSO_HDM                         -0.022276                    LASSO_HDM  \n",
       "LASSO_partialling_out              0.015258        LASSO_partialling_out  "
      ]
     },
     "metadata": {},
     "execution_count": 90
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "source": [
    "errors = coef_df['Estimator'] - coef_df['lower bound CI']"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "source": [
    "coef_df['errors'] = errors"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "source": [
    "# Define figure, axes, and plot\n",
    "fig, ax = plt.subplots(figsize=(15, 10))\n",
    "    \n",
    "# Error bars for 95% confidence interval\n",
    "# Can increase capsize to add whiskers\n",
    "coef_df.plot(x='variables', y='Estimator', kind='bar',\n",
    "            ax=ax, color='none', fontsize=22, \n",
    "            ecolor='steelblue',capsize=0,\n",
    "            yerr='errors', legend=False)\n",
    "    \n",
    "# Set title & labels\n",
    "plt.title('Coefficients of Features w/ 95% Confidence Intervals',fontsize=30)\n",
    "ax.set_ylabel('Coefficients',fontsize=22)\n",
    "ax.set_xlabel('',fontsize=22)\n",
    "    \n",
    "# Coefficients\n",
    "ax.scatter(x=pd.np.arange(coef_df.shape[0]), \n",
    "         marker='o', s=80, \n",
    "         y=coef_df['Estimator'], color='steelblue')\n",
    "    \n",
    "# Line to define zero on the y-axis\n",
    "ax.axhline(y=0, linestyle='--', color='red', linewidth=1)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stderr",
     "text": [
      "<ipython-input-93-6a909340e248>:17: FutureWarning: The pandas.np module is deprecated and will be removed from pandas in a future version. Import numpy directly instead\n",
      "  ax.scatter(x=pd.np.arange(coef_df.shape[0]),\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
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   "source": [
    "#### This graph shows the comparison of the coefficients in the different model approaches: OLS, Lasso (with $\\alpha$ = 0.00077), Lasso (with $\\alpha$ = 0.1), Lasso (with $\\alpha$ = 0.8), Lasso with the HDM package and the Lasso by the \"partialling out\" method. These are the following inferences:\n",
    "\n",
    "\n",
    "- First of all, Ordinal Least squares provides a rather noisy estimate (high standard error) of the speed of convergence, and does not allow us to answer the question about the convergence hypothesis since the confidence interval includes zero.\n",
    "\n",
    "- Secondly, on the one hand, for  sample splitting via Lasso provides a more precise estimate. \n",
    "\n",
    "- The Lasso (Train sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-8.14\\%,1.03\\%]$ only includes negative numbers. This empirical evidence does NOT support the convergence hypothesis.\n",
    "\n",
    "- On the other hand, The Lasso (Test sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-17.38\\%,-0.87\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "- Thirdly, these are the $\\beta$'s for Lasso when $\\alpha$ = 0.1. On the one hand, for  sample splitting via Lasso provides a more precise estimate. \n",
    "\n",
    "- The Lasso (Train sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-17.38\\%,-0.87\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "- On the other hand, The Lasso (Test sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-17.38\\%,-0.87\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "- Fourthly, these are the $\\beta$'s for Lasso when $\\alpha$ = 0.8\n",
    "\n",
    "- One the one hand, The Lasso (Train sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-8.06\\%,-0.12\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "- On the other hand, The Lasso (Test sample) based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-8.06\\%,-0.12\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "- Fifthly, The Lasso via HDM package based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-7.73\\%,-2.22\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "- Sixthly, The Lasso via partialling out method based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-8.05\\%,-0.94\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis.\n",
    "\n",
    "In conclusion, only lasso in almost all the methods used give us significant results (only not in the train sample with $\\alpha$=0.00077). In other words, according to this empirical research we can say that poor countries grow faster than rich countries."
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