Chapter21IVexperiments.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 21: An Experimental Perspective on the Instrumental Variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "graphviz         : 0.20.1\n",
      "scipy            : 1.11.1\n",
      "linearmodels     : 5.3\n",
      "statsmodels      : 0.14.0\n",
      "pandas           : 2.0.3\n",
      "matplotlib       : 3.7.2\n",
      "numpy            : 1.24.3\n",
      "seaborn          : 0.13.0\n",
      "matplotlib_inline: 0.1.6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "import linearmodels as lm\n",
    "from joblib import Parallel, delayed\n",
    "\n",
    "# viz\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
    "plt.rc(\"font\", **font)\n",
    "plt.rcParams[\"figure.figsize\"] = (10, 10)\n",
    "%matplotlib inline\n",
    "\n",
    "from utils import *\n",
    "\n",
    "np.random.seed(42)\n",
    "%load_ext autoreload\n",
    "%autoreload 1\n",
    "\n",
    "%load_ext watermark\n",
    "%watermark --iversions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def IV_Wald(Z, D, Y):\n",
    "    tau_D = np.mean(D[Z == 1]) - np.mean(D[Z == 0])\n",
    "    tau_Y = np.mean(Y[Z == 1]) - np.mean(Y[Z == 0])\n",
    "    CACE = tau_Y / tau_D\n",
    "    return np.array([tau_D, tau_Y, CACE])\n",
    "\n",
    "\n",
    "def IV_Wald_delta(Z, D, Y):\n",
    "    est = IV_Wald(Z, D, Y)\n",
    "    AdjustedY = Y - D * est[2]\n",
    "    VarAdj = np.var(AdjustedY[Z == 1], ddof=1) / np.sum(Z) + np.var(\n",
    "        AdjustedY[Z == 0], ddof=1\n",
    "    ) / np.sum(1 - Z)\n",
    "    return np.array([est[2], np.sqrt(VarAdj) / abs(est[0])])\n",
    "\n",
    "\n",
    "def IV_Wald_bootstrap(Z, D, Y, n_boot=200, k=-1):\n",
    "    est = IV_Wald(Z, D, Y)\n",
    "    n = len(Z)\n",
    "\n",
    "    def bootfn(*args):\n",
    "        # draw indices\n",
    "        ids = np.random.choice(np.arange(n), size=n, replace=True)\n",
    "        return IV_Wald(Z[ids], D[ids], Y[ids])[2]\n",
    "\n",
    "    boot_est = Parallel(n_jobs=k)(delayed(bootfn)(i) for i in range(int(n_boot)))\n",
    "    boot_est = np.vstack(boot_est)\n",
    "    return np.array([est[2], boot_est.flatten().std()])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## without covariates\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ivsim_nocovars(shares=[1 / 2, 1 / 4, 1 / 4], *args):\n",
    "    n = 200\n",
    "    D0 = np.r_[\n",
    "        np.repeat(0, int(n * shares[0])),\n",
    "        np.repeat(1, int(n * shares[1])),\n",
    "        np.repeat(0, int(n * shares[2])),\n",
    "    ]\n",
    "    D1 = np.r_[\n",
    "        np.repeat(1, int(n * shares[0])),\n",
    "        np.repeat(1, int(n * shares[1])),\n",
    "        np.repeat(0, int(n * shares[2])),\n",
    "    ]\n",
    "    Y0 = np.r_[\n",
    "        np.random.normal(1, size=int(n * shares[0])),\n",
    "        np.random.normal(0, size=int(n * shares[1])),\n",
    "        np.random.normal(2, size=int(n * shares[2])),\n",
    "    ]\n",
    "    Y1 = Y0.copy()\n",
    "    Y1[np.arange(int(n * shares[0]))] = np.random.normal(3, 1, int(n * shares[0]))\n",
    "    Z = np.random.binomial(1, 0.5, n)\n",
    "    D = Z * D1 + (1 - Z) * D0\n",
    "    Y = Z * Y1 + (1 - Z) * Y0\n",
    "    ret = np.array(\n",
    "        [\n",
    "            IV_Wald(Z, D, Y)[2],\n",
    "            IV_Wald_delta(Z, D, Y)[1],\n",
    "            IV_Wald_bootstrap(Z, D, Y, k=1)[1],\n",
    "        ]\n",
    "    )\n",
    "    return ret"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### strong IV "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "MC = 2000\n",
    "res = Parallel(n_jobs=-1)(\n",
    "    delayed(ivsim_nocovars)([1 / 2, 1 / 4, 1 / 4], i) for i in range(int(MC))\n",
    ")\n",
    "res = np.vstack(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0459278335318825 0.5337581637120559\n",
      "0.5562637573206064\n"
     ]
    }
   ],
   "source": [
    "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
    "print(cent, sd)\n",
    "print(res[:, 2].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.hist(res[:, 0], bins=50, density=True, alpha=0.5)\n",
    "x_axis = np.arange(-1, 5, 0.01)\n",
    "\n",
    "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
    "ax.vlines(2, 0, 1, color=\"k\")\n",
    "ax.set_title(r\"strong IV: $\\pi_c = 0.5$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## weak IV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "MC = 2000\n",
    "res = Parallel(n_jobs=-1)(\n",
    "    delayed(ivsim_nocovars)([1 / 5, 2 / 5, 2 / 5], i) for i in range(int(MC))\n",
    ")\n",
    "res = np.vstack(res)\n",
    "res = np.ma.masked_invalid(res)  # remove infs from divide by zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.2980928526598845 9.060489740223025\n",
      "11.430861088387783\n"
     ]
    }
   ],
   "source": [
    "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
    "print(cent, sd)\n",
    "print(res[:, 1].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/alal/anaconda3/envs/metrics/lib/python3.11/site-packages/numpy/lib/function_base.py:4737: UserWarning: Warning: 'partition' will ignore the 'mask' of the MaskedArray.\n",
      "  arr.partition(\n"
     ]
    },
    {
     "data": {
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      ],
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "minr, maxr = np.percentile(res[:, 0], [0.5, 99.5])\n",
    "\n",
    "f, ax = plt.subplots(figsize=(5, 5))\n",
    "sims = res[:, 0]\n",
    "ax.hist(\n",
    "    np.where((sims > minr) & (sims < maxr), sims, 0), bins=50, density=True, alpha=0.5\n",
    ")\n",
    "x_axis = np.arange(minr, maxr, 0.01)\n",
    "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
    "ax.vlines(2, 0, 1, color=\"k\")\n",
    "ax.set_title(r\"weak IV: $\\pi_c = 0.2$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## weakest IV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "MC = 2000\n",
    "res = Parallel(n_jobs=-1)(\n",
    "    delayed(ivsim_nocovars)([1 / 10, 2 / 5, 1 / 2], i) for i in range(int(MC))\n",
    ")\n",
    "res = np.vstack(res)\n",
    "res = np.ma.masked_invalid(res)  # remove infs from divide by zero"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.9621044093432425 44.27081120055434\n",
      "280.39027826364907\n"
     ]
    }
   ],
   "source": [
    "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
    "print(cent, sd)\n",
    "print(res[:, 1].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
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     },
     "metadata": {},
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    }
   ],
   "source": [
    "minr, maxr = np.percentile(res[:, 0], [0.5, 99.5])\n",
    "\n",
    "f, ax = plt.subplots(figsize=(5, 5))\n",
    "sims = res[:, 0]\n",
    "ax.hist(\n",
    "    np.where((sims > minr) & (sims < maxr), sims, 0), bins=50, density=True, alpha=0.5\n",
    ")\n",
    "x_axis = np.arange(minr, maxr, 0.01)\n",
    "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
    "ax.vlines(2, 0, 1, color=\"k\")\n",
    "ax.set_title(r\"weakest IV: $\\pi_c = 0.1$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## With Covariates\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def IV_Lin(Z, D, Y, X):\n",
    "    X = (X - X.mean(axis=0)) / X.std(axis=0)\n",
    "    tau_D = (\n",
    "        sm.OLS(D, np.c_[sm.add_constant(Z), X, Z.reshape(-1, 1) * X]).fit().params[1]\n",
    "    )\n",
    "    tau_Y = (\n",
    "        sm.OLS(Y, np.c_[sm.add_constant(Z), X, Z.reshape(-1, 1) * X]).fit().params[1]\n",
    "    )\n",
    "    CACE = tau_Y / tau_D\n",
    "    return np.array([tau_D, tau_Y, CACE])\n",
    "\n",
    "\n",
    "def IV_Lin_bootstrap(Z, D, Y, X, n_boot=200, k=-1):\n",
    "    X = (X - X.mean(axis=0)) / X.std(axis=0)\n",
    "    est = IV_Lin(Z, D, Y, X)\n",
    "    n = len(Z)\n",
    "\n",
    "    def bootfn(*args):\n",
    "        id = np.random.choice(np.arange(n), size=n, replace=True)\n",
    "        return IV_Lin(Z[id], D[id], Y[id], X[id, :])[2]\n",
    "\n",
    "    boot_est = Parallel(n_jobs=k)(delayed(bootfn)(i) for i in range(int(n_boot)))\n",
    "    boot_est = np.vstack(boot_est)\n",
    "    return np.array([est[2], boot_est.flatten().std()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ivsim_covars(shares=[1 / 2, 1 / 4, 1 / 4], *args):\n",
    "    n = 200\n",
    "    X = np.random.normal(size=int(n * 2)).reshape((n, 2))\n",
    "    D0 = np.r_[\n",
    "        np.repeat(0, int(n * shares[0])),\n",
    "        np.repeat(1, int(n * shares[1])),\n",
    "        np.repeat(0, int(n * shares[2])),\n",
    "    ]\n",
    "    D1 = np.r_[\n",
    "        np.repeat(1, int(n * shares[0])),\n",
    "        np.repeat(1, int(n * shares[1])),\n",
    "        np.repeat(0, int(n * shares[2])),\n",
    "    ]\n",
    "    Y0 = np.r_[\n",
    "        np.random.normal(1, size=int(n * shares[0])),\n",
    "        np.random.normal(0, size=int(n * shares[1])),\n",
    "        np.random.normal(2, size=int(n * shares[2])),\n",
    "    ] + X @ np.array([1, -1])\n",
    "    Y1 = Y0.copy()\n",
    "    Y1[np.arange(int(n * shares[0]))] = np.random.normal(3, 1, int(n * shares[0])) + +X[\n",
    "        np.arange(int(n * shares[0])), :\n",
    "    ] @ np.array([1, -1])\n",
    "    Z = np.random.binomial(1, 0.5, n)\n",
    "    D = Z * D1 + (1 - Z) * D0\n",
    "    Y = Z * Y1 + (1 - Z) * Y0\n",
    "    return IV_Lin_bootstrap(Z, D, Y, X, k=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### Strong IV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "MC = 2000\n",
    "res = Parallel(n_jobs=-1)(\n",
    "    delayed(ivsim_covars)([1 / 2, 1 / 4, 1 / 4], i) for i in range(int(MC))\n",
    ")\n",
    "res = np.vstack(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.041022022570901 0.5542291812774217\n",
      "0.5594014563842343\n"
     ]
    }
   ],
   "source": [
    "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
    "print(cent, sd)\n",
    "print(res[:, 1].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.hist(res[:, 0], bins=50, density=True, alpha=0.5)\n",
    "x_axis = np.arange(-1, 5, 0.01)\n",
    "\n",
    "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
    "ax.vlines(2, 0, 1, color=\"k\")\n",
    "ax.set_title(r\"strong IV: $\\pi_c = 0.5$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weak IV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "MC = 2000\n",
    "res = Parallel(n_jobs=-1)(\n",
    "    delayed(ivsim_covars)([1 / 5, 2 / 5, 2 / 5], i) for i in range(int(MC))\n",
    ")\n",
    "res = np.vstack(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1504851844132458 20.437946561705076\n",
      "101.34710547345787\n"
     ]
    }
   ],
   "source": [
    "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
    "print(cent, sd)\n",
    "print(res[:, 1].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "minr, maxr = np.percentile(res[:, 0], [0.5, 99.5])\n",
    "\n",
    "f, ax = plt.subplots(figsize=(5, 5))\n",
    "sims = res[:, 0]\n",
    "ax.hist(\n",
    "    np.where((sims > minr) & (sims < maxr), sims, 0), bins=50, density=True, alpha=0.5\n",
    ")\n",
    "x_axis = np.arange(minr, maxr, 0.01)\n",
    "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
    "ax.vlines(2, 0, 1, color=\"k\")\n",
    "ax.set_title(r\"weak IV: $\\pi_c = 0.2$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weakest IV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "MC = 2000\n",
    "res = Parallel(n_jobs=-1)(\n",
    "    delayed(ivsim_covars)([1 / 10, 2 / 5, 1 / 2], i) for i in range(int(MC))\n",
    ")\n",
    "res = np.vstack(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-19.37707093642744 1170.4776931064248\n",
      "3529.2840088053103\n"
     ]
    }
   ],
   "source": [
    "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
    "print(cent, sd)\n",
    "print(res[:, 1].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "minr, maxr = np.percentile(res[:, 0], [0.5, 99.5])\n",
    "\n",
    "f, ax = plt.subplots(figsize=(5, 5))\n",
    "sims = res[:, 0]\n",
    "ax.hist(\n",
    "    np.where((sims > minr) & (sims < maxr), sims, 0), bins=50, density=True, alpha=0.5\n",
    ")\n",
    "x_axis = np.arange(minr, maxr, 0.01)\n",
    "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
    "ax.vlines(2, 0, 1, color=\"k\")\n",
    "ax.set_title(r\"weakest IV: $\\pi_c = 0.2$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## WeakIV Robust Inference: Fieller Anderson Rubin Confidence Interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def FARci(Z, D, Y, Lower, Upper, grid):\n",
    "    CIrange = np.arange(Lower, Upper, grid)\n",
    "\n",
    "    def pvfun(t):\n",
    "        Y_t = Y - t * D\n",
    "        TauAdj = Y_t[Z == 1].mean() - Y_t[Z == 0].mean()\n",
    "        VarAdj = np.var(Y_t[Z == 1], ddof=1) / np.sum(Z) + np.var(\n",
    "            Y_t[Z == 0], ddof=1\n",
    "        ) / np.sum(1 - Z)\n",
    "        Tstat = TauAdj / np.sqrt(VarAdj)\n",
    "        return (1 - sp.stats.norm.cdf(np.abs(Tstat))) * 2\n",
    "\n",
    "    Pvalue = Parallel(n_jobs=-1)(delayed(pvfun)(t) for t in CIrange)\n",
    "    return CIrange, Pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linestimator(Z, Y, X):\n",
    "    X = (X - X.mean(axis=0)) / X.std(axis=0)\n",
    "    n, p = X.shape\n",
    "    # fully interacted OLS\n",
    "    Xmat = np.c_[sm.add_constant(Z), X, Z.reshape(-1, 1) * X]\n",
    "    m = sm.OLS(Y, Xmat).fit(cov_type=\"HC2\")\n",
    "    est, vehw = m.params[1], m.bse[1] ** 2\n",
    "    # super-population correction\n",
    "    inter = m.params[-p:]  # (β_1 - β_0) term - last p elements of coef\n",
    "    # (β_1 - β_0)' Σ (β_1 - β_0) / n\n",
    "    superCorr = np.sum(inter * (np.cov(X.T) @ inter)) / n\n",
    "    vsuper = vehw + superCorr\n",
    "    return est, np.sqrt(vehw), np.sqrt(vsuper)\n",
    "\n",
    "\n",
    "def FARciX(Z, D, Y, X, Lower, Upper, grid):\n",
    "    CIrange = np.arange(Lower, Upper, grid)\n",
    "\n",
    "    def pvfun(t):\n",
    "        Y_t = Y - t * D\n",
    "        linest = linestimator(Z, Y_t, X)\n",
    "        Tstat = linest[0] / linest[2]\n",
    "        return (1 - sp.stats.norm.cdf(np.abs(Tstat))) * 2\n",
    "\n",
    "    Pvalue = Parallel(n_jobs=-1)(delayed(pvfun)(t) for t in CIrange)\n",
    "    return CIrange, Pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ivsim_covars(shares=[1 / 2, 1 / 4, 1 / 4], *args):\n",
    "    n = 200\n",
    "    X = np.random.normal(size=int(n * 2)).reshape((n, 2))\n",
    "    D0 = np.r_[\n",
    "        np.repeat(0, int(n * shares[0])),\n",
    "        np.repeat(1, int(n * shares[1])),\n",
    "        np.repeat(0, int(n * shares[2])),\n",
    "    ]\n",
    "    D1 = np.r_[\n",
    "        np.repeat(1, int(n * shares[0])),\n",
    "        np.repeat(1, int(n * shares[1])),\n",
    "        np.repeat(0, int(n * shares[2])),\n",
    "    ]\n",
    "    Y0 = np.r_[\n",
    "        np.random.normal(1, size=int(n * shares[0])),\n",
    "        np.random.normal(0, size=int(n * shares[1])),\n",
    "        np.random.normal(2, size=int(n * shares[2])),\n",
    "    ] + X @ np.array([1, -1])\n",
    "    Y1 = Y0.copy()\n",
    "    Y1[np.arange(int(n * shares[0]))] = np.random.normal(3, 1, int(n * shares[0])) + +X[\n",
    "        np.arange(int(n * shares[0])), :\n",
    "    ] @ np.array([1, -1])\n",
    "    Z = np.random.binomial(1, 0.5, n)\n",
    "    D = Z * D1 + (1 - Z) * D0\n",
    "    Y = Z * Y1 + (1 - Z) * Y0\n",
    "    return Z, D, Y, X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'strong IV: $\\\\pi_c = 0.5$')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p20b342de8e\">\n",
       "   <rect x=\"27.479688\" y=\"34.68\" width=\"179.520312\" height=\"227.56\"/>\n",
       "  </clipPath>\n",
       "  <clipPath id=\"pc6ddb9367a\">\n",
       "   <rect x=\"238.079687\" y=\"34.68\" width=\"179.520312\" height=\"227.56\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(1, 2, figsize=(6, 4))\n",
    "Z, D, Y, _ = ivsim_covars([1 / 2, 1 / 4, 1 / 4])\n",
    "CI, Pv = FARci(Z, D, Y, 0, 5, 0.001)\n",
    "\n",
    "ax[0].plot(CI, Pv)\n",
    "ax[0].hlines(0.05, 0, 5, color=\"k\", linestyle=\"--\")\n",
    "\n",
    "Z, D, Y, _ = ivsim_covars([1 / 2, 1 / 4, 1 / 4])\n",
    "CI, Pv = FARci(Z, D, Y, 0, 5, 0.001)\n",
    "\n",
    "ax[1].plot(CI, Pv)\n",
    "ax[1].hlines(0.05, 0, 5, color=\"k\", linestyle=\"--\")\n",
    "\n",
    "f.set_tight_layout(True)\n",
    "f.suptitle(r\"strong IV: $\\pi_c = 0.5$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'strong IV: $\\\\pi_c = 0.2$')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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+++7Dfffdh7S0NDz33HMYMWKE4j9ALDvZ0FWj0W5zoK7FiqzkOBVHRBRanI96snTaPR+3e31MRMrwO3A6dOhQn1975JFHPB9PmjQJW7duHdioyCdl9W3dPj9W18bAiWIK56OeOryyTJZOZpyIlMYtVyLYyYbugdPx+laVRkJE4cK7OLzNysCJSGkMnCLYCfdSnV7rKgc9XtfW3+lEFAO8s0ztNi7VESmNgVMEO+Feqps9KgsAcLyOGSeiWNfeyaU6omBi4BShnE6Bk+5u4XLgdHbNExHFHtY4EQUXA6cIVdXcgU67EzqNhEtGZAIAys+0o5MN74himneNUzsDJyLFMXCKUKfc9U0Fg+KRlxKHBIMWDqfAqUZmnYhimYVLdURBxcApQsmb+g5OT4AkSRiWmQDA1ZKAiGJXR7eME4vDiZTGwClCnZIDp7R4AEBRRiIA3llHFOtYHE4UXAycIlRX4OTaqLTInXHinXVEsc27xolbrhApj4FThOoZOLkzTryzjiimdevjxIwTkeIYOEUoucapUA6cMlwZJ7YkIIpt3dsRsMaJSGkMnCJQq9WOhrZOAF6Bk3uprrGtE2fcXyOi2NPOPk5EQcXAKQLJ2aZBJj2S4/QAAJNBh7wU1wa/x1jnRBSzWBxOFFwMnCLQ2fVNsuLsJADA4RoGTkSxioETUXAxcIpAZ9c3yUqyXAXiR2pbQj4mIgoP7ezjRBRUDJwiUF8ZpxHZ7sCJGSeimMUaJ6LgYuAUgfoOnFxLdcw4EcUmp1Ogw9a1XyXbERApj4FTBOqzxsm9VFfTbIW53RbycRGRujrs3QMli80BIYRKoyGKTgycIozTKXC6sR1Azxqn5Dg9ct131h1l1oko5pydYXI4BTodzj7OJqKBYOAUYWpaOtDpcEKnkTxBkjc568Q764hij1zfpNNIXce4XEekKAZOEeZUg2uZLn9QPHTanv/7SuQ6JwZORDFH7hqeGKeDwT0/sECcSFkMnCJMX/VNshFsSUAUs+QgyaTXIt6g7XaMiJTBwCnC9NXDSTaCGSeimCUvy8UZtDB5Aif2ciJSEgOnCHOujJNc41Td3ME764hijFzjFM+ME1HQMHCKMOcKnFLi9chONgIAjtYy60QUSzq8Aic548TicCJlMXCKMKfcrQj6CpwA7wJx1jkRxRI5uxRv0MKk13U7RkTKYOAUQdo7HahvtQIACgf1HTgVewrEmXEiiiXeS3UmI2uciIJBp/YAyHcVTa5sU6JRh+T4vv/XyRmnw8w4EcWUdq+Mk87h6uXkvXcdEQWOgVMEOX3GVd9UMCgekiT1eZ4cOB2qZuBEFEu8a5x0GvZxIgoGLtVFEDnjlJ8a3+95o3JcgVNtixUN7qU9Iop+3WqceFcdUVAwcIogFWfcgdOg/gOnBKMOQ9JdNVAHmXUiihntvd5VxxonIiUxcIogp92BU8E5AiegK+tUWtUc1DERUfjoYB8noqBj4BRBupbq+r6jTjY6NxkAUFrFjBNRrGjvZamOfZyIlMXi8Aji61IdAIzKcQVOB6uZcSKKFd41Tk7hOtbGpToiRTFwihCddidqWjoA+LZUN8adcTpS0wqbwwm9lslFomjnXeMk3IETl+qIlMW/phGiytwOIYA4vQbpCYZznl8wKB4JBi06HU6U1beFYIREpDbvGqcEI5fqiIKBgVOEkJfp8lL77+Ek02gkjPLUOXG5jigWyNmlOIMW8QZuuUIUDAycIkTXHXXnLgyXdd1ZxwJxolggL9WZvNsRsHM4kaJY4xQhTvvY/NKbfGcdC8SJYkOHV3G4xp2Z5l51RMpi4BQhKvzo4SQbncteTkSxxLs4XKuRAydmnIiUxKW6CCHvU+dPxmmkuyVBTbMVjW2dQRkXEYUPT42TXguTu8aJxeFEymLgFCHk5pf+ZJwSjToMTpO3XmHWiSiaOZ0CVrsTAGAydHUOtzsFOt3HiShwDJwigN3hRLXZ1cPJl+aX3uTlugOVDJyIolmHvSuz5N05HGDWiUhJDJwiQE2LFXangE4jISspzq/vHZeXAgDYV2EOxtCIKEx4B0dxOi30Wg30Wnedk40F4kRKYeAUAbx7OMkFn74aV8DAiSgWyPVNRp0GGvc8Ea93ZZ3arMw4ESmFgVMEqGjyvzBcNj7fFTiV1beh1cp3nUTRSu4a7r1El2BkgTiR0hg4RYDTjb5v7nu2jEQjclPiIATrnIiimXcrAplcIM6NfomU43fgVFZWhrlz5yIvLw8lJSVYtmxZr+e98sorGDFiBHJzc1FQUIB7770XnZ28JX4gBnJHnbexrHOiKMX5qEu713YrskSjvO0KAycipfgdOC1atAhz585FRUUFNm/ejBUrVmDjxo3dzmlubsa9996L119/HVVVVdi/fz8+/PBDfPjhh4oNPJZUDKBruDd5uW4/AyeKMpyPuvSWcZKX7VjjRKQcvwKnhoYGbNu2DYsXL4YkScjNzcWiRYvw3nvvdTsvPj4e+fn5sFhctTkdHR2QJAlFRUXKjTyGyMXhA1mqA4DxBa5GmMw4UTThfNRdRy+Bk5xxamN9I5Fi/NpypaysDGlpadDpur4tNzcXW7Zs6XaeXq/Hhx9+iOuuuw61tbUAgL/85S+YMGFCr9e1Wq2wWq2ez5ubWYsjE0J49qkrSPV9g19v49wZp2N1rWiz2j0Fo0SRLFjzERCZc5In42Twzji5AycWhxMpxq+Mk8VigSR1vx1ekiTPOzlZa2srrr32Wjz//PNoaWnB9u3bsWTJEmzfvr3X6y5duhQpKSmeR2FhoZ8/RvRqaOtEp90JSQJyUvzr4STLSopDVpIRQnDfOooewZqPgMick+R2BN4ZpwRmnIgU51fgZDKZIITodkwIAZOpeyZk48aNSElJwYIFC6DRaDB27FgsWLAAr732Wq/XXbJkCcxms+dRXl7u548RvaqaXB3DMxKNMOgGfhOkXOfE5TqKFsGaj4DInJPk4vD4bsXhco0TAycipfi1ZjN06FA0NjbCbrd70uOVlZUoLi7udp4QAhpN9z/yGo0Gdnvvv7xGoxFGo9GfocSMSrO7+eUAs02ycfkp+PhgLQMnihrBmo+AyJyTeqtx6lqqY+BEpBS/UhgZGRmYOnUqli9fDiEEqqursWrVKsyfPx+rV6/GwoULAQDTpk3DiRMn8NFHHwEATp48ibfffhtz585V/ieIclXu+qbclIEVhst4Zx1FG85H3ck1TnG9FoezxolIKX6v/axcuRLr169HXl4eZsyYgbvuuguzZ89GZWUlSktLAQBZWVl455138MgjjyAnJwezZ8/G4sWLcc011yj+A0S7KvfmvrmpgWWcxru3Xjla28q0PUUNzkdd2judAM4qDudSHZHi/L69qqioCBs2bOhx/JFHHsEjjzzi+fzyyy/H7t27AxsdodIdOOUFmHHKTo5Dbkocqswd+Pq0GdOHpysxPCJVcT7q0lsfJ0/GiUt1RIrhlithzrNUF2DGCQAuGJwKANhb3hTwtYgovPRb48SlOiLFMHAKc56lugAzTgBwfmEqAGDPqTMBX4uIwou8rUp8t01+uVRHpDQGTmHM4RSobnYv1SmScRoEANhT3tTjNm4iimztNneNk3cfJwP7OBEpjYFTGKtrscLhFNBqJGQlBR44jctLgU4joa7F6qmdIqLo0NFLHydPA0x2DidSDAOnMCb3cMpOMkKrkc5x9rnFG7QYlZsEgMt1RNGm3+Jwq51ZZiKFMHAKY3LX8NzUwOubZBcUupbr9p5qUuyaRKS+3vo4ye0I7E6BTodTlXERRRsGTmGsyiw3vwx8mU7mKRDnnXVEUaW3LVfkGieAd9YRKYWBUxirbJILwxXMOLlbEuyvMKPTznegRNGit3YEWo2EOL1rmmeBOJEyGDiFsWBknIZlJCAlXg+r3YmD1c2KXZeI1GVxZ5xMXhkngE0wiZTGwCmMVSrYw0kmSZJnuY6NMImigxCi1xonwLsJJgMnIiUwcApjctdwJXo4eZOX63ae4J11RNHA6rXsHn9WximBG/0SKYqBU5jqtDtR12oFoGzGCQCmDE0DAOw80ajodYlIHe1efZridN2n9QQDu4cTKYmBU5iqae6AEIBBq0F6gkHRa18wOBU6jYRKcwdOn7Eoem0iCj15mc6g1UCnPStwcmecWhk4ESmCgVOYkveoy0mJg0aB5pfeTAYdxuanAAB2MOtEFPG66pt6TulycbiF3cOJFMHAKUwF4446b1OHuhphbi9jnRNRpOuth5NMvsuOGSciZTBwClPB6OHkbTLrnIiihpxxMnk1vJQleDJODJyIlMDAKUwFO+MkF4gfqW3FmbbOoDwHEYWGnHE6uxUBACQY5eJwLtURKYGBU5iqDMI+dd7SEgwozkoEwDonokjXtcFvzyk9wcg+TkRKYuAUpuSMU16QMk5AV9aJgRNRZPNst9JLjZO8Xx07hxMpg4FTmKoKQtfws02RC8TZCJMoonmKw3tdqpPbEXCpjkgJDJzCUIfNgUZ33ZHSXcO9yRmnbyrMLBwlimB9bbcCdDXAtHCpjkgRDJzCkJxtitdrkRKvD9rzFAyKR15KHOxOgV0nmXUiilRdNU79ZZwYOBEpgYFTGPLcUZcaB0lStvmlN0mSMG14OgBg67GGoD0PEQWXvFRn6q3GiQ0wiRTFwCkMVXvqm4K3TCe7eHgGAAZORJHM046g18CJe9URKYmBUxiqbnYFTtnJwQ+cLip2ZZz2nW6Cud0W9OcjIuX1u1Rn4FIdkZIYOIWhGnmfuhAETrkp8SjKSIBTANvL2JaAKBL5UuNktTthdzhDOi6iaMTAKQzJGaecECzVAcB0d53T50frQ/J8RKSsfvs4GbuOtbHOiShgDJzCUHWzFUBoluoA4OJiV53TF6xzIopI/W25YtBqoNe6bjJhnRNR4Bg4haFQLtUBwPQiV8bpUE0L6lqsIXlOIlJOf0t1kiQhKc7V1qSlg4ETUaAYOIUZh1OgrtUVvIRqqW5QggFjcpMBAF8cZ9aJKNL0144AABI9vZx4AwhRoBg4hZn6ViscTgGtRkJGojFkz3ux++66L46xzoko0vSXcQKApDhX4MSME1HgGDiFGbmHU2aiEVpN8Jpfnu0idz+nTw/XQwgRsuclosB5tlw5R8aJgRNR4Bg4hRlPD6cQLdPJLixKg0GnQUVTO47VtYX0uYkoMO2drjYD58o4sZcTUeAYOIWZGrkVQXLolukAwGTQ4cJhrk1/Nx2qDelzE1FgOs65VCcXh7PGiShQDJzCTHWI76jzNqskEwCw+XBdyJ+biAZGCNFV43Su4nAu1REFjIFTmFFrqQ4ALh2ZBQDYdrwRlk5OsESRwOYQcDhddYm99XECvIrDuVRHFDAGTmGma6ku9IHT8MwE5KfGo9PhxJdsS0AUEdq9uoH32Y6Ad9URKYaBU5iRl+pC1TXcmyRJuHSka7lu0yEu1xFFAnmZTqeRoNf2PqUncamOSDEMnMJMTYi3WzmbvFzHOieiyHCuHk6AV3E4G2ASBYyBUxhptdo9twuHqmv42aYPT4deK+FkgwVl9WxLQBTuPPvU9bFMB7A4nEhJDJzCiLxMl2jUeSa6UEs06jBlqKstwcaDbEtAFO58yzixOJxIKQycwkitfEddiHs4nW32KNdy3YYDNaqOg4jO7Vw9nAAWhxMpiYFTGJFbEai1TCebOyYHALD9RCOaLJ2qjoWI+ufLUl2S0VXjxKU6osAxcAojnh5OKhWGywanmzAqJwkOp8AnXK4jCmsWd8bJ5MNSXbvNAbvDGZJxEUUrBk5hpEbFruFnmzsmGwDw0TdcriMKZx2d/XcNB7qW6gDuV0cUKAZOYSRcluoAYI57ue7TI3WeGgoiCj++FIfrtRrE6V3TPeuciALDwCmMVKvcw8nbuPxk5KbEwdLpwOdH69UeDhH1QQ6c+tpuRZZolDf6ZeBEFAi/A6eysjLMnTsXeXl5KCkpwbJly/o8t66uDjNnzsQvf/lLOBzMWpxLOC3VSZKEOe7lOt5dR+GK81FXcXi8of/pPNm9XMelOqLA+B04LVq0CHPnzkVFRQU2b96MFStWYOPGjT3Os1qtuP7663HHHXfg6aefhlbb/7uhWOdwCtS1ujJO4bBUB3TdXfef0hrPJqJE4YTzkW/tCICuOqdWdg8nCohfgVNDQwO2bduGxYsXQ5Ik5ObmYtGiRXjvvfd6nPvss89i2rRpuP3225Uaa1Srb7XC4RTQaiRkJKrbx0l2YVEakuN0qG/txM4TjWoPh6gbzkcuvtQ4AV3dw7lURxQYvwKnsrIypKWlQafrukMjNzcXR44c6XZee3s7/vSnPyE5ORn5+fkYNmwYli9f3ud1rVYrmpubuz1ijdw1PDPRCK1GUnk0LnqtBnPHurJOa76uUnk0RN0Faz4CImtOsniW6vrfbSCJTTCJFOFX4GSxWCBJ3f+oS5IEi8XS7diXX36J9vZ2TJo0CadOncJrr72GX/3qV/jiiy96ve7SpUuRkpLieRQWFvr5Y0Q+Tw+nMFmmk10zIRcAsHZ/Ffu/UFgJ1nwERNac1JVx6n86Z3E4kTL8CpxMJhOE6F7rIoSAyWTqdqyqqgqDBw/GtddeC61Wi+nTp2Pu3Ln4/PPPe73ukiVLYDabPY/y8nI/f4zIVyO3IlB5u5WzXVycgVSTHvWtndhexuU6Ch/Bmo+AyJqTfOnjBHRlnFjjRBQYvwKnoUOHorGxEXZ71zuWyspKFBcXdzsvKysLGk33S2s0GhgMhl6vazQakZyc3O0Ra6rD6I46b3qtBle5l+s+4HIdhZFgzUdAZM1JvrYj8AROzDgRBcSvwCkjIwNTp07F8uXLIYRAdXU1Vq1ahfnz52P16tVYuHAhAODCCy9EVVUVNm/eDAA4cOAANm7ciCuuuEL5nyBKyEt1WWEWOAHANRPyAADr9lfBxuU6ChOcj1xYHE4UWn63I1i5ciXWr1+PvLw8zJgxA3fddRdmz56NyspKlJaWAgCSkpLw9ttv46GHHkJubi4WLFiAl19+GWPGjFH8B4gWXUt14Rc4TStKQ3qCAWcsNmw91qD2cIg8OB9593E6V8bJXePEPk5EAen/NoxeFBUVYcOGDT2OP/LII3jkkUc8n8+YMQM7d+4MbHQxxLNUF2bF4QCg02owb3wO/vHlKaz5qhKzSjLVHhIRAM5HwAD6ODHjRBQQbrkSJmrCaLuV3nQt11Vz7zqiMGLxszi8uYPF4USBYOAUBlqtds82COGYcQKAqUPTkJ8ajxarHR9xCxaisOFrjVNKvGupztzOwIkoEAycwoC8TJdo1HkKOMONRiNhwcR8AMD/7Tqt8miISOZZqjtHxkkOnJoZOBEFhIFTGJALw7PDrIfT2RZMLAAAbDlS5xkzEanH5nDC5nD1sjpXxinZqzjcyb0niQaMgVMYCOfCcG/DMhIwcXAqnAL4554KtYdDFPO86w3P1ccpOd6VzRaCLQmIAsHAKQzUtMgZp/AOnADghkmurNP/7T7do2szEYWW3IpAkgCjrv/p3KjTIs69LQsLxIkGjoFTGKgJ067hvblmQh4MOg0O17Rif0X4bnxKFAvkO+pMem2Pfft6wwJxosAxcAoDctfwcF+qA1wT75wx2QCAt3eF7/5dRLGgqxWBbzeVsECcKHAMnMJAdZj3cDrbTZNdO8W/t6fCs1RARKHXbnPVKpnOcUedTC4QZ8aJaOAYOIWBSFqqA4AZxRkoTItHS4cdH3xdqfZwiGKWZ6nOx8CJS3VEgWPgpDKHU6Cu1ZVxioSlOsDV0+nWqUMAAP+77ZTKoyGKXb52DZd5lupYHE40YAycVFbfaoXDKaDVSMhIDO8+Tt5unFwAvVbCV+VN2F9hVns4RDGp3c+MUzIzTkQBY+CkMrmHU2aiEVrNue+KCRcZiUZcOTYHAPDadmadiNTgyTjpfSsOZ+BEFDgGTiqT76jLjpBlOm+3XjgYAPD+ngrPXntEFDqWTn+Lw90b/bbz95VooBg4qcyz3UpS5CzTyaYXpaMoIwFtnQ68t5v71xGFmr9LdSwOJwocAyeVRcp2K72RJAnfn+4qEl/5+Qnuf0UUYhYfN/iVsTicKHAMnFTmWaqLkFYEZ7txciGS4nQ4Xt+GTYdr1R4OUUxhcThR6DFwUpm8VBcpPZzOlmDU4TtTXbVOf/2sTOXREMWWrhondg4nChUGTiqL5KU62Q8uGgqtRsLnRxtQWsX964hCxd8GmMmewMnOTbqJBoiBk8pqImy7ld7kp8bjqnGu1gR/Y9aJKGQG2jm80+FEh80ZtHERRTMGTipqtdo9t/FHcsYJAO68ZBgA4P29laht6VB5NESxQV6q83WT3wSD1tMvjnVORAPDwElF8jJdolGHRKNvE1+4mjh4ECYOTkWnw8laJ6IQ8RSH633LOEmS1NXLiXfWEQ0IAycVeXo4JUdeD6fe3HtZMQDgH1+cRJOlU+XREEU/f5fqAPZyIgoUAycVRUNhuLfZo7IwOjcZbZ0OrPz8hNrDIYp6/m7yC3gFThYGTkQDwcBJRZHew+lskiTh3suGAwBWbT3BbViIgqzdJmecfF/qZy8nosAwcFJRpPdw6s28cbkoykyAud2Gf3x5Uu3hEEU1f/eqA4BUkwEA0MTAiWhAGDipyBM4RclSHQBoNRJ+fKmr1ukvW457ileJSFlOp/C0FPBnqW6QyZVxYh0i0cAwcFJRdRT0cOrN9efnoTAtHvWtnXj1ixNqD4coKsnLdMDAMk6NbQyciAaCgZOKaszRt1QHAHqtBosvLwEAvLLpGGspiILA4pXNjdP5HjileTJO/L0kGggGTipxOAXqWl0Zp2haqpN9+4J8jMhKhLndhr9sOa72cIiijrwMHq/XQuNuaumLQQmujNMZLtURDQgDJ5XUt1rhcApoJCDdPZFFE61GwkNzRwJwbf5b12JVeURE0cVi878wHAAGcamOKCAMnFQi93DKTDJCp43O/w1Xjs3GeQUpsHQ68MdNR9UeDlFUGUgPJ6ArcOJSHdHAROdf7AhQHYWtCM4mSRJ+duUoAMD/fnkKpxosKo+IKHq0D6BrOACkumucGi2dEEIoPi6iaMfASSU1Udb8si8XF6fjkuIMdDqcWLq2VO3hEEWNroyTf/tcprlLAzrtzm535hGRbxg4qSTatlvpiyRJ+NU1o6GRgLX7q/Hl8Qa1h0QUFTzNL33c4FdmMmhhcJcHnOFyHZHfGDipJNq2W+nPqJxk3HrhYADAUx8cgMPJ5QGiQA10qU6SJM9y3RkWiBP5jYGTSqJxu5X+PHhFCZLidDhQ1Yx3dpWrPRyiiDfQ4nCga7mOLQmI/MfASSU1zdHbw6k36YlGPHD5CADAc+sPsSkmUYDkpboEP2ucgK4CcS7VEfmPgZNK5K7hsbBUJ/v+9KEoykxAfWsnfrf+kNrDIYpoimScuFRH5DcGTipos9rRYnW9W4yVjBMAGHQa/Obb4wAA/9h2EntOnVF5RESRyzLAGiega786LtUR+Y+BkwrkwvBEow6JRv/T7JHsouEZWDAxH0IAS97dB5vDqfaQiCLSQIvDAWAQ96sjGjAGTiroWqYzqjwSdfzy6tFINelxsLoFKz8vU3s4RBHJYhtYHyeA264QBYKBkwo8XcNjaJnOW3qiEY/OGw0AeGHDEXYUJxqA9s6B7VUHdAVOXKoj8h8DJxV4ejglxWbgBAA3Ti7AhcPS0G5z4OF3voKTvZ2I/BJIjdOgBC7VEQ0UAycVeJbqYjTjBLia8D238DyYDFpsL2vEyq0n1B4SUUTx3FXnZ+dwgEt1RIFg4KSCWNjg1xeD00345bdcS3bL1h3EsbpWlUdEFDm6isP9r3GS2xEwcCLyHwMnFVS7m1/GUg+nvtw6dTBmjMiA1e7EQ299BTvvsiPyicXmqnEaSB+n9ETXjSntNoenkSYR+cbvwKmsrAxz585FXl4eSkpKsGzZsn7PX716NfR6PZ544omBjjHq1MZ4cbg3SZLw7A0TkBSnw97yJry88ajaQ6IIEsvzUZvVlXEaSEuTBIMWcXrX9F/fwqwTkT/8DpwWLVqEuXPnoqKiAps3b8aKFSuwcePGXs81m8347W9/i3vuuSfggUYLh1OgtsW93QozTgCAvNR4T2PMlz4+gi+ONag8IooUsTwftbmb6CYY/c84SZKEDHfWqb7Nqui4iKKdX4FTQ0MDtm3bhsWLF0OSJOTm5mLRokV47733ej3/V7/6FX7yk58gIyNDkcFGg4ZWKxxOAY0EZCQa1B5O2Lj+/HzcOKkATgE88MYeNLRyMqf+xfJ8ZHc4YbW7lrUHslcd0LVcV9/C3zUif/gVOJWVlSEtLQ06Xdcvam5uLo4cOdLj3L1792Lr1q0+vbuzWq1obm7u9ohWcmF4ZpIROi1LzLw9ef1YFGclorbFiofeZosC6l+w5iMg/OekNndhOAAkDHD3gUz3G7cGFogT+cWvv9wWiwWSJHU7JkkSLJbuDQyFELj33nuxfPlyaLXnTiMvXboUKSkpnkdhYaE/w4oo1WbeUdcXk0GHl2+9AEadBpsO1eHPnx5Xe0gUxoI1HwHhPyfJy3R6rQSDbmBvwNITmHEiGgi/fuNMJhOE6J4FEELAZDJ1O/a3v/0NQ4YMwYwZM3y67pIlS2A2mz2P8vJyf4YVUWrk5pcMnHo1KicZj187FgDw3PqD2Hy4TuURUbgK1nwEhP+cJN8JN9BsEwBkJLkyTvVcFifyi1+/dUOHDkVjYyPsdrsnPV5ZWYni4uJu5/3nP//Bhg0bkJOTAwBobXX15/n666/x7rvv9riu0WiE0Rgb+7bF+nYrvvjO1EJ8Vd6EN3eW477XduNfP7kEQzMS1B4WhZlgzUdA+M9Jre476gZa3wTAqzicS3VE/vAr45SRkYGpU6di+fLlEEKguroaq1atwvz587F69WosXLgQAPD666+jvr4e1dXVqK6uxsMPP4yHH364z0kqllSb2cPpXCRJwlPfHosLBqeiucOOu/++07M0QSSL5fkokDvqZCwOJxoYvxfHV65cifXr1yMvLw8zZszAXXfdhdmzZ6OyshKlpaXBGGNUqWHXcJ8YdVr86buTkJVkxOGaVvz0rb0sFqceYnU+6gqcAsk4camOaCAkcXaRQBhobm5GSkoKzGYzkpOT1R6Ooq74/WYcrW3FP+68EJeMiPzbooNt96kzuOXPX6LT4cQPZwzDL781Ru0hkY+i6fc43H6W9/acxoNvfoVLijPwj7suHNA1Dte0YO4LnyLVpMfex+YqPEKi8KPU7zHvhw8xT8YpJXzrJ8LJxMGD8NyNEwAAK7aUYdXnZSqPiEh9ctfwQJbq5BqnJosNNm51ROQzBk4hZOm0o6XDlWJnjZPvrj8/Hz+/aiQA4Mk1B7D+m2qVR0SkLs9SXQDF4anxemg1rnYODa0sECfyFQOnEJJ7OCUYtEiK06s8msjyX7OG49YLB0MI4P7X92DXyUa1h0SkGrkBZiA1ThqNhLQE1jkR+YuBUwjJrQiy2YrAb5Ik4anrxmL2qCxY7U7c/rcd2F9hVntYRKqQM06mAJbqAK+WBAyciHzGwCmEeEddYHRaDf7frRMxdWgaWqx2fO+v23CoukXtYRGFnNwAMzGApTqg6846LtUR+Y6BUwjJPZwYOA1cvEGLv94+GecVpOCMxYbv/nUbyurb1B4WUUh5GmAGsFQHAJnujFMtezkR+YyBUwjVcKlOEUlxerx6x1SMyklCXYsVt674ksETxRSLAg0wASDL/SZOnpuI6NwYOIVQlbkdAJDLwClgqSYD/nHXhRiemYAqcwdu/vMXOFLDZTuKDa0KNMAEgOxkOePEwInIVwycQqjKfVddbkq8yiOJDhmJRrxx93SMyklCbYsVN//PlywYp5jQ1hl4OwKgq2xAvuOXiM6NgVMIVTbJgRMzTkrJTDLi9R9Ow4SCFDS2deLWFV9i96kzag+LKKgsCtU4dS3VscaJyFcMnEKk0+703PLLwElZgxJcy3aThwxCc4cdt63Yho9La9QeFlHQyEt1JkNgNU457rmotqWDe0ES+YiBU4jIxZdGncbTdI6Ukxynx+o7p2JmSSbabQ78cPVO/O+2k2oPiygoLO4GmIkK3VVncwicsbAlAZEvGDiFSGVTV2G4JEkqjyY6mQw6/PUHk3HT5AI4BfDL9/Zj2bqDCMN9rIkGTAjRVeMUYOBk0Gk8vZy4XEfkGwZOIVLt2dyXy3TBpNdq8OwNE7D4ihEAgD9uOob7Xt+Ddvc7dKJI125zQH4vEGg7AgDISmJLAiJ/MHAKEbkwPI931AWdJElYfEUJli2cAJ1Gwpqvq3DDK1tR3mhRe2hEAZPrmyQJiNcHHjjJb+YYOBH5hoFTiHh6OKUy4xQqN00uxGs/nIaMRAMOVDXjupc/w9Zj9WoPiyggnjvqDDpFlv3lXk7VDJyIfMLAKUS6WhEw4xRKU4el4V8/uQTj811btHzvr9ux4tPjrHuiiNWqUNdwWTZbEhD5hYFTiFQ3s2u4WvJS4/H2j6ZjwQX5cDgFnv6wFHe+uhONbbyLiCKPfEddoM0vZdncdoXILwycQqSKGSdVxem1eP6m8/Df3x4Hg06DTw7W4uoXt2Db8Qa1h0bkl1arDUDgd9TJchg4EfmFgVMIdNgcaHBnN/JY46QaSZLwvWlD8M8fX4yizARUN3fgOyu+xAsbDsPmcKo9PCKftHS4luqS4pQJnLLkGiduu0LkEwZOISC/k4vXa5ESr1d5NDQmLxkf/OQS3DDR1e/pxY+PYMEft+IwNwmmCKB04JSf6sqCN7R1osPGth1E58LAKQS896hj88vwkGDU4fmbzsOLt5yPlHg99lWYcc1Ln+FPm4/Bwa0nKIzJxeGJRmXehKXE65Hg3rqlwt2ol4j6xsApBNiKIHxdf34+PnpwJmaPykKnw4nfrj2IhX/aikPVzD5ReGrpcNU4KZVxkiQJ+YNcWaeKMwyciM6FgVMIVJlZGB7OspPj8NcfTMayhROQZNRhz6kmfOulLfjt2oOwuLe2IAoXSi/VAV3Ldcw4EZ0bA6cQ8GSc2IogbEmShJsmF2L9gzMxd0w27E6BP20+hjm//xQfl9aoPTwij9ZgBE7MOBH5jIFTCLAVQeTIS43H/3x/MlZ8fzLyU+NR0dSOO1/diR+u3okT9W1qD48IzZ7ASbkbTfJTTQCYcSLyBQOnEKiUl+pY4xQx5ozJxoafzsQ9s4qg00jYcKAGc17YjP9ecwBmi03t4VEMk2ucEhXq4wQw40TkDwZOIVDtXqrjBr+RxWTQYcm80Vj7wAxcOjITNofAXz8rw6zfbcSqz8vY+4lUId9VxxonInUwcAqy9k4HzrgzFDmscYpII7KTsGrRVLx6x1SUZCeiyWLDEx8cwBW/34z39pxm+wIKqZYgLNUVuDNO1c0dsPMNAVG/GDgFWaU725Rg0CJZwXeIFHqzSjLx4f0z8PT8cUhPMOBkgwUPvvkVrlz+Kf79dRWcDKAoBJRuRwAAmYlGGLQaOJwC1dx6hahfDJyCTK4ZKBhkYvPLKKDTanDbhUPw6c8vw8+uHImUeD2O1rbi3td241t/+Azrv6lmAEVBI4QIylKdRiN5ajBZ50TUPwZOQSbXDMjFlxQdEow63HtZMbb84jI8cPkIJBp1KK1qxj1/34W5yz/F2zvL0Wnnkgcpy2p3wuZwBeZKLtUBXXVOpxk4EfWLgVOQnT5jAdBVQ0DRJTlOjwfnlGDLzy/Djy8djiSjDkdrW/Gzd77GrOc24q+flaHNyiaapIxm9zKdJAEmvVbRaw9Oc7UkONVoUfS6RNGGgVOQyWlv+d0cRadBCQb8/KpR+HzJbDwybxQyk4yoMnfgv9ccwEW//QRL15Z6gmiigZKbXyYaddBolF36H5qRAAA40cB+ZUT9YeAUZHLam0t1sSE5To8fzRqOLT+/DEsXjMfQdBPM7Tb8efNxzFy2EXev3onPj9ZDCNZBkf88d9Qp2MNJNjTdlXE60cAAn6g/vM0ryOQap4JBJpVHQqEUp9fiO1MH46bJhfjkYC1e3XoCnx2tx0cHavDRgRqMyErE96cPwXXn5yMlXtlaFYpewWhFIBuS7s44sUM+Ub8YOAVRp93pubWXS3WxSauRMGdMNuaMycbR2has/uIk/m/XaRypbcWv3/8Gv/l3KeaNy8FNUwoxbVi64ssvFF1arcq3IpANcWeczO02NFk6kWoyKP4cRNGAS3VBVG3ugBCAUadBRiInoVhXnJWEp64fhy8evRyPXzsGI7OTYLU78c+9lbh1xTbM+t1GvPTxEVSyezP1Qd6nLjEIgZPJoEN2shEAUMasE1GfmHEKIrkYOH9QPHs4kUdynB6LLh6G2y8aiq9Pm/HmznJ8sLcS5Y3t+P2Gw3jhP4cxdWgarj8/H/PG5WBQAoNucgnmUh0ADE1PQE2zFScbLLhg8KCgPAdRpGPgFESnm3hHHfVNkiScV5iK8wpT8etvjcHa/VV4c0c5tpU1eh6Pvb8fM0sycd15eZgzJhsJQSgKpsjR2qF880tvQ9MTsK2skRknon5wFg4i767hRP2JN2ixYGIBFkwswOkzFqz5ugrv761EaVUzPjlYi08O1iJOr8FlI7Nw5dgcXDYqi0XlMag5CNuteJNbEpxkSwKiPjFwCqLTnsCJGSfyXcEgE340azh+NGs4jta24F97K/H+V5U42WDB2v3VWLu/GjqNhOnD0zF3bA7mjM7mBtIxosm9YXhqfHCWb+WWBGVsSUDUJwZOQVTRxK7hFJjirCT8dO5IPDinBPsqzFj/TTU++qYGR2pbseVIPbYcqcev/7kf5xWmYs7oLMwqycLYvGTenRelzO2uwClY2caizEQAwPHaVgghWJtJ1AsGTkF0ml3DSSGSJGFCQSomFKTiZ1eOwvG6VldPqG+qsftUE74qdz1+99FhZCQaMHNEJmaNzMSMEZlIY3F51DC3dwIAUk1BKg7PMEGrkdBitaO6uQO5KZy7iM7GwClI7A4nqs3uHk7MOJHCijIT8aNZifjRrOGobe7AhtIabDpUh61H61Hf2ol391Tg3T0VkCRgQkEqZpVk4qLh6bhgcCqMOmX3OKPQCXbGyajTYmi6Ccfq2nC4ppWBE1EvGDgFSU2LFXangF4rISuJ9ScUPFnJcbjtwiG47cIh6LQ7sfNkIzYfrsPmQ3U4WN3iyUa99PERGHUaTBoyCBcNT8f04emYUJAKvZbt3CJFsAMnACjJTsKxujYcqWnBrJLMoD0PUaRi4BQk5e4dxvNS46FlvQmFiEGnwUXDM3DR8AwsmTca1eYObD5ciy1H6vHl8QbUt3Zi67EGbD3WAAAwGbSYPDQN04vSMXnoIIzPT0GcnhmpcCUXhwczcBqRnYS1+6txpKY1aM9BFMn8fqtZVlaGuXPnIi8vDyUlJVi2bFmv523cuBFTpkxBbm4uRo8ejQ8//DDgwUaSU+67UgansRUBqScnJQ43TxmMl2+diB2/vAIbHpyJp64f62qsadLD0unAp4fr8Oy6g7jxT19g/BPrMf+Pn+M3aw5g7b4q1Lq3DApXsTQfddgcsNqdAICUINU4AUBJtqtA/HBtS9CegyiS+Z1xWrRoEa655hqsX78e1dXVmDlzJqZMmYLLLrvMc05VVRVuvvlmrFu3DhMnTsS7776L2267DfX19dBqY+Pd7MlGVx8Uef8nIrVJkoQR2UkYkZ2E708fCqdT4FBNC7441oBtZQ3YdfIM6ls7sedUE/acasJfPisDABSmxWPS4EGYOMSVkRqdmxw2WalYmo+a3ct0Wo2EpCA2Qh2RlQQAOFrDO+uIeuPXb19DQwO2bduG//znP5AkCbm5uVi0aBHee++9bhNVbm4udu/ejYKCAgDAtddei6amJlRXVyM/P1/ZnyBMnXRnnIakJag8EqLeaTQSRucmY3RuMu64ZBiEEChvbMfOk43YdfIMdp08g0M1LShvbEd5Yzv+ubcSAKDTSCjJTsKEghSML0jBhPxUjMxJgkEX2lqpWJuPmtyBU3KcLqjBzLCMBOjcd9ZVmTuQx7uCibrxK3AqKytDWloadLqub8vNzcWWLVt6nCtPUvL3JScnIzOz90JDq9UKq9Xq+by5udmfYYWlU+4ap8HMOFGEkCQJg9NNGJxuwoKJrt/f5g4b9p5qws6TZ/D16SZ8fdqMxrZOHKhqxoGqZryxoxwAYNBqMCo3CePyUzAuLwVj8pKRGy+COt5gzUdAeM5JcmF4qim47SUMOg2GZiTgaG0rDtW0MHAiOotfgZPFYunxTkeSJFgsfXeZtdvtuP/++/H444/DYOj9F37p0qV48skn/RlK2PNknBg4UQRLjtNjZkkmZrrvrhJCoNLcgX3uIGpfhRlfnzbD3G7D16ddH3t0Brf7dLDmIyA85yS5MDw5BFvtjM5NxtHaVhyobMZlI7OC/nxEkcSvwMlkMkGI7u8ihRAwmXoPDjo7O3HLLbdgxIgR+OlPf9rndZcsWdLt683NzSgsLPRnaGHFbLF53h2yOJyiiSRJyE+NR35qPK4alwsAniW+ryuasK/CjAOVzThQ2Yw6a3ADp2DNR0B4zkmejFMIAqdxecn44KtK7K8wn/tkohjjV+A0dOhQNDY2wm63e9LjlZWVKC4u7nFue3s75s+fj5EjR+LFF1/s97pGoxFGo9GfoYQ1uTA8M8kIk4EdHyi6eS/xXTMhD4ArgDleUYfi5cF73mDNR0B4zkmh6OEkG5+fAgDYX8nAiehsflVzZmRkYOrUqVi+fDmEEKiursaqVaswf/58rF69GgsXLgQAtLa24qqrrsL48eN9mqSiTVdhOLNNFJskSUJmcnAbv8bafGS2uLZbCUXgNDbPFTiVN7ajyf28ROTi920wK1euxPr165GXl4cZM2bgrrvuwuzZs1FZWYnS0lIAwM6dO/Hpp5/i73//O3JycjyPV155RfEfIByxMJwoNGJpPuoqDg9+4JRi0nvKDL6pVL8wniic+L2OVFRUhA0bNvQ4/sgjj+CRRx4BAFx66aU9ag9iyckGdw8ntiIgCqpYmo+aQrhUBwDj8pNxqtGCfRVmXFycEZLnJIoE3KQqCHhHHREprbHNtWSWlhDcdgSycXKdEwvEibph4BQEXKojIqU1tIY2cJILxPeWN4Xk+YgiBQMnhVk6Xd12AWBoOpfqiEgZcsYpPSE0d/udX5gKjQScPtOOmjDfs5AolBg4Kays3lXfNMikD9k7QyKKbkIINLS5OpmnJYZmXkmK02NUTjIAYOeJMyF5TqJIwMBJYcfqXIHT8MxElUdCRNGixWqHzeEqcE8P4RuyyUMHAQB2nGgM2XMShTsGTgo7XtcKACjK5DIdESmj0V3fZDJoEafXhux5Jw9NAwDsOsmME5GMgZPCmHEiIqU1hPiOOtnkIa6M04GqZrRZ7SF9bqJwxcBJYcdq5YwTAyciUkZXYXhoA6c8976EDqfA7lPMOhEBDJwU5XQKT3H4cC7VEZFCGuXCcBVuOJlWlA4A+OxofcifmygcMXBSUFVzB9ptDui1Egq5Tx0RKaRrqS70Gw/PLHF1Dd9ymIETEcDASVFyYfjgNBP0Wr60RKQMuTg8PUStCLzJ260cqGpGXYs15M9PFG74111Bcn0TC8OJSEmh3m7FW0aiEWPzXP2cth5j1omIgZOCjsiBUxYDJyJSTl2rK9OTkRj6pToAuGSEK+u0+XCdKs9PFE4YOCnoUHULAGBUTpLKIyGiaCJveZKTHKfK888qyQQAbDpUB7vDqcoYiMIFAyeFCCE8gdNIBk5EpKCaZlfGKTtZnYzT1KFpSDXp0djWiR3cfoViHAMnhVQ0taPFaodeK6Eog0t1RKSMDpsD5nYbACArSZ2Mk06rwZzR2QCA9d9UqzIGonDBwEkhcrZpeGYiDDq+rESkDPlONqNOg+R4nWrjuGpcDgBg3f5qOJ1CtXEQqY1/4RVykPVNRBQEcn1TdnIcJElSbRwXF2cgwaBFdXMH9pQ3qTYOIrUxcFLIQU99U7LKIyGiaKJ2fZMsTq/F3LGurNO7u0+rOhYiNTFwUsih6mYAwKhcZpyISDlyxilLpTvqvC2cVAAA+NdXleiwOVQeDZE6GDgpoMPmwLE61x51XKojIiXVtLgDpyR1M04AML0oHfmp8WjpsOOjAzVqD4dIFQycFHCgqhkOp0BGolG1PitEFJ1qzF01TmrTaCTcMDEfAPDWjnKVR0OkDgZOCvjaXSh5XkGKqsWbRBR9KpraAQD5qfEqj8TlxsmF0EjAZ0frcbimRe3hEIUcAycFfH3aDAAYX5Ci8kiIKNqcPuMKnAoGhUfgVJhmwpXuIvG/fVam8miIQo+BkwK+Ot0EADivIFXVcRBRdOm0O1HtLg4vGGRSeTRd7poxDADw7p4K1Lv30SOKFQycAtTSYcPxeldh+ARmnIhIQVXmdggBxOk1yEg0qD0cj4mDB+H8wlR02p1YseW42sMhCikGTgHaV2GGEK76g3SVdi4noujUtUxnCqv6SUmScP/lxQCAV7eeQK07K0YUCxg4BWine8PLCwanqjsQIoo6p89YAIRPfZO3y0ZmYdKQQeiwOfHyxqNqD4coZBg4BWh7WSMA4MJhaSqPhIiiTXljeN1R502SJDw8dyQA4LVtpzz7dRJFOwZOAbA5nNh10pVxmjosXeXREFG0KXPXTw7LSFB5JL2bPjwdc8dkw+4U+PU/90MIbv5L0Y+BUwD2VZjRbnNgkEmPEVmJag+HiKLM0dpWAMDwMJ5fHr9uLOL1Wmw/0Yi3d3IPO4p+DJwCIC/TTRmaBo0mfAo3iSjyOZzCk3EqzgzfwCk/NR4PzhkBAHjyg29wwj1momjFwCkAnx2pBwBcWMRlOiJSVnmjBZ0OJ4w6TVjWOHm785IiTB2WhrZOBx54Yw867U61h0QUNAycBqjNase2sgYAwGUjM1UeDRFFm2N1rmW6oszEsM9oazUSlt98PpLjdPjqtJn1ThTVGDgN0OdH62FzCAxJN4Vt4SYRRa6D7rvUisO4vslbXmo8XrzlAmgk4M2d5fjTZjbGpOikU3sA/Wlra4NWq+1xXKvVIi4urtt5fdFoNIiPjx/QuRaLpc93TR99fQqAq5eJJEn9nitJEkymru0S2tvb4XT2ncpOSEgY0LkdHR1wOByKnGsydTXcs1qtsNvtipwbHx8PjcYVr3d2dsJmsylyblxcnOffij/n2mw2dHZ29nmu0WiETqfz+1y73Q6rte+tKAwGA/R6vd/nOhwOdHT03WxQr9fDYDD4fa7T6UR7e7si5+p0OhiN0dkMNpRz0p5j1XDarBiXl+w55s88o8acNLUwAY9dMwZPfHAAz647CD3s+M6UAp+uyzmJc1LEzEkiDJnNZgGgz8fVV1/d7XyTydTnubNmzep2bkZGRp/nTp48udu5Q4YM6fPcuMwhYsgv1ohNh2qFEEKMGTOmz3OHDBnS7bqTJ0/u89yMjIxu586aNavPc00mU7dzr7766n5fN28LFy7s99zW1lbPuT/4wQ/6Pbe2ttZz7o9//ON+zy0rK/Oc+/DDD/d77v79+z3nPv744/2eu337ds+5y5Yt6/fcjRs3es59+eWX+z13zZo1nnNXrlzZ77lvvfWW59y33nqr33NXrlzpOXfNmjX9nvvyyy97zt24cWO/5y5btsxz7vbt2/s99/HHH/ecu3///n7Pffjhhz3nlpWV9Xvuj3/8YyFE1++x2WwWkU6tOcmQM0J8fqTOc25/c9KYMWO6XVfNOemZDw+IIb9YI+KL+r4uwDlJfnBOiqw5iUt1A+RwCgwy6XHRcBaGE1HwjM1PUXsIfnvkqlH40azhag+DKCgkIcKvgq+5uRkpKSmorKxEcnJyj6+rvVT36Lv78N7eCnzvkhI8PX98v+cCXKrzxrS4SyykxeXfY7PZ3OvvcSQJ9Zy0+XAtfvT33RiSkYAtj17lOR7uS3Xe5woh8OJHB/D79QcBuHZX+O0N45GTEt/jXIBzEuekyJmTwjpwCscJt9Vqx7RnPka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      "text/plain": [
       "<Figure size 600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l, h = -5, 30\n",
    "f, ax = plt.subplots(1, 2, figsize=(6, 4))\n",
    "Z, D, Y, _ = ivsim_covars([1 / 5, 2 / 5, 2 / 5])\n",
    "CI, Pv = FARci(Z, D, Y, l, h, 0.001)\n",
    "\n",
    "ax[0].plot(CI, Pv)\n",
    "ax[0].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
    "ax[0].set_xlim(l, h)\n",
    "\n",
    "Z, D, Y, _ = ivsim_covars([1 / 5, 2 / 5, 2 / 5])\n",
    "CI, Pv = FARci(Z, D, Y, l, h, 0.001)\n",
    "\n",
    "ax[1].plot(CI, Pv)\n",
    "ax[1].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
    "ax[1].set_xlim(l, h)\n",
    "f.set_tight_layout(True)\n",
    "f.suptitle(r\"strong IV: $\\pi_c = 0.2$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'strong IV: $\\\\pi_c = 0.1$')"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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",
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      ],
      "text/plain": [
       "<Figure size 600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l, h = -10, 25\n",
    "f, ax = plt.subplots(1, 2, figsize=(6, 4))\n",
    "Z, D, Y, _ = ivsim_covars([1 / 10, 2 / 5, 1 / 2])\n",
    "CI, Pv = FARci(Z, D, Y, l, h, 0.001)\n",
    "\n",
    "ax[0].plot(CI, Pv)\n",
    "ax[0].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
    "ax[0].set_xlim(l, h)\n",
    "\n",
    "Z, D, Y, _ = ivsim_covars([1 / 10, 2 / 5, 1 / 2])\n",
    "CI, Pv = FARci(Z, D, Y, l, h, 0.001)\n",
    "\n",
    "ax[1].plot(CI, Pv)\n",
    "ax[1].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
    "ax[1].set_xlim(l, h)\n",
    "f.set_tight_layout(True)\n",
    "f.suptitle(r\"strong IV: $\\pi_c = 0.1$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Application"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "import formulaic as fm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "jobsdata = pd.read_csv(\"jobsdata.csv\")\n",
    "Z, D, Y = jobsdata.treat.values, jobsdata.comply.values, jobsdata.job_seek.values\n",
    "X = (\n",
    "    fm.Formula(\"~ -1 + sex + age + marital + nonwhite + educ + income\")\n",
    "    .get_model_matrix(data=jobsdata)\n",
    "    .values\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "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>CACE</th>\n",
       "      <th>SE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>delta</th>\n",
       "      <td>0.108790</td>\n",
       "      <td>0.081027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bootstrap</th>\n",
       "      <td>0.108790</td>\n",
       "      <td>0.081694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>linestimator</th>\n",
       "      <td>0.117633</td>\n",
       "      <td>0.081463</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  CACE        SE\n",
       "delta         0.108790  0.081027\n",
       "bootstrap     0.108790  0.081694\n",
       "linestimator  0.117633  0.081463"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(\n",
    "    np.c_[\n",
    "        IV_Wald_delta(Z, D, Y),\n",
    "        IV_Wald_bootstrap(Z, D, Y, n_boot=1e3),\n",
    "        IV_Lin_bootstrap(Z, D, Y, X, n_boot=1e3),\n",
    "    ].T,\n",
    "    index=[\"delta\", \"bootstrap\", \"linestimator\"],\n",
    "    columns=[\"CACE\", \"SE\"],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "l, h = -0.2, 0.4\n",
    "CI1, Pv1 = FARci(Z, D, Y, l, h, 0.001)\n",
    "CI2, Pv2 = FARciX(Z, D, Y, X, l, h, 0.001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'AR Intervals')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "f, ax = plt.subplots(2, 1, figsize=(6, 4))\n",
    "ax[0].plot(CI1, Pv1)\n",
    "ax[0].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
    "ax[0].set_xlim(l, h)\n",
    "ax[0].set_title(\"No Covariates\")\n",
    "\n",
    "ax[1].plot(CI2, Pv2)\n",
    "ax[1].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
    "ax[1].set_xlim(l, h)\n",
    "ax[1].set_title(\"With Covariates\")\n",
    "f.set_tight_layout(True)\n",
    "f.suptitle(r\"AR Intervals\")"
   ]
  }
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