01_OLS_causal.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "21b19548",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "pd.options.mode.chained_assignment = None  # default='warn'\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as ppt\n",
    "from sklearn import linear_model\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.discrete.discrete_model import Probit\n",
    "from statsmodels.discrete.discrete_model import Logit\n",
    "from linearmodels import OLS\n",
    "from scipy.spatial import distance\n",
    "\n",
    "from stargazer.stargazer import Stargazer\n",
    "import evaluation_functions\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "416a5c88-63cd-4a3b-b890-e4ed313a00b2",
   "metadata": {},
   "source": [
    "# Treatment independent of covariates"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8e8a6c8",
   "metadata": {},
   "source": [
    "## Create data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3150c6d1-4f55-412a-8327-b1be7b83e201",
   "metadata": {},
   "outputs": [],
   "source": [
    "a_true = 10.\n",
    "b1_true = 2.\n",
    "b2_true = 0.\n",
    "tau_true = 10.\n",
    "sigma = 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b05256c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>w</th>\n",
       "      <th>eps</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.562850</td>\n",
       "      <td>5.858894</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.268386</td>\n",
       "      <td>22.857315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.722447</td>\n",
       "      <td>5.002097</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.551508</td>\n",
       "      <td>30.893386</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.880598</td>\n",
       "      <td>7.857356</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.787702</td>\n",
       "      <td>26.973495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.797264</td>\n",
       "      <td>4.913460</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.235991</td>\n",
       "      <td>17.358537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8.347151</td>\n",
       "      <td>5.642156</td>\n",
       "      <td>0</td>\n",
       "      <td>-0.948044</td>\n",
       "      <td>25.746259</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x1        x2  w       eps          y\n",
       "0  6.562850  5.858894  0 -0.268386  22.857315\n",
       "1  5.722447  5.002097  1 -0.551508  30.893386\n",
       "2  8.880598  7.857356  0 -0.787702  26.973495\n",
       "3  3.797264  4.913460  0 -0.235991  17.358537\n",
       "4  8.347151  5.642156  0 -0.948044  25.746259"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create data\n",
    "df_data = pd.DataFrame(index=range(1000))\n",
    "df_data['x1'] = np.random.uniform(0, 10, df_data.shape[0])\n",
    "df_data['x2'] = np.random.uniform(0, 10, df_data.shape[0]) # not important\n",
    "df_data['w'] = np.random.choice([0,1], df_data.shape[0])\n",
    "df_data['eps'] = np.random.normal(0, sigma, df_data.shape[0])\n",
    "df_data['y'] = a_true + tau_true*df_data['w'] + b1_true*df_data['x1'] + b2_true*df_data['x2'] + df_data['eps']\n",
    "df_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bd2fe2c",
   "metadata": {},
   "source": [
    "## Estimate model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "87610fc7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Estimation Summary                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                      0.9847\n",
      "Estimator:                        OLS   Adj. R-squared:                 0.9846\n",
      "No. Observations:                1000   F-statistic:                 6.392e+04\n",
      "Date:                Wed, Aug 16 2023   P-value (F-stat)                0.0000\n",
      "Time:                        16:20:21   Distribution:                  chi2(3)\n",
      "Cov. Estimator:                robust                                         \n",
      "                                                                              \n",
      "                             Parameter Estimates                              \n",
      "==============================================================================\n",
      "            Parameter  Std. Err.     T-stat    P-value    Lower CI    Upper CI\n",
      "------------------------------------------------------------------------------\n",
      "const          9.9793     0.0833     119.74     0.0000      9.8160      10.143\n",
      "w              9.9014     0.0614     161.25     0.0000      9.7810      10.022\n",
      "x1             2.0150     0.0106     189.86     0.0000      1.9942      2.0358\n",
      "x2            -0.0001     0.0104    -0.0113     0.9910     -0.0206      0.0203\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "exog = df_data[['w','x1','x2']]\n",
    "exog = sm.add_constant(exog)\n",
    "endog = df_data['y']\n",
    "mod = OLS(endog, exog) #, entity_effects=True,time_effects=True)\n",
    "res = mod.fit() #cov_type='clustered', cluster_entity=True)\n",
    "a_est = res.params[0]\n",
    "b1_est = res.params[1]\n",
    "b2_est = res.params[2]\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbbc4ed1-af88-43b1-9c46-2babd50eb788",
   "metadata": {},
   "source": [
    "# Treatment dependent on covariates"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9d4c88f-4db0-45d3-83c6-d4788cb11a6a",
   "metadata": {},
   "source": [
    "## Create data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "47db6ef3-1eb6-412b-9397-e7982885ad36",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 1915.13it/s]\n"
     ]
    },
    {
     "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>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>w</th>\n",
       "      <th>eps</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.044239</td>\n",
       "      <td>1.283057</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.806114</td>\n",
       "      <td>23.282363</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.089057</td>\n",
       "      <td>9.505502</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.726744</td>\n",
       "      <td>37.904857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.470742</td>\n",
       "      <td>9.674889</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.598968</td>\n",
       "      <td>15.540452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.200621</td>\n",
       "      <td>2.329253</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.369771</td>\n",
       "      <td>11.771012</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.684132</td>\n",
       "      <td>8.770907</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.641086</td>\n",
       "      <td>28.009351</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x1        x2    w       eps          y\n",
       "0  7.044239  1.283057  0.0 -0.806114  23.282363\n",
       "1  8.089057  9.505502  1.0  1.726744  37.904857\n",
       "2  2.470742  9.674889  0.0  0.598968  15.540452\n",
       "3  0.200621  2.329253  0.0  1.369771  11.771012\n",
       "4  3.684132  8.770907  1.0  0.641086  28.009351"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create data\n",
    "df_data = pd.DataFrame(index=range(1000))\n",
    "df_data['x1'] = np.random.uniform(0, 10, df_data.shape[0])\n",
    "df_data['x2'] = np.random.uniform(0, 10, df_data.shape[0]) # not important\n",
    "df_data['w'] = np.nan\n",
    "for ind in tqdm(df_data.index):\n",
    "    prob_w = df_data['x1'].loc[ind]/df_data['x1'].max() # if x1 is small, probability of treatment is low\n",
    "    df_data['w'].loc[ind] = np.random.choice([0,1],p=[1.-prob_w,prob_w])\n",
    "df_data['eps'] = np.random.normal(0, sigma, df_data.shape[0])\n",
    "df_data['y'] = a_true + tau_true*df_data['w'] + b1_true*df_data['x1'] + b2_true*df_data['x2'] + df_data['eps']\n",
    "df_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9cd927b6-1c8c-4467-839d-c635ee476422",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>w</th>\n",
       "      <th>x1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>w</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.555483</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>0.555483</td>\n",
       "      <td>1.000000</td>\n",
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      "text/plain": [
       "           w        x1\n",
       "w   1.000000  0.555483\n",
       "x1  0.555483  1.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_data[['w','x1']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "582c32d4-4ea8-4e42-95d5-2e0f823f5e98",
   "metadata": {},
   "source": [
    "## Estimate naive model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "19a0114b-51b6-4948-b45f-5dae9b6a32c7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Estimation Summary                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                      0.7382\n",
      "Estimator:                        OLS   Adj. R-squared:                 0.7380\n",
      "No. Observations:                1000   F-statistic:                    2818.4\n",
      "Date:                Wed, Aug 16 2023   P-value (F-stat)                0.0000\n",
      "Time:                        16:20:24   Distribution:                  chi2(1)\n",
      "Cov. Estimator:                robust                                         \n",
      "                                                                              \n",
      "                             Parameter Estimates                              \n",
      "==============================================================================\n",
      "            Parameter  Std. Err.     T-stat    P-value    Lower CI    Upper CI\n",
      "------------------------------------------------------------------------------\n",
      "const          16.749     0.2148     77.989     0.0000      16.328      17.169\n",
      "w              16.407     0.3090     53.088     0.0000      15.801      17.012\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "exog = df_data[['w']]\n",
    "exog = sm.add_constant(exog)\n",
    "endog = df_data['y']\n",
    "mod = OLS(endog, exog) #, entity_effects=True,time_effects=True)\n",
    "res = mod.fit() #cov_type='clustered', cluster_entity=True)\n",
    "a_est = res.params[0]\n",
    "w_est = res.params[1]\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d03d3423-c639-4bfd-873e-ad5ac0b75886",
   "metadata": {},
   "source": [
    "## Include relevant covariates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d2293644-07b6-4272-8489-16c49b213f36",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Estimation Summary                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                      0.9885\n",
      "Estimator:                        OLS   Adj. R-squared:                 0.9885\n",
      "No. Observations:                1000   F-statistic:                 8.503e+04\n",
      "Date:                Wed, Aug 16 2023   P-value (F-stat)                0.0000\n",
      "Time:                        16:20:27   Distribution:                  chi2(3)\n",
      "Cov. Estimator:                robust                                         \n",
      "                                                                              \n",
      "                             Parameter Estimates                              \n",
      "==============================================================================\n",
      "            Parameter  Std. Err.     T-stat    P-value    Lower CI    Upper CI\n",
      "------------------------------------------------------------------------------\n",
      "const          9.9134     0.0856     115.78     0.0000      9.7456      10.081\n",
      "w              10.025     0.0783     128.10     0.0000      9.8715      10.178\n",
      "x1             2.0140     0.0140     143.64     0.0000      1.9865      2.0414\n",
      "x2             0.0061     0.0117     0.5190     0.6037     -0.0168      0.0289\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "exog = df_data[['w','x1','x2']]\n",
    "exog = sm.add_constant(exog)\n",
    "endog = df_data['y']\n",
    "mod = OLS(endog, exog) #, entity_effects=True,time_effects=True)\n",
    "res = mod.fit() #cov_type='clustered', cluster_entity=True)\n",
    "a_est = res.params[0]\n",
    "b1_est = res.params[1]\n",
    "b2_est = res.params[2]\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec5e1eda-7c10-4852-ab42-be18446f7c6b",
   "metadata": {},
   "source": [
    "## Large sample"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "384dc482-323c-4a06-b4ad-f96b5a9e9e4c",
   "metadata": {},
   "source": [
    "### Create sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7340b54a-c961-4934-afc4-e877355e6772",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_data(a_true,tau_true,b1_true,b2_true):\n",
    "    df_data = pd.DataFrame(index=range(1000))\n",
    "    df_data['x1'] = np.random.uniform(0, 10, df_data.shape[0])\n",
    "    df_data['x2'] = np.random.uniform(0, 10, df_data.shape[0]) # not important\n",
    "    df_data['w'] = np.nan\n",
    "    for ind in (df_data.index):\n",
    "        prob_w = df_data['x1'].loc[ind]/df_data['x1'].max() # if x1 is small, probability of treatment is low\n",
    "        df_data['w'].loc[ind] = np.random.choice([0,1],p=[1.-prob_w,prob_w])\n",
    "    df_data['eps'] = np.random.normal(0, sigma, df_data.shape[0])\n",
    "    df_data['y'] = a_true + tau_true*df_data['w'] + b1_true*df_data['x1'] + b2_true*df_data['x2'] + df_data['eps']\n",
    "    return df_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4b03e100-86f7-48d0-be8b-59861c44bf5e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 100/100 [00:42<00:00,  2.33it/s]\n"
     ]
    }
   ],
   "source": [
    "# Run large number of estimations\n",
    "for i in tqdm(range(100)):\n",
    "    # Naive model\n",
    "    df_data = create_data(a_true,tau_true,b1_true,b2_true)\n",
    "    exog = df_data[['w']]\n",
    "    exog = sm.add_constant(exog)\n",
    "    endog = df_data['y']\n",
    "    mod = OLS(endog, exog) #, entity_effects=True,time_effects=True)\n",
    "    res = mod.fit() #cov_type='clustered', cluster_entity=True)\n",
    "    df_param_i = pd.DataFrame(data=[res.params])\n",
    "    df_conflow_i = res.conf_int(0.95)[['lower']].transpose()\n",
    "    df_confhigh_i = res.conf_int(0.95)[['upper']].transpose()\n",
    "    if i == 0:\n",
    "        df_param_naive = df_param_i.copy()\n",
    "        df_conflow_naive = df_conflow_i.copy()\n",
    "        df_confhigh_naive = df_confhigh_i.copy()\n",
    "    else:\n",
    "        df_param_naive = df_param_naive.append(df_param_i)\n",
    "        df_conflow_naive = df_conflow_naive.append(df_conflow_i)\n",
    "        df_confhigh_naive = df_confhigh_naive.append(df_confhigh_i)\n",
    "    # Full model\n",
    "    exog = df_data[['w','x1','x2']]\n",
    "    exog = sm.add_constant(exog)\n",
    "    endog = df_data['y']\n",
    "    mod = OLS(endog, exog) #, entity_effects=True,time_effects=True)\n",
    "    res = mod.fit() #cov_type='clustered', cluster_entity=True)\n",
    "    df_param_i = pd.DataFrame(data=[res.params])\n",
    "    df_conflow_i = res.conf_int(0.95)[['lower']].transpose()\n",
    "    df_confhigh_i = res.conf_int(0.95)[['upper']].transpose()\n",
    "    if i == 0:\n",
    "        df_param_full = df_param_i.copy()\n",
    "        df_conflow_full = df_conflow_i.copy()\n",
    "        df_confhigh_full = df_confhigh_i.copy()\n",
    "    else:\n",
    "        df_param_full = df_param_full.append(df_param_i)\n",
    "        df_conflow_full = df_conflow_full.append(df_conflow_i)\n",
    "        df_confhigh_full = df_confhigh_full.append(df_confhigh_i)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c4703ce-7dd6-4fde-9230-df1d28a673e9",
   "metadata": {},
   "source": [
    "### Visualize difference in estimates for naive and full model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "714e7ea7-4691-4bb2-9b0f-53c1f2622444",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12398f040>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_param_naive['w'].hist(color='blue',alpha=0.5,label='naive')\n",
    "df_param_full['w'].hist(color='green',alpha=0.5,label='full')\n",
    "ppt.axvline(tau_true,color='red',label='true tau')\n",
    "ppt.axvline(df_param_naive['w'].mean(),color='blue',label='naive mean tau')\n",
    "ppt.axvline(df_param_full['w'].mean(),color='green',label='full mean tau')\n",
    "ppt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ee00be6-bfe3-4bc1-bbba-6fc5f99e7e5e",
   "metadata": {},
   "source": [
    "Treatment is more likely if x1 is large. Therefore, the naive model over-estimates the treatment effect if x1 is ommitted."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a312fb0-d60b-4060-8658-7537e3111424",
   "metadata": {},
   "source": [
    "## Solve with matching"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53568110-f14e-4537-bd0a-4180ccc3aacb",
   "metadata": {},
   "source": [
    "This follows roughly Imbens (2014) - Mathcing Methods in Practice."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c654546-a8bc-4d84-af44-fb425cf4229c",
   "metadata": {},
   "source": [
    "### Step 1: Assess overlap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9c0e742f-4346-4e34-bbdc-c3e3be487491",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x12fd9caf0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_data.loc[df_data['w'] == 1]['x1'].hist(label='treated',alpha=0.5)\n",
    "df_data.loc[df_data['w'] == 0]['x1'].hist(label='control',alpha=0.5)\n",
    "ppt.legend()"
   ]
  },
  {
   "attachments": {
    "d6182048-1478-484c-a6c0-d797635fb9f0.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "688b2e13-9987-415e-998c-d63b0f4d77d8",
   "metadata": {},
   "source": [
    "![grafik.png](attachment:d6182048-1478-484c-a6c0-d797635fb9f0.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9d9995cd-4a21-4ea2-800c-d436f47e2db8",
   "metadata": {},
   "outputs": [],
   "source": [
    "N_c = (1 - df_data['w']).sum()\n",
    "N_t = (df_data['w']).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ea5cf4e5-9e0d-4b21-872e-432fe755a78f",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_ck = 1/N_c*(df_data.loc[df_data['w'] == 0]['x1'].sum())\n",
    "x_tk = 1/N_t*(df_data.loc[df_data['w'] == 1]['x1'].sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0b29b65d-3b85-4b41-80ef-9b3a010774f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "S2_Xck = 1/(N_c-1)*(((df_data.loc[df_data['w'] == 0]['x1'] - x_ck)**2).sum())\n",
    "S2_Xtk = 1/(N_t-1)*(((df_data.loc[df_data['w'] == 1]['x1'] - x_tk)**2).sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ea72429d-f4b5-432a-9098-6919ec27080c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3345532444619126"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_Xk = (x_tk - x_ck)/np.sqrt((S2_Xtk + S2_Xck)/2)\n",
    "delta_Xk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7e3a91d4-c7ee-478a-8511-fef00bfc3eb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26.4775155710109"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_Xk = (x_tk - x_ck)/(np.sqrt((S2_Xtk)/N_t) + (S2_Xck/N_c))\n",
    "t_Xk"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aca7e97f-63e9-411e-8c54-e1153ad53df4",
   "metadata": {},
   "source": [
    "### Step 2: Estimate propensity score"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55ebb0b2-bcc0-4569-bfff-df0247c5e841",
   "metadata": {},
   "source": [
    "#### Lasso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "81970c40-f8ad-4314-b1fb-9d2d9af094fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully    (Exit mode 0)\n",
      "            Current function value: 0.5230550482468894\n",
      "            Iterations: 22\n",
      "            Function evaluations: 23\n",
      "            Gradient evaluations: 22\n",
      "                           Logit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:                      w   No. Observations:                 1000\n",
      "Model:                          Logit   Df Residuals:                      997\n",
      "Method:                           MLE   Df Model:                            2\n",
      "Date:                Wed, 16 Aug 2023   Pseudo R-squ.:                  0.2494\n",
      "Time:                        16:20:38   Log-Likelihood:                -520.15\n",
      "converged:                       True   LL-Null:                       -692.95\n",
      "Covariance Type:            nonrobust   LLR p-value:                 9.012e-76\n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -2.4003      0.216    -11.102      0.000      -2.824      -1.977\n",
      "x1             0.4908      0.032     15.418      0.000       0.428       0.553\n",
      "x2            -0.0146      0.027     -0.551      0.582      -0.067       0.037\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "# which covariates to include\n",
    "formula = 'w ~ x1 + x2'\n",
    "lasso = Logit.from_formula(formula, df_data).fit_regularized(method='l1', alpha=1.0, L1_wt=1.0, start_params=None, profile_scale=False, refit=False)\n",
    "print(lasso.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54f6f2eb-91c0-4117-a6fc-f4a965e9b970",
   "metadata": {},
   "source": [
    "#### Imbens and Rubin (2014), as described in Imbens (2014) on page 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "aba0fa36-2fcc-42fb-ad44-1d6aaf789896",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c6e3d854-3a17-436c-9186-2db524274ca0",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_data['x1x2'] = df_data['x1']*df_data['x2']\n",
    "cols = ['x1','x2','x1x2']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b77b7984-cd96-4b2a-ac5e-3699621019cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "C_lin = 1\n",
    "C_qua = 2.71"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "bb24be90-e057-48eb-aada-18ee43a21993",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_B = [1]\n",
    "K_B = len(X_B)\n",
    "K = 2 # x1 and x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "b0149a81-a1d8-4b60-b1ac-4a3d6e875761",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.692947\n",
      "         Iterations 3\n",
      "                           Logit Regression Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:                      w   No. Observations:                 1000\n",
      "Model:                          Logit   Df Residuals:                      999\n",
      "Method:                           MLE   Df Model:                            0\n",
      "Date:                Wed, 16 Aug 2023   Pseudo R-squ.:               5.131e-12\n",
      "Time:                        17:05:21   Log-Likelihood:                -692.95\n",
      "converged:                       True   LL-Null:                       -692.95\n",
      "Covariance Type:            nonrobust   LLR p-value:                       nan\n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         -0.0400      0.063     -0.632      0.527      -0.164       0.084\n",
      "==============================================================================\n"
     ]
    }
   ],
   "source": [
    "# Step 1: Estimate logistic regresion model, with basic covs X_B\n",
    "df_data['const'] = 1\n",
    "step1 = Logit(endog=df_data['w'],exog=df_data['const'],offset=False)\n",
    "step1_res = step1.fit()\n",
    "llf1 = step1_res.llf\n",
    "print(step1_res.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "ef11976c-bf38-4cd5-9e96-187daa9f6fb5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.520225\n",
      "         Iterations 6\n",
      "0.5733839438659721\n",
      "x2\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.692946\n",
      "         Iterations 3\n",
      "4.407817728798138e-06\n",
      "x1x2\n",
      "Optimization terminated successfully.\n",
      "         Current function value: 0.617790\n",
      "         Iterations 5\n",
      "0.22960970523552418\n"
     ]
    }
   ],
   "source": [
    "# Estimate K+1-K_B additional logistic regression models where each model includes a single additional element\n",
    "# Compute: likelihood-ratio test assesses the goodness of fit of two competing statistical models, specifically one found by maximization \n",
    "# over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods\n",
    "# Other: https://www.statsmodels.org/dev/generated/statsmodels.regression.linear_model.RegressionResults.compare_lr_test.html\n",
    "for col in cols:\n",
    "    print(col)\n",
    "    step2 = Logit(endog=df_data['w'],exog=df_data[['const'] + [col]],offset=False)\n",
    "    step2_res = step2.fit()\n",
    "    llf2 = step2_res.llf\n",
    "    print(-2.*np.log(llf2/llf1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b6d4e8c-c70d-416c-b9b5-1babe706f734",
   "metadata": {},
   "source": [
    "--> This is possibly wrong. Procedure says to stop here."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "851e5705-8b0b-4d5b-9db2-d2016e435649",
   "metadata": {},
   "source": [
    "#### Estimate propensity score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "3db02f5f-ea92-4fe7-a4d1-2ab7789cbd99",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.520225\n",
      "         Iterations 6\n"
     ]
    }
   ],
   "source": [
    "# treatment selection model\n",
    "formula = 'w ~ x1'\n",
    "res_probit = Logit.from_formula(formula, df_data).fit()\n",
    "df_data['propensity_score'] = res_probit.predict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "8e499710-81a5-4263-8f50-360b9e9f4110",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Logit Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>w</td>        <th>  No. Observations:  </th>  <td>  1000</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                 <td>Logit</td>      <th>  Df Residuals:      </th>  <td>   998</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                 <td>MLE</td>       <th>  Df Model:          </th>  <td>     1</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Wed, 16 Aug 2023</td> <th>  Pseudo R-squ.:     </th>  <td>0.2493</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>17:28:59</td>     <th>  Log-Likelihood:    </th> <td> -520.23</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>converged:</th>             <td>True</td>       <th>  LL-Null:           </th> <td> -692.95</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>  LLR p-value:       </th> <td>4.162e-77</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   -2.5067</td> <td>    0.177</td> <td>  -14.124</td> <td> 0.000</td> <td>   -2.855</td> <td>   -2.159</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>        <td>    0.4964</td> <td>    0.032</td> <td>   15.491</td> <td> 0.000</td> <td>    0.434</td> <td>    0.559</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/latex": [
       "\\begin{center}\n",
       "\\begin{tabular}{lclc}\n",
       "\\toprule\n",
       "\\textbf{Dep. Variable:}   &        w         & \\textbf{  No. Observations:  } &     1000    \\\\\n",
       "\\textbf{Model:}           &      Logit       & \\textbf{  Df Residuals:      } &      998    \\\\\n",
       "\\textbf{Method:}          &       MLE        & \\textbf{  Df Model:          } &        1    \\\\\n",
       "\\textbf{Date:}            & Wed, 16 Aug 2023 & \\textbf{  Pseudo R-squ.:     } &   0.2493    \\\\\n",
       "\\textbf{Time:}            &     17:28:59     & \\textbf{  Log-Likelihood:    } &   -520.23   \\\\\n",
       "\\textbf{converged:}       &       True       & \\textbf{  LL-Null:           } &   -692.95   \\\\\n",
       "\\textbf{Covariance Type:} &    nonrobust     & \\textbf{  LLR p-value:       } & 4.162e-77   \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "\\begin{tabular}{lcccccc}\n",
       "                   & \\textbf{coef} & \\textbf{std err} & \\textbf{z} & \\textbf{P$> |$z$|$} & \\textbf{[0.025} & \\textbf{0.975]}  \\\\\n",
       "\\midrule\n",
       "\\textbf{Intercept} &      -2.5067  &        0.177     &   -14.124  &         0.000        &       -2.855    &       -2.159     \\\\\n",
       "\\textbf{x1}        &       0.4964  &        0.032     &    15.491  &         0.000        &        0.434    &        0.559     \\\\\n",
       "\\bottomrule\n",
       "\\end{tabular}\n",
       "%\\caption{Logit Regression Results}\n",
       "\\end{center}"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                           Logit Regression Results                           \n",
       "==============================================================================\n",
       "Dep. Variable:                      w   No. Observations:                 1000\n",
       "Model:                          Logit   Df Residuals:                      998\n",
       "Method:                           MLE   Df Model:                            1\n",
       "Date:                Wed, 16 Aug 2023   Pseudo R-squ.:                  0.2493\n",
       "Time:                        17:28:59   Log-Likelihood:                -520.23\n",
       "converged:                       True   LL-Null:                       -692.95\n",
       "Covariance Type:            nonrobust   LLR p-value:                 4.162e-77\n",
       "==============================================================================\n",
       "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -2.5067      0.177    -14.124      0.000      -2.855      -2.159\n",
       "x1             0.4964      0.032     15.491      0.000       0.434       0.559\n",
       "==============================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_probit.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "7b2619ef-4331-4c79-9255-fc3bda41aa22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x130160e50>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_data['propensity_score'].loc[df_data['w'] == 1].hist(alpha=0.5,label='treated')\n",
    "df_data['propensity_score'].loc[df_data['w'] == 0].hist(alpha=0.5,label='control')\n",
    "ppt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "id": "fd8ca46f-23b0-4522-9bf7-29dd7b5205f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "w\n",
       "0.0    0.316973\n",
       "1.0    0.672719\n",
       "Name: propensity_score, dtype: float64"
      ]
     },
     "execution_count": 295,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_data.groupby('w')['propensity_score'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "2fbe7b3b-5a77-48a6-9d00-83103d49890d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Cut off extremes\n",
    "df_data_sub = df_data.loc[df_data['propensity_score'] < 0.8]\n",
    "df_data_sub = df_data_sub.loc[df_data_sub['propensity_score'] > 0.2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17ffce7d-b7ee-4b39-b006-c03622e207c0",
   "metadata": {},
   "source": [
    "### Matching with replacement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "324fb871-637c-4259-b746-d61e4aa7669d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.spatial import distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "3acbf692-247a-42d7-82a2-75fc1e9ff187",
   "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>x1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x1</th>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     x1\n",
       "x1  1.0"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iv = df_data[['x1']].corr()\n",
    "iv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "74c459e7-b3ac-40da-9bc6-a466766603eb",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 563/563 [01:22<00:00,  6.85it/s]\n"
     ]
    }
   ],
   "source": [
    "df_data_sub['match_ind'] = -1\n",
    "df_data_sub['match_x1'] = -1\n",
    "df_data_sub['match_y'] = -1\n",
    "for ind in tqdm(df_data_sub.index):\n",
    "    X0 = df_data_sub[['x1']].loc[ind]\n",
    "    w = df_data_sub['w'].loc[ind]\n",
    "    max_distance = 100000.\n",
    "    max_ind = -1\n",
    "    max_x1 = -1.\n",
    "    df_data_sub_w = df_data_sub.loc[df_data_sub['w'] == (1-w)]\n",
    "    for ind2 in df_data_sub_w.index:\n",
    "        X1 = df_data_sub[['x1']].loc[ind2]\n",
    "        dist = distance.mahalanobis(X0, X1, iv)\n",
    "        if dist < max_distance:\n",
    "            max_distance = dist\n",
    "            max_ind = ind2\n",
    "            max_x1 = df_data_sub['x1'].loc[ind2]\n",
    "            max_y = df_data_sub['y'].loc[ind2]\n",
    "    df_data_sub['match_ind'].loc[ind] = max_ind\n",
    "    df_data_sub['match_x1'].loc[ind] = max_x1\n",
    "    df_data_sub['match_y'].loc[ind] = max_y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20e088b5-7f5c-4280-8484-ebceee021137",
   "metadata": {},
   "source": [
    "#### Simple matching estimator discussed in Abadie and Imbens (2006)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "a749438b-4d4a-4179-9758-b6e4a71d748d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.03442179609474"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_data_sub_w0 = df_data_sub.loc[df_data_sub['w'] == 0]\n",
    "df_data_sub_w0['diff_10'] = df_data_sub_w0['match_y']-df_data_sub_w0['y']\n",
    "sum_10 = df_data_sub_w0['diff_10'].sum()\n",
    "df_data_sub_w1 = df_data_sub.loc[df_data_sub['w'] == 1]\n",
    "df_data_sub_w1['diff_01'] = df_data_sub_w1['y']-df_data_sub_w1['match_y']\n",
    "sum_01 = df_data_sub_w1['diff_01'].sum()\n",
    "(sum_10 + sum_01)/len(df_data_sub)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "287d72e3-88cb-46cf-ab6c-782a3a4d65e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>w</th>\n",
       "      <th>eps</th>\n",
       "      <th>y</th>\n",
       "      <th>x1x2</th>\n",
       "      <th>const</th>\n",
       "      <th>propensity_score</th>\n",
       "      <th>match_ind</th>\n",
       "      <th>match_x1</th>\n",
       "      <th>match_y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.044239</td>\n",
       "      <td>1.283057</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.806114</td>\n",
       "      <td>23.282363</td>\n",
       "      <td>9.038156</td>\n",
       "      <td>1</td>\n",
       "      <td>0.729108</td>\n",
       "      <td>252</td>\n",
       "      <td>7.046820</td>\n",
       "      <td>33.576206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.470742</td>\n",
       "      <td>9.674889</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.598968</td>\n",
       "      <td>15.540452</td>\n",
       "      <td>23.904157</td>\n",
       "      <td>1</td>\n",
       "      <td>0.217519</td>\n",
       "      <td>219</td>\n",
       "      <td>2.475713</td>\n",
       "      <td>24.722025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.684132</td>\n",
       "      <td>8.770907</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.641086</td>\n",
       "      <td>28.009351</td>\n",
       "      <td>32.313181</td>\n",
       "      <td>1</td>\n",
       "      <td>0.336739</td>\n",
       "      <td>951</td>\n",
       "      <td>3.671397</td>\n",
       "      <td>17.619988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5.954231</td>\n",
       "      <td>2.001568</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.750974</td>\n",
       "      <td>22.659436</td>\n",
       "      <td>11.917801</td>\n",
       "      <td>1</td>\n",
       "      <td>0.610406</td>\n",
       "      <td>480</td>\n",
       "      <td>5.957477</td>\n",
       "      <td>31.132311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4.712546</td>\n",
       "      <td>8.971891</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.667362</td>\n",
       "      <td>28.757730</td>\n",
       "      <td>42.280449</td>\n",
       "      <td>1</td>\n",
       "      <td>0.458259</td>\n",
       "      <td>581</td>\n",
       "      <td>4.682588</td>\n",
       "      <td>18.262975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>989</th>\n",
       "      <td>4.282613</td>\n",
       "      <td>2.626623</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.395814</td>\n",
       "      <td>18.169411</td>\n",
       "      <td>11.248811</td>\n",
       "      <td>1</td>\n",
       "      <td>0.405941</td>\n",
       "      <td>201</td>\n",
       "      <td>4.276962</td>\n",
       "      <td>29.035899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>990</th>\n",
       "      <td>3.774673</td>\n",
       "      <td>8.673752</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.496838</td>\n",
       "      <td>18.046184</td>\n",
       "      <td>32.740576</td>\n",
       "      <td>1</td>\n",
       "      <td>0.346850</td>\n",
       "      <td>771</td>\n",
       "      <td>3.777025</td>\n",
       "      <td>27.125095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>991</th>\n",
       "      <td>4.674225</td>\n",
       "      <td>2.352609</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-0.597614</td>\n",
       "      <td>28.750836</td>\n",
       "      <td>10.996624</td>\n",
       "      <td>1</td>\n",
       "      <td>0.453541</td>\n",
       "      <td>669</td>\n",
       "      <td>4.677338</td>\n",
       "      <td>19.004508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>992</th>\n",
       "      <td>3.645073</td>\n",
       "      <td>3.088727</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.307770</td>\n",
       "      <td>28.597917</td>\n",
       "      <td>11.258637</td>\n",
       "      <td>1</td>\n",
       "      <td>0.332423</td>\n",
       "      <td>645</td>\n",
       "      <td>3.648922</td>\n",
       "      <td>18.253897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>2.351854</td>\n",
       "      <td>1.449033</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.847497</td>\n",
       "      <td>13.856211</td>\n",
       "      <td>3.407915</td>\n",
       "      <td>1</td>\n",
       "      <td>0.207641</td>\n",
       "      <td>791</td>\n",
       "      <td>2.343078</td>\n",
       "      <td>25.940493</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>563 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           x1        x2    w       eps          y       x1x2  const  \\\n",
       "0    7.044239  1.283057  0.0 -0.806114  23.282363   9.038156      1   \n",
       "2    2.470742  9.674889  0.0  0.598968  15.540452  23.904157      1   \n",
       "4    3.684132  8.770907  1.0  0.641086  28.009351  32.313181      1   \n",
       "6    5.954231  2.001568  0.0  0.750974  22.659436  11.917801      1   \n",
       "7    4.712546  8.971891  1.0 -0.667362  28.757730  42.280449      1   \n",
       "..        ...       ...  ...       ...        ...        ...    ...   \n",
       "989  4.282613  2.626623  0.0 -0.395814  18.169411  11.248811      1   \n",
       "990  3.774673  8.673752  0.0  0.496838  18.046184  32.740576      1   \n",
       "991  4.674225  2.352609  1.0 -0.597614  28.750836  10.996624      1   \n",
       "992  3.645073  3.088727  1.0  1.307770  28.597917  11.258637      1   \n",
       "998  2.351854  1.449033  0.0 -0.847497  13.856211   3.407915      1   \n",
       "\n",
       "     propensity_score  match_ind  match_x1    match_y  \n",
       "0            0.729108        252  7.046820  33.576206  \n",
       "2            0.217519        219  2.475713  24.722025  \n",
       "4            0.336739        951  3.671397  17.619988  \n",
       "6            0.610406        480  5.957477  31.132311  \n",
       "7            0.458259        581  4.682588  18.262975  \n",
       "..                ...        ...       ...        ...  \n",
       "989          0.405941        201  4.276962  29.035899  \n",
       "990          0.346850        771  3.777025  27.125095  \n",
       "991          0.453541        669  4.677338  19.004508  \n",
       "992          0.332423        645  3.648922  18.253897  \n",
       "998          0.207641        791  2.343078  25.940493  \n",
       "\n",
       "[563 rows x 11 columns]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_data_sub"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ad722a4-ed2a-4f7c-a217-40b7613761cc",
   "metadata": {},
   "source": [
    "#### Bias-correcting matching estimator discussed in Abadie and Imbens (2006, 2010)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "cc1e6506-c953-4586-bcaf-419e1a8bbafa",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_data_sub_w0.rename(columns={'y':'y0','match_y':'y1'},inplace=True)\n",
    "df_data_sub_w1.rename(columns={'y':'y1','match_y':'y0'},inplace=True)\n",
    "df_data_sub_comp = df_data_sub_w0.append(df_data_sub_w1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "97c434d0-8f91-4f93-9fd1-2ab275975c11",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run least squares regressions\n",
    "exog = df_data_sub_comp[['x1']]\n",
    "exog = sm.add_constant(exog)\n",
    "endog = df_data_sub_comp['y1']\n",
    "mod_t = OLS(endog, exog) #, entity_effects=True,time_effects=True)\n",
    "res_t = mod_t.fit() #cov_type='clustered', cluster_entity=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "9e04e532-c591-4223-a84b-25278e404ced",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_data_sub_comp['est_y_1'] = res_t.params[0] + res_t.params[1]*df_data_sub_comp['x1']\n",
    "df_data_sub_comp['est_y_1'].loc[df_data_sub_comp['w'] == 1] = df_data_sub_comp['y1'].loc[df_data_sub_comp['w'] == 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "fe57da37-727f-495f-b2a3-18d426a5930a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run least squares regressions\n",
    "exog = df_data_sub_comp[['x1']]\n",
    "exog = sm.add_constant(exog)\n",
    "endog = df_data_sub_comp['y0']\n",
    "mod_c = OLS(endog, exog) #, entity_effects=True,time_effects=True)\n",
    "res_c = mod_c.fit() #cov_type='clustered', cluster_entity=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "66a4229d-94bc-4bdb-8f41-b3ccfb81c642",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_data_sub_comp['est_y_0'] = res_c.params[0] + res_c.params[1]*df_data_sub_comp['x1']\n",
    "df_data_sub_comp['est_y_0'].loc[df_data_sub_comp['w'] == 0] = df_data_sub_comp['y0'].loc[df_data_sub_comp['w'] == 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "233531ac-9221-4a9e-bbfb-d29b7ba95f48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.059520236328652"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Biased-adjusted matching estimator\n",
    "(df_data_sub_comp['est_y_1'] - df_data_sub_comp['est_y_0']).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "4b9b9092-c43b-4a85-8e9f-e0e87da80f39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.911837951199686"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Biased-adjusted matching estimator for the treated\n",
    "(df_data_sub_comp['est_y_1'].loc[df_data_sub_comp['w'] == 1] - df_data_sub_comp['est_y_0'].loc[df_data_sub_comp['w'] == 1]).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e619033e-3221-41cc-82ee-a1711525f224",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44178a7f-ce49-486e-8010-9cc542e66c6c",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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