notebooks/causal_inference_kang_schafer.ipynb

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      "source": [
        "#@title Copyright 2019 The Empirical Calibration Authors.\n",
        "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "#     https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License.\n",
        "# ============================================================================"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "RYsS3JrpHaJI"
      },
      "source": [
        "# Causal Inference of Kang-Schafer simulation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "s_FngMAZGxLG"
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      "source": [
        "\u003ctable align=\"left\"\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/google/empirical_calibration/blob/master/notebooks/causal_inference_kang_schafer.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" /\u003eRun in Google Colab\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://github.com/google/empirical_calibration/blob/master/notebooks/causal_inference_kang_schafer.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" /\u003eView source on GitHub\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "\u003c/table\u003e"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "toc",
        "id": "FDLqKjdKKZMV"
      },
      "source": [
        "\u003e[Causal Inference of Kang-Schafer simulation.](#scrollTo=RYsS3JrpHaJI)\n",
        "\n",
        "\u003e\u003e[Imports](#scrollTo=VGDMBD7TRIf4)\n",
        "\n",
        "\u003e\u003e[Correctly Specified Model](#scrollTo=X1D4OBiEZhnT)\n",
        "\n",
        "\u003e\u003e[Misspecified Model](#scrollTo=0zuCvTGVdMVj)\n",
        "\n",
        "\u003e\u003e[Benchmark Execution Time](#scrollTo=ITCnSqDiyjIx)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "XhdK9tifRPYR"
      },
      "source": [
        "We illustrate empirical calibration to estimate the average treatment effect on the treated (ATT) on Kang-Schafer simulation under both correctly specified and misspecified models, and benchmark the execution time.  For details of simulation setup, please refer to [kang_schafer_population_mean.ipynb](./kang_schafer_population_mean.ipynb)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "VGDMBD7TRIf4"
      },
      "source": [
        "## Imports"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "hzy_rdy7WXyS"
      },
      "outputs": [],
      "source": [
        "from matplotlib import pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import patsy\n",
        "import seaborn as sns\n",
        "import timeit\n",
        "\n",
        "# install and import ec\n",
        "!pip install -q git+https://github.com/google/empirical_calibration\n",
        "import empirical_calibration as ec\n",
        "\n",
        "sns.set_style('whitegrid')\n",
        "%config InlineBackend.figure_format='retina'\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "X1D4OBiEZhnT"
      },
      "source": [
        "## Correctly Specified Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "5gUCcNuhcSBf"
      },
      "source": [
        "We run the simulation 1000 times under correctly specified logistic propensity score and linear outcome regression. For each simulation we estimate the average treatment effect on the treated (ATT) using empirical calibration."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "0lcgAuqwiVLv"
      },
      "outputs": [],
      "source": [
        "def estimate_att(formula):\n",
        "  simulation = ec.data.kang_schafer.Simulation(size=1000)\n",
        "\n",
        "  t = simulation.treatment\n",
        "  y = simulation.outcome\n",
        "\n",
        "  df = pd.DataFrame(\n",
        "      np.column_stack(\n",
        "          [simulation.covariates, simulation.transformed_covariates]))\n",
        "  df.columns = [\"z1\", \"z2\", \"z3\", \"z4\", \"x1\", \"x2\", \"x3\", \"x4\"]\n",
        "  x = patsy.dmatrix(formula, df, return_type=\"dataframe\").values\n",
        "\n",
        "\n",
        "  weights = ec.maybe_exact_calibrate(covariates=x[t == 0],\n",
        "                                     target_covariates=x[t == 1])[0]\n",
        "\n",
        "  return (np.mean(y[t == 1]) - np.mean(y[t == 0]),\n",
        "          np.mean(y[t == 1]) - np.sum(y[t == 0] * weights))\n",
        "\n",
        "\n",
        "def show_estimates(estimates, col='weighted'):\n",
        "  ax = estimates[col].hist(bins=20, alpha=0.8, edgecolor='none')\n",
        "  plt.axvline(estimates[col].mean(), linestyle='dashed', color='red')\n",
        "  print('bias of {} is {}'.format(col, estimates[col].mean()))\n",
        "  print('rmse of {} is {}'.format(col, np.sqrt(np.mean((estimates[col] - 0.) ** 2))))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "qgVOrpBNN0AP"
      },
      "outputs": [],
      "source": [
        "estimates = pd.DataFrame(\n",
        "    [estimate_att(\"-1 + z1 + z2 + z3 + z4\") for i in xrange(1000)])\n",
        "estimates.columns = ['raw', 'weighted']"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "f0VIHhXycouh"
      },
      "source": [
        "The mean of the 1000 ATT estimates after weight correction is very close to the true zero ATT."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "height": 313
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 143,
          "status": "ok",
          "timestamp": 1563456747099,
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          "user_tz": 240
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      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "bias of raw is -19.9628369399\n",
            "rmse of raw is 20.0889440518\n"
          ]
        },
        {
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QHgAAAAAYITwAAAAAMEJ4AAAAAGCE8AAAAADACOEBAAAAgBHCAwAAAAAjhAcAAAAARggP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\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7fc7f2f41b90\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 262,
              "width": 391
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "show_estimates(estimates,'raw')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "colab": {
          "height": 313
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 143,
          "status": "ok",
          "timestamp": 1563456747286,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "irPv3UCLLMeu",
        "outputId": "d82b6d15-56b3-4165-bb6e-4ad82c4bcd1d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "bias of weighted is 0.00108065962091\n",
            "rmse of weighted is 0.0854238555451\n"
          ]
        },
        {
          "data": {
            "image/png": 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bVgcAwDsEBQBAQGRVlriXCQoAEPyCIihcuHBB69evV0VFhf7617/q4sWLuuGG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\nIhKwUCAiIiIiIgELBSIiIiIiEvwFfKoYpZmrZXcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7fc7f2e5fe50\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 262,
              "width": 389
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "show_estimates(estimates,'weighted')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "0zuCvTGVdMVj"
      },
      "source": [
        "## Misspecified Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "sA_480Flh5gz"
      },
      "source": [
        "If the transformed covariates are observed in place of the true covariates, both the propensity score model and outcome regression model become misspecified. We run 1000 simulations and for each simulation estimate the ATT by balancing the transformed covariates. The causal estimate is no longer unbiased."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "ReZeU-vUdk-j"
      },
      "outputs": [],
      "source": [
        "estimates_miss = pd.DataFrame([estimate_att(\"-1 + x1 + x2 + x3 + x4\") for i in xrange(1000)])\n",
        "estimates_miss.columns = ['raw', 'weighted']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "height": 313
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 138,
          "status": "ok",
          "timestamp": 1563456757689,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "O1mUMQqFq4XI",
        "outputId": "2b4462dd-3e6f-4090-c536-8627fd21e24b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "bias of weighted is -4.37849137373\n",
            "rmse of weighted is 4.50105698077\n"
          ]
        },
        {
          "data": {
            "image/png": 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U06ZNazQ3oUOHDlq2bJmys7OVk5Ojv//97+rYsaOio6OVkpKiBx54wKYjAQAA\nANo+2wOCJP3gBz/QD37wgyvaZtKkSZo0aVIrVQQAAAD4J58ICAAA1MuNm2x3CQDg1wgIAACfkudI\ns7sEAPBrtt7FCAAAAIBvISAAAAAAMAgIAAAAAAwCAgAAAACDgAAAAADAICAAAAAAMAgIAAAAAAwC\nAgAAAACDgAAAAADA4EnKAACggVmLt3itr8WzRnutLwDuISAAAHxKfG6mWc5zpNlWBwD4KwICAMCn\nODZmmWUCAgB4H3MQAAAAABgEBAAAAAAGAQEAAACAQUAAAAAAYBAQAAAAABgEBAAAAAAGAQEAAACA\nQUAAAAAAYBAQAAAAABgEBAAAAABGJ7sLAADgUrlxk+0uAQD8GgEBAOBT8hxpdpcAAH6NS4wAAAAA\nGAQEAAAAAAYBAQAAAIBBQAAAAABgEBAAAAAAGAQEAAAAAAYBAQAAAIBBQAAAAABgEBAAAAAAGAQE\nAAAAAEYnuwsAAOBS8bmZZjnPkWZbHQDgrwgIAACf4tiYZZYJCADgfVxiBAAAAMAgIAAAAAAwCAgA\nAAAADAICAAAAAIOAAAAAAMAgIAAAAAAwCAgAAAAADAICAAAAAIOAAAAAAMAgIAAAAAAwOtldAAAA\nl8qNm2x3CQDg1wgIAACfkudIs7sEAPBrXGIEAAAAwCAgAAAAADAICAAAAAAMAgIAAAAAg4AAAAAA\nwCAgAAAAADC4zSkAALDNrMVbLru+qrpakhS87fLt3LF41ugW7wPwBz53BuE3v/mNBg0apEGDBun1\n119vtt369euVkpKi22+/XcOHD9ePfvQjZWdny+VyebFaAAAAoH3xqTMIH3/8sV577TV16NDhsh/0\nMzIy5HQ61aVLF40cOVIBAQHKz8/X/PnztWPHDi1ZskSWZXmxcgAAAKB98JmAUFNTo9mzZ6tXr166\n5ZZb9Le//a3Jdnl5eXI6nQoNDVV2drYiIiIkSadOnVJqaqo2bdqk1atXKzU11ZvlAwAAAO2Cz1xi\ntGTJEn3yySfKyMhQ165dm223fPlyWZal9PR0Ew4kqWfPnpo3b55cLpdWrFjhjZIBAK0gPjfT/AEA\neJ9PBISPPvpImZmZGjdunEaPHt1suxMnTqi4uFgBAQFyOByN1o8YMUJ9+vTRyZMntWfPnlasGADQ\nWhwbs8wfAID32R4Qampq9NRTT6lHjx761a9+ddm2xcXFkqQBAwaoc+fOTbaJjo5u0BYAAACA+2yf\ng/Cb3/wFckfJAAAcs0lEQVRGR44c0eLFi9W9e/fLtj127JgkKTw8vNk2YWFhDdoCAAAAcJ+tZxA+\n/PBDvfHGGxozZkyTlwx9U/X/3Qs5MDCw2TZBQUFyuVyqqqryWJ0AAACAv7AtIJw/f16zZ89Wt27d\nNHfuXLe2qb/1KbcwBQAAAFqHbZcYLVq0SKWlpXruued0zTXXuLVNcHCwpH+dSWhKdXW1LMsybd2R\nk5OjtWvXutU2OTlZ/fr1U2VlpXbt2uV2H/Acxt1evjD+VZd5D2jv/O3Yfel4fakWf+SJ8feF96+2\nirGzz/79+7VgwQK32iYmJiopKanFfdoWEP72t7+pQ4cOysnJUU5OToN1n376qSRpzZo12rx5s667\n7jotWLDAzD0oKytrdr/l5eWSLj9P4ZvKyspUUFDgVtu4uDi39wsAAAC0xNmzZ93+nBobG+uRPm2d\npFxXV6fCwsJm1x87dkzHjh0z8wmioqIkSYcOHVJNTU2TdzIqKipq0NYd4eHhbg9oSEiIJKlr164a\nOHCg232g5eq/vYiJibG5Ev/kS+MfvG2L3SV4Xf23p8FBQTZX4l2+cLz+Ova+wpPj7wvvX22NL733\n+5v6sQ8JCXH7c+qVfEF+ObYFhM2bNze7bvbs2Vq3bp2eeuoppaWlmdf79u2rqKgolZSUaMOGDRo/\nfnyD7QoKClReXq7Q0FANHz7c7VqSkpLcPh1z4MABVVZWur1vAAAA4LsaNGiQVq1a5dU+bX8OwuXU\nT0q+1IwZM+RyubRw4UKVlpaa1ysqKpSRkSHLsjR9+nRvlgkAAAC0G7Y/B6E5TYUDSYqPj1dKSoqc\nTqfGjRunUaNGKSAgQPn5+aqqqtKYMWM0adIkL1cLYNbiLXaXAAAAPMBnA8LlbmU6Z84cxcTEKDs7\nW4WFhaqtrVVkZKSSk5M1ceJEL1YJAPC03LjJdpcAAH7NJwPC888/r+eff/6ybRISEpSQkOCligAA\n3pLnSLO7BADwaz49BwEAAACAdxEQAAAAABgEBAAAAAAGAQEAAACAQUAAAAAAYBAQAAAAABgEBAAA\nAAAGAQEAAACAQUAAAAAAYBAQAAAAABid7C4AAIBLxedmmuU8R5ptdQCAvyIgAAB8imNjllkmIMCT\nZi3e4rW+Fs8a7bW+AE/jEiMAAAAABgEBAAAAgEFAAAAAAGAQEAAAAAAYBAQAAAAABgEBAAAAgEFA\nAAAAAGAQEAAAAAAYBAQAAAAABgEBAAAAgNHJ7gIAALhUbtxku0sAAL9GQAAA+JQ8R5rdJQCAX+MS\nIwAAAAAGAQEAAACAQUAAAAAAYBAQAAAAABgEBAAAAAAGAQEAAACAQUAAAAAAYBAQAAAAABgEBAAA\nAAAGAQEAAACA0cnuAgAAuFR8bqZZznOk2VYHAPgrAgIAwKc4NmaZZQICAHgflxgBAAAAMAgIAAAA\nAAwCAgAAAACDgAAAAADAICAAAAAAMAgIAAAAAAwCAgAAAACDgAAAAADAICAAAAAAMHiSMtCOzVq8\nxWP7qqquliQFb/PcPgEAgO8hIAAAfEpu3GS7SwAAv0ZAAAD4lDxHmt0lAIBfYw4CAAAAAIOAAAAA\nAMAgIAAAAAAwCAgAAAAADAICAAAAAIOAAAAAAMAgIAAAAAAwCAgAAAAADB6UBnjRrMVb7C4BAADg\nsmwLCBcvXtTOnTu1detW7d69W2VlZTp9+rR69uypYcOG6cc//rFiY2Ob3X79+vVyOp06ePCgamtr\nFRkZqaSkJKWkpMiyLC8eCQAAANB+2BYQdu7cqUceeUSWZalXr14aOnSogoKCdOjQIW3atEkbN27U\nY489pp///OeNts3IyJDT6VSXLl00cuRIBQQEKD8/X/Pnz9eOHTu0ZMkSQgIAtFHxuZlmOc+RZlsd\nAOCvbAsIlmUpPj5ekydP1m233dZg3YYNG5Senq5ly5bpjjvuaHAmIS8vT06nU6GhocrOzlZERIQk\n6dSpU0pNTdWmTZu0evVqpaamevV4AACe4diYZZYJCADgfbZNUh45cqSWLFnSKBxI0v3336/ExERJ\n0p///OcG65YvXy7LspSenm7CgST17NlT8+bNk8vl0ooVK1q3eAAAAKCd8tm7GA0ePFgul0vl5eXm\ntRMnTqi4uFgBAQFyOByNthkxYoT69OmjkydPas+ePd4sFwAAAGgXfDYgHD58WJLUu3dv81pxcbEk\nacCAAercuXOT20VHRzdoCwAAAMB9PhkQTp48qXXr1pl5CvWOHTsmSQoPD29227CwsAZtAQAAALjP\n5wJCbW2t0tPT9eWXX+p73/ueRo8ebdZVV1dLkgIDA5vdPigoSC6XS1VVVa1dKgAAANDu+FxAmDNn\njj744ANde+21evHFFxusc7lcksQtTAEAAIBW4lNPUl6wYIHefvtthYaGKisrS9dcc02D9cHBwZL+\ndSahKdXV1bIsy7R1R05OjtauXetW2+TkZPXr10+VlZXatWuX233Ac9ryuFdd5me3rWgPx9CW+dv4\n+9Lx+lIt/qitjX9b/l3VlPZ2PG3J/v37tWDBArfaJiYmKikpqcV9+kxAeOGFF7R69Wr16tVLmZmZ\nDW5hWq9+7kFZWVmz+6m/69Hl5il8U1lZmQoKCtxqGxcX5/Z+0TYszz1hdwkAgHbGm79bZjj6eK0v\neN/Zs2fd/px66bPDWsInAsKLL76ozMxM9ezZUytXrlRkZGST7aKioiRJhw4dUk1NTZN3MioqKmrQ\n1h3h4eFuD2hISIgkqWvXrho4cKDbfaDl6r+9iImJ8eh+g7dt8ej+2qv6b++Cg4JsrsQ/+ev4+8Lx\n+uvY+wrG/9t5+vfipVrrdy++Xf3Yh4SEuP059Uq+IL8c2wPCwoULtXLlSvXo0UMrV67UzTff3Gzb\nvn37KioqSiUlJdqwYYPGjx/fYH1BQYHKy8sVGhqq4cOHu11DUlKS26djDhw4oMrKSrf3DQAAAHxX\ngwYN0qpVq7zap62TlF966SW9+uqr6t69u1auXKlBgwZ96zYzZsyQy+XSwoULVVpaal6vqKhQRkaG\nLMvS9OnTW7NsAEAryo2bbP4AALzPtjMImzdv1iuvvCLLstS/f/9mk9ENN9zQ4AN/fHy8UlJS5HQ6\nNW7cOI0aNUoBAQHKz89XVVWVxowZo0mTJnnrMAAAHpbnSLO7BADwa7YFhDNnzpjble7du1d79+5t\nst2IESManRGYM2eOYmJilJ2drcLCQtXW1ioyMlLJycmaOHFiq9cOAAAAtFe2BYTExEQlJiZ+5+0T\nEhKUkJDgwYoAAAAA+NyD0gAAAADYh4AAAAAAwCAgAAAAADAICAAAAAAMAgIAAAAAg4AAAAAAwCAg\nAAAAADAICAAAAAAM2x6UBgBAU+JzM81yniPNtjoAwF8REAAAPsWxMcssExAAwPu4xAgAAACAQUAA\nAAAAYBAQAAAAABgEBAAAAAAGAQEAAACAQUAAAAAAYBAQAAAAABgEBAAAAAAGAQEAAACAQUAAAAAA\nYHSyuwAAAC6VGzfZ7hIAwK8REAAAPiXPkWZ3CQDg17jECAAAAIDBGQQAAIA2bNbiLa2276rqaklS\n8Lav+1g8a3Sr9QXfwRkEAAAAAAYBAQAAAIBBQAAAAABgEBAAAAAAGAQEAAAAAAYBAQAAAIBBQAAA\nAABgEBAAAAAAGDwoDQDgU+JzM81yniPNtjoAwF8REAAAPsWxMcssExAAwPu4xAgAAACAQUAAAAAA\nYBAQAAAAABgEBAAAAAAGAQEAAACAQUAAAAAAYBAQAAAAABg8BwE+Kb/oM52/UNfgtU8PV0uSvrSO\nebSv2jqXOnawPLpPAACAtoqAAJ+U+8ERna083+C1quqvA8LHpYc82tfFi3Xq2LmjR/cJAADQVnGJ\nEQAAAACDMwgAAJ+SGzfZ7hIAwK8REAAAPiXPkWZ3CQDg17jECAAAAIBBQAAAAABgEBAAAAAAGMxB\nAAAAgFtmLd7i1f4Wzxrt1f7wNc4gAAAAADAICAAAAAAMAgIAAAAAg4AAAAAAwCAgAAAAADAICAAA\nAAAMbnMKAPAp8bmZZjnPkWZbHQDgrwgIAACf4tiYZZYJCADgfW06IKxfv15Op1MHDx5UbW2tIiMj\nlZSUpJSUFFmWZXd5AAAAQJvTZgNCRkaGnE6nunTpopEjRyogIED5+fmaP3++duzYoSVLlhASAAAA\ngCvUJgNCXl6enE6nQkNDlZ2drYiICEnSqVOnlJqaqk2bNmn16tVKTU21uVIAAACgbWmTdzFavny5\nLMtSenq6CQeS1LNnT82bN08ul0srVqywsUIAAACgbWpzAeHEiRMqLi5WQECAHA5Ho/UjRoxQnz59\ndPLkSe3Zs8eGCgEAAIC2q80FhOLiYknSgAED1Llz5ybbREdHN2gLAAAAwD1tbg7CsWPHJEnh4eHN\ntgkLC2vQFgAAAG3PrMVbvNbX4lmjvdaXr2tzZxCqq6slSYGBgc22CQoKksvlUlVVlbfKAgAAANqF\nNhcQXC6XJHELUwAAAKAVtLlLjIKDgyX960xCU6qrq2VZlmn7bXJycrR27Vq32k6ZMkXdunVTZWWl\ndu3a5dY2uHKjB3VQneubZ4maP2vUElVf1Ym86Y6r7C7Az/nP+B9Yvtws33eDLxy3L9Tgzxh/e/nP\n+Pvq57rjx49rwYIFbrVNTExUUlJSi/tscwGhfu5BWVlZs23Ky8sbtP02ZWVlKigocKvttGnT3GqH\nlgkJ8t6PZg/3ciQAL6nsGWOWr7WxDgDwBR06dHD7c2psbKxH+mxzASEqKkqSdOjQIdXU1DR5J6Oi\noqIGbb9NeHi42wNaUVEhSaqrqzOToeEd+/fv19mzZxUSEqJBgwbZXY7fYfztxfjbh7G3F+NvL8bf\nPsePH1eHDh1UUVHh9udUd78c/zaWq/6i/jYkKSlJJSUleuGFFzR+/PgG6woKCvSTn/xEoaGh2rZt\nm8f7Tk1NVUFBgWJjY7Vq1SqP7x/NY+ztxfjbi/G3D2NvL8bfXoy/fewc+zY3SVmSZsyYIZfLpYUL\nF6q0tNS8XlFRoYyMDFmWpenTp9tYIQAAANA2tblLjCQpPj5eKSkpcjqdGjdunEaNGqWAgADl5+er\nqqpKY8aM0aRJk+wuEwAAAGhz2mRAkKQ5c+YoJiZG2dnZKiwsVG1trSIjI5WcnKyJEyfaXR4AAADQ\nJrXZgCBJCQkJSkhIsLsMAAAAoN1ok3MQAAAAALQOAgIAAAAAg4AAAAAAwCAgAAAAADAICAAAAACM\njvPmzZtndxFtzeDBgxUbG6vBgwfbXYrfYeztxfjbi/G3D2NvL8bfXoy/fewae8vlcrm82iMAAAAA\nn8UlRgAAAAAMAgIAAAAAg4AAAAAAwCAgAAAAADAICAAAAAAMAgIAAAAAo5PdBbQHdXV1+sMf/qA/\n//nP+sc//qFz584pJCREQ4YM0b/927/pBz/4gd0ltkv33XefPvvss29t94tf/EIzZ870QkX+a/v2\n7frDH/6gjz76SKdPn1b37t11/fXX6/vf/74effRRu8trlwoKCvSTn/zksm3++Mc/6pZbbvFSRf7t\n4MGDSkpK0sWLF3XTTTdp/fr1dpfUbu3evVvr1q1TSUmJjh8/rtOnT6tTp06KiIjQPffco0ceeUQ9\ne/a0u8x269NPP9XWrVv13nvv6ciRIyovL1fnzp01YMAA3X///UpJSVFAQIDdZbZL586d09/+9jcV\nFRWpqKhIJSUl+uqrrzR69Gi98sorHu2LgNBCtbW1mjp1qvLz83XVVVcpJiZGV199tY4ePaq///3v\n2r59u9LS0vT000/bXWq743A49MUXXzS57syZM9q8ebMsy9Idd9zh5cr8h8vl0pw5c/TWW28pICBA\nw4YNU2hoqCoqKvS///u/evPNNwkIraxXr1666667Gr1uWZauvvpqGyryP7W1tXr66adVV1cny7Ls\nLqfd27p1q/74xz8qPDxcN910k66++mqdOXNGRUVF+v3vf6+cnBytWrVKkZGRdpfaLk2ePFmff/65\nrrrqKg0dOlTR0dGqqKjQnj17tGfPHr3zzjvKzMxUSEiI3aW2O0eOHNGTTz7Z4H2mtd5zCAgt9Kc/\n/Un5+fkKDw/XmjVr1KdPH7Puvffe04wZM5SVlaXx48fzBEIP+4//+I9m17366qvavHmzrr/+esXE\nxHixKv+yaNEivfXWWxo2bJiWLFnS4Off5XJp3759NlbnHyIjI/X888/bXYZf+93vfqeSkhJNmjRJ\nq1evtrucdm/8+PF6+OGH1bdv3wavf/XVV3rmmWf017/+VXPnztWqVatsqrB9u/HGGzVr1iw5HA4F\nBgaa1z/77DPNmDFDJSUlev7553lfagXBwcFKTk7W0KFDNWTIEBUXF2vu3Lmt0hdzEFqooKBAlmXp\n4YcfbvDhSJL+3//7f+bb6z179thRnt/605/+JMuylJycbHcp7dY//vEPvf7667r66qv1yiuvNPr5\ntyxLQ4cOtak6wDv279+vV155RXFxcYqLi7O7HL9www03NAoHktSlSxfzxdGuXbt04cIFb5fmF15/\n/XUlJiY2CAeSdO2112revHlyuVzasGGDLl68aFOF7VdERIQWLFighx9+WNHR0ercuXOr9UVAaCF3\n/+dwqt97PvzwQx0+fFgdO3bU+PHj7S6n3VqzZo3q6uo0YcIE9ejRw+5yAK+7ePGinn76aQUHB7fa\nt3i4Mh07djT/rV+G90RFRUmSzp8/r9OnT9tcDVqCS4xa6K677tLatWvldDo1duxYhYWFmXXbt2/X\njh071KdPH91zzz02Vulf/vSnP0mSRo8erV69etlcTfv13nvvSfr6TNnJkyf1l7/8RYcPH1aXLl00\ndOhQxcXFteq3G/haRUWFli5dqn/+858KDAzUzTffrO9///uENi9YtmyZDhw4oP/6r/9iUqwPuHDh\ngl566SVJ0j333KMOHfgO1NuOHDkiSQoICFD37t1trgYtQUBooQceeEAffPCB3nrrLcXHx+v2229X\njx49dOzYMX388ce67bbb9Pzzzzc6FYfWce7cOeXm5nJ5USurqakxvwgOHTqkmTNnqrq62qx3uVwK\nCwvT0qVLNWTIELvK9AuffPKJXn75ZfN3l8ulBQsW6IknntCPf/xjGytr34qLi7VixQrdfffd+uEP\nf2h3OX7pyJEj+t3vfifLsvTFF1+oqKhIp06d0q233soZHZssX75cknTvvfdyJ6M2joDgAc8++6wi\nIyO1aNEi5efnm9e7d++uUaNG8S22F/31r39VdXW1evfurbvvvtvuctqts2fPyuVyybIsPf/88xoy\nZIh+9atf6aabblJZWZkWL16s//mf/9GMGTP0l7/8hW+zW0G3bt30yCOPaMyYMbr++usVGBioI0eO\naM2aNXr77bf1n//5n7rqqqs0YcIEu0ttdy5cuKCnnnpKXbp00bPPPmt3OX7r5MmTeueddxq8NmrU\nKD377LPq3bu3TVX5r5ycHG3YsEGBgYGaNWuW3eWghfw6ILz44ot69913r3i7rKwshYaGSpIqKyv1\nxBNPKD8/XzNnztS4cePUu3dvHT58WCtWrNDLL7+szZs3Kzs7W0FBQZ4+hDbLE2PflPrJyYmJiZxe\nvoyWjn9dXZ15rVu3blq5cqWCg4MlSQMGDNDSpUv14IMP6uDBg8rOztZjjz3msdrbA0/8/A8ePLjR\nndEGDRqkZ599VgMHDtT8+fO1aNEiPfjgg3yTdwlPjP3SpUt16NAhZWRkNJqcj8vz5Ht/TEyMSkpK\nJEknTpxQQUGBlixZorFjx+rFF19k0ngTWut3b35+vubOnasOHTpo/vz5uv7661tQZfvUWmPfWvw6\nIHz++ec6fPjwFW1jWVaDmfkvvPCCtm3bpieeeEJTp041rw8cOFCLFi3S6dOn9f7772vlypV6/PHH\nPVV6m+eJsf+mw4cPa/fu3bIsS0lJSS2ssH1r6fjXhwFJuv/++xv8vb7tQw89pPnz5+uDDz4gIHxD\na/z8XyolJUVLly7V6dOn9dFHH+n222//DlW2Ty0d+3379um1115TbGysHnrooVaosH1rrZ/9Pn36\naNy4cRo+fLgefPBBzZ49W8OHD+dMwje0xvgXFhZq5syZunjxon79619r7NixLayyfWrt931Ps1wu\nl8uWntuBuro6DRs2TBcuXNCWLVua/CZp3bp1evrpp3XbbbdpzZo1NlTpPxYuXKhXX31VI0aM4P7X\nXjBy5EidOXNGTz75ZJMPQ9u6datmzJih66+/Xrm5uTZU6N8efvhhffTRR1q0aJEeeOABu8tpN5Yu\nXaqlS5fqxhtvbDQx+csvv9T+/fsVGBhobvH73HPPKSIiwo5S/dZPf/pTbd26Vc8995wSExPtLqdd\n+/DDDzV16lSdO3eu2d8FaD1r167V7NmzeZKyr6moqFBNTY0sy1LXrl2bbNOtWzdJXz/ZF62nrq5O\n77zzjizL0o9+9CO7y/ELQ4YM0fvvv9/srezqn3LNpXX2qP//wvh7nmVZ+uSTT/TJJ580uf6rr75S\nYWGhLMtSVVWVl6tDfXCrqKiwuZL2bc+ePZo2bZrOnTunWbNmEQ7aGQJCC/To0UOdO3fWhQsX9NFH\nH+l73/teoza7d++WJPXr18/b5fmVrVu36vPPP1fXrl3lcDjsLscvjBkzRu+9916DifmXev/99yVJ\n0dHR3iwL+vrhXYcPH1aHDh14WJ2HPf74481eLlpQUKCf/OQnGjBggNavX+/lyiBJtbW1KiwslCSu\ng29FH3/8saZOnarq6mr9/Oc/1/Tp0+0uCR7GLM4WCAgI0L333mtuK3j06NEG6//+97/rjTfekGVZ\nSkhIsKlK/1A/OTkhIUFdunSxuxy/kJiYqL59+2rv3r1asWJFg3W5ubn6y1/+ok6dOmnixIk2Vdi+\nrVq1qsmzN7t379YvfvELWZalBx54gLuood1ZsmSJysvLG71+6tQpzZ49W6WlpQoLC9Ndd91lQ3Xt\n3969ezVlyhRVVVVp5syZmjlzpt0loRUwB6GFTpw4oUmTJqmsrEwBAQG69dZbdc0116i0tFTFxcWy\nLEtjx47Vf//3f9tdart16tQp3X333aqtrdWbb76pW265xe6S/MZHH32kRx99VNXV1br++uvNbU73\n7dunDh066Ne//rVSUlLsLrNdGjFihM6dO6fIyEiFhYWpS5cuOnLkiA4cOCDp6zu8LF++vNEEcrSe\n+jMIN910E2cQWtGgQYPUsWNHDRw4UBEREerYsaPKy8tVXFys8+fPq1evXlq+fLl5qi88KzY2VmfP\nnlX37t113333Ndvuqaee4hbXreCxxx7TyZMnJX39+efo0aMKCQnRDTfcYNrMnDmzxQ/o5RKjFurT\np4/WrVunrKwsvfvuuyopKdFX/799O1RVLYgCMLzmAbb4ELYTBKsWg00QTFajwVfwNXwN9QUsgkUM\nll3sdjfoKcJJd6V708F74N7vazNMGKb9DOvzM1qtVgwGg5hOpwYE32y73cbr9YpOpyMO/rJutxu7\n3S7W63UcDofY7/dRVVWMRqOYz+fR6/V++or/rMViEafTKa7Xa5zP53g+n9Fut6Pf78d4PI7JZBKl\nlJ++5n+nlOLd32y1WsXpdIq6ruN4PMbj8YiqquLj4yOGw2HMZrM/zgXyfU3TRCkl7vd7bDab354p\npcRyuRQIb1DXddxut1yXUqJpmrhcLrn3awbwO/wgAAAAyQwCAACQBAIAAJAEAgAAkAQCAACQBAIA\nAJAEAgAAkAQCAACQBAIAAJAEAgAAkAQCAACQBAIAAJAEAgAAkAQCAACQBAIAAJAEAgAAkAQCAACQ\nBAIAAJC+AAJZV7dfEkXjAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7fc7f279a190\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 262,
              "width": 388
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "show_estimates(estimates_miss)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "y4uYEPCnoUzG"
      },
      "source": [
        "One reasonable strategy is to expand the set of balancing covariates and hope it will make the model less \"misspecified\". If we additional balance the two-way interactions and the log transformation, the bias indeed reduces."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "eY4OL0uFmbgk"
      },
      "outputs": [],
      "source": [
        "formula = (\"-1 + (x1 + x2 + x3 + x4)**2 + I(np.log(x1)) + I(np.log(x2)) + \"\n",
        "           \"I(np.log(x3)) + I(np.log(x4))\")\n",
        "\n",
        "estimates_expanded = pd.DataFrame([estimate_att(formula) for i in xrange(1000)])\n",
        "estimates_expanded.columns = ['raw', 'weighted']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "height": 313
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 290,
          "status": "ok",
          "timestamp": 1563456781447,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "o9TjJbMIq8dv",
        "outputId": "eae4313d-03ba-4e62-d8fd-5932d11aa09b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "bias of weighted is -1.88003551222\n",
            "rmse of weighted is 2.07831395567\n"
          ]
        },
        {
          "data": {
            "image/png": 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4BwAAACyC8A8AAABYBOEfAAAAsIiBZhcAAIA721JnmV0CAAQcwj8AwCeVp+eZXQIABBym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\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7fc7f2cda510\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 262,
              "width": 383
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "show_estimates(estimates_expanded)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "1Ji6iROgDYfv"
      },
      "source": [
        "If the model was misspecified in the sense that more covariates are included than necessary, the causal estimate remains unbiased."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "8ZsBSFkVB6-E"
      },
      "outputs": [],
      "source": [
        "formula = \"-1 + z1 + z2 + z3 + z4 + x1 + x2 + x3 + x4\"\n",
        "estimates_redundant = pd.DataFrame([estimate_att(formula) for i in range(1000)])\n",
        "estimates_redundant.columns = ['raw', 'weighted']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "height": 313
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 159,
          "status": "ok",
          "timestamp": 1563456798742,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "gG0ToCi4rUzx",
        "outputId": "86ad654b-4a66-4ec7-cdb2-1d7b5ca37c43"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "bias of weighted is -0.00229483538445\n",
            "rmse of weighted is 0.0891054715229\n"
          ]
        },
        {
          "data": {
            "image/png": 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Sbdy4UZMmTWrXLz8/Xy6XSwMHDlRycrICAwNVVlamFStWaP/+/Vq7di1hAQAA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\nhBBCCCFE5H//ol0nbkW00wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x7fc7f2576a90\u003e"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 262,
              "width": 389
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "show_estimates(estimates_redundant)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "ITCnSqDiyjIx"
      },
      "source": [
        "## Benchmark Execution Time"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "IknZ8jA51hbE"
      },
      "source": [
        "The execution time is generally linear with respect to the sample size. With 1 million control units, it takes around 1 second to find the weights."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "height": 170
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 202,
          "status": "ok",
          "timestamp": 1563456798977,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "i21mXoaxywOn",
        "outputId": "7de07cb5-9799-4caa-dc04-c18287336c5b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "count    100.000000\n",
              "mean       0.001823\n",
              "std        0.000230\n",
              "min        0.001637\n",
              "25%        0.001699\n",
              "50%        0.001750\n",
              "75%        0.001873\n",
              "max        0.003199\n",
              "dtype: float64"
            ]
          },
          "execution_count": 13,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.random.seed(123)\n",
        "simulation = ec.data.kang_schafer.Simulation(size=2000)\n",
        "x1 = simulation.covariates[simulation.treatment == 1]\n",
        "x0 = simulation.covariates[simulation.treatment == 0]\n",
        "pd.Series(timeit.repeat(\n",
        "    'ec.maybe_exact_calibrate(x0, x1)',\n",
        "    setup='from __main__ import x1, x0, ec',\n",
        "    repeat=100,\n",
        "    number=1)).describe()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "height": 170
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 1117,
          "status": "ok",
          "timestamp": 1563456800133,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 240
        },
        "id": "pIdIjcpi077X",
        "outputId": "d12c2681-eaa2-41af-a8f5-83c04078688d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "count    100.000000\n",
              "mean       0.010971\n",
              "std        0.000702\n",
              "min        0.010231\n",
              "25%        0.010383\n",
              "50%        0.010658\n",
              "75%        0.011522\n",
              "max        0.013335\n",
              "dtype: float64"
            ]
          },
          "execution_count": 14,
          "metadata": {
            "tags": []
          },
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.random.seed(123)\n",
        "simulation = ec.data.kang_schafer.Simulation(size=20000)\n",
        "x1 = simulation.covariates[simulation.treatment == 1]\n",
        "x0 = simulation.covariates[simulation.treatment == 0]\n",
        "pd.Series(timeit.repeat(\n",
        "    'ec.maybe_exact_calibrate(x0, x1)',\n",
        "    setup='from __main__ import x1, x0, ec',\n",
        "    repeat=100,\n",
        "    number=1)).describe()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "last_runtime": {
        "build_target": "",
        "kind": "local"
      },
      "name": "causal_inference_kang_schafer.ipynb",
      "provenance": [],
      "version": "0.3.2"
    },
    "kernelspec": {
      "display_name": "Python 2",
      "name": "python2"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}