Experimentos_Aleatorizados.ipynb

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      "name": "Experimentos Aleatorizados.ipynb",
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/rpasquini/herramientas-econometricas/blob/main/Experimentos_Aleatorizados.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "code",
      "metadata": {
        "id": "z27Cwxw3dlH7",
        "outputId": "59e7f013-eec6-40ff-823c-3830e34bacfe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        }
      },
      "source": [
        "import pandas as pd\n",
        "import statsmodels.api as sm  \n",
        "from scipy import stats  \n",
        "import numpy as np"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FQxEYR1Fdist"
      },
      "source": [
        "df=pd.read_csv('https://raw.githubusercontent.com/rpasquini/econometrics_and_causality/master/happiness_on_tap_extract.csv')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z79v6Q66f5Ju"
      },
      "source": [
        "Extracto de datos de: \n",
        "\n",
        "[Devoto, F., Duflo, E., Dupas, P., Parienté, W., & Pons, V. (2012). Happiness on tap: piped water adoption in urban Morocco. American Economic Journal: Economic Policy, 4(4), 68-99.](https://web.stanford.edu/~pdupas/MoroccoWaterConnections.pdf\n",
        ")\n",
        "\n",
        "Las variables fueron modificadas para el proposito de este ejercicio. \n",
        "\n",
        "**Descripción de variables**\n",
        "\n",
        "\n",
        "motivacion: Dummy = 1 si el hogar recibió motivación para conexión \\\n",
        "conectado: Dummy = 1 si el hogar se conectó a la red de agua \\\n",
        "sexojefe: Dummy = 1 Masculino, 0 Femenino \\\n",
        "edadjefe: Edad Jefe de Hogar \\\n",
        "jefesabeleer: Dummy=1 Jefe sabe leer \\\n",
        "jefesabeescribir: Dummy=1 Jefe sabe escribir \\\n",
        "pdiasfueaescuela: Porcentaje dias hijos fueron a la escuela.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p1Xb2xlweJEP",
        "outputId": "02567998-242c-4e06-98c8-7849b6a83928",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        }
      },
      "source": [
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>random_id</th>\n",
              "      <th>motivacion</th>\n",
              "      <th>conectado</th>\n",
              "      <th>sexojefe</th>\n",
              "      <th>edadjefe</th>\n",
              "      <th>jefesabeleer</th>\n",
              "      <th>jefesabeescribir</th>\n",
              "      <th>pdiasfueaescuela</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>37.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
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              "      <th>1</th>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>45.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>57.142860</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>50.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>85.714287</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>7</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>54.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>85.714287</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>8</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>66.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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            ],
            "text/plain": [
              "   random_id  motivacion  ...  jefesabeescribir  pdiasfueaescuela\n",
              "0          1           0  ...               1.0               NaN\n",
              "1          3           1  ...               0.0         57.142860\n",
              "2          5           0  ...               1.0         85.714287\n",
              "3          7           1  ...               1.0         85.714287\n",
              "4          8           0  ...               0.0               NaN\n",
              "\n",
              "[5 rows x 8 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c4O9WsOMps3b",
        "outputId": "9035dbe1-4d7c-4abe-bc6a-58b1a15f1dc9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        }
      },
      "source": [
        "df.groupby('motivacion').count()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "    .dataframe thead th {\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>random_id</th>\n",
              "      <th>conectado</th>\n",
              "      <th>sexojefe</th>\n",
              "      <th>edadjefe</th>\n",
              "      <th>jefesabeleer</th>\n",
              "      <th>jefesabeescribir</th>\n",
              "      <th>pdiasfueaescuela</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>motivacion</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>377</td>\n",
              "      <td>377</td>\n",
              "      <td>377</td>\n",
              "      <td>372</td>\n",
              "      <td>372</td>\n",
              "      <td>372</td>\n",
              "      <td>147</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>411</td>\n",
              "      <td>411</td>\n",
              "      <td>411</td>\n",
              "      <td>407</td>\n",
              "      <td>404</td>\n",
              "      <td>404</td>\n",
              "      <td>173</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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            ],
            "text/plain": [
              "            random_id  conectado  ...  jefesabeescribir  pdiasfueaescuela\n",
              "motivacion                        ...                                    \n",
              "0                 377        377  ...               372               147\n",
              "1                 411        411  ...               404               173\n",
              "\n",
              "[2 rows x 7 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kOVdGbUGjcvu"
      },
      "source": [
        "df=df.dropna()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WC4uhOw9ePqL"
      },
      "source": [
        "dias_tratados=df.pdiasfueaescuela.loc[df.motivacion==1]\n",
        "dias_control=df.pdiasfueaescuela.loc[df.motivacion==0]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qMJzBFXLrogW"
      },
      "source": [
        "## Test de medias (supuesto varianzas son iguales)\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0floEgWJjq7u",
        "outputId": "824af8e2-6c4e-4d08-f591-1fc268102053",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "stats.ttest_ind(dias_tratados, dias_control, equal_var=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_indResult(statistic=-1.5002574789125818, pvalue=0.13454932763122404)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_v5YvTRQtEuL"
      },
      "source": [
        "#Equivalencia del test a través de estimar OLS \n",
        "\n",
        "\n",
        "\n",
        "$pdiasescuela_i=\\beta_0+\\beta_1motivacion_i+\\epsilon_i$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "svIPzXUDjVlI"
      },
      "source": [
        "def ols(lista, data):\n",
        "  \"\"\" \n",
        "  Funcion que realiza la regresion OLS\n",
        "  La primera variable de la lista es la dependiente, el resto son las explicativas\n",
        "  data es la base de datos\n",
        "  \"\"\"\n",
        "  datos=data[lista]\n",
        "  # el metodo dropna() me permite eliminar las filas que tienen algun valor missing\n",
        "  datos=datos.dropna()\n",
        "  Y=datos[lista[0]]\n",
        "  X=datos[lista[1:]]\n",
        "  X=sm.add_constant(X)\n",
        "  modelo=sm.OLS(Y,X)\n",
        "  modeloajustado=modelo.fit()\n",
        "  print(modeloajustado.summary())\n",
        "  return modeloajustado"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Up6QXV-MkAfd",
        "outputId": "b1c43fb7-740e-4953-fa0b-fa15c09951f9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 474
        }
      },
      "source": [
        "ols(['pdiasfueaescuela', 'motivacion'], df)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:       pdiasfueaescuela   R-squared:                       0.007\n",
            "Model:                            OLS   Adj. R-squared:                  0.004\n",
            "Method:                 Least Squares   F-statistic:                     2.251\n",
            "Date:                Thu, 30 Jul 2020   Prob (F-statistic):              0.135\n",
            "Time:                        21:32:20   Log-Likelihood:                -1476.3\n",
            "No. Observations:                 317   AIC:                             2957.\n",
            "Df Residuals:                     315   BIC:                             2964.\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==============================================================================\n",
            "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const         62.1331      2.116     29.366      0.000      57.970      66.296\n",
            "motivacion    -4.3219      2.881     -1.500      0.135      -9.990       1.346\n",
            "==============================================================================\n",
            "Omnibus:                       33.768   Durbin-Watson:                   1.885\n",
            "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               40.136\n",
            "Skew:                          -0.847   Prob(JB):                     1.93e-09\n",
            "Kurtosis:                       2.586   Cond. No.                         2.72\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<statsmodels.regression.linear_model.RegressionResultsWrapper at 0x7f81ea06bb70>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fsZ0Fn8PzMt3"
      },
      "source": [
        "# Randomnization Inference Approach\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P48CytdafqA7"
      },
      "source": [
        "lista=[[\"Buenos Aires\",1,1],[\"Catamarca\",1,1],[\"Chaco\",1,1],[\"Chubut\",1,1],[\"Córdoba\",1,0],[\"Corrientes\",0,0],[\"Entre Ríos\",0,0],[\"Formosa\",0,0],[\"Jujuy\",0,0],[\"La Pampa\",0,0]]\n",
        "variables=['provincia',\"T\",\"Y\"]\n",
        "df=pd.DataFrame(lista, columns=variables)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DdPN8Y1jmrhD",
        "outputId": "9aa38f87-7b35-4fa0-c7de-de7af2b400c1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 356
        }
      },
      "source": [
        "df"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>provincia</th>\n",
              "      <th>T</th>\n",
              "      <th>Y</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Buenos Aires</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Catamarca</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Chaco</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Chubut</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Córdoba</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Corrientes</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>Entre Ríos</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Formosa</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Jujuy</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>La Pampa</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      provincia  T  Y\n",
              "0  Buenos Aires  1  1\n",
              "1     Catamarca  1  1\n",
              "2         Chaco  1  1\n",
              "3        Chubut  1  1\n",
              "4       Córdoba  1  0\n",
              "5    Corrientes  0  0\n",
              "6    Entre Ríos  0  0\n",
              "7       Formosa  0  0\n",
              "8         Jujuy  0  0\n",
              "9      La Pampa  0  0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qrww9UchpaMQ",
        "outputId": "50014456-59eb-407d-ac13-1567c53f0eae",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "  Y_tratadas=df['Y'].loc[df['T']==1]\n",
        "  Y_control=df['Y'].loc[df['T']==0]\n",
        "  dif_means=np.mean(Y_tratadas)-np.mean(Y_control) #computamos la diferencia de medias\n",
        "  dif_means"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tInPgE61vZ5Z",
        "outputId": "75672844-c3c7-4593-fd41-447b6714a3fb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        }
      },
      "source": [
        "from itertools import permutations \n",
        "import numpy as np\n",
        "iteradorcomb=combinations(df.index,5)  #Generamos un iterador de permutaciones. Cada vez que invoquemos la funcion next() sobre él me devolverá una iteracion.\n",
        "listadediferencias=[]\n",
        "for i in range(0,252):\n",
        "  posicionestratadosfalso=next(iteradorcomb)\n",
        "  df.loc[df.index.isin(posicionestratadosfalso),'falsotratamiento']=1\n",
        "  df.loc[~df.index.isin(posicionestratadosfalso),'falsotratamiento']=0\n",
        "  Y_tratadas=df['Y'].loc[df['falsotratamiento']==1]\n",
        "  Y_control=df['Y'].loc[df['falsotratamiento']==0]\n",
        "  dif_means=np.mean(Y_tratadas)-np.mean(Y_control) #computamos la diferencia de medias\n",
        "  listadediferencias.append(dif_means)\n",
        "\n",
        "pd.DataFrame(listadediferencias).hist()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f81ea032198>]],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QMVHgTg4o2A6",
        "outputId": "296ed1db-486e-440c-c9d1-dcda35acb28d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "stats.percentileofscore(listadediferencias,0.8)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "99.0079365079365"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        }
      ]
    }
  ]
}