python-dml-401k-Sensitivity.ipynb

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   "source": [
    "# Inference on Predictive and Causal Effects in High-Dimensional Nonlinear Models"
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    "## Impact of 401(k) on  Financial Wealth\n",
    "\n",
    "As a practical illustration of the methods developed in this lecture, we consider estimation of the effect of 401(k) eligibility and participation \n",
    "on accumulated assets. 401(k) plans are pension accounts sponsored by employers. The key problem in determining the effect of participation in 401(k) plans on accumulated assets is saver heterogeneity coupled with the fact that the decision to enroll in a 401(k) is non-random. It is generally recognized that some people have a higher preference for saving than others. It also seems likely that those individuals with high unobserved preference for saving would be most likely to choose to participate in tax-advantaged retirement savings plans and would tend to have otherwise high amounts of accumulated assets. The presence of unobserved savings preferences with these properties then implies that conventional estimates that do not account for saver heterogeneity and endogeneity of participation will be biased upward, tending to overstate the savings effects of 401(k) participation.\n",
    "\n",
    "One can argue that eligibility for enrolling in a 401(k) plan in this data can be taken as exogenous after conditioning on a few observables of which the most important for their argument is income. The basic idea is that, at least around the time 401(k)’s initially became available, people were unlikely to be basing their employment decisions on whether an employer offered a 401(k) but would instead focus on income and other aspects of the job. "
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   "source": [
    "### Data\n",
    "\n",
    "The data set can be downloaded from the github repo\n"
   ]
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  {
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   "source": [
    "# Import relevant packages\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.model_selection import cross_val_score, cross_val_predict, KFold\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.linear_model import LassoCV, RidgeCV, ElasticNetCV, LinearRegression, Ridge, Lasso, LogisticRegressionCV\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.ensemble import GradientBoostingRegressor, GradientBoostingClassifier\n",
    "from sklearn.ensemble import RandomForestRegressor, RandomForestClassifier\n",
    "from sklearn.tree import DecisionTreeRegressor, DecisionTreeClassifier\n",
    "import patsy\n",
    "import warnings\n",
    "from sklearn.base import BaseEstimator, clone\n",
    "import statsmodels.api as sm\n",
    "from IPython.display import Markdown\n",
    "import wget\n",
    "import os\n",
    "import seaborn as sns\n",
    "warnings.simplefilter('ignore')\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6e66e77f",
   "metadata": {},
   "outputs": [],
   "source": [
    "file = \"https://raw.githubusercontent.com/CausalAIBook/MetricsMLNotebooks/main/data/401k.csv\"\n",
    "data = pd.read_csv(file)"
   ]
  },
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       "count  9.915000e+03  ...  9915.000000  9915.000000  9915.000000  9915.000000   \n",
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       "\n",
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       "      <td>1800</td>\n",
       "      <td>0</td>\n",
       "      <td>200000</td>\n",
       "      <td>15900</td>\n",
       "      <td>184100</td>\n",
       "      <td>7549</td>\n",
       "      <td>7049</td>\n",
       "      <td>9349</td>\n",
       "      <td>8849</td>\n",
       "      <td>192949</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2487</td>\n",
       "      <td>-6013</td>\n",
       "      <td>2487</td>\n",
       "      <td>-6013</td>\n",
       "      <td>-6013</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>300000</td>\n",
       "      <td>90000</td>\n",
       "      <td>210000</td>\n",
       "      <td>10625</td>\n",
       "      <td>-2375</td>\n",
       "      <td>10625</td>\n",
       "      <td>-2375</td>\n",
       "      <td>207625</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 44 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    ira  a401    hval  hmort  hequity   nifa  net_nifa    tfa  net_tfa  \\\n",
       "0     0     0   69000  60150     8850    100     -3300    100    -3300   \n",
       "1     0     0   78000  20000    58000  61010     61010  61010    61010   \n",
       "2  1800     0  200000  15900   184100   7549      7049   9349     8849   \n",
       "3     0     0       0      0        0   2487     -6013   2487    -6013   \n",
       "4     0     0  300000  90000   210000  10625     -2375  10625    -2375   \n",
       "\n",
       "   tfa_he  ...  i3  i4  i5  i6  i7  a1  a2  a3  a4  a5  \n",
       "0    5550  ...   1   0   0   0   0   0   1   0   0   0  \n",
       "1  119010  ...   0   1   0   0   0   0   0   0   1   0  \n",
       "2  192949  ...   0   0   0   1   0   0   0   0   1   0  \n",
       "3   -6013  ...   0   0   1   0   0   1   0   0   0   0  \n",
       "4  207625  ...   0   1   0   0   0   0   0   1   0   0  \n",
       "\n",
       "[5 rows x 44 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1d3dc85c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r",
      "  0% [                                                                                ]    0 / 2314\r",
      "100% [................................................................................] 2314 / 2314"
     ]
    },
    {
     "data": {
      "text/markdown": [
       "# Pension 401(k) data set\n",
       "\n",
       "## Description\n",
       "Data set on financial wealth and 401(k) plan participation. The source of this data set is the `hdm` package in `R`. It was created on 2/20/2023, by calling the `data(pension)` command in `R` after loading the `hdm` package and then writing the created dataframe to a csv file.\n",
       "\n",
       "## Format\n",
       "Dataframe with the following variables (amongst others):\n",
       "\n",
       "**p401**\n",
       "\n",
       "participation in 401(k)\n",
       "\n",
       "**e401**\n",
       "\n",
       "eligibility for 401(k)\n",
       "\n",
       "**a401**\n",
       "\n",
       "401(k) assets\n",
       "\n",
       "**tw**\n",
       "\n",
       "total wealth (in US $)\n",
       "\n",
       "**tfa**\n",
       "\n",
       "financial assets (in US $)\n",
       "\n",
       "**net_tfa**\n",
       "\n",
       "net financial assets (in US $)\n",
       "\n",
       "**nifa**\n",
       "\n",
       "non-401k financial assets (in US $)\n",
       "\n",
       "**net_nifa**\n",
       "\n",
       "net non-401k financial assets\n",
       "\n",
       "**net_n401**\n",
       "\n",
       "net non-401(k) assets (in US $)\n",
       "\n",
       "**ira**\n",
       "\n",
       "individual retirement account (IRA)\n",
       "\n",
       "**inc**\n",
       "\n",
       "income (in US $)\n",
       "\n",
       "**age**\n",
       "\n",
       "age\n",
       "\n",
       "**fsize**\n",
       "\n",
       "family size\n",
       "\n",
       "**marr**\n",
       "\n",
       "married\n",
       "\n",
       "**pira**\n",
       "\n",
       "participation in IRA\n",
       "\n",
       "**db**\n",
       "\n",
       "defined benefit pension\n",
       "\n",
       "**hown**\n",
       "\n",
       "home owner\n",
       "\n",
       "**educ**\n",
       "\n",
       "education (in years)\n",
       "\n",
       "**male**\n",
       "\n",
       "male\n",
       "\n",
       "**twoearn**\n",
       "\n",
       "two earners\n",
       "\n",
       "**nohs, hs, smcol, col**\n",
       "\n",
       "dummies for education: no high-school, high-school, some college, college\n",
       "\n",
       "**hmort**\n",
       "\n",
       "home mortage (in US $)\n",
       "\n",
       "**hequity**\n",
       "\n",
       "home equity (in US $)\n",
       "\n",
       "**hval**\n",
       "\n",
       "home value (in US $)\n",
       "\n",
       "## Details\n",
       "The sample is drawn from the 1991 Survey of Income and Program Participation (SIPP) and consists of 9,915 observations. The observational units are household reference persons aged 25-64 and spouse if present. Households are included in the sample if at least one person is employed and no one is self-employed. The data set was analysed in Chernozhukov and Hansen (2004) and Belloni et al. (2014) where further details can be found. They examine the effects of 401(k) plans on wealth using data from the Survey of Income and Program Participation using 401(k) eligibility as an instrument for 401(k) participation.\n",
       "\n",
       "## References\n",
       "V. Chernohukov, C. Hansen (2004). The impact of 401(k) participation on the wealth distribution: An instrumental quantile regression analysis. The Review of Economic and Statistics 86 (3), 735â€“751.\n",
       "\n",
       "A. Belloni, V. Chernozhukov, I. Fernandez-Val, and C. Hansen (2014). Program evaluation with high-dimensional data. Working Paper."
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "readme = \"https://raw.githubusercontent.com/CausalAIBook/MetricsMLNotebooks/main/data/401k.md\"\n",
    "filename = wget.download(readme)\n",
    "display(Markdown(open(filename, 'r').read()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "looking-invention",
   "metadata": {
    "papermill": {
     "duration": 0.037509,
     "end_time": "2021-03-24T14:13:52.250583",
     "exception": false,
     "start_time": "2021-03-24T14:13:52.213074",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The data consist of 9,915 observations at the household level drawn from the 1991 Survey of Income and Program Participation (SIPP).  All the variables are referred to 1990. We use net financial assets (*net\\_tfa*) as the outcome variable, $Y$,  in our analysis. The net financial assets are computed as the sum of IRA balances, 401(k) balances, checking accounts, saving bonds, other interest-earning accounts, other interest-earning assets, stocks, and mutual funds less non mortgage debts. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "received-nutrition",
   "metadata": {
    "papermill": {
     "duration": 0.038843,
     "end_time": "2021-03-24T14:13:52.327055",
     "exception": false,
     "start_time": "2021-03-24T14:13:52.288212",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Among the $9915$ individuals, $3682$ are eligible to participate in the program. The variable *e401* indicates eligibility and *p401* indicates participation, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0d26d552",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.countplot(data['e401'],)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "material-sending",
   "metadata": {
    "papermill": {
     "duration": 0.039406,
     "end_time": "2021-03-24T14:13:53.435306",
     "exception": false,
     "start_time": "2021-03-24T14:13:53.395900",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Eligibility is highly associated with financial wealth:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a7741bb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1058.88x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.displot(data=data, x='net_tfa', kind='kde', col='e401', hue='e401', fill=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "awful-antigua",
   "metadata": {
    "papermill": {
     "duration": 0.040645,
     "end_time": "2021-03-24T14:13:54.245822",
     "exception": false,
     "start_time": "2021-03-24T14:13:54.205177",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The unconditional APE of e401 is about $19559$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ef070d79",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19559\n"
     ]
    }
   ],
   "source": [
    "e1 = data[data['e401'] == 1]['net_tfa']\n",
    "e0 = data[data['e401'] == 0]['net_tfa']\n",
    "print(f'{np.mean(e1) - np.mean(e0):.0f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cross-priority",
   "metadata": {
    "papermill": {
     "duration": 0.041187,
     "end_time": "2021-03-24T14:13:54.437695",
     "exception": false,
     "start_time": "2021-03-24T14:13:54.396508",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Among the $3682$ individuals that  are eligible, $2594$ decided to participate in the program. The unconditional APE of p401 is about $27372$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "33cd014e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "27372\n"
     ]
    }
   ],
   "source": [
    "e1 = data[data['p401'] == 1]['net_tfa']\n",
    "e0 = data[data['p401'] == 0]['net_tfa']\n",
    "print(f'{np.mean(e1) - np.mean(e0):.0f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "suitable-vulnerability",
   "metadata": {
    "papermill": {
     "duration": 0.041678,
     "end_time": "2021-03-24T14:13:54.640532",
     "exception": false,
     "start_time": "2021-03-24T14:13:54.598854",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "As discussed, these estimates are biased since they do not account for saver heterogeneity and endogeneity of participation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "a9354414",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['age', 'inc', 'fsize', 'educ', 'db', 'marr', 'male', 'twoearn', 'pira',\n",
       "       'nohs', 'hs', 'smcol', 'col', 'hown'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = data['net_tfa'].values\n",
    "D = data['e401'].values\n",
    "D2 = data['p401'].values\n",
    "D3 = data['a401'].values\n",
    "X = data.drop(['e401', 'p401', 'a401', 'tw', 'tfa', 'net_tfa', 'tfa_he',\n",
    "               'hval', 'hmort', 'hequity',\n",
    "               'nifa', 'net_nifa', 'net_n401', 'ira',\n",
    "               'dum91', 'icat', 'ecat', 'zhat',\n",
    "               'i1', 'i2', 'i3', 'i4', 'i5', 'i6', 'i7',\n",
    "               'a1', 'a2', 'a3', 'a4', 'a5'], axis=1)\n",
    "X.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4c3e489",
   "metadata": {},
   "source": [
    "### We define a transformer that constructs the engineered features for controls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a2cfdf4c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Defaulting to user installation because normal site-packages is not writeable\n",
      "Requirement already satisfied: formulaic in c:\\programdata\\anaconda3\\lib\\site-packages (0.5.2)\n",
      "Requirement already satisfied: interface-meta>=1.2.0 in c:\\programdata\\anaconda3\\lib\\site-packages (from formulaic) (1.3.0)\n",
      "Requirement already satisfied: numpy>=1.16.5 in c:\\programdata\\anaconda3\\lib\\site-packages (from formulaic) (1.21.5)\n",
      "Requirement already satisfied: typing-extensions>=4.2.0 in c:\\programdata\\anaconda3\\lib\\site-packages (from formulaic) (4.3.0)\n",
      "Requirement already satisfied: pandas>=1.0 in c:\\programdata\\anaconda3\\lib\\site-packages (from formulaic) (1.4.4)\n",
      "Requirement already satisfied: wrapt>=1.0 in c:\\programdata\\anaconda3\\lib\\site-packages (from formulaic) (1.14.1)\n",
      "Requirement already satisfied: scipy>=1.6 in c:\\programdata\\anaconda3\\lib\\site-packages (from formulaic) (1.9.1)\n",
      "Requirement already satisfied: astor>=0.8 in c:\\programdata\\anaconda3\\lib\\site-packages (from formulaic) (0.8.1)\n",
      "Requirement already satisfied: python-dateutil>=2.8.1 in c:\\programdata\\anaconda3\\lib\\site-packages (from pandas>=1.0->formulaic) (2.8.2)\n",
      "Requirement already satisfied: pytz>=2020.1 in c:\\programdata\\anaconda3\\lib\\site-packages (from pandas>=1.0->formulaic) (2022.1)\n",
      "Requirement already satisfied: six>=1.5 in c:\\programdata\\anaconda3\\lib\\site-packages (from python-dateutil>=2.8.1->pandas>=1.0->formulaic) (1.16.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install formulaic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "53b1283d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.base import TransformerMixin, BaseEstimator\n",
    "from formulaic import Formula\n",
    "\n",
    "class FormulaTransformer(TransformerMixin, BaseEstimator):\n",
    "    \n",
    "    def __init__(self, formula, array=False):\n",
    "        self.formula = formula\n",
    "        self.array = array\n",
    "    \n",
    "    def fit(self, X, y=None):\n",
    "        return self\n",
    "    \n",
    "    def transform(self, X, y=None):\n",
    "        df = Formula(self.formula).get_model_matrix(X)\n",
    "        if self.array:\n",
    "            return df.values\n",
    "        return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "824ee320",
   "metadata": {},
   "outputs": [],
   "source": [
    "transformer = FormulaTransformer(\"0 + poly(age, degree=6, raw=True) + poly(inc, degree=8, raw=True) \"\n",
    "                                 \"+ poly(educ, degree=4, raw=True) + poly(fsize, degree=2, raw=True) \"\n",
    "                                 \"+ male + marr + twoearn + db + pira + hown\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b35bbd34",
   "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>db</th>\n",
       "      <th>hown</th>\n",
       "      <th>male</th>\n",
       "      <th>marr</th>\n",
       "      <th>pira</th>\n",
       "      <th>poly(age, degree=6, raw=True)[0]</th>\n",
       "      <th>poly(age, degree=6, raw=True)[1]</th>\n",
       "      <th>poly(age, degree=6, raw=True)[2]</th>\n",
       "      <th>poly(age, degree=6, raw=True)[3]</th>\n",
       "      <th>poly(age, degree=6, raw=True)[4]</th>\n",
       "      <th>...</th>\n",
       "      <th>poly(fsize, degree=2, raw=True)[1]</th>\n",
       "      <th>poly(inc, degree=8, raw=True)[0]</th>\n",
       "      <th>poly(inc, degree=8, raw=True)[1]</th>\n",
       "      <th>poly(inc, degree=8, raw=True)[2]</th>\n",
       "      <th>poly(inc, degree=8, raw=True)[3]</th>\n",
       "      <th>poly(inc, degree=8, raw=True)[4]</th>\n",
       "      <th>poly(inc, degree=8, raw=True)[5]</th>\n",
       "      <th>poly(inc, degree=8, raw=True)[6]</th>\n",
       "      <th>poly(inc, degree=8, raw=True)[7]</th>\n",
       "      <th>twoearn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>9915.000000</td>\n",
       "      <td>9915.000000</td>\n",
       "      <td>9915.000000</td>\n",
       "      <td>9915.000000</td>\n",
       "      <td>9915.000000</td>\n",
       "      <td>9915.000000</td>\n",
       "      <td>9915.000000</td>\n",
       "      <td>9915.000000</td>\n",
       "      <td>9.915000e+03</td>\n",
       "      <td>9.915000e+03</td>\n",
       "      <td>...</td>\n",
       "      <td>9915.000000</td>\n",
       "      <td>9915.000000</td>\n",
       "      <td>9.915000e+03</td>\n",
       "      <td>9.915000e+03</td>\n",
       "      <td>9.915000e+03</td>\n",
       "      <td>9.915000e+03</td>\n",
       "      <td>9.915000e+03</td>\n",
       "      <td>9.915000e+03</td>\n",
       "      <td>9.915000e+03</td>\n",
       "      <td>9915.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.271004</td>\n",
       "      <td>0.635199</td>\n",
       "      <td>0.205951</td>\n",
       "      <td>0.604841</td>\n",
       "      <td>0.242158</td>\n",
       "      <td>41.060212</td>\n",
       "      <td>1792.938981</td>\n",
       "      <td>82850.255371</td>\n",
       "      <td>4.022991e+06</td>\n",
       "      <td>2.036867e+08</td>\n",
       "      <td>...</td>\n",
       "      <td>10.581241</td>\n",
       "      <td>37200.623197</td>\n",
       "      <td>1.997590e+09</td>\n",
       "      <td>1.437534e+14</td>\n",
       "      <td>9.104568e+17</td>\n",
       "      <td>-1.945721e+16</td>\n",
       "      <td>-9.132838e+16</td>\n",
       "      <td>1.934747e+16</td>\n",
       "      <td>2.234841e+16</td>\n",
       "      <td>0.380837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.444500</td>\n",
       "      <td>0.481399</td>\n",
       "      <td>0.404415</td>\n",
       "      <td>0.488909</td>\n",
       "      <td>0.428411</td>\n",
       "      <td>10.344505</td>\n",
       "      <td>899.134499</td>\n",
       "      <td>61725.701911</td>\n",
       "      <td>3.939869e+06</td>\n",
       "      <td>2.448502e+08</td>\n",
       "      <td>...</td>\n",
       "      <td>11.391608</td>\n",
       "      <td>24774.288006</td>\n",
       "      <td>3.026128e+09</td>\n",
       "      <td>4.129207e+14</td>\n",
       "      <td>3.249753e+18</td>\n",
       "      <td>5.290488e+18</td>\n",
       "      <td>5.317962e+18</td>\n",
       "      <td>5.317873e+18</td>\n",
       "      <td>5.262071e+18</td>\n",
       "      <td>0.485617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>25.000000</td>\n",
       "      <td>625.000000</td>\n",
       "      <td>15625.000000</td>\n",
       "      <td>3.906250e+05</td>\n",
       "      <td>9.765625e+06</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-2652.000000</td>\n",
       "      <td>0.000000e+00</td>\n",
       "      <td>-1.865179e+10</td>\n",
       "      <td>-9.222694e+18</td>\n",
       "      <td>-9.221958e+18</td>\n",
       "      <td>-9.221276e+18</td>\n",
       "      <td>-9.223372e+18</td>\n",
       "      <td>-9.221563e+18</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>32.000000</td>\n",
       "      <td>1024.000000</td>\n",
       "      <td>32768.000000</td>\n",
       "      <td>1.048576e+06</td>\n",
       "      <td>3.355443e+07</td>\n",
       "      <td>...</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>19413.000000</td>\n",
       "      <td>3.768646e+08</td>\n",
       "      <td>7.316072e+12</td>\n",
       "      <td>3.677463e+16</td>\n",
       "      <td>-4.537058e+18</td>\n",
       "      <td>-4.603302e+18</td>\n",
       "      <td>-4.539584e+18</td>\n",
       "      <td>-4.508422e+18</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>1600.000000</td>\n",
       "      <td>64000.000000</td>\n",
       "      <td>2.560000e+06</td>\n",
       "      <td>1.024000e+08</td>\n",
       "      <td>...</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>31476.000000</td>\n",
       "      <td>9.907386e+08</td>\n",
       "      <td>3.118449e+13</td>\n",
       "      <td>4.226261e+17</td>\n",
       "      <td>3.660147e+16</td>\n",
       "      <td>-2.199258e+17</td>\n",
       "      <td>3.665403e+16</td>\n",
       "      <td>4.447478e+16</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>48.000000</td>\n",
       "      <td>2304.000000</td>\n",
       "      <td>110592.000000</td>\n",
       "      <td>5.308416e+06</td>\n",
       "      <td>2.548040e+08</td>\n",
       "      <td>...</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>48583.500000</td>\n",
       "      <td>2.360356e+09</td>\n",
       "      <td>1.146744e+14</td>\n",
       "      <td>2.117477e+18</td>\n",
       "      <td>4.485390e+18</td>\n",
       "      <td>4.471642e+18</td>\n",
       "      <td>4.613388e+18</td>\n",
       "      <td>4.509509e+18</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>64.000000</td>\n",
       "      <td>4096.000000</td>\n",
       "      <td>262144.000000</td>\n",
       "      <td>1.677722e+07</td>\n",
       "      <td>1.073742e+09</td>\n",
       "      <td>...</td>\n",
       "      <td>169.000000</td>\n",
       "      <td>242124.000000</td>\n",
       "      <td>5.862403e+10</td>\n",
       "      <td>1.419428e+16</td>\n",
       "      <td>9.222042e+18</td>\n",
       "      <td>9.218801e+18</td>\n",
       "      <td>9.219035e+18</td>\n",
       "      <td>9.223289e+18</td>\n",
       "      <td>9.220028e+18</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                db         hown         male         marr         pira  \\\n",
       "count  9915.000000  9915.000000  9915.000000  9915.000000  9915.000000   \n",
       "mean      0.271004     0.635199     0.205951     0.604841     0.242158   \n",
       "std       0.444500     0.481399     0.404415     0.488909     0.428411   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "50%       0.000000     1.000000     0.000000     1.000000     0.000000   \n",
       "75%       1.000000     1.000000     0.000000     1.000000     0.000000   \n",
       "max       1.000000     1.000000     1.000000     1.000000     1.000000   \n",
       "\n",
       "       poly(age, degree=6, raw=True)[0]  poly(age, degree=6, raw=True)[1]  \\\n",
       "count                       9915.000000                       9915.000000   \n",
       "mean                          41.060212                       1792.938981   \n",
       "std                           10.344505                        899.134499   \n",
       "min                           25.000000                        625.000000   \n",
       "25%                           32.000000                       1024.000000   \n",
       "50%                           40.000000                       1600.000000   \n",
       "75%                           48.000000                       2304.000000   \n",
       "max                           64.000000                       4096.000000   \n",
       "\n",
       "       poly(age, degree=6, raw=True)[2]  poly(age, degree=6, raw=True)[3]  \\\n",
       "count                       9915.000000                      9.915000e+03   \n",
       "mean                       82850.255371                      4.022991e+06   \n",
       "std                        61725.701911                      3.939869e+06   \n",
       "min                        15625.000000                      3.906250e+05   \n",
       "25%                        32768.000000                      1.048576e+06   \n",
       "50%                        64000.000000                      2.560000e+06   \n",
       "75%                       110592.000000                      5.308416e+06   \n",
       "max                       262144.000000                      1.677722e+07   \n",
       "\n",
       "       poly(age, degree=6, raw=True)[4]  ...  \\\n",
       "count                      9.915000e+03  ...   \n",
       "mean                       2.036867e+08  ...   \n",
       "std                        2.448502e+08  ...   \n",
       "min                        9.765625e+06  ...   \n",
       "25%                        3.355443e+07  ...   \n",
       "50%                        1.024000e+08  ...   \n",
       "75%                        2.548040e+08  ...   \n",
       "max                        1.073742e+09  ...   \n",
       "\n",
       "       poly(fsize, degree=2, raw=True)[1]  poly(inc, degree=8, raw=True)[0]  \\\n",
       "count                         9915.000000                       9915.000000   \n",
       "mean                            10.581241                      37200.623197   \n",
       "std                             11.391608                      24774.288006   \n",
       "min                              1.000000                      -2652.000000   \n",
       "25%                              4.000000                      19413.000000   \n",
       "50%                              9.000000                      31476.000000   \n",
       "75%                             16.000000                      48583.500000   \n",
       "max                            169.000000                     242124.000000   \n",
       "\n",
       "       poly(inc, degree=8, raw=True)[1]  poly(inc, degree=8, raw=True)[2]  \\\n",
       "count                      9.915000e+03                      9.915000e+03   \n",
       "mean                       1.997590e+09                      1.437534e+14   \n",
       "std                        3.026128e+09                      4.129207e+14   \n",
       "min                        0.000000e+00                     -1.865179e+10   \n",
       "25%                        3.768646e+08                      7.316072e+12   \n",
       "50%                        9.907386e+08                      3.118449e+13   \n",
       "75%                        2.360356e+09                      1.146744e+14   \n",
       "max                        5.862403e+10                      1.419428e+16   \n",
       "\n",
       "       poly(inc, degree=8, raw=True)[3]  poly(inc, degree=8, raw=True)[4]  \\\n",
       "count                      9.915000e+03                      9.915000e+03   \n",
       "mean                       9.104568e+17                     -1.945721e+16   \n",
       "std                        3.249753e+18                      5.290488e+18   \n",
       "min                       -9.222694e+18                     -9.221958e+18   \n",
       "25%                        3.677463e+16                     -4.537058e+18   \n",
       "50%                        4.226261e+17                      3.660147e+16   \n",
       "75%                        2.117477e+18                      4.485390e+18   \n",
       "max                        9.222042e+18                      9.218801e+18   \n",
       "\n",
       "       poly(inc, degree=8, raw=True)[5]  poly(inc, degree=8, raw=True)[6]  \\\n",
       "count                      9.915000e+03                      9.915000e+03   \n",
       "mean                      -9.132838e+16                      1.934747e+16   \n",
       "std                        5.317962e+18                      5.317873e+18   \n",
       "min                       -9.221276e+18                     -9.223372e+18   \n",
       "25%                       -4.603302e+18                     -4.539584e+18   \n",
       "50%                       -2.199258e+17                      3.665403e+16   \n",
       "75%                        4.471642e+18                      4.613388e+18   \n",
       "max                        9.219035e+18                      9.223289e+18   \n",
       "\n",
       "       poly(inc, degree=8, raw=True)[7]      twoearn  \n",
       "count                      9.915000e+03  9915.000000  \n",
       "mean                       2.234841e+16     0.380837  \n",
       "std                        5.262071e+18     0.485617  \n",
       "min                       -9.221563e+18     0.000000  \n",
       "25%                       -4.508422e+18     0.000000  \n",
       "50%                        4.447478e+16     0.000000  \n",
       "75%                        4.509509e+18     1.000000  \n",
       "max                        9.220028e+18     1.000000  \n",
       "\n",
       "[8 rows x 26 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transformer.fit_transform(X).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "8c5e20e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "transformer = FormulaTransformer(\"0 + poly(age, degree=6, raw=True) + poly(inc, degree=8, raw=True) \"\n",
    "                                 \"+ poly(educ, degree=4, raw=True) + poly(fsize, degree=2, raw=True) \"\n",
    "                                 \"+ male + marr + twoearn + db + pira + hown\", array=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "957a6d85",
   "metadata": {},
   "source": [
    "# Semi-Synthetic Data Generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "39483bf1",
   "metadata": {},
   "outputs": [],
   "source": [
    "class semisynth:\n",
    "    \n",
    "    def fit(self, X, D, y):\n",
    "        self.X_ = X.copy()\n",
    "        self.est0_ = make_pipeline(transformer,\n",
    "                                   RandomForestRegressor(min_samples_leaf=20, ccp_alpha=0.001)).fit(X[D==0], y[D==0])\n",
    "        self.res0_ = y[D==0] - self.est0_.predict(X[D==0])\n",
    "        self.res0_ -= np.mean(self.res0_)\n",
    "        self.est1_ = make_pipeline(transformer,\n",
    "                                   RandomForestRegressor(min_samples_leaf=20, ccp_alpha=0.001)).fit(X[D==1], y[D==1])\n",
    "        self.res1_ = y[D==1] - self.est1_.predict(X[D==1])\n",
    "        self.res1_ -= np.mean(self.res1_)\n",
    "        self.prop_ = make_pipeline(transformer,\n",
    "                                   RandomForestClassifier(min_samples_leaf=20, ccp_alpha=0.001)).fit(X, D)\n",
    "        return self\n",
    "\n",
    "    def generate(self, n):\n",
    "        X = self.X_.iloc[np.random.choice(self.X_.shape[0], n, replace=True)]\n",
    "        D = np.random.binomial(1, self.prop_.predict_proba(X)[:, 1])\n",
    "        y0 = self.est0_.predict(X) + self.res0_[np.random.choice(self.res0_.shape[0], n, replace=True)]\n",
    "        y1 = self.est1_.predict(X) + self.res1_[np.random.choice(self.res1_.shape[0], n, replace=True)]\n",
    "        y = y0 * (1 - D) + y1 * D\n",
    "        return X, D, y, y1, y0\n",
    "    \n",
    "    def generate_with_confounding(self, n, gamma, delta):\n",
    "        X = self.X_.iloc[np.random.choice(self.X_.shape[0], n, replace=True)]\n",
    "        A = np.random.uniform(-np.sqrt(3), np.sqrt(3), size=n)\n",
    "        prop = self.prop_.predict_proba(X)[:, 1] + gamma * A\n",
    "        D = np.random.binomial(1, np.clip(prop, 0, 1))\n",
    "        y0 = self.est0_.predict(X) + self.res0_[np.random.choice(self.res0_.shape[0], n, replace=True)]\n",
    "        y1 = self.est1_.predict(X) + self.res1_[np.random.choice(self.res1_.shape[0], n, replace=True)]\n",
    "        y = y0 * (1 - D) + y1 * D + delta * A\n",
    "        return X, D, y, y1, y0, A\n",
    "    \n",
    "    def y_cef(self, X, D):\n",
    "        return self.est1_.predict(X) * D + self.est0_.predict(X) * (1 - D)\n",
    "    \n",
    "    def D_cef(self, X):\n",
    "        return self.prop_.predict_proba(X)[:, 1]\n",
    "\n",
    "    @property\n",
    "    def true_ate(self):\n",
    "        return np.mean(self.est1_.predict(self.X_) - self.est0_.predict(self.X_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e38d8ffb",
   "metadata": {},
   "outputs": [],
   "source": [
    "synth = semisynth().fit(X, D, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a04c998c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7531.0676100128085"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "synth.true_ate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b1d121fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "X, D, y, y1, y0 = synth.generate(20000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9ffb0bc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7261.916568708302"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(y1 - y0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a745a6f2",
   "metadata": {},
   "source": [
    "## Estimating the ATE of 401(k) Eligibility on Net Financial Assets"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10538ad3",
   "metadata": {},
   "source": [
    "We are interested in valid estimators of the average treatment effect of `e401` and `p401` on `net_tfa`. We start using ML approaches to estimate the function $g_0$ and $m_0$ in the following PLR model:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fcf3165",
   "metadata": {},
   "source": [
    "\\begin{eqnarray}\n",
    " &  Y = D\\theta_0 + g_0(X) + \\zeta,  &  E[\\zeta \\mid D,X]= 0,\\\\\n",
    " & D = m_0(X) +  V,   &  E[V \\mid X] = 0.\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42354b51",
   "metadata": {},
   "source": [
    "### Double Lasso without Sample Splitting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1e3c38b",
   "metadata": {},
   "source": [
    "We first look at the treatment effect of e401 on net total financial assets. We give estimates of the ATE and ATT that corresponds to the linear model\n",
    "\n",
    "\\begin{equation*}\n",
    "Y = D \\alpha + f(X)'\\beta+ \\epsilon,\n",
    "\\end{equation*}\n",
    "\n",
    "where $f(X)$ includes indicators of marital status, two-earner status, defined benefit pension status, IRA participation status, and home ownership status, and  orthogonal polynomials of degrees 2, 4, 6 and 8 in family size, education, age and  income, respectively. The dimensions of $f(X)$ is 25. \n",
    "\n",
    "In the first step, we report estimates of the average treatment effect (ATE) of 401(k) eligibility on net financial assets both in the partially linear regression (PLR) model and in the interactive regression model (IRM) allowing for heterogeneous treatment effects. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "051af0ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "modely = make_pipeline(transformer, StandardScaler(), LassoCV())\n",
    "modeld = make_pipeline(transformer, StandardScaler(), LassoCV())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "53bc1c83",
   "metadata": {},
   "outputs": [],
   "source": [
    "resy = y - modely.fit(X, y).predict(X)\n",
    "resD = D - modeld.fit(X, D).predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "51244ab4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7775.63821483496"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(resy * resD) / np.mean(resD**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "625b9c67",
   "metadata": {},
   "source": [
    "## Let's add some confounding to our data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "2a1730a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "X, D, y, y1, y0, A = synth.generate_with_confounding(20000, .1, 7000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "0da9e208",
   "metadata": {},
   "outputs": [],
   "source": [
    "modely = make_pipeline(transformer, StandardScaler(), LassoCV())\n",
    "modeld = make_pipeline(transformer, StandardScaler(), LassoCV())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "5221a251",
   "metadata": {},
   "outputs": [],
   "source": [
    "resy = y - modely.fit(X, y).predict(X)\n",
    "resD = D - modeld.fit(X, D).predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "198e5511",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10850.120017713394"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = np.mean(resy * resD) / np.mean(resD**2)\n",
    "theta"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67e98f1c",
   "metadata": {},
   "source": [
    "### Understanding Degree of Confounding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "8348bc61",
   "metadata": {},
   "outputs": [],
   "source": [
    "modelA = make_pipeline(transformer, StandardScaler(), LassoCV())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "22323f23",
   "metadata": {},
   "outputs": [],
   "source": [
    "resA = A - modelA.fit(X, A).predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "bf392b63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04734637615348802"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resDhat = LinearRegression().fit(resA.reshape(-1, 1), resD).predict(resA.reshape(-1, 1))\n",
    "etaD = 1 - np.mean((resD - resDhat)**2) / np.var(resD)\n",
    "etaD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "9e1a0344",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.018897848649871762"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "partialresy = resy - theta * resD\n",
    "partialresA = resA - LinearRegression().fit(resD.reshape(-1, 1), resA).predict(resD.reshape(-1, 1))\n",
    "partialresyhat = LinearRegression().fit(partialresA.reshape(-1, 1), partialresy).predict(partialresA.reshape(-1, 1))\n",
    "etaY = 1 - np.mean((partialresy - partialresyhat)**2) / np.var(partialresy)\n",
    "etaY"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "938c0610",
   "metadata": {},
   "source": [
    "### Sensitivity Bounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "dad9b796",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bounds(etaD, etaY):\n",
    "    nusq = np.mean(resD ** 2)\n",
    "    theta = np.mean(resy * resD) / nusq\n",
    "    sigmasq = np.mean((resy - resD * theta)**2)\n",
    "    S = np.sqrt(sigmasq / nusq)\n",
    "    CD = etaD / (1 - etaD)\n",
    "    CY = etaY\n",
    "    error = S * np.sqrt(CD * CY)\n",
    "    return theta - error, theta + error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "779c6c3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(7307.083629513094, 14393.156405913694)"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bounds(0.05, 0.02)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "dfa371a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def contour(etaD, error):\n",
    "    nusq = np.mean(resD ** 2)\n",
    "    theta = np.mean(resy * resD) / nusq\n",
    "    sigmasq = np.mean((resy - resD * theta)**2)\n",
    "    S = np.sqrt(sigmasq / nusq)\n",
    "    CD = etaD / (1 - etaD)\n",
    "    etaY = error**2 / (CD * S**2)\n",
    "    return etaY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "678b0adf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CdDwJLK3UOIbFXVVFFxmnLIQQQpwxJLC0UmMPCy4X3tra8DZGCCGEOMtIYGklTUQESkQEIJeFhBBCiI4mgaUNdI3jWGTyOCGEEKJDSWBpg8bnCbnlTiEhhBCiQ0lgaQO5U0gIIYQIDwksbXBstlu5JCSEEKLj9OrVC0VRmiy/+c1vAFBVlYULF5Kenk5ERAQXX3wxO3bsCKjD4XBw++23k5SURFRUFNOmTePw4cMBZaqqqsjJycFsNmM2m8nJyaG6urqjvuZJSWBpg8bJ4+SSkBBCiI701VdfUVRU5F/WrVsHwI9//GMAHnvsMZ588kmef/55vvrqK1JTU5kwYQI1NTX+OubOncuqVatYvnw5mzZtora2lqlTp+LxePxlZs6cSX5+PmvWrGHNmjXk5+eTk5PTsV+2BfK05jaQS0JCCCHCoVu3bgHv//KXv9C3b18uuugiVFXl6aefZsGCBVx33XUA/OMf/yAlJYW3336bW2+9FYvFwquvvsobb7zB5ZdfDsCbb75Jjx49+PTTT5k0aRK7du1izZo1fPHFF4wePRqAV155hezsbPbs2cOAAQM69kufQAJLG2gT5C4hIYToSlRVxea2heXYEboIFEVp8+ecTidvvvkm8+bNQ1EU9u/fT3FxMRMnTvSXMRqNXHTRRWzevJlbb72VvLw8XC5XQJn09HSGDBnC5s2bmTRpErm5uZjNZn9YARgzZgxms5nNmzdLYDmT6BrvEpIeFiGE6BJsbhuj3x596oIhsGXmFiL1kW3+3HvvvUd1dTU33XQTAMXFxQCkpKQElEtJSeHgwYP+MgaDgfjGSVCPK9P4+eLiYpKTk5scLzk52V8mnGQMSxvIJSEhhBDh9uqrrzJlyhTS09MDtp/YW6Oq6il7cE4s01z51tTTEaSHpQ20MnGcEEJ0KRG6CLbM3BK2Y7fVwYMH+fTTT3n33Xf921JTUwFfD0laWpp/e2lpqb/XJTU1FafTSVVVVUAvS2lpKWPHjvWXKSkpaXLMsrKyJr034SA9LG3QeEnIW1eH1+kMc2uEEEKcLkVRiNRHhmVpT6/Fa6+9RnJyMldeeaV/W+/evUlNTfXfOQS+cS7r16/3h5GsrCz0en1AmaKiIrZv3+4vk52djcVi4csvv/SX2bJlCxaLxV8mnKSHpQ00MTGg1YLHg6eqCk0nSJxCCCHODl6vl9dee40bb7wRne7Yz7eiKMydO5dHHnmEfv360a9fPx555BEiIyOZOXMmAGazmVmzZnH33XeTmJhIQkIC99xzD0OHDvXfNTRo0CAmT57M7NmzeemllwC45ZZbmDp1atgH3IIEljZRNBq08fF4ysvxVFail8AihBCig3z66acUFhbyq1/9qsm+e++9F5vNxm233UZVVRWjR49m7dq1xMTE+Ms89dRT6HQ6pk+fjs1m47LLLmPp0qVotVp/mbfeeos77rjDfzfRtGnTeP7550P/5VpBUVVVDXcjgsFqtWI2m7FYLMTGxobsOPuvmoZj7156vPo3oseNC9lxhBBCBJfdbqegoIDevXtjMpnC3ZyzysnOfWt/v2UMSxsdu1OoOrwNEUIIIc4i7Qosixcv9qekrKwsNm7c2GLZTZs2MW7cOBITE4mIiGDgwIE89dRTTcqtXLmSwYMHYzQaGTx4MKtWrWpP00Ku8YnNcqeQEEII0XHaHFhWrFjB3LlzWbBgAVu3bmX8+PFMmTKFwsLCZstHRUXx29/+lg0bNrBr1y7uv/9+7r//fl5++WV/mdzcXGbMmEFOTg7btm0jJyeH6dOns2VLeG41O5nGByC65QGIQgghRIdp8xiW0aNHM3LkSJYsWeLfNmjQIK655hoWLVrUqjquu+46oqKieOONNwCYMWMGVquVjz/+2F9m8uTJxMfHs2zZslbV2VFjWMqefY7yxYuJ+8kM0hYuDNlxhBBCBJeMYQmfDh/D4nQ6ycvLC3gWAcDEiRPZvHlzq+rYunUrmzdv5qKLLvJvy83NbVLnpEmTTlqnw+HAarUGLB3h2CUhme1WCCGE6ChtCizl5eV4PJ5mn1dwqucMZGRkYDQaGTVqFL/5zW+4+eab/fuKi4vbXOeiRYswm83+pUePHm35Ku3WeElIpucXQgghOk67Bt2253kFGzdu5Ouvv+bFF1/k6aefbnKpp611zp8/H4vF4l8OHTrUxm/RPo13Cbll0K0QQgjRYdo0cVxSUhJarbZJz8fxzytoSe/evQEYOnQoJSUlLFy4kJ/+9KeA7/kFba3TaDRiNBrb0vyg0HXrBoC7rKzDjy2EEEKcrdrUw2IwGMjKygp4FgHAunXr2vScAVVVcTgc/vfZ2dlN6ly7dm2neHbBiXQND5nyWq146+rC3BohhBDi7NDmqfnnzZtHTk4Oo0aNIjs7m5dffpnCwkLmzJkD+C7VHDlyhNdffx2AF154gZ49ezJw4EDANy/LX//6V26//XZ/nXfeeScXXnghjz76KFdffTXvv/8+n376KZs2bQrGdwwqbXQ0muhovLW1uEpKMPbpE+4mCSGEEF1em8ewzJgxg6effpqHHnqI4cOHs2HDBlavXk1mZibge/rj8XOyeL1e5s+fz/Dhwxk1ahTPPfccf/nLX3jooYf8ZcaOHcvy5ct57bXXOO+881i6dCkrVqxg9OjRQfiKwadL9V2qchUVhbklQgghzgYbNmzgqquuIj09HUVReO+99wL233TTTSiKErCMGTMmoIzD4eD2228nKSmJqKgopk2bxuHDhwPKVFVVkZOT47+hJScnh+rq6oAyhYWFXHXVVURFRZGUlMQdd9yB0+kMxdcO0K6HH952223cdtttze5bunRpwPvbb789oDelJTfccAM33HBDe5rT4fSpaTh/2Ie7uCTcTRFCCHEWqKurY9iwYfzyl7/k+uuvb7bM5MmTee211/zvDQZDwP65c+fy4Ycfsnz5chITE7n77ruZOnUqeXl5/gcgzpw5k8OHD7NmzRrA97TmnJwcPvzwQwA8Hg9XXnkl3bp1Y9OmTVRUVHDjjTeiqirPPfdcKL66nzytuR38PSzF0sMihBAi9KZMmcKUKVNOWsZoNJLaMM7yRBaLhVdffZU33niDyy+/HIA333yTHj168OmnnzJp0iR27drFmjVr+OKLL/xXOF555RWys7PZs2cPAwYMYO3atezcuZNDhw6Rnp4OwBNPPMFNN93Eww8/HNKJW+Xhh+2gT00DkB4WIYQ4w6mqire+PixLGyeaP6XPPvuM5ORk+vfvz+zZsyktLfXvy8vLw+VyBUzSmp6ezpAhQ/yTtObm5mI2mwOGY4wZMwaz2RxQZsiQIf6wAr6JXh0OB3l5eUH9PieSHpZ20Pt7WE4+WZ4QQojOTbXZ2DMyKyzHHvBNHkpkZFDqmjJlCj/+8Y/JzMykoKCABx54gEsvvZS8vDyMRiPFxcUYDAbiG+YSa3T8JK3FxcUkJyc3qTs5OTmgzIlTjsTHx2MwGE45gezpksDSDjp/D4sEFiGEEOE3Y8YM/+shQ4YwatQoMjMz+eijj7juuuta/NyJk7Q2N2Fre8qEggSWdpAeFiGE6BqUiAgGfBPaSxknO3aopKWlkZmZyd69ewHfBK1Op5OqqqqAXpbS0lL/nGepqamUlDQd6lBWVubvVUlNTWXLli0B+6uqqnC5XKecQPZ0yRiWdmjsYfHW1OCplcnjhBDiTKUoCprIyLAsoeyRqKio4NChQ6Sl+X6vsrKy0Ov1AZO0FhUVsX37dn9gyc7OxmKx8OWXX/rLbNmyBYvFElBm+/btFB03rcfatWsxGo1kZYX20pr0sLSDNjrKP3mcu6QYbXTfcDdJCCFEF1ZbW8sPP/zgf19QUEB+fj4JCQkkJCSwcOFCrr/+etLS0jhw4AC///3vSUpK4tprrwXAbDYza9Ys7r77bhITE0lISOCee+5h6NCh/ruGBg0axOTJk5k9ezYvvfQS4LuteerUqQwYMACAiRMnMnjwYHJycnj88ceprKzknnvuYfbs2SG9Qwikh6Xd9Gm+W8fkspAQQohQ+/rrrxkxYgQjRowAfLPOjxgxgj/84Q9otVq+++47rr76avr378+NN95I//79yc3NJSYmxl/HU089xTXXXMP06dMZN24ckZGRfPjhh/45WADeeusthg4dysSJE5k4cSLnnXceb7zxhn+/Vqvlo48+wmQyMW7cOKZPn84111zDX//615CfA0UN9n1VYWK1WjGbzVgslpCnPIDCm2dTt2kTaQ//mbgWJvERQgjRedjtdgoKCujduzcmkynczTmrnOzct/b3W3pY2kl6WIQQQoiOI4GlnXQpvsAitzYLIYQQoSeBpZ2O9bDIbLdCCCFEqElgaadjPSzyPCEhhBAi1CSwtJP0sAghhBAdRwJLOzX2sMjkcUIIIUToSWBpJ210FJqG+9vdJTLwVgghhAglCSynwf9MoSIJLEIIIUQoSWA5Df6nNksPixBCCBFSElhOg/SwCCGEEB1DAstp0KU23NosPSxCCCFCaMOGDVx11VWkp6ejKArvvfdewP6bbroJRVECljFjxgSUcTgc3H777SQlJREVFcW0adM4fPhwQJmqqipycnIwm82YzWZycnKorq4OKFNYWMhVV11FVFQUSUlJ3HHHHTidzlB87QASWE6DviGwSA+LEEKIUKqrq2PYsGE8//zzLZaZPHkyRUVF/mX16tUB++fOncuqVatYvnw5mzZtora2lqlTp+LxePxlZs6cSX5+PmvWrGHNmjXk5+eTk5Pj3+/xeLjyyiupq6tj06ZNLF++nJUrV3L33XcH/0ufQBfyI3Rh0sMihBCiI0yZMoUpU6actIzRaCS14XfpRBaLhVdffZU33niDyy+/HIA333yTHj168OmnnzJp0iR27drFmjVr+OKLLxg9ejQAr7zyCtnZ2ezZs4cBAwawdu1adu7cyaFDh0hPTwfgiSee4KabbuLhhx8O6cOHpYflNEgPixBCdA0uh6fFxe3ytL6ss3VlQ+Gzzz4jOTmZ/v37M3v2bEpLS/378vLycLlcTJw40b8tPT2dIUOGsHnzZgByc3Mxm83+sAIwZswYzGZzQJkhQ4b4wwrApEmTcDgc5OXlheR7NZIeltPgnzyuthZPbS3a6Ogwt0gIIUR7vHzn+hb3ZQ5JZOpvh/nf//3/NuJ2epstm94vjmvvHul///qCzdhrXU3K/ebFS0+jtU1NmTKFH//4x2RmZlJQUMADDzzApZdeSl5eHkajkeLiYgwGA/Hx8QGfS0lJobjhIb7FxcUkJyc3qTs5OTmgTEpKSsD++Ph4DAaDv0yoSGA5DY2Tx3lranAXF6M955xwN0kIIcRZaMaMGf7XQ4YMYdSoUWRmZvLRRx9x3XXXtfg5VVVRFMX//vjXp1MmFCSwnCZ9aiqOmhpcxSUYJbAIIcQZ6ZZnLmpxn3LC4IlfPT6+5bIn/Gb/4uGxp9OsdktLSyMzM5O9e/cCkJqaitPppKqqKqCXpbS0lLFjx/rLlJQ0fT5eWVmZv1clNTWVLVu2BOyvqqrC5XI16XkJNhnDcpr8A2/lqc1CCHHG0hu1LS46vbb1ZQ2tKxtqFRUVHDp0iLQ03wSnWVlZ6PV61q1b5y9TVFTE9u3b/YElOzsbi8XCl19+6S+zZcsWLBZLQJnt27dTVHTsN2/t2rUYjUaysrJC+p2kh+U0+QfeylObhRBChEhtbS0//PCD/31BQQH5+fkkJCSQkJDAwoULuf7660lLS+PAgQP8/ve/JykpiWuvvRYAs9nMrFmzuPvuu0lMTCQhIYF77rmHoUOH+u8aGjRoEJMnT2b27Nm89NJLANxyyy1MnTqVAQMGADBx4kQGDx5MTk4Ojz/+OJWVldxzzz3Mnj07pHcIgQSW06ZrnO1WeliEEEKEyNdff80ll1zifz9v3jwAbrzxRpYsWcJ3333H66+/TnV1NWlpaVxyySWsWLGCmIaH9AI89dRT6HQ6pk+fjs1m47LLLmPp0qVotcd6fN566y3uuOMO/91E06ZNC5j7RavV8tFHH3Hbbbcxbtw4IiIimDlzJn/9619DfQpQVFVVQ36UDmC1WjGbzVgslpCnvONVr3yXogULiPrRj+j5t1c67LhCCCHaxm63U1BQQO/evTGZTOFuzlnlZOe+tb/fMoblNEkPixBCCBF6ElhOk75hQJNbxrAIIYQQISOB5TTpG27japw8TgghhBDBJ4HlNGmiotA0XHNzh3iWPyGEEOJsJYElCBp7WeSZQkIIIURoSGAJAl1a41wsMvBWCCE6uy5yc+wZJRjnvF2BZfHixf5bk7Kysti4cWOLZd99910mTJhAt27diI2NJTs7m08++SSgzNKlS1EUpclit9vb07wOZ8jIAMBVeCjMLRFCCNESvV4PQH19fZhbcvZpPOeN/w3ao80Tx61YsYK5c+eyePFixo0bx0svvcSUKVPYuXMnPXv2bFJ+w4YNTJgwgUceeYS4uDhee+01rrrqKrZs2cKIESP85WJjY9mzZ0/AZ8+U++QNvXoB4Dx4MLwNEUII0SKtVktcXBylpaUAREZGhvyBfWc7VVWpr6+ntLSUuLi4gEnq2qrNgeXJJ59k1qxZ3HzzzQA8/fTTfPLJJyxZsoRFixY1Kf/0008HvH/kkUd4//33+fDDDwMCi6IopDZMc3+mMWRmAuA8cCC8DRFCCHFSjb8zjaFFdIy4uLjT/o1vU2BxOp3k5eVx3333BWyfOHEimzdvblUdXq+XmpoaEhISArbX1taSmZmJx+Nh+PDh/OlPfwoINCdyOBw4HA7/e6vV2oZvElzH97CoXi+KRoYGCSFEZ6QoCmlpaSQnJ+NyucLdnLOCXq8/rZ6VRm0KLOXl5Xg8niaPkE5JSaG4lbf0PvHEE9TV1TF9+nT/toEDB7J06VKGDh2K1WrlmWeeYdy4cWzbto1+/fo1W8+iRYt48MEH29L8kNF37w46HarDgbukxD+ZnBBCiM5Jq9UG5UdUdJx2dQWceM1PVdVWXQdctmwZCxcuZMWKFSQnJ/u3jxkzhp///OcMGzaM8ePH884779C/f3+ee+65FuuaP38+FovFvxw6FL4Br4pO5x94K5eFhBBCiOBrU2BJSkpCq9U26U0pLS1t0utyohUrVjBr1izeeecd/6OsW2yURsP555/P3r17WyxjNBqJjY0NWMJJBt4KIYQQodOmwGIwGMjKymLdunUB29etW8fYsWNb/NyyZcu46aabePvtt7nyyitPeRxVVcnPzyftDLq04h94W3AgvA0RQgghuqA23yU0b948cnJyGDVqFNnZ2bz88ssUFhYyZ84cwHep5siRI7z++uuAL6z84he/4JlnnmHMmDH+3pmIiAjMZjMADz74IGPGjKFfv35YrVaeffZZ8vPzeeGFF4L1PUPO0LsXIJeEhBBCiFBoc2CZMWMGFRUVPPTQQxQVFTFkyBBWr15NZkMPQ1FREYWFhf7yL730Em63m9/85jf85je/8W+/8cYbWbp0KQDV1dXccsstFBcXYzabGTFiBBs2bOCCCy44za/XceSSkBBCCBE6itpF5ii2Wq2YzWYsFktYxrO4ior44ZJLQadj4NZvUE5jNj8hhBDibNHa32+ZMCRIdCkpKCYTuN24jhwJd3OEEEKILkUCS5AoGg2GhkcTyGUhIYQQIrgksASRfxyLDLwVQgghgkoCSxD5b22WHhYhhBAiqCSwBJH0sAghhBChIYEliBrnYnFIYBFCCCGCSgJLEDVeEnIXFeO128PcGiGEEKLrkMASRNqEBDQxMaCqOI+bPE8IIYQQp0cCSxApiiIDb4UQQogQkMASZDLwVgghhAg+CSxBJoFFCCGECD4JLEEml4SEEEKI4JPAEmTHelgksAghhBDBIoElyAy9fD0snvJyPLW1YW6NEEII0TVIYAkybUwM2sREQHpZhBBCiGCRwBICMvBWCCGECC4JLCFwbODtgfA2RAghhOgiJLCEgAy8FUIIIYJLAksI+HtY5JKQEEIIERQSWELg+DEsqqqGtzFCCCFEFyCBJQQMvXuBToe3pgZ3cXG4myOEEEKc8SSwhIDGYMDYpw8A9l27w9waIYQQ4swngSVETIMGAmDfvSvMLRFCCCHOfBJYQsQ4cBAADulhEUIIIU6bBJYQMQ0cAIB9twQWIYQQ4nRJYAkR40DfJSHXoUN4amrC3BohhBDizCaBJUR08fHoUlMBcOzZE+bWCCGEEGc2CSwhZGroZZE7hYQQQojTI4ElhIxyp5AQQggRFBJYQsgkdwoJIYQQQSGBJYQa52Jx7N2L6nKFuTVCCCHEmUsCSwjpMzLQREWhulw49heEuzlCCCHEGUsCSwgpGo3/9maHjGMRQggh2k0CS4jJnUJCCCHE6ZPAEmL+ZwrtkcAihBBCtJcElhA7/plCqqqGuTVCCCHEmaldgWXx4sX07t0bk8lEVlYWGzdubLHsu+++y4QJE+jWrRuxsbFkZ2fzySefNCm3cuVKBg8ejNFoZPDgwaxatao9Tet0jP3OAa0WT3U17pKScDdHCCGEOCO1ObCsWLGCuXPnsmDBArZu3cr48eOZMmUKhYWFzZbfsGEDEyZMYPXq1eTl5XHJJZdw1VVXsXXrVn+Z3NxcZsyYQU5ODtu2bSMnJ4fp06ezZcuW9n+zTkJjNGLs0wcA+y4ZeCuEEEK0h6K28TrF6NGjGTlyJEuWLPFvGzRoENdccw2LFi1qVR3nnnsuM2bM4A9/+AMAM2bMwGq18vHHH/vLTJ48mfj4eJYtW9aqOq1WK2azGYvFQmxsbBu+UegdufderB98SLc77yDp178Od3OEEEKITqO1v99t6mFxOp3k5eUxceLEgO0TJ05k8+bNrarD6/VSU1NDQkKCf1tubm6TOidNmnTSOh0OB1arNWDprBpnvJU7hYQQQoj2aVNgKS8vx+PxkJKSErA9JSWF4uLiVtXxxBNPUFdXx/Tp0/3biouL21znokWLMJvN/qVHjx5t+CYdy3+n0G4JLEIIIUR7tGvQraIoAe9VVW2yrTnLli1j4cKFrFixguTk5NOqc/78+VgsFv9y6NChNnyDjtU4eZyrsBBPbW2YWyOEEEKcedoUWJKSktBqtU16PkpLS5v0kJxoxYoVzJo1i3feeYfLL788YF9qamqb6zQajcTGxgYsnZUuPh5daioAjj17wtwaIYQQ4szTpsBiMBjIyspi3bp1AdvXrVvH2LFjW/zcsmXLuOmmm3j77be58sorm+zPzs5uUufatWtPWueZxj/j7U65U0gIIYRoK11bPzBv3jxycnIYNWoU2dnZvPzyyxQWFjJnzhzAd6nmyJEjvP7664AvrPziF7/gmWeeYcyYMf6elIiICMxmMwB33nknF154IY8++ihXX30177//Pp9++imbNm0K1vcMO9PgwdR+9hm2774Nd1OEEEKIM06bx7DMmDGDp59+moceeojhw4ezYcMGVq9eTWZmJgBFRUUBc7K89NJLuN1ufvOb35CWluZf7rzzTn+ZsWPHsnz5cl577TXOO+88li5dyooVKxg9enQQvmLnEDFiBAC2b7aeoqQQQgghTtTmeVg6q848DwuAp7aW7y8YDV4v56xfjz4l+dQfEkIIIbq4kMzDItpPGx2NsX9/AGxbvwlza4QQQogziwSWDhQ5ciQA9XkSWIQQQoi2kMDSgSIaAovtGwksQgghRFtIYOlAkVm+wGLfvRtvXV2YWyOEEEKcOSSwnELF0Vr2bCmmqvj0A4Y+LQ1dehp4PNi+ldubhRBCiNaSwHIKX/37AJ++tpOD2yuCUl/kCBnHIoQQQrSVBJZTiE+NBKCquD4o9UVkyTgWIYQQoq0ksJxCXEpjYAnOmJPGO4Vs+fmobndQ6hRCCCG6Ogksp9DYw1JdEpweFmO/fmiio/HW12OXByEKIYQQrSKB5RQae1hsNS7sda7Trk/RaokYPtxXp0zTL4QQQrSKBJZTMJh0RMUZgeD1sjTe3lz/TV5Q6hNCCCG6OgksrXBsHEuQBt423Clky/uGLvIoJyGEECKkdOFuwJlg1JRMRkzoSXJmTFDqizhvKOh0uEtLcR05iiGje1DqFUIIIboq6WFphYyBCWQOSSQixhCU+jSRkZgGDwbkQYhCCCFEa0hgCZPIESMAqM+TcSxCCCHEqUhgaQWPx8ver0r48t8FeD3eoNR5bAI5uVNICCGEOBUJLK2gURT++/ouvvp3AdZye1DqbJxAzrF3L57q6qDUKYQQQnRVElhaQdEomFOCO4GcLikJwzl9QVWpy80NSp1CCCFEVyWBpZWC/UwhgOjxFwJQu2Fj0OoUQgghuiIJLK0U5+9hCc4zhQCix/8IgNpNG2U+FiGEEOIkJLC0kr+HJUiXhAAiRo1CiYjAU1aOY/fuoNUrhBBCdDUSWFopPiUKCN4YFgCNwUDU6NEA1G7cFLR6hRBCiK5GAksrmZMjgOA9BLFRVMNlobqNMo5FCCGEaIlMzd9KBpOOqbcPIzbRhCEieKct+sILKQHqt27FU1uLNjo6aHULIYQQXYX0sLRB5rmJxKdGodEoQavT0KMHhsxMcLvl9mYhhBCiBRJYOoGoC323N9fJOBYhhBCiWRJY2sBSVs/XHx9g238OBbVe/+3NG+X2ZiGEEKI5EljawFpmZ8v7+9mx8UhQ64284AIUoxF3URHOffuCWrcQQgjRFUhgaYO4hrlYLKU2PEF6CCKAxmQi8vzzAbm9WQghhGiOBJY2iI4zojNo8HpVaoL0EER/3f7bmzcEtV4hhBCiK5DA0gaKRvFP0R/MGW8BohqeK1T/1dd464NbtxBCCHGmk8DSRvGNgaU4eM8UAjD07oW+e3dUl4u6L78Mat1CCCHEmU4CSxsdewhicHtBFEUh6sLxANSuXx/UuoUQQogznQSWNmoceBvswAIQc8klANR8+imqxxP0+oUQQogzlUzN30Y9Byfykz9cQFy3yKDXHTVmDBqzGU9ZOfVf5xE1+oKgH0MIIYQ4E0kPSxuZovQkpkej1Qf/1CkGAzETLgfA+vHqoNcvhBBCnKna9au7ePFievfujclkIisri40nedJwUVERM2fOZMCAAWg0GubOndukzNKlS1EUpclitwf31uEzQezkKQDUrF2H6naHuTVCCCFE59DmwLJixQrmzp3LggUL2Lp1K+PHj2fKlCkUFhY2W97hcNCtWzcWLFjAsGHDWqw3NjaWoqKigMVkMrW1eR2ieL+F/7y+i68/PhD0uqPGjEYbF4enspJ6uVtICCGEANoRWJ588klmzZrFzTffzKBBg3j66afp0aMHS5YsabZ8r169eOaZZ/jFL36B2WxusV5FUUhNTQ1YOquaSju7Nxexf2tZ0OtWdDpiJk4EwPrxx0GvXwghhDgTtSmwOJ1O8vLymNjwg9po4sSJbN68+bQaUltbS2ZmJhkZGUydOpWtW7eetLzD4cBqtQYsHSWldywAFYdrcTuDfzdP7BXHXRZyuYJevxBCCHGmaVNgKS8vx+PxkJKSErA9JSWF4uLidjdi4MCBLF26lA8++IBly5ZhMpkYN24ce/fubfEzixYtwmw2+5cePXq0+/htFZNgIiJGj9erUn64Nuj1R44ahTYxEY/FQt0XXwS9fiGEEOJM065Bt4qiBLxXVbXJtrYYM2YMP//5zxk2bBjjx4/nnXfeoX///jz33HMtfmb+/PlYLBb/cujQoXYfv60URSGlt+/yVklB8Ht2FJ2O2EmNl4XWBL1+IYQQ4kzTpsCSlJSEVqtt0ptSWlrapNfltBql0XD++eeftIfFaDQSGxsbsHSklF4xAJQcCM2lqJjJk4GGSeSczpAcQwghhDhTtCmwGAwGsrKyWLduXcD2devWMXbs2KA1SlVV8vPzSUtLC1qdwZbSq7GHxRKS+iOzstB164bXaqX2NMcHCSGEEGe6Nl8SmjdvHn/729/4+9//zq5du7jrrrsoLCxkzpw5gO9SzS9+8YuAz+Tn55Ofn09tbS1lZWXk5+ezc+dO//4HH3yQTz75hP3795Ofn8+sWbPIz8/319kZJfeKQVFAq9PgCsHAW0WrJWbSJABq5G4hIYQQZ7k2T80/Y8YMKioqeOihhygqKmLIkCGsXr2azMxMwDdR3IlzsowYMcL/Oi8vj7fffpvMzEwOHDgAQHV1NbfccgvFxcWYzWZGjBjBhg0buOCCzjs1vTFSz81PXYjBFLqnG8ReMYWqN9+k5tP/4HU40BiNITuWEEII0Zkpqqqq4W5EMFitVsxmMxaLpcPHs4SK6vXyw2WX4y4qovuTTxB7xRXhbpIQQggRVK39/ZZnCQVBqDKfotEQd+21AFS988+QHEMIIYQ4E0hgOQ21VQ7e/Wsery/YHLLQEnf9daAo1H/xBc6DB0NyDCGEEKKzk8ByGiJi9JQeqKG20oGlzBaSY+i7dydq/I8AqP7Xv0JyDCGEEKKzk8ByGrQ6DUk9ogEoDdF8LADx06cDUP3uKpmTRQghxFlJAstpSunlGyAUihlvG0VfdBG6bt3wVFRQ89//hew4QgghRGclgeU0JTcGlhD2sCh6PebrrwOg+p13QnYcIYQQorOSwHKaGp/cXH6oFo/bG7LjxN1wAygKdZs34+zA5yYJIYQQnYEEltNk7haBMVKHx+2l4kjwn9zcyJCRQVTD4w+q/ymDb4UQQpxdJLCcJkVRyBgYT6/zktBo2//E6taIaxx8u+pdVJcrpMcSQgghOpPQzSt/Fpk0ewiKEtqwAhBz6SVok5LwlJVT89lnxE6YEPJjCiGEEJ2B9LAEQUeEFfANvm2c+bZ62bIOOaYQQgjRGUhgCSJruY2aSntIjxE3YwZotdRtzsV+3BOvhRBCiK5MAkuQbH73B964P5dv/xvaO3gMGd2JnTwZgIpX/x7SYwkhhBCdhQSWIOnWMwaAwp2VIT9W4s2zALB+/DHOw4dDfjwhhBAi3CSwBEmPQQkoClQerQv5ZSHToEFE/ehH4PVS+drSkB5LCCGE6AwksASJKUrvn0TuUAf2slSvXIm7MvTHE0IIIcJJAksQ9RicCEDhjoqQHyty9GhMQ4ag2u1UvfV2yI8nhBBChJMEliDqeW4CAId2V+H1hG6afvDdSt3Yy1L15pt46+tDejwhhBAinCSwBFFyZizGKB1OmzukT29uFDNhAvrMnngsFqpXvhvy4wkhhBDhIoEliDQahexr+jL51iEkZkSH/HiKVkviL38FQOVrr8l0/UIIIbosCSxBdu747vQdkYzB1DFPPTBfczXaxERcR49i+eCDDjmmEEII0dEksJzhNCYTibN8Y1nKnn8Br8MR5hYJIYQQwSeBJQTKD9fw5Yf7KdwZ+ruFAOJ/NhNdairuoiKq5BlDQgghuiAJLCGw96sSvvroAN9vKemQ42mMRrrd/lsAKl58CU9NTYccVwghhOgoElhCoGfjfCw7K0J+e3Mj89VXY+jTB091NZWvvdYhxxRCCCE6igSWEEg9x4wpSo+txsXhPVUdckxFp6PbXXMBqFj6D9zl5R1yXCGEEKIjSGAJAa1WwzlZyQB8/2XHXBYCiLn8ckznnYdaX0/5khc77LhCCCFEqElgCZH+o1MB2L+1DJfT0yHHVBSF5HnzAKh65x2chw51yHGFEEKIUJPAEiKpfWKJTTLhcng4sK3jLs9EjRnte5Kzy0XZM8922HGFEEKIUJLAEiKKotD/glSMkToc9R07A23yvLtAUbD++9/Uf/VVhx5bCCGECAUJLCE0YkJPfvnYjxhyUUaHHtc0eDBx06cDUPzQQzJlvxBCiDOeBJYQMkTo0OrCc4qT75qLNj4ex94fqHzjzbC0QQghhAgWCSwdQFVVyg517GRu2rg4ku+5G4Cy55/HVVzcoccXQgghgkkCS4h5XF7e+uMXvPPwV1SX1nfosc3XXkvEiBGo9fWU/OXRDj22EEIIEUwSWEJMq9dgTooAfFP2dyRFoyH1j38AjYaaNWuo3fR5hx5fCCGECBYJLB2gcU6WPVuKUVW1Q49tGjiQ+J//DICSP/0Jr9PZoccXQgghgqFdgWXx4sX07t0bk8lEVlYWGzdubLFsUVERM2fOZMCAAWg0GubOndtsuZUrVzJ48GCMRiODBw9m1apV7Wlap9R7WBI6gwZLqY3SAx3/YMJud9yBrls3nAcPUv7C4g4/vhBCCHG62hxYVqxYwdy5c1mwYAFbt25l/PjxTJkyhcLCwmbLOxwOunXrxoIFCxg2bFizZXJzc5kxYwY5OTls27aNnJwcpk+fzpYtW9ravE7JYNLRe1g3AHZuPtrhx9dGR5Ny//0AVLzyCrb8/A5vgxBCCHE6FLWN1yhGjx7NyJEjWbJkiX/boEGDuOaaa1i0aNFJP3vxxRczfPhwnn766YDtM2bMwGq18vHHH/u3TZ48mfj4eJYtW9aqdlmtVsxmMxaLhdjY2NZ/oQ5ydG81q574Bq1ew42LxhIRbejwNhy5916sH3yIITOT3qveRRMZ2eFtEEIIIY7X2t/vNvWwOJ1O8vLymDhxYsD2iRMnsnnz5va1FF8Py4l1Tpo06aR1OhwOrFZrwNKZpZ1jplvPGDwuL/vySsPShtT770eXkoLz4EFK//pEWNoghBBCtEebAkt5eTkej4eUlJSA7SkpKRSfxjwfxcXFba5z0aJFmM1m/9KjR492H78jKIrCuBvO4Zq7RnDuhd3D0gZtbCxpjzwMQNXbb1P7udw1JIQQ4szQrkG3iqIEvFdVtcm2UNc5f/58LBaLfzl0BjyZuHv/eLoPiD/tc3U6oseNI37mTACKfr8Aj8UStrYIIYQQrdWmwJKUlIRWq23S81FaWtqkh6QtUlNT21yn0WgkNjY2YDmTOO3uDr/FuVHyPXdjyMzEXVJC8Z/+HLZ2CCGEEK3VpsBiMBjIyspi3bp1AdvXrVvH2LFj292I7OzsJnWuXbv2tOrszLZ8uJ9/3Pc5h/dUheX4mshI0h/9C2g0WP/9b6r/+c+wtEMIIYRorTZfEpo3bx5/+9vf+Pvf/86uXbu46667KCwsZM6cOYDvUs0vfvGLgM/k5+eTn59PbW0tZWVl5Ofns3PnTv/+O++8k7Vr1/Loo4+ye/duHn30UT799NMW52w50znq3TjtHrZ9Gr7LWBHDh9PtrrkAlPz5YWzbd4StLUIIIcSp6Nr6gRkzZlBRUcFDDz1EUVERQ4YMYfXq1WRmZgK+ieJOnJNlxIgR/td5eXm8/fbbZGZmcuDAAQDGjh3L8uXLuf/++3nggQfo27cvK1asYPTo0afx1TqvYZdm8N1nhzm4vYLKojoS0qLC0o7Em2/GtjWf2v/+lyN33knvlf9CGxcXlrYIIYQQJ9PmeVg6q84+D8uJVi/5loJt5Qwen84lPxsYtnZ4rFYKrr8B16FDRF90ERlLFqNo5IkNQgghOkZI5mERwTP88p4A7PmimLpqR9jaoY2NJePZZ1CMRmrXr6fi5ZfD1hYhhBCiJRJYwiTtHDOpfcx4XF6++qggrG0xDRpE6h/+AEDZs8/JU52FEEJ0OhJYwkRRFLKv6wvAni9LsNe5wtqeuOuvI+7HN4DXy5G5c3Hs3RvW9gghhBDHk8ASRunnxPGjH/fjp3+4AFOUPtzNIeWBB4gcNQpvbS2Ft96Ku6ws3E0SQgghAAksYTfssh7EJkaEuxkAaAwGMp5/DkOvXriPFnHo17fhtdnC3SwhhBBCAktnUnGkNuyzzmrj4ujx0oto4+Kwb9/O0XvvRfV4wtomIYQQQgJLJ6CqKp++tpPlf/qSg99VhLs5GDIzyVj8AopeT826Tyl9/K/hbpIQQoiznASWTkBRFKLijADkvrcPrzf8U+NEjhxJ2qJFAFQuXUr5iy+FuUVCCCHOZhJYOomRk3pijNRRebSO3blF4W4OAOapV5J8770AlD39NJWvvx7mFgkhhDhbSWDpJIyRekZd0QuA3Hf3YatxhrdBDRJ/9UuSfvtbAEoeWUSVPChRCCFEGEhg6USGXpJBYkY09joXG9/pPPOgJP3mNhJ+9SsAiv/wRywffhjmFgkhhDjbSGBphY66c0er1XBpzkAUBfZ+VcKBb8s75LinoigKyf93D3E//QmoKkfvm491zSfhbpYQQoiziASWk/B4PTz7zbNMeXcK5baOCQ/JmbEMu7wnkWYDilbpkGO2hqIopD7wAOZrrgGPhyPz5mF5//1wN0sIIcRZQgLLSWg1WrYUb+FI7RE+2v9Rhx33gqt6M/OPo8k8N7HDjtkaikZD2sN/xnzddeD1cvR391G1bFm4myWEEOIsIIHlFK7uezUA7+97v8MuDekNWoyRx6bqD/dkcsdTtFrS/vwn4n/+cwCKH3yIildfDXOrhBBCdHUSWE5hUq9JGDQG9lbtZU/Vng49tqqq7P6iiJWP5eFydp7ZZhWNhpQFvyfx1lsBKH38r5Q9+2ynClZCCCG6Fgksp2A2mrm4x8UAvP9Dx47ZcDk8fLFqHyUFVjYs/75Dj30qiqKQfNdcus2bB0D54iUU3X8/qiu8T50WQgjRNUlgaYWrz/FdFlpdsBqXt+N+kA0mHZf/6lwUBXZvLmLX5qMdduzWSrplNqkL/wgaDZaV71J4yy14rNZwN0sIIUQXI4GlFbLTs0kwJVBpr+TzI5936LEzBsRzwVV9AFi/7HvKD9d26PFbI/4nP/E9eygykvrcLzj4s5/hOnIk3M0SQgjRhUhgaQW9Rs+Vfa4E4IN9H3T48bMmZ9Lz3EQ8Li9rXv4Op83d4W04lZiLL6bXm2+gS07GsfcHCmb8BNu334a7WUIIIboICSyt1Hi30GeHPsPisHTosRWNwoRfDiY63oil1Mb/3tzdKQe4mgYPptc7KzAOGICnvJyDP8+heuXKcDdLCCFEFyCBpZUGJAxgQPwAXF4XHxd83OHHN0XrmTR7CBqdQmxSBJ0wrwCgT00l8603ib70UlSnk6IF91P0x4V4nZ3j2UhCCCHOTBJY2mBa32kAfLgvPM/SSe1j5ucPZZN9bV80ms4zC+6JtNHRZDz/HN3uvAMUheoVKziYk4OruDjcTRNCCHGGksDSBlf0uQKtouXb8m8psBSEpQ0xCSb/a5fTQ8WRzjcIF3xztST9+tf0eOlFNGYz9m3fUnD9DdRu6thBy0IIIboGCSxtkBSRxLju44DwDL49nq3WyXtPbuW9p7ZSXVIf1racTPSFF9L7X//EOHAgnooKDt18MyWPPY4ql4iEEEK0gQSWNmq8LLRq7ypsblvY2qHVaVC9KvZaFx8+v416a+cNAIYePei1fBnxM38KQOXf/86Bn87EeeBAeBsmhBDijCGBpY0u7XEp3aO7U2Gv4J0974StHQaTjqm/HUZskglrmY2PXtiG0975bndupDGZSP3DH8h4/jm0ZjP2HTvYf931VK9c2SnveBJCCNG5SGBpI71Wz63n+Z6h8+p3r1LvCt/lmMhYA1fdPhxTlJ7SgzX8+7ltnXKOluPFXH45vd9/j8gLLkCtr6dowf0cmjMHV0lJuJsmhBCiE5PA0g5X9b2KnjE9qXJU8fbut8PalriUSK66YxjGSB1F+yx88Gw+jk4eWvSpqfR87e8k33M3isFA3foN7J96FdUr35XeFiGEEM2SwNIOOo2OOcPmAPDa9teocdaEtT3JmbFcPXcExigd1go7tk48nqWRotWSePPN9H53JabzzsNbU0PRggW+3pajne+ZSUIIIcJLAks7XdH7CvqY+2B1Wnlz55vhbg7desZwzV0juGbuCOJSIsPdnFYznnMOvd5+i253z0PR66lbv4F9V06l4tW/y5OfhRBC+ElgaSetRsuvh/8agNd3vt7h0/U3JykjhoT0KP/7g9srsFaE706m1lJ0OpJmz6b3e6uIyMpCtdkoffxxCq6/gfpvtoa7eUIIIToBCSynYWLmRPrH96fWVcs/dvwj3M0JUFxg4eOXvmPlo3mUHrSGuzmtYuzbl8w3Xift4YfRxsXh+P57Ds6cydEFC3CXl4e7eUIIIcJIAstp0Cgabht+GwBv7nqTSntlmFt0TJTZSFxyBPVWJ6v++g3788vC3aRWUTQa4q6/jj4fr8Z8w/UAWFa+y75Jkyl/5RW8DkeYWyiEECIcJLCcpkt7XMrgxMHY3Dae+PqJcDfHLybBxHX3ZNFzcAJul5ePX/qObf85dMbchaOLjyf9z38m8+23MQ0direujrInnmT/lVOxfrL2jPkeQgghgqNdgWXx4sX07t0bk8lEVlYWGzduPGn59evXk5WVhclkok+fPrz44osB+5cuXYqiKE0Wu93enuZ1KEVRmH/BfBQUPtj3Af8r/F+4m+RniNBxxW/OY/D4dFBh0z/38t9/7MLl9IS7aa0WOXIEvVYsJ/3Rv6BLTsZ1+DBH7ryTgz+dSf1XX4W7eUIIITpImwPLihUrmDt3LgsWLGDr1q2MHz+eKVOmUFhY2Gz5goICrrjiCsaPH8/WrVv5/e9/zx133MHKlSsDysXGxlJUVBSwmEymZuvsbIYnD+fGc28E4MHcB6m2V4e3QcfRajVcPHMAY687B0WB3V8Us3tzUbib1SaKRoP56qvpu+Zjkm77NYrJhC0/n4M5v6Bw9i3Yd+4MdxOFEEKEmKK2sW999OjRjBw5kiVLlvi3DRo0iGuuuYZFixY1Kf+73/2ODz74gF27dvm3zZkzh23btpGbmwv4eljmzp1LdXV1O78GWK1WzGYzFouF2NjYdtfTXg6Pgx9/+GMKLAVM6T2Fxy58rMPbcCqH91SxO7eIy34xCEWjhLs57eYqLaV8yRKq//kvcPsmyYuZMplut92GsV+/MLdOCCFEW7T297tNPSxOp5O8vDwmTpwYsH3ixIls3ry52c/k5uY2KT9p0iS+/vprXMfNs1FbW0tmZiYZGRlMnTqVrVvPrNtZjVojD497GI2i4eOCj1l3cF24m9RExoB4Lr9psD+suJ0evl5dgMtx5lwiAtAnJ5P2xz/Sd/VHxE6dCkDNx2vYP+1qDs+9C/ue78PcQiGEEMHWpsBSXl6Ox+MhJSUlYHtKSgrFxcXNfqa4uLjZ8m63m/KGW1UHDhzI0qVL+eCDD1i2bBkmk4lx48axd+/eFtvicDiwWq0BS7gN7TaUWUNmAfCn3D9RYasIc4tObsOK79nyQQEr/vwlRfvCP49MWxl69qT7Xx+n9/vvETNxIqgqNWvWUHD11Ry+/Q5sO3aEu4lCCCGCpF2DbhUl8HKCqqpNtp2q/PHbx4wZw89//nOGDRvG+PHjeeedd+jfvz/PPfdci3UuWrQIs9nsX3r06NGerxJ0c4bNoV98P6ocVTyU+1CnvpulX1YK0fFGLGU2Vv01j80rf8DtOrN6WwBMAwaQ8ewz9H7/fWImTwZFoWbdOg5cfwOFv/oVtZ9/3qn/OwghhDi1NgWWpKQktFptk96U0tLSJr0ojVJTU5str9PpSExMbL5RGg3nn3/+SXtY5s+fj8Vi8S+HDh1qy1cJGYPWwMPjHkan6Pjvof+yeNvicDepRT0GJ/CTBy5gYHYqqgpb1xXyziNfU7z/zOttATAN6E/G00/R54P3ib3qKtBqqducy6FZN1Nw3fVYPvy3TPcvhBBnqDYFFoPBQFZWFuvWBY7PWLduHWPHjm32M9nZ2U3Kr127llGjRqHX65v9jKqq5Ofnk5aW1mJbjEYjsbGxAUtnMShxEA9kPwDAi9te5IN9H4S5RS0zRuq57MbBXPHroUTEGqgqqmPlY3ns/PzMfQChsV8/uj/+GOes/YT4X+SgRETg2LWLo//3f/xw2eWUL1mCu7LzTPInhBDi1Np8l9CKFSvIycnhxRdfJDs7m5dffplXXnmFHTt2kJmZyfz58zly5Aivv/464LuteciQIdx6663Mnj2b3Nxc5syZw7Jly7j+et9Mpg8++CBjxoyhX79+WK1Wnn32Wd544w0+//xzLrjggla1K9x3CTXnmW+e4W/f/Q2dRsfLE17m/NTzw92kk7LVOtn87j4K8sv46R9HE2U2hrtJQeGuqqJ6+XIq334bT5lv3JRiMBB75ZXE/+xnRAw5N8wtFEKIs1drf7/bHFjAN3HcY489RlFREUOGDOGpp57iwgsvBOCmm27iwIEDfPbZZ/7y69ev56677mLHjh2kp6fzu9/9jjlz5vj333XXXbz77rsUFxdjNpsZMWIECxcuJDs7O+hfuCN5VS/3briXTw58QowhhjeveJM+5j7hbtYp2WqcRMQY/O+3fLCfnoMTSDsnLnyNCgLV6cT6ySdUvv4G9u++8283DRlC/E9mEHvFFWgiz5wnXQshRFcQ0sDSGXXGwAJgd9u5ee3NbCvbRvfo7rx1xVskRjQ/dqczOri9gn8/vw2APsO7MeaaPsSnRp3iU52bqqrYt22j8s23qPnkE/+4Fk10NOZp04i74XpMgweHuZVCCHF2kMDSiVTaK/nZRz/jcO1h+pj78NKEl0iNSg13s1qlzuLgy38XsGvTUVQVFI3CuT9KZ9SVvbrEJSN3ZSWWVauoWvEOruNmazYOHEjcddcRe9VUdPHxYWyhEEJ0bRJYgqmmGGJOL2ActB5k1iezKKkvIT0qnVcmvkLP2J5BamDoVR6tI/e9fRz41jcGRKvXcO6P0hl9dR8MJl2YW3f6VK+XutxcLCtXUrPu02N3E+n1xFx8MbHTriL6oovQGAwnr0gIIUSbSGAJBrcDPvk9bFsBczZAwumNPzlae5Rb1t3CQetBEk2JvDThJQYkDAhOWzvIke+r+OK9fRTvtxLbLYKfLRyNRtu1Hvrtqa7G8tFHWFa+G/CcIk1sLLGTJ2O+aioRWVkomq71vYUQIhwksASDxw3/uAoKN0P6SPjVJ6A7vX9hl9vKmbNuDnuq9hBjiGHJ5UsY1m1YcNrbQVRV5fDuKrxelcxzfeNx3C4Pm//1A+de2J3E7tFhbmHw2Pfswfrhh1g+/DfukhL/dl1KCrGTJxEzeTIRw4efdOJEIYQQLZPAEizVh+DFH4G9GsbdCRMeOu0qLQ4Lv/nPb9hWtg2T1sQD2Q8wre+0029rGO3cdJT/vbkbgJ7nJjB8Qk8yBsR3mR9y1eOh/quvsXz4ATWfrMVbW+vfp0tPI3biJGImTvCFF+l5EUKIVpPAEkw7P4B3cnyvf/4unHPZaVdZ76rnnvX3sPHIRgBu6H8D911wH0btmTmQtaywhrw1B9i/tYzGP1EJ6VEMvag7/UendolxLo28Tid1mz7H+vHH1P7nP3jr6/37tN2SiLnsMmIun0DUBeejyJgXIYQ4KQkswfbvu+Drv0NUMvx6M0R3O+0qPV4PL3/7Mku2LUFFZXDiYJ646AkyYjKC0ODwsJTZ2PbfQ+z6/ChupxcAg0lLzsNjMUU1P7Pxmcxrt1O7cSM169ZR+7/P8NbU+PdpoqOJGv8jYi65hOgLL0QbFxe+hgohRCclgSXYXDZ4+RIo2wXnXA4z/wlB6vr//Mjn3LfxPqod1cQaYvlj9h+Z2GtiUOoOF0e9iz1bitm+/gjRCSam3THcv6/g23LS+pq7XIBRnU7qtnxJzbp11PznP3gqjntat1ZLxIjhRF94EdEXjsc4YECXuVwmhBCnQwJLKJTshFcuAbcdJvwJxt0RtKqLaou4Z/09fFv+LQCX9byM34/+PcmRyUE7Rjioqoqj3u0PJ3XVDv4x/3M0Wg29hycxcEwaGYPi0XaxO41Urxf7d99R87//Ufvf/+H4/vuA/brkZKLG/4jo8eOJGjNGel+EEGctCSyh8tXf4KO7AQWmPQcjc4JWtcvj4qVvX+LV717FrbqJ0ccwb9Q8ru93fZf513jpQSv/fX0XFUfq/NtMUXr6ZiXT//xk0vrGoWi6xnc9nvPwEeo2bqB2/QbqtmxBtdmO7VQUTEOGEDVuLFFjxxIxfLjM9yKEOGtIYAkVVYWP74UvX/a9n/YcjPxFUA+xp3IPCzcvZHvFdgBGpYzi3vPvZVDioKAeJ1xUVaWssIbducX8kFeCrcbl33f5TYMYMKblp3R3BV6Hg/qvvqZu4wbqNm/GsfeHgP2KyUTkyJFEjhlD1JjRmAYPRtF1nUHLQghxPAksodQBocXj9fDmrjd5fuvz2D12FBSm9pnKb0f8lvTo9KAeK5y8Hi+H91Sx98sSDu6o4GcPjsEY6bt8tGPjEUoLa+gzvBsZ/ePR6rvWZaNGrpIS6jbnUvf559R98QWe8vKA/ZqoKCJGjiTy/POJuuB8TOeei6LvWuN/hBBnLwksoaaq8PHv4MuXfO9DEFoAjtQe4ZlvnuHjgo8BMGgM/GzQz5g1dBZmoznoxwsnr8cbMGvuvx79mpICKwA6o5aegxLIHJpIr6FJRMZ2zUsmqqri/OEH6r7YQt2WL6j/8iu8VmtAGSUigohhw4gcOZKIkSOJGD4MbXTXmaxPCHF2kcDSEU4MLRf/Hi68BzTaoB9qR/kOnsh7gq+KvwIgUhfJj/v/mJzBOaREpQT9eJ3BoZ2V/LC1lAPfllNvcQbs6z4gjqvnjugyY3taono8OPbsof7rr6n/6ivqv/oaT3V1YCGNBuOAAUQMH0bkiBFEDB+OvkePLn9uhBBdgwSWjqKq8MkC+OIF3/s+l8B1rwRlnpamh1LZeGQjz37zLHuq9gCg0+iY1ncavzz3l/Qy9wr6MTsDVVUpP1RLwbflHPyunNKDvstEU+YM9Zf53xu7SEiPJmNgPAlpUV1y4C747j5y7t9Pfd432L7Joz7vG1yHDzcpp01MJGLoUCKGnYdp6HlEnDcUbSd7irkQQoAElo5vQP7b8O954LZBTBrc8HfIHBuSQzUGl1e/e5VvSr/xbx+XPo7pA6ZzYcaF6DRdd5BmncWBy+4hLiUSAEtZPW8+8IV/f0SMnu794+neP460c+K6dIAB3xgY29Z8bPn52LZuxb5z57GnTR/HkJmJaehQTEPOJWLIEEyDBqGJigpDi4UQ4hgJLOFQshP+eSOUfw+KFi6e73v+0Gk+MPFktpZu5dXvXmX94fX+bSmRKVzf/3quPedaUqNSQ3bszqLe6mT3F0Uc2VPF0b3V/hl2G42Y0JOx158DgMfjBS9ddgAv+O5Csu/cif2777Bt+xbbd9/hKixsWlBRMPTpg2nw4GPLoIHSEyOE6FASWMLFUeubxv+7d3zvE8+BKY/6ZscNoUPWQ/xz7z95b+97VDmqAFBQuCD1Aq7scyUTMicQbej6AzM9bi8lB6z+8FK838LlvxxM3xG+CfgO767kw+e3kdwzltS+ZlJ6xZLSO5boeGOXHvPhrqrCvn0H9h3bsW3fjn37DtzFxc2W1XfvjnHQQEwDB2EaOADjwIHo09PloY5CiJCQwBJOqgrfvgNr74e6Ut+2gVNh0iMQnxnSQzs9TtYdXMc/v/8neSV5/u1GrZGLMi5iQq8JjO8+nij92XEpwOPxggpane/H9ptPDpK7al+TcpGxBpJ7xXLB1N506xnT0c0MC3dZGfZdu7Dv2IF9505sO3bgPlrUbFlNVBTG/v0xDuiPsX9/TP36YezXT2boFUKcNgksnYHdAp89ClteBNUDOhOM+hWMvR1iQz+XypHaI6zev5p/7/83+y37/dsNGgNj0sdwWc/LuCjjIhIjEkPels5CVVUsZTaK91so3meh5ICViiN1qF7f/w2m//58f2D5/qti9uWV0a1nNEkZMST1iCYqrmv3xHiqq7Hv+R7H7l3Yd+3Gvns3zn37mh0TA6Dr1g1jv34Y+52DoW9fjOf0w9i3D1pz17rlXggROhJYOpPSXbD6/+DARt97jR6Gz4QfzYWEPiE/vKqq7K7czccHPua/hf/loPWgf5+CwuDEwYzrPo4fdf8RQ5OGdukBu81xOT2UF9ZQcsDK0Esy/M81+u8bu9j1eWCPgylKT2JGNEndo8makklETNecD+Z4qsuF88ABX5DZswfH3r04vv8e19GjLX5G2y0JY5++GPv2wdCnL8Y+vTH06YMuJaVLBz4hRNtJYOlsVBX2/Qc2PgkHP/dtUzQw+GrI+iX0Gh+0pz+fvBkq+6r38Wnhp/y38L/sqtwVsD/GEMOolFFckHoB56eeT7/4fmiUs3PsQulBK0f3VlN+qJbywzVUFtX7e2IAZj91IYYIX7j7evUBSg5YSUiPIiEtioT0KOJTItEZgj8nT2fhqa3F+cMP2PfuxfnDPhz79uH44YcWx8YAKJGRGHplYuzVG0Pv3hh69WpYMtHGnB2X4oQQgSSwdGYHc2HTk7B37bFt8b19M+UOnwkxHXdnT1l9GZuPbmbTkU1sProZqzNwVtU4Yxwjk0cyInkEw5OHMzhxMAZt1+9VaI7b5aHyaB3lh2uprbRzwVXHesfee+objuypDvyAArGJJuJTo5hy61D/nUkuhwedQdNlexo8tbU49+3Dsb8A5/6G9b59OA8dAo+nxc9pExMxZGZi6NkTQy/fWt8zE0PPHnLnkhBdmASWM0Hxd/D13+Hbf4KzxrdN0UKfi309LwOnQlTHjS/xeD3srNjJl8Vf8lXxV3xT+g02ty2gjF6j59zEcxnabShDEodwbtK59Izp2WV/fFur6Idqyg7VUHm0jsqiOiqP1uGodwO+eWF+9fh4f9kPns2neL+F+JRIzMmRmLtFYE6OwNzN97rLPnbA5cJ56DDOAwU4CwpwFBTgOnAQx8EDeMrKT/pZrdmMvmdPDD16oO/ZA0NGBvqMHugzMtCnpsjDIYU4g0lgOZM462DHKvjmdTi05dh2RQu9fgSDroJ+EyC+V4c2y+V1saN8B1tLt5Jfmk9+WT6V9som5WIMMQxOHMyghEEMSBjAwPiB9DL3OuvGwhxPVVVsNS6qin3Bpc/wYzMfv3H/Zqzl9mY/Z4rWM+uvx8LNzk1H8Xq8xCRFEJtoIibRhE7f9S4zeWprcR44iKvwIM7CQpwHC3Ee9L0+8WGQTeh06NPS0Hfvjj6jO4bu3X2v09PRd++OLjkZRdv1zpkQXYUEliAprbFj1GoxR3bQ03HLf4Bd78PO96FoW+C+hL6++VzOucw3i66xY6/5q6rKoZpD5Jfls718OzvKd7C7cjdOr7NJWaPWSB9zH/rF9+OcuHP8S2pU6lnfG+NxebGU26guqcdSaqO6rB5Lqe91dLyR6+8d5S/75gO5WMoCe7kizQZiE00kZcRw0cwB/u3WChumKD0GU9cKit66OpyHD+MsLMRVeAjXkcM4Dx3GdegQriNHWryDyU+nQ5+S4gsw6Wno0tN9ASctHX1aKvq0NJnxV4gwksASJPPeyWfdjhJ+Oa4Xv/pRb+IiO7C7vrLAF1z2roXCL3y3RjdStJB2HvQc6wsvPbM79PJRI5fHxd7qveyu3M2uil3sqdrDnso91Lvrmy0foYugV2wvept708fch0xzJpkxmWTGZhKpj+zg1nc+Xq+K5rjHCHy+8geqS+qpqbBhLbfjchz7M5CcGcOP55/vf//mH3KxlNowRuqIjjcSHW8iKt5ITLyRuJQozslK7tDv0hFUrxd3SQmuI0dwHTmC8/BhXIeP4Dp61LcUFYHbfcp6NLGxvhCTmoouNRV9agq61DTfOiUFfUqKhBohQkQCSxA43V6ueeFzdhb5BqJGG3XcNLYXs37Um/ioDh5nYLdAwQb44T++u42qm5lqPS4TumdB95G+derQDu+FAfCqXg7XHGZv9V5+qPqBH6p9ywHLAdxqyz8e3SK60TO2Jz1iepARnUFGTAY9YnrQPbo7CaaEs75nRlVV7HUurOV2airsaHUKvYd18+9bet/nTZ5q3ejEcLPi4S/xuLxExRmJMhuJijMQafa9jk0ykZx5hl1WbYHq8eAuK/MFmqNFuIqKcBX5woz7aBGu4mK8NTWtqksTHY0uNQV9cgq65GR0KSnokruhT2l4n5yMLjERRd9BvbFCdBESWILE61X5ZEcxz/xnL7uLfX+xRRm0/HhUD64b2Z2h3c3h+SG1HPbdbXTwcyjMhbLdzZeL7w0p5/rCS8q50G2QbyyMtuMvG7i8Lg7XHGa/ZT8FlgIKLAUcsB6g0FpItaP6pJ81aU2kR6f7lqh00qLTSIlMIS0qjdSoVFIiU9Br5YfCaXdTW+mgpspOXZWD2io7tVUOYhJNnH9lb8AXbl66fT0et7fZOpJ7xfLj+45dlnr/6a2oXpXIWAORsUYizQYiYgxExOiJSTCR2P3MfuSDp7YWd5EvvLiKinAXl+AqKfati4txl5Tgra1tXWWKgjYhAV23boFLUpJvndzwOikJTaT0KAoBEliCXr/Xq7JuVwnPfLrX3+MC0KdbFNcO787Vw7vTMzGMfwHZquBoPhzJg6Nbfeua5qdZR2vwPeMoqb9vSezrGx+T2BciEzq02Y0sDguF1kIKawo5XHOYw7WHOVRziEM1hyirL0Pl1H9ME02JpESlkByZTEqkb90tohvJkckkRSSRHJmM2Wg+a+eVaaSqKtUl9dRWO6ivdlBncVJX7fAtFieJGdFc3DA25lThJqV3LDf87li4ee/Jb/B6VV+gidb7g01EtIGYRBOpfc7MGXA9tXW4S0twFxfjKi3FXVKKu7QUd2kJrpJS3GVluMvKWnX5qZEmMhJttyR0iUnoEhPRJiX6Xiclok087nVCIpqoyLO+h1F0XRJYQkRVVdZ/X8bKb46wdkcxjuP+Ij8nOZrx/ZK4sF83RvdJINIQ5sGPdeVQsh2Kt/vWJTugfC+ccKtyAFOc73lHcZnH1nGZYM7wLaaOv1Tg9DgprivmSO0RjtYe5UjtEUrqSyiuK/YvzQ38bY5O0ZEQkUBSRBJJEUkkmBJINCWSGJHoex2RSLwxngRTAnGmOPSas7vXRvWqHN1bTZ3VQb3FSb3Vt9isTuprnHTrGcOlOYN8ZU8RblL7mLn+3iz/+7cf3ILH5cEUpccUbcAUrcMUpSciWo85OZJ+o1L8ZeuqHehNWvRGbaf94Va9XjzV1b4gU1aGu7TMH2TcZWW4y8v9r1V783eJtUQxGtEmJqBLTEKbEI8uIfG4dQK6hHi0CQlo432vlYiITnuehDiRBJYOUGN38cmOEt7beoTN+8o5bhJU9FqF8zLiGN7j2JIR3wn+EvF6wXIIyvZA+R6o+AEq9kHlfrAeOfXnjWYwd/c9Cykm7dg6Jg1iUiA6BaKSO/SSk6qqVDmqKKkrobS+1B9mym3llNpKKasvo6y+zP8U67aINcT6wosxjjhTHPHGeOKMcZiNZt+2417HGmMxG80YtcYQfMvOT/WqHP2hGluNC1uN07fUuvzvEzOiuXBGf1/ZU4SbtL5mrvu/Y+Fm6e82UWdxotEqGKP0mCJ1GCP1mKJ0JHaPZsw1ff1l9+eXoWgUjBE6jJG+xRCh6zRhR1VVvHX1uMtK8VRU4C6v8IWZ8jI8FZW4Kyp82xsW1XaSf2C0QDEaGwJMHLr4BLTx8Q1LHLr4eLRxcb7luNcakykE31aIU5PA0sEs9S427ytnw95yNu4t43BV079kEqMMDEyLoX9KDANSYhiQGsM5ydHEmDrJv+Kd9VB1AKoPQtXBY68th3xjZmyt/cFXIDIRopMhqttxS5JviUzy7Y9qWJvMoAn9PBkuj4sKewUVtgrKbeWU2cqotFdSYavwre0VVNoqqXJUUe2oxqs2/2N6KiatiVhDLLHGWN/6uNcxhhhiDDFE66OJNcQSbYgm2hBNrP7Y67OhV6fxspS9zo291om9zoWt1oWjzoW91kVstwiyJvfyl3/lrg04bc1fbkk7x8x19xwLN6/9blOzg481GoWUPrEBZTeu+B6nw4MxwhdqfGsthggdkTEG0s6J85f1uLxodEqHhx5vfT3uyio8FeW4KyrxVFX61pWVuCsrfCGnqhJPZRWeykpUZ+t6G0+kmEy+8GI2Hws0ja/NZrRxZt/abEZjNqM1x6GNM6Mxnp0BXQSPBJYwUlWVgxX1fFNYRf6havIPVbOryIrL0/ypTowy0CspiszESHolRpERH0F6XATd4yJIiTVh0HWSMReOWl8vjOUQWIt8Y2SsR6GmGGqOQm2pb1Fbnn69eYovtEQmQEQCRMQ3LHG+tSnOt99k9m0zmcEY67s8ZYwNSdjxeD1YnVaq7FVUOar862p7NVWOKiwOC9WOaqod1VgcFqwOKxanpd0h53hGrZFovS+8ROt9S6Q+kmh9NFH6KP8SqY8kSh/l3x+pizy2Xedb6zX6TtGrcLpUVcXt8mKvdeGod+Goc2Ovd+God2OM1NF3xLFbtj9a/C31FgcOmxtHvRtnvRtvQ/dna8MNQEJ6FD/9w2j/+7cXfoGl1IY+QovBpPMtEVr0Rh3mJBMX/vTYnDjff1mMy+HBYNKhN2kxmHzl9MaGMBSi2Ywbe2881VV4qo4t7soqPNXVAds8lmrcVdV4qqvbNPbmRIrRiDY21hdeYs2+17GxaMyxaBvfm2PRNGzXxh57rZhMXeLPpzg9Elg6GbvLw+7iGr4vrmFPSQ3fl9Swu7iGshrHST+nKNAt2khKrImUWCPJsSaSY4x0izGSGGUkKdpAUrSRhGgDMUZd+P/P7/VCfQXUFkNdGdSW+dZ1pb4xNfUVDetyqKs49kiC02GI9gUXY4xvMcU2bItpWEcHvjdENSzHv25Y9JG+k96er656qXPVYXFYsDh9IcbqtFLjrPGvj39tdVqpddZS66ylxlXT5DEIwaBVtETqIonQR/jWuggidBFE6o+9bm4x6UzHXmtNmHS+JULr22fUGYnQRqDTdII/c6egqiouhwenzYOqqsQkHLv0sXPTUWy1Thz1bhw2Ny6bG4fNg9PmJrabiQm/PNdftvGyVHPi06KY+cfAcFNV3PxcRNHxRm5cNM7//qMXtlFVUu8LN0atf9EZtUTGGMi+9tjlroPbK3Da3OiMWvQGjW9t1KI3+NbteXq4L+TU+UJMtcUXbKqr8Vgsx9aWhm3VFrwWi2+b1er7//vp0OvRxsSgjYnxhZiYaDQxsWhiotE2WcegaSwbE4M2OhpNdLQ8lqELaO3vt/yX7iAmvdY/luV4NXYXByvqOVBR51uX13HUYuNotZ0j1Tacbi+lNQ5Kaxx8d4ohJjqNQlyknvhIA/GRBmIj9JgDFh0xJj0xJh3RJh2xJj3RRt/raKMOoy4ID+TTaCC6m29pDbcT7NVQXwm2St/aXu27/GRrWNstDUu1b22rBocV3A0DF521viUI2QfwhRZ9JBgij732v49oeB8BuoiG9ybQRaDRm4jRRxKjM5GhjwCdCXSxvktjugjQGRu2Na5NAU/odnvdvgDjqqXOVUeNs8b/+lRLvbueele9f233+M6NR/VQ46qhxhWskxNIq2gxao2+QKP1BRmT1oRRawx8fdx7g9ZwbK3zrY1ao2+tMR573bBu7rVeo2/13V6Kovh7RE40+Efprf6uMx8cg9Pmxmnz4LS7cdrduOweHDY3emNgL1+PQQmYkyNx2d047R5fYLK7fb0uEYHtsFbYsZQ2H1aj4owBgeXr1QUU77c2W9Zg0jL76Yv87z95ZTslBdZj4cagRWfQojdq0Jt0XPYL32BpRVE4uNdGTRXoDQloDUnoM7To+jR+RkNKjxiUhgkN3S4PGo2CovhmIfY0BBiv1YrHYm0IM8e9r7HitVjx1NQ0bK/xhR2PB1wuPJW+y1vtpURE+MOLL8hEoYmO8b2PjkIb8DoaTVRUw/uG11FRaKOiUAxd8xleXUm7AsvixYt5/PHHKSoq4txzz+Xpp59m/PjxLZZfv3498+bNY8eOHaSnp3PvvfcyZ86cgDIrV67kgQceYN++ffTt25eHH36Ya6+9tj3NO6PEmPQM6W5mSPemt3uqqkpFnZOiajulNXZKrA5KrL7X5bVOKmod/nWd04Pbq1Je66S8tn3XsLUahWijjiiDlsjGtUFHpEGLyaAlUq8l0qAlwqAjQq/FpNcQYdBi0jcsOg0mvRZjw7rxtVGvwajzvTboNOg0x40D0Bl8P+jR7ZiF1e30BRe7BRw1JyxW39pZ67uU5axteF/XsDS8d9X7xu646o7V66r3Lc3/Azm4NHp/iNHpjMTpjMRpjQ2hpmFpfK81HFtrDb7PaWMhwuA7j9pji0ejw6Yo1Csq9ajU4cGmeqlXPdhUDzbVTb3qxuZ1Y/e6sHld2LxO7F4nNo8Dm8eJzWPH5rbhcDuwN7y2u+3YPXb/pS+P6vGFpBZmNg4lnUaHQeMLMQaNAb1WfyzYaAy+/drA/XqNHoPW4Fs3bDt+n16jP7at4bV/e+N7gx6dSeffFqnRo9NoqLZXo9fq0Wl0jJt+TouB6sRO7Uk3D8Fe78LVEGyOLW60J1wO7tYzFq1O49vv9OJ2eHA5PbgdniahqbbKQU1l83cj6Y1af2AB2LHpCIU7Wg4Nty2+xP/609d2su+bMjQaBa1Bg06vQaf3BRutPp7r/+9ydAZfW7avP0xxgRWt/lg532sFjephwLkRKLZavDU1VBRaqKuyodjrUOx1UFeDYquBulqUWgua2grUGl9ZT22tfzCyarPhttmgrKzF9reGYjAEhBhN9LEwo4mKQhMZhSYq8th+//bIY+vGJSpKen5CoM1ndMWKFcydO5fFixczbtw4XnrpJaZMmcLOnTvp2bNnk/IFBQVcccUVzJ49mzfffJPPP/+c2267jW7dunH99dcDkJuby4wZM/jTn/7Etddey6pVq5g+fTqbNm1i9OjRTeo8WyiKQlK0kaRoI3Dy+SvsLg/V9S4q65xU1zupqndRbXNisbmw2twNaxdWu4sau5uahnWdw02d0zfmxONVsdhcWGyneDbLadIoYND5QoxBp8Gg1QSs9VqlYa3B2LDWaRu2azXotAp6raZhUdBpNOi1Uei0Meg0x/bpTAq6KAWd1heSdBoFXUP5wLWCVlHRex3oPTb0Hhs6jw2tx47OU+9bu20oHhtatx2Nux6Nx47itqO4bL5w47aDy9awtjdsc/huIXc7GvY1vD9+nIvXBU5XcC6NHUcLRDcsp1eRwReqtLqGtR5Vo8et1WLT6LFrtb5Fo8Oh0WLXaLArCg6NFoeiwaGAXaPgUMCBgkNRcYBvu6riUlQcqhcHKnbViwsvDtWDEy9O1Yvd68apenCqHhwnzJLs9rpxe91hCUutoVE06BSdP8ToFB06jS/o6DTHXh//3r8oOnQmHVqNln9uOu7zvXXo+vq265Rjdek1WhR0vLXrIHqNHq2ihUv0pI7VofFoUVxaFI8WXBrwKGjQ8E3JN8fqyXCRqo3A6/b9kfS6wOtU8bi8oCrUumvRKlp0Gh2uhr8vvF4Vr92Dy+4Bjv2doTkuZB3ZW80PX5e2eI4GXXQhxghfL9eWnbvY+WUREAEkBRbUw40vjiM63jfAN3fVPnZ+fgStVkGrAY2iolW8aPCiUd2M6VeJyVWDt6aGQ+VGimujUVwOFJcdjdMGDhuKw4Ziryf5aC4GVx2q00mNTUc9sWhq3GjUajTeMjReN4rXjUb1YHRY0DT8OVRR/P/bHMVgaBpmoiJRIiIDw01ERMP2iIb3jfsi0EREHNveUPZsDkJtHsMyevRoRo4cyZIlS/zbBg0axDXXXMOiRYualP/d737HBx98wK5du/zb5syZw7Zt28jNzQVgxowZWK1WPv74Y3+ZyZMnEx8fz7Jly1rVrs4+hqUz83pV6pxu6hweah1ubE7fut7pptbhxu7yUO/0LbaGtd3twd6wtjk92FweHG4vdpcXh8uD3eXB6Wl47/a0OOD4TKfVKL5FUY691ihoFN9fpFpF8f1LtKGMRqOgx4tJ4yJCcWLCjVFxYVTcGHFhxOl/bcCFERf6htd61Y1ecfrWuNHjQqe60asudLjQqy60qhsd7obXDe+Pe31s7UbrdaJR3WhUN1qvGw1tHSzdsVR8P4tORfEvLkXBoSg4Ffzv/fsJ3OY6oZyLhrVyrE43BJR3KRpcGgW3v6yCW6Hhs+BuPAagdu6hPEGj9erQeQwYVSNG1YTea8CgGjF4DehUA+WJ+9EqGjSKhrSK/sTUd0PnNaBT9Wi9enRe31rj1XFoxHoUrYJW0ZKyZwSxRT1RPFo0Xl/AUrxaFI8GRdVQed16lEgPWkVLxJb+6L9Pa7GNETmH0JlVtBod9s/N2PNafg5U5i9dREY50NldlG3RU/xdyzF/ZMwG4lwlYLNT6OzHD8YxaFQ3itfjW3tcaBrCzaBdr2OuOQBAeeIQDne/yBd+VE9ACNJ43aQf3UR0vW+iz9qodCoSBh8rq3r8ZRWvB7PtMBE6F5qICNxR8dijUtAY9eiMerQmA7oIAxqjEV2EEX2kHn2UL/hoIkwopsa1ybfNZPIFouNeKwZDh49LC8kYFqfTSV5eHvfdd1/A9okTJ7J58+ZmP5Obm8vEiRMDtk2aNIlXX30Vl8uFXq8nNzeXu+66q0mZp59+usW2OBwOHI5jA1at1uav64pT02iUhrEtobud1uNVcbq9ON2+AONwe3E0vHd6vLg8Xv/+E9+7vCout2+b26vicHtxN7x2ur24vV5cbhWX14vbo/ree1Q8XtX3mRO2ub2q//Meb+M2XzmXx4tXBbfXi9cLLq+Xk0X6xs+3jwLoG5bw0+BFjxsdHnR40OPxvVfc6I/bpmsoo1c8aP3bGvc3fF7xoMXr3964aPGiV9y+Nb7PN27X4UaLik5p3OarW4M3oK7Gf0nr8DZ83vc+uuEzWrz+4x9fTttQT+M2jRLcEO0B3Ao4UXA3BhulMezg29bw2tUQjnzljn+NPxw1hidPw7bj9zeuPf56A9eehtfHf9bb0D5Pw+cb125FaWi7b+057r27mR8uj8aNR+PG0dI10+OuSB+JKoeTPTPy+JkSEr6BFibaVlQN6lEvjd0ZpthoIoZF+QOQRtWh9ep871UdB/Z8h1vr6/XpXt+f1Iw+aP1ltGhVHRqvDp2q5/Vv36Xe4Pv9GFQ3lkFR2b5QpurRNJTVenVoVC3ze+dSEXUUgBGH4xl9CLyKDrQ6PBgDflEfv15PnV6LyQl9qrrR1zq4xdNwNGYHkXXFmFzgMWVSldLycIgh21/BWJ6P12KhJLk7O3r8+NhON76xfA0dtoN2/YO0ki8BKE84l++GzEbjdaCo9ceFId+694GPSCnNQwWq4nqwv891+P5Ue1HxgOIlofoD0n97CyOnzGyxfaHUpsBSXl6Ox+MhJSUlYHtKSgrFxcXNfqa4uLjZ8m63m/LyctLS0los01KdAIsWLeLBBx9sS/NFGGk1ChEGLREGLZ3lB7q1vF4Vj3p8uFEDtvnfn1DO41XxqsevCdjmUX2f86o0KdtY3tu4XfWV8x5Xr6riP97x7WwspxL4GRWOfa6hrKo23CXS+DlVhYZ143uVhjJe/G1TjyvjUVU8gO2E7Rz3+cbj07BPxff9Gjt4Gz+jqo3ljj82AcdUGz7f0FTfZxpeH1+O4/Z7T/iMb58XjeoLMIrq9r/2BRu1Idh40CjegLDT+FpBbbq98bJEwz7NcfuP3+Z/rZy4vbG8GvDafyzFF7YMqAFllGbfN9bju1wSuO3YPg1eFPAfv/F4mobzoCpe37lTvKB4fedZ8QIqqtLw50xRj3vvxavg364CXo3vc756fD+BqqLiBbwNa7WhrOe4z3pRjpVpCFm+tQVvQ2DzNKy9WvDqfEFtUH3DNsCjz8ebkO/76W0IY04F3+eBgV7w2BuOE/c/dsV91lD2+OP5Lv7oFUh2+7YfSvkPR5I+R/HqAJ1vrepRVB2KqqU8qginzpewKuL3cKD2DV9g8gcgDRpVh8ar5fvhlVgjfON+0i1VDCjbgqYhJGlVrS9cebXoPFqeu7KOWoMWowvSrV76VVegUXUoqgYNOhS0oGpRFC3f9vKyO0XB4AJNw+VcTwvzPLkbJrxUAFWJxhrbv0mZQbs/orx0f9v+Ag2idl0MO7G7SFXVk3YhNVf+xO1trXP+/PnMmzfP/95qtdKjR49TN16INtJoFDQo6EM/t53oBNTjwxEEBqSGTpkmgamhXGDQCvz8sQDVQh2N25sLZP7PqceVaaZ847GOP04L9R1fBo47fsBnm34HAE0z3+PYZ1X/a5orE9D2E9vS/Pfzrb0NdaugelFVL4qqoqgN4UlVUVQV8NB4MlSvL6jRWMbbEIEa6lFU1VcPXvwpm8YT6W3+NSqK14Pi+1YNx/TtU1TVPw+Vr72+Hgqv2YtX9fjCnOpBVb2gevGoXsDLFNLwqr5Y5DV5UVM8eFVHw39LXxu9qgcvXnoyBFUd1HCuPah80VCv17duOBeqqqIQjYMfYQdUjwLud1FVBa8XFFVB9WrAq6CqCl8O86JRhqC4POhsRnQ1H6F4FBQ3aDwKGq+G/AsNZA/NJlzaFFiSkpLQarVNej5KS0ub9JA0Sk1Nbba8TqcjMTHxpGVaqhPAaDRilBkWhRBBpii+W3Y1LQ6nFEKEQ5umUDUYDGRlZbFu3bqA7evWrWPs2LHNfiY7O7tJ+bVr1zJq1Cj0ev1Jy7RUpxBCCCHOLm2+JDRv3jxycnIYNWoU2dnZvPzyyxQWFvrnVZk/fz5Hjhzh9ddfB3x3BD3//PPMmzeP2bNnk5uby6uvvhpw98+dd97JhRdeyKOPPsrVV1/N+++/z6effsqmTZuC9DWFEEIIcSZrc2CZMWMGFRUVPPTQQxQVFTFkyBBWr15NZmYmAEVFRRQWFvrL9+7dm9WrV3PXXXfxwgsvkJ6ezrPPPuufgwVg7NixLF++nPvvv58HHniAvn37smLFirN6DhYhhBBCHCPPEhJCCCFE2LT297uTPAZYCCGEEKJlEliEEEII0elJYBFCCCFEpyeBRQghhBCdngQWIYQQQnR6EliEEEII0elJYBFCCCFEpyeBRQghhBCdngQWIYQQQnR6bZ6av7NqnLDXarWGuSVCCCGEaK3G3+1TTbzfZQJLTU0NAD169AhzS4QQQgjRVjU1NZjN5hb3d5lnCXm9Xo4ePUpMTAyKooS7OWcNq9VKjx49OHTokDzDKQzk/IeXnP/wkvMfXsE6/6qqUlNTQ3p6OhpNyyNVukwPi0ajISMjI9zNOGvFxsbKXxhhJOc/vOT8h5ec//AKxvk/Wc9KIxl0K4QQQohOTwKLEEIIITo9CSzitBiNRv74xz9iNBrD3ZSzkpz/8JLzH15y/sOro89/lxl0K4QQQoiuS3pYhBBCCNHpSWARQgghRKcngUUIIYQQnZ4EFiGEEEJ0ehJYxCktXryY3r17YzKZyMrKYuPGjS2Wfffdd5kwYQLdunUjNjaW7OxsPvnkkw5sbdfTlvN/vM8//xydTsfw4cND28Aurq3n3+FwsGDBAjIzMzEajfTt25e///3vHdTarqet5/+tt95i2LBhREZGkpaWxi9/+UsqKio6qLVdx4YNG7jqqqtIT09HURTee++9U35m/fr1ZGVlYTKZ6NOnDy+++GJwG6UKcRLLly9X9Xq9+sorr6g7d+5U77zzTjUqKko9ePBgs+XvvPNO9dFHH1W//PJL9fvvv1fnz5+v6vV69ZtvvunglncNbT3/jaqrq9U+ffqoEydOVIcNG9Yxje2C2nP+p02bpo4ePVpdt26dWlBQoG7ZskX9/PPPO7DVXUdbz//GjRtVjUajPvPMM+r+/fvVjRs3queee656zTXXdHDLz3yrV69WFyxYoK5cuVIF1FWrVp20/P79+9XIyEj1zjvvVHfu3Km+8sorql6vV//1r38FrU0SWMRJXXDBBeqcOXMCtg0cOFC97777Wl3H4MGD1QcffDDYTTsrtPf8z5gxQ73//vvVP/7xjxJYTkNbz//HH3+sms1mtaKioiOa1+W19fw//vjjap8+fQK2Pfvss2pGRkbI2ng2aE1guffee9WBAwcGbLv11lvVMWPGBK0dcklItMjpdJKXl8fEiRMDtk+cOJHNmze3qg6v10tNTQ0JCQmhaGKX1t7z/9prr7Fv3z7++Mc/hrqJXVp7zv8HH3zAqFGjeOyxx+jevTv9+/fnnnvuwWazdUSTu5T2nP+xY8dy+PBhVq9ejaqqlJSU8K9//Ysrr7yyI5p8VsvNzW3y32rSpEl8/fXXuFyuoByjyzz8UARfeXk5Ho+HlJSUgO0pKSkUFxe3qo4nnniCuro6pk+fHoomdmntOf979+7lvvvuY+PGjeh08n/v09Ge879//342bdqEyWRi1apVlJeXc9ttt1FZWSnjWNqoPed/7NixvPXWW8yYMQO73Y7b7WbatGk899xzHdHks1pxcXGz/63cbjfl5eWkpaWd9jGkh0WckqIoAe9VVW2yrTnLli1j4cKFrFixguTk5FA1r8tr7fn3eDzMnDmTBx98kP79+3dU87q8tvz593q9KIrCW2+9xQUXXMAVV1zBk08+ydKlS6WXpZ3acv537tzJHXfcwR/+8Afy8vJYs2YNBQUFzJkzpyOaetZr7r9Vc9vbS/4JJlqUlJSEVqtt8q+Z0tLSJkn6RCtWrGDWrFn885//5PLLLw9lM7ustp7/mpoavv76a7Zu3cpvf/tbwPcDqqoqOp2OtWvXcumll3ZI27uC9vz5T0tLo3v37pjNZv+2QYMGoaoqhw8fpl+/fiFtc1fSnvO/aNEixo0bx//93/8BcN555xEVFcX48eP585//HJR/5YvmpaamNvvfSqfTkZiYGJRjSA+LaJHBYCArK4t169YFbF+3bh1jx45t8XPLli3jpptu4u2335Zrx6ehrec/NjaW7777jvz8fP8yZ84cBgwYQH5+PqNHj+6opncJ7fnzP27cOI4ePUptba1/2/fff49GoyEjIyOk7e1q2nP+6+vr0WgCf9a0Wi1w7F/7IjSys7Ob/Ldau3Yto0aNQq/XB+cgQRu+K7qkxtsKX331VXXnzp3q3Llz1aioKPXAgQOqqqrqfffdp+bk5PjLv/3226pOp1NfeOEFtaioyL9UV1eH6yuc0dp6/k8kdwmdnrae/5qaGjUjI0O94YYb1B07dqjr169X+/Xrp958883h+gpntLae/9dee03V6XTq4sWL1X379qmbNm1SR40apV5wwQXh+gpnrJqaGnXr1q3q1q1bVUB98skn1a1bt/pvKT/x3Dfe1nzXXXepO3fuVF999VW5rVl0vBdeeEHNzMxUDQaDOnLkSHX9+vX+fTfeeKN60UUX+d9fdNFFKtBkufHGGzu+4V1EW87/iSSwnL62nv9du3apl19+uRoREaFmZGSo8+bNU+vr6zu41V1HW8//s88+qw4ePFiNiIhQ09LS1J/97Gfq4cOHO7jVZ77//e9/J/27vLlz/9lnn6kjRoxQDQaD2qtXL3XJkiVBbZOiqtJPJoQQQojOTcawCCGEEKLTk8AihBBCiE5PAosQQgghOj0JLEIIIYTo9CSwCCGEEKLTk8AihBBCiE5PAosQQgghOj0JLEIIIYTo9CSwCCGEEKLTk8AihBBCiE5PAosQQgghOj0JLEIIIYTo9P4fhM2VxjwW1GsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "etaDgrid = np.linspace(0.05, .99, 100)\n",
    "for level in [3000, 5000, 7000, 15000]:\n",
    "    etaYgrid = [contour(t, level) for t in etaDgrid]\n",
    "    plt.plot(etaDgrid, etaYgrid, label=f'{level}')\n",
    "etaYgrid = [contour(t, theta) for t in etaDgrid]\n",
    "plt.plot(etaDgrid, etaYgrid, '--', label=f'{level}')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "7a7313ba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-4.723336120010572\n",
      "Robustness value = 0.0946\n"
     ]
    }
   ],
   "source": [
    "# Find the \"robustness value\" such that if both partial R^2 for D and Y are larger\n",
    "# than this value, then the effect is zero\n",
    "for t in np.linspace(0.01, .99, 10000):\n",
    "    if bounds(t, t)[0] <= 0:\n",
    "        print(bounds(t, t)[0])\n",
    "        break\n",
    "print(f\"Robustness value = {t:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bd7a8e80",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  },
  "papermill": {
   "default_parameters": {},
   "duration": 537.547458,
   "end_time": "2021-03-24T14:22:44.931595",
   "environment_variables": {},
   "exception": null,
   "input_path": "__notebook__.ipynb",
   "output_path": "__notebook__.ipynb",
   "parameters": {},
   "start_time": "2021-03-24T14:13:47.384137",
   "version": "2.3.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}