diff --git a/pyfixest/Chapter01CorrAssocSimpsons.ipynb b/pyfixest/Chapter01CorrAssocSimpsons.ipynb
new file mode 100644
index 0000000..e58860e
--- /dev/null
+++ b/pyfixest/Chapter01CorrAssocSimpsons.ipynb
@@ -0,0 +1,491 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 1: Correlation, Association, and the Yule-Simpson Paradox"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import scipy as sp\n",
+ "import pyfixest as pf\n",
+ "\n",
+ "# viz\n",
+ "from IPython.core.interactiveshell import InteractiveShell\n",
+ "\n",
+ "InteractiveShell.ast_node_interactivity = \"all\"\n",
+ "\n",
+ "\n",
+ "%load_ext autoreload\n",
+ "%autoreload 1\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Unadjusted and Adjusted Regression\n",
+ "Lalonde Observational Data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# read CPS data\n",
+ "dat = pd.read_table(\"cps1re74.csv\", delimiter=\" \")\n",
+ "dat[\"u74\"] = np.where(dat[\"re74\"] == 0, 1, 0)\n",
+ "dat[\"u75\"] = np.where(dat[\"re75\"] == 0, 1, 0)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Unadjusted regression"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "pf.feols(\"re78 ~ treat\", data=dat, vcov=\"HC2\").tidy().loc[\"treat\"]\n",
+ "# %%\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Adjusted Regression"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "rhs = list(set(dat.columns) - {\"re78\", \"treat\"})\n",
+ "pf.feols(f're78 ~ treat + {\"+\".join(rhs)}', data=dat, vcov=\"hetero\").tidy().loc[\n",
+ " \"treat\"\n",
+ "]\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Fisher's exact test for contingency tables\n",
+ "Bertrand and Mullainathan (2004) experiment "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "call 0 1\n",
+ "race \n",
+ "black 2278 157\n",
+ "white 2200 235\n"
+ ]
+ }
+ ],
+ "source": [
+ "resume = pd.read_csv(\"resume.csv\")\n",
+ "print(xtab := pd.crosstab(resume[\"race\"], resume[\"call\"]))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "SignificanceResult(statistic=1.5498841922408801, pvalue=4.758747107909523e-05)"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "sp.stats.fisher_exact(xtab)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## simpson's paradox \n",
+ "UCB admissions data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Admit | \n",
+ " Gender | \n",
+ " Dept | \n",
+ " Freq | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " Admitted | \n",
+ " Male | \n",
+ " A | \n",
+ " 512 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " Rejected | \n",
+ " Male | \n",
+ " A | \n",
+ " 313 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " Admitted | \n",
+ " Female | \n",
+ " A | \n",
+ " 89 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " Rejected | \n",
+ " Female | \n",
+ " A | \n",
+ " 19 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " Admitted | \n",
+ " Male | \n",
+ " B | \n",
+ " 353 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | Admit | \n",
+ " Admitted | \n",
+ " Rejected | \n",
+ "
\n",
+ " \n",
+ " | Gender | \n",
+ " | \n",
+ " | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | Female | \n",
+ " 557 | \n",
+ " 1278 | \n",
+ "
\n",
+ " \n",
+ " | Male | \n",
+ " 1198 | \n",
+ " 1493 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Admit | \n",
+ " Gender | \n",
+ " Dept | \n",
+ " Freq | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " Admitted | \n",
+ " Male | \n",
+ " A | \n",
+ " 512 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " Rejected | \n",
+ " Male | \n",
+ " A | \n",
+ " 313 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " Admitted | \n",
+ " Female | \n",
+ " A | \n",
+ " 89 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " Rejected | \n",
+ " Female | \n",
+ " A | \n",
+ " 19 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " Admitted | \n",
+ " Male | \n",
+ " B | \n",
+ " 353 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 1241,
+ "width": 691
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(3, 2, figsize=(8, 15))\n",
+ "for i, (y0, y1, res, v) in enumerate(\n",
+ " zip([y0_1, y0_2, y0_3], [y1_1, y1_2, y1_3], [res1, res2, res3], [v1, v2, v3])\n",
+ "):\n",
+ " ax[i][0].plot(y0, y1, \"o\")\n",
+ " ax[i][0].set_xlabel(r\"$Y^0$\", fontsize=12)\n",
+ " ax[i][0].set_ylabel(r\"$Y^1$\", fontsize=12)\n",
+ " ax[i][1].hist(res[:, 0] - tautrue, bins=50, density=True)\n",
+ " ax[i][1].set_xlabel(r\"$\\hat{\\tau} - \\tau$\", fontsize=12)\n",
+ " x = np.linspace(-1, 1, 100)\n",
+ " y = sp.stats.norm.pdf(x, loc=0, scale=np.sqrt(v))\n",
+ " ax[i][1].plot(x, y, label=\"Neyman variance\")\n",
+ "ax[0][1].set_title(r\"$\\tau_i = \\tau$\")\n",
+ "ax[1][1].set_title(r\"Negative Corr between $Y^1$ and $Y^0$\")\n",
+ "ax[2][1].set_title(r\"Uncorrelated $Y^1$ and $Y^0$\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Constant | \n",
+ " Negative | \n",
+ " Independent | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | Variance | \n",
+ " 0.031073 | \n",
+ " 0.006261 | \n",
+ " 0.019115 | \n",
+ "
\n",
+ " \n",
+ " | Estimated Variance | \n",
+ " 0.030088 | \n",
+ " 0.030094 | \n",
+ " 0.030080 | \n",
+ "
\n",
+ " \n",
+ " | Coverage | \n",
+ " 0.941100 | \n",
+ " 0.999900 | \n",
+ " 0.982800 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 836,
+ "width": 446
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "n, n1, n0 = 1000, 600, 400\n",
+ "tautrue = 1\n",
+ "\n",
+ "# cauchy contamination: prob combination = 0.1\n",
+ "eps = np.random.binomial(1, 0.1, n)\n",
+ "y0_1 = (1 - eps) * np.random.exponential(1, n) + eps * np.random.standard_cauchy(n)\n",
+ "y1_1 = y0_1 + tautrue\n",
+ "tautrue_1 = np.mean(y1_1) - np.mean(y0_1)\n",
+ "z_1 = z_2 = z_3 = np.repeat([0, 1], [n0, n1])\n",
+ "MC = int(1e4)\n",
+ "res1 = np.zeros((MC, 3))\n",
+ "for i in range(MC):\n",
+ " res1[i] = sampling_dist(z_1, y1_1, y0_1, n=n, n1=n1, n0=n0, tautrue=1)\n",
+ "v1 = np.var(y1_1) / n1 + np.var(y0_1) / n0 - np.var(y1_1 - y0_1) / n\n",
+ "v1\n",
+ "\n",
+ "# cauchy contamination: prob combination = 0.3\n",
+ "eps = np.random.binomial(1, 0.3, n)\n",
+ "y0_2 = (1 - eps) * np.random.exponential(1, n) + eps * np.random.standard_cauchy(n)\n",
+ "y1_2 = y0_2 + tautrue\n",
+ "tautrue_2 = np.mean(y1_2) - np.mean(y0_2)\n",
+ "res2 = np.zeros((MC, 3))\n",
+ "for i in range(MC):\n",
+ " res2[i] = sampling_dist(z_2, y1_2, y0_2, n=n, n1=n1, n0=n0, tautrue=1)\n",
+ "v2 = np.var(y1_2) / n1 + np.var(y0_2) / n0 - np.var(y1_2 - y0_2) / n\n",
+ "v2\n",
+ "\n",
+ "\n",
+ "# cauchy contamination: prob combination = 0.5\n",
+ "eps = np.random.binomial(1, 0.5, n)\n",
+ "y0_3 = (1 - eps) * np.random.exponential(1, n) + eps * np.random.standard_cauchy(n)\n",
+ "y1_3 = y0_3 + tautrue\n",
+ "tautrue_3 = np.mean(y1_3) - np.mean(y0_3)\n",
+ "res3 = np.zeros((MC, 3))\n",
+ "for i in range(MC):\n",
+ " res3[i] = sampling_dist(z_3, y1_3, y0_3, n=n, n1=n1, n0=n0, tautrue=1)\n",
+ "v3 = np.var(y1_3) / n1 + np.var(y0_3) / n0 - np.var(y1_3 - y0_3) / n\n",
+ "\n",
+ "v1, v2, v3\n",
+ "\n",
+ "f, ax = plt.subplots(3, 1, figsize=(5, 10))\n",
+ "for i, (res, v) in enumerate(zip([res1, res2, res3], [v1, v2, v3])):\n",
+ " ax[i].hist(res[:, 0] - tautrue, bins=100, density=True)\n",
+ " ax[i].set_xlabel(r\"$\\hat{\\tau} - \\tau$\", fontsize=12)\n",
+ " x = np.linspace(-10, 10, 1000)\n",
+ " y = sp.stats.norm.pdf(x, loc=0, scale=np.sqrt(v))\n",
+ " ax[i].plot(x, y)\n",
+ " ax[i].set_xlim(-4, 4)\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Application"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from causalinference.utils import lalonde_data\n",
+ "\n",
+ "y, z, _ = lalonde_data()\n",
+ "y *= 1000"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(1794.3430782016621, 670.9967300240978)"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "n0, n1 = np.sum(1 - z), np.sum(z)\n",
+ "tauhat = np.mean(y[z == 1]) - np.mean(y[z == 0])\n",
+ "vhat = np.var(y[z == 1], ddof=1) / n1 + np.var(y[z == 0], ddof=1) / n0\n",
+ "sehat = np.sqrt(vhat)\n",
+ "tauhat, sehat"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Homoskedastic"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "reg_data = pd.DataFrame({\"y\": y, \"z\": z})\n",
+ "pf.feols(\"y ~ z\", data=reg_data).tidy()\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Heteroskedastic"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# PyFixest's heteroskedastic covariance is HC1.\n",
+ "reg_data = pd.DataFrame({\"y\": y, \"z\": z})\n",
+ "pf.feols(\"y ~ z\", data=reg_data, vcov=\"hetero\").tidy()\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "reg_data = pd.DataFrame({\"y\": y, \"z\": z})\n",
+ "pf.feols(\"y ~ z\", data=reg_data, vcov=\"HC2\").tidy()\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "econometrics",
+ "language": "python",
+ "name": "econometrics"
+ },
+ "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"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pyfixest/Chapter05StratandPostStrat.ipynb b/pyfixest/Chapter05StratandPostStrat.ipynb
new file mode 100644
index 0000000..2294b9e
--- /dev/null
+++ b/pyfixest/Chapter05StratandPostStrat.ipynb
@@ -0,0 +1,847 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 5: Stratification and Post-Stratification in Randomized Experiments"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import scipy as sp\n",
+ "\n",
+ "# viz\n",
+ "import matplotlib\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
+ "plt.rc(\"font\", **font)\n",
+ "plt.rcParams[\"figure.figsize\"] = (6, 6)\n",
+ "%matplotlib inline\n",
+ "%config InlineBackend.figure_format = 'retina'\n",
+ "\n",
+ "%load_ext autoreload\n",
+ "%autoreload 1\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " duration | \n",
+ " treatment | \n",
+ " female | \n",
+ " black | \n",
+ " hispanic | \n",
+ " ndependents | \n",
+ " recall | \n",
+ " young | \n",
+ " old | \n",
+ " quarter | \n",
+ " durable | \n",
+ " lusd | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 1 | \n",
+ " 18.011343 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 2 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 5 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 1.003399 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 5 | \n",
+ " 0 | \n",
+ " 1 | \n",
+ "
\n",
+ " \n",
+ " | 5 | \n",
+ " 26.960396 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 4 | \n",
+ " 0 | \n",
+ " 1 | \n",
+ "
\n",
+ " \n",
+ " | 6 | \n",
+ " 7.009044 | \n",
+ " 1 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 2 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ "
\n",
+ " \n",
+ " | 12 | \n",
+ " 9.022409 | \n",
+ " 1 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 1 | \n",
+ " 0 | \n",
+ " 3 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | col_0 | \n",
+ " 0 | \n",
+ " 1 | \n",
+ " 2 | \n",
+ " 3 | \n",
+ " 4 | \n",
+ " 5 | \n",
+ "
\n",
+ " \n",
+ " | row_0 | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 234 | \n",
+ " 41 | \n",
+ " 687 | \n",
+ " 794 | \n",
+ " 738 | \n",
+ " 860 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 87 | \n",
+ " 48 | \n",
+ " 757 | \n",
+ " 866 | \n",
+ " 811 | \n",
+ " 461 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 525,
+ "width": 509
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(2, 1)\n",
+ "ax[0].hist(statSREMC[:, 0], bins=50)\n",
+ "ax[0].vlines(stat_obs[0], 0, 50, color=\"red\")\n",
+ "ax[0].set_xlabel(r\"$\\hat{\\tau}_s$\")\n",
+ "ax[1].hist(statSREMC[:, 1], bins=30)\n",
+ "ax[1].vlines(stat_obs[1], 0, 50, color=\"red\")\n",
+ "ax[1].set_xlabel(r\"$W_s$\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Neyman"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def neyman_SRE(z, y, x):\n",
+ " xlevels = np.unique(x)\n",
+ " K = len(xlevels)\n",
+ " PiK, TauK, varK = np.zeros(K), np.zeros(K), np.zeros(K)\n",
+ " for k in range(K):\n",
+ " id = np.where(x == xlevels[k])\n",
+ " zk, yk = z[id], y[id]\n",
+ " PiK[k] = zk.shape[0] / z.shape[0]\n",
+ " TauK[k] = np.mean(yk[zk == 1]) - np.mean(yk[zk == 0])\n",
+ " varK[k] = np.var(yk[zk == 1], ddof=1) / sum(zk) + np.var(\n",
+ " yk[zk == 0], ddof=1\n",
+ " ) / sum(1 - zk)\n",
+ " return np.sum(PiK * TauK), np.sum(PiK**2 * varK)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def sim_cluster(K, n, n1, n0):\n",
+ " x = np.repeat(range(K), n)\n",
+ " y0 = np.random.exponential(1, n * K)\n",
+ " y1 = y0 + 1\n",
+ " # block level assignment vector\n",
+ " zb = np.repeat([0, 1], [n0, n1])\n",
+ " MC = int(1e4)\n",
+ " TauHat, VarHat = np.zeros(MC), np.zeros(MC)\n",
+ " for k in range(MC):\n",
+ " z = np.concatenate([np.random.permutation(zb) for i in range(K)])\n",
+ " y = z * y1 + (1 - z) * y0\n",
+ " TauHat[k], VarHat[k] = neyman_SRE(z, y, x)\n",
+ " plt.hist(TauHat, bins=50)\n",
+ " plt.vlines(1, 0, 500, color=\"red\")\n",
+ " return np.var(TauHat), np.mean(VarHat)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(0.009649300175537943, 0.00978208282388499)"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 505,
+ "width": 517
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sim_cluster(5, 80, 50, 30)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(0.010911041476145415, 0.010650749123757628)"
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 505,
+ "width": 517
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "sim_cluster(50, 8, 5, 3)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### application to Penn bonus experiment"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(-0.0899064590011073, 0.030797749686469634)"
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "est, var = neyman_SRE(z, y, block)\n",
+ "est, np.sqrt(var)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## chong et al (2016)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | class_level | \n",
+ " 1.0 | \n",
+ " 2.0 | \n",
+ " 3.0 | \n",
+ " 4.0 | \n",
+ " 5.0 | \n",
+ "
\n",
+ " \n",
+ " | treatment | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | Soccer Player | \n",
+ " 16 | \n",
+ " 19 | \n",
+ " 15 | \n",
+ " 10 | \n",
+ " 10 | \n",
+ "
\n",
+ " \n",
+ " | Physician | \n",
+ " 17 | \n",
+ " 20 | \n",
+ " 15 | \n",
+ " 11 | \n",
+ " 10 | \n",
+ "
\n",
+ " \n",
+ " | Placebo | \n",
+ " 15 | \n",
+ " 19 | \n",
+ " 16 | \n",
+ " 12 | \n",
+ " 10 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | class_level | \n",
+ " 1.0 | \n",
+ " 2.0 | \n",
+ " 3.0 | \n",
+ " 4.0 | \n",
+ " 5.0 | \n",
+ "
\n",
+ " \n",
+ " | z | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 15 | \n",
+ " 19 | \n",
+ " 16 | \n",
+ " 12 | \n",
+ " 10 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 17 | \n",
+ " 20 | \n",
+ " 15 | \n",
+ " 11 | \n",
+ " 10 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Estimate | \n",
+ " Std. Error | \n",
+ " z value | \n",
+ " Pr(>|z|) | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | Stratify | \n",
+ " 0.405890 | \n",
+ " 0.202391 | \n",
+ " 2.005480 | \n",
+ " 0.044912 | \n",
+ "
\n",
+ " \n",
+ " | Stratify and post-stratify | \n",
+ " 0.463343 | \n",
+ " 0.190393 | \n",
+ " 2.433609 | \n",
+ " 0.014949 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " coef | \n",
+ " se | \n",
+ " t | \n",
+ " p | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | unadjusted | \n",
+ " 0.0518 | \n",
+ " 0.078 | \n",
+ " 0.669 | \n",
+ " 0.504 | \n",
+ "
\n",
+ " \n",
+ " | adjusted | \n",
+ " 0.0682 | \n",
+ " 0.074 | \n",
+ " 0.925 | \n",
+ " 0.355 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 526,
+ "width": 535
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "design_adjustment_fig(0.1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 526,
+ "width": 535
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "design_adjustment_fig(0.25)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "econometrics",
+ "language": "python",
+ "name": "econometrics"
+ },
+ "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"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pyfixest/Chapter07MatchedPairs.ipynb b/pyfixest/Chapter07MatchedPairs.ipynb
new file mode 100644
index 0000000..c011423
--- /dev/null
+++ b/pyfixest/Chapter07MatchedPairs.ipynb
@@ -0,0 +1,572 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 7: Matched-Pairs Experiment"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import pyfixest as pf\n",
+ "import scipy as sp\n",
+ "\n",
+ "# viz\n",
+ "import matplotlib\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
+ "plt.rc(\"font\", **font)\n",
+ "plt.rcParams[\"figure.figsize\"] = (6, 6)\n",
+ "%matplotlib inline\n",
+ "%config InlineBackend.figure_format = 'retina'\n",
+ "%load_ext autoreload\n",
+ "%autoreload 1\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def MP_enumerate(i, n_pairs):\n",
+ " if i > 2**n_pairs:\n",
+ " return None\n",
+ " a = 2 ** np.arange(n_pairs)[::-1]\n",
+ " b = 2 * a\n",
+ " return 2 * (i % b >= a) - 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " pair | \n",
+ " pot | \n",
+ " cross | \n",
+ " self | \n",
+ " diff | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 1 | \n",
+ " 1 | \n",
+ " 23.500 | \n",
+ " 17.375 | \n",
+ " 6.125 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 2 | \n",
+ " 1 | \n",
+ " 12.000 | \n",
+ " 20.375 | \n",
+ " -8.375 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 3 | \n",
+ " 1 | \n",
+ " 21.000 | \n",
+ " 20.000 | \n",
+ " 1.000 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 4 | \n",
+ " 2 | \n",
+ " 22.000 | \n",
+ " 20.000 | \n",
+ " 2.000 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 5 | \n",
+ " 2 | \n",
+ " 19.125 | \n",
+ " 18.375 | \n",
+ " 0.750 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 526,
+ "width": 524
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.hist(t_ran, bins=50)\n",
+ "plt.axvline(t_obs, color=\"red\")\n",
+ "plt.title(\"Exact Randomization Distribution: Darwin Data\")\n",
+ "plt.annotate(f\"p-value = {p_value:.3f}\", xy=(0.05, 0.9), xycoords=\"axes fraction\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "IR(2015) : Children's TV Data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " x_control | \n",
+ " x_treatment | \n",
+ " y_control | \n",
+ " y_treatment | \n",
+ " diffx | \n",
+ " diffy | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 1 | \n",
+ " 12.9 | \n",
+ " 12.0 | \n",
+ " 54.6 | \n",
+ " 60.6 | \n",
+ " -0.9 | \n",
+ " 6.0 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 15.1 | \n",
+ " 12.3 | \n",
+ " 56.5 | \n",
+ " 55.5 | \n",
+ " -2.8 | \n",
+ " -1.0 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 16.8 | \n",
+ " 17.2 | \n",
+ " 75.2 | \n",
+ " 84.8 | \n",
+ " 0.4 | \n",
+ " 9.6 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 15.8 | \n",
+ " 18.9 | \n",
+ " 75.6 | \n",
+ " 101.9 | \n",
+ " 3.1 | \n",
+ " 26.3 | \n",
+ "
\n",
+ " \n",
+ " | 5 | \n",
+ " 13.9 | \n",
+ " 15.3 | \n",
+ " 55.3 | \n",
+ " 70.6 | \n",
+ " 1.4 | \n",
+ " 15.3 | \n",
+ "
\n",
+ " \n",
+ " | 6 | \n",
+ " 14.5 | \n",
+ " 16.6 | \n",
+ " 59.3 | \n",
+ " 78.4 | \n",
+ " 2.1 | \n",
+ " 19.1 | \n",
+ "
\n",
+ " \n",
+ " | 7 | \n",
+ " 17.0 | \n",
+ " 16.0 | \n",
+ " 87.0 | \n",
+ " 84.2 | \n",
+ " -1.0 | \n",
+ " -2.8 | \n",
+ "
\n",
+ " \n",
+ " | 8 | \n",
+ " 15.8 | \n",
+ " 20.1 | \n",
+ " 73.7 | \n",
+ " 108.6 | \n",
+ " 4.3 | \n",
+ " 34.9 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 526,
+ "width": 974
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(1, 2, figsize=(12, 6))\n",
+ "ax[0].hist(t_randist[:, 0], bins=50)\n",
+ "ax[0].axvline(unadj_t, color=\"red\")\n",
+ "ax[0].set_title(\"Unadjusted Randomization Distribution\")\n",
+ "ax[0].annotate(\n",
+ " f\"p-value = {p_unadjusted:.3f}\", xy=(0.05, 0.9), xycoords=\"axes fraction\"\n",
+ ")\n",
+ "ax[1].hist(t_randist[:, 1], bins=50)\n",
+ "ax[1].axvline(adj_t, color=\"red\")\n",
+ "ax[1].set_title(\"Adjusted Randomization Distribution\")\n",
+ "ax[1].annotate(f\"p-value = {p_adjusted:.3f}\", xy=(0.05, 0.9), xycoords=\"axes fraction\")"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "econometrics",
+ "language": "python",
+ "name": "econometrics"
+ },
+ "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"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pyfixest/Chapter08UnifyingFisherNeyman.ipynb b/pyfixest/Chapter08UnifyingFisherNeyman.ipynb
new file mode 100644
index 0000000..332f9d4
--- /dev/null
+++ b/pyfixest/Chapter08UnifyingFisherNeyman.ipynb
@@ -0,0 +1,579 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 8: Unification of the Fisherian and Neymanian Inferences in Randomized Experiments"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from joblib import Parallel, delayed\n",
+ "\n",
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import pyfixest as pf\n",
+ "import scipy as sp\n",
+ "import seaborn as sns\n",
+ "\n",
+ "# viz\n",
+ "import matplotlib\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
+ "plt.rc(\"font\", **font)\n",
+ "plt.rcParams[\"figure.figsize\"] = (6, 6)\n",
+ "%matplotlib inline\n",
+ "%config InlineBackend.figure_format = 'retina'\n",
+ "\n",
+ "%load_ext autoreload\n",
+ "%autoreload 1\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import warnings\n",
+ "\n",
+ "warnings.filterwarnings(\"ignore\", category=FutureWarning)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## FRT Simulation Study (sec 8.3)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def cafrt_stat_n(z, y):\n",
+ " data = pd.DataFrame({\"y\": y, \"z\": z})\n",
+ " m1 = pf.feols(\"y ~ z\", data=data)\n",
+ " m2 = pf.feols(\"y ~ z\", data=data, vcov=\"HC2\")\n",
+ " est, vse, rse = m1.coef().loc[\"z\"], m1.se().loc[\"z\"], m2.se().loc[\"z\"]\n",
+ " return est, est / vse, est / rse\n",
+ "\n",
+ "\n",
+ "def cafrt_stat_f(z, y, x):\n",
+ " covariates = pd.DataFrame(np.asarray(x))\n",
+ " covariates.columns = [f\"x{i}\" for i in range(covariates.shape[1])]\n",
+ " data = covariates.assign(y=y, z=z)\n",
+ " rhs = \" + \".join(covariates.columns)\n",
+ " m1 = pf.feols(\"y ~ z + \" + rhs, data=data)\n",
+ " m2 = pf.feols(\"y ~ z + \" + rhs, data=data, vcov=\"HC2\")\n",
+ " est, vse, rse = m1.coef().loc[\"z\"], m1.se().loc[\"z\"], m2.se().loc[\"z\"]\n",
+ " return est, est / vse, est / rse\n",
+ "\n",
+ "\n",
+ "def cafrt_stat_l(z, y, x):\n",
+ " covariates = pd.DataFrame(np.asarray(x))\n",
+ " covariates.columns = [f\"x{i}\" for i in range(covariates.shape[1])]\n",
+ " covariates = covariates - covariates.mean()\n",
+ " data = covariates.assign(y=y, z=z)\n",
+ " rhs = \" + \".join(covariates.columns)\n",
+ " m1 = pf.feols(\"y ~ z * (\" + rhs + \")\", data=data)\n",
+ " m2 = pf.feols(\"y ~ z * (\" + rhs + \")\", data=data, vcov=\"HC2\")\n",
+ " est, vse, rse = m1.coef().loc[\"z\"], m1.se().loc[\"z\"], m2.se().loc[\"z\"]\n",
+ " return est, est / vse, est / rse\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def cafrt_pvalue(z, y, x, nfrt, k=6):\n",
+ " covariates = pd.DataFrame(np.asarray(x))\n",
+ " covariates.columns = [f\"x{i}\" for i in range(covariates.shape[1])]\n",
+ " residual_data = covariates.assign(y=y)\n",
+ " rr = pf.feols(\"y ~ \" + \" + \".join(covariates.columns), data=residual_data).resid()\n",
+ " cafrt_stat_obs = np.r_[\n",
+ " cafrt_stat_n(z, y),\n",
+ " cafrt_stat_f(z, y, x),\n",
+ " cafrt_stat_l(z, y, x),\n",
+ " cafrt_stat_n(z, rr),\n",
+ " ]\n",
+ "\n",
+ " def run_cafrt_pvalue(*args):\n",
+ " zperm = np.random.permutation(z)\n",
+ " return np.r_[\n",
+ " cafrt_stat_n(zperm, y),\n",
+ " cafrt_stat_f(zperm, y, x),\n",
+ " cafrt_stat_l(zperm, y, x),\n",
+ " cafrt_stat_n(zperm, rr),\n",
+ " ]\n",
+ "\n",
+ " results = Parallel(n_jobs=k)(delayed(run_cafrt_pvalue)(i) for i in range(nfrt))\n",
+ " cafrt_stat_perm = np.vstack(results)\n",
+ " summ = 1 * (np.abs(cafrt_stat_perm) - np.abs(cafrt_stat_obs) >= 0)\n",
+ " return summ.mean(axis=0)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([0.742, 0.742, 0.816, 0.722, 0.722, 0.822, 0.68 , 0.66 , 0.772,\n",
+ " 0.72 , 0.72 , 0.822])"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "nfrt = int(500)\n",
+ "n, r = 100, 0.2\n",
+ "n1, n0 = int(r * n), int((1 - r) * n)\n",
+ "sigma1, sigma0 = 1, 0.5\n",
+ "x = np.random.uniform(low=-1, high=1, size=n)\n",
+ "y1 = x**3 + np.random.normal(scale=sigma1, size=n)\n",
+ "y0 = -(x**3) + np.random.normal(scale=sigma0, size=n)\n",
+ "y1, y0 = y1 - y1.mean(), y0 - y0.mean()\n",
+ "zz = np.r_[np.ones(n1), np.zeros(n0)]\n",
+ "\n",
+ "\n",
+ "def simulation_frt():\n",
+ " z = np.random.permutation(zz)\n",
+ " y = z * y1 + (1 - z) * y0\n",
+ " return cafrt_pvalue(z, y, x, nfrt, k=8)\n",
+ "\n",
+ "\n",
+ "simulation_frt()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "CPU times: user 1min 23s, sys: 2.2 s, total: 1min 25s\n",
+ "Wall time: 1min 34s\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "array([[0.01 , 0.01 , 0.024, 0.004, 0.004, 0.028, 0.01 , 0.004, 0.022,\n",
+ " 0.004, 0.004, 0.026],\n",
+ " [0.274, 0.274, 0.446, 0.37 , 0.372, 0.556, 0.102, 0.066, 0.27 ,\n",
+ " 0.368, 0.368, 0.564],\n",
+ " [0.134, 0.134, 0.286, 0.102, 0.1 , 0.316, 0.148, 0.122, 0.322,\n",
+ " 0.1 , 0.1 , 0.314],\n",
+ " [0.936, 0.936, 0.952, 0.708, 0.71 , 0.824, 0.456, 0.41 , 0.57 ,\n",
+ " 0.71 , 0.71 , 0.822],\n",
+ " [0.08 , 0.08 , 0.208, 0.176, 0.19 , 0.372, 0. , 0. , 0.01 ,\n",
+ " 0.204, 0.204, 0.422]])"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "%%time\n",
+ "nmc = 500\n",
+ "res = []\n",
+ "for i in range(nmc):\n",
+ " res.append(simulation_frt())\n",
+ "simres = np.vstack(res)\n",
+ "simres[:5, :]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "simdata = [\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Unstudentized\",\n",
+ " \"fac2\": \"Neyman\",\n",
+ " \"frt_pv\": simres[:, 0],\n",
+ " }\n",
+ " ),\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Studentized OLS\",\n",
+ " \"fac2\": \"Neyman\",\n",
+ " \"frt_pv\": simres[:, 1],\n",
+ " }\n",
+ " ),\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Studentized EHW\",\n",
+ " \"fac2\": \"Neyman\",\n",
+ " \"frt_pv\": simres[:, 2],\n",
+ " }\n",
+ " ),\n",
+ " # fisher\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Unstudentized\",\n",
+ " \"fac2\": \"Fisher\",\n",
+ " \"frt_pv\": simres[:, 3],\n",
+ " }\n",
+ " ),\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Studentized OLS\",\n",
+ " \"fac2\": \"Fisher\",\n",
+ " \"frt_pv\": simres[:, 4],\n",
+ " }\n",
+ " ),\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Studentized EHW\",\n",
+ " \"fac2\": \"Fisher\",\n",
+ " \"frt_pv\": simres[:, 5],\n",
+ " }\n",
+ " ),\n",
+ " # lin\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Unstudentized\",\n",
+ " \"fac2\": \"Lin\",\n",
+ " \"frt_pv\": simres[:, 6],\n",
+ " }\n",
+ " ),\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Studentized OLS\",\n",
+ " \"fac2\": \"Lin\",\n",
+ " \"frt_pv\": simres[:, 7],\n",
+ " }\n",
+ " ),\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Studentized EHW\",\n",
+ " \"fac2\": \"Lin\",\n",
+ " \"frt_pv\": simres[:, 8],\n",
+ " }\n",
+ " ),\n",
+ " # rosenbaum\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Unstudentized\",\n",
+ " \"fac2\": \"Rosenbaum\",\n",
+ " \"frt_pv\": simres[:, 9],\n",
+ " }\n",
+ " ),\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Studentized OLS\",\n",
+ " \"fac2\": \"Rosenbaum\",\n",
+ " \"frt_pv\": simres[:, 10],\n",
+ " }\n",
+ " ),\n",
+ " pd.DataFrame(\n",
+ " {\n",
+ " \"fac1\": \"Studentized EHW\",\n",
+ " \"fac2\": \"Rosenbaum\",\n",
+ " \"frt_pv\": simres[:, 11],\n",
+ " }\n",
+ " ),\n",
+ "]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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6+4UVffqY1fVOvbE2V8XV5o5lDptF50wZqowz/tXpMX5x5jgZbndvhehT0aEOPbJgmh5atkMPfrTNdN/6nHKd+9DnevqaGVxIHiACsqjtcrk8CWRL7hZ/+E3bZWZmavLkydqyZYsuueSSdo9dXl7e6eO3fAwAAAD4N/LHvrG/tEY1DebneVxK//pgOigiWDfOHq6/N/uwvWLbQX2xo0gzR8b7MDIAANDXyCEBAB2paXDq9bW5KmlR0A5xWHXe5DQlRzEDWZKsVot+euoojUmO1M9fWqfqZucNCivrdemjX+nxq6br2OGDfBgl+kJAFrWXL1/e7X2io6M9V0m2dPXVV+vqq68+sqAAAADgt8gf+8bWFrO0EyODFRce5KNoeu66E4bpua/3qrCy3jP21/e36K1bZslq7T+zzgEAwJEhhwQAtKe2waXX17QuaEcE23X+5FQNigj2UWT+64wJyXrjlpn60bNZ2ltc4xmvrHfqyv9+o39fNkVnTkz2YYTobVZfBwAAAAAALrehnUXVprGxyZE+iubIhAXZ9bPTRpvGNuVW6O0NB3wUEQAAAADAX9Q2uvT62pxWLcejQx26eFo6Be0OjE6K1Ju3zNSMoXGm8QanWzc//60Wf7PPR5GhL1DUBgAAAOBz+0tq1OA0t8gcldg/i9qSdMn0dI1ICDeN/d/Srap3tt2CFAAAAAAw8NU1uvTG2lwVVZkL2lEhdl00NU1RoQ4fRdZ/xIQF6dnrZmjO+CTTuNuQfvv6Rj28bIePIkNvo6gNAAAAwOe2F1aZbqdEhygipP+ulmS3WfXrM8eaxvaX1GrxKq4aBwAAAIBAVO88VNA+2GypKkmKDLHroqnpigyhoN1VIQ6bFi6YqsuOzmh13wMfbqWwPUBR1AYAAADgUy63oV0HzUXtkYkRPorGe+aMT9L0IbGmsYeW7VB1vdNHEQEAAAAAfMHpcuvt9XkqbFHQjgg+VNBmhnb32W1W/fXCTP3klJGt7nvgw6169LOdPogKvYmiNgAAAACfyimtUV2L1uMjE/p/UdtiseiOs8yztYuqGvTUF7t9FBEAAAAAoK+53Ybe35Sv3LJa0/ihgnaaoilo95jFYtEv5ozR3eeMb3XfX9/P1hMrd/kgKvQWitoAAAAAfGpHi9bjSVHBA+Yq9aOHxumUsYmmsUc/26XS6oZ29gAAAAAADBSGYejj7ALtKqo2jYcF2XTh1DTFhAX5KLKB5ZqZw3TPuRNajd/77hY9zYXlAwZFbQAAAAA+4zYM7Txo/nA/EFqPN/fLOWNMtyvrnVpEGzQAAAAAGNAMw9DKHUXakldpGg+yW3X+5DTFUtD2qquOH6q75o5rNf7HtzfrhVX7fBARvI2iNgAAAACfyS+vU22jyzQ2EFqPNzc+NUrnTU41jT395R7ll9f5KCIAAAAAQG/L2luqtfvKTGM2q0XnHpWqhMhg3wQ1wF1/wnD9psUyYJJ015KN+mRLgQ8igjdR1MaAVO90aXthpVbvKVHosZdr0Nk/k3XKhXrmyz36amexGl3uzg8CAACAXteyBdug8KAB2X7t56ePlt1q8dyud7r1r0+2+zAiAAAAAEBv2ZJXoS93FpvGLBbp7MxkpcWG+iiqwPDjE0fol3NGm8bchnTrC2u1MafcR1HBG+y+DgDwFsMwtKuoWptyy7W/pFYuw5AkBU84TU3XPN391neSpOhQh04dm6gFxw7WtCFxPooYAAAAe1oUtYfFh/sokt41ZFC4Lj06Q883a3n2ctZ+3TB7+ID9ngEAAAAgEO0rqdHHbcwKnjMuScPjB1ZnMn916ymjVNfo1kPLdnjGahtduvaZ1Xr9puOVERfmw+jQU8zUxoCQX16nV77N0Tsb8rSnuMZT0G5PeW2jXl+bq4se+Uo/fHKV1uwr7aNIAQAA0KS8tlHF1Q2mseEJA7fA+9NTRynEcfgjmMtt6MGPtvkwIgAAAACANxVV1evdDXlytyhRzB4Vr7EpUb4JKkD9Ys5oXTglzTR2sLJe1zy9WuU1jT6KCkeCojb6Nbdh6IsdRXopa7/yergm4crtRbpw4Ze6a8lGVdc7vRwhAAAA2rO7xSztUIdNSVEhPoqm9yVFhejq44eZxt5ef0Cbcml/BgAAAAD9XVWdU2+uO6CGFsufThkcoymDY30UVeCyWCy676KjdNzwQabxHYVVuvF/Wap3unwUGXqKojb6rbpGl95cd0BZe9ueZW21SOkxoWrY9oUqst6Se0+WxnVwJdT/vt6ns/61Ut+2czwAAAB4166iKtPtofFhslos7Ww9MNx04ghFhphXgfq/pVt9FA0AAAAAwBvqnS69uT5XVS0mzo1MjNAJI+N9FBWC7FYt+uE0jUo0t33/eleJfr9kk4xOuv7Cv1DURr9UXe/US1n7ta+kptV9USF2nT4uSTfMHq6LpqWrZuV/VfrJY3J//rjev+0EffmbU3Tn2WOVEBncat99JTW6/LGv9dq3OX3xbQAAAASseqdLuaW1prFAWFs6OsyhH584wjS2fOtBrdpV7KOIAAAAAABHwuU29N7GfBVVmZfXSokO0Rnjk2QZ4Bdv+7voUIeeuuboVjWhl7Ny9L9V+3wUFXqCojb6ndoGl95Ym6uyFmseWC3SzBGD9MPjhmh8apSC7bY290+NCdUNs0do5a9P1p1njzWtayhJDS63fvHKet33frbcLRe+AAAAgFfsK64xrTFms1g0JG7gF7Ul6ZqZQxUfYf4wff+HW7lCHAAAAAD6GcMw9Gl2YasJeDGhDp0zKVV2G2U4f5AeG6anrj5aYUHmutGf3v5OWXtKfBQVuou/JvQr9U6XlqzLVXG1+YqnsCCbLpyarulD42S3du3XOsRh0w2zR+iD22Zr+pDW61ks+myn7nxjI4VtAACAXrC3xQf+tNhQBdkD4+NJWJBdPz11pGns272l+jS70EcRAQAAAAB6YtXuEm3OqzCNhTpsOm9yqkIdbU+8g29MTIvW/108yTTW6DJ00/NrdLCy3kdRoTsC46wRBgTDMPThdwUqbPHiEh3q0GVHZygtJrRHxx0aH64XbzhW18wc2uq+F1fv169e3SAXhW0AAACvMQxDe4vNRe0hg8J8FI1vXHb0YGXEmfPXBz7cygWVAAAAANBPbD5QoVW7zbN87VaLzp2UqpiwIB9FhY6cnZmim04yLwl2sLJet7+0jjpQP0BRG/1G1t5S7S6qNo1Fhth14dQ0RYY4jujYdptVd58zQX+9MFN2q3l9i9fW5OjXr26gHSQAAICXlFQ3qKreaRobEhdYRe0gu1U/P320aSw7v1JvrT/go4gAAAAAAF21t7han2QXmMYsks6amKzk6BDfBIUu+eWcMTphVLxp7PMdRXp42Q4fRYSuoqiNfmF/SY2+2llsGgt12HThlDRFHWFBu7nLZwzWwgVT5bC1Lmz/7YOtXnscAACAQNay9XhEsF1x4YF3Ffu5k9I0JinSNPbgR9vU4HT7KCIAAAAAQGcOVtbrvY35ajmx98TRCRqeEOGboNBlNqtF/7x0spKjzBcf/PPjbfp6V3E7e8EfUNSG36trdOmD7/LVcp70mROTe6WFx5wJyXrsh9Nbrem46LOdemLlLq8/HgAAQKDZV9K69bjFYmln64HLZrXoV2eMMY3tK6nRS6v3+SgiAAAAAEBHKusa9db6A2pwmS9GnjY4VpMyYnwTFLptUESw/n35FNmade51G9LPX1qn8tpGH0aGjlDUht/7fEeRahpcprHjhg/S4F5sUXny2EQ9smCq6QVNkv783hYt/S6/1x4XAABgoHO63MotrTWNBVrr8eZOHZeoqYNjTGP//nSHahqcbe8AAAAAAPCJeqdLb60/0Go5rVGJEZo5cpCPokJPzRgW12pZsAPldfrDm5t8FBE6Q1Ebfm1fSY2+O1BhGhsSF6ajh8b2+mOfOi5J912YaRozDOlnL61Tdn5FO3sBAACgI7lltXI269FmkZQRwEVti8WiX5851jR2sLJeT32xxzcBAQAAAABacbkNvbcxX0VVDabx1OgQzRmfFJDdxwaCm04coeOGmy9IeHPdAb25LtdHEaEjdl8HALSn0eXWp9mFpjGHzaJTxyX22RvExdMzdLCqXvc3W0+7psGl65/J0pu3zNSgiOA+iQMAAGCgaNl6PCkqRCEOm4+i8Q/HDh+kE0cn6LNtBz1jj362U1ccM0TRYQ4fRgb0P9OnT1d+fv/vrpWcnKysrCxfhwEAAABJhmFo2dbCVp9nY8IcmjcpVXYb80f7K6vVor9fMkln/nOFKuoOz8D//ZJNOnb4ICW1WHcbvkVRG37r272lrdYumDkyXpEhfXti76YTR2hHYZVeX3P4ypyc0lrd9uI6PXPtjFYtygEAANC+vW2spw3pV2eMMRW1K+qcWrRip+5oMYsbQMfy8/OVm8usCgAAAHjP6r2lrTrKhjpsOn9ymkID/CLtgSA1JlR/viBTP1m81jNWUefU797YpMevnMYsfD9CURt+qbreqW/3lprGUqNDdFRadJ/HYrFY9JcLMrW7qFpr95V5xj/fUaR/fbK91ZoLAAAAaFtNg1PFLVq1DQ7g1uPNTUyL1ryjUvTOhjzP2FNf7NY1xw9VIleGA91msVoVFZfg6zC6raLkoAy329dhAAAA4HvZ+RX6amexacxmteicSSmKDqWz1kBxzqRUfbS5QG+tP+AZ+3jLodvnTU7zYWRojqI2/NJXu4pbrbV48ti+azveUojDpkd/OE3n/OdzFVTUe8b/8+l2TR0co5PGJPokLgAAgP4kp7TWdNths9DKq5lfzBmj9zfly/V9HlzX6Na/P92ue8/P9HFkQP8TFZegu19Y4eswuu2e+bNVXlTg6zAAAAAgKae0Rh9vLmw1fuaEZKVEh/ogIvSmP547QV/uLDKtm373W99p5sh4xbMUrV+g0T/8TlFVvTa3aOUxITXK5y8aiZEhenj+VFO7ccOQbn9pnQor6nwYGQAAQP+wv9TcejwtJpSlXJoZFh+uS6anm8Ze/Ga/9hZX+ygiAAAAAAhMJdUNemdDnlyGYRqfPSpeIxMjfBQVelNceJD+33kTTWNlNY3687tbfBQRWqKoDb/zxY4iNX+bcNgsOnb4IJ/F09z0oXH6TYt1DUtrGvXLVzfIaPHmBgAAALOcEvNM7YxYWo+39NNTRynYfvhjmtNt6MGPtvkwIgAAAAAILNX1Tr25Llf1TvOyMJPSozU5I8Y3QaFPnJWZormZKaaxN9bm6osdRT6KCM1R1IZfKaio055i8wyeaYNjFR7sP53yrz9hmE4fn2QaW7HtoJ75co9vAgIAAOgHKusaVVbbaBpLj6NdW0sp0aG66vihprG31h9o1ckIAAAAAOB9jS633t5wQBV1TtP48PhwzR6d4LMlUtF37j53vCJDzDWpu5ZsUl2jy0cRoQlFbfiV1XtKTLdDHTZNHRLro2jaZrFYdP9FRykx0twO/a/vZ2tbQaWPogIAAPBvLdfTDrZblcCaVG266cQRimx2UadhSH/7INuHEQEAAABAALBY9MGmfBVU1JuGk6KCdebEZFkpaAeExMgQ3dGiY+/uomot+mynjyJCE4ra8BtFVfXaedC8XuDUwTFy2Pzv1zQ2PEj/d/Ek01i9063bXlyneidX6wAAALS0v8TcjSc9NpQr3NsRGx6kG2YPN419tu2gPtt20EcRAQAAAMDAF3rcFdpVZK5RRIXYdc5RqX5Zp0DvmT9jsKYMjjGNPbJ8p3JKa9reAX2Cv0L4jZaztIPtVh2VHuObYLpg9ugEXTNzqGlsS16F/r6UNQ8BAACaMwxD+0tZT7s7rp01TAktOgPd+85mOV3udvYAAAAAAPRU9Kz5Ch53kmks2G7VeZPT/Gp5VPQNq9WiP5+fKZv18MX49U63/vLeFh9GBYra8AtlNQ3aVlBlGpuSEaMgu3//it5x5liNSYo0jT2+cpe+3FHko4gAAAD8T1lto6rqzeuRZcRR1O5IeLBdv5ozxjS2vbBKi1fv91FEAAAAADAwWUafqJiZ801jNotF845KUVx4kI+igq+NT43SFccMNo29tzFfX+6k/uMr/l0xRMBYt7/MdDvIZtWkjBifxNIdIQ6b/nnZZAU1az1iGNKvXt3Q6sQtAABAoMptMUs7LMim2DCHj6LpPy6alq7xKVGmsX98tE3ltY0+iggAAAAABpZ3NhyQ9ejLWo2fMSFJ6XQYC3i3nz661fmLP71NFzVfoagNn6t3urQ5r8I0lpkWrRCHzUcRdc+4lCj9+kzzLJrcslr9lTYUAAAAkg7lRs2lx7CedlfYrBb9ft5401hJdYMWLtvho4gAAAAAYOD4YkeRbn9pnSwWc6ns5DEJGtWiQysCU0xYkH7eootadn6lXluT46OIAhsLAcDnNh+oUKPL8Ny2SDoqPdprx68qK5Yk5eXlKT093WvHNbPIetrPZE0e6xl5ftU+PXvvz2QUbPXKIyQnJysrK8srxwIAAOhLLYvaqbGhPoqk/zluxCDNGZ+kpZsLPGNPfbFHC44ZosGD2p81MH36dOXn5/dFiL2KHBgAAABAb9iYU64bns0y1SYk6ZhhcToqPcY3QcEvzZ8xWM9/vVfZ+ZWesQc/2qZzJqX6MKrARFEbPuU2DK3PKTeNjUiIUFSo99pRut1uz7+5ubleO25L9iUPKOXah2UNCvGMGUfP14H/3iqjsa7XHhcAAMCfWSIGqbLOvCxLWgxF7e648+xxWra10HOypcHl1l/f36JHrpjW7j75+fm9mvsCAAAAQH+1u6haVz/1jaobXKbx+s2f6phTbvBRVPBXNqtFd80dryueXOUZK6io15Mrd/swqsBEURs+taeoutWagJN7bS1ti6LjE3vp2IfUffuawo5b4Lltj0lW0hk3qfbrF3p8zIqSgzLcrM8AAAD6J3vSKNPtELtVg8KDfBRN/zQ0PlxXHTdUT3x++APz+5vytWpXsY4ZPqjDfS1Wq6LiEno7RK8jBwYAAADQGwoq6vTDJ1epuLrBNF6dvVKNX78gy09u9FFk8GezRsVr9ugErdh20DO26LOdUjBt6vsSRW341IZc8yzthMhgpcaEtLP1kbEFh+nuF1b0yrGbGIahV9fk6EDZ4ZnZwRNO1YIfXqW0HrbZvGf+bJUXFXS+IQAAgB+yp5jXnkqLZT3tnvjJKaP02pocldYcviD0D29+p3d+OksOm7Xd/aLiEno9B+4N5MAAAAAAvK2oql4LnlilnFLzElnuvC0qeufvio7t+KJhBLbfnDlWK7cflPF9x/rqBpesmWdLu7J9G1gAaf/sB9DLKmobtbe4xjQ2KT26X5/ktFgsOm1ckmxW8/fw0ZYCNbqYaQIAAAKPPWm06XYqrcd7JDrModtPNz+XWwsq9cyXe3wTEAAAAAD0I2U1DbriiVXaUVhlGp+YFiX3Z49ILmc7ewKHjE+N0gVT0kxjllEnyBYZ76OIAg9FbfjM5rwK0+0gu1Wjk/p/q4bYsCAdP8J8RVd5baO+2lnso4gAAAB8wxoeI1tMsmmM9bR7bv6MwRqXEmUa+8dH25RfXtfOHgAAAACAirpGXfnfb5SdX2kaHxYfrqevmSE5630UGfqbn58+Wg7b4UmNFptD0cdf6sOIAgtFbfiE2zD03QFzUXtsUmSHrRP7k8kZMUqJNrdRX7u/THnlte3sAQAAMPCEpE8w3Q6yWZUQEeyjaPo/u82qe8+faBqrbnDp/7272UcRAQAAAIB/q6536pqnVmtDjnkp1PTYUD1//TGK5zMquiE9NkyXzxhsGovIPF3WyAQfRRRYWFMbPrGvpEZV9eZ2HhPSotrZuv+xft+G/IVv9snlNjzjH28u1OXHZMhuHRjFewAAgI4EZ5gLsCkxIbJa++9SM/5g2pBYXTo9Qy9l7feMvbshT5cdfVAnjOJDNAAAAIC+N336dOXn5/s6jNZsDllPvlXW5LGmYaO6VHveuFMz/nOou2peXp4kqbq6us9DDHRVZYd/Bunp6T6OpotCo2U7715Z7EGSJIvNLnvmWT4OKjBQ1IZPbMo1XxWVGBmsxMiQdrbun+LCg3TMsDh92azteElNg1bvLtVxLdqTAwAADEQh6eNNt1lP2zvuOGusPtycr7KaRs/YH978Th/87AQF220+jAwAAABAIMrPz1dubq6vwzCxOEKUeNEfFNKioO2qKlX+C3fIWXqg1T5Gswlq6Btut9vzr7/9DrUvVzFr3lH0jAs9I6FjTlBZTYNiwoJ8GNfAR1Ebfa62waXdReYrniakDpxZ2s1NGxyrHYVVKqw8vCZH1t4SjUyMUEIkbU0AAMAAZg+WI2GoaSgtmqK2N8SFB+mOM8fqt69v9IztLqrW4yt26dZTRvkwMgAAAACBzGK1KirODzpIOUIUMec22ZNHm4bddZWqXvoPhdtcUnySZ7y8qKCvI0QrFkXHJ/o6iK7b/pmMKWfL4jg0WdNitSprb6lOG5fUyY44EhS10ee2FVaq+QVPNqtFY5IifRdQL7JaD7Uhf3H1Ps/37Dakj7cU6NLpGbTfBAAAA5Ylfrgs1sOzhq0WKSmKi/q85dLpGXpp9X6t21/mGfvPpzt0zqRUDRkU7rvAAAAAAASsqLgE3f3CCp/GUO90acnaA8qvqDONB9utunD2eCXOXdxqn1+cOU7G9zOG4Ru24DCf/+501+c7ivTt3lLP7S15FZoxLE5RIQ4fRjWwsbAv+tzW/ErT7RHx4Qp2DNw2iQmRwZo2JNY0VlhZrzX7StvZAwAAYABIGGG6mRgZIruNjx/eYrVadO/5E9X8Gsl6p1t3vLZBblrmAQAAAAhAdY0uvb4mt1VBO8Rh1UVT0wfcEqjwrSkZMXI3Hu7S6zZkKnLD+wL+rNIdd9whi8Xi+Vq0aNERHe/ZZ5/VSSedpPj4eIWEhGj48OG66aabtG/fPi9F3L+V1TQor9z8hjImZWDO0m5uxrA4xbVYS+Hr3SUqrW7wUUQAAKCnyB+7xtKiqJ0Sw8kDb5uYFq0rjxtqGvt6V4meX7XXNwEBAIB2kUMCQO+qrnfq9TW5pqVAJSnUYdNFU9NZDhReFx5sV/WGD01j3x2oUHW900cRDXwBW9Q2DEO33HKL7r//fsXGxio09MjX97vyyit11VVX6bPPPlNJSYksFot2796tRYsWKTMzU1lZWV6IvH/bWmCepR3isGpI3MBvj2i3WnXaePN6EC63oY+3FMgwmEkDAEB/QP7YdS63IUv8MNNYKutp94pfnjFGaTHm5/av72dL4YN8FBEAAGiOHBIAel95baNe+TZHB6vMBe2wIJt+MC1d8REUtNE7Kr55Q4ar0XPb5Ta0ttkyYfCugFxT2+Vy6frrr9fTTz+txMRELV26VOedd5727u35jIannnpKzz33nKKiovTwww/rBz/4gUJCQrRz50796le/0htvvKGLL75Y27Ztk8MRmP30DcNQdovW46MTI2ULkHWlU6JDNTkjxrTu4YHyOm3IKdekjBifxYWBbfr06crPz/d1GD1SWFgol8slm82mxMTEznfwU8nJyZxQAAYA8sfuyc6vkCXIfMI2JZqZ2r0hItiu+39wlBY8scozVtPgkvW4K6Vtv/JhZIGrP+dfzZHDAMCRI4cEgN53sLJeS9blqqbBZRqPCLbrwqlpim3RQRXwJldVsao2fqLIyWd6xjbmlmvG0DgF2QN2XnGvCbiidmNjo6644gq9/PLLSk9P18cff6wxY8Yc8XH/9re/SZIWLVqkyy+/3DM+YsQIvfTSS5o+fbo2bNigxYsX68orrzzix+uPCivrVVbTaBobGwCtx5s7fsQg7S6qVnnt4efhi51FGhYfrqhQPmjA+/Lz85Wbm+vrMI6I2+3u998DgP6N/LH7Wq4hFR3qUHhwwH306DMzR8Zr/jGD9cKqw+1GrcljFTH5TClnjQ8jC0wDIf8CABw5ckgA6H25pbV6a/0BNbjcpvHoUIfOn5yqGAra6AMV37yuiElzZLEcKmI3ON3adKBcUwfH+jiygSfgzixlZ2fr7bff1vDhw/XJJ59o6NChR3zMrVu3auvWrUpKStKll17a6n6Hw6Fbb71VN9xwg958882ATShbth6PDnUoOSqwZuw4bFadOjZRr689fJKr0WXok+xCnT85VRZLYMxaR9+zWK2KikvwdRjdUl5U8P3/LIqO738ztStKDspwuzvfEIDfI3/svqw95qJ2KrO0e91vzxqrz7YeVG5ZrWcs9qRrVLWE9bV9pT/mXxI5DAB4CzkkAPSunQer9P6mfLnc5uU94yOCdP7kNC6sRp9xlh5Q3c4shY6c4Rlbu69Mk9JjAqZTcV8JuL/qzMxMLVmyRBMnTlRqaqpXjvn5559Lko4//nhZrW23E5g9e7YkacWKFV55zP7GMAztKKwyjY1OigjIIm5GXJgmpkZp04EKz9i+khptyavU+NQoH0aGgSwqLkF3v9C/Xn9+ceY4GW63bMFh/S52Sbpn/uxmhXkA/Rn5Y/e1nKmdEsN62r0tMsSh+y7K1A+f/MYzZg0OU+isq2UYRkDm3b7WH/MviRwGALyFHBIAeodhGFq7r0wrdxS1ui8tJlTnTEpRsN3mg8gQyCq/fdtU1K6qd2p7QaXGplDz8aaAbOg+Z84cryWTkrR9+3ZJUkZGRrvbNN1XVFSk8vJyrz12f1FQUa/KOqdpbFRiYLUeb27WqHiFB5vfWFdsP6jqemc7ewAAAF8if+y6vPJa02xhifW0+8oJoxJ0+Qzz75QjbbzW7CvzTUAAAAQ4ckgA8C6X29Cn2YVtFrRHJITr/MmpFLThEw1521qd+1izr0yGYbSzB3oiIIva3rZv36G160JD25+BEhYW1mr7QLK90Nx6PCbUofiIwF3PIthu0yljzO2U651uLdtayIscAAABYCDnjy1nabvrqzUoPHDzvr5259njWrV7/3JnkfLL63wUEQAA8JaBnEMCQGfqG116c32uqQNqkwmpUTp7YorsNkpe8J1pQ8xraB+sqteBMj6Le1PAtR/vDVVVVZ1v1MPtc3JyOrw/Ly+vW4/tC221Hh8VoK3HmxueEKHRSRHaVnD4udl5sFo7Cqs0KilwZ7EDABAIejN/lHybQ84YFqe/XzxJt//lP3LGDJGltkwWy+ReezyYRYY49H8XT9Llj38li+XQCR23Ib2/KU/zZwxWsINZCwAA9FcDOYcEgI6U1TTo7fV5KqlpaHXf8SMGafqQ2ICvN8D3hsWHKzrUofLaRs/Yuv1lSotlSTZvoajtBbW1tZ1v1ExNTU2Xt+2onVBLjz32mGJiYjrcJiUlRZdffrlpbPHixR0mpZdffrncbrfWbthoGjdcjapa+26ncbndhhz1wySFe8ZGh1SqMuvzTve12OyKmDLPNFa3Z60ai/Z2uq89NlWhI2aYxqrWfyijsfOfV8iQyXIkDPXcdtVWqOa7TzvdT5LCjzpD1qDDL1IN+TtUn7OpzW1nGtKUEKcMSRXuEH3QMEbLth5UelyYQh021Wz7Utdf/UMZbresVqsefPDBNo8zdepUnXTSSaax9rZt6cILL9TQoUM9t/fs2aPXX3+9S/v+/Oc/N91evny51qxZ0+l+Q4cO1YUXXmgae+aZZ1RcXNzpvieeeKKmTZvmuV1ZWanHH3+8S/FeeeWVio+P99zeuHGjPvroo073i4iI0A033GAae/vttz1tvzoyceJEzZkzxzT20EMPqaGhdQLW0rx58zR69GjP7QMHDujFF1/sdD9JuuWWWxQcHOy5PXXyUarMWtLpfrbwOIWNm20aq9myQq7qkk73DUodq+DUsZ7bXX2NkKSwsbNli4jz3G4sydXtP/vZ97cs7cbuz68R7f3t/uhHP1Jk5OELV7799lt99tlnnT7moEGDdNVVV5nGXn/9de3Zs6fTfXmN4DWiubKysk63Qe/rzfxR8o8c8tLhbrndO7V23yZJP/CMH+n7Q92u1Z3u5+33h8cee6xLJ4VPP/10ZWZmem4XFRXp2Wef7XQ/ybvvD/kbVuhS+zrJYZ6xXZG1RiHNitpBSSMUnJFp2qYr+YIkhY46TvboJM9tZ3mBard/1aV9I6efb7pdv3+jGgp2msbaeh/tL+8PTZ+fautaX5Ffu/MbOUsPdPqYjvghChk6xTRWtfYdGa7OlysKGX60HHFpntuuqhLVZHdtXdWIKXNNt7/66it99VXnP9eevEY0Oe6443Tcccd5btfX1+vhhx/uUryXXXaZqa3vtm3bPM+/xWolhxQ5pD++RjTpTzkk+aP/CIQcsom33x/eeeedTvcLCgrSrbfeahpbunSpNm1q+7xec6NGjdI555xjGutvOSTvD63x/tD185DN1R/IVsOB7E736+p5SJfbUF2jS6dJ0vcfcb5zJinbnaIzxidpVFKkDFejKgP4PGR78XenVtGcNSRS4RNPNY3VbPtSrorCTvft7ufM5rE7ywt69XNmW2xRiQobfbxprHrTJ3LXVbazx2HB6RPNA411Ote2RvUh7sNjlVLFartaXnMRNuEU2UIPr7fdeHCP6vau6/QxLY5QRUw6wzR2JJ8zr1pwmew2W4f1J8l/ckiK2gNIVVWVbLaOZ15ER0e3GqupqVFlZft/oBEREZIOJXYmhmQ0dP6ia5FktRjS9121o0Mdigq2qK4L+xq21r+ihrOhS49rOFu/WRuNtV3b1+1qMWB0ab+mbc3Hcna4b9j3L2YNlkM/u9pGl1ZsO6gzJiTLcNYr8vvnX1K7P6f6+vpWYx39TJtzOp2tbnd137bi6Mq+bX2oqq6u7tK+LZMwwzC6HK/b7Tbdbmxs7PH3WldX16V969o4mVlZWdmlZLKxsdF02+Vy9TjeoKCgrv3uB7WO12is6+LfXGOLga69RkiSYZh/NnK7FBV1+E29veP482tEe3+7LZcYaGho6NLPNSSk9Xq0nb1+N+E1gteI5ro7WwMDX+/nkA7zHUf4/tCl12kvvz9UVVV16e+r5d+l2+3u8uuIt98fwoNsktp6b252s+V7t7r+s5G75c/G3fV9Wz6ms7FL76P95f2h6XffYm3d+vBIfg/dDbVSF4raapGnGEY3fjYtVkLq6nt3T14jmj9GS1392bhc5u+1sbHR8/xL5JASOaQ/vkZ0xF9zSPJHtKW3csgm3n5/6Mq+rc596sj+LvtjDsn7gxnvDz2Lt638vs3tunge0qrD59CbhNkM/WByupKbll4K8POQ7cbfzVqFZzubo/WYs75n54hbxtRC89h7+3Nm29u1fk3r8vlwd4vPZ4Yhu6te9pZNAxobW37UauNn07XzHW3GcQS/h+Hh4Qr+/v2vo795f8khKWp7QUfr2LSl+do2ndm/f3+H9+fl5WnGjENX+ERERJiuzOvqY4eFhXW4X15entxud+s3P4tkCer8e69pcMltHP4rHpUYIYu1vkv7Wtp4o7DYg7q2r711ImpxdO1nZbG2SMotli49ZtO25mPZO923rtGlOuPwG0V2fqVGJ0UqyR6syqoqz5X6KSkpbe7ffEZuk85+F5rY7fZWt7u6b1txdGXftn4Pw8PD20y8Wmr5AcNisXQ5XmuLE4sOh6NL+zY/MdYkJCSkS/u29SEhMjKyS8mkw2FOHmw2W49/Ng0NDV37u3G0jtfiCOni31yLZKeLrxGSPO1RPaw2VVQ0rY9jUXR8Yqt9JP9+jagoOdjm327LVkhBQUFd+rmGh4e3Guvs9bsJrxG8RjTX8gQPfKM380dpYOSQUtvvD77IIdv6O29Ly79Lq9Xa5dcgb78/VFVVyW1ItvCYVvlpWJBNVoul9Xu3uv6zUcuCrdXa9X1bPqbd0aX30f7y/tD0u9/WTO0j+T20BoV2aaa2WuQpFks3fjYtTr4cyXt3X+QpLYspDofj0O/+9zO1o+IS2tyPHJIcsiVyyI4fk/zRfwRCDtnE2+8PXdm3raL2kfxd9scckvcHM94fevazaSu/b3O7Ds5DGoZU73TJ6W5VCpTVYtHEjEGKim62f4CfhywvKmi60xx/D2oVh2Jr42djD+7ZOWJ1/LNpHntYL3/ObHu71q9pFkeILK7WxflW21lb/E58/7Opd7rV6DpcoLdICgtqMVu71c+mi+c72vi9OZLfw+rqatXX1XVYf5L8J4e0GC0v5wpQQ4cO1d69e/XII4/oxz/+cbf2nT9/vhYvXqw77rhD9913X7vbNSUZGzZsMLWUORI5OTme1kD79+9Xenq6V47bXHp6unJzcxUdn6S7X+ha27omxVX1+t+qfaaxy47OUFJU6xfF3vKLM8fJcLtlCw7XA2933pLGF6rqnXru671qcB5+oQsPsmnBsUN0/1Unq7yoQGlpaZ2ubQS0dCR/v77WH/52O3LP/Nn87cIv9UXuECj6a/4o+X8O6Q/6++t40/M/aOocRZz+U9N9sWEOXXp0hoLt/ru+dn9+/vnd9y2ef8D7yB+9ixwSwEDkzRzsYGW93tuUp7Ka1kXFkYkROn1ckoLsrbsiHYn+fh6yP8ffn2OX2o6/tLpBz35tbkt/2rhETUht3cHE13rz80dv5A3e/csPUIMHD5bUdnuPJs3bnDRtHwh2FlWbbkcE25UY2frKl0AXEWzXCSPjTWPVDS59uqXzNSoAAED/Q/6IvuLct16TM2JMY6U1jfrwu4JW7SoBAIB/I4cEMJAZhqH1OWV6KWt/q4K2RdKskfE6e2Ky1wvagLfFhgdpyCBzl4iNueU+imZg4a/fC0aOHCmp4xY9TffFx8e3uZ7MQLXroLln/vCE8FZtcXDIhNSoVi90Ow5WyTHyOB9FBAAAegv5I/rSzJGDWl1YuruoWl/vLvFRRAAAoCfIIQEMVHWNLr27MU/Ltx6Uq0XL8RCHVedPSdO0IbHUFtBvHJVmfg8uqKhXQUXnyx6gYxS1veCEE06QJH311Vftznb4/PPPTdsGgqp6pwoq6k1jw+Nbr9eCQywWi04fl6QQh/nPMuy4BbJFtb2OBwAA6J/IH9GX7Far5mamKNRhbjf+ze4SbSuo9FFUAACgu8ghAQxEB8pq9fyqfdp5sLrVfYmRwbr86MEaHNd6bXTAnw2ND1dEsHnNbWZrHzmK2l4wZswYjRkzRnl5eXr55Zdb3e90OvXQQw9Jks4777y+Ds9ndrd4EwqyWZUey5tPR8KD7Tp1bJJpzBIUqvi5t0tchQYAwIBB/oi+FhXq0FkTk1ullEs3FyivvNY3QQEAgG4hhwQwkLjchr7cWaRXv81RVb2z1f1TMmJ08fR0RYU6fBAdcGSsFosmpkWZxrbmV6re6fJRRAMDRe0uKi8v19SpUxUaGqorr7yy1f2//vWvJUk33nijXnjhBdXXH5qhvGvXLl122WVat26dhgwZossvv7xP4/alXUXm1uNDB4XJZqUw25mRiREalxJpGgsZnCnLuNN9FBEAAOgJ8kf4m4y4MM0elWAac7kNvb0+T+W1je3sBQAA+hI5JIBAUFRVrxdX79PqPaVq2XcixGHVuZNSNXt0guxWSljovyamRpsuLHe6DW3Jo1vakQjIV4RTTz1Vdrvd9LV3715J0i233GIaP/XUUyVJGzdu1Nq1a1VXV6fFixe3Oua1116rBQsWqLy8XAsWLFBYWJhCQ0M1YsQIvfbaa4qKitIrr7yioKCgPv1efaXB6db+UvOMj+EJET6Kpv85cXSCIkPMrSmsk87TJtpTAADgE+SPGCgmpUe3ulq8ttGlJetyVdPQenYEAADoOXJIADBzG4a+3VuqF7/Zr6Kqhlb3p8eEasGMIRrGMqYYAMKD7RoRb66LfXegvN0lRNC5gCxqu1yuVl9N3G53m/dlZmZq8uTJCg4ObvdKx//973968sknNWvWLEVHR8swDA0ZMkQ/+tGPtH79eh199NF98v35g30lNXK5D/9hWi2HZmqja4LtNp0xPtk0ZrHZdesLa1RZxywaAAD6GvkjBgqLxaKTRie2WpOurKZRb647oAan20eRAQAw8JBDAsBhJdUNevXbHH2+o0iuFkU9q0U6bvggXTA1TREtJnsB/VlmerTpdlFVgwor630UTf8XkK8Oy5cv7/Y+0dHRWrt2bafbXXvttbr22mt7ENXAsqfYvJ52Wkyogh02H0XTP6XFhmrakFh9u7fUM7anuEa/eW2jHpo/RRbW2B6Q6hpd2nmwSnuLa1RQUafCynoVVtSrsLJOpTUNqm1wqa7RrdpGl2obXHK5DdmsFtmtFtlsh/4NcdgUHepQVIhD1tk3alBZkezuRq3fX6bwYLsigu0KD7YpItjO7xEAdBH5IwYSm9WiszOT9UpWjoqrD8+OKKys1zsbD+jco1JltwXk9c8AAHgVOSQAHFryKGtviVbvLm1VzJakQeFBmjMhSYmRIT6IDuhdGbGhigqxq6LucGe07w5UKCmK3/eeCMiiNnqXYRjaU2Quag+lXUiPHDd8kFat/lb2xOGesXc35umYr+N05XFDfRcYjphhGMorr9OafaXakFOu7QWV2nGwSjmltep29xFX66Gc79v/WwdPVcTgQ2PLtx00bWOzWhQd4lB0mEMxoYf/jQkLUmSIXVYK3gAADFjBdpvOn5yml7/dr8pmH673l9Tq3Y15mndUqmxWcgEAAAAAPZdfXqePtxSYLqZtbtrgWB07PI6LajFgWSwWjU+J0te7SzxjW/MrdcKoeDn4ve82itrwuqKqBlU3mKtswwZR1O4Jm9Wi6mWLFHHu72ULjfSM/793NmtyRoyOSo/xXXDoFsMwtLWgUp9vL9K3e0u1Zl+pCip822bE5TZUUtOgkprWSaXNYlFMmEOx4UGKCwtSbLhDsWFBig0LUpCdN1sAAAaCiBC7Lpicple+zVFt4+H8fU9xjd7flKezJqZQ2AYAAADQbQ1Ot77aVax1+8vavD861KHTxyUpLTa0bwMDfGBcqrmo3eBya0dhlcalRPkwqv6pT4vaDQ0NCgoK6suHhA/sbtF6PDrUoZgwh4+i6f+MqmIVv/ugEn9wt2es0WXo5ufX6N2fnKBonlu/VV7TqM93FOmzbYX6bNtBnxexu8NlGCqubmjzKsqIYLviwoMU26zoHRcepLAgG+3MAfQKckig98SGB+m8yal6fU2uGlyH19PeebBa723M01kTk5k1AQDol8ghAcA39hRX69PsQlNHqCYWSVMHx+qY4XHMUkXAiApxaEhcmPaW1HjGvjtQQVG7B/q0qD1o0CCdfvrpmjt3rubOnavk5OS+fHj0kVatxweFUeg6QrU7V8v93YeyTjjDM5ZTWqtfvrpej/1wGs+vHymradDS7wr07sY8fbGjSE53d3uJH5IaHaLUmFAlRYUoITJYiVHBio8IVniQXaFBVoU4bAp12GS3WuUyDLncbjldhpxuQ9X1TlXUOVVe26h7/vI3VTUYChmUqiGTZ6mq3qnqeqd6GJYkqareqap6p/aVmMeDbFbFhju+L3gHef6NDnUwywvAESGHBHpXUlSIzp+SqjfW5qrRdThJ2FVUrbc35GneUSmccAIA9DvkkADQt2yRgxR2yk16c92BNu9PiAjWqeMSWUsYAWlCapSpqJ1bVquymgbFhHEBXnf0aVG7trZWS5Ys0ZtvvimLxaKpU6dq3rx5mjdvnqZOndqXoaCX1Da6lF9eZxpjPW3vcK9boqPPvkzf7i31jH20uUAPL9uhW08Z5cPIUNPg1Psb8/X2hgP6fHv3CtlRIXZNGRyriWlRGpkYoZEJkRqeEK7wYO+8PN+94R2V5uYqOj5Jl1x/uaRDrdBrGlwqr21UWW2jymsaVVbboLKaQ7cbnO5Ojtq2BpdbBRX1rWakWy2HOjY0Fbljw4MUE+pQRIhdEUF2WSl4A+gEOSTQ+1KiQ3XepDQtWZdrymX2ldTojbW5OndSqkIcNh9GCABA95BDAkDfaHS5ZRk/R6kTz5Y1qHU7cZvVomOHxWnK4FgmviBgDUsIV4jDqrrGw+fes/MrdezwQT6Mqv/p06J2cXGxli5dqvfee08ffvihsrKylJWVpXvuuUcpKSmaO3eu5s2bp9NOO02hoayl0B/tK65R83Ke3WpRegw/S68w3Hpo/hSd/a+VKq1p9Az/39JtGp0UqTkTuOK4LxmGobX7y/RK1n69vT5PVfWt2+m0JS0mVCeMite0IbGaMjhWw+PD+7yoa7FYFB5sV3iwXakt/j4Nw1Bto0ulNY0qrT603nZpdYNKaxpVXtvYzhE75jZ06Hg1jZLMnRwsksKD7YoM+f4r2KHwYJvCguwKHnyUXFUlkrNBbsOQlY4EQMAihwT6RlpsqM6fkqa31h0wtSLPK6/TK1k5Om9KqqJCWPoGANA/kEMCQO/7amex/vDmJtmmXtTm/WkxoTp1XKJimY2KAGe3WjUmKVLrc8o9Y9n5lTpmWBydeLuhT4va0dHRuvjii3XxxRdLktauXav3339f7777rr755hs9/vjjeuKJJxQcHKxTTjlF8+bN09y5c5WRkdGXYeII7GmxnnZ6bChr8HlRSnSo/nXZFF391Dem9tG3v7ROr918vMYmswZDb6uoa9SrWTla/M0+bS+s6nT7ILtVxw4fpJNGJ+jEMQkaHh/u129SFotFYUF2hQXZldai4O10ub8vTjc0K3gfut3TNuuGDrczzys335d06b2e/z/06Q6FBtkUGmRTmONQ0Ts06FAL9hCHVaGOQ/c1tWUPcdi48hMYQMghgb6TFhOqC6amacnaXNU3695SUtOgl1fv17yjUpUcTbtAAID/I4cEgN5TWFmnv7y7RUvaaTUe4rBq5sh4TUiJ8utzoUBfGpsSZSpql9c26kB5Xavz8Ghfnxa1W5oyZYqmTJmiO++8U+Xl5VqxYoXnq+lKSovFoszMTE97oGOPPdaXIaMDhmFoX7M1ASRp6CBaj3vb7NEJ+u1Z4/Tn97Z4xqobXLru6Sy9cfPxSmRNkl6xu6haz3y5R69k7Vd1g6vDbYPsVp08JkFzj0rVqWMTvdZK3NfsNqsSIoOVEBlsGjcMQ5V1Ts+s7qZid0l1g2obO36uusqQVNPgUk2DS8Vd3CfYfnjt8UMF70PF77AguyK+nx0eEWJXeJCdAjjQz5BDAr0rOSpEP5iWrjfXHTB1o6lucOnVb3N08tgETUiN9mGEAAB0HzkkABw5p8utZ7/aq398tE2VbXSuNAy3MtNidPzIeIWyfBFgkhQZrNgwh6kTb3ZeBUXtbvCbSkt0dLTOOeccnXPOOZKkmpoavfDCC/r1r3+tjRs3auPGjfrrX/+q+Ph4nX322brkkkt01lln+ThqNFdU1aCaFsW+IYPCfBTNwHb9CcO0Ja9Cr6/N9YzlltXq2mdW66UbjhswRVRfMwxDk864VGWJU2RJmyiLpf2uA4bbLSNvs4zdX6smZ4Peddbr3T6MtT15eXmSpOrq6k627DmLxaKoUIeiQh2tLmSpa3SptKZBJdXfF7q/L3xX1jvl6uHs7q6qd7pV73R32jbdIiks2KbIYIciQ+yKCXMoJixIsWEOxYYFsX4o4OfIIYHeER8RrIunHypsl1Q3eMZdhqGPtxSqsLJes0clcGEYAKBfIocEgO77dm+J7lrynbbkVbR5f33+DjV886JO/dczfRwZ0D9YLBaNS4nSlzsPT9vaVlilE0cn0PG4i/yq8rV161atXLlSK1as0MqVK7Vv3z4ZhiGHw6FZs2bJZrPp888/1zPPPKNnn31WP/rRj7Ro0SJfh43v7S0xF82iQw8VhuB9FotFf7kwU7uLq7V2X5lnfFNuhW59YY0eu3K6HLwI9lhdo0uvr8nVU1/sVsXUq9TRM9lYmqeqjR+petMnclV2dQ5x3zN6uYDcnhCHTSnRoUqJbnvt7so6pyrrDrUfr6xrVGWd8/sZ2U4VFZfIFhrZ6zEakqrrXaqudym/jZw81GFTfGSQEiKClRARrPjIYMWFBfX5WugA2kcOCfSOqBCHLp6Wrnc35imntNZ034acchVV1evsiSlcUAkA6JfIIQGga4qr6vW3D7L1clZOm/dHhthVtuJZ5S9/UdGDEvo4OqB/GZscaSpqNzjd2lVUrdFJvX8efCDw6dmH8vJyffTRR3rvvff0wQcfqKCgQNKhYkd8fLyuuOIKzZs3T2eccYaiog6tFVxXV6fPPvtMl1xyiV544QWSST+yr9jcenxwHLO0e1OIw6YnrpyuCx/5UnubPffLth7UL19Zr39cMpmiWzdV1zv1/Kq9enzlbh2srG93O8PtVuPeNWrY8qmcedtkkaGIYLsUnNSH0XZNeVGBr0NoU/O1u5PaWQr+F2eeJUNWOWKS9YvH31Xt9+3HPf82Hvqqazw0VtvoMq396S21jS7tL6nV/pLDJ/PtVouSo0KUEhPyfdE+hBndQB8ihwT6TojDpgsmp+nzHUVau7/MdN+Bsjq98M0+nTYuScPiWXYIAODfyCEBoHtcbkMvrt6n+z/Y2m4nxAunpum3Z43TlCeukwzvn5cDBprIEIcyYkO1v9mF49sKKilqd1GfF7XXr1+v999/X++9956+/vpruVwuGcahGYQt16yxWFoX5EJCQnTGGWcoLCxMhYWFfR0+2tHocutAWZ1pjNbjvW9QRLCeuvpoXfjIlyprtg7Dm+sOKCrEoT+dN6HNvyOYldU06Okv9+jpL/eYnseWgu1WTUyN1lHp0Yo6fYyky/suyB76xZnjZLj7cULpdspdXarEyK6tFe92G4cL3U1F7wa35/+1jS5V1ztVVec8ohboTrehnLJa5ZTVSiqVJA2KCNLguDANiQtTKuugAF5HDgn4jtVq0ezRCUqMDNbH2YWm98+aBpfeWn9AE1OjdMKoBAXZ6RYEAPAf5JAA0DMbcsr0+yWbtD6nvM37xyRF6v+dP1EzhsX1cWRA/zcmOdJU1N5TXKN6p0vBdiZNdaZPi9ppaWnKz8+XdOgqyJCQEJ1++umeBDIjI6PLx7rkkktUUdH22g3oe7mltXIZh09uWSxSeixFnb4wPCFCT141XQueWKW6xsPFy+e+3qsgu1V3zR1HYbsdhZV1enLlbv3v672qbrEefHONxfvVmL1cN//uj7R193NWq0XhwfYutUE1DEN1je7Drc/rnaqobVRpTaPKahpUXtuo7tS8i6saVFzVoLX7ymSzWBR+1i/lzv5Sqth9BN8RAIkcEvAXY1OiFBsepHc25Kmq3mm6b9OBCu0vrdWc8Ulc3AUA8AvkkADQfeU1jXpgabaeX7VPRhvnxcKDbLr99NG66vihnCcFemhEQoQ+zS70nHt2uQ3tOlitcSnttDSFR58WtfPy8pSamqq5c+dq3rx5Ou200xQa2rMTHv/617+8HB2OxN4Sc+vx5KgQrirpQ9OGxOnRH07X9c+sVqPrcLbx5Oe7ZRjS7+dR2G4up7RGj362Sy9l7VdDB+2qjx8xSCsf+4MOZH2s6PhEErUBxmKxKDTIptAgmxIig1vd73YbKq9rVHFVgw5W1utgVb0OVta3OonfFpdhyJE6TnGp4yRJZ/xjheZMSNKc8cmamBbF3yPQTeSQgP9IigrR5TMy9NHmAu1psfxQeW2jXv02R5MyYnTs8Dg+DwAAfIocEgC6zu029OqaHN33frZKqhva3GbeUSm6a+54JUd3raMigLaFOGwaMihcu4uqPWNbCyopandBnxa1v/32W02ZMqUvHxJ9ZF+Lojatx/veiaMT9M9Lp+gni9eYZpf+94vdanC5dM+5E2UL8DW2dxRW6ZHlO/Xmulw5O5iCe9q4RN188khNHRyr9Hs2S+pZi2r0b1arRbFhQYoNC9LIxAjPeE2DU/nldcorr9OB8loVVNR32sZ8a0GlthZU6j+f7tDguDCdOylV501O1SjWSgG6hBwS8C9hQXadOylV3x2o0IrtB00XVRqS1u0v09b8Ss0aFa9xyZFczAUA8AlySADoms0HKvSHNzcpa29pm/cPTwjX/ztvomaOjO/jyICBa3RShKmovb+kRrWNLoU6uDi8I31a1B40aJBycnKUnp7elw+LXlZV52x19daQuHAfRRPY5h6VIqd7sm5/aZ2psP2/r/eptKZRD14yKSBnzGzKLdfC5Tv0/qb8NtvmSJLVIs09KlU3nzSCK6LQobAgu4YnRGh4wqFCt8ttqKCiTvtKarSvpEb5FXXt/p5Jhy4CemjZDj20bIfGJkfqvMlpunBqmpKiuMoVaA85JOB/LBaLJqZFKz02VEs3FyivvM50f22jSx9tLtDGnHKdNCaB9zkAQJ8jhwS6Z/r06Z6W/f1ZcnKysrKyfB1Gv1BZ16gHP9qmZ7/a2+aEjVCHTT85daSunzVcQXY6WALeNDw+QnZroWfynduQdhZWaWJatI8j8299WtQeOnSoYmNjVVxc3OV9MjIyVFhYqPr6+l6MDEcip9Q8SzvYblViVOtWvujulGGFAAEAAElEQVQb501Ok6RWhe13N+SptLpBjyyYpugwh4+i61ur95To4WU7tHzrwXa3cdgsunBKun580ggNi+diDHSfzWpRakyoUmNCdezwQap3upRTWqvXXn5R9oyjZAuPbXff7PxKZX+QrQc+zNYpYxN16dGDdfKYBNlpdQ+YkEMC/ismLEg/mJaub/eWatXuklYnw/Ir6vTi6v0alRihY4bFaVAEnxMAAH2DHBLonvz8fOXm5vo6DPQBwzD01voDuvfdLTpY2fbr3ZzxSfrDOeOVHktHVqA3BNmtGhofrh2FVZ6xrQWVFLU70adFbenQC2Z3OJ1OOZ2dr18K39lfWmu6nRYTKistBn3qvMlpslut+tlLa03tIL/cWazzF36hJ66arhEJER0cof9yuw19ml2oRZ/tbLdljiSFOKy67OjBumH2cKXG9GxNLaAtwXabRiREqPaLZ1VefFBpR83ULX95VB9+l99q7dEmbkP6eEuhPt5SqMTIYF08PV2XTM/QkEFcaAE0IYcE/JfVYtHRQ+M0OilSK7Yd1K5mLdSabC+s0vbCKo1OitAxwwYpLjzIB5ECAAINOSTQfRarVVFxCb4Oo9sqSg7KcLt9HYbf21FYqd8v+U5f7Wr7gp/BcWG659wJOnlsYh9HBgSe0UkRpqJ2TmmtquudCg/u89Jtv9Grz8yGDRu0bt0601hDQ4Oee+65LieVtbW1slqZsebP9reYqZ0Rx9Vb/mDuUSmKDnXoxueyVN3g8ozvLqrW+Q9/oQcvmazTxyf5MELvanS59da6A3p0xU5tK6hqd7vIYLt+eNwQXTtrmOKZKYTeZrilol367dnj9JuzxmpTboXeXJertzccUEFF21fCFlbW6+FlO/Xwsp06fsQgLThmiOZMSJKD2dsIIOSQQP8UHerQOZNStaeoWp9tO6iy2sZW22wrqNK2gkPF7ckZMUqOCmHNbQCAV5BDAt4RFZegu19Y4eswuu2e+bNVXlTg6zD8VnW9U//+dLueXLnb0+64uSC7VTedOEI3nTRCIazpC/SJYYPC5bBZTBMTtxdWaXJGjO+C8nO9WtR+4403dM8995hOUtTW1urqq6/u8jEMw9CECRN6ITp4Q3ltoyrrzFewpscy69VfzBoVr8U3HKtrn85SUdXhAlplnVM/ejZL180apjvOHNuv10SpaXDqpdX79cTK3cotq213u7jwIF07c6h+eNxQRYcGRvt1+BeLxaLM9Ghlpkfrt2eP0ze7S7Rk7aECd02zC0+a+3Jnsb7cWayU6BBdcewQXXZ0Bm1bERDIIYH+bWh8uNLjQrV2X5my9paqwdl6xkxTcTsxMliTM2I0KilCdooIAIAjQA4JAK0ZhqEPNuXr/72zWQfK69rc5qQxCbrn3Al0DAT6mN1m1fCECP1/9u48Pq663v/4+8ySSSb7vjbd0qYLbaGUHVoWRbwIXCyiiBcXlFXkIqLXewUKeH/36uUKyGIF0QsoiCwiqCAKhbJT6Ard0yVLJ/ueyTLL+f1RmvYkaZq0kzmTzOv5eMyjne/5zplPAk0+cz7n+/luqe3oH9ta10FRexhjWtQ+/fTT+/++YcMGPfvss3I6nTrllFNG9HqHw6GioiLddNNNYxQhjtTAVdpJbqeyaSUYU+aXZOj5b5+ibz36gT7e02459vCbO/Xujib9z0ULNKcozaYID09Vs1+PvrNLT66qUnvPwVuDFaUn6vLTpumS4yfJm0DbDsQGp8PQSdOzddL0bN183hz9Zf0ePfF+ldZWtQ4539fWo//52xbd88o2XbCgSF89eQr7q2BCI4cExj+Xw6HjpmRpXnG61lS2am1Vq/pCg4vb9R29enljnd7Y1qg5RWkqz09Vbio3cAEARo8cEgCsdjZ26dbnP9bKrQ1DHi/OSNIt583R2XPy6Z4E2GRmvrWo7WvrUXtPQGmJLMwbyphWeJYsWaIlS5ZI2rsnTUJCglJSUrRixYqxfFtEUfWA/bRLMpP4BRiDijKS9NRVJ+n7T6/Xn9f7LMc+3tOu8+97U9ecPl3XnFEW0+1lTNPUOxVN+s3bu/SPTXUarnvYzPwUXbl4us4/uoi2zYhpKR6Xvnhcqb54XKk217bryVVV+uOaGrX6B7ds7QuG9dSH1Xrqw2odNyVTXz9lqj4zt0BOBz93MbGQQwITR6LbqZOmZ+uY0gytrmzR2qpWS2u1fboDIX24u0Uf7m5RdnKCPPM/K+eqv9gQMQBgvCKHBIC9egIhPbBiu5a/vmPIG0vdTkPfOm2avn1mGYuAAJtNzkqWx+VQ7wEdzrbVderYyZk2RhW7ovYTy+VyqbS0VBkZGdF6S4wx0zRV3WxdqU3r8cjrbG2SJPl8PpWUlBzx+YwZi+VYdLEM5/47fYJhUz9/dbvuef49hVc/I7PywyN+n4EKCgr0wQcfHNZra9t69Mzqaj39YbV2NnYNO/fYyZm6esl0nTkrTw4KfRhnZhWk6dbz5uoH58zS3z6u1SNv79LqytYh567a1aJVu1pUmuXVN0+bqi8cO0lJCZG7KWXRokWqra2N2PnsciQ/exAbyCGBiSHR7dTJ03O0sDRTH+1p0/rqtkHbGO3T1NWnpOMuUslxF8ls2q2f/X2rzijP1YKSDPI77f0c1hsMqzcYVl8wrGA4rEDIVCAU/uRhKhgKK2xKYdOUOeDPsGnKkCHD0N7Hvr9r73Ypnvn/pLTOdhlpKfr1mzvldBhyOgy59v3pNOR0OPY/dxhyHHjc4Rg839h/zOGQHJ88N4y9f9/72Pv+jgPG9h//5E/++wMYIXJIAONNpK7DGMXz5Fj0RRmpuUMeD/s2q3vV4/r5I3X6+RG/234+396FVF1dw1+7BWDldBgqy0uxdNndWtdBUfsgonobzq5du6L5dhhjrf6AugbsAzspy2tTNBNXOBzu/7OmpubIT1jzhNwb31XO525UQu4UyyEjJVvOxVeot3a72t7+vbq3vXvk73eYuvtCWrGlXk99UKXXtzYoPMyqbMOQzizP01WnT9dxU7KiFyQwRhLdTl1wdLEuOLpY66pa9cjbu/Tn9b4h766tbPbrlj99rLv+vlX/ctIUffWkyRHZd7u2tjYyP3OACCCHBCaORLdTiyZnaeGkTO1o7NK66tZB3Z8OZGRP1s9f2aafv7JN2ckJWjwzV8dNydKiKZkqy02ZMEXOYCisrr6QunqD6uoNqrM3qK6+kPx9QfUEwuoJhNQdCKknEFJvIKxhUuMjlnTcUu27Vfn2P28cw3c6PA5DSnA55E1wyZvg/OThUrLHqSS3S46Tv6aMRp8SFNQmX7u8CU6leFxKS3LTwQmIM+SQAMaTI70O40zLU9anrpB3xolDHg92NKllxcPyb1p52O8xEuZwF3EBDGnGgKJ2fUevWv19yvCy1e9A9JbAYRu4n3ayx6mMJPr8jx1D6Tl5kTlV2C//n/9L4aM/J8+Cf5LhsK7u9BSUKe/zP1KodY96N61Q37Z3pMDBLzYOp725QWZ4cCFuKG3+gF7ZXKe/fVyr17c2qCcw/OtSPS59YdEkXXbSZE3JST6s+IBYt2BShn72xaP1w3+arSfer9Rv392t+o7eQfNa/AH9/JVt+uXrFbro2BJ987RpmhqBfxeGw6G0rKHv7o1lo/nZAwCIPscnd6OX5aWoqbNXm2o7tKW2Q529Q6/elvau4P7jmhr9cc3ei31piS4tnJypYyZlqrwgVeUFqSrN8sbUthyhsCl/X1BdvaG9hereoLr6Pila9+4vYvcE+Z01UmFTnxT6+9Q8xEIgx7STlD5t799f3lhnOZac4FRaklsZSW5lJicoL9WjnBSPkj1cGgEAALFh1NdhHC555n1GiUefK8M1eJGDGQ6pd+Mr6ln9J7kDPUrPyY9gtPu1NdYdehKAIU3K9CrJ7VR3YP8i0oqGLh07maL2QGPyye21117T22+/rXPPPVcLFizoH1+58vDvAlq8eHEkQkMEVQ1YUTEp08t+2mPI6fHq1scjfyddQ0evVm5tUHXr4KK1M6NI3pMuVeopX9HU7GTNyE/R5CyvPKPYd/u2Ly8+aFLT3RfSmsoWvb+rWe/taNaqXc0KjuBuvum5yfrqyVP0+YUlSuECFOJEbqpH3zlrhq5aMl0vfuTTr97YqQ01bYPm9QbD+t17lXr8/UqdPSdfVyyefkTtatKycsfkZ89YG+5nD2IXOSQQn7JTPDq1zKNTpmerprVbW2o7tH6nTw7P8DdntfcE9dqWBr22paF/LNHt0Iy8VE3JSVZxRpKKM5NUnJGooowkZSUnKD3JLY/r8LfrCIVNdfYG1dETUEdPUC1dfWro7FV9e68aOnvV0NErx1n/qkKXV67ULN23Yvthvxcir6svpK6+kHxtPZbx5ASnclI9Kkrf+/9MQVpiTN0cAWB45JAAJpLRXIfZ3dSl17Y2qNUfGPJ4UXqizpiVp5xPXyvp2ghGOdiN58xmcQFwmBwOQ9Nzk/XRAau1KxrYV3soY1INuvDCC9Xe3q4XXnhB77zzTv/46aefflhFT8MwFAwe/I59RJ9pmqoZUNRmP+3xKTfVo88vLFZFQ5fermhUyxBJUChsantDp7Y3dMqQlJfmUWF6knJTPcpOTlBakluJLsfB/30bDsmbqfd2NKmioUtb6zq0rrpVG6rbRlTElvZeaDpvQZG+sGiSFpZmcAMF4laCy6ELji7W+QuK9M6OJj24coflYv4+pin97eM6/e3jOh0/NUvXnlGmxTNy+LeDmEYOCcQ3wzBUkulVSaZXb/7nl9STmK28BWdo5umf1/b6zhGdoycQ1oaatiFv/NrHm7C3w1RqolsJLofcTuOTPx1yGIaC4bCCIVPB8N69qf19IXX07C1kD9x+aSiOwtmK5v30bqcht3Nv/C6nIbdj79fkcAy9V7VhSDIlU3v32JYphbX3M55pSls+fEuBYECJSV4tXrxEwXBYofDe70f4kz9Dlj/DCoX2Pw+ZpuV5MBwediuhWNDVF1JXk1+7m/Z2I3M5DBVmJKokw6upOcnKSUkghwJiGDkkgHjT0RPQG9sate0gOXKS26nTZuRoVkEqOQwwTkzPTbEUtX1tPerqDdJVaoAx+W5MmTJF69at09SpUy3jpaWl/BCdIBo7+yytEKS9K7UxPhnG3vaP03KTtbWuQ6t2tai5q2/IuaakuvZe1bVb2x+7HIYS3c69F9AMQ6b2FsPTLr1H6QlJMhxOffHB0e3R7XQYOmFqlpYuLNFn5xXIm8APcGAfwzB08vQcnTw9R1tqO/TQGzv0p7U1CoQGXzV+f2ez3t/5vuYVp+vaM6br7DkFE2YPUkws5JAA+oVD6q3coHCoWf94/h5VNfv12tYGrdrZrA93t6hmiC5DI+XvC8nfF5IGrNaNBS6HoWSPSymevXtEexNcSnI7leh2fPLnvodDiW6nXA4j4j8fV//kXrU11qm4uFi/ffT7ETlneF+x+5NCd9g0FTb3FtLDpj55vreovu9YOLz3eaj/2N7xUNhUbzAsf19Q/t6QuvqC6v5kBba/N6j/+fkD8oed8mTkqaD8GPl7Q4M+ux5KMGyqqrlbVc3demdHk9ISXZqem6LpuSkqzEiUg99JQEwhhwQQL0JhU2urWvXezqYhr/8YkuaVpOvkadmj6rQJwH4lWUlKcDrUF9rf8WBHQ5fmlaTbGFXsGZMK0apVq1RXV6fCwkLL+K5du8bi7WCD6gH7aaclupTGftrjnsMwNKsgTeX5qapu6db66jbtaOwc0cqK4CetGAedMzFlVDEkuBxaPCNHn5lboE/NzldmMvtGAIdSXpCqO7+wQN87u1y/eXunHn+3Uh1D/HvcUNOmq367WmV5Kbp6yXSdf3SR3E6HDREDQyOHBHAwk7K8+pcTJ+tfTpwsSfK1deuDXS1aXdmiLZ/sx910kJsyY4HD0AHFapdSEvYWrZP3Pf+kiJ3gHKb70TjmcBhyyFA0rq3+5KtPqammRuk5+frKZXtbdwZCYbV1B9TeHVBrd0Ct/oAaP2kXP5LOUe09Qa2patWaqlYluZ0qL0jVnMI05aYO3rcSQPSRQwKRZXgzVNPSrc7eoLoDIfUEQv03pUmS65OuMIkJTnndTqUmupXhdXN9YYztbOzSyq0Nau0eutV4fppHZ5bnKS8tMcqRAYgEl8OhKdlebT2gA0NFQydF7QHGpKjtcrlUXFw8FqdGjKge1HqcVdoTiWEYmpTl1aQsr7oDIVXUd2pbfadqWrsVinDvQKfD0FFFaTpuSpaOm5qlU8tyaKkBHKaC9ET98LOz9e0zyvTkqio9/ObOQXtGStL2+k7d+NQ63fWPrbpyyXR94dgSJXIHL2IAOSRiSWdrkyTJ5/OppKTE5mhGz+fzSZK6urpsjmRsFKYn6bwFSTpvQVH/WENHr7bWdWhbXYdqWrs/efSopqVbjZ29w5zt8BiGlOpxKS8tUXmpHuWmepSb4tEvf36nWmp2KtElXbns50pOcCnRPTGL1eOF2+lQTopHOSnWInTYNNXmD6i+o1e17T2qbvGrsXP4myO6AyGtrWrV2qpW5aV6NKcwTeUFqeRSgI3IIYHD19zVp7crGvXBrhY5z75JkzKK5UhI0tOrq0d9rrRElzKTE5TpTVBeqkfFGUlKTXSRAx2hlq4+vb6toX+blIESXQ6dUpajuUVpfK+BcW56XoqlqF3V4ldvMCSPi88a+1A5wqiFTVPVA9r9TcpiP+2JKsnt1FHF6TqqOF3BUFh72nrka+1WwycrGzp6ghppmTvR7VBpllcz8lM1My9VCydnaGFpJkVsIMJSE9365mnTdNlJU/THNdX6xWsV2jXEh5/qlm7d/NxH+vkr2/St06bqKydOps0/AHwiHA73/1lTU2NzNIfPjPXNjCMo95PC8illOYOOBUJhyyrdtu4+dfQE1RcMKxAyFQiFFQiFFTZNuRx796Z2ORx7t9hJcCo10aVUj0upie69f090KTnBNeR2HsuvelldNTVy5eQPKqIitjgMY+/F9+QElRekStpbtK5p6VZ1i187G7vU3nPwfXXrO3pV39GgN7Y3alZBqo6ZlKFs/psDAGLc9vpOvbjBp5c+rtXHB+zfauSV6UhKou09QbX3BC3F1xSPS0UZiSrOSFJpllcZXjoyjlRvMKT3djZrXVXrQbtozi1K0ynTc5SUQMELmAgmZ3vlNAyFPumMETalXY3+/s8qsKmovWvXLk2ZMmXQeFNTkx599FFt375d6enp+tSnPqUzzzwz+gFiWA0dveoLhi1jrNSODy7n3qJ0adb+/96hT9qOd/UG1RcKqy8YlmnuXbniMAw9+ZMb1F5XpbyUBG3avok7BoEoSnA59MXjSnXRsZP01w0+3b9iuzbXdgya19DRq//318365es7dMXiafqXkybbEC1waOSQsIeh9Jw8u4MYtbbGOrtDiClup0PZKR4KjjikJLdTZXkpKstL0ZKZpho7+7S9oVMVDZ1qOsgq7lDY1Md72vXxnnaVZnl1TGmGJmd5+ewDxAhySEDq6Ano+XV79MT7lfqopv3QL4iQzt6gttZ1amvd3pWHmV63puWmaGpOsgrTE+Xgd+VghqGPatr0dkWTugOhIafkp3l0+sw8FaTTahyYSDwup0qykiw3B1U0dFLUPkDUi9rf+c539Mgjj+jVV1/Vscce2z++atUqffazn1VLS4vMT+5C+MlPfqKlS5fqySef5MNgDKkasJ92ptetFFbaxi2nw1B6klvpB9lTPejbokBjneQu5t8xYBOnw9B5C4r0ufmFenVzve5bsV1rKlsHzWvq6tN/vbhZD67cIWP2p2XUPxH9YIGDIIeEXZwer259fKXdYYzajefMlhkOH3oigIMyDKO/A8BJ07LV4u/TJl+7Nvk61Nk79Aruyma/Kpv9ykpO0PFTsjQjP4UL9oCNyCER72rbevTwmzv0+HuV6uobukA6FKfDUFqiS95PtlFxORxyOCSZUjBsqi8UVndfSP6+0EF/Jw6lxR/Qh7tb9OHuFiW6HSrLTVF5QaqKMpL4fSkpqewEpZ75Db2yuX7I494Ep04ty9GsglR+TgETVFluiqWovaupS8FQWC6nw8aoYkdUK5HPPvus7rvvPhUVFSkrK8ty7Oqrr1Zzc7M+//nP66yzzlJFRYUeeOABPfPMM/r5z3+u66+/PpqhYhjspw0A45NhGDprdr7OnJWnd3Y06YEVFXpze+OgeU1dfXIee5GKZ31KfR+9rEAoLDeJE2xEDgkAiAWZ3gSdPD1HJ07LVmWzXxv3tKuioXPIlqDNXX166eNavbfTreOnZmlmfioX64EoI4dEPKtv79E9r2zTHz6oUiA0/HY03gSnjp+apVf+8Cs1bl2jxGCnbn7ouREXTQOhsFr9ATV39anZ36fGjl752noOusp4n55AWB/taddHe9qV7HFqZn6qyvNTlZfqibuC7apdzXKefZPy8sqGPO40DB1dmqHjp2QpwcX1GWAim5qTbHkeCJmqaukeNB6volrUvu+++2QYhu69915NnTq1f3zr1q1avXq1zj77bD399NP944sWLdKXv/xlPfrooySTMSIcNrVn4H7ameynDQDjiWEYOnl6jk6enqO1Va2695VtQ94F7EzOUNIJF+s3b+3S8VOzdFRxmlwOPjwh+sghAQCxxGEYmpKdrCnZyerqDWp9dZs21LQNefG+xR/Q3z6u03s7m3XC1CyV57OyCogWckjEI39fUL94rUK/emPnsEXlvFSPPntUgT5zVIEWTd5bKC25+fPqqamRJyd/VL+r3E5Hf2eTfUzTVIs/oJrWbu1p7VZls1/+YVaKd/WGtKayVWsqW5WR5FZ5QarKC1KVOcH34F5d2aL7Xt2uVzfXyzhIQXtaTrJOm5HDfuRAnEj2uFSYnihfW0//WEVDJ0XtT0S1qL1hwwYZhqHzzjvPMv72229Lki6++GLL+Oc//3k5HA5t2bIlajFieA2dvYPu7ivKoKgNAOPV0ZMy9PDXjtO6qlbd88o2vTpEcbs7ENLrWxu0prJFJ03P5mIsoo4cEgAQq5I9Lp00PVvHTcnU5toOralqVXPX4L23Wz8pbn+4u0WnluWolD23gTFHDol4Ypqm/vZxne7480bVDFiQtI/DkM6ana8vH1+qxTNz5XSM3e8hwzCUlZygrOQEzStOl2maqmvv1Y7GTu1s7FJj5+Dflfu0dgf03s5mvbezWflpHs0qSNOMvBQlT6DtL9/d0aT7Xt0+ZPe8fXJTPDqlLFuTsylkAfGmLDfFUtTe0dCl8CyTzk+KclG7u7tbbrdbLpf1bT/88EMZhqGFCxdaxt1ut5xOpxysCosZA5OiTK97QiUUiLzO1iZJks/nU0lJic3RjJ7P55MkdXV12RwJMLYWTMrQr792nNZWteqef2zVii0Ng+a09wT1t4/rtHp3q04py+ZiLKKGHBIAEOtcToeOKk7X3KI07Wjs0ns7mtXQ2TtoXmNnn55bu0eTMpN0SlmO8tMSbYgWiA/kkIgXjZ29+o8/btDfPq4b8rjH5dAXFpXoW6dNs61AahiGCtITVZCeqJOn56i9O6Ct9R3aUtsxbIG7rr1Xde0NWrmtQaVZXs0qSNX03JRxuUVaKGzq1c31emjlDr2/q/ng89obdO5J8zQzP4VrLkCcmpabrDcOuOmlOxCSr61HxSwwjW5Re8qUKdq0aZPWrVunBQsWSJLC4bBeeuklpaSkaP78+Zb569evVyAQ0KxZs6IZJoYxsPU4q7RxKOFwuP/Pmpoam6M5fOZQG+UBE9DRkzL0m68fr5IFp6pv5qfknX7coDkNnb1cjEVUkUMCAMYLwzA0PTdF03KS9xa3dzaroWNwcbuqpVu/X1Wl8oJUnTI9W6mJbhuiBSY2ckjEg5c+qtW//3HDkF1CnA5DFy8q0fVnzVRBemx9bk9LcmvR5Cwtmpylps5ebanbW+Bu7wkOOd80pd1Nfu1u8svtrNf03BTNKkjVpEyvHGO44jwSWrr69OQHVXrsnd0HXUUvSWZPu1reeFyO6tUqv3BFFCMEEGsyvAnKTklQ0wE3/VQ0dFLUVpSL2kuWLNHGjRt18cUX6+abb1ZWVpaeeOIJ7dixQ1//+tcH3Qn5wx/+UIZh6KKLLopmmBjGntYey3P+EWHkDKXn5NkdxKi1NQ59lysw4TXtUsPTtylr7imaeeltlpY3+/RfjM1P1allOUpJpHMHxgY5JABgvDmwuL2zsUtvVzSpaYiCw5baDlXUd+q4KVlaWJoR/UCBCYwcEhNZbzCk//eXTXrknd1DHj95erZuO3+uZuSnRjmy0ctO8ejkFI9OmpatuvZeba5t19a6zoPuCR4Imdpc26HNtR3yJjg1LTdZ03NTJIczypEfXChs6t0dTXp2dY1eWL9HfcHwQefmpnp05eJpWvaVT6mjcqfSc/KjGCmAWDU9J0VNnfu7OlTUd+q0spy47+AQ1avPy5Yt04svvqht27bpq1/9qqS9+33k5eVp2bJllrmXXnqpXnrpJU2bNk3f+c53ohkmDsKRXjgomWClNkbK6fHq1sdX2h3GqN14zmyZ4YMnnsBEF6rbri8cW6KdjV16q6JpyLu/t9R1aEfj3ouxx5RmyEW7PkQYOSQAYLwyDEPTclM0JSdZm3ztendHszp7ravQgmFT7+xo0sd72uSefIzU+JJN0QITCzkkJqrqFr+u+d1qra9uG3QsOzlBt5w3R+cvKBp3hY8DW5QvnpGryha/Nn9y81fwIB0U/X0hfVTTro9q2pV+6d1yb18lo3mbGjt7lZPiiWr84bCpVbua9ef1Pr34kW/YtuqSVJSeqKtOn66LF01SotupZaHh5wOIL9Pzki1bFbT3BNXc1afsKP9sizVRLWrn5uZqzZo1uu+++/T+++/L4XDoqKOO0r/+678qOzvbMnfevHl6++239ec//1np6enRDBMH4SqYYXme4nEpjVV5ADDh9V+MzU7WptqhL8YGQqbermjSx3vatWRmrqbm2LNPFyYmckgAwHjnMAzNLUrXzPxUra1q1Qe7Wwat2mrvCSr5U9+Wo+xUacNz9gQKTCDkkJiIPtjVrCsf+3DI7h9nz8nX//v8vKgXc8eCw2FoSnaypmQnq688rB2Nndpc26HKJr8OtkGgkeBV8pwlkpZo0Y//ofL8VJ00PVsnTc/WosmZES8EmaapHY1dendHk96paNK7O5rV2Dl4y5GBjipO02UnTdE/H12sBBeLAgAMLTfFoxSPy3INdmdTF0XtaL9henq6/uM//uOQ8/7t3/5N11xzjdLS0qIQFUbCVTDT8rwoI3Hc3fEHADh8Dsfei7Hl+alaV92mVbua1TvgYmxbd0DPr9uj6bnJOr08Tykebn5CZJBDAgAmArfToeOmZGluUZreqWjSR3vaB81JmnK0zNJ5Wvb8x7rh0zOVnsR+28DhIofERPLMh9X64bMb1Beyfg73uBy6/YK5unjRpAl5rTbB5dCsgjTNKkhTV29QW+v2th6v7xi+gLylrkNb6jr0f2/vkiTlpXo0uzBNswpTNbsgTZOzvSrOSFJOimfYfbnDYVOt3QFVt/hV1dz9yfu3a3VlqxoOEcM+bqehc+cV6rKTp+iYSRkT8r8TgMgyDENTc5K1oWZ/V45djX4tmpxlY1T2i+krzSSSscWVb12pTetxAIhPLqdDx07O1OzC1INejK1o6FJVy26dVpajuUVpfGBDVJFDAgBinTfBpbNm52tecbpe39qgPW09luOGw6n/e3uXXli3Rz/47CxdtLBk2AvuAI4cOSRilWma+sXrFfrpS1sGHZuWm6wHLl2oWQXx8f9vsselY0ozdUxpplr8fapo6NSOhi75BvweHUp9R6/qOxr0+tYGy7hhSOlJbqUnueV2OuRyGAqbpnqDYXX1BtXiDyh0kPbnhzK3KE3nLSjS0oUlyk2N79WVAEZvSo7XUtTe09atnkBIiW6njVHZK6aL2ogdztQcOVJzLGPFFLUBIK7tuxh7VHG6XtvSoNp264fIvmBYr2yu15baDp05O0+Z3oSoxdbZ2iRJ8vl8Kikpidr7RlpBQYE++OADu8MAAABjJC8tURcdW6KtdZ16c3vjoC1emrr69P2n1+uJ9yt1+/lHaV4JbZEBTGyLFi1SbW2t3WEctvr6eoVCITmdTuXl5UXgjIYcx14kx+xPDToSrtmgrU/+Sp+669AF3ZHw+XySpK6uroicb6xlehO0aHKWFk3OUldvUD//79ukwtlKKp0nw5044vOYptTqD6jVH4hIXOX5qfrc/EJ9bkERW7MBOCKTMr1yOoz+G2tMU6ps9mtmfqrNkdkn6kXtQCCgRx55RC+++KIqKirU2dmpcDg87GsMw1BFRUWUIsRQPCVzrc9dDmUnR684AQCIXflpibp4UYk213bojW2N6g6ELMerW7v1u/cqdWpZjhaUpEdl1fa+3CIcDqumpmbM3w9jjxwSADBRGYah8oJUTctN1s/uukueeefIcFk/b6+pbNX597+pS44v1U1nlyuTz+PAiJBDjj+1tbUT4jNcZD6LGso659tKHaKg3b7qObWs+LVkDv//8+EwD3NVsp2SPS71bXldbW/9QcUlk/T8W+v0TkWT3q5o1Ie7W9QTiPz3aZ/8NI9OnJatk6Zl68Rp2ZpCIRtAhLidDpVkJml3k79/bGdjF0XtaGlsbNRZZ52ljz76SKY58l+OtCy1X+Ika1G7KCOJ/y4AgH6GYWh2YZqmZCdr5bYGba7tsBwPhU29vrVBu5u69Ok5+fImRCsFMZSeE4m746OrvblB5iEutsUTckgAQDxwOx3qWf0nNb33JxX+07flKD3Gctw0pcffq9RfN/j0vbPLdcnxpXLSkhw4KHLI8c1wOJSWlWt3GKPW1lj3yd+O8LOoYSjp1K/JM/PUQYf87z6h8Mf/UHp2ZL8/+2Mf58ywFpZmamFppq49o0yhsKmdjV3a5GvX5tp2bfJ1aFt9h3ytPQqOooDvMPZeE5+SnazyglTNKkjVoilZmpLt5ecGgDEzNTvZUtTe3eRX2DTliNOfO1Etan//+9/Xhg0b5HA4tHTpUn3uc59TcXGxXC66oMe6gSu1aT0OABhKUoJTn5lboPKCVL26uV4dPdYWmrua/Prtu5U6e26+pmSP/d3LTo9Xtz6+cszfJ9Ju+/LiiXNBIQLIIQEA8STYVqfwyuV69JXVuu2FjdrZaG0D2+oP6EfPfaTfr6rUbecfpWMnZ9oUKRDbyCHHt7Ss3HH5We7Gc2bLDIeP6LOoaZr6+6Y6bfJZbxZ3GNKn5+Rr1lm3SLolAtFa7Yt9onE6DJXlpagsL0XnLSjqHw+FTTV29qq5q0+t/oA6egIKhEwFQmE5HIY8LoeS3E5lJScoMzlBeakeuZ0OG78SAPFoak6yXtva0P+8OxBSXXuPCtPjs0YX1SzuhRdekGEYuvPOO/Wv//qv0XxrHImEZCXkTrYMFWWMfF8SAED8mZKdrK+cMFlvVzRqXXWb5Vh3IKQ/rd2joydl6NSyHFYY4ZDIIQEA8ej08jydND1bD7+5U/e+sn3QFi8f1bRr6S/e1kXHlugH58xSbqrHpkiB2EQOifHINE2t3No4ZEH73HmFmpabYlNkE4/TYSg/LVH5aVznBhC70pLcykpOUHNXX//YrkZ/3Ba1o3prUU9PjwzD0De/+c1ovu1BvfXWW7roootUVFQkj8ejwsJCLV26VG+++eZhnW/btm269tprNWfOHCUnJyshIUFFRUU677zz9Nxzz0U2+Cgy8sosz10OQ3mp/LIHAAwvweXQ6eV5+ueji+RNcA46vraqVc+srlZXb3CIVwP7kUMCAOKVx+XUNaeX6ZUbl+jc+YVDznn6w2qd+b+v6Tdv7VQwNPFW2AGHK5ZySPJHjNR7O5u1trrVMuY0DH1ufhEFbQCIU1MHdLvc2dR1kJkTX1SL2rNmzZLT6VRiov0F0YceekiLFy/WM888I5/PJ6fTqdraWj377LNasmSJli9fPqrz/eUvf9G8efP0wAMPaNOmTeru7pZhGPL5fPrzn/+sCy+8UF//+tfH6KsZWwOL2gXpiayqAwCM2OTsZF16QqmmZHsHHfO19ej3q6pU295jQ2QYL8ghx2cOCQCInKKMJN3/5YV6/JsnaEbe4KJGR09Qt72wUZ+79029t6PJhgiB2BMrOST5I0ZqQ02b3tvZbBlzGNI/zS/Q1Jyx374LABCbpuRYr6k2dPSqM04XCUW1qH3zzTcrFArplVdeiebbDrJlyxZde+21CofDuvnmm9XY2Ci/36+mpibdeuutCofDuu6667Rx48YRna+np0df//rX1dvbqzlz5mjFihXq7u5WT0+Pdu7cqcsvv1yS9H//93/64x//OJZf2pgw8mZYnhexnzYAYJS8CS6dv6BIp8/MHXRjVGdvUE9/WK1NvnabokOsI4ccnzkkACDyTi7L0V+vP00/One2UjyDd5TbXNuhLz74rq7//RrVcdMg4lws5JDkjxipXU1dWrGlftD42XMKNC2HFdoAEM8K05OU4LKWc3c1xudq7agWtc8//3y9/PLL+vWvf33Y7XUi4a677lIgENAVV1yh22+/XdnZ2ZKkrKwsLVu2TFdffbWCwaDuvPPOEZ3v7bffVkPD3o3af//73+v000+Xx+ORYRiaMmWKHnroIS1cuFCSxl0LIH9fUMoqtYwVU9QGABwGwzC0YFKGLl5UotRE60XYUNjUyxvrtHJrg8KmaVOEiFXkkOMvhwQAjB2306FvnjZNr964RJ8/pnjIOX9au0dn3vmafvl6hfqCtCRHfIqFHJL8ESPR0NGrFzfUauBH4TPKc1VekGpPUACAmOF0GJqcZV2tvStOW5APvq13DE2bNk2S1N3draefflopKSn9ydxwDMNQRUVFxOJ4/vnnJUnXX3/9kMdvuOEG/eIXv9ALL7wg0zRlGMO32q6rq5Mkpaamat68eYOOG4ahk08+WatXr1Ztbe0RRh9daypbZTj274PqMKTCdPtbfwIAxq+81ER96bhJenFDrapbuy3H1lS1qrM3qLPn5svliOq9d4hh5JDjL4cEAIy9vLRE/eyLR+uSE0p183MfaXNth+V4V19I//XiZv3hgyotO3+uTpuRa1OkgD1iIYckf8Sh+PuCemH9HvWFrDcgHTclU/NLMuwJCgAQc6bmJGtbfWf/88pmv4LhcNxdP41qUXvXrl2W5x0dHero6Bh68gEOldCNRkVFhXw+nzIzMzVnzpwh58yYMUMFBQWqra3Vxo0bNXfu3GHPWVhYOOL3LyoqGlW8dnt/wD4uuakeuZ3x9Y8EABB53gSX/vmYYr25rVFrq1stx7bVd6onENLn5hcNaq2D+EQOOf5ySABA9Bw3JUt/vu5UPf5+pe782xa191j316to6NK/PPy+zijP1Q8+O0uzCtJsihSILrtzSPJHHEoobOrFDbXqGPBze2Z+ik6adugbMAAA8WNytnWldiBkqqalW5Ozk22KyB5RLWqvWLEimm83pG3btkmSJk2aNOy8SZMmqba2Vtu3bz9kQnnMMccoPT1dbW1t2rBhw6A7JU3T1DvvvCNJOv300w8/eBus2mUtatN6HAAQKU6HoSXlucpN9ejVzfUKHdBrraqlW8+srtYFRxfJmxDVdAUxiBxy/OWQAIDocjkduuykKTp3XqF++tIWPflB1aA5K7Y06LWtDVq6sETf/fRMFfH5HhOc3Tkk+SMO5c1tjYO6lxWmJ+rTs/MjeoMuAGD88ya4VJCWqNr2nv6xXU1+itpjacmSJdF8uyFVVlZKkpKShv/w5vV6LfOHk56erh//+Me67rrr9KUvfUkPPPCATjrpJLndblVWVurHP/6xPvzwQ5144on6yle+Mqp4q6urhz3u8/lGdb7RCITCWlPZahnjQy8AINLmFKUpNdGlF9bvUSC0v7Bd39Grpz6s1oVHFystyW1jhLAbOeT4yiEBAPbJTvHoJxfN1yUnlOqWP32k9dVtluOmKT39YbVeWLdHXztliq45vUzp5FmYoOzOIcdb/iiRQ0bT1rqOQV3LUjwunTuvUC66ZAIAhjAlx2stajd2acnM+NpiKO6WPnV2dh560mHM//a3v638/Hz993//t04//XQZhiG3262+vj5lZWXppptu0rJly+R0Og99sgMc6m7OsRQMmfreZ8p12wO/k5kzTU5vOkVtABihztYmSXs/9JeUlNgczejtu1jR1dUVlfeblOXV0oUl+tPaPeoOhPrHW/0BPfVhtZYuLFaGNyEqsQBDIYcEAIwnR0/K0HPXnKInP6jS/768VY2dvZbjvcGwfvn6Dv3+/Sp9+4wy/ctJk5XoHt3vGgDDG2/5o0QOGS0t/j79Y1OdZczpMHTu/EIle+Lucj0AYISmZifr3R37uyu3dgfU1h2Iq5tUbf0t2dTUpHXr1qm+vl6dnZ365je/Oebv2d3dfehJB/D7/SOe29vbq7S0vXtTmaapvr4+SXvvyExMTJTf7++/+3I8SEpw6vJTp+rWLy1XTU2NMqcepaSznrE7LAAYF8LhcP+fNTU1Nkdz+MyweehJEZKflqgvLCrRH9fUWPYU6+wN6pnVNRS20Y8cEgCAQ3M4DF1yfKnOX1Ckh97YoQdX7pC/L2SZ09Yd0H/+dZN+9eYOXb1kur50fCnFbUxY0c4hyR8xlGAorL9u8Fm6lEnSGeW5KkhLtCkqAMB4kJvqUZLbaVkQtLupS/NLMuwLKspsKWo/88wz+t///V+99957lvF9yaRpmjr77LO1aNEi3X777XK7Y/suA9M09dWvflWPPfaYZsyYoaefflonnXSSUlNTtWXLFv3P//yP7rjjDj322GP6xz/+oenTp4/43FVVg/fBOpDP59Pxxx9/pF/CiIQ7GqLyPgAwsRhKz8mzO4hRa2usO/SkMZDpTdDFx07Sc2tr1NTV1z++r7D9hWNLaEUex8ghx2cOCQCwV7LHpX/91ExdesJk/fyVbXri/UoFB9y4WNfeq2UvbNQvXq+guI0JZyLlkGOZP0rkkNHwxvZGNXb2WcbmFKZpblG6TREBAMYLwzBUmuXVlrqO/rHKZj9F7bF05ZVX6le/+pVM05RhGMrLy1N9fb1lzvbt27V161a9+uqr2rp1q55++mkZhhGR9z/UPjYDjeSuxscff1yPPfaYMjMz9cYbbyg/P7//2KJFi/Tkk09Kkv7whz/ommuu0d/+9rcRv/94bFkLANjP6fHq1sdX2h3GqN14zmyZn6w2j7aURJcuOrZEz66pUUPH/laZnb1BPbtmb2GblmzxhxySHBIAcGRyUz2645+P0jdOnar/+dtm/XVD7aA5FLcx0diZQ463/FEihxxrOxu7tL66zTKWnZyg08vjaz9UAMDhm5xtLWpXNXcrFDbldETm+lesc0TzzR5//HE99NBDysjI0K9//Wv5/X75fL7+djn7zJgxQ+vXr9eCBQv03HPP6fHHH49YDCkpKRGf/4c//EGSdMkll1iSyQN997vflST9/e9/V0tLy6hiAAAg3iS6nfr8McXKTfFYxtu6A3pubY16A6GDvBITETkkOSQAIHKm5iTrgUuP1R+vOVmnlGUPOWdfcXvJ/6zQr97Yoc7e4JDzgFhmdw5J/ogD+fuC+vtGa0c0l8PQP80rlNsZ1Uv0AIBxrDTLehNcXyisuvYem6KJvqj+xnzwwQdlGIbuv/9+fe1rX5PH4zno3PT0dP3sZz+TaZp68MEHIxZDaWmpJKmnZ/j/yPv2sdk3fzjbtm2TtDcJPpjy8nJJe9sEbd++fUSxAgAQzxLdTl24sFjZydZ9tBs7+/T8+j0KhuxZSY7oI4ckhwQARN4xpZn63TdP1B+uPGnY4vaP/7JJJ//XK7rzb1ssXXSAWGd3Dkn+iH1M09Qrm+ote6BK0mkzcpQ14PMuAADDSfa4lJNi/d2xu8lvUzTRF9Wi9rp16yRJ55133ojmn3rqqXI4HNq8eXPEYigrK5N06D1i9h3fN384odDehMThOPi388C2RfvmAwCA4SW5nbrwmGKlD9hHe09rj/6+sU6maR7klZhIyCGt8wEAiKTjp2Ydsrjd3hPUfSu265SfvKp//+MG7WzsinKUwOjZnUOSP2KfLbUd2jHg5+bUnGTNK2YfbQDA6E3OSrY8390cP7l5VDek7O3tldvtHvGeMi6XSwkJCero6Dj05BEqKytTYWGhfD6fNm/erFmzZg2aU1FRodraWmVnZ2vOnDmHPGdhYaG2bt3af7fkULZu3dr/96KiosMLHgCAOJTscenCY4r11AdV6urbf1Fma32nUiuadGpZjo3RIRrIIfcihwQAjKV9xe33dzbrnle26q3tTYPm9AXDevy9Sj3xfqXOmVugKxZP0zGlmTZEOzYWLVqk2trBe42PJwUFBfrggw/sDiMm2J1Dkj9Ckrp6g3pta4NlLMnt1Kdm50Vk73YAQPwpzfbqw8r9W4zUtfeqJxBSottpY1TREdWV2lOmTFEgENCmTZtGNH/jxo3q6enRlClTIhrH+eefL0m65557hjx+9913S9p7J+dIkoszzjhD0t59bZqbm4ecc//990uSpk2bNqJ2QgAAYL/0JLcuOLpYCQP2Gvtwd4s+2tNmU1SIFnJIckgAQPTsK24/c/VJ+tTsoffsNU3pxY9qdeEDb+uiX7ytlz7yKRQe/x10amtrVVNTM64f470oH0mxkEOSP8Y30zS1Yku9eoPWrbPOnJUnb0JU15oBACaQovREuRzWvKGyOT5akEe1qH3eeefJNE394Ac/UDg8/D6YwWBQN954owzD6E8AI+WGG26Q2+3W8uXLtWzZsv4ksKWlRXfccYfuv/9+uVwu3XTTTf2vaWtr08KFC5WUlKTLLrvMcr6rrrpK6enpqq+v11lnnaVXX31Vfr9f4XBYFRUVuuqqq/TII49Ikn74wx9G9GsBACBe5KZ69E/zCjTwWs+KzfXa09ptT1CICnJIckgAQPQdOzlLv/rqIv3ju4t18aISuZ1DF9w+2N2iq367Wmfc+Zr+762d6uoNRjnSyDMcDqXn5I+rhzFMO+p4FQs5JPljfNte36mKBmtL2Jn5KSrLS7EpIgDAROByOlScae1EEy9F7ajeEnbTTTfpscce04svvqgFCxboG9/4hqZNm6ZgcO8Hnr///e/y+/3avHmzHnnkEW3evFnFxcWWxC4SysvLdd999+nqq6/Wbbfdpttuu01er1d+/97/6IZh6N5777W0/dmwYYPWrFkjSXriiSf06KOP9h/Lz8/XH/7wB1100UVau3atzjrrLBmGIZfLpUAg0D/v2muv1Te/+c2Ifi0AAMSTydnJOmtWnv6xqb5/LGxKf17v05eOn6S0RPcwr8Z4RQ5JDgkAsE9ZXqp+etEC3Xh2uX791k49/m6lOoYoXFc2+7XshY362d+36pITSvW1k6eoMH1kbZ9jTVpWrm59fKXdYYzKbV9erLbGOrvDiCmxkEOSP8YvIyFpyLbjp8/MsykiAMBEMjnLq91N+wvZu5v8Mk1zwm9tEdWidk5Ojl555RV96Utf0oYNG/S9733Pcvycc87p/7tpmpo/f75+//vfKzs7O+KxXHHFFZo1a5Z+9rOf6b333lNTU5Py8/N14okn6oYbbtCSJUss8+fNm6ejjz5amzZt0sUXXzzofGeffbY2bNigu+++W3//+9+1a9cu9fX1qaioSCeccIKuvPJKfeYzn4n41wEAQLyZW5Supq4+rals7R/rDoT0l/U+fWFRiVysUplwyCHJIQEA9stPS9QPPztb155Rpsffq9T/vbVLte09g+a19wT1y9d36OE3dupz8wv1zdOm6ajidBsiRryLlRyS/DE+pZ9yifx9IcvY6eW5SkqY+PudAgDGXmmW1/K8szeoFn9AWckJNkUUHVHfvGP27NlavXq1nnvuOT3zzDP68MMPVVdXp66uLiUnJys/P1+LFi3S0qVLdcEFF8jpHLtf9IsXL9bixYtHNDc9Pb3/LsmDmTx5su66665IhAYAAIZx6vQcNXf2afcBrXXqO3r1xtZGnTGLO98nInJIAABiQ1qiW1ctma7LT52qv27w6aE3duijmvZB84JhU8+t3aPn1u7RidOy9M1Tp+nMWXlyOCb26hHElljJIckf40tC4Uwlz/+0ZWxKtlczaDsOAIiQrOQEpXhc6jygg9Lupi6K2mPB6XRq6dKlWrp0qR1vDwAAxjmHw9BnjyrQ71dVqbV7f5u99TVtKsxItDEyjCVySAAAYofb6dAFRxfr/AVFem9ns371xg7LFjEHendHs97d0axpOcn6xqlTtXRhCasVETXkkIgqw6Gss6+RYezvIOZyGDqjPG/Ct4QFAESPYRianO3Vx3v231y6u9mvY0ozbYxq7EW9qN3c3KzNmzerpaVFnZ2dkqSUlBRlZWWpvLxcWVlZ0Q4JAACMQx63U+fOL9STq6oUDJv9469sqpcrq1iBxiobo0OkkUMCABCbDMPQidOydeK0bO1o6NSv39qppz+sVk8gPGjujsYu/ei5j/S/L2/RV06crH85abLyUrkhEWOHHBLRljL/bHkKyixjJ0zLUlqS26aIAAATVWmWtahd09KtYCgsl3Pibs0YlaL2hg0b9OCDD+q5557Tnj17hp1bXFysCy+8UN/61rd01FFHRSM8AAAwTuWkeHTGrDz9fWNd/1gwbCrnc9+T77EbbYwMkUAOCQDA+DItN0U//ud5+u6ny/X4e7v1yDu71dDRO2heiz+ge1/drl++vkNLjy3WNaeXadKAfQGBw0UOCbv0BEJKP+0rlrHs5AQdM2lir5oDANhj4L7awbCpPW09g8YnkjEv13/3u9/VwoUL9cADD6impkamaQ77qK6u1r333qtjjjlGN954o0zTPPSbAACAuDWnME1HFaVZxhLypytz8VdtigiRQA4JAMD4lZWcoG+fOUNv/uAM3fmFBZpVkDrkvL5QWE+8X6Uz7nxN//bMelU1+6McKSYackjY6Z2KJjmTrJ9Nl8zMldNB23EAQOQlup3KT/NYxnY3ddkUTXSMaVH7W9/6lu655x6Fw2Fdeumleumll1RbW6tAIKBwOGx5BAIB1dbW6qWXXtKll16qcDisu+++W9/61rfGMkQAADABLJ6Zq6zkBMtY2vEXyjN5gU0R4UiQQwIAMDF4XE5ddGyJXrz+NP328hN0ennukPOCYVO/X7W3uP39p9epuoXiNkaPHBJ2auzs1YaaNstYWV4KXSgAAGNqclay5XlVc7dNkUTHmBW1//73v+vhhx9WYmKi/vrXv+rRRx/V2Wefrby8PDmdzkHznU6n8vLydPbZZ+uxxx7TX/7yF3k8Hv3mN7/RK6+8MlZhAgCACcDtdOicuQWD7oDP+vRV6gmEbIoKh4McEgCAiccwDJ06I0f/9/Xj9fINi/Wl4yYpwTX4klQwbOoPH1TrzP99Xf/1101q6w7YEC3GI3JI2O2t7Y06cJ1/ONCr08pybIsHABAfBrYab+jsVXffxL0WOmZF7YcffliGYejWW2/VZz7zmVG//pxzztEtt9wi0zT10EMPjUGEAABgIslN9ejUARcNnClZem1rg00R4XCQQwIAMLHNzE/Vfy+drze/f4a+ccpUeYYobvcFw/rlyh1a8j8r9Os3d6ovGLYhUown5JCwU3WLX7uarB0mOj98QWlJbpsiAgDEi4L0RLkGLPKpmsBdj8asqP3OO+9Ikr7xjW8c9jkuv/xySdLbb78dkZgAAMDEtqAkXZMH3KG4pbZD2+o7bIoIo0UOCQBAfMhLS9Qt583RGz84Q988daoS3YMvUbX6A7r9zxv16bte14rN9TZEifGCHBJ2MU1Tb25vtIyFulrU8eELNkUEAIgnToeh4swky1hV88QtarvG6sS1tbXyer3KyTn8Niu5ublKTk5WXV1dBCMDAAATlWEY+tTsfD30ygY5ElP6x1dsblBJhldJCYNbDyK2kEMCkKTO1iZJks/nU0lJic3RjI7P55MkdXV12RwJxqPx/P/+gQoKCvTBBx+MaG5eaqJ+9Lk5unLJdN2/Yrt+++5uBcOmZc7uJr++/n+rdO68Qt1y3hzlpyWORdgYx8ghYZft9Z2qa++1jLW+9YTMQI9NEQEA4k1pple7D+gYUtUycffVHrOidiAQUHJy8qEnHoLL5ZLfP3HvKgAAAJGVkuhS8ysPKufc7/aPdQdCWrmtQZ+ZW2BjZBgJckgAkhQOh/v/rKmpsTmaw2MOKMoBIzER/t8/XLmpHi07f66+evIU/fSlzXrxo9pBc/6ywaeVWxv0/XPK9eUTJss5oNUi4hc5JOwQCpt6u6LJMhZorlHnur/J6ebmGwBAdEwa0LWyrTugtu6A0ifgNhhjVtQGAACwi3/ja/LPOEnemSf1j22u7VB5QaqmZB/5xS4AQLQYSs/JszuIUWlrZIUfImH8/b8vSe3NDTLDR7b/9dScZP3iK8fqw93N+s+/bNLqylbL8Y7eoG7+08d6ZnWN/vfiBZqemzL0iQBgjH20p02t3QHLWOsbj0nhkE0RAQDiUU5KgpLcTnUH9v/+qWr2K7043caoxgZFbQAAMCE1//0XSpw8Xw7P/iL2q5vr9ZUTJivBNXjPRgBA7HF6vLr18ZV2hzEqN54z+4iLesB4/H9fkm778uKI3dhx7OQsPXP1yXr6w2r9v79uUovfWjhaW9Wqz/38Td163hx98bhJMgxWbQOInr5gWO/taLaM5ad5VLmVPdkBANFlGIZKMpO0rb6zf6yqxa+jKGqPTk9Pj/793//9iM8BAAAwWqHOZrW98VtlfurK/rGOnqDe29mk02bk2hgZDoUcEgAASHsv0H1h0SSdNTtf/++vm/T0h9WW492BkP7t2Q16fWuD/uvz85ThTbApUsQCckhE0+rKFsuKOEk6tSxHq2yKBwAQ30qzvNaidnO3TNOccDd+jmlRu7e3Vz/5yU+O6BwT8ZsOAACio+ujVzXvon9VdWt3/9iaqlbNLkxTTorHxsgwHHJIAABwoKzkBN35hQX6/MJi/eiPH2lHY5fl+Isf1WptVat+dvHROml6tk1Rwm7kkIiW7r6QVle2WMamZHtVkuk9yCsAABhbA/fV7g6E1NjZp9zUiXX9c8yK2osXLyYJBAAAtjtzdp5+926lQqYpSTJNacWWel20sIRcJQaRQwIAgIM5eXqO/vKd0/Tjv2zU796rtBzztfXo0l+9q++fM0tXLp5GPhFnyCERTWuqWhQImf3PDUmnlOXYFxAAIO6lJ7mVluhSe0+wf6yqxU9Re6Ree+21sTo1AADAiGV6E3Ts5Ey9v2v/fmd7Wnu0ubZDswvTbIwMQyGHBAB7dbY2SZJ8Pp9KSkpsjmb0fD6fJKmrq+sQMzFeJSU49Z8XztOSmbn6wTPrLXtth03pv1/crA01bfrp0vlK9oxpg0LEEHJIREtPIKR1VW2WsfKCVDqBAQBsNynLq4/3tPc/r2r2a2Fppo0RRR7ZPQAAmPCOm5KpzbXtlrsV39zeqOm5KUpwOWyMDACA2BIOh/v/rKmpsTmaw2eGzUNPwrh29twCLZiUoe/+Ya3e2t5kOfaX9T7tauzSw189TgXpiTZFCGAiWlvVqr5Q2DJ23JQsm6IBAGC/0gFF7ZrWboXCppyOidPNhqI2AACY8FxOh5aU5+qFdb7+MX9fSB/ubmHfRQAAhmQoPSfP7iBGra2xzu4QEEX5aYl67Bsn6IHXtut//75V5gH3Mny8p13/fP9bevhrizS3KN2+IAFMGL3BkNZWtVrGZuanKCs5wZ6AAAA4QElmkuV5IGSqrr1HRRlJB3nF+ENRGwAAxIVpOSmaku3VriZ//9iHlS06qjhNqYluGyMDACD2OD1e3fr4SrvDGLUbz5ktMxw+9ERMGA6HoW+fOUNzi9N1/RNrLJ15att7dPHyd/TgZYvY7xbAEVtX1abeIKu0AQCxyZvgUk5Kgho7+/rHKpv9E6qoTb9NAAAQN04ty5FxQMedUNjU2xVNB38BAAAAxoUzyvP0p2+fqqk5yZbxrr6Qvv6bVXpxg+8grwSAQ+sLhrWmssUyVpabwl7aAICYMinLa3le1eI/yMzxiaI2AACIG9kpHs0b0H5yc22Hatt7bIoIAAAAkTI1J1nPXn2yjp9qXTnZFwrr2sdX66kPqmyKDMB4t76mVT0DVmkP/FkDAIDdSjOtRe3ath71BSdOJyuK2gAAIK6cMC1LCU5rCvTG1gaZB27CCAAAgHEpMzlBj11+vM6dV2gZD5vS959ZrydXVdoUGYDxKhAKa/XuVsvYtJxk5aayShsAEFuKMpLkOKBLZdiU9rR22xdQhLGnNgAAiCveBJeOn5qlN7c39o/taevR9oZOzchLtTEyAACA8a2zde+2Lj6fTyUlJfYGYxhyHHeJHDOX9A+ZpvSDZzboezf9QOb2Nwa9xOfb26K8q6sramECiH0batrUHQhZxlilDQCIRQkuhwrSE7WndX9XyqoWv6YM2KJnvKKoDQAA4s6CknStr25Ve0+wf+yt7U2ampMsl4NGNgAAAIcjHA73/1lTU2NzNJKq/0cZi+uVftIXLMOOE76spoZadW18bciXmWE6+ADYKxQ2tXrAXtqTs73KT0u0KSIAAIY3KdNrKWpXt7BSGwAAYNxyOR06pSxHL35U2z/W1h3Q+uo2LSzNtDEyAACAicBQek6e3UFIksyNL6knMVGJx5zXP2YYDmWfe4OSkhIV2L2mf7ytsc6OEAHEsK11Herqta7SPoFV2gCAGFaSmaT3du5/Xt/Rq55ASIlup31BRQhFbQAAEJdm5KVobXqifG3771z8YFeLjipKV4KL1doAAACHy+nx6tbHV9odRj/TNPXuzma9v7O5f8xwOJX26et0wdFFmpTllSTdeM5smZ+sNgcA0xy8Srs4I0mF6Uk2RQQAwKEVpCfK6TAUOqD7UE1rt6bnptgYVWRwxRYAAMQlwzB02owcy1h3IKR11a32BAQAAIAxYRiGTpyapYWlGZbxkGnqz+t9auzstScwADGtqqVbjZ19lrFjBvwcAQAg1rgcDhWmW7fJmCgtyClqAwCAuFWYnqSpOcmWsQ93t6g3GDrIKwAAADAeGYahU8tydFRRmmW8LxTWn9buUUdPwKbIAMSqgau0M5Lcmjbg8yMAALFoUqbX8ry6xW9TJJFFURsAAMS1E6dZ90PrDYa1prLVnmAAAAAwZgzD0Bmz8jQ911qU6uwN6vl1e2S4Ew/ySgDxpqmzV7ubrAWAY0ozZBiGTREBADByJZnWrTIaO/vU3Tf+F/GwpzYAAIhreamJmp6brIqGrv6xNZWtOnpShhLdThsjAwAAQKQ5DEPnzC3Qs2tq5Gvr6R9v7OxT9j/9qxr++F82RgcgVqyparU8T3Q7NLswbejJiAmdrU2SJJ/Pp5KSEpujGT2fzydJ6urqOsRMADi0/LREuRyGggfsq13d6teMvFQbozpyFLUBAEDcO3FatqWo3RcKa3Vli06enjPMqwAAADAeuZwOnbegSH/4oEqt/v1tx70zT1b6qZeoc9WfbIwOgN26eoPa7OuwjM0vzpDbSdPTWBYOh/v/rKmpsTmaw2ceUIACgMPldBgqykhSZfP+riPVLd0UtQEAAMa7nBSPZualaGt9Z//Y2qpWHTMpU0kJrNYGAACYaJLcTp2/oEhPrqpSbzDcP55xypcVbN5jY2QA7La+uk0hc39h0WkYml+SbmNEGB1D6Tl5dgcxam2NdXaHAGCCKckcXNQe7yhqAwAASDphWra21Xdq36WLQMjUh5UtOrWM1doAAAATUaY3Qf80r1DPra3RAfUrZZ19jVr8fcr0JtgXHABbBEJhra9ptYyVF6Qq2cNl9PHC6fHq1sdX2h3GqN14zmyZ4fChJwLACE3K9Epq6n/e3NWnrt7guP6dRs8UAAAASVnJCSovsLbgWVfVqq7eoE0RAQAAYKyVZnm1ZEauZczh8eov630KhCguAPFmk69dPQHrv/1jSjPsCQYAgCOQl+pRwoCtM2pax/dqbYraAAAAnzhhapYMY//zYNjU6soW+wICAADAmJtfkq5ZA25ubOrq04rN9TZFBMAOpmlqXXWbZWxyllc5KR6bIgIA4PA5HIaKMhItY+O9BTlFbQAAgE9keBM0uyDNMrahpk09gZBNEQEAAGCsGYahM2flqa9hl2V8U22HNvva7QkKQNTVtHaruavPMsYqbQDAeFaS6bU8r27xH2Tm+EBRGwAA4ADHTcnUAYu1FQiZWl/TdtD5AAAAGP/cTocan/svhXu7LOOvbqlXi7/vIK8CMJGsH7BKO8PrVmmW9yCzAQCIfSWZSZbnLf6AOsfxVosUtQEAAA6Q4U3QjLwUy9jaylYF2VMRAABgQgu2+tT0t/stY4GQqZc+qlUobNoUFYBo6OoNqqKh0zI2vzhdxoH7UwEAMM7kpnqU4LKWgsfzam2K2gAAAAMcOyXT8rw7ENLHtJ4EAACY8PybVqrr4xWWsfqOXr2/s9mmiABEw0d72nTgvSsuh6HZhWkHfwEAAOOAwzBUnGFdrT2e99WmqA0AADBAXmqiJg9oM7d6d4vCrNABAACY8FpX/EaZXrdlbNXuZtW29dgUEYCxFA6b+qjGehNzeUGqEt1OmyICACByBrYgp6gNAAAwwSwasFq7vSeorfUdNkUDAACAaDGDvfrM3AI5Dug6bJrS3zbWKsCWNMCEs6Oxa9D+ovOL022KBgCAyJqUaV2409YdUEdPwKZojgxFbQAAgCEUZySpIC3RMvbB7haZJqu1AQAAJrr8tEQdPzXLMtbqD+idHU02RQRgrKyvbrU8L0hLVN6Az4IAAIxXOSkJShy0r/b4XK1NURsAAGAIhmHo2MnW1dpNnX3a1eS3KSIAAABE03GTs5Sf5rGMra1sVV07bciBiaK5q09VAy7szy9hlTYAYOIwDEPFA1qQV7WMz+ubFLUBAAAOYnpu8qD9FD/Y3WxTNAAAAIgmh8PQZ+YUyHlAH3JT0iub6xUO070HmAg21LRZnie6HZqRl2JTNAAAjI2SAS3IWakNAAAwwQy1WntPa498beMz8QMAAMDoZCYn6Pgp1jbkDR29WlPVak9AACImEApro6/dMja3KF0uJ5fMAQATS8mAldodPUG1dY+/fbX5DQ0AADCMWQVpSvG4LGNrK1vtCQYAAABRd+zkTGUnJ1jG3t3RNC4vBALYb0tth/qCYcvYvGJajwMAJp7s5AQluZ2Wsepx2IKcojYAAMAwnA5DR0/KsIxta+hURw8XMQEAAOKB02HorNl5lrFg2NSrm+tlmrQhB8arj/dYV2lPyfYqPcl9kNkAAIxfhmEMWq09HluQU9QGAAA4hLlFaXIduJeiKa2vbhvmFQAAAJhICtOTNL/EuoKzstmvLbUdNkUE4Eg0dvaqtr3HMsYqbQDAREZRe5x76623dNFFF6moqEgej0eFhYVaunSp3nzzzSM+99atWzV79mwZhqETTjhBNTU1EYgYAADYIdHt1JzCNMvYhpo2BULhg7wCExX5IwAA8evk6dmDtqV5fVuDuvtCNkWE8YIcMvYMXKWdnODUlOxkm6IBAGDslWR6Lc87e4NypOUdZHZsitui9kMPPaTFixfrmWeekc/nk9PpVG1trZ599lktWbJEy5cvP+xzb9y4Uaeddpo2b96sL3zhC1q5cqWKi4sjGD0AAIi2gS3Ie4NhbWZlTlwhfwQAIL55XE6dXp5rGesJhPXujiabIsJ4QA4Ze4LhsDbXWovaswvT5DigOxcAABNNptctb4J1X21X4Sybojk8cVnU3rJli6699lqFw2HdfPPNamxslN/vV1NTk2699VaFw2Fdd9112rhx46jPXVdXp8985jOqr6/X5ZdfrieffFIej2cMvgoAABBNmckJmpxtvaNxbVUr+yjGCfJHAAAgSdNzU1SWm2IZ21DTpsbOXpsiQiwjh4xNOxu61BOwdt2aU5R2kNkAAEwMQ+2rTVF7HLjrrrsUCAR0xRVX6Pbbb1d2drYkKSsrS8uWLdPVV1+tYDCoO++8c9TnvvTSS1VdXa0LL7xQDz74oAyDO/wAAJgojhmwWru5q0+VzX57gkFUkT8CAIB9TpuZI9cBKzpNSSu3NXCzIwYhh4xNA1uPF2ckKdObYFM0AABEz6QBLchdBeU2RXJ44rKo/fzzz0uSrr/++iGP33DDDZKkF154YVQfSH7zm9/olVde0eTJk/Xoo4/K4YjLby8AABNWaZZXmV63ZWxtVas9wSCqyB8BAMA+aYluLZycaRmrau7WzsYumyJCrCKHjD3t3QHtHnBj8lxWaQMA4kTxgJXajuQMuTKLbIpm9OIu46moqJDP51NmZqbmzJkz5JwZM2aooKBAjY2NI27/09fXp1tuuUWS9NOf/lQpKSmHeAUAABhvDMMYtLf2ria/Wvx99gSEqCB/BAAAAy2anKkUj8sytnJbo4Lh8EFegXhDDhmbNvqsq7QTnA6V5fE9BADEh4wkt5I91n21E0vn2RTN6MVdUXvbtm2SpEmTJg07b9/x7du3j+i8jz/+uKqrq3XKKafo4osvPrIgAQBAzJpdmCaPy5pCrWO19oRG/ggAAAZyOx06pSzbMtbWHdC6qjabIkKsIYeMPaZpDipqlxekyu2Mu0vkAIA4ZRiGSjKsLcgpasewyspKSVJSUtKw87xer2X+oTzyyCOS9rYNeuONN3T22WcrPz9fGRkZOvnkk/XrX//6sPZWqq6uHvbh8/lGfU4AAHD43E6HjipKt4xt9LWrNxiyKSKMtfGWP0rkkAAAREN5fqoK0xMtY+/vbJa/L2hTRIgl5JCxp7LZr44e679PWo8DAOJNyYAW5J5J46eo7Tr0lImls7Mz4vMbGxu1cuVKJScny+Fw6Mwzz1QwuD9Beuedd/TOO+9oxYoVeuyxx0b1/oe6mxMAAETf/EnpWl3Von3XigIhU5t9HVowoDU5Jobxlj9K5JAAAESDYRhaPDNXT66q6h/rC4X1TkWTzpqdb2NkiAXkkLFn4x7rKu2clATlpXpsigYAAHsM3FfblZqtYGqeTdGMTtyt1O7u7h7VfL/ff8g57733nsLhsI466ijdeuut+uUvf6mGhgb19vZq3bp1Wrp0qSTpt7/9rX73u98dVtwAACB2pCW6NS0n2TK2oabtsFdEILaRPwIAgIMpSEvU7IJUy9hHe9rV1NlrU0SIFeSQsaU7EFJFQ5dlbG5RugzDsCkiAADsMdS+2kZ+uU3RjE7crdQeC+vWrZO0N7H861//qs9+9rP9x+bPn6+nnnpKp59+ulauXKkHHnhAl1566YjPXVVVNexxn8+n448//vACBwAAh21ecbrlokhTV5/2tPYMutsRGMpY5o8SOSQAANF0clmOtjd0KhDaf4PjOzua9Ln5RTZGhYmIHPLwba3tUOiAm5CdDkOzBtyQAgBAPNi3r/aWuo79Y/kzbYxo5OKuqH2ofWwG2revzXAaGxslSVOnTrUkk/sYhqFrrrlGK1eu1AcffKBAICC32z2i9y8pKRlVvAAAIDpKs7xKT3KrrTvQP7ahpo2i9gQ03vJHiRwSAIBoSvG4tLA0U+/tbO4fq2joUm1bjwoG7LmN+EEOGVs21Vpbj0/PSVai23mQ2QAATGwlmUmDitqmacZ8B5O4az+ekpIS8fnt7XuTorlz5x50zr5jfX19qq+vH1UMAAAg9hiGofnF6Zax7fWd8vcFD/IKjFfkjwAA4FCOKc1Qott6me2tikabokEsIIeMHc1dfaprt24JMLsozaZoAACw38BFOYY3Qzsbuw4yO3bEXVG7tLRUktTT0zPsvH372OybP5x9d14mJycfdM6Biemh3hsAAIwPs4vS5HTsv4MxZJrauKd9mFdgPCJ/BAAAh+JxOXXclCzLWHVLtyqbD71PMiYmcsjYscln/YzmTXCqNPPQK+MBAJiohtpX+90dzQeZHTvirqhdVlYm6dB7xOw7vm/+cPLz8yVJ3d3dB53T1bX/Dof09PSDzgMAAONHktupGXnWFRUbatpkHrBXG8Y/8kcAADAS84vTleKx7vT3dkUjuWGcIoeMDaZpanNth2VsVkGqHI7Ybq8KAMBY2revthnoVffO1QqteU7HT8069AttFpdF7cLCQjU3N2vz5s1DzqmoqFBtba2ys7M1Z86cQ57zmGOOkSRt3LjxoHM2bdokScrLy1NOTs5hRA4AAGLR/BLrhaL2nqB2syJnQiF/BAAAI+FyOnTCgIuBde29qmiI/VaOiDxyyNhQ3dKtzl7rFlGzCmg9DgDA4pk5avvtdar/wy0yP35RZXmj2zrFDnFX1Jak888/X5J0zz33DHn87rvvliSdd955I9oU/cwzz1Rqaqq2b9+u1157bcg5Dz30kCTpnHPOGX3AAAAgZhWkJSonJcEytqG6zaZoMFbIHwEAwEjMKUxTRpLbMvbOjiaFWa0dl8gh7bep1tp6PCclQbmpHpuiAQAgdngTXFI4ZHcYoxKXRe0bbrhBbrdby5cv17Jly9TcvLdPfEtLi+644w7df//9crlcuummm/pf09bWpoULFyopKUmXXXaZ5XxJSUm64YYbJElf/OIX9eyzz6qvr0/S3hZCl19+uV5++WW53W5973vfi9JXCQAAosEwDM0rtq7W3tnYpfaegE0RYSyQPwIAgJFwOAydND3bMtbc1actA9ofIz6QQ9orEApre32nZWx2Iau0AQAYr+KyqF1eXq777rtPDodDt912m7Kzs5WcnKysrCzdcsstkqR7773X0vZnw4YNWrNmjXp6evTEE08MOud//Md/6Nxzz1V9fb2WLl0qr9er5ORklZaW6te//rUcDoeWL1+uefPmRe3rBAAA0TGrIE1u5/6VFaakj2vaD/4CjDvkjwAAYKRm5KUoN8W6EvTdHU0KhVmtHW/IIe1VUd+pQGj/vztDUnl+qn0BAQCAIxKXRW1JuuKKK7RixQpdcMEFKigoUCAQUH5+vi644AKtWLFCV111lWX+vHnzdPTRR8vj8eiSSy4ZdL6EhAQ9//zz+tWvfqVTTz1VKSkpCgaDKikp0Ze//GWtWrVK3/jGN6L15QEAgChKcDkG7cv28Z42hblwOaGQPwIAgJEwjMGrtdt7gqzWjlPkkPbZNODfXGm2V8kel03RAACAIxXXv8UXL16sxYsXj2huenq61qxZM+wch8Ohyy+/XJdffnkkwgMAAOPI/JJ0bajZv5d2V19Iu5q6NC03xcaoEGnkjwAAYCSmZHtVmJ4oX1tP/9iqXc2aVZAqh+PQeydjYiGHjL7OnqAqm/2WsdkFtB4HAGA8i9uV2gAAAJGUk+JRQVqiZezjPbQgBwAAiEeGYej4KVmWsdbugLbWs1obiIbNddbPYglOh6blJtsUDQAAiASK2gAAABEyt8h65//Opi519QZtigYAAAB2mpztVV6qdW/tVTtbZJpsUQOMJdM0tclnvYGkLC9FbieXwgEAGM/4TQ4AABAhM/NT5XbubydpmtJGH6u1AQAA4pFhGDp+qnW1drO/T9vrO22KCIgPDZ29au7qs4zNLky1KRoAABApFLUBAAAiJMHl0Iw868WSj/e0sxoHAAAgTk3LSVZ2SoJl7P1dzeSHwBjaUmtdpZ2a6FJxRpJN0QAAgEihqA0AABBBRxVbW5C3dQdU09ptUzQAAACw01B7azd29mlHY5dNEQETm2ma2lpn7YZQnp8qwzAO8goAADBeUNQGAACIoIK0RGV5ratxPt5DC3IAAIB4VZaXokyv2zL2/k5WawNjoaa1W529QctYeQGtxwEAmAgoagMAAESQYRiaO2C19rb6TvUEQjZFBAAAADs5hlitXd/Rq91NfpsiAiauga3Hs1MSlJPisSkaAAAQSRS1AQAAImxWQaocB3S3C4XNQRdXAAAAED9m5qcqPWnAau1dzTZFA0xMobCpbfWDW48DAICJgaI2AABAhHkTXJqWm2IZ+9hHC3IAAIB45XAYOm5KpmXM19YjX1u3TREBE8/upi71BsOWMYraAABMHBS1AQAAxsBRRdYW5A0dvapv77EpGgAAANhtVkGaUjwuy9iHu1tsigaYeAZ2xypMT1TagA4JAABg/KKoDQAAMAYmZXkHXbT8aA+rtQEAAOKV02HomEkZlrGKhi61+PvsCQiYQPqCYe1o7LKMzSpglTYAABMJRW0AAIAx4DAMzR2wWntrXYeCofBBXgEAAICJbm5xmhKc1stxq1mtDRyxHQ2dCobN/ucOQ5qRR1EbAICJhKI2AADAGJlTaC1q9wbD2jlg9QAAAADih8fl1LySdMvYptoOdfUGbYoImBg211lbj5dmeZWU4LQpGgAAMBYoagMAAIyRtCS3SjKSLGMbfbQgBwAAiGdHT8qQw9j/PBQ2tb66zb6AgHHO3xdUZbPfMlZO63EAACYcitoAAABjaPaAFuS7m/2sxAEAAIhjKR6XZhVYc8R11a3qC7JNDXA4ttV3ytzfeVwuh6FpOSn2BQQAAMYERW0AAIAxVJabIrdz/1Ic05S21HYM8woAAABMdAtLMyzPe4NhOvoAh2ng56tpuclKcHHZGwCAiYbf7gAAAGMoweVQWa51lcBGX7vMA5cSAAAAIK5kp3g0NSfZMra6skXhMDkiMBrtPQH52nosY7QeBwBgYqKoDQAAMMZmF1rbSzZ19amho9e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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 1488,
+ "width": 986
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# create a figure with subplots\n",
+ "fig, axes = plt.subplots(nrows=4, ncols=3, figsize=(10, 15))\n",
+ "\n",
+ "# loop through each dataframe and plot histogram\n",
+ "for i, df in enumerate(simdata):\n",
+ " row = i // 3\n",
+ " col = i % 3\n",
+ " sns.histplot(\n",
+ " data=df,\n",
+ " x=\"frt_pv\",\n",
+ " hue=\"fac2\",\n",
+ " ax=axes[row, col],\n",
+ " kde=True,\n",
+ " stat=\"density\",\n",
+ " legend=False,\n",
+ " )\n",
+ " axes[row, col].set_ylim(0, 1.7)\n",
+ " axes[row, col].set_title(f\"{df['fac1'][0]} - {df['fac2'][0]}\")\n",
+ "[ax.axhline(y=1, linestyle=\"--\", color=\"grey\", linewidth=1) for ax in axes.flat]\n",
+ "# adjust spacing between subplots\n",
+ "plt.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Case Study"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def cre_stat(z, y, x):\n",
+ " covariates = pd.DataFrame(np.asarray(x))\n",
+ " covariates.columns = [f\"x{i}\" for i in range(covariates.shape[1])]\n",
+ " neyman_data = pd.DataFrame({\"y\": y, \"z\": z})\n",
+ " lin_data = (covariates - covariates.mean()).assign(y=y, z=z)\n",
+ " rhs = \" + \".join(covariates.columns)\n",
+ " tau_n_fit = pf.feols(\"y ~ z\", data=neyman_data, vcov=\"HC2\")\n",
+ " tau_l_fit = pf.feols(\"y ~ z * (\" + rhs + \")\", data=lin_data, vcov=\"HC2\")\n",
+ " return np.r_[\n",
+ " tau_n_fit.coef().loc[\"z\"],\n",
+ " tau_n_fit.se().loc[\"z\"],\n",
+ " tau_n_fit.tstat().loc[\"z\"],\n",
+ " tau_l_fit.coef().loc[\"z\"],\n",
+ " tau_l_fit.se().loc[\"z\"],\n",
+ " tau_l_fit.tstat().loc[\"z\"],\n",
+ " ]\n",
+ "\n",
+ "\n",
+ "def cre_frt(z, y, x, n_frt=1e3):\n",
+ " test_stat = cre_stat(z, y, x)\n",
+ " # normal dist pvalue\n",
+ " asy_p_n = 2 * sp.stats.norm.cdf(-np.abs(test_stat[2]))\n",
+ " asy_p_l = 2 * sp.stats.norm.cdf(-np.abs(test_stat[5]))\n",
+ " # FRT p value\n",
+ " null_dist = Parallel(n_jobs=8)(\n",
+ " delayed(cre_stat)(np.random.permutation(z), y, x) for i in range(n_frt)\n",
+ " )\n",
+ " null_dist = np.vstack(null_dist)\n",
+ " comparisons = 1 * (np.abs(null_dist) >= np.abs(test_stat))\n",
+ " frt_p_n, frt_p_l = comparisons[:, 2].mean(), comparisons[:, 5].mean()\n",
+ "\n",
+ " restable = np.c_[\n",
+ " np.r_[test_stat[0], test_stat[3]],\n",
+ " np.r_[test_stat[1], test_stat[4]],\n",
+ " np.r_[asy_p_n, asy_p_l],\n",
+ " np.r_[frt_p_n, frt_p_l],\n",
+ " ]\n",
+ " res = pd.DataFrame(\n",
+ " restable,\n",
+ " index=[\"Neyman\", \"Lin\"],\n",
+ " columns=[\"Estimate\", \"Std. Error\", \"Asy. p-value\", \"FRT p-value\"],\n",
+ " )\n",
+ " return res, null_dist\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | class_level | \n",
+ " 1.0 | \n",
+ " 2.0 | \n",
+ " 3.0 | \n",
+ " 4.0 | \n",
+ " 5.0 | \n",
+ "
\n",
+ " \n",
+ " | treatment | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ " | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | Soccer Player | \n",
+ " 16 | \n",
+ " 19 | \n",
+ " 15 | \n",
+ " 10 | \n",
+ " 10 | \n",
+ "
\n",
+ " \n",
+ " | Physician | \n",
+ " 17 | \n",
+ " 20 | \n",
+ " 15 | \n",
+ " 11 | \n",
+ " 10 | \n",
+ "
\n",
+ " \n",
+ " | Placebo | \n",
+ " 15 | \n",
+ " 19 | \n",
+ " 16 | \n",
+ " 12 | \n",
+ " 10 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " naive | \n",
+ " fisher | \n",
+ " lin | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | est | \n",
+ " 0.533904 | \n",
+ " 0.061248 | \n",
+ " -0.016954 | \n",
+ "
\n",
+ " \n",
+ " | se | \n",
+ " 0.225701 | \n",
+ " 0.220883 | \n",
+ " 0.223635 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {
+ "image/png": {
+ "height": 390,
+ "width": 1189
+ }
+ },
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(1, 3, figsize=(12, 4))\n",
+ "ax[0].hist(pscores[z == 1], bins=5, alpha=0.5, density=True)\n",
+ "ax[0].hist(pscores[z == 0], bins=5, alpha=0.5, density=True, edgecolor=\"black\")\n",
+ "ax[1].hist(pscores[z == 1], bins=10, alpha=0.5, density=True)\n",
+ "ax[1].hist(pscores[z == 0], bins=10, alpha=0.5, density=True, edgecolor=\"black\")\n",
+ "ax[2].hist(pscores[z == 1], bins=30, alpha=0.5, density=True, label=\"treated\")\n",
+ "ax[2].hist(\n",
+ " pscores[z == 0],\n",
+ " bins=30,\n",
+ " alpha=0.5,\n",
+ " density=True,\n",
+ " label=\"control\",\n",
+ " edgecolor=\"black\",\n",
+ ")\n",
+ "ax[2].legend()\n",
+ "\n",
+ "# Hide the y-axis\n",
+ "ax[0].set_ylim(0, 4.5), ax[1].set_ylim(0, 4.5), ax[2].set_ylim(0, 4.5)\n",
+ "ax[0].set_xlim(0, 1), ax[1].set_xlim(0, 1), ax[2].set_xlim(0, 1)\n",
+ "ax[0].set_yticks([]), ax[1].set_yticks([]), ax[2].set_yticks([])\n",
+ "ax[0].set_yticklabels([]), ax[1].set_yticklabels([]), ax[2].set_yticklabels([])\n",
+ "ax[0].set_title(\"5 bins\"), ax[1].set_title(\"10 bins\"), ax[2].set_title(\"30 bins\")\n",
+ "f.tight_layout()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/alal/Desktop/code/00_causal/CausalinferencePy/causalinference/core/summary.py:102: RuntimeWarning: invalid value encountered in divide\n",
+ " return (mean_t - mean_c) / np.sqrt((sd_c**2 + sd_t**2) / 2)\n",
+ "/home/alal/Desktop/code/00_causal/CausalinferencePy/causalinference/estimators/ols.py:21: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
+ "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
+ " olscoef = np.linalg.lstsq(Z, Y)[0]\n",
+ "/home/alal/Desktop/code/00_causal/CausalinferencePy/causalinference/core/summary.py:28: RuntimeWarning: Degrees of freedom <= 0 for slice\n",
+ " self._dict[\"Y_t_sd\"] = np.sqrt(data[\"Y_t\"].var(ddof=1))\n",
+ "/home/alal/anaconda3/envs/metrics/lib/python3.11/site-packages/numpy/core/_methods.py:261: RuntimeWarning: invalid value encountered in scalar divide\n",
+ " ret = ret.dtype.type(ret / rcount)\n",
+ "/home/alal/Desktop/code/00_causal/CausalinferencePy/causalinference/core/summary.py:33: RuntimeWarning: Degrees of freedom <= 0 for slice\n",
+ " self._dict[\"X_t_sd\"] = np.sqrt(data[\"X_t\"].var(0, ddof=1))\n",
+ "/home/alal/anaconda3/envs/metrics/lib/python3.11/site-packages/numpy/core/_methods.py:258: RuntimeWarning: invalid value encountered in divide\n",
+ " ret = um.true_divide(\n",
+ "/home/alal/Desktop/code/00_causal/CausalinferencePy/causalinference/core/summary.py:27: RuntimeWarning: Degrees of freedom <= 0 for slice\n",
+ " self._dict[\"Y_c_sd\"] = np.sqrt(data[\"Y_c\"].var(ddof=1))\n",
+ "/home/alal/Desktop/code/00_causal/CausalinferencePy/causalinference/core/summary.py:32: RuntimeWarning: Degrees of freedom <= 0 for slice\n",
+ " self._dict[\"X_c_sd\"] = np.sqrt(data[\"X_c\"].var(0, ddof=1))\n"
+ ]
+ },
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\n",
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\n",
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\n",
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\n",
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+ " 27.0 | \n",
+ " 11.0 | \n",
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+ " 0.0 | \n",
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+ " 1.0 | \n",
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+ " 0.0 | \n",
+ " 7506.1460 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 1.0 | \n",
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+ " 0.0 | \n",
+ " 0.0 | \n",
+ " 1.0 | \n",
+ " 0.0 | \n",
+ " 0.0 | \n",
+ " 289.7899 | \n",
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\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
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\n",
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+ " \n",
+ " | 0 | \n",
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\n",
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\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
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\n",
+ " \n",
+ " \n",
+ " \n",
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+ " -8506.495361 | \n",
+ " 583.442609 | \n",
+ " -14.579832 | \n",
+ "
\n",
+ " \n",
+ " | fisher | \n",
+ " 1067.546135 | \n",
+ " 628.438879 | \n",
+ " 1.698727 | \n",
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\n",
+ " \n",
+ " | lin | \n",
+ " -4265.800513 | \n",
+ " 3211.771843 | \n",
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+ "
\n",
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\n",
+ "
\n",
+ "\n",
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\n",
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\n",
+ " \n",
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+ " 862.221261 | \n",
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\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "# Figure 17.1\n",
+ "# bias factor and hyperbola\n",
+ "RR = rr\n",
+ "RR_L = lower\n",
+ "xmax = 40\n",
+ "x = np.arange(0, xmax, 0.01)\n",
+ "f, ax = plt.subplots(1, 1, figsize=(6, 6))\n",
+ "ax.plot(x, x, linestyle=\"--\", color=\"grey\", alpha=0.1, linewidth=2)\n",
+ "ax.set_xlabel(r\"$RR_{ZU}$\")\n",
+ "ax.set_ylabel(r\"$RR_{UY}$\")\n",
+ "x = np.arange(RR, xmax, 0.01)\n",
+ "x_L = np.arange(RR_L, xmax, 0.01)\n",
+ "y = RR * (RR - 1) / (x - RR) + RR\n",
+ "y_L = RR_L * (RR_L - 1) / (x_L - RR_L) + RR_L\n",
+ "ax.axhline(y=RR, linestyle=\"-\", color=\"grey\")\n",
+ "ax.axhline(y=RR_L, linestyle=\"--\", color=\"grey\")\n",
+ "ax.axvline(x=RR, linestyle=\"-\", color=\"grey\")\n",
+ "ax.axvline(x=RR_L, linestyle=\"--\", color=\"grey\")\n",
+ "ax.plot(x, y, linestyle=\"-\", color=\"black\")\n",
+ "ax.plot(x_L, y_L, linestyle=\"--\", color=\"black\")\n",
+ "high = RR + np.sqrt(RR * (RR - 1))\n",
+ "high_L = RR_L + np.sqrt(RR_L * (RR_L - 1))\n",
+ "ax.scatter(high, high, marker=\"o\", color=\"black\")\n",
+ "ax.scatter(high_L, high_L, marker=\"o\", color=\"black\")\n",
+ "ax.text(high_L + 5, high_L, \"(15.52, 15.52)\")\n",
+ "ax.text(high + 5, high, \"(20.95, 20.95)\")\n",
+ "ax.set_xlim(0, 40)\n",
+ "ax.set_ylim(0, 40)\n",
+ "ax.legend(\n",
+ " [\n",
+ " r\"$RR_{ZU} * RR_{UY} / (RR_{ZU} + RR_{UY} - 1) = 10.73$\",\n",
+ " r\"$RR_{ZU} * RR_{UY} / (RR_{ZU} + RR_{UY} - 1) = 8.02$\",\n",
+ " ],\n",
+ ")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## application"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [
+ {
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+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0.0 | \n",
+ " 0.0 | \n",
+ " 0.0 | \n",
+ " 0.0 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 2 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 1.0 | \n",
+ " 0.0 | \n",
+ " 0.0 | \n",
+ " NaN | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 2 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 1 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 1 | \n",
+ " 0 | \n",
+ " 0.0 | \n",
+ " 0.0 | \n",
+ " 0.0 | \n",
+ " 0.0 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 1 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " 0.0 | \n",
+ " 0.0 | \n",
+ " 1.0 | \n",
+ " 0.0 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(1, 3, figsize=(10, 4))\n",
+ "RR1 = np.arange(1, 1.5, 0.01)\n",
+ "ax[0].plot(RR1, evalue(RR1), linestyle=\"-\", color=\"black\")\n",
+ "ax[0].set_xlabel(r\"$RR$\")\n",
+ "ax[0].set_ylabel(r\"E-Value\")\n",
+ "ax[0].set_xlim(1, 1.5)\n",
+ "\n",
+ "RR2 = np.arange(1, 3, 0.01)\n",
+ "ax[1].plot(RR2, evalue(RR2), linestyle=\"-\", color=\"black\")\n",
+ "ax[1].set_xlabel(r\"$RR$\")\n",
+ "ax[1].set_ylabel(r\"$RR$\")\n",
+ "ax[1].set_xlim(1, 3)\n",
+ "\n",
+ "RR3 = np.arange(1, 10, 0.01)\n",
+ "ax[2].plot(RR3, evalue(RR3), linestyle=\"-\", color=\"black\")\n",
+ "ax[2].set_xlabel(r\"$RR$\")\n",
+ "ax[2].set_ylabel(r\"$RR$\")\n",
+ "ax[2].set_xlim(1, 10)\n",
+ "plt.show()"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "metrics",
+ "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": "3.11.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pyfixest/Chapter18SensitivityAnalysis.ipynb b/pyfixest/Chapter18SensitivityAnalysis.ipynb
new file mode 100644
index 0000000..39fd83a
--- /dev/null
+++ b/pyfixest/Chapter18SensitivityAnalysis.ipynb
@@ -0,0 +1,304 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 18: Sensitivity Analysis for the Average Causal Effect with Unmeasured Confounding"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import pyfixest as pf\n",
+ "from utils import *\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "%load_ext autoreload\n",
+ "%autoreload 1\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def OS_est(z, y, x, lb=0, ub=1, e1=1, e0=1):\n",
+ " covariates = pd.DataFrame(np.asarray(x))\n",
+ " covariates.columns = [f\"x{i}\" for i in range(covariates.shape[1])]\n",
+ " data = covariates.assign(y=y, z=z)\n",
+ " rhs = \" + \".join(covariates.columns)\n",
+ " pscore = pf.feglm(\"z ~ \" + rhs, data=data, family=\"logit\").predict(\n",
+ " data, type=\"response\"\n",
+ " )\n",
+ " pscore = np.clip(pscore, lb, ub)\n",
+ " # fitted potential outcomes\n",
+ " outcome1 = pf.feols(\"y ~ \" + rhs, data=data.loc[data.z == 1]).predict(data)\n",
+ " outcome0 = pf.feols(\"y ~ \" + rhs, data=data.loc[data.z == 0]).predict(data)\n",
+ "\n",
+ " ## outcome regression estimator\n",
+ " ace_reg = (\n",
+ " np.mean(z * y)\n",
+ " + np.mean((1 - z) * outcome1 / e1)\n",
+ " - np.mean(z * outcome0 * e0)\n",
+ " - np.mean((1 - z) * y)\n",
+ " )\n",
+ " ## IPW estimators\n",
+ " w1 = pscore + (1 - pscore) / e1\n",
+ " w0 = pscore * e0 + (1 - pscore)\n",
+ " ace_ipw0 = np.mean(z * y * w1 / pscore) - np.mean((1 - z) * y * w0 / (1 - pscore))\n",
+ " ace_ipw = np.mean(z * y * w1 / pscore) / np.mean(z / pscore) - np.mean(\n",
+ " (1 - z) * y * w0 / (1 - pscore)\n",
+ " ) / np.mean((1 - z) / (1 - pscore))\n",
+ " ## doubly robust estimator\n",
+ " aug = outcome1 / pscore / e1 + outcome0 * e0 / (1 - pscore)\n",
+ " ace_dr = ace_ipw0 - np.mean((z - pscore) * aug)\n",
+ "\n",
+ " return np.array([ace_reg, ace_ipw0, ace_ipw, ace_dr])\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "nhanes_bmi = pd.read_csv(\"nhanes_bmi.csv\").iloc[:, 1:]\n",
+ "z, y, x = (\n",
+ " nhanes_bmi.School_meal.values,\n",
+ " nhanes_bmi.BMI.values,\n",
+ " nhanes_bmi.iloc[:, 2:].values,\n",
+ ")\n",
+ "x = (x - x.mean(0)) / x.std(0)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "E1 = np.array([1 / 2, 1 / 1.7, 1 / 1.5, 1 / 1.3, 1, 1.3, 1.5, 1.7, 2])\n",
+ "E0 = E1.copy()\n",
+ "est = np.zeros((len(E1), len(E0)))\n",
+ "\n",
+ "for i in range(len(E1)):\n",
+ " for j in range(len(E0)):\n",
+ " est[i, j] = OS_est(z, y, x, e1=E1[i], e0=E0[j])[3]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " 0.500000 | \n",
+ " 0.588235 | \n",
+ " 0.666667 | \n",
+ " 0.769231 | \n",
+ " 1.000000 | \n",
+ " 1.300000 | \n",
+ " 1.500000 | \n",
+ " 1.700000 | \n",
+ " 2.000000 | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0.500000 | \n",
+ " 14.62 | \n",
+ " 13.62 | \n",
+ " 12.73 | \n",
+ " 11.57 | \n",
+ " 8.96 | \n",
+ " 5.57 | \n",
+ " 3.30 | \n",
+ " 1.04 | \n",
+ " -2.36 | \n",
+ "
\n",
+ " \n",
+ " | 0.588235 | \n",
+ " 11.93 | \n",
+ " 10.93 | \n",
+ " 10.04 | \n",
+ " 8.88 | \n",
+ " 6.27 | \n",
+ " 2.87 | \n",
+ " 0.61 | \n",
+ " -1.66 | \n",
+ " -5.05 | \n",
+ "
\n",
+ " \n",
+ " | 0.666667 | \n",
+ " 10.13 | \n",
+ " 9.13 | \n",
+ " 8.24 | \n",
+ " 7.08 | \n",
+ " 4.47 | \n",
+ " 1.08 | \n",
+ " -1.19 | \n",
+ " -3.45 | \n",
+ " -6.85 | \n",
+ "
\n",
+ " \n",
+ " | 0.769231 | \n",
+ " 8.33 | \n",
+ " 7.33 | \n",
+ " 6.45 | \n",
+ " 5.29 | \n",
+ " 2.67 | \n",
+ " -0.72 | \n",
+ " -2.98 | \n",
+ " -5.25 | \n",
+ " -8.64 | \n",
+ "
\n",
+ " \n",
+ " | 1.000000 | \n",
+ " 5.64 | \n",
+ " 4.64 | \n",
+ " 3.75 | \n",
+ " 2.59 | \n",
+ " -0.02 | \n",
+ " -3.41 | \n",
+ " -5.68 | \n",
+ " -7.94 | \n",
+ " -11.34 | \n",
+ "
\n",
+ " \n",
+ " | 1.300000 | \n",
+ " 3.57 | \n",
+ " 2.57 | \n",
+ " 1.68 | \n",
+ " 0.52 | \n",
+ " -2.09 | \n",
+ " -5.49 | \n",
+ " -7.75 | \n",
+ " -10.01 | \n",
+ " -13.41 | \n",
+ "
\n",
+ " \n",
+ " | 1.500000 | \n",
+ " 2.65 | \n",
+ " 1.65 | \n",
+ " 0.76 | \n",
+ " -0.40 | \n",
+ " -3.01 | \n",
+ " -6.41 | \n",
+ " -8.67 | \n",
+ " -10.93 | \n",
+ " -14.33 | \n",
+ "
\n",
+ " \n",
+ " | 1.700000 | \n",
+ " 1.94 | \n",
+ " 0.94 | \n",
+ " 0.06 | \n",
+ " -1.11 | \n",
+ " -3.72 | \n",
+ " -7.11 | \n",
+ " -9.38 | \n",
+ " -11.64 | \n",
+ " -15.03 | \n",
+ "
\n",
+ " \n",
+ " | 2.000000 | \n",
+ " 1.15 | \n",
+ " 0.15 | \n",
+ " -0.74 | \n",
+ " -1.90 | \n",
+ " -4.51 | \n",
+ " -7.90 | \n",
+ " -10.17 | \n",
+ " -12.43 | \n",
+ " -15.83 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
+ "ax[0].hist(ytreated - yctrl, bins=20, density=True)\n",
+ "ax[0].set_xlabel(r\"$\\hat{\\tau}_i$\")\n",
+ "\n",
+ "ax[1].plot(Gamma, Pvalue)\n",
+ "ax[1].set_xlabel(r\"$\\Gamma$\")\n",
+ "ax[1].set_ylabel(r\"$P$-value\")\n",
+ "ax[1].axhline(0.05, color=\"red\", linestyle=\"--\")\n",
+ "ax[1].axvline(Gamma[np.array(Pvalue) >= 0.05][0], color=\"red\", linestyle=\"--\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 101,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([0.07943202])"
+ ]
+ },
+ "execution_count": 101,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "res[0]"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "metrics",
+ "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": "3.11.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pyfixest/Chapter20OverlapRD.ipynb b/pyfixest/Chapter20OverlapRD.ipynb
new file mode 100644
index 0000000..d175051
--- /dev/null
+++ b/pyfixest/Chapter20OverlapRD.ipynb
@@ -0,0 +1,18142 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 20: Overlap in Observational Studies: Difficulties and Opportunities"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import scipy as sp\n",
+ "import pyfixest as pf\n",
+ "\n",
+ "# viz\n",
+ "import matplotlib\n",
+ "import matplotlib.pyplot as plt\n",
+ "import seaborn as sns\n",
+ "\n",
+ "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
+ "plt.rc(\"font\", **font)\n",
+ "plt.rcParams[\"figure.figsize\"] = (10, 10)\n",
+ "%matplotlib inline\n",
+ "\n",
+ "from utils import *\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "%load_ext autoreload\n",
+ "%autoreload 1\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## drinking age RD figure"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " agecell | \n",
+ " all | \n",
+ " internal | \n",
+ " external | \n",
+ " alcohol | \n",
+ " homicide | \n",
+ " suicide | \n",
+ " mva | \n",
+ " drugs | \n",
+ " externalother | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 19.068493 | \n",
+ " 92.825401 | \n",
+ " 16.617590 | \n",
+ " 76.207817 | \n",
+ " 0.639138 | \n",
+ " 16.316818 | \n",
+ " 11.203714 | \n",
+ " 35.829327 | \n",
+ " 3.872425 | \n",
+ " 8.534373 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 19.150684 | \n",
+ " 95.100739 | \n",
+ " 18.327684 | \n",
+ " 76.773056 | \n",
+ " 0.677409 | \n",
+ " 16.859964 | \n",
+ " 12.193368 | \n",
+ " 35.639256 | \n",
+ " 3.236511 | \n",
+ " 8.655786 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 19.232876 | \n",
+ " 92.144295 | \n",
+ " 18.911053 | \n",
+ " 73.233238 | \n",
+ " 0.866443 | \n",
+ " 15.219254 | \n",
+ " 11.715812 | \n",
+ " 34.205650 | \n",
+ " 3.202071 | \n",
+ " 8.513741 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 19.315069 | \n",
+ " 88.427757 | \n",
+ " 16.101770 | \n",
+ " 72.325981 | \n",
+ " 0.867308 | \n",
+ " 16.742825 | \n",
+ " 11.275010 | \n",
+ " 32.278957 | \n",
+ " 3.280689 | \n",
+ " 8.258285 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 19.397261 | \n",
+ " 88.704941 | \n",
+ " 17.363520 | \n",
+ " 71.341415 | \n",
+ " 1.019163 | \n",
+ " 14.947726 | \n",
+ " 10.984314 | \n",
+ " 32.650967 | \n",
+ " 3.548198 | \n",
+ " 8.417533 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(figsize=(10, 10))\n",
+ "mlda.set_index(\"agecell\").plot(\n",
+ " ax=ax,\n",
+ ")\n",
+ "ax.axvline(21, color=\"k\", linestyle=\"--\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## simulated data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 500\n",
+ "\n",
+ "\n",
+ "def sim_rd_dgp(tau, x0=1, x1=0, y01=1, n=500):\n",
+ " df, gr = simulate(\n",
+ " x=lambda: np.random.normal(0, 1, n),\n",
+ " y0=lambda x: x0 * x + np.random.normal(0, 0.5, n),\n",
+ " y1=lambda y0, x: y0 * y01 + x1 * x + tau + x1 * np.random.normal(0, 0.5, n),\n",
+ " z=lambda x: 1 * (x >= 0),\n",
+ " y=lambda y0, y1, z: z * y1 + (1 - z) * y0,\n",
+ " )\n",
+ " return df\n",
+ "\n",
+ "\n",
+ "def plot_rd(df, ax):\n",
+ " ax.scatter(df[\"x\"], df[\"y0\"], color=\"grey\", s=1)\n",
+ " ax.scatter(df[\"x\"], df[\"y1\"], color=\"grey\", s=1)\n",
+ " ax.scatter(df[\"x\"], df[\"y\"], color=\"black\", s=1)\n",
+ " ax.axvline(0, color=\"k\", linestyle=\"--\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(2, 2, figsize=(10, 10))\n",
+ "plot_rd(sim_rd_dgp(5), ax[0, 0])\n",
+ "plot_rd(sim_rd_dgp(1), ax[0, 1])\n",
+ "plot_rd(sim_rd_dgp(5, y01=0, x1=0.5), ax[1, 0])\n",
+ "plot_rd(sim_rd_dgp(1, y01=0, x1=0.5), ax[1, 1])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Lee (2008)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Unnamed: 0 | \n",
+ " x | \n",
+ " y | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 1 | \n",
+ " 2 | \n",
+ " 0.1393 | \n",
+ " 0.4611 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 3 | \n",
+ " -0.0736 | \n",
+ " 0.5434 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 4 | \n",
+ " 0.0868 | \n",
+ " 0.5846 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 5 | \n",
+ " 0.3994 | \n",
+ " 0.5803 | \n",
+ "
\n",
+ " \n",
+ " | 5 | \n",
+ " 6 | \n",
+ " 0.1681 | \n",
+ " 0.6244 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f = plt.figure(figsize=(7, 5))\n",
+ "plt.scatter(house.x, house.y, s=1)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "house[\"z\"] = 1 * (house.x >= 0)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "hh = np.arange(0.05, 1, 0.01)\n",
+ "\n",
+ "\n",
+ "def fit_rd(h):\n",
+ " mod = pf.feols(\"y ~ z * x\", data=house.loc[np.abs(house.x) <= h], vcov=\"HC2\")\n",
+ " return mod.coef().loc[\"z\"], mod.se().loc[\"z\"]\n",
+ "\n",
+ "\n",
+ "res = np.array([fit_rd(h) for h in hh])\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 1.0, 'Subset Linear Regression: |X| < h')"
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(figsize=(7, 5))\n",
+ "\n",
+ "ax.scatter(hh, res[:, 0], marker=\"o\", color=\"k\", s=1)\n",
+ "ax.scatter(hh, res[:, 0] + 1.96 * res[:, 1], color=\"grey\", marker=\"o\", s=1)\n",
+ "ax.scatter(hh, res[:, 0] - 1.96 * res[:, 1], color=\"grey\", marker=\"o\", s=1)\n",
+ "ax.set_xlabel(\"Bandwidth\")\n",
+ "ax.set_ylabel(\"Point and Interval Estimates\")\n",
+ "ax.set_title(\"Subset Linear Regression: |X| < h\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "metrics",
+ "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": "3.11.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pyfixest/Chapter21IVexperiments.ipynb b/pyfixest/Chapter21IVexperiments.ipynb
new file mode 100644
index 0000000..4357435
--- /dev/null
+++ b/pyfixest/Chapter21IVexperiments.ipynb
@@ -0,0 +1,13254 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 21: An Experimental Perspective on the Instrumental Variable"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import pyfixest as pf\n",
+ "import scipy as sp\n",
+ "from joblib import Parallel, delayed\n",
+ "\n",
+ "# viz\n",
+ "import matplotlib\n",
+ "import matplotlib.pyplot as plt\n",
+ "import seaborn as sns\n",
+ "\n",
+ "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
+ "plt.rc(\"font\", **font)\n",
+ "plt.rcParams[\"figure.figsize\"] = (10, 10)\n",
+ "%matplotlib inline\n",
+ "\n",
+ "from utils import *\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "%load_ext autoreload\n",
+ "%autoreload 1\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def IV_Wald(Z, D, Y):\n",
+ " tau_D = np.mean(D[Z == 1]) - np.mean(D[Z == 0])\n",
+ " tau_Y = np.mean(Y[Z == 1]) - np.mean(Y[Z == 0])\n",
+ " CACE = tau_Y / tau_D\n",
+ " return np.array([tau_D, tau_Y, CACE])\n",
+ "\n",
+ "\n",
+ "def IV_Wald_delta(Z, D, Y):\n",
+ " est = IV_Wald(Z, D, Y)\n",
+ " AdjustedY = Y - D * est[2]\n",
+ " VarAdj = np.var(AdjustedY[Z == 1], ddof=1) / np.sum(Z) + np.var(\n",
+ " AdjustedY[Z == 0], ddof=1\n",
+ " ) / np.sum(1 - Z)\n",
+ " return np.array([est[2], np.sqrt(VarAdj) / abs(est[0])])\n",
+ "\n",
+ "\n",
+ "def IV_Wald_bootstrap(Z, D, Y, n_boot=200, k=-1):\n",
+ " est = IV_Wald(Z, D, Y)\n",
+ " n = len(Z)\n",
+ "\n",
+ " def bootfn(*args):\n",
+ " # draw indices\n",
+ " ids = np.random.choice(np.arange(n), size=n, replace=True)\n",
+ " return IV_Wald(Z[ids], D[ids], Y[ids])[2]\n",
+ "\n",
+ " boot_est = Parallel(n_jobs=k)(delayed(bootfn)(i) for i in range(int(n_boot)))\n",
+ " boot_est = np.vstack(boot_est)\n",
+ " return np.array([est[2], boot_est.flatten().std()])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "## without covariates\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def ivsim_nocovars(shares=[1 / 2, 1 / 4, 1 / 4], *args):\n",
+ " n = 200\n",
+ " D0 = np.r_[\n",
+ " np.repeat(0, int(n * shares[0])),\n",
+ " np.repeat(1, int(n * shares[1])),\n",
+ " np.repeat(0, int(n * shares[2])),\n",
+ " ]\n",
+ " D1 = np.r_[\n",
+ " np.repeat(1, int(n * shares[0])),\n",
+ " np.repeat(1, int(n * shares[1])),\n",
+ " np.repeat(0, int(n * shares[2])),\n",
+ " ]\n",
+ " Y0 = np.r_[\n",
+ " np.random.normal(1, size=int(n * shares[0])),\n",
+ " np.random.normal(0, size=int(n * shares[1])),\n",
+ " np.random.normal(2, size=int(n * shares[2])),\n",
+ " ]\n",
+ " Y1 = Y0.copy()\n",
+ " Y1[np.arange(int(n * shares[0]))] = np.random.normal(3, 1, int(n * shares[0]))\n",
+ " Z = np.random.binomial(1, 0.5, n)\n",
+ " D = Z * D1 + (1 - Z) * D0\n",
+ " Y = Z * Y1 + (1 - Z) * Y0\n",
+ " ret = np.array(\n",
+ " [\n",
+ " IV_Wald(Z, D, Y)[2],\n",
+ " IV_Wald_delta(Z, D, Y)[1],\n",
+ " IV_Wald_bootstrap(Z, D, Y, k=1)[1],\n",
+ " ]\n",
+ " )\n",
+ " return ret"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "### strong IV "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "MC = 2000\n",
+ "res = Parallel(n_jobs=-1)(\n",
+ " delayed(ivsim_nocovars)([1 / 2, 1 / 4, 1 / 4], i) for i in range(int(MC))\n",
+ ")\n",
+ "res = np.vstack(res)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "2.0459278335318825 0.5337581637120559\n",
+ "0.5562637573206064\n"
+ ]
+ }
+ ],
+ "source": [
+ "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
+ "print(cent, sd)\n",
+ "print(res[:, 2].mean())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(figsize=(5, 5))\n",
+ "ax.hist(res[:, 0], bins=50, density=True, alpha=0.5)\n",
+ "x_axis = np.arange(-1, 5, 0.01)\n",
+ "\n",
+ "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
+ "ax.vlines(2, 0, 1, color=\"k\")\n",
+ "ax.set_title(r\"strong IV: $\\pi_c = 0.5$\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## weak IV"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "MC = 2000\n",
+ "res = Parallel(n_jobs=-1)(\n",
+ " delayed(ivsim_nocovars)([1 / 5, 2 / 5, 2 / 5], i) for i in range(int(MC))\n",
+ ")\n",
+ "res = np.vstack(res)\n",
+ "res = np.ma.masked_invalid(res) # remove infs from divide by zero"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "2.2980928526598845 9.060489740223025\n",
+ "11.430861088387783\n"
+ ]
+ }
+ ],
+ "source": [
+ "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
+ "print(cent, sd)\n",
+ "print(res[:, 1].mean())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "/home/alal/anaconda3/envs/metrics/lib/python3.11/site-packages/numpy/lib/function_base.py:4737: UserWarning: Warning: 'partition' will ignore the 'mask' of the MaskedArray.\n",
+ " arr.partition(\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "minr, maxr = np.percentile(res[:, 0], [0.5, 99.5])\n",
+ "\n",
+ "f, ax = plt.subplots(figsize=(5, 5))\n",
+ "sims = res[:, 0]\n",
+ "ax.hist(\n",
+ " np.where((sims > minr) & (sims < maxr), sims, 0), bins=50, density=True, alpha=0.5\n",
+ ")\n",
+ "x_axis = np.arange(minr, maxr, 0.01)\n",
+ "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
+ "ax.vlines(2, 0, 1, color=\"k\")\n",
+ "ax.set_title(r\"weak IV: $\\pi_c = 0.2$\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## weakest IV"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "MC = 2000\n",
+ "res = Parallel(n_jobs=-1)(\n",
+ " delayed(ivsim_nocovars)([1 / 10, 2 / 5, 1 / 2], i) for i in range(int(MC))\n",
+ ")\n",
+ "res = np.vstack(res)\n",
+ "res = np.ma.masked_invalid(res) # remove infs from divide by zero"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "3.9621044093432425 44.27081120055434\n",
+ "280.39027826364907\n"
+ ]
+ }
+ ],
+ "source": [
+ "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
+ "print(cent, sd)\n",
+ "print(res[:, 1].mean())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "minr, maxr = np.percentile(res[:, 0], [0.5, 99.5])\n",
+ "\n",
+ "f, ax = plt.subplots(figsize=(5, 5))\n",
+ "sims = res[:, 0]\n",
+ "ax.hist(\n",
+ " np.where((sims > minr) & (sims < maxr), sims, 0), bins=50, density=True, alpha=0.5\n",
+ ")\n",
+ "x_axis = np.arange(minr, maxr, 0.01)\n",
+ "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
+ "ax.vlines(2, 0, 1, color=\"k\")\n",
+ "ax.set_title(r\"weakest IV: $\\pi_c = 0.1$\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## With Covariates\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def IV_Lin(Z, D, Y, X):\n",
+ " X = (X - X.mean(axis=0)) / X.std(axis=0)\n",
+ " covariates = pd.DataFrame(X, columns=[f\"x{i}\" for i in range(X.shape[1])])\n",
+ " data = covariates.assign(D=D, Y=Y, Z=Z)\n",
+ " rhs = \" + \".join(covariates.columns)\n",
+ " tau_D = pf.feols(\"D ~ Z * (\" + rhs + \")\", data=data).coef().loc[\"Z\"]\n",
+ " tau_Y = pf.feols(\"Y ~ Z * (\" + rhs + \")\", data=data).coef().loc[\"Z\"]\n",
+ " CACE = tau_Y / tau_D\n",
+ " return np.array([tau_D, tau_Y, CACE])\n",
+ "\n",
+ "\n",
+ "def IV_Lin_bootstrap(Z, D, Y, X, n_boot=200, k=-1):\n",
+ " X = (X - X.mean(axis=0)) / X.std(axis=0)\n",
+ " est = IV_Lin(Z, D, Y, X)\n",
+ " n = len(Z)\n",
+ "\n",
+ " def bootfn(*args):\n",
+ " id = np.random.choice(np.arange(n), size=n, replace=True)\n",
+ " return IV_Lin(Z[id], D[id], Y[id], X[id, :])[2]\n",
+ "\n",
+ " boot_est = Parallel(n_jobs=k)(delayed(bootfn)(i) for i in range(int(n_boot)))\n",
+ " boot_est = np.vstack(boot_est)\n",
+ " return np.array([est[2], boot_est.flatten().std()])\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def ivsim_covars(shares=[1 / 2, 1 / 4, 1 / 4], *args):\n",
+ " n = 200\n",
+ " X = np.random.normal(size=int(n * 2)).reshape((n, 2))\n",
+ " D0 = np.r_[\n",
+ " np.repeat(0, int(n * shares[0])),\n",
+ " np.repeat(1, int(n * shares[1])),\n",
+ " np.repeat(0, int(n * shares[2])),\n",
+ " ]\n",
+ " D1 = np.r_[\n",
+ " np.repeat(1, int(n * shares[0])),\n",
+ " np.repeat(1, int(n * shares[1])),\n",
+ " np.repeat(0, int(n * shares[2])),\n",
+ " ]\n",
+ " Y0 = np.r_[\n",
+ " np.random.normal(1, size=int(n * shares[0])),\n",
+ " np.random.normal(0, size=int(n * shares[1])),\n",
+ " np.random.normal(2, size=int(n * shares[2])),\n",
+ " ] + X @ np.array([1, -1])\n",
+ " Y1 = Y0.copy()\n",
+ " Y1[np.arange(int(n * shares[0]))] = np.random.normal(3, 1, int(n * shares[0])) + +X[\n",
+ " np.arange(int(n * shares[0])), :\n",
+ " ] @ np.array([1, -1])\n",
+ " Z = np.random.binomial(1, 0.5, n)\n",
+ " D = Z * D1 + (1 - Z) * D0\n",
+ " Y = Z * Y1 + (1 - Z) * Y0\n",
+ " return IV_Lin_bootstrap(Z, D, Y, X, k=1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "\n",
+ "### Strong IV"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "MC = 2000\n",
+ "res = Parallel(n_jobs=-1)(\n",
+ " delayed(ivsim_covars)([1 / 2, 1 / 4, 1 / 4], i) for i in range(int(MC))\n",
+ ")\n",
+ "res = np.vstack(res)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "2.041022022570901 0.5542291812774217\n",
+ "0.5594014563842343\n"
+ ]
+ }
+ ],
+ "source": [
+ "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
+ "print(cent, sd)\n",
+ "print(res[:, 1].mean())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(figsize=(5, 5))\n",
+ "ax.hist(res[:, 0], bins=50, density=True, alpha=0.5)\n",
+ "x_axis = np.arange(-1, 5, 0.01)\n",
+ "\n",
+ "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
+ "ax.vlines(2, 0, 1, color=\"k\")\n",
+ "ax.set_title(r\"strong IV: $\\pi_c = 0.5$\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Weak IV"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "MC = 2000\n",
+ "res = Parallel(n_jobs=-1)(\n",
+ " delayed(ivsim_covars)([1 / 5, 2 / 5, 2 / 5], i) for i in range(int(MC))\n",
+ ")\n",
+ "res = np.vstack(res)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "2.1504851844132458 20.437946561705076\n",
+ "101.34710547345787\n"
+ ]
+ }
+ ],
+ "source": [
+ "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
+ "print(cent, sd)\n",
+ "print(res[:, 1].mean())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "minr, maxr = np.percentile(res[:, 0], [0.5, 99.5])\n",
+ "\n",
+ "f, ax = plt.subplots(figsize=(5, 5))\n",
+ "sims = res[:, 0]\n",
+ "ax.hist(\n",
+ " np.where((sims > minr) & (sims < maxr), sims, 0), bins=50, density=True, alpha=0.5\n",
+ ")\n",
+ "x_axis = np.arange(minr, maxr, 0.01)\n",
+ "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
+ "ax.vlines(2, 0, 1, color=\"k\")\n",
+ "ax.set_title(r\"weak IV: $\\pi_c = 0.2$\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Weakest IV"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "MC = 2000\n",
+ "res = Parallel(n_jobs=-1)(\n",
+ " delayed(ivsim_covars)([1 / 10, 2 / 5, 1 / 2], i) for i in range(int(MC))\n",
+ ")\n",
+ "res = np.vstack(res)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "-19.37707093642744 1170.4776931064248\n",
+ "3529.2840088053103\n"
+ ]
+ }
+ ],
+ "source": [
+ "cent, sd = res[:, 0].mean(), res[:, 0].std()\n",
+ "print(cent, sd)\n",
+ "print(res[:, 1].mean())"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 23,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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HzAAA1iNmAADrETMAgPWIGQDAesQMAGA9YgYAsB4xAwBYj5gBAKxHzAAA1iNmAADrETMAgPWIGQDAesQMAGA9YgYAsB4xAwBYj5gBAKxHzAAA1iNmAADrETMAgPWIGQDAesQMAGA9YgYAsB4xAwBYj5gBAKxHzAAA1iNmAADrETMAgPWIGQDAesQMAGA9YgYAsB4xAwBYj5gBAKxHzAAA1iNmAADrETMAgPWIGQDAesQMAGA9YgYAsB4xAwBYj5gBAKxHzAAA1iNmAADrETMAgPUCjll+fr5SUlLkdruVkJCguXPnVjtu0aJF6tGjh1wulzp27KiJEyfqxIkT5z1hAADOFnDMMjIylJKSogMHDig3N1eLFy9WTk6O35jS0lJNnDhR77zzjg4ePKhvv/1WK1eu1MqVKxts4gAAnBZQzIqKirRx40ZNmjRJDodDLpdLGRkZWrFihd+41q1bKzY2VuXl5ZKkn3/+WQ6HQ926dWu4mQMA8H+CAxmcn5+vqKgoBQf/upvL5dIXX3zhN65ly5ZauXKlxowZo0OHDkmS3njjDfXr16/a41ZUVKiiosL3cWlpaSDTAgA0cwE9MisvL5fD4fDb5nA4fI/ATjt69KhuueUWzZ8/X2VlZdq0aZOmTZumTZs2VXvcOXPmKDIy0neLi4sL8DQAAM1ZQDFzOp0yxvhtM8bI6XT6bcvJyVFkZKTS0tLUokUL9enTR2lpaXr77berPe60adNUUlLiuxUUFAR4GgCA5iygpxm7dOmi4uJieb1e31ONHo9H8fHxfuOMMWrRwr+TLVq0kNfrrfa4oaGhCg0NDWQqAAD4BPTILDo6WsnJyVqwYIGMMSosLNTSpUuVmpqqrKwspaenS5KuueYa7d27V//+978lSfv27dPy5cuVkpLS8GcAAGj2Ar40f8mSJcrOzpbb7dbgwYM1fvx4DR8+XB6PR3l5eZKk9u3b691339WTTz6pmJgYDR8+XJMmTdLo0aMb/AQAAHCYs38JdgkoLS1VZGSkSkpKFBER0djTAaxz7NgxhYeHSzp1QVZYWFgjzwg4N/XtAS9nBQCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6AccsPz9fKSkpcrvdSkhI0Ny5c2sce/jwYQ0ZMkTTp0/XL7/8cl4TBQCgJsGB7pCRkaHRo0crOztbhYWFGjJkiJKSkjRs2DC/cRUVFbr11ls1YcIE3XfffQ01XwAAqgjokVlRUZE2btyoSZMmyeFwyOVyKSMjQytWrKgy9ve//72uueYaQgYAuOACill+fr6ioqIUHPzrAzqXy6Vdu3b5jTt+/Lhef/11RUREKDY2Vl27dtWCBQtqPG5FRYVKS0v9bgAA1FdAMSsvL5fD4fDb5nA4VF5e7rdtw4YNOn78uBITE/Wf//xHb7/9tp5++mmtX7++2uPOmTNHkZGRvltcXFyApwEAaM4CipnT6ZQxxm+bMUZOp9Nv28GDB9WpUyfdcsstCgoK0rXXXquUlBR9+eWX1R532rRpKikp8d0KCgoCPA0AQHMW0AUgXbp0UXFxsbxer++pRo/Ho/j4eL9x7du3V4sW/p1s0aKFQkJCqj1uaGioQkNDA5kKAAA+AT0yi46OVnJyshYsWCBjjAoLC7V06VKlpqYqKytL6enpkqSBAwfq4MGDys3NlSR99913ysnJ0Y033tjwZwAAaPYC/juzJUuWKDs7W263W4MHD9b48eM1fPhweTwe5eXlSZLatGmj5cuXa8qUKXK5XEpLS9Mf//hH9e7du8FPAAAAhzn7l2CXgNLSUkVGRqqkpEQRERGNPR3AOseOHVN4eLgk6ejRowoLC2vkGQHnpr494OWsAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArEfMAADWI2YAAOsRMwCA9YgZAMB6xAwAYD1iBgCwHjEDAFiPmAEArBdwzPLz85WSkiK3262EhATNnTu31vFZWVlq2bKlZs6cea5zBACgVgHHLCMjQykpKTpw4IByc3O1ePFi5eTkVDu2pKREL774oh588MHznigAADUJKGZFRUXauHGjJk2aJIfDIZfLpYyMDK1YsaLa8U8//bQeeughRUdHN8hkAQCoTkAxy8/PV1RUlIKDg33bXC6Xdu3aVWXs9u3btW7duno9KquoqFBpaanfDQCA+gooZuXl5XI4HH7bHA6HysvL/bYZYzRx4kQtWLBAQUFBdR53zpw5ioyM9N3i4uICmRYAoJkLKGZOp1PGGL9txhg5nU6/bX/5y1/UuXNnDR48uF7HnTZtmkpKSny3goKCQKYFAGjmguse8qsuXbqouLhYXq/X91Sjx+NRfHy837hPPvlEq1evVkxMjCTp6NGjkqQdO3bo/fffr3Lc0NBQhYaGntMJAAAQ0COz6OhoJScna8GCBTLGqLCwUEuXLlVqaqqysrKUnp4uSXrnnXd05MgRFRYWqrCwUFOnTtXUqVOrDRkAAOcr4EvzlyxZouzsbLndbg0ePFjjx4/X8OHD5fF4lJeXdyHmCABArRzm7F+CXQJKS0sVGRmpkpISRURENPZ0AOscO3ZM4eHhkk49zR8WFtbIMwLOTX17wMtZAQCsR8wAANYjZgAA6xEzAID1iBkAwHrEDABgPWIGALAeMQMAWI+YAQCsR8wAANYjZgAA6xEzAID1iBkAwHrEDABgPWIGALAeMQMAWI+YAQCsR8wAANYjZgAA6xEzAID1iBkAwHrEDABgPWIGALAeMQMAWI+YAQCsR8wAANYjZgAA6xEzAID1iBkAwHrEDABgPWIGALAeMQMAWI+YAQCsR8wAANYjZgAA6xEzAID1iBkAwHrEDABgPWIGALAeMQMAWI+YAQCsR8wAANYjZgAA6xEzAID1iBkAwHrEDABgPWIGALAeMQMAWI+YAQCsR8wAANYjZgAA6xEzAID1iBkAwHrEDABgPWIGALAeMQMAWI+YAQCsR8wAANYjZgAA6xEzAID1iBkAwHrEDABgPWIGALBewDHLz89XSkqK3G63EhISNHfu3GrH5eTkKCkpSS6XS5dffrlWrlx53pMFAKA6wYHukJGRodGjRys7O1uFhYUaMmSIkpKSNGzYMN+YgwcPaty4cVq1apUGDBig999/X3fffbeOHDmioKCgBj0BAAAcxhhT38FFRUXq2LGjysrKFBx8qoOzZ89WYWGh/vCHP/iN3b9/vzp27ChJOnnypEJCQrR//37FxsbW+XlKS0sVGRmpkpISRUREBHI+ACQdO3ZM4eHhkqSjR48qLCyskWcEnJv69iCgR2b5+fmKioryhUySXC6XvvjiiypjT4fs9H4RERFq165dtcetqKhQRUWF3+QBAKivgH5nVl5eLofD4bfN4XCovLy8xn28Xq8eeeQRZWZmKiQkpNoxc+bMUWRkpO8WFxcXyLQAAM1cQDFzOp06+1lJY4ycTme140+cOKGxY8eqR48eeuyxx2o87rRp01RSUuK7FRQUBDItAEAzF9DTjF26dFFxcbG8Xq/vqUaPx6P4+PgqY48fP67U1FT17NlTCxcurPW4oaGhCg0NDWQqAAD4BPTILDo6WsnJyVqwYIGMMSosLNTSpUuVmpqqrKwspaenSzr1C+eRI0eqb9++dYYMAIDzFfDfmS1ZskTZ2dlyu90aPHiwxo8fr+HDh8vj8SgvL0+StHnzZn3++edatmyZYmJifLdFixY1+AkAABDQpfkXC5fmA+eHS/PRVNS3B7ycFQDAesQMAGA9YgYAsB4xAwBYj5gBAKxHzAAA1iNmAADrETMAgPWIGQDAesQMAGA9YgYAsB4xAwBYj5gBAKxHzAAA1iNmAADrETMAgPWIGQDAesQMAGA9YgYAsB4xAwBYj5gBAKxHzAAA1iNmAADrETMAgPWIGQDAesQMAGA9YgYAsB4xAwBYj5gBAKxHzAAA1iNmAADrETMAgPWIGQDAesQMAGC94MaeAICG9+qnu/z+Hdra6ft48k0JjTEl4ILikRkAwHrEDABgPWIGALAeMQMAWI+YAQCsR8wAANYjZgAA6xEzAID1iBkAwHrEDABgPWIGALAeMQMAWI+YAQCsx6vmA5Z6ZfX/a+wpAJcMHpkBAKxHzAAA1iNmAADrETMAgPWIGQDAesQMAGA9YgYAsB4xAwBYj5gBAKxHzAAA1iNmAADr8dqMQDNT22s6Tr4p4SLOBGg4PDIDAFiPmAEArBdwzPLz85WSkiK3262EhATNnTu32nFbt27VoEGD5HK51Lt3by1btuy8JwsAQHUCjllGRoZSUlJ04MAB5ebmavHixcrJyfEbU1lZqfT0dE2aNEkHDx7UihUrNHXqVO3evbvBJg4AwGkBXQBSVFSkjRs36pNPPpHD4ZDL5VJGRoZWrFihYcOG+cZt375dDodDd9xxhySpZ8+euvXWW/XRRx/psccea9gzANBguDgEtgooZvn5+YqKilJw8K+7uVwuffHFF37j9uzZo5iYGL9tLpdLu3btqva4FRUVqqio8H1cUlIiSSotLQ1kev52rZaynzr3/YGLpOxn7zntN7aW+8pPVmra//379vWpcrY8/1+PH/ii5vvatOLCaNTgf7+UgkPOeffTHTDG1DouoK/A8vJyORwOv20Oh0Pl5eXnNO60OXPmaNasWVW2x8XFBTI9ANVIeHFvY08Bzdn0dg1ymLKyMkVGRtZ4f0AxczqdVepojJHT6TyncadNmzbN7+nHyspKFRcXq23btr4olpaWKi4uTgUFBYqIiAhk2k0Oa+GP9fgVa+GP9fiVrWthjFFZWZncbnet4wKKWZcuXVRcXCyv1+t7qtHj8Sg+Pt5vXNeuXVVYWOi3zePxqFevXtUeNzQ0VKGhoX7bfvOb31Q7NiIiwqr/EBcSa+GP9fgVa+GP9fiVjWtR2yOy0wJ6Ij06OlrJyclasGCBjDEqLCzU0qVLlZqaqqysLKWnp0uSrrrqKlVWVmr58uWSpJ07d+rDDz/UmDFjzuE0AACoXcC/FV6yZImys7Pldrs1ePBgjR8/XsOHD5fH41FeXt6pg7ZooXfffVevvPKKYmJilJqaqnnz5qlHjx4NfgIAAAR8CVK3bt20evXqKtuffPJJPfnkk76PExMTtW7duvOb3RlCQ0OVmZlZ5enI5oi18Md6/Iq18Md6/Kqpr4XD1HW9IwAAlzhemxEAYD1iBgCwHjEDAFiPmAEArHdJxmzdunXq3r27HA5HlVfanzFjhiIiIhQTE+O7bdq0yXf/Sy+9pISEBLndbt14443as2fPxZ5+g6ptLep6O56mthZn+uWXXxQcHOz3dTB27K+vVljftypqSprjOZ+ptp8NTfl7QZJOnjypjIwMRURE6J577vG7r7Zzb1JfM+YSs3z5cpOQkGB27NhhJJldu3b53T9x4kSzZMmSavfNyckx8fHx5sCBA6aystLMnz/fDBky5CLM+sKoay2uv/56M2/ePFNZWWk8Ho+Jj483a9asMcY0vbU42+HDh03nzp1rvL+2tWmqmuM5n6mmnw1N/XuhtLTUDBs2zEyZMsU888wz5u677/bdV9e5N6WvmUsuZlu2bDGFhYXGGFPtD/C77rrL/POf/6x234cfftg8++yzvo+9Xq9xOp3myJEjF27CF1Bta3HkyBHTqlUrc/LkSd+2F154wTz88MPGmKa3FmfbuXOnSUxMrPa+utamKWqO53y2mn42NPXvBa/Xa1atWmWMMSYzM9MvZrWde1P7mrnknmYcMGCAOnToUOP9xcXF2rNnj/r06aMuXbpoxowZvvvOfuuZoKAgRUdHW/umoLWtRU1vx3P6bXaa2lqcrbi4WNHR0XrwwQflcrk0dOhQffvtt5LqXpumqDme89lq+tnQ1L8XgoKCNGLEiGrvq+3cm9rXTKPEbP/+/erYsWOV23333VfnvomJiXI6nfrmm2+Uk5OjrKwsvfvuu5ICf+uZS8G5rkVd52rjWpyttrUJCwtTTEyMpk+froKCAt1www268847JTWNcw9Uczzns9X0s6E5r01t597U1qVR3lGvY8eO2r9//znt+8ILL/j+3bVrV6Wnpys3N1fp6ekBv/XMpeBc16Kuc7VxLc5W19osXbrU9+/JkydrxowZKioqahLnHqjmeM5nq+lnQ3Nem9rOPSgoqEmtyyX3NGNdTpw44fexw+FQy5YtJVV96xmv16vDhw+re/fuF3WOF8OZb8dz2plvx9Mc1uLMr4XT/4fZsmXLOtemKWqO53y2mn42NIfvhZrUdu5N7WvGqpgZYzRo0CC99957kqQff/xRH3zwgW666SZJUlpamrKysuTxeGSM0cKFC3X11VcrOjq6Mad9QdT2djxS01+LDz74QCNHjtRPP/0kSXr99deVnJysiIiIOtemKWqO53ym2n42NPXvhdrUdu5N7mvmYl1pUl9vvPGGadu2rWnbtq2RZC677DLTtm1bs3z5cmOMMdu2bTODBw82HTp0MN26dTPz58/323/u3LkmPj7euFwuc8MNN5jdu3c3xmk0iLrW4ocffjA33nijiYmJMfHx8ebFF1/0278prcXZvF6vmTFjhomLizMxMTEmJSXF72rPutamKWqO53ym2n42NOXvBWOMSUhIMG3btjWtW7c2oaGhpm3btiYpKckYU/u5N6WvGV41HwBgPaueZgQAoDrEDABgPWIGALAeMQMAWI+YAQCsR8wAANYjZgAA6xEzAID1iBkAwHrEDABgPWIGALAeMQMAWO//A8Pgl1mmiHLIAAAAAElFTkSuQmCC",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "minr, maxr = np.percentile(res[:, 0], [0.5, 99.5])\n",
+ "\n",
+ "f, ax = plt.subplots(figsize=(5, 5))\n",
+ "sims = res[:, 0]\n",
+ "ax.hist(\n",
+ " np.where((sims > minr) & (sims < maxr), sims, 0), bins=50, density=True, alpha=0.5\n",
+ ")\n",
+ "x_axis = np.arange(minr, maxr, 0.01)\n",
+ "ax.plot(x_axis, sp.stats.norm.pdf(x_axis, loc=cent, scale=sd))\n",
+ "ax.vlines(2, 0, 1, color=\"k\")\n",
+ "ax.set_title(r\"weakest IV: $\\pi_c = 0.2$\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## WeakIV Robust Inference: Fieller Anderson Rubin Confidence Interval"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def FARci(Z, D, Y, Lower, Upper, grid):\n",
+ " CIrange = np.arange(Lower, Upper, grid)\n",
+ "\n",
+ " def pvfun(t):\n",
+ " Y_t = Y - t * D\n",
+ " TauAdj = Y_t[Z == 1].mean() - Y_t[Z == 0].mean()\n",
+ " VarAdj = np.var(Y_t[Z == 1], ddof=1) / np.sum(Z) + np.var(\n",
+ " Y_t[Z == 0], ddof=1\n",
+ " ) / np.sum(1 - Z)\n",
+ " Tstat = TauAdj / np.sqrt(VarAdj)\n",
+ " return (1 - sp.stats.norm.cdf(np.abs(Tstat))) * 2\n",
+ "\n",
+ " Pvalue = Parallel(n_jobs=-1)(delayed(pvfun)(t) for t in CIrange)\n",
+ " return CIrange, Pvalue"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def linestimator(Z, Y, X):\n",
+ " X = (X - X.mean(axis=0)) / X.std(axis=0)\n",
+ " n, p = X.shape\n",
+ " # fully interacted OLS\n",
+ " covariates = pd.DataFrame(X, columns=[f\"x{i}\" for i in range(p)])\n",
+ " data = covariates.assign(y=Y, z=Z)\n",
+ " m = pf.feols(\"y ~ z * (\" + \" + \".join(covariates.columns) + \")\", data=data, vcov=\"HC2\")\n",
+ " est, vehw = m.coef().loc[\"z\"], m.se().loc[\"z\"] ** 2\n",
+ " # super-population correction\n",
+ " inter = m.coef().loc[[f\"z:x{i}\" for i in range(p)]].to_numpy()\n",
+ " # (β_1 - β_0)' Σ (β_1 - β_0) / n\n",
+ " superCorr = np.sum(inter * (np.cov(X.T) @ inter)) / n\n",
+ " vsuper = vehw + superCorr\n",
+ " return est, np.sqrt(vehw), np.sqrt(vsuper)\n",
+ "\n",
+ "\n",
+ "def FARciX(Z, D, Y, X, Lower, Upper, grid):\n",
+ " CIrange = np.arange(Lower, Upper, grid)\n",
+ "\n",
+ " def pvfun(t):\n",
+ " Y_t = Y - t * D\n",
+ " linest = linestimator(Z, Y_t, X)\n",
+ " Tstat = linest[0] / linest[2]\n",
+ " return (1 - sp.stats.norm.cdf(np.abs(Tstat))) * 2\n",
+ "\n",
+ " Pvalue = Parallel(n_jobs=-1)(delayed(pvfun)(t) for t in CIrange)\n",
+ " return CIrange, Pvalue\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def ivsim_covars(shares=[1 / 2, 1 / 4, 1 / 4], *args):\n",
+ " n = 200\n",
+ " X = np.random.normal(size=int(n * 2)).reshape((n, 2))\n",
+ " D0 = np.r_[\n",
+ " np.repeat(0, int(n * shares[0])),\n",
+ " np.repeat(1, int(n * shares[1])),\n",
+ " np.repeat(0, int(n * shares[2])),\n",
+ " ]\n",
+ " D1 = np.r_[\n",
+ " np.repeat(1, int(n * shares[0])),\n",
+ " np.repeat(1, int(n * shares[1])),\n",
+ " np.repeat(0, int(n * shares[2])),\n",
+ " ]\n",
+ " Y0 = np.r_[\n",
+ " np.random.normal(1, size=int(n * shares[0])),\n",
+ " np.random.normal(0, size=int(n * shares[1])),\n",
+ " np.random.normal(2, size=int(n * shares[2])),\n",
+ " ] + X @ np.array([1, -1])\n",
+ " Y1 = Y0.copy()\n",
+ " Y1[np.arange(int(n * shares[0]))] = np.random.normal(3, 1, int(n * shares[0])) + +X[\n",
+ " np.arange(int(n * shares[0])), :\n",
+ " ] @ np.array([1, -1])\n",
+ " Z = np.random.binomial(1, 0.5, n)\n",
+ " D = Z * D1 + (1 - Z) * D0\n",
+ " Y = Z * Y1 + (1 - Z) * Y0\n",
+ " return Z, D, Y, X"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 0.98, 'strong IV: $\\\\pi_c = 0.5$')"
+ ]
+ },
+ "execution_count": 27,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(1, 2, figsize=(6, 4))\n",
+ "Z, D, Y, _ = ivsim_covars([1 / 2, 1 / 4, 1 / 4])\n",
+ "CI, Pv = FARci(Z, D, Y, 0, 5, 0.001)\n",
+ "\n",
+ "ax[0].plot(CI, Pv)\n",
+ "ax[0].hlines(0.05, 0, 5, color=\"k\", linestyle=\"--\")\n",
+ "\n",
+ "Z, D, Y, _ = ivsim_covars([1 / 2, 1 / 4, 1 / 4])\n",
+ "CI, Pv = FARci(Z, D, Y, 0, 5, 0.001)\n",
+ "\n",
+ "ax[1].plot(CI, Pv)\n",
+ "ax[1].hlines(0.05, 0, 5, color=\"k\", linestyle=\"--\")\n",
+ "\n",
+ "f.set_tight_layout(True)\n",
+ "f.suptitle(r\"strong IV: $\\pi_c = 0.5$\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 28,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 0.98, 'strong IV: $\\\\pi_c = 0.2$')"
+ ]
+ },
+ "execution_count": 28,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "l, h = -5, 30\n",
+ "f, ax = plt.subplots(1, 2, figsize=(6, 4))\n",
+ "Z, D, Y, _ = ivsim_covars([1 / 5, 2 / 5, 2 / 5])\n",
+ "CI, Pv = FARci(Z, D, Y, l, h, 0.001)\n",
+ "\n",
+ "ax[0].plot(CI, Pv)\n",
+ "ax[0].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
+ "ax[0].set_xlim(l, h)\n",
+ "\n",
+ "Z, D, Y, _ = ivsim_covars([1 / 5, 2 / 5, 2 / 5])\n",
+ "CI, Pv = FARci(Z, D, Y, l, h, 0.001)\n",
+ "\n",
+ "ax[1].plot(CI, Pv)\n",
+ "ax[1].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
+ "ax[1].set_xlim(l, h)\n",
+ "f.set_tight_layout(True)\n",
+ "f.suptitle(r\"strong IV: $\\pi_c = 0.2$\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 0.98, 'strong IV: $\\\\pi_c = 0.1$')"
+ ]
+ },
+ "execution_count": 29,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "l, h = -10, 25\n",
+ "f, ax = plt.subplots(1, 2, figsize=(6, 4))\n",
+ "Z, D, Y, _ = ivsim_covars([1 / 10, 2 / 5, 1 / 2])\n",
+ "CI, Pv = FARci(Z, D, Y, l, h, 0.001)\n",
+ "\n",
+ "ax[0].plot(CI, Pv)\n",
+ "ax[0].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
+ "ax[0].set_xlim(l, h)\n",
+ "\n",
+ "Z, D, Y, _ = ivsim_covars([1 / 10, 2 / 5, 1 / 2])\n",
+ "CI, Pv = FARci(Z, D, Y, l, h, 0.001)\n",
+ "\n",
+ "ax[1].plot(CI, Pv)\n",
+ "ax[1].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
+ "ax[1].set_xlim(l, h)\n",
+ "f.set_tight_layout(True)\n",
+ "f.suptitle(r\"strong IV: $\\pi_c = 0.1$\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Application"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import formulaic as fm"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "jobsdata = pd.read_csv(\"jobsdata.csv\")\n",
+ "Z, D, Y = jobsdata.treat.values, jobsdata.comply.values, jobsdata.job_seek.values\n",
+ "X = (\n",
+ " fm.Formula(\"~ -1 + sex + age + marital + nonwhite + educ + income\")\n",
+ " .get_model_matrix(data=jobsdata)\n",
+ " .values\n",
+ ")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 32,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " CACE | \n",
+ " SE | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | delta | \n",
+ " 0.108790 | \n",
+ " 0.081027 | \n",
+ "
\n",
+ " \n",
+ " | bootstrap | \n",
+ " 0.108790 | \n",
+ " 0.081694 | \n",
+ "
\n",
+ " \n",
+ " | linestimator | \n",
+ " 0.117633 | \n",
+ " 0.081463 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(2, 1, figsize=(6, 4))\n",
+ "ax[0].plot(CI1, Pv1)\n",
+ "ax[0].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
+ "ax[0].set_xlim(l, h)\n",
+ "ax[0].set_title(\"No Covariates\")\n",
+ "\n",
+ "ax[1].plot(CI2, Pv2)\n",
+ "ax[1].hlines(0.05, l, h, color=\"k\", linestyle=\"--\")\n",
+ "ax[1].set_xlim(l, h)\n",
+ "ax[1].set_title(\"With Covariates\")\n",
+ "f.set_tight_layout(True)\n",
+ "f.suptitle(r\"AR Intervals\")"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "metrics",
+ "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": "3.11.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/Chapter22IVmixtureDist.ipynb b/pyfixest/Chapter22IVmixtureDist.ipynb
similarity index 100%
rename from Chapter22IVmixtureDist.ipynb
rename to pyfixest/Chapter22IVmixtureDist.ipynb
diff --git a/pyfixest/Chapter23IVeconometrics.ipynb b/pyfixest/Chapter23IVeconometrics.ipynb
new file mode 100644
index 0000000..96f74c7
--- /dev/null
+++ b/pyfixest/Chapter23IVeconometrics.ipynb
@@ -0,0 +1,200 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 23: An Econometric Perspective on the Instrumental Variable"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import scipy as sp\n",
+ "import pyfixest as pf\n",
+ "\n",
+ "# viz\n",
+ "import matplotlib\n",
+ "import matplotlib.pyplot as plt\n",
+ "import seaborn as sns\n",
+ "\n",
+ "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
+ "plt.rc(\"font\", **font)\n",
+ "plt.rcParams[\"figure.figsize\"] = (10, 10)\n",
+ "%matplotlib inline\n",
+ "\n",
+ "from utils import *\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "%load_ext autoreload\n",
+ "%autoreload 1\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "card_data = pd.read_csv(\"card1995.csv\")\n",
+ "yn, dn, zn = [\"lwage\", \"educ\", \"nearc4\"]\n",
+ "Y, D, Z = card_data[yn], card_data[dn], card_data[zn]\n",
+ "xs = [\n",
+ " \"exper\",\n",
+ " \"expersq\",\n",
+ " \"black\",\n",
+ " \"south\",\n",
+ " \"smsa\",\n",
+ " \"reg661\",\n",
+ " \"reg662\",\n",
+ " \"reg663\",\n",
+ " \"reg664\",\n",
+ " \"reg665\",\n",
+ " \"reg666\",\n",
+ " \"reg667\",\n",
+ " \"reg668\",\n",
+ " \"smsa66\",\n",
+ "]\n",
+ "X = card_data[xs].values"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "formula = f\"{yn} ~ {' + '.join(xs)} | {dn} ~ {zn}\"\n",
+ "iv_res2 = pf.feols(formula, data=card_data, vcov=\"hetero\")\n",
+ "\n",
+ "iv_est, iv_se = iv_res2.coef().loc[dn], iv_res2.se().loc[dn]\n",
+ "{\"tsls\": iv_est, \"lower CI\": iv_est - 1.96 * iv_se, \"upper CI\": iv_est + 1.96 * iv_se}\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# PyFixest's native IV estimator performs both stages and computes valid IV inference.\n",
+ "iv_est2, iv_se2 = iv_res2.coef().loc[dn], iv_res2.se().loc[dn]\n",
+ "\n",
+ "{\n",
+ " \"tsls\": iv_est2,\n",
+ " \"lower CI\": iv_est2 - 1.96 * iv_se2,\n",
+ " \"upper CI\": iv_est2 + 1.96 * iv_se2,\n",
+ "}\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Anderson Rubin"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from joblib import Parallel, delayed\n",
+ "\n",
+ "CIrange = np.arange(-0.1, 0.4, 0.001)\n",
+ "\n",
+ "\n",
+ "def pvfun(t):\n",
+ " ar_data = card_data.assign(Y_t=Y - t * D)\n",
+ " mod = pf.feols(\"Y_t ~ \" + zn + \" + \" + \" + \".join(xs), data=ar_data, vcov=\"HC2\")\n",
+ " Tstat = mod.tstat().loc[zn]\n",
+ " return (1 - sp.stats.norm.cdf(np.abs(Tstat))) * 2\n",
+ "\n",
+ "\n",
+ "Pvalue = Parallel(n_jobs=-1)(delayed(pvfun)(t) for t in CIrange)\n",
+ "Pvalue = np.stack(Pvalue)\n",
+ "lb, ub = CIrange[Pvalue >= 0.05].min(), CIrange[Pvalue >= 0.05].max()\n",
+ "\n",
+ "f, ax = plt.subplots(figsize=(6, 5))\n",
+ "ax.plot(CIrange, Pvalue)\n",
+ "ax.hlines(0.05, -0.1, 0.4, color=\"k\", linestyle=\"--\")\n",
+ "ax.vlines([lb, iv_est2, ub], 0, 1, color=\"grey\", linestyle=\"--\")\n",
+ "ax.set_title(\"Fieller-Anderson-Rubin Interval \\n Card's IV data\")\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 95,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "{'tsls': 0.13150383624468942,\n",
+ " 'lower CI': 0.02900000000000011,\n",
+ " 'upper CI': 0.28100000000000036}"
+ ]
+ },
+ "execution_count": 95,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "{\n",
+ " \"tsls\": iv_est2,\n",
+ " \"lower CI\": lb,\n",
+ " \"upper CI\": ub,\n",
+ "}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### bonus: control function"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# One-shot native IV estimate and heteroskedasticity-robust SE.\n",
+ "iv_res2.coef().loc[dn], iv_res2.se().loc[dn]\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "metrics",
+ "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": "3.11.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pyfixest/Chapter24IVfuzzyRD.ipynb b/pyfixest/Chapter24IVfuzzyRD.ipynb
new file mode 100644
index 0000000..3c54247
--- /dev/null
+++ b/pyfixest/Chapter24IVfuzzyRD.ipynb
@@ -0,0 +1,2745 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 24: Application of the Instrumental Variable Method: Fuzzy Regression Discontinuity Design"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from joblib import Parallel, delayed\n",
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import scipy as sp\n",
+ "import pyfixest as pf\n",
+ "\n",
+ "# viz\n",
+ "import matplotlib\n",
+ "import matplotlib.pyplot as plt\n",
+ "import seaborn as sns\n",
+ "\n",
+ "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
+ "plt.rc(\"font\", **font)\n",
+ "plt.rcParams[\"figure.figsize\"] = (10, 10)\n",
+ "%matplotlib inline\n",
+ "\n",
+ "from utils import *\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "%load_ext autoreload\n",
+ "%autoreload 1\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Asher Novosad (2020)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | r2012 | \n",
+ " 0 | \n",
+ " 1 | \n",
+ "
\n",
+ " \n",
+ " | t | \n",
+ " | \n",
+ " | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 4517 | \n",
+ " 1501 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 2821 | \n",
+ " 2593 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(figsize=(7, 5))\n",
+ "ax.plot(res.h, res.est, color=\"black\")\n",
+ "ax.fill_between(res.h, res.lb, res.ub, color=\"black\", alpha=0.2)\n",
+ "ax.hlines(0, 10, 80, color=\"black\", linestyle=\"--\")\n",
+ "ax.set_title(\"Asher-Novosad Roads Fuzzy RD\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Li et al (2015)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " outcome | \n",
+ " rv0 | \n",
+ " apply | \n",
+ " Z | \n",
+ " D | \n",
+ " left | \n",
+ " right | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 0 | \n",
+ " -0.366618 | \n",
+ " 1 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " -0.366618 | \n",
+ " 0.000000 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 0 | \n",
+ " -0.381168 | \n",
+ " 1 | \n",
+ " 0 | \n",
+ " 0 | \n",
+ " -0.381168 | \n",
+ " 0.000000 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 0 | \n",
+ " 0.632612 | \n",
+ " 1 | \n",
+ " 1 | \n",
+ " 1 | \n",
+ " 0.000000 | \n",
+ " 0.632612 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 0 | \n",
+ " 0.613000 | \n",
+ " 1 | \n",
+ " 1 | \n",
+ " 1 | \n",
+ " 0.000000 | \n",
+ " 0.613000 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 0 | \n",
+ " 0.991360 | \n",
+ " 1 | \n",
+ " 1 | \n",
+ " 1 | \n",
+ " 0.000000 | \n",
+ " 0.991360 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "f, ax = plt.subplots(figsize=(7, 5))\n",
+ "ax.plot(res.h, res.est, color=\"black\")\n",
+ "ax.fill_between(res.h, res.lb, res.ub, color=\"black\", alpha=0.2)\n",
+ "ax.hlines(0, 0.1, 1, color=\"black\", linestyle=\"--\")\n",
+ "ax.set_title(\"Li et al (2015) Fuzzy RD\")"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "metrics",
+ "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": "3.11.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pyfixest/Chapter25IVmendelian.ipynb b/pyfixest/Chapter25IVmendelian.ipynb
new file mode 100644
index 0000000..9501a84
--- /dev/null
+++ b/pyfixest/Chapter25IVmendelian.ipynb
@@ -0,0 +1,3119 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 25: Application of The Instrumental Variable Method: Mendelian Randomization"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from joblib import Parallel, delayed\n",
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import scipy as sp\n",
+ "import pyfixest as pf\n",
+ "\n",
+ "# viz\n",
+ "import matplotlib\n",
+ "import matplotlib.pyplot as plt\n",
+ "import seaborn as sns\n",
+ "\n",
+ "font = {\"family\": \"IBM Plex Sans Condensed\", \"weight\": \"normal\", \"size\": 10}\n",
+ "plt.rc(\"font\", **font)\n",
+ "plt.rcParams[\"figure.figsize\"] = (10, 10)\n",
+ "%matplotlib inline\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "%load_ext autoreload\n",
+ "%autoreload 1\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def fisher_weight(est, se):\n",
+ " n, d = np.sum(est / se**2), np.sum(1 / se**2)\n",
+ " return n / d, np.sqrt(1 / d)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " Unnamed: 0 | \n",
+ " beta_exposure | \n",
+ " beta_outcome | \n",
+ " se_exposure | \n",
+ " se_outcome | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0 | \n",
+ " 14 | \n",
+ " -0.0051 | \n",
+ " 0.003490 | \n",
+ " 0.0066 | \n",
+ " 0.012048 | \n",
+ "
\n",
+ " \n",
+ " | 1 | \n",
+ " 15 | \n",
+ " -0.0254 | \n",
+ " 0.040681 | \n",
+ " 0.0051 | \n",
+ " 0.010801 | \n",
+ "
\n",
+ " \n",
+ " | 2 | \n",
+ " 17 | \n",
+ " 0.0077 | \n",
+ " -0.040866 | \n",
+ " 0.0073 | \n",
+ " 0.012936 | \n",
+ "
\n",
+ " \n",
+ " | 3 | \n",
+ " 22 | \n",
+ " 0.0173 | \n",
+ " 0.028683 | \n",
+ " 0.0059 | \n",
+ " 0.010865 | \n",
+ "
\n",
+ " \n",
+ " | 4 | \n",
+ " 58 | \n",
+ " 0.0063 | \n",
+ " -0.009085 | \n",
+ " 0.0095 | \n",
+ " 0.017261 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "bmisbp[\"dotsize\"] = 1 / bmisbp.se_exposure**2\n",
+ "\n",
+ "\n",
+ "# Plot miles per gallon against horsepower with other semantics\n",
+ "sns.regplot(\n",
+ " x=\"beta_exposure\",\n",
+ " y=\"beta_outcome\", # size=\"dotsize\",\n",
+ " data=bmisbp,\n",
+ " ci=None,\n",
+ " scatter_kws={\"s\": bmisbp.dotsize / 1000},\n",
+ ")"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "metrics",
+ "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": "3.11.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/pyfixest/Chapter26principalStratification.ipynb b/pyfixest/Chapter26principalStratification.ipynb
new file mode 100644
index 0000000..8f2bb1c
--- /dev/null
+++ b/pyfixest/Chapter26principalStratification.ipynb
@@ -0,0 +1,445 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 26: Principal Stratification"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import matplotlib.pyplot as plt\n",
+ "import pyfixest as pf\n",
+ "\n",
+ "np.random.seed(42)\n",
+ "\n",
+ "%load_ext watermark\n",
+ "%watermark --iversions\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Partial ID\n",
+ "\n",
+ "### SACE with grouped data"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(0.03698057577458183, 0.19404122726930068)"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "## Chapter 26.4.2\n",
+ "## truncation by death example\n",
+ "## data from Yang and Small (2016)\n",
+ "pi11 = 277 / (277 + 152)\n",
+ "pi00 = 109 / (109 + 322)\n",
+ "pi10 = 1 - pi11 - pi00\n",
+ "\n",
+ "## observed means\n",
+ "mu11 = 54 / 322\n",
+ "mu01 = 59 / 277\n",
+ "\n",
+ "## bounds on the treatment potential outcomes\n",
+ "lb = ((pi11 + pi10) * mu11 - pi10) / pi11\n",
+ "ub = ((pi11 + pi10) * mu11) / pi11\n",
+ "lb, ub"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(-0.17601581411711492, -0.018955162622396077)"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "## bounds on the sace\n",
+ "lb - mu01, ub - mu01"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### SACE with microdata"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "## function for SACE with a binary outcome\n",
+ "def SACE01_fit(Z, M, Y):\n",
+ " ## summary statistics\n",
+ " pM1 = np.mean(M[Z == 1])\n",
+ " pM0 = np.mean(M[Z == 0])\n",
+ " mu11 = np.mean(Y[(Z == 1) & (M == 1)])\n",
+ " mu01 = np.mean(Y[(Z == 0) & (M == 1)])\n",
+ " ## proporitions of the strata\n",
+ " pi11 = pM0\n",
+ " pi00 = 1 - pM1\n",
+ " pi10 = 1 - pi11 - pi00\n",
+ " ## bounds on the treatment potential outcomes\n",
+ " lb = ((pi11 + pi10) * mu11 - pi10) / pi11\n",
+ " ub = ((pi11 + pi10) * mu11) / pi11\n",
+ " ## bounds on the SACE\n",
+ " return np.array([lb - mu01, ub - mu01])\n",
+ "\n",
+ "\n",
+ "def SACE01(Z, M, Y, nboot=1e3):\n",
+ " from joblib import Parallel, delayed\n",
+ "\n",
+ " bounds = SACE01_fit(Z, M, Y)\n",
+ " n = len(Z)\n",
+ "\n",
+ " def bootfn(*args):\n",
+ " idx = np.random.choice(n, n, replace=True)\n",
+ " return SACE01_fit(Z[idx], M[idx], Y[idx])\n",
+ "\n",
+ " res = Parallel(n_jobs=-1, verbose=0)(delayed(bootfn)() for _ in range(int(nboot)))\n",
+ " res = np.vstack(res)\n",
+ " b_se = np.std(res, axis=0)\n",
+ " # IM CI\n",
+ " l_ci, u_ci = bounds[0] - 1.96 * b_se[0], bounds[1] + 1.96 * b_se[1]\n",
+ " res = pd.DataFrame(\n",
+ " np.c_[bounds, b_se, np.array([l_ci, u_ci])],\n",
+ " columns=[\"est\", \"se\", \"ci\"],\n",
+ " index=[\"lb\", \"ub\"],\n",
+ " )\n",
+ " return res"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "## truncation by death example\n",
+ "## data from Yang and Small (2016)\n",
+ "Z = np.r_[np.repeat(1, 322 + 109), np.repeat(0, 277 + 152)]\n",
+ "\n",
+ "M = np.r_[np.repeat(1, 322), np.repeat(0, 109), np.repeat(1, 277), np.repeat(0, 152)]\n",
+ "Y = np.r_[\n",
+ " np.repeat(1, 54),\n",
+ " np.repeat(0, 268),\n",
+ " np.repeat(np.nan, 109),\n",
+ " np.repeat(1, 59),\n",
+ " np.repeat(0, 218),\n",
+ " np.repeat(np.nan, 152),\n",
+ "]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " est | \n",
+ " se | \n",
+ " ci | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | lb | \n",
+ " -0.176016 | \n",
+ " 0.055382 | \n",
+ " -0.284565 | \n",
+ "
\n",
+ " \n",
+ " | ub | \n",
+ " -0.018955 | \n",
+ " 0.036026 | \n",
+ " 0.051657 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | col_0 | \n",
+ " 0.0 | \n",
+ " 1.0 | \n",
+ "
\n",
+ " \n",
+ " | row_0 | \n",
+ " | \n",
+ " | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | 0.0 | \n",
+ " 299 | \n",
+ " 0 | \n",
+ "
\n",
+ " \n",
+ " | 1.0 | \n",
+ " 228 | \n",
+ " 372 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
\n",
+ "\n",
+ "
\n",
+ " \n",
+ " \n",
+ " | \n",
+ " est | \n",
+ " se | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | tau10 | \n",
+ " 0.167204 | \n",
+ " 0.101708 | \n",
+ "
\n",
+ " \n",
+ " | tau00 | \n",
+ " -0.095306 | \n",
+ " 0.151533 | \n",
+ "
\n",
+ " \n",
+ "
\n",
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "res = Parallel(n_jobs=-1)(delayed(simulation)(1, 1, 1) for _ in range(1000))\n",
+ "res = np.vstack(res)\n",
+ "print(res[:, 0].std(), res[:, 1].mean())\n",
+ "print(res[:, 3].std(), res[:, 4].mean())\n",
+ "\n",
+ "f, ax = plt.subplots(1, 2, figsize=(6, 3))\n",
+ "ax[0].hist(res[:, 0], bins=30, density=True)\n",
+ "ax[0].vlines(1, 0, 1, color=\"red\")\n",
+ "ax[0].set_title(\"NDE\")\n",
+ "ax[1].hist(res[:, 3], bins=30, density=True)\n",
+ "ax[1].vlines(\n",
+ " 1,\n",
+ " 0,\n",
+ " 1,\n",
+ " color=\"red\",\n",
+ ")\n",
+ "ax[1].set_title(\"NIE\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$\\theta_2$ = 0"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.16070039875959033 0.15894602890501858\n",
+ "0.07139184520607268 0.07184486066517198\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "res = Parallel(n_jobs=-1)(delayed(simulation)(1, 0, 1) for _ in range(1000))\n",
+ "res = np.vstack(res)\n",
+ "print(res[:, 0].std(), res[:, 1].mean())\n",
+ "print(res[:, 3].std(), res[:, 4].mean())\n",
+ "\n",
+ "f, ax = plt.subplots(1, 2, figsize=(6, 3))\n",
+ "ax[0].hist(res[:, 0], bins=30, density=True)\n",
+ "ax[0].vlines(1, 0, 3, color=\"red\")\n",
+ "ax[0].set_title(\"NDE\")\n",
+ "ax[1].hist(res[:, 3], bins=30, density=True)\n",
+ "ax[1].vlines(\n",
+ " 0,\n",
+ " 0,\n",
+ " 3,\n",
+ " color=\"red\",\n",
+ ")\n",
+ "ax[1].set_title(\"NIE\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "$\\beta_1 = 0$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.13398443810512395 0.1421209837224335\n",
+ "0.010519116540859337 0.012717706993520813\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "image/svg+xml": [
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "res = Parallel(n_jobs=-1)(delayed(simulation)(0, 0, 1) for _ in range(1000))\n",
+ "res = np.vstack(res)\n",
+ "print(res[:, 0].std(), res[:, 1].mean())\n",
+ "print(res[:, 3].std(), res[:, 4].mean())\n",
+ "\n",
+ "f, ax = plt.subplots(1, 2, figsize=(6, 3))\n",
+ "ax[0].hist(res[:, 0], bins=30, density=True)\n",
+ "ax[0].vlines(1, 0, 3, color=\"red\")\n",
+ "ax[0].set_title(\"NDE\")\n",
+ "ax[1].hist(res[:, 3], bins=30, density=True)\n",
+ "ax[1].vlines(\n",
+ " 0,\n",
+ " 0,\n",
+ " 3,\n",
+ " color=\"red\",\n",
+ ")\n",
+ "ax[1].set_title(\"NIE\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import formulaic as fm\n",
+ "\n",
+ "jobsdata = pd.read_csv(\"jobsdata.csv\")\n",
+ "X = (\n",
+ " fm.Formula(\n",
+ " \"\"\"\n",
+ " ~ econ_hard + depress1 + sex + age + occp + marital +\n",
+ " nonwhite + educ + income -1\n",
+ " \"\"\"\n",
+ " )\n",
+ " .get_model_matrix(data=jobsdata)\n",
+ " .values\n",
+ ")\n",
+ "Z, M, Y = jobsdata[[\"treat\", \"job_seek\", \"depress2\"]].values.T"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "\n",
+ "\n",
+ "
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+ " \n",
+ " \n",
+ " | \n",
+ " coef | \n",
+ " se | \n",
+ " t | \n",
+ "
\n",
+ " \n",
+ " \n",
+ " \n",
+ " | NDE | \n",
+ " -0.036789 | \n",
+ " 0.040794 | \n",
+ " -0.901813 | \n",
+ "
\n",
+ " \n",
+ " | NIE | \n",
+ " -0.013733 | \n",
+ " 0.009008 | \n",
+ " -1.524646 | \n",
+ "
\n",
+ " \n",
+ "
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+ "