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"Target units: ate\n",
"\n",
"## Estimate\n",
"Mean value: 3.987497536617294\n",
"Mean value: 4.122408234201723\n",
"p-value: [0, 0.001]\n",
"\n"
]
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"text": [
"Refute: Use a Placebo Treatment\n",
"Estimated effect:3.987497536617294\n",
"New effect:-0.025021095946670787\n",
"p value:0.86\n",
"Estimated effect:4.122408234201723\n",
"New effect:-0.022474970252860365\n",
"p value:0.92\n",
"\n"
]
}
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"<table class=\"simpletable\">\n",
"<caption>IV2SLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>income</td> <th> R-squared: </th> <td> 0.889</td> \n",
" <th>Dep. Variable:</th> <td>income</td> <th> R-squared: </th> <td> 0.904</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>IV2SLS</td> <th> Adj. R-squared: </th> <td> 0.889</td> \n",
" <th>Model:</th> <td>IV2SLS</td> <th> Adj. R-squared: </th> <td> 0.904</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Two Stage</td> <th> F-statistic: </th> <td> 1361.</td> \n",
" <th>Method:</th> <td>Two Stage</td> <th> F-statistic: </th> <td> 1876.</td> \n",
"</tr>\n",
"<tr>\n",
" <th></th> <td>Least Squares</td> <th> Prob (F-statistic):</th> <td>1.30e-188</td>\n",
" <th></th> <td>Least Squares</td> <th> Prob (F-statistic):</th> <td>2.04e-231</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Fri, 25 Oct 2024</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>14:43:26</td> <th> </th> <td> </td> \n",
" <th>Time:</th> <td>14:44:13</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 1000</td> <th> </th> <td> </td> \n",
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" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[0.025</th> <th>0.975]</th> \n",
"</tr>\n",
"<tr>\n",
" <th>Intercept</th> <td> 9.6387</td> <td> 0.977</td> <td> 9.865</td> <td> 0.000</td> <td> 7.721</td> <td> 11.556</td>\n",
" <th>Intercept</th> <td> 8.9729</td> <td> 0.877</td> <td> 10.231</td> <td> 0.000</td> <td> 7.252</td> <td> 10.694</td>\n",
"</tr>\n",
"<tr>\n",
" <th>education</th> <td> 3.9875</td> <td> 0.108</td> <td> 36.889</td> <td> 0.000</td> <td> 3.775</td> <td> 4.200</td>\n",
" <th>education</th> <td> 4.1224</td> <td> 0.095</td> <td> 43.308</td> <td> 0.000</td> <td> 3.936</td> <td> 4.309</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td> 2.539</td> <th> Durbin-Watson: </th> <td> 1.959</td>\n",
" <th>Omnibus:</th> <td> 1.392</td> <th> Durbin-Watson: </th> <td> 1.913</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.281</td> <th> Jarque-Bera (JB): </th> <td> 2.587</td>\n",
" <th>Prob(Omnibus):</th> <td> 0.499</td> <th> Jarque-Bera (JB): </th> <td> 1.460</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 0.121</td> <th> Prob(JB): </th> <td> 0.274</td>\n",
" <th>Skew:</th> <td>-0.067</td> <th> Prob(JB): </th> <td> 0.482</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 2.940</td> <th> Cond. No. </th> <td> 24.5</td>\n",
" <th>Kurtosis:</th> <td> 2.870</td> <th> Cond. No. </th> <td> 25.1</td>\n",
"</tr>\n",
"</table>"
],
"text/latex": [
"\\begin{center}\n",
"\\begin{tabular}{lclc}\n",
"\\toprule\n",
"\\textbf{Dep. Variable:} & income & \\textbf{ R-squared: } & 0.889 \\\\\n",
"\\textbf{Model:} & IV2SLS & \\textbf{ Adj. R-squared: } & 0.889 \\\\\n",
"\\textbf{Method:} & Two Stage & \\textbf{ F-statistic: } & 1361. \\\\\n",
"\\textbf{} & Least Squares & \\textbf{ Prob (F-statistic):} & 1.30e-188 \\\\\n",
"\\textbf{Dep. Variable:} & income & \\textbf{ R-squared: } & 0.904 \\\\\n",
"\\textbf{Model:} & IV2SLS & \\textbf{ Adj. R-squared: } & 0.904 \\\\\n",
"\\textbf{Method:} & Two Stage & \\textbf{ F-statistic: } & 1876. \\\\\n",
"\\textbf{} & Least Squares & \\textbf{ Prob (F-statistic):} & 2.04e-231 \\\\\n",
"\\textbf{Date:} & Fri, 25 Oct 2024 & \\textbf{ } & \\\\\n",
"\\textbf{Time:} & 14:43:26 & \\textbf{ } & \\\\\n",
"\\textbf{Time:} & 14:44:13 & \\textbf{ } & \\\\\n",
"\\textbf{No. Observations:} & 1000 & \\textbf{ } & \\\\\n",
"\\textbf{Df Residuals:} & 998 & \\textbf{ } & \\\\\n",
"\\textbf{Df Model:} & 1 & \\textbf{ } & \\\\\n",
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"\\begin{tabular}{lcccccc}\n",
" & \\textbf{coef} & \\textbf{std err} & \\textbf{t} & \\textbf{P$> |$t$|$} & \\textbf{[0.025} & \\textbf{0.975]} \\\\\n",
"\\midrule\n",
"\\textbf{Intercept} & 9.6387 & 0.977 & 9.865 & 0.000 & 7.721 & 11.556 \\\\\n",
"\\textbf{education} & 3.9875 & 0.108 & 36.889 & 0.000 & 3.775 & 4.200 \\\\\n",
"\\textbf{Intercept} & 8.9729 & 0.877 & 10.231 & 0.000 & 7.252 & 10.694 \\\\\n",
"\\textbf{education} & 4.1224 & 0.095 & 43.308 & 0.000 & 3.936 & 4.309 \\\\\n",
"\\bottomrule\n",
"\\end{tabular}\n",
"\\begin{tabular}{lclc}\n",
"\\textbf{Omnibus:} & 2.539 & \\textbf{ Durbin-Watson: } & 1.959 \\\\\n",
"\\textbf{Prob(Omnibus):} & 0.281 & \\textbf{ Jarque-Bera (JB): } & 2.587 \\\\\n",
"\\textbf{Skew:} & 0.121 & \\textbf{ Prob(JB): } & 0.274 \\\\\n",
"\\textbf{Kurtosis:} & 2.940 & \\textbf{ Cond. No. } & 24.5 \\\\\n",
"\\textbf{Omnibus:} & 1.392 & \\textbf{ Durbin-Watson: } & 1.913 \\\\\n",
"\\textbf{Prob(Omnibus):} & 0.499 & \\textbf{ Jarque-Bera (JB): } & 1.460 \\\\\n",
"\\textbf{Skew:} & -0.067 & \\textbf{ Prob(JB): } & 0.482 \\\\\n",
"\\textbf{Kurtosis:} & 2.870 & \\textbf{ Cond. No. } & 25.1 \\\\\n",
"\\bottomrule\n",
"\\end{tabular}\n",
"%\\caption{IV2SLS Regression Results}\n",
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"\"\"\"\n",
" IV2SLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: income R-squared: 0.889\n",
"Model: IV2SLS Adj. R-squared: 0.889\n",
"Method: Two Stage F-statistic: 1361.\n",
" Least Squares Prob (F-statistic): 1.30e-188\n",
"Dep. Variable: income R-squared: 0.904\n",
"Model: IV2SLS Adj. R-squared: 0.904\n",
"Method: Two Stage F-statistic: 1876.\n",
" Least Squares Prob (F-statistic): 2.04e-231\n",
"Date: Fri, 25 Oct 2024 \n",
"Time: 14:43:26 \n",
"Time: 14:44:13 \n",
"No. Observations: 1000 \n",
"Df Residuals: 998 \n",
"Df Model: 1 \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept 9.6387 0.977 9.865 0.000 7.721 11.556\n",
"education 3.9875 0.108 36.889 0.000 3.775 4.200\n",
"Intercept 8.9729 0.877 10.231 0.000 7.252 10.694\n",
"education 4.1224 0.095 43.308 0.000 3.936 4.309\n",
"==============================================================================\n",
"Omnibus: 2.539 Durbin-Watson: 1.959\n",
"Prob(Omnibus): 0.281 Jarque-Bera (JB): 2.587\n",
"Skew: 0.121 Prob(JB): 0.274\n",
"Kurtosis: 2.940 Cond. No. 24.5\n",
"Omnibus: 1.392 Durbin-Watson: 1.913\n",
"Prob(Omnibus): 0.499 Jarque-Bera (JB): 1.460\n",
"Skew: -0.067 Prob(JB): 0.482\n",
"Kurtosis: 2.870 Cond. No. 25.1\n",
"==============================================================================\n",
"\"\"\""
]
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