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"Target units: ate\n",
"\n",
"## Estimate\n",
"Mean value: 4.130869232919477\n",
"Mean value: 4.15323575009908\n",
"p-value: [0, 0.001]\n",
"\n"
]
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"output_type": "stream",
"text": [
"Refute: Use a Placebo Treatment\n",
"Estimated effect:4.130869232919477\n",
"New effect:0.019853343491346664\n",
"p value:0.94\n",
"Estimated effect:4.15323575009908\n",
"New effect:0.05746995723853913\n",
"p value:0.8200000000000001\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> 0.904</td> \n",
" <th>Dep. Variable:</th> <td>income</td> <th> R-squared: </th> <td> 0.903</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>IV2SLS</td> <th> Adj. R-squared: </th> <td> 0.904</td> \n",
" <th>Model:</th> <td>IV2SLS</td> <th> Adj. R-squared: </th> <td> 0.902</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Two Stage</td> <th> F-statistic: </th> <td> 1815.</td> \n",
" <th>Method:</th> <td>Two Stage</td> <th> F-statistic: </th> <td> 1853.</td> \n",
"</tr>\n",
"<tr>\n",
" <th></th> <td>Least Squares</td> <th> Prob (F-statistic):</th> <td>8.27e-227</td>\n",
" <th></th> <td>Least Squares</td> <th> Prob (F-statistic):</th> <td>9.90e-230</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Sat, 19 Oct 2024</td> <th> </th> <td> </td> \n",
" <th>Date:</th> <td>Tue, 22 Oct 2024</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>23:43:13</td> <th> </th> <td> </td> \n",
" <th>Time:</th> <td>01:09:22</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> 8.7593</td> <td> 0.893</td> <td> 9.811</td> <td> 0.000</td> <td> 7.007</td> <td> 10.511</td>\n",
" <th>Intercept</th> <td> 8.8450</td> <td> 0.899</td> <td> 9.836</td> <td> 0.000</td> <td> 7.080</td> <td> 10.610</td>\n",
"</tr>\n",
"<tr>\n",
" <th>education</th> <td> 4.1309</td> <td> 0.097</td> <td> 42.604</td> <td> 0.000</td> <td> 3.941</td> <td> 4.321</td>\n",
" <th>education</th> <td> 4.1532</td> <td> 0.096</td> <td> 43.050</td> <td> 0.000</td> <td> 3.964</td> <td> 4.343</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td> 3.915</td> <th> Durbin-Watson: </th> <td> 2.128</td>\n",
" <th>Omnibus:</th> <td> 0.661</td> <th> Durbin-Watson: </th> <td> 1.971</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.141</td> <th> Jarque-Bera (JB): </th> <td> 4.009</td>\n",
" <th>Prob(Omnibus):</th> <td> 0.719</td> <th> Jarque-Bera (JB): </th> <td> 0.575</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 0.096</td> <th> Prob(JB): </th> <td> 0.135</td>\n",
" <th>Skew:</th> <td>-0.054</td> <th> Prob(JB): </th> <td> 0.750</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 3.243</td> <th> Cond. No. </th> <td> 25.2</td>\n",
" <th>Kurtosis:</th> <td> 3.048</td> <th> Cond. No. </th> <td> 25.9</td>\n",
"</tr>\n",
"</table>"
],
"text/latex": [
"\\begin{center}\n",
"\\begin{tabular}{lclc}\n",
"\\toprule\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: } & 1815. \\\\\n",
"\\textbf{} & Least Squares & \\textbf{ Prob (F-statistic):} & 8.27e-227 \\\\\n",
"\\textbf{Date:} & Sat, 19 Oct 2024 & \\textbf{ } & \\\\\n",
"\\textbf{Time:} & 23:43:13 & \\textbf{ } & \\\\\n",
"\\textbf{Dep. Variable:} & income & \\textbf{ R-squared: } & 0.903 \\\\\n",
"\\textbf{Model:} & IV2SLS & \\textbf{ Adj. R-squared: } & 0.902 \\\\\n",
"\\textbf{Method:} & Two Stage & \\textbf{ F-statistic: } & 1853. \\\\\n",
"\\textbf{} & Least Squares & \\textbf{ Prob (F-statistic):} & 9.90e-230 \\\\\n",
"\\textbf{Date:} & Tue, 22 Oct 2024 & \\textbf{ } & \\\\\n",
"\\textbf{Time:} & 01:09:22 & \\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} & 8.7593 & 0.893 & 9.811 & 0.000 & 7.007 & 10.511 \\\\\n",
"\\textbf{education} & 4.1309 & 0.097 & 42.604 & 0.000 & 3.941 & 4.321 \\\\\n",
"\\textbf{Intercept} & 8.8450 & 0.899 & 9.836 & 0.000 & 7.080 & 10.610 \\\\\n",
"\\textbf{education} & 4.1532 & 0.096 & 43.050 & 0.000 & 3.964 & 4.343 \\\\\n",
"\\bottomrule\n",
"\\end{tabular}\n",
"\\begin{tabular}{lclc}\n",
"\\textbf{Omnibus:} & 3.915 & \\textbf{ Durbin-Watson: } & 2.128 \\\\\n",
"\\textbf{Prob(Omnibus):} & 0.141 & \\textbf{ Jarque-Bera (JB): } & 4.009 \\\\\n",
"\\textbf{Skew:} & 0.096 & \\textbf{ Prob(JB): } & 0.135 \\\\\n",
"\\textbf{Kurtosis:} & 3.243 & \\textbf{ Cond. No. } & 25.2 \\\\\n",
"\\textbf{Omnibus:} & 0.661 & \\textbf{ Durbin-Watson: } & 1.971 \\\\\n",
"\\textbf{Prob(Omnibus):} & 0.719 & \\textbf{ Jarque-Bera (JB): } & 0.575 \\\\\n",
"\\textbf{Skew:} & -0.054 & \\textbf{ Prob(JB): } & 0.750 \\\\\n",
"\\textbf{Kurtosis:} & 3.048 & \\textbf{ Cond. No. } & 25.9 \\\\\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: 0.904\n",
"Model: IV2SLS Adj. R-squared: 0.904\n",
"Method: Two Stage F-statistic: 1815.\n",
" Least Squares Prob (F-statistic): 8.27e-227\n",
"Date: Sat, 19 Oct 2024 \n",
"Time: 23:43:13 \n",
"Dep. Variable: income R-squared: 0.903\n",
"Model: IV2SLS Adj. R-squared: 0.902\n",
"Method: Two Stage F-statistic: 1853.\n",
" Least Squares Prob (F-statistic): 9.90e-230\n",
"Date: Tue, 22 Oct 2024 \n",
"Time: 01:09:22 \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 8.7593 0.893 9.811 0.000 7.007 10.511\n",
"education 4.1309 0.097 42.604 0.000 3.941 4.321\n",
"Intercept 8.8450 0.899 9.836 0.000 7.080 10.610\n",
"education 4.1532 0.096 43.050 0.000 3.964 4.343\n",
"==============================================================================\n",
"Omnibus: 3.915 Durbin-Watson: 2.128\n",
"Prob(Omnibus): 0.141 Jarque-Bera (JB): 4.009\n",
"Skew: 0.096 Prob(JB): 0.135\n",
"Kurtosis: 3.243 Cond. No. 25.2\n",
"Omnibus: 0.661 Durbin-Watson: 1.971\n",
"Prob(Omnibus): 0.719 Jarque-Bera (JB): 0.575\n",
"Skew: -0.054 Prob(JB): 0.750\n",
"Kurtosis: 3.048 Cond. No. 25.9\n",
"==============================================================================\n",
"\"\"\""
]
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