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@SandraMartinezGutierrez
SandraMartinezGutierrez committed Mar 8, 2022
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138 changes: 69 additions & 69 deletions Julia_Notebooks/.ipynb_checkpoints/Julia_pm2_notebook_jannis-checkpoint.ipynb
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{
"cell_type": "code",
"execution_count": 14,
"id": "339de597",
"id": "9dd1e0db",
"metadata": {},
"outputs": [
{
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},
{
"cell_type": "code",
"execution_count": 21,
"execution_count": 77,
"id": "48763755",
"metadata": {},
"outputs": [
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"────────────────────────────────────────────────────────────────────────────────\n",
" Coef. Std. Error t Pr(>|t|) Lower 95% Upper 95%\n",
"────────────────────────────────────────────────────────────────────────────────\n",
"(Intercept) 1.23713e-17 0.0041763 0.00 1.0000 -0.00829952 0.00829952\n",
"r_D -0.0502399 0.0151951 -3.31 0.0014 -0.080437 -0.0200428\n",
"(Intercept) -5.44341e-18 0.00417979 -0.00 1.0000 -0.00830646 0.00830646\n",
"r_D -0.0500007 0.0152165 -3.29 0.0015 -0.0802403 -0.0197611\n",
"────────────────────────────────────────────────────────────────────────────────"
]
},
"execution_count": 21,
"execution_count": 77,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Seat values for Lasso\n",
"\n",
"lasso_model = fit(LassoModel, term(:Y) ~ sum(term.(names(data[!, Not([\"Y\", \"D\"])]))), data; α = 0.9999)\n",
"lasso_model = fit(LassoModel, term(:Y) ~ sum(term.(names(data[!, Not([\"Y\", \"D\"])]))), data; α = 0.8)\n",
"r_Y = residuals(lasso_model)\n",
"r_Y = DataFrame([r_Y], [:r_Y])\n",
"\n",
"# Part. out d\n",
"\n",
"lasso_model = fit(LassoModel, term(:D) ~ sum(term.(names(data[!, Not([\"Y\", \"D\"])]))), data; α = 0.9999)\n",
"lasso_model = fit(LassoModel, term(:D) ~ sum(term.(names(data[!, Not([\"Y\", \"D\"])]))), data; α = 0.8)\n",
"r_D = residuals(lasso_model)\n",
"r_D = DataFrame([r_D], [:r_D])\n",
"\n",
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},
{
"cell_type": "code",
"execution_count": 22,
"execution_count": 78,
"id": "47debbc4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-0.02004279098812973"
"-0.01976108418900473"
]
},
"execution_count": 22,
"execution_count": 78,
"metadata": {},
"output_type": "execute_result"
}
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},
{
"cell_type": "code",
"execution_count": 23,
"execution_count": 79,
"id": "c4e19d41",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Coefficient for D via partialling-out using lasso is: -0.05023991997750313\n"
"Coefficient for D via partialling-out using lasso is: -0.05000069917512743\n"
]
}
],
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},
{
"cell_type": "code",
"execution_count": 24,
"execution_count": 87,
"id": "cd77ef49",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1×4 Named Matrix{Float64}\n",
"A ╲ B │ 1 2 3 4\n",
"──────┼───────────────────\n",
"LASSO │ 0.0 0.0 0.0 0.0"
" A ╲ B │ 1 2 3 4\n",
"─────────────┼───────────────────\n",
"DOUBLE LASSO │ 0.0 0.0 0.0 0.0"
]
},
"execution_count": 24,
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"table_2 = NamedArray(zeros(1, 4))\n",
"setnames!(table_2, [\"LASSO\"], 1)\n",
"setnames!(table_2, [\"DOUBLE LASSO\"], 1)\n",
"table_2"
]
},
{
"cell_type": "code",
"execution_count": 25,
"execution_count": 88,
"id": "17fbb3c1",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1×4 Named Matrix{Float64}\n",
"A ╲ B │ 1 2 3 4\n",
"──────┼───────────────────────────────────────────────\n",
"LASSO │ -0.0502399 0.0151951 -0.080437 -0.0200428"
" A ╲ B │ 1 2 3 4\n",
"─────────────┼───────────────────────────────────────────────\n",
"DOUBLE LASSO │ -0.0500007 0.0152165 -0.0802403 -0.0197611"
]
},
"execution_count": 25,
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
}
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},
{
"cell_type": "code",
"execution_count": 26,
"execution_count": 89,
"id": "0aad650b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div class=\"data-frame\"><p>1 rows × 5 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>model</th><th>Estimator</th><th>Std. Error</th><th>lower bound CI</th><th>upper bound CI</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>LASSO</td><td>-0.0502399</td><td>0.0151951</td><td>-0.080437</td><td>-0.0200428</td></tr></tbody></table></div>"
"<div class=\"data-frame\"><p>1 rows × 5 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>model</th><th>Estimator</th><th>Std. Error</th><th>lower bound CI</th><th>upper bound CI</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>DOUBLE LASSO</td><td>-0.0500007</td><td>0.0152165</td><td>-0.0802403</td><td>-0.0197611</td></tr></tbody></table></div>"
],
"text/latex": [
"\\begin{tabular}{r|ccccc}\n",
"\t& model & Estimator & Std. Error & lower bound CI & upper bound CI\\\\\n",
"\t\\hline\n",
"\t& String & Float64 & Float64 & Float64 & Float64\\\\\n",
"\t\\hline\n",
"\t1 & LASSO & -0.0502399 & 0.0151951 & -0.080437 & -0.0200428 \\\\\n",
"\t1 & DOUBLE LASSO & -0.0500007 & 0.0152165 & -0.0802403 & -0.0197611 \\\\\n",
"\\end{tabular}\n"
],
"text/plain": [
"\u001b[1m1×5 DataFrame\u001b[0m\n",
"\u001b[1m Row \u001b[0m│\u001b[1m model \u001b[0m\u001b[1m Estimator \u001b[0m\u001b[1m Std. Error \u001b[0m\u001b[1m lower bound CI \u001b[0m\u001b[1m upper bound CI \u001b[0m\n",
"\u001b[1m \u001b[0m│\u001b[90m String \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
"─────┼────────────────────────────────────────────────────────────────\n",
" 1 │ LASSO -0.0502399 0.0151951 -0.080437 -0.0200428"
"\u001b[1m Row \u001b[0m│\u001b[1m model \u001b[0m\u001b[1m Estimator \u001b[0m\u001b[1m Std. Error \u001b[0m\u001b[1m lower bound CI \u001b[0m\u001b[1m upper bound CI \u001b[0m\n",
"\u001b[1m \u001b[0m│\u001b[90m String \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
"─────┼──────────────────────────────────────────────────────────────────────\n",
" 1 │ DOUBLE LASSO -0.0500007 0.0152165 -0.0802403 -0.0197611"
]
},
"execution_count": 26,
"execution_count": 89,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"table_2_pandas = DataFrame( table_2, [ :\"Estimator\", :\"Std. Error\", :\"lower bound CI\", :\"upper bound CI\"])\n",
"model_2 = DataFrame(model = [\"LASSO\"])\n",
"model_2 = DataFrame(model = [\"DOUBLE LASSO\"])\n",
"table_2_pandas = hcat(model_2,table_2_pandas)\n",
"table_2_pandas"
]
},
{
"cell_type": "code",
"execution_count": 39,
"execution_count": 90,
"id": "c1caa31d",
"metadata": {},
"outputs": [
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" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <td style = \"text-align: center;\">LASSO</td>\n",
" <td style = \"text-align: center;\">-0.05024</td>\n",
" <td style = \"text-align: center;\">0.015195</td>\n",
" <td style = \"text-align: center;\">-0.080437</td>\n",
" <td style = \"text-align: center;\">-0.020043</td>\n",
" <td style = \"text-align: center;\">DOUBLE LASSO</td>\n",
" <td style = \"text-align: center;\">-0.050001</td>\n",
" <td style = \"text-align: center;\">0.015217</td>\n",
" <td style = \"text-align: center;\">-0.08024</td>\n",
" <td style = \"text-align: center;\">-0.019761</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
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},
{
"cell_type": "code",
"execution_count": 35,
"execution_count": 91,
"id": "56ba8e89",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2×4 Named Matrix{Float64}\n",
"vcat ╲ B │ 1 2 3 4\n",
"─────────┼───────────────────────────────────────────────────\n",
"OLS │ -0.00937799 0.0298877 -0.0706002 0.0518442\n",
"LASSO │ -0.0502399 0.0151951 -0.080437 -0.0200428"
" vcat ╲ B │ 1 2 3 4\n",
"─────────────┼───────────────────────────────────────────────────\n",
"OLS │ -0.00937799 0.0298877 -0.0706002 0.0518442\n",
"DOUBLE LASSO │ -0.0500007 0.0152165 -0.0802403 -0.0197611"
]
},
"execution_count": 35,
"execution_count": 91,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"table_3 = vcat(table_1, table_2)\n",
"setnames!(table_3, [\"OLS\", \"LASSO\"], 1)\n",
"setnames!(table_3, [\"OLS\", \"DOUBLE LASSO\"], 1)\n",
"table_3"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "981f7a24",
"execution_count": 92,
"id": "84462180",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div class=\"data-frame\"><p>2 rows × 5 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>model</th><th>Estimator</th><th>Std. Error</th><th>lower bound CI</th><th>upper bound CI</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>OLS</td><td>-0.00937799</td><td>0.0298877</td><td>-0.0706002</td><td>0.0518442</td></tr><tr><th>2</th><td>LASSO</td><td>-0.0502399</td><td>0.0151951</td><td>-0.080437</td><td>-0.0200428</td></tr></tbody></table></div>"
"<div class=\"data-frame\"><p>2 rows × 5 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>model</th><th>Estimator</th><th>Std. Error</th><th>lower bound CI</th><th>upper bound CI</th></tr><tr><th></th><th title=\"String\">String</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody><tr><th>1</th><td>OLS</td><td>-0.00937799</td><td>0.0298877</td><td>-0.0706002</td><td>0.0518442</td></tr><tr><th>2</th><td>DOUBLE LASSO</td><td>-0.0500007</td><td>0.0152165</td><td>-0.0802403</td><td>-0.0197611</td></tr></tbody></table></div>"
],
"text/latex": [
"\\begin{tabular}{r|ccccc}\n",
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"\t& String & Float64 & Float64 & Float64 & Float64\\\\\n",
"\t\\hline\n",
"\t1 & OLS & -0.00937799 & 0.0298877 & -0.0706002 & 0.0518442 \\\\\n",
"\t2 & LASSO & -0.0502399 & 0.0151951 & -0.080437 & -0.0200428 \\\\\n",
"\t2 & DOUBLE LASSO & -0.0500007 & 0.0152165 & -0.0802403 & -0.0197611 \\\\\n",
"\\end{tabular}\n"
],
"text/plain": [
"\u001b[1m2×5 DataFrame\u001b[0m\n",
"\u001b[1m Row \u001b[0m│\u001b[1m model \u001b[0m\u001b[1m Estimator \u001b[0m\u001b[1m Std. Error \u001b[0m\u001b[1m lower bound CI \u001b[0m\u001b[1m upper bound CI \u001b[0m\n",
"\u001b[1m \u001b[0m│\u001b[90m String \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
"─────┼─────────────────────────────────────────────────────────────────\n",
" 1 │ OLS -0.00937799 0.0298877 -0.0706002 0.0518442\n",
" 2 │ LASSO -0.0502399 0.0151951 -0.080437 -0.0200428"
"\u001b[1m Row \u001b[0m│\u001b[1m model \u001b[0m\u001b[1m Estimator \u001b[0m\u001b[1m Std. Error \u001b[0m\u001b[1m lower bound CI \u001b[0m\u001b[1m upper bound CI \u001b[0m\n",
"\u001b[1m \u001b[0m│\u001b[90m String \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\u001b[90m Float64 \u001b[0m\n",
"─────┼───────────────────────────────────────────────────────────────────────\n",
" 1 │ OLS -0.00937799 0.0298877 -0.0706002 0.0518442\n",
" 2 │ DOUBLE LASSO -0.0500007 0.0152165 -0.0802403 -0.0197611"
]
},
"execution_count": 36,
"execution_count": 92,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"table_3_pandas = DataFrame( table_3, [ :\"Estimator\", :\"Std. Error\", :\"lower bound CI\", :\"upper bound CI\"])\n",
"model_3 = DataFrame(model = [\"OLS\", \"LASSO\"])\n",
"model_3 = DataFrame(model = [\"OLS\", \"DOUBLE LASSO\"])\n",
"table_3_pandas = hcat(model_3, table_3_pandas)\n",
"table_3_pandas"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "e6b8b04d",
"execution_count": 93,
"id": "33d2533b",
"metadata": {},
"outputs": [
{
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" <td style = \"text-align: center;\">0.051844</td>\n",
" </tr>\n",
" <tr>\n",
" <td style = \"text-align: center;\">LASSO</td>\n",
" <td style = \"text-align: center;\">-0.05024</td>\n",
" <td style = \"text-align: center;\">0.015195</td>\n",
" <td style = \"text-align: center;\">-0.080437</td>\n",
" <td style = \"text-align: center;\">-0.020043</td>\n",
" <td style = \"text-align: center;\">DOUBLE LASSO</td>\n",
" <td style = \"text-align: center;\">-0.050001</td>\n",
" <td style = \"text-align: center;\">0.015217</td>\n",
" <td style = \"text-align: center;\">-0.08024</td>\n",
" <td style = \"text-align: center;\">-0.019761</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
Expand All @@ -1460,7 +1460,7 @@
"source": [
"The least square method provides a rather noisy estimate of the speed of convergence. We can not answer the question if poor countries grow faster than rich countries. The least square method does not work when the ratio $p/n$ is large.\n",
"\n",
"In sharp contrast, partialling-out via Lasso provides a more precise estimate. The Lasso based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-7.8\\%,-2.2\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis."
"In sharp contrast, partialling-out via Lasso provides a more precise estimate. The Lasso based point estimate is $-5\\%$ and the $95\\%$ confidence interval for the (annual) rate of convergence $[-8\\%,-1.9\\%]$ only includes negative numbers. This empirical evidence does support the convergence hypothesis."
]
},
{
Expand All @@ -1487,11 +1487,11 @@
" <td>0.051844</td>\n",
" </tr>\n",
" <tr>\n",
" <th>LASSO</th>\n",
" <td>-0.05024</td>\n",
" <td>0.015195</td>\n",
" <td>-0.080437</td>\n",
" <td>-0.020043</td>\n",
" <th>DOUBLE LASSO</th>\n",
" <td>-0.050001</td>\n",
" <td>0.015217</td>\n",
" <td>-0.08024</td>\n",
" <td>-0.019761</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>"
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