From f4968a7e54e951b9806e31ba73a212a9e090203d Mon Sep 17 00:00:00 2001 From: John Ryan Date: Tue, 16 Apr 2024 14:32:59 -0500 Subject: [PATCH] Add model notes, compare ln & Pln dists --- CompareIncomeDist.ipynb | 341 +++++----------------------------------- Model.md | 181 +++++++++++++++++++++ 2 files changed, 219 insertions(+), 303 deletions(-) create mode 100644 Model.md diff --git a/CompareIncomeDist.ipynb b/CompareIncomeDist.ipynb index b481e2c..7f91a6a 100644 --- a/CompareIncomeDist.ipynb +++ b/CompareIncomeDist.ipynb @@ -14,7 +14,7 @@ }, { "cell_type": "code", - "execution_count": 221, + "execution_count": 5, "id": "16ed9b3c", "metadata": {}, "outputs": [ @@ -22,10 +22,8 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/2m/db9b_l2950xckts1f65_rc2m0000gn/T/ipykernel_5865/831081070.py:5: DeprecationWarning:\n", - "\n", - "Importing display from IPython.core.display is deprecated since IPython 7.14, please import from IPython display\n", - "\n" + "/var/folders/2m/db9b_l2950xckts1f65_rc2m0000gn/T/ipykernel_54033/831081070.py:5: DeprecationWarning: Importing display from IPython.core.display is deprecated since IPython 7.14, please import from IPython display\n", + " from IPython.core.display import display, HTML\n" ] }, { @@ -485197,16 +485195,12 @@ "id": "3b4bdbe5", "metadata": {}, "source": [ - "## Analyze the performance of the income density estimates\n", - "\n", - "Outstanding problems:\n", - "1. maximum likelihood estimator which simultaneously estimates pareto parameter, cutoff and lognormal parameters either sends the cutoff to the end of the data or kinks more severely at the cutoff.\n", - "2. when including a pareto cutoff, the derivative of the income density, $\\hat{f}'$ is not continuous at the cutoff, which leads to a large discontinuity in the $\\theta_z$ and thereby $g_z$" + "## Analyze the performance of the income density estimates" ] }, { "cell_type": "code", - "execution_count": 225, + "execution_count": 1, "id": "9b7c81a3", "metadata": {}, "outputs": [], @@ -485215,67 +485209,43 @@ "from iot.inverse_optimal_tax import IOT\n", "import numpy as np\n", "# get data\n", - "data = gen_microdata()" + "data = gen_microdata()\n", + "data = data[data[\"expanded_income\"] > 0]" ] }, { "cell_type": "code", - "execution_count": 226, - "id": "bfa674b6", - "metadata": {}, - "outputs": [], - "source": [ - "data = data[data[\"expanded_income\"] > 0]\n", - "data[\"log_expanded_income\"] = np.log(data[\"expanded_income\"])\n" - ] - }, - { - "cell_type": "code", - "execution_count": 227, + "execution_count": 3, "id": "ac8fa99d", "metadata": {}, "outputs": [], "source": [ - "#instantiate IOT object with different distribution types\n", - "cutoff = 300_000\n", - "iot2 = IOT(data=data, income_measure=\"expanded_income\", dist_type=\"kde_pareto\", pareto_cutoff=cutoff)\n", - "# iot3 = IOT(data=data, income_measure=\"expanded_income\", dist_type=\"log_normal_pareto_mle\", pareto_cutoff=200_000)\n", - "# iot4 = IOT(data=data, income_measure=\"expanded_income\", dist_type=\"log_normal_pareto_sequential\", pareto_cutoff=200_000)\n", - "iot5 = IOT(data=data, income_measure=\"expanded_income\", dist_type=\"log_normal\") " - ] - }, - { - "cell_type": "code", - "execution_count": 228, - "id": "0a2e7159", - "metadata": {}, - "outputs": [], - "source": [ - "df2 = iot2.df()\n", - "# df3 = iot3.df()\n", - "# df4 = iot4.df()\n", - "df5 = iot5.df()" + "iot_ln = IOT(data=data, income_measure=\"expanded_income\", dist_type=\"log_normal\") \n", + "iot_Pln = IOT(data=data, income_measure=\"expanded_income\", dist_type=\"Pln\")\n", + "\n", + "df_ln = iot_ln.df()\n", + "df_Pln = iot_Pln.df()" ] }, { "cell_type": "code", - "execution_count": 229, + "execution_count": 7, "id": "e7dc7302", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 229, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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", + "image/png": 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", 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" ] @@ -485293,73 +485263,35 @@ "\n", "# plot weighted histogram of income from data.expanded_income, with weights s006\n", "fig, ax = plt.subplots()\n", - "ax.hist(data[\"expanded_income\"], bins=100, density=True, weights=data[\"s006\"])\n", + "ax.hist(data[\"expanded_income\"], bins=50, density=True, weights=data[\"s006\"])\n", "ax.set_xlabel(\"income\")\n", "ax.set_ylabel(\"density\")\n", - "ax.set_xlim(left=0)\n", - "# overlay the income distribution, f across z on the same plot, for the different dist_types\n", - "ax.plot(df2[\"z\"], df2[\"f\"], 'g-', label='kde pareto')\n", - "# ax.plot(df3[\"z\"], df3[\"f\"], 'r-', label='log normal mle')\n", - "# ax.plot(df4[\"z\"], df4[\"f\"], 'b-', label='log normal sequential')\n", - "ax.plot(df5[\"z\"], df5[\"f\"], 'y-', label='log normal')\n", + "ax.set_xlim(left=0, right=500_000)\n", + "ax.plot(df_ln[\"z\"], df_ln[\"f\"], 'y-', label='log normal')\n", + "ax.plot(df_Pln[\"z\"], df_Pln[\"f\"], 'm-', label='Pln')\n", + "\n", "ax.legend()" ] }, { "cell_type": "code", - "execution_count": 230, - "id": "293ba8a7", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(-49998.950000000004, 500000.0)" - ] - }, - "execution_count": 230, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# plot f_prime from df2 and df3\n", - "fig, ax = plt.subplots()\n", - "ax.plot(df2[\"z\"], df2[\"f_prime\"], 'g-', label='kde pareto')\n", - "ax.plot(df5[\"z\"], df5[\"f_prime\"], 'r-', label='log normal')\n", - "# ax.plot(df4[\"z\"], df4[\"f_prime\"], 'b-', label='log normal sequential')\n", - "ax.set_xlim(right=500_000)" - ] - }, - { - "cell_type": "code", - "execution_count": 231, + "execution_count": 10, "id": "7a0b71a4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[]" + "" ] }, - "execution_count": 231, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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MBAAgejhWVIqKinTjjTfq7rvvrvDnJSUlGjhwoIqKirRq1SrNnTtXc+bM0bhx45yKFNbat5fi4qTCQumbb0ynAQAgNBwrKhMnTtSIESPUqVOnCn++ZMkSbdq0SS+//LLOP/98XXHFFZo0aZJmzpypoqIip2KFrYSEEwNqv/zSbBYAAELF2BiV1atXq1OnTmrcuHHZa/3795fP59NXX31V6fv8fr98Pl+5R7Q4+fQPAADRwFhRyc/PL1dSJJU9z8/Pr/R9U6ZMUWpqatkjMzPT0ZxuEjg4xYBaAEC0CKqojB49Wh6Pp8rHFodnJBszZowKCwvLHnv37nX097kJR1TcgcHMABA6ccFsPGrUKA0ZMqTKbbKysqr1WRkZGfr000/LvVbwn/nhMzIyKn2f1+uV1+ut1u+INIEjKlu3Sn6/FKW7AQAQRYIqKunp6UpPT6+VX5yTk6PJkyfr22+/VaNGjSRJS5cuVUpKis4JzG6Gcpo1k+rVs+/5s2WLdN55phNFNyZ8AwDnOTZGZc+ePcrNzdWePXtUUlKi3Nxc5ebm6ujRo5Kkyy+/XOecc44GDx6sf/7zn3r//ff1u9/9TsOHD4/aIyan4/Fw+gcAEF2COqISjHHjxmnu3Lllz7t06SJJ+vDDD9WnTx/Fxsbq3Xff1d13362cnBydddZZuv322/Xwww87FSkidOokffwxA2oBANHBsaIyZ84czZkzp8ptWrRoocWLFzsVISJxRAUAEE2410+Y4Z4/AIBoQlEJMx072sv9+6WDB81mAQDAaRSVMJOcLAWuAP/nP81mAQDAaRSVMHTBBfbyiy/M5gAAwGkUlTBEUTGLmWkBIHQoKmEoO9teUlTMYsI3AHAeRSUM/WdKGn39tRRFN48GAEQhikoYSk+XAjeNZkAtACCSUVTCFONUAADRgKISpgJFZd06szkAAHASRSVMcUQFABANKCphKnDlz+bN0vffm80CAIBTKCphqkkTKSNDKi3lBoUAgMhFUQljnP4xgwnfACB0KCphLFBUPv/cbA4AAJxCUQlj3brZy08/NZsjWjEzLQA4j6ISxrp3t5ebNjFDLQAgMlFUwlijRlLLlvaYic8+M50GAIDaR1EJcxddZC/XrDGbAwAAJ1BUwlzg9M/atWZzAADgBIpKmDv5iAqXzQIAIg1FJcydf74UHy8dOCDt2mU6DQAAtYuiEuYSE6UuXex1xqkAACINRSUCME4ltDjFBgChQ1GJAFz5YwYTvgGA8ygqESBQVL74QvrhB7NZAACoTRSVCNCqldS0qXT8OKd/AACRhaISATweqVcve/0f/zCbBQCA2kRRiRCXXGIvP/7YbA4AAGoTRSVCBIrK6tX2KSAAACIBRSVCnHOOlJYmHTsmrV9vOg0AALWDohIhYmIYpwIAiDwUlQgSKCqMU3EWE74BQOhQVCJIYJzKypVSaanZLAAA1AaKSgTp0kWqW1c6dEj66ivTaSIfM9MCgPMoKhEkPv7E6Z8PPjCbBQCA2uBYUZk8ebJ69OihunXrql69ehVu4/F4TnnMnz/fqUhRoV8/e7lsmdkcAADUhjinPrioqEg33nijcnJy9OKLL1a63ezZszVgwICy55WVGlRPoKisWGHPpxIfbzQOAABnxLGiMnHiREnSnDlzqtyuXr16ysjIcCpG1OncWWrYUDp4UPr0U+nii00nAgCg5oyPURk+fLgaNmyobt26adasWbJOc+2n3++Xz+cr98AJMTHSpZfa65z+AQCEO6NF5eGHH9Zrr72mpUuX6vrrr9c999yjGTNmVPmeKVOmKDU1teyRmZkZorThg3EqAIBIEVRRGT16dIUDYE9+bNmypdqf9/vf/14XX3yxunTpogcffFC//e1v9cQTT1T5njFjxqiwsLDssXfv3mD+CFEhUFTWrJGOHDGbBQCAMxHUGJVRo0ZpyJAhVW6TlZVV4zDdu3fXpEmT5Pf75fV6K9zG6/VW+jPYWrWSsrKkHTvsWWoHDjSdKLIwMy0AhE5QRSU9PV3p6elOZVFubq7S0tIoIrWgXz/p+eelJUsoKk5hwjcAcJ5jV/3s2bNHhw4d0p49e1RSUqLc3FxJUps2bZSUlKR33nlHBQUFuuiii5SYmKilS5fq0Ucf1f333+9UpKjSv79dVP7+d+kPfzCdBgCAmnGsqIwbN05z584te96lSxdJ0ocffqg+ffooPj5eM2fO1IgRI2RZltq0aaPp06dr2LBhTkWKKv362XOobNtmP37yE9OJAAAInsc63fXALufz+ZSamqrCwkKlpKSYjuMql11mT6X/1FPSb35jOk3k+OILKTtbatZMYiw3ANRMdb+/jc+jAucExqYsXmw2BwAANUVRiWCBovLRR9LRo2azAABQExSVCNa2rdS6tVRUxORvAIDwRFGJYB6PdOWV9vqiRWazAABQExSVCHfyOJXwHjbtHuxHAAgdikqE691bqltX2r9fWr/edBoAAIJDUYlwiYn25G+S9PbbZrNEGmamBQDnUVSiwKBB9vLNN43GAAAgaBSVKPCzn0mxsdKGDdL27abTAABQfRSVKFC/vtSnj73OURUAQDihqESJa6+1l2+9ZTQGAABBoahEiWuusZerVkkFBWazAABQXRSVKNGsmXThhfYcIFz9AwAIFxSVKMLpHwBAuKGoRJHAZcrLl0s+n9EoYY2ZaQEgdCgqUaRDB6ldO/smhYsXm04T/pjwDQCcR1GJMtddZy8XLDCbAwCA6qCoRJlAUVm8WPrhB7NZAAA4HYpKlMnOlpo3l44dk5YsMZ0GAICqUVSijMdz4qjKG2+YzQIAwOlQVKLQ9dfby4UL7YG1AAC4FUUlCuXkSI0bS4WF0ocfmk4DAEDlKCpRKDb2xORvnP4BALgZRSVKBcapvPWWVFJiNErYYcI3AAgdikqU6tNHSkuTDhyQVq40nQYAgIpRVKJUfPyJOyoz+VvNMDMtADiPohLFTp6ltrTUbBYAACpCUYliP/2plJQkffON9NlnptMAAHAqikoUS0yUBg601zn9AwBwI4pKlAtM/vbGG1zNAgBwH4pKlLviCvvIyvbt0oYNptMAAFAeRSXKJSVJ/fvb60z+BgBwG4oKyk7/ME4FAOA2FBXoZz+T4uKkjRulr782ncb9GMsDAKFDUYHS0qTLLrPXOf1TfUz4BgDOo6hAUvnJ3wAAcAvHisquXbs0dOhQtWrVSnXq1FHr1q01fvx4FRUVldvuyy+/VK9evZSYmKjMzEw9/vjjTkVCFQYNso8QfP65tHu36TQAANgcKypbtmxRaWmpnnvuOX311Vd66qmn9Oyzz+qhhx4q28bn8+nyyy9XixYttG7dOj3xxBOaMGGCnn/+eadioRKNGkm9etnrb75pNgsAAAFxTn3wgAEDNGDAgLLnWVlZ2rp1q5555hlNmzZNkjRv3jwVFRVp1qxZSkhIUMeOHZWbm6vp06frjjvucCoaKnH99dLHH9vjVH7zG9NpAAAI8RiVwsJC1a9fv+z56tWrdckllyghIaHstf79+2vr1q367rvvKvwMv98vn89X7oHace219vKTT6T8fLNZAACQQlhU8vLyNGPGDN15551lr+Xn56tx48bltgs8z6/km3LKlClKTU0te2RmZjoXOspkZkrdutmX3771luk0AADUoKiMHj1aHo+nyseWLVvKvWffvn0aMGCAbrzxRg0bNuyMAo8ZM0aFhYVlj717957R56G8k+/9AwCAaUGPURk1apSGDBlS5TZZWVll6/v371ffvn3Vo0ePUwbJZmRkqKCgoNxrgecZGRkVfrbX65XX6w02NqrpuuukBx+UPvxQOnRIOulMHf6DCd8AIHSCLirp6elKT0+v1rb79u1T3759lZ2drdmzZysmpvwBnJycHI0dO1bHjx9XfHy8JGnp0qVq166d0tLSgo2GWtCmjdS5s/Tll9LChdJpOikAAI5ybIzKvn371KdPHzVv3lzTpk3TgQMHlJ+fX27sya233qqEhAQNHTpUX331lV599VX94Q9/0MiRI52KhWpg8rfqYWZaAHCeY5cnL126VHl5ecrLy1OzZs3K/cz6z7Hz1NRULVmyRMOHD1d2drYaNmyocePGcWmyYddfL02YIC1ZIh05IiUnm04EAIhWHssK7zPuPp9PqampKiwsVEpKiuk4EcGypHbtpG3bpPnzpZtvNp3IXdaulS66SGrVStqxw3QaAAhP1f3+5l4/OIXHw9U/AAB3oKigQoGisnix9MMPZrMAAKIXRQUVys6WmjeXjh2zx6oAAGACRQUV8nhOXP3D6R8AgCkUFVQqUFTeeUcqKjKbBQAQnSgqqFSPHlLjxtLhw/ZMtbCF93VyABBeKCqoVGysNGiQvc7kb6diwjcAcB5FBVUKXP3z1ltSSYnRKACAKERRQZX69JHS0qRvv5VWrjSdBgAQbSgqqFJ8vHT11fY6p38AAKFGUcFpBU7/LFgglZaazQIAiC4UFZzWT38qJSVJ33wjff656TQAgGhCUcFpJSZKAwfa60z+BgAIJYoKqiUw+duCBcwjAgAIHYoKquXKKyWvV8rLkzZsMJ3GLIoaAIQORQXVkpQk9e9vr3P1DwAgVCgqqLbA6Z833zSbwy2YmRYAnEdRQbVddZU9rf6XX0o7dphOAwCIBhQVVFv9+lLv3vY6R1UAAKFAUUFQrr3WXlJUAAChQFFBUAJ3U161SiooMBoFABAFKCoISrNm0oUX2pfovv226TQAgEhHUUHQOP0DAAgVigqCFigqy5dLhYVmswAAIhtFBUFr395+HD8uLV5sOk3oMTMtAIQORQU1wukfJnwDgFCgqKBGAkXl73+XfvzRbBYAQOSiqKBGuna1rwA6elRatsx0GgBApKKooEY8nhNzqkTz6R8AgLMoKqixwOmfhQul4mKzWQAAkYmighq75BL7/j8HD0qffGI6DQAgElFUUGNxcfYdlSVO/wAAnEFRwRm57jp7+cYbUmmp2SwAgMhDUcEZufxyKSVF+uYb+0aF0YAJ3wAgdCgqOCOJiScG1b7yitksocaEbwDgPMeKyq5duzR06FC1atVKderUUevWrTV+/HgVFRWV28bj8ZzyWLNmjVOx4IBbbrGXr7/O1T8AgNoV59QHb9myRaWlpXruuefUpk0bbdy4UcOGDdOxY8c0bdq0ctsuW7ZMHTt2LHveoEEDp2LBAZdeKjVsKB04IH3wgX06CACA2uBYURkwYIAGDBhQ9jwrK0tbt27VM888c0pRadCggTIyMpyKAofFx0s33CA9+6x9+oeiAgCoLSEdo1JYWKj69euf8vrVV1+tRo0aqWfPnlq4cGGVn+H3++Xz+co9YF7g9M+CBZLfbzYLACByhKyo5OXlacaMGbrzzjvLXktKStKTTz6p119/XYsWLVLPnj01aNCgKsvKlClTlJqaWvbIzMwMRXycRs+e0tlnSz6ffaNCAABqg8eygrvYcvTo0Xrssceq3Gbz5s1q37592fN9+/apd+/e6tOnj/785z9X+d5f/OIX2rlzp/7xj39U+HO/3y//Sf/L7vP5lJmZqcLCQqWkpATxJ0FtGzVKmj7dnlvljTdMp3HOJ5/YxewnP5G+/tp0GgAITz6fT6mpqaf9/g56jMqoUaM0ZMiQKrfJysoqW9+/f7/69u2rHj166Pnnnz/t53fv3l1Lly6t9Oder1der7faeRE6Q4bYRWXhQntgbXq66UQAgHAXdFFJT09XejW/gfbt26e+ffsqOztbs2fPVkzM6c805ebmqkmTJsHGggt06iR17Sp9/rn0l79II0eaTgQACHeOXfWzb98+9enTRy1atNC0adN04MCBsp8FrvCZO3euEhIS1KVLF0nSggULNGvWrNOeHoJ7DR1qF5UXX5RGjIjMSdGYmRYAQsexorJ06VLl5eUpLy9PzZo1K/ezk4fFTJo0Sbt371ZcXJzat2+vV199VTfccINTseCw//f/7IKyaZP02WdSt26mEzknEksYALhN0INp3aa6g3EQOoMHSy+/LN1xh/Tcc6bT1L6VK6VevaS2baWtW02nAYDwVN3vb+71g1o3dKi9nDdPOnzYaBQAQJijqKDW9e4tnXuudOyYPVYFAICaoqig1nk80n332et//KNUUmI2DwAgfFFU4IjbbpMaNJB27bLnVQEAoCYoKnBEnTpS4G4JTz7JJb0AgJqhqMAxw4dLXq895fyHH5pOAwAIRxQVOKZpU2nYMHt94sTIOaoSKX8OAAgHFBU4avRoKSFB+vhjacUK02lqFxO+AYDzKCpw1NlnnziqMmaMVFpqNg8AILxQVOC4sWOlpCRp7Vrpr381nQYAEE4oKnBckyZ2WZGkBx+Ujh41mwcAED4oKgiJ3/xGatVK2r9fmjDBdBoAQLigqCAkEhOlGTPs9enTpVWrzOYBAIQHigpCZuBA6fbb7ct7hwyRvv/edCIAgNtRVBBSTz9tz6+ybZt0113MSQIAqBpFBSFVr540b54UGyv95S/Ss8+aTgQAcDOKCkKuTx9p6lR7/b77wm8iOI4CAUDoUFRgxKhR0k03ScePS4MGSRs3mk4UPGamBQDnUVRghMcjzZ0r9eolFRZKAwZIe/aYTgUAcBuKCoxJTJTefls65xxp3z7pssvseVYAAAigqMCotDTpvfekli2lvDy7rBQUmE4FAHALigqMy8yUPvjAXm7ZIvXrJx08aDoVAMANKCpwhVat7LLSpIk9sPanP5W++850KgCAaRQVuEabNnZZadRIys2V+veXfD7TqQAAJlFU4Crt20vLl0sNGkiffSZde63044+mUwEATKGowHXOPVd6/30pKck+wnLbbVJJielUJzDhGwCEDkUFrpSdbV+6nJAgLVgg3XOP+woCE74BgPMoKnCtSy+V/vpXuxA8/7w0caLpRACAUKOowNWuv1565hl7feJE6ZVXzOYBAIQWRQWud+ed0v332+u//KW0Zo3ZPACA0KGoICxMnSpdfbXk90vXXCPt3m06EQAgFCgqCAuxsdK8eVLnztK330pXXSUdOWI6FQDAaRQVhI2kJOmdd6TGjaUNG6Sf/9xdly0DAGofRQVhpXlz+7Jlr1dauFB66CHTiQAATqKoIOx07y7NmmWvP/64NHeu2TwAAOdQVBCWbr1VGjvWXh82TFq5MnS/220TzwFAJHO0qFx99dVq3ry5EhMT1aRJEw0ePFj79+8vt82XX36pXr16KTExUZmZmXr88cedjIQI8vDD0nXXSceP2/cE2rUrtL+fmWkBwHmOFpW+ffvqtdde09atW/XGG29o+/btuuGGG8p+7vP5dPnll6tFixZat26dnnjiCU2YMEHPP/+8k7EQIWJipJdekrp0kQ4e5EogAIhEcU5++IgRI8rWW7RoodGjR2vQoEE6fvy44uPjNW/ePBUVFWnWrFlKSEhQx44dlZubq+nTp+uOO+5wMhoixFln2YNqL7xQ2rjRPiX01lv25cwAgPAXsjEqhw4d0rx589SjRw/Fx8dLklavXq1LLrlECQkJZdv1799fW7du1XfffVfh5/j9fvl8vnIPRLdmzewrgRITpXfflUaPNp0IAFBbHC8qDz74oM466yw1aNBAe/bs0dtvv132s/z8fDVu3Ljc9oHn+fn5FX7elClTlJqaWvbIzMx0LjzCRrduJ64EmjZN+tOfzOYBANSOoIvK6NGj5fF4qnxs2bKlbPsHHnhA69ev15IlSxQbG6tf/OIXss7gsokxY8aosLCw7LF3794afxYiyy23SOPH2+v33ssNDAEgEgQ9RmXUqFEaMmRIldtkZWWVrTds2FANGzZU27Zt1aFDB2VmZmrNmjXKyclRRkaGCgoKyr038DwjI6PCz/Z6vfJ6vcHGRpQYP146cMA+ovKLX0ipqdKVV5pOBQCoqaCLSnp6utLT02v0y0pLSyXZ40wkKScnR2PHji0bXCtJS5cuVbt27ZSWllaj34Ho5vFIM2ZIhw9Lf/2rdP310pIlUq9eppMBAGrCsTEqa9eu1R//+Efl5uZq9+7d+uCDD3TLLbeodevWysnJkSTdeuutSkhI0NChQ/XVV1/p1Vdf1R/+8AeNHDnSqViIAjEx0pw50sCB0o8/2kdUPvmk9j6fCd8AIHQcKyp169bVggULdNlll6ldu3YaOnSoOnfurI8++qjs1E1qaqqWLFminTt3Kjs7W6NGjdK4ceO4NBlnLD5eeu016dJLpaNHpf79pX/8o3Z/BxO+AYDzPNaZjGx1AZ/Pp9TUVBUWFiolJcV0HLjM999L11wjLVtmz7myaJHUu/eZfeaHH9oFqGNHe+4WAEDwqvv9zb1+ENHq1rUnhLv8cunYMfs00AcfmE4FAKguigoiXp069oRwAwbYR1iuuEJasMB0KgBAdVBUEBUSE6U337RvYlhUJN14o8QtpQDA/SgqiBqJifYA22HDpNJS6c47pcmTuYoHANyMooKoEhsrPfecNHas/fx3v5PuuUc6ftxsLgBAxSgqiDoej/TII9LTT9vrzz5rD7Y9eNB0MgDAf6OoIGrdd589yDYpSVqxQrrwQmndOtOpAAAno6ggql11lbRmjdS6tbRrl3TRRdKkSVJxceXvYUwLAIQORQVRr2NH6dNP7SuBioulceOkLl2k99+v+n3MTAsAzqOoAJLq15defVV6+WUpLc2ecXbAAKlrV3vw7d69phMCQHSiqAD/4fFIt90m5eVJI0ZICQn2mJW77pKaN5eaNrVPDV12memkABA9KCrAf6lfX5o+Xdq3T3r8calbN/uOzP/6l7R27YntMjPNZQSAaMFNCYFqKCyUtm2zTwGVltp3Z+7bV0pONp0MAMJTdb+/40KYCQhbqan2eJWuXU0nAYDowqkfAADgWhQVAADgWhQVAADgWhQVAADgWhQVAADgWhQVAADgWhQVAADgWhQVAADgWhQVAADgWhQVAADgWhQVAADgWhQVAADgWhQVAADgWmF/92TLsiTZt4sGAADhIfC9Hfger0zYF5UjR45IkjIzMw0nAQAAwTpy5IhSU1Mr/bnHOl2VcbnS0lLt379fycnJ8ng8tfrZPp9PmZmZ2rt3r1JSUmr1s3EC+zk02M+hwX4ODfZzaDi5ny3L0pEjR9S0aVPFxFQ+EiXsj6jExMSoWbNmjv6OlJQU/kUIAfZzaLCfQ4P9HBrs59Bwaj9XdSQlgMG0AADAtSgqAADAtSgqVfB6vRo/fry8Xq/pKBGN/Rwa7OfQYD+HBvs5NNywn8N+MC0AAIhcHFEBAACuRVEBAACuRVEBAACuRVEBAACuFdVFZebMmWrZsqUSExPVvXt3ffrpp1Vu//rrr6t9+/ZKTExUp06dtHjx4hAlDX/B7OsXXnhBvXr1UlpamtLS0tSvX7/T/rOBLdi/0wHz58+Xx+PRoEGDnA0YIYLdz4cPH9bw4cPVpEkTeb1etW3blv9+VEOw+/npp59Wu3btVKdOHWVmZmrEiBH68ccfQ5Q2PH388ce66qqr1LRpU3k8Hr311lunfc+KFSt0wQUXyOv1qk2bNpozZ46zIa0oNX/+fCshIcGaNWuW9dVXX1nDhg2z6tWrZxUUFFS4/SeffGLFxsZajz/+uLVp0ybrd7/7nRUfH29t2LAhxMnDT7D7+tZbb7VmzpxprV+/3tq8ebM1ZMgQKzU11frmm29CnDy8BLufA3bu3GmdffbZVq9evaxrrrkmNGHDWLD72e/3W127drWuvPJKa+XKldbOnTutFStWWLm5uSFOHl6C3c/z5s2zvF6vNW/ePGvnzp3W+++/bzVp0sQaMWJEiJOHl8WLF1tjx461FixYYEmy3nzzzSq337Fjh1W3bl1r5MiR1qZNm6wZM2ZYsbGx1nvvvedYxqgtKt26dbOGDx9e9rykpMRq2rSpNWXKlAq3v+mmm6yBAweWe6179+7WnXfe6WjOSBDsvv5vxcXFVnJysjV37lynIkaEmuzn4uJiq0ePHtaf//xn6/bbb6eoVEOw+/mZZ56xsrKyrKKiolBFjAjB7ufhw4dbl156abnXRo4caV188cWO5owk1Skqv/3tb62OHTuWe+3mm2+2+vfv71iuqDz1U1RUpHXr1qlfv35lr8XExKhfv35avXp1he9ZvXp1ue0lqX///pVuD1tN9vV/+/7773X8+HHVr1/fqZhhr6b7+eGHH1ajRo00dOjQUMQMezXZzwsXLlROTo6GDx+uxo0b69xzz9Wjjz6qkpKSUMUOOzXZzz169NC6devKTg/t2LFDixcv1pVXXhmSzNHCxHdh2N+UsCYOHjyokpISNW7cuNzrjRs31pYtWyp8T35+foXb5+fnO5YzEtRkX/+3Bx98UE2bNj3lXw6cUJP9vHLlSr344ovKzc0NQcLIUJP9vGPHDn3wwQe67bbbtHjxYuXl5emee+7R8ePHNX78+FDEDjs12c+33nqrDh48qJ49e8qyLBUXF+uuu+7SQw89FIrIUaOy70Kfz6cffvhBderUqfXfGZVHVBA+pk6dqvnz5+vNN99UYmKi6TgR48iRIxo8eLBeeOEFNWzY0HSciFZaWqpGjRrp+eefV3Z2tm6++WaNHTtWzz77rOloEWXFihV69NFH9ac//UlffPGFFixYoEWLFmnSpEmmo+EMReURlYYNGyo2NlYFBQXlXi8oKFBGRkaF78nIyAhqe9hqsq8Dpk2bpqlTp2rZsmXq3LmzkzHDXrD7efv27dq1a5euuuqqstdKS0slSXFxcdq6datat27tbOgwVJO/z02aNFF8fLxiY2PLXuvQoYPy8/NVVFSkhIQERzOHo5rs59///vcaPHiwfv3rX0uSOnXqpGPHjumOO+7Q2LFjFRPD/5fXhsq+C1NSUhw5miJF6RGVhIQEZWdna/ny5WWvlZaWavny5crJyanwPTk5OeW2l6SlS5dWuj1sNdnXkvT4449r0qRJeu+999S1a9dQRA1rwe7n9u3ba8OGDcrNzS17XH311erbt69yc3OVmZkZyvhhoyZ/ny+++GLl5eWVFUFJ+vrrr9WkSRNKSiVqsp+///77U8pIoBxa3NKu1hj5LnRsmK7LzZ8/3/J6vdacOXOsTZs2WXfccYdVr149Kz8/37Isyxo8eLA1evTosu0/+eQTKy4uzpo2bZq1efNma/z48VyeXE3B7uupU6daCQkJ1t/+9jfrX//6V9njyJEjpv4IYSHY/fzfuOqneoLdz3v27LGSk5Ote++919q6dav17rvvWo0aNbIeeeQRU3+EsBDsfh4/fryVnJxsvfLKK9aOHTusJUuWWK1bt7ZuuukmU3+EsHDkyBFr/fr11vr16y1J1vTp063169dbu3fvtizLskaPHm0NHjy4bPvA5ckPPPCAtXnzZmvmzJlcnuykGTNmWM2bN7cSEhKsbt26WWvWrCn7We/eva3bb7+93Pavvfaa1bZtWyshIcHq2LGjtWjRohAnDl/B7OsWLVpYkk55jB8/PvTBw0ywf6dPRlGpvmD386pVq6zu3btbXq/XysrKsiZPnmwVFxeHOHX4CWY/Hz9+3JowYYLVunVrKzEx0crMzLTuuece67vvvgt98DDy4YcfVvjf28C+vf32263evXuf8p7zzz/fSkhIsLKysqzZs2c7mtFjWRwTAwAA7hSVY1QAAEB4oKgAAADXoqgAAADXoqgAAADXoqgAAADXoqgAAADXoqgAAADXoqgAAIBTfPzxx7rqqqvUtGlTeTwevfXWW0F/hmVZmjZtmtq2bSuv16uzzz5bkydPDuozovKmhAAAoGrHjh3Teeedp1/96le67rrravQZ9913n5YsWaJp06apU6dOOnTokA4dOhTUZzAzLQAAqJLH49Gbb76pQYMGlb3m9/s1duxYvfLKKzp8+LDOPfdcPfbYY+rTp48kafPmzercubM2btyodu3a1fh3c+oHAAAE7d5779Xq1as1f/58ffnll7rxxhs1YMAAbdu2TZL0zjvvKCsrS++++65atWqlli1b6te//nXQR1QoKgAAICh79uzR7Nmz9frrr6tXr15q3bq17r//fvXs2VOzZ8+WJO3YsUO7d+/W66+/rpdeeklz5szRunXrdMMNNwT1uxijAgAAgrJhwwaVlJSobdu25V73+/1q0KCBJKm0tFR+v18vvfRS2XYvvviisrOztXXr1mqfDqKoAACAoBw9elSxsbFat26dYmNjy/0sKSlJktSkSRPFxcWVKzMdOnSQZB+RoagAAABHdOnSRSUlJfr222/Vq1evCre5+OKLVVxcrO3bt6t169aSpK+//lqS1KJFi2r/Lq76AQAApzh69Kjy8vIk2cVk+vTp6tu3r+rXr6/mzZvr5z//uT755BM9+eST6tKliw4cOKDly5erc+fOGjhwoEpLS3XhhRcqKSlJTz/9tEpLSzV8+HClpKRoyZIl1c5BUQEAAKdYsWKF+vbte8rrt99+u+bMmaPjx4/rkUce0UsvvaR9+/apYcOGuuiiizRx4kR16tRJkrR//379z//8j5YsWaKzzjpLV1xxhZ588knVr1+/2jkoKgAAwLW4PBkAALgWRQUAALgWRQUAALgWRQUAALgWRQUAALgWRQUAALgWRQUAALgWRQUAALgWRQUAALgWRQUAALgWRQUAALgWRQUAALjW/weDmvtQdVKDXgAAAABJRU5ErkJggg==", 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", "text/plain": [ "
" ] @@ -485370,30 +485302,31 @@ ], "source": [ "fig, ax = plt.subplots()\n", - "ax.plot(df2[\"z\"], df2[\"theta_z\"], 'b-')\n", - "ax.plot\n", - "ax.plot()" + "ax.plot(df_ln[\"z\"], df_ln[\"theta_z\"], 'r-')\n", + "ax.plot(df_Pln[\"z\"], df_Pln[\"theta_z\"], 'b-')\n", + "ax.set_xlim(left=1000, right=1_000_000)\n", + "ax.legend([\"log normal\", \"Pln\"])" ] }, { "cell_type": "code", - "execution_count": 232, + "execution_count": 12, "id": "e90ef79d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "Text(0, 0.5, 'g_z')" + "" ] }, - "execution_count": 232, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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", + "image/png": 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", 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" ] @@ -485405,211 +485338,13 @@ "source": [ "# plot g_z across z\n", "fig, ax = plt.subplots()\n", - "ax.plot(df2[\"z\"], df2[\"g_z\"])\n", - "\n", - "ax.set_xlim(right=500_000)\n", - "ax.set_xlabel(\"income\")\n", - "ax.set_ylabel(\"g_z\")" - ] - }, - { - "cell_type": "code", - "execution_count": 233, - "id": "24beb49b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'Smoothed f_prime, convolution')" - ] - }, - "execution_count": 233, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import numpy as np\n", - "z = df2[\"z\"]\n", - "y = df2[\"f_prime\"].copy()\n", - "\n", - "window_size = 10000\n", - "\n", - "# Find the index of the cutoff value\n", - "cutoff_index = np.abs(z - cutoff).argmin()\n", - "\n", - "# Apply moving average filter to smooth the values of y around the cutoff\n", - "smoothed_y = np.convolve(y, np.ones(window_size)/window_size, mode='same')\n", - "\n", - "# Extract the smoothed values around the cutoff\n", - "smoothed_y_around_cutoff = smoothed_y[cutoff_index - window_size//2 : cutoff_index + window_size//2 + 1]\n", - "\n", - "# update y to include the smoothed values around the cutoff\n", - "y[cutoff_index - window_size//2 : cutoff_index + window_size//2 + 1] = smoothed_y_around_cutoff\n", - "\n", - "# Plot the smoothed values for all of y\n", - "fig, ax = plt.subplots()\n", - "ax.plot(z, df2[\"f_prime\"], 'b-')\n", - "\n", - "ax.plot(z, y, 'r-')\n", - "# set labels\n", - "ax.set_xlabel(\"income\")\n", - "ax.set_ylabel(\"f_prime\")\n", - "# set title\n", - "ax.set_title(\"Smoothed f_prime, convolution\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": 234, - "id": "c6ee5216", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'g_z with convlution smoothing')" - ] - }, - "execution_count": 234, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "theta_z = 1 + ((df2.z * smoothed_y) / df2.f)\n", - "\n", - "g_z = (\n", - " 1\n", - " + (theta_z * iot2.eti * df2.mtr) / (1 - df2.mtr)\n", - " + ((iot2.eti * df2.z * df2.mtr_prime) / (1 - iot2.mtr) ** 2)\n", - ")\n", - "\n", - "# plot g_z across z for z < 500_000\n", - "fig, ax = plt.subplots()\n", - "ax.plot(df2[\"z\"][df2[\"z\"] < 500_000], g_z[df2[\"z\"] < 500_000])\n", - "# set labels\n", - "ax.set_xlabel(\"income\")\n", - "ax.set_ylabel(\"g_z\")\n", - "# set title\n", - "ax.set_title(\"g_z with convlution smoothing\")" - ] - }, - { - "cell_type": "code", - "execution_count": 235, - "id": "de84815e", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'Smoothed f_prime, gaussian filter')" - ] - }, - "execution_count": 235, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from scipy.ndimage import gaussian_filter1d\n", - "z = df2[\"z\"]\n", - "y = df2[\"f_prime\"]\n", - "\n", - "cutoff = 250_000\n", - "smooth_region_width = 40000\n", - "\n", - "# Apply Gaussian smoothing to the function around the discontinuity point\n", - "smoothed_y = np.copy(y)\n", - "smoothed_y[z >= cutoff - smooth_region_width/2] = gaussian_filter1d(y[z >= cutoff - smooth_region_width/2], sigma=500)\n", - "\n", - "\n", - "# Plot the smoothed values for all of y\n", - "fig, ax = plt.subplots()\n", - "ax.plot(z, smoothed_y)\n", - "# set labels\n", - "ax.set_xlabel(\"income\")\n", - "ax.set_ylabel(\"f_prime\")\n", - "# set title\n", - "ax.set_title(\"Smoothed f_prime, gaussian filter\")" - ] - }, - { - "cell_type": "code", - "execution_count": 236, - "id": "5470b68e", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0.5, 1.0, 'g_z with gaussian smoothing')" - ] - }, - "execution_count": 236, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "theta_z = 1 + ((df2.z * smoothed_y) / df2.f)\n", + "ax.plot(df_ln[\"z\"], df_ln[\"g_z\"])\n", + "ax.plot(df_Pln[\"z\"], df_Pln[\"g_z\"])\n", "\n", - "g_z = (\n", - " 1\n", - " + (theta_z * iot2.eti * df2.mtr) / (1 - df2.mtr)\n", - " + ((iot2.eti * df2.z * df2.mtr_prime) / (1 - iot2.mtr) ** 2)\n", - ")\n", - "\n", - "# plot g_z across z for z < 500_000\n", - "fig, ax = plt.subplots()\n", - "ax.plot(df2[\"z\"][df2[\"z\"] < 500_000], g_z[df2[\"z\"] < 500_000])\n", - "# set labels\n", + "ax.set_xlim(left=1000)\n", "ax.set_xlabel(\"income\")\n", "ax.set_ylabel(\"g_z\")\n", - "# set title\n", - "ax.set_title(\"g_z with gaussian smoothing\")" + "ax.legend([\"log normal\", \"Pln\"])" ] } ], diff --git a/Model.md b/Model.md new file mode 100644 index 0000000..69815d7 --- /dev/null +++ b/Model.md @@ -0,0 +1,181 @@ +# Model + +Based Saez (2001), Diamond (1998), Saez, Slemrod, Giertz (2012), lecture notes by Rishabh Kirpalani. + +We derive the Diamond-Saez-Mirrlees optimal tax formula, and invert it following Lockwood and Weinzierl (2016) and Jacobs, Jongen and Zoutman (2017) + +## Environment + +Suppose households have an ability type, $\theta \in \Theta$ with distribution $f(\theta)$, which is private information. The production technology is such that type $\theta$ has production (or taxable income) $z(\theta) = \theta * l(\theta)$. The planner or policy maker can observe income / production $z$ for each type, but not labor $l$. The government has exogenous expenditures $E$, which must be funded by labor of households or (in the decentralized problem) taxes on labor. + + An allocation is a set of consumption and output $\{ c(\theta), z(\theta) \}_{\forall \theta \in \Theta}$. The household has preferences given by + + $$ U(\theta) = u(c(\theta)) - v(l(\theta)) = u(c(\theta)) - v\left (\frac{z(\theta)}{\theta}\right ),$$ + +where $u', v' > 0$, and $u'' \leq 0 \leq v''$. The marginal rate of substitution for the household between $c$ and $z$ is + + $$MRS_{c, z} = -\theta\frac{u'(c)}{v'(\frac{z}{\theta})}.$$ + + +Now, note that + +$$\frac{\partial}{\partial \theta} MRS_{c, z} = -u'(c) \left[\frac{1}{v'(\frac{z}{\theta})}+ \frac{zv''(\frac{z}{\theta})}{\theta v'(\frac{z}{\theta})}\right] < 0 $$ + +by assumptions on $u$ and $v$. Thus, the single crossing property holds. +## Incentive Compatibility + +Since labor effort and productivity type are unobservable, the planner or policy maker cannot achieve the first best outcome in which policy can be a function of ability directly. By the revelation principle, a decentralized equilibrium in which agents truthfully reveal their type is equivalent to planner's problem with incentive compatibility constraints. Thus, policy makers must design the tax system to ensure that agents truthfully reveal their productivity through their income choice. An allocation is incentive compatible (globally) if + +$$ u(c(\theta)) - v\left (\frac{z(\theta)}{\theta}\right ) > c(\hat \theta) - v\left (\frac{z(\hat \theta)}{\theta}\right ), \forall \theta, \hat{\theta}.$$ + +However, it can be shown that this global incentive compatibility constraint can be replaced by the following conditions for local incentive compatibility: + +1. $U'(\theta) = \frac{z(\theta)}{\theta^2}v'\left (\frac{z(\theta)}{\theta}\right )$ +2. $z(\theta)$ increasing + +Mechanism design literature drops condition 2, to be verified ex-post. + +## Constrained Social Planner's Problem + +The constrained social planner wants to maximize welfare subject to incentive compatibility and resource constraints. The constrained social planner's problem is: + +$$\begin{align*} +\max_{c(\theta),z(\theta)} & \int_{\Theta} G(U(\theta)) dF(\theta) \\ +\text{subject to} & \\ +& \int_{\Theta} (z(\theta) - c(\theta)) dF(\theta) \geq E \quad (\text{RC}) \\ +& U'(\theta) = \frac{z(\theta)}{\theta^2} v'\left(\frac{z(\theta)}{\theta}\right) \quad \forall \theta \in \Theta \quad (\text{LIC}) \\ +& U(\theta) = u(c(\theta)) - v\left(\frac{z(\theta)}{\theta}\right) \quad \forall \theta \in \Theta \\ +& z(\theta) \text{ increasing in } \theta +\end{align*}$$ + +Where G is a weighting function for the social planner which determines their redistributive preferences. We will drop the monotonicity condition to be verified later. The Lagrangian for the social planner's problem is: + +$$ +\begin{align*} +L =& \int_{\Theta} G(U(\theta)) + \lambda[z(\theta) - c(\theta) - E] dF(\theta) \\ +& + \int_{\Theta} \gamma(\theta) \left [u(c(\theta)) - v\left(\frac{y(\theta)}{\theta}\right) - U(\theta)\right ] + \mu(\theta)\left [U'(\theta)- \frac{z(\theta)}{\theta^2} v'\left(\frac{z(\theta)}{\theta}\right)\right]d\theta\\ +\end{align*} +$$ + + +Where $\lambda, \gamma(\theta), \mu(\theta)$ are Lagrange multipliers. There is an equivalent social planner's problem in which the planner has an exogenous value of raising public funds; another interpretation of $\lambda$ is the marginal value of public funds. + + +Using integration by parts on $\int_{\Theta} \mu(\theta)U'(\theta)d\theta$, we have: + +$$ +\begin{align*} +L =& \int_{\Theta} G(U(\theta)) + \lambda[z(\theta) - c(\theta)- E] dF(\theta) \\ +& + \int_{\Theta} \gamma(\theta) \left [u(c(\theta)) - v\left(\frac{y(\theta)}{\theta}\right) - U(\theta)\right ] - \mu(\theta)\left [\frac{z(\theta)}{\theta^2} v'\left(\frac{z(\theta)}{\theta}\right)\right]d\theta\\ \\ +&+ \mu(\bar{\theta}) U(\bar{\theta}) - \mu(\underline{\theta}) U(\underline{\theta}) +\end{align*} +$$ + +It must be the case that $\mu(\underline\theta) = \mu(\bar\theta) = 0$. Otherwise, the planner would like to set $U(\barθ) = ∞$ $(U (\underlineθ) = −∞)$ which would violate incentive constraints. + +Taking first order conditions: + +$$ +\begin{align*} +U(\theta): \quad & G'(U(\theta)) f(\theta) - \gamma(\theta) - \mu'(\theta) = 0 \\ +c(\theta): \quad & \gamma(\theta) u'(c(\theta)) - \lambda f(\theta) = 0 \\ +z(\theta): \quad & -\gamma(\theta) \frac{1}{\theta} v'\left(\frac{z(\theta)}{\theta}\right) + \lambda f(\theta) - \mu(\theta) \left[\frac{1}{\theta^2} v'\left(\frac{z(\theta)}{\theta}\right) + \frac{z(\theta)}{\theta^3} v''\left(\frac{z(\theta)}{\theta}\right)\right] = 0 +\end{align*} +$$ + +Boundary conditions: $\mu(\bar{\theta}) = \mu(\underline{\theta}) = 0$. + +Using the first order conditions for $U(\theta)$ and $c(\theta)$, we have: + +$$ +\mu(\theta) = \int_\theta^{\bar\theta} \left[\frac{\lambda f(y)}{u'(c(y))} - G'(U(y)) f(y)\right] dy +$$ + +Substituting this into the first order condition for $z(\theta)$ yields: + +$$ +\frac{1}{\frac{1}{\theta} v'\left(\frac{z(\theta)}{\theta}\right)} - \frac{1}{u'(c(\theta))} = \frac{1-F(\theta)}{\theta f(\theta)} \left[1 + \frac{z(\theta)}{\theta} \frac{v''\left(\frac{z(\theta)}{\theta}\right)}{v'\left(\frac{z(\theta)}{\theta}\right)}\right] \int_\theta^{\bar{\theta}} \left[\frac{1}{u'(c(y))} - \frac{G'(U(y))}{\lambda}\right] \frac{dF(y)}{1-F(\theta)} +$$ + +This, togethether with the resource constraint characterizes optimal allocations. + +## The Diamond-Saez-Mirrlees Optimal Tax Formula + +The policy maker wants to implement the constrained planner's problem with a tax policy $T(z)$. The household's problem is: + +$$\begin{align*} +\max_{c, z} \quad &u(c) - v(\frac{z}{\theta}) \\ +\text{subject to} & \\ +& c = z - T(z) +\end{align*}$$ + +Assuming households do not optimize with respect to a highly nonlinear tax code, the first order condtion of the household is $\frac{1}{\theta} v'(\frac{z}{\theta}) = u'(c)(1-T'(z))$. +Letting $T(z)$ be the tax function that implements the efficient allocation and substituting the household FOC, the formula becomes: + +$$ +\frac{T'(\theta)}{1-T'(\theta)} = u'(c(\theta)) \frac{1-F(\theta)}{\theta f(\theta)} \left[1 + \frac{z(\theta)}{\theta} \frac{v''\left(\frac{z(\theta)}{\theta}\right)}{v'\left(\frac{z(\theta)}{\theta}\right)}\right] \int_\theta^{\bar{\theta}} \left[\frac{1}{u'(c(y))} - \frac{G'(U(y))}{\lambda}\right] \frac{dF(y)}{1-F(\theta)} +$$ + +As per Diamond (1998), we take preferences to be GHH, which has the interpretation of no income effects, so that the formula does not depend on both consumption and income simultaneously. This also has the benefit of being able to interpret utility in dollars. + +$$U(c, l) = c - \psi (\varepsilon l^{\frac{1}{\varepsilon}})$$ + +where $\varepsilon$ is the elasticity of taxable income. Thus, $u'(c) = 1$, and $x \frac{v''(x)}{v'(x)} = \frac{1}{\epsilon}-1$. Also note that there is a 1 to 1 mapping between $\theta$ and $z$ under incentive compatibility. Thus, we can replace $\theta$ with $z$ in the formula. However, one should be careful that we now are using $f$ as the virtual density, which makes the assumption that taxes are linearized around $T(z)$. This is fine as long as individuals are not optimizing with respect to a highly nonlinear tax code. Therefore, the formula becomes: + + +$$ +\frac{T'(z)}{1-T'(z)} = \frac{1-F(z)}{\varepsilon z f(z)} \int_z^{\bar{z}} \left[1 - \frac{G'(U(y))}{\lambda}\right] \frac{dF(y)}{1-F(z)} +$$ + + +Let $g(z) = G'(U(z))/\lambda$ be the marginal social welfare weight. The interpretation is that $g(z)$ is the social welfare or value to the policy maker from giving an additional dollar of income or consumption to an agent earning $z$. Therefore, we get the formula used in Lockwood and Weinzierl (2015) and Jacobs, Jongen and Zoutman (2017): + +$$ +\frac{T'(z)}{1-T'(z)} = \frac{1-F(z)}{\varepsilon z f(z)} \int_z^{\bar{z}} \left[1 - g(y)\right] \frac{dF(y)}{1-F(z)} +$$ + + +We assume there is an unbounded distribution of income, so $\bar{z} = \infty$. The key components are: + +1. A hazard ratio $\frac{1-F(z)}{zf(z)}$. For a thin-tailed distribution such as the lognormal distribution, this converges to 0, giving us the "no distortion at the top" result of a 0 marginal tax rate at the top of the income distribution. For a Pareto distribution, this term is $\alpha$, which represents the thinness of the tail. +2. The elasticity of taxable income $\varepsilon$. This has estimates ranging from .12 to .4, with .25 as a middle of the road estimate. See Saez, Slemrod, Giertz (2012). +3. The planner's redistributionary motives, captured by $g(z)$. Note in general that these are endogenous; they depend on the equilibrium allocation. + + +## Inverting the optimal tax formula + +As per Lockwood and Weinzierl (2016), we can invert this formula: + +$$\bar{g}(z) = 1-F(z) - \frac{\varepsilon z f(z) T'(z)}{1-T'(z)}$$ + +Where $\bar{g}(z) \equiv \int_z^\infty g(y)dF(y)$. By the fundamental theorem of calculus, $\frac{d}{dz}\bar{g}(z) = - g(z)f(z)$. Thus, + +$$ +\begin{align*} +g(z) &= -\frac{1}{f(z)}\frac{d}{dz}\left[ 1-F(z) - \varepsilon z f(z)\frac{ T'(z)}{1-T'(z)}\right]\\ +&=1 + \frac{1}{f(z)}\frac{d}{dz}\left[\varepsilon z f(z)\frac{ T'(z)}{1-T'(z)}\right] \\ +& = 1 + \theta_z \varepsilon \frac{T'(z)}{1-T'(z)} + \varepsilon \frac{zT''(z)}{(1-T'(z))^2} +\end{align*} +$$ + +Where $\theta_z \equiv 1 + \frac{zf'(z)}{f(z)}$ is the elasticity of the local tax base with respect to income. In the case of constant ETI, we get the formula used by Lockwood & Weinzierl (2016) on the first line, and Jacobs, Jongen and Zoutman (2017) on the 3rd line. + +In the case of variable ETI, we get an extra term for the JJZ formula: + +$$g(z) = 1 + \theta_z \varepsilon(z) \frac{T'(z)}{1-T'(z)} + \varepsilon(z) \frac{zT''(z)}{(1-T'(z))^2}+ \varepsilon'(z)\frac{zT'(z)}{1-T'(z)}$$ + +However, note that this is subject to the constraint that + +$$\int_0^\infty g(z) dF(z) = 1$$ + +To see why this is true, consider a reform in which the government collects an additional dollar from everyone. Since we have GHH preferences and utility is in terms of dollars, the welfare loss from this reform is + +$$ \int_0^\infty G(U(z)) - G(U(z)-1) dF(z) \approx \int_0^\infty G'(U(z))dF(z).$$ + +The gain to the social planner of collecting this dollar is $\lambda$, the value (or shadow price) of relaxing the government budget constraint. At optimum, the marginal benefit equals the marginal cost, so + +$$\int_0^\infty G'(U(z))dF(z) = \lambda$$ + +$$\implies \int_0^\infty g(z) dF(z) = 1$$ + +by definition of $g$.