{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# The use of axes\n", "\n", "Axes are a great option to define at the simulation declaration in order to make a variable v evolves in a given interval.\n", "\n", "We'll show this opportunity with the illustration of the evolution of average rate and marginal rate of the French Income Tax." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Initialisation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We import essential modules and initialize the tax and benefit system\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from openfisca_france import FranceTaxBenefitSystem\n", "from openfisca_france.scenarios import init_single_entity\n", "\n", "tax_benefit_system = FranceTaxBenefitSystem() # Create an instance of French Tax and Benefit system" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Income Tax Concavity : a progressive system ?\n", "\n", "Let's observe how to declare a simulation with an income (`salaire_de_base`) evolving between 0 euros and 100000 euros per year." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "scenario = init_single_entity(\n", " tax_benefit_system.new_scenario(),\n", " \n", " # Axe declaration\n", " axes = [[\n", " dict( # in a dictionary\n", " count = 100, # 'count' : indicates the number of step\n", " min = 0,\n", " max = 100000,\n", " name = 'salaire_de_base', # the variable you want to make evolve\n", " ),\n", " ]],\n", " \n", " period = 2014,\n", " parent1 = dict(\n", " date_naissance = '1980-01-01',\n", " )\n", ")\n", "\n", "simulation = scenario.new_simulation()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 1010.10114, 2020.2023 , 3030.3027 ,\n", " 4040.4045 , 5050.5054 , 6060.6055 , 7070.707 ,\n", " 8080.809 , 9090.909 , 10101.011 , 11111.11 ,\n", " 12121.211 , 13131.315 , 14141.414 , 15151.515 ,\n", " 16161.618 , 17171.717 , 18181.818 , 19191.918 ,\n", " 20202.021 , 21212.121 , 22222.22 , 23232.326 ,\n", " 24242.422 , 25252.525 , 26262.63 , 27272.725 ,\n", " 28282.828 , 29292.932 , 30303.03 , 31313.13 ,\n", " 32323.236 , 33333.332 , 34343.434 , 35353.54 ,\n", " 36363.637 , 37373.74 , 38383.836 , 39393.938 ,\n", " 40404.043 , 41414.14 , 42424.242 , 43434.344 ,\n", " 44444.44 , 45454.547 , 46464.652 , 47474.75 ,\n", " 48484.844 , 49494.94 , 50505.05 , 51515.152 ,\n", " 52525.26 , 53535.363 , 54545.45 , 55555.55 ,\n", " 56565.656 , 57575.76 , 58585.863 , 59595.953 ,\n", " 60606.06 , 61616.16 , 62626.26 , 63636.37 ,\n", " 64646.473 , 65656.555 , 66666.664 , 67676.766 ,\n", " 68686.87 , 69696.98 , 70707.08 , 71717.164 ,\n", " 72727.27 , 73737.375 , 74747.48 , 75757.586 ,\n", " 76767.67 , 77777.78 , 78787.875 , 79797.97 ,\n", " 80808.086 , 81818.164 , 82828.28 , 83838.38 ,\n", " 84848.484 , 85858.586 , 86868.69 , 87878.805 ,\n", " 88888.88 , 89899. , 90909.09 , 91919.19 ,\n", " 92929.305 , 93939.38 , 94949.5 , 95959.59 ,\n", " 96969.69 , 97979.805 , 98989.88 , 100000.01 ],\n", " dtype=float32)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "simulation.calculate_add('salaire_de_base', 2014)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "income_tax = - simulation.calculate('irpp', 2014)\n", "gross_wage = simulation.calculate_add('salaire_de_base', 2014)\n", "taxable_income = simulation.calculate_add('salaire_imposable', 2014)\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'Gross Wage')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(gross_wage,income_tax)\n", "plt.ylabel(u\"Tax Income\")\n", "plt.xlabel(u\"Gross Wage\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**NB** : The Income Tax is flat in opposite to common opinion." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Average rate" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python3.7/site-packages/ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in true_divide\n", " \"\"\"Entry point for launching an IPython kernel.\n" ] } ], "source": [ "average_rate = income_tax / gross_wage\n", "# the 1st value of gross_wage is zero, so there's a warning" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'Gross Wage')" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(gross_wage, average_rate)\n", "plt.ylabel(\"Averate Tax Rate\")\n", "plt.xlabel(\"Gross Wage\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Marginal rate" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "marginal_rate = (income_tax[:-1] - income_tax[1:]) / (taxable_income[:-1] - taxable_income[1:] ) " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'Gross Wage')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(gross_wage[:-1], marginal_rate)\n", "plt.ylabel(\"Marginal Tax Rate\")\n", "plt.xlabel(\"Gross Wage\")" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.1259707, 0.26955944)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "marginal_rate[25], marginal_rate[90]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see the step in the French Tax scale of 14% and 30% (applied after a 10% deduction on the taxable income) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Notice : dedicated fonctions in OpenFisca" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Marginal and Average rate exist as functions implemented in OpenFisca. You can apply them on several income concept" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "from openfisca_core.rates import average_rate, marginal_rate" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0. , -74.434586, -148.86015 , -223.29471 ,\n", " -297.7293 , -372.15488 , -446.58942 , -521.024 ,\n", " -595.4586 , -669.8843 , -744.3187 , -818.7533 ,\n", " -893.17883 , -967.61346 , -1042.048 , -1116.4736 ,\n", " -1190.9083 , -1265.3428 , -1339.7686 , -1414.203 ,\n", " -1488.6375 , -1563.072 , -1637.4978 , -1711.9324 ,\n", " -1786.367 , -1860.7925 , -1935.2269 , -2009.6617 ,\n", " -2084.0872 , -2158.5217 , -2232.9565 , -2307.3813 ,\n", " -2381.8167 , -2456.2505 , -2530.6855 , -2605.1108 ,\n", " -2679.5457 , -2753.9802 , -2828.406 , -2902.84 ,\n", " -2977.275 , -3051.7007 , -3126.1353 , -3200.5698 ,\n", " -3275.0044 , -3349.4302 , -3423.8647 , -3498.2988 ,\n", " -3572.724 , -3647.1592 , -3721.5942 , -3796.019 ,\n", " -3870.4539 , -3944.8887 , -4019.3145 , -4093.7483 ,\n", " -4168.183 , -4242.618 , -4317.0435 , -4391.4775 ,\n", " -4465.913 , -4540.339 , -4614.773 , -4689.2065 ,\n", " -4763.6333 , -4838.0674 , -4912.501 , -4986.9272 ,\n", " -5061.3623 , -5135.797 , -5210.2305 , -5284.657 ,\n", " -5359.0913 , -5433.5264 , -5507.951 , -5582.386 ,\n", " -5656.821 , -5731.247 , -5805.68 , -5880.1157 ,\n", " -5954.541 , -6028.975 , -6103.4097 , -6177.8447 ,\n", " -6252.2705 , -6326.7046 , -6401.1396 , -6475.5654 ,\n", " -6550. , -6624.4346 , -6698.8604 , -6773.295 ,\n", " -6847.7295 , -6922.163 , -6996.589 , -7071.024 ,\n", " -7145.458 , -7219.884 , -7294.3184 , -7368.753 ],\n", " dtype=float32)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "csg = simulation.calculate_add('csg', period = 2014)\n", "csg" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.07369024, 0.07368577, 0.07368726, 0.07368797, 0.07368666,\n", " 0.07368726, 0.07368767, 0.07368797, 0.07368726, 0.07368755,\n", " 0.07368779, 0.07368726, 0.07368749, 0.07368767, 0.07368726,\n", " 0.07368743, 0.07368761, 0.07368726, 0.07368743, 0.07368755,\n", " 0.07368767, 0.07368743, 0.07368749, 0.07368767, 0.07368737,\n", " 0.07368749, 0.07368761, 0.07368737, 0.07368743, 0.07368755,\n", " 0.07368731, 0.07368743, 0.07368749, 0.07368761, 0.07368743,\n", " 0.07368749, 0.07368755, 0.07368743, 0.07368749, 0.07368755,\n", " 0.07368743, 0.07368749, 0.07368755, 0.07368761, 0.07368743,\n", " 0.07368749, 0.07368755, 0.07368743, 0.07368749, 0.07368755,\n", " 0.07368743, 0.07368749, 0.07368755, 0.07368743, 0.07368749,\n", " 0.07368755, 0.07368755, 0.07368743, 0.07368749, 0.07368755,\n", " 0.07368749, 0.07368749, 0.07368755, 0.07368743, 0.07368749,\n", " 0.07368749, 0.07368743, 0.07368749, 0.07368749, 0.07368755,\n", " 0.07368749, 0.07368749, 0.07368755, 0.07368743, 0.07368749,\n", " 0.07368755, 0.07368743, 0.07368749, 0.07368755, 0.07368743,\n", " 0.07368749, 0.07368749, 0.07368755, 0.07368749, 0.07368749,\n", " 0.07368755, 0.07368743, 0.07368749, 0.07368755, 0.07368743,\n", " 0.07368749, 0.07368749, 0.07368755, 0.07368749, 0.07368749,\n", " 0.07368755, 0.07368749, 0.07368749, 0.07368755], dtype=float32)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1 - average_rate(-csg[1:], gross_wage[1:])" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.ylim(0,0.1)\n", "plt.plot(gross_wage[1:], 1-average_rate(-csg[1:], gross_wage[1:]))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 1 }