├── .DS_Store ├── .gitattributes ├── Hugget - Continuum Income Types.ipynb ├── MIT_shock_aiyagari.ipynb ├── README.md ├── Ramsey.ipynb ├── Skiba.ipynb ├── Two_assets.ipynb ├── Y_butterfly.pdf ├── aiyagari_continuous_time.ipynb ├── aiyagari_irfs_A_shock.pdf ├── distributions_cont_incomeType.pdf └── policy_functions.pdf /.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jbduarte/Numerical_Continuous_Time/2f42aa8002c28f84242f0838c5f4aeb6978e9889/.DS_Store -------------------------------------------------------------------------------- /.gitattributes: -------------------------------------------------------------------------------- 1 | # Auto detect text files and perform LF normalization 2 | * text=auto 3 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Numerical Methods in Continuous Time 2 | 3 | ### By Joao B. Duarte (www.jbduarte.com) 4 | 5 | I have replicated in Python codes of Benjamin Moll, SeHyoun Ahn, and Pontus Rendahl for a variety of economic models set in continuous time. 6 | I am indebted to their rich publicly available material. 7 | 8 | Please let me know of any bugs you may find. (joao.duarte@novasbe.pt) 9 | -------------------------------------------------------------------------------- /Ramsey.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "## Ramsey Model in Continuous Time" 8 | ] 9 | }, 10 | { 11 | "cell_type": "code", 12 | "execution_count": 2, 13 | "metadata": {}, 14 | "outputs": [], 15 | "source": [ 16 | "import numpy as np" 17 | ] 18 | }, 19 | { 20 | "cell_type": "code", 21 | "execution_count": 525, 22 | "metadata": {}, 23 | "outputs": [], 24 | "source": [ 25 | "# 1. Set parameters\n", 26 | "\n", 27 | "γ = 2.0\n", 28 | "ρ = 0.05\n", 29 | "α = 1/3\n", 30 | "δ = 0.05\n", 31 | "\n", 32 | "def kss():\n", 33 | " return ((δ+ρ)/α)**(1/(α-1))\n", 34 | "kss = kss()\n", 35 | "\n", 36 | "kmax = 2*kss\n", 37 | "kmin = 0.01*kss\n", 38 | "N = 400\n", 39 | "maxit=20000\n", 40 | "crit = 10**-6" 41 | ] 42 | }, 43 | { 44 | "cell_type": "code", 45 | "execution_count": 526, 46 | "metadata": {}, 47 | "outputs": [], 48 | "source": [ 49 | "# 2. Create Grid for K\n", 50 | "k = np.linspace(kmin, kmax, N)\n", 51 | "dk = (kmax-kmin)/(N-1)\n", 52 | "\n", 53 | "dV = np.zeros(N)\n", 54 | "dVb = np.zeros(N)\n", 55 | "dVf = np.zeros(N)\n", 56 | "c = np.zeros(N)\n", 57 | "\n", 58 | "V0 = (((k**α)**(1-γ))/(1-γ))/ρ # Initial guess for v is steady state v\n", 59 | "v = V0\n", 60 | "\n", 61 | "\n", 62 | "# Construct matrix to get fast the finite differences in v vector\n", 63 | "# D = np.zeros((N, N))\n", 64 | "\n", 65 | "# for i in range(1,N-1):\n", 66 | "# for j in range(0,N):\n", 67 | "# if i-j == 1:\n", 68 | "# D[i,j] = -0.5/(dk)\n", 69 | "# if i-j == -1:\n", 70 | "# D[i,j] = 0.5/(dk)\n", 71 | "\n", 72 | "# D[0,0], D[0,1] = -1/dk, 1/dk\n", 73 | "# D[-1,-2], D[-1,-1] = -1/dk, 1/dk " 74 | ] 75 | }, 76 | { 77 | "cell_type": "code", 78 | "execution_count": 527, 79 | "metadata": {}, 80 | "outputs": [ 81 | { 82 | "name": "stderr", 83 | "output_type": "stream", 84 | "text": [ 85 | "/Users/joaobduarte/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:19: RuntimeWarning: divide by zero encountered in power\n", 86 | "/Users/joaobduarte/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:22: RuntimeWarning: divide by zero encountered in power\n" 87 | ] 88 | }, 89 | { 90 | "name": "stdout", 91 | "output_type": "stream", 92 | "text": [ 93 | "Value Function Converged, Iteration = 14416\n", 94 | "It took 3.93 seconds\n" 95 | ] 96 | } 97 | ], 98 | "source": [ 99 | "# 3. Solve!\n", 100 | "from time import time\n", 101 | "dist = []\n", 102 | "\n", 103 | "start = time()\n", 104 | "for i in range(0,maxit):\n", 105 | " V = v\n", 106 | " \n", 107 | " # forward difference\n", 108 | " dVf[0:N-1] = (V[1:N]-V[0:N-1])/dk\n", 109 | " dVf[N-1] = 0 #will never be used\n", 110 | " # backward difference\n", 111 | " dVb[1:N] = (V[1:N]-V[0:N-1])/dk\n", 112 | " dVb[0] = 0 #will never be used\n", 113 | " \n", 114 | " I_concave = dVb > dVf #indicator whether value function is concave (problems arise if this is not the case)\n", 115 | " \n", 116 | " #consumption and savings with forward difference\n", 117 | " cf = dVf**(-1/γ)\n", 118 | " muf = k**α - δ*k - cf\n", 119 | " #consumption and savings with backward difference\n", 120 | " cb = dVb**(-1/γ)\n", 121 | " mub = k**α - δ*k - cb\n", 122 | " #consumption and derivative of value function at steady state\n", 123 | " c0 = k**α - δ*k \n", 124 | " dV0 = c0**(-γ)\n", 125 | " \n", 126 | " # dV_upwind makes a choice of forward or backward differences based on\n", 127 | " # the sign of the drift \n", 128 | " If = muf > 0 #below steady state\n", 129 | " Ib = mub < 0 #above steady state\n", 130 | " I0 = (1-If-Ib) #at steady state\n", 131 | " #make sure the right approximations are used at the boundaries\n", 132 | " Ib[0] = 0\n", 133 | " If[0] = 1\n", 134 | " Ib[N-1] = 1\n", 135 | " If[N-1] = 0\n", 136 | " dV_Upwind = dVf*If + dVb*Ib + dV0*I0 #important to include third term\n", 137 | " \n", 138 | " c = dV_Upwind**(-1/γ)\n", 139 | " Vchange = c**(1-γ)/(1-γ) + dV_Upwind*(k**α - δ*k - c) - ρ*V\n", 140 | " \n", 141 | " ## This is the update\n", 142 | " # the following CFL condition seems to work well in practice\n", 143 | " Delta = .9*dk/max(k**α - δ*k)\n", 144 | " v = v + Delta*Vchange\n", 145 | " \n", 146 | " dist.append( max(abs(Vchange)) )\n", 147 | " if dist[i] < crit:\n", 148 | " print('Value Function Converged, Iteration = %5.0f' % i)\n", 149 | " break\n", 150 | "end = time()\n", 151 | "\n", 152 | "print('It took %1.2f seconds' % (end-start))" 153 | ] 154 | }, 155 | { 156 | "cell_type": "code", 157 | "execution_count": 528, 158 | "metadata": {}, 159 | "outputs": [ 160 | { 161 | "data": { 162 | "image/png": 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nVfWeqrrPHM/NApjADQAAYBhzC+OttWcl+e5MZlL/wST/UFUvqaoj53UNFkfLOAAAQH/m2TKe1tonWmvfn+RpSa5K8suZdF3/0Xleh/mYncANAACAvsw1jK9orb0pyelJfiPJXZO8tareVVWnLeJ6HJjZburiOAAAQF8WEsaTpLV2Q2vteZnc2uw9Sf5Fks9U1X+pqq2Lui77bmYCt53DlQMAAGBsFhbGV7TWLm6tPS7JkzK5F/nzk3y2qp606GuzZzO3NtNRHQAAoDcLD+MrWmt/meT+SV6Y5KQkf1ZV7+jr+qxldxrfKYsDAAD0prcwXlWbkpya5KIkb8kkCT62r+tzezMt48I4AABAb7Ys4qRVdfck39k9HtAtz0hyxMou3fLGRVyffWMCNwAAgGHMLYxX1auzO4Afv7J6apfLk3xq1eOSeV2/K8OvJ3loJjO53ynJTUm+lOTtSX67tXbVGsecleQFSb4vydauTH+Y5NWttR3zLN9GMzOBmzAOAADQm3m2jD+7W96c5OPZHbg/neRTrbWr53it9fxsd+2/TnJlkqMzCdnnJvl/q+r7WmuXr+zcTSL3tq7Mb06yLckTkrwiydlJntJDmQfjPuMAAADDmGcY/7FMwvdFrbWhbpR1bGvt5tUrq+olSX4lyS8n+ffdumOTvDbJjiSPbK19rFv/wiTvS3JOVT21tXZeX4Xv3UzL+HDFAAAAGJu5TeDWWjuvtXbhgEE8awXxzp92y/tMrTsnk1ndz1sJ4lPneEH39KfmXsgNxJhxAACAYfQ2m/rAntAtPz217tHd8t1r7H9+JpPLnVVVR6yxfSmYTR0AAGAYC5lNfWhV9QtJjklyXCYTun1/JkH8pVO73bdbXrz6+Nba9qr6YpLvSHKvJBfu5XoXrLPpfvtX8n7VzH3GpXEAAIC+LGUYT/ILSe4y9fzdSX6itfaNqXXHdctr1jnHyvrj19l+yNMyDgAAMIylDOOttbsmSVXdJclZmbSIf6KqHt9a+/g+nmYlqu41prbWzlzzBJMW84fs4/X659ZmAAAAg1jqMeOttStaa3+e5DFJTkzyxqnNKy3fx93uwIljV+23dNzaDAAAYBhLHcZXtNa+lOSzSb6jqu7Urb6oW56+ev+q2pLk1CTbk1zaSyEHYDZ1AACAYfQSxqvqjVX1a31caw/u3i13dMv3dcvHrrHvw5McleTDrbVbFl2woZT7jAMAAAyir5bxf53kSYu8QFXdr6ruusb6TVX1kiR3ziRcf6vb9NYk30zy1Kp66NT+W5P8avf0NYss89BmJ3CTxgEAAPqyTBO4PTbJb1TV+Um+kOSqTGZUf0Qmtyf7epJnruzcWru2qp6ZSSh/f1Wdl2RbkidmctuztyZ5c6//gt5N39pswGIAAACMzDKF8f+d5PeTnJ3kgZnckuyGTO4j/sdJXtVa2zZ9QGvt7VX1iCTPT/LkJFuTXJLk57r9lzqizrSMD1cMAACA0VmaMN5a+0ySZx/AcR9K8rj5l2jjM4EbAADAMEYxmzprK/cZBwAAGIQwPmKzLeMDFgQAAGBkhHGSmMANAACgT8L4iBkzDgAAMAxhfMQ2TdW+LA4AANAfYXzEauY+49I4AABAX4TxEXOfcQAAgGH0Fcb/KclXeroW+8itzQAAAIaxpY+LtNZO6eM67J8qTeMAAABD0E19xKZnU9cyDgAA0B9hfMSm2sXdZxwAAKBHwviIzdxnXD91AACA3gjjIzYzgdvO4coBAAAwNsL4iE2HcQAAAPojjI+YCdwAAACGsdAwXlX3rKo/XOQ1OHDuMw4AADCMRbeMn5Dk6Qu+BgdoZgI3WRwAAKA3Ww7m4Kp62l52+baDOT+L5dZmAAAAwzioMJ7kDUluTNa9L5Yx6RtYzczgJo0DAAD05WDD8leTPK21doe1HknOnkMZWZBNM2PGhysHAADA2BxsGL8gyUP2sL1ltjc0G0iZTR0AAGAQB9tN/WVJjtnD9kuSPOogr8GCTLeMy+IAAAD9Oagw3lr74F6235DkAwdzDRanomUcAABgCCZYG7Garn1ZHAAAoDfC+IhtMmYcAABgEML4iLnPOAAAwDDmHsar6uyqOmLe52X+plvGm37qAAAAvVlEy/i7ktxjAedlzsp9xgEAAAaxiDDuvuKHiOkwrmEcAACgP8aMj5gJ3AAAAIZxUPcZT5Kq+k+rVh2e5DlVtW1lRWvtxQd7HeZvdgI3YRwAAKAvBx3Gk5y66nklOTnJcd1zKW+Dmp3ADQAAgL4cdBhvrf3k9POqOifJL7bWLj3Yc7NY02PGNYwDAAD0x5jxEauanWuvSeQAAAC9EMZHbpPbmwEAAPRuEWH8vybZtte92BDKjOoAAAC9m8cEbjNaa78273OyOJursqObvk0YBwAA6Idu6iM3PWx8587hygEAADAmwvjIbZ4aNL5DyzgAAEAvhPGR22zMOAAAQO+E8ZGb7aYujAMAAPRhLhO4VdUjkrw8yUlJLknyyanHZ1tr2+dxHeZvppu6MA4AANCLec2m/rokn0nyiiT3TvLgJOckOTnJrUm2zuk6zNl0GJfFAQAA+jGvMH7XJI9prV06vbKqTsgkmLNBuc84AABA/+Y1ZvyDSU5ZvbK1tq219t45XYMFmJ7ATTd1AACAfswrjL8myQur6qQ5nY+ezHZTF8YBAAD6MK9u6m/vlhdX1TuSfCTJJ5J8srV245yuwQLMzqY+XDkAAADGZF5h/J5JHpTkgd3yOUlOS9Kq6vOttfvP6TrM2cxs6lrGAQAAejGXMN5a+0qSryR5x8q6qjoqk3D+XfO4Boux2QRuAAAAvZvXmPFU1Uu7AJ4kaa3d2Fr7SGvt9+Z1DeZvtpu6MA4AANCHuYXxJL+Y5MKqevIcz8mC6aYOAADQv3mG8d9Pco8kf1pV76mq+8zx3CzIpulu6iZwAwAA6MXcwnhr7VlJvjuTmdR/MMk/VNVLqurIeV2D+dtkzDgAAEDv5tkyntbaJ1pr35/kaUmuSvLLmXRd/9F5Xof5memmbsw4AABAL+Yaxle01t6U5PQkv5HkrkneWlXvqqrTFnE9DtymTVrGAQAA+raQMJ4krbUbWmvPy+TWZu9J8i+SfKaq/ktVbV3Uddk/m6ZnUxfGAQAAerGwML6itXZxa+1xSZ6Uyb3In5/ks1X1pEVfm72bvs/4DhO4AQAA9GLhYXxFa+0vk9w/yQuTnJTkz6rqHX1dn7Xppg4AANC/3sJ4VW1KcmqSi5K8JUkleewcz39iVT2jqv68qi6pqpuq6pqq+tuq+rfd9dc67qyqemdVbauqG6vq01X13KraPK+ybWQz3dRN4AYAANCLLYs4aVXdPcl3do8HdMszkhyxsku3vHGOl31Kktck+VqSv0nyT0nukuRfJvmDJD9UVU9pbXfzb9dV/m1Jbk7y5iTbkjwhySuSnN2dc6nNzKauZRwAAKAXcwvjVfXq7A7gx6+sntrl8iSfWvW4ZF7XT3JxkicmeUdrbdfo56r6lSR/n+TJmQTzt3Xrj03y2iQ7kjyytfaxbv0Lk7wvyTlV9dTW2nlzLOOGM3uf8QELAgAAMCLzbBl/dre8OcnHsztwfzrJp1prV8/xWrfTWnvfOuu/XlW/m+QlSR6ZLownOSeTsetvXAni3f43V9ULkrw3yU8lGU8Yl8YBAAB6Mc8w/mOZhO+LplumN4jbuuX2qXWP7pbvXmP/8zPpQn9WVR3RWrtlkYUb0kw3dWEcAACgF3ML4xu1O3dVbUnytO7pdPC+b7e8ePUxrbXtVfXFJN+R5F5JLtzLNS5YZ9P99q+0/Zvtpi6MAwAA9KG32dQH9NJMJpF7Z2vtPVPrj+uW16xz3Mr649fZvhRmZlMXxgEAAHqxkNnUN4qqek6Sn0/yuSQ/vr+Hd8u9JtTW2pnrXP+CJA/Zz+v2arab+oAFAQAAGJG5hPGq+rZ5nKdzdWvt2oM9SVU9O8lvJflskh9orW1btctKy/dxWduxq/ZbSps26aYOAADQt3m1jF+WfWhB3kcvSvLigzlBVT03k3uFfyaTIH7lGrtdlOShSU5PMjPmuxtnfmomE75dejBl2eiMGQcAAOjfvML4izO/MP6Bgzm4qp6XyTjxTyb5wdbaN9fZ9X1J/p8kj03yP1Zte3iSo5Kcv8wzqSfJ5qkx42ZTBwAA6Mdcwnhr7dx5nOdgVdULM/li4IIkj1mja/q0tyb59SRPrapXr9xrvKq2JvnVbp/XLLK8G8Fsy/iABQEAABiRpZnAraqenkkQ35Hkg0meU1NBs3NZa+0NSdJau7aqnplJKH9/VZ2XZFuSJ2Zy27O3JnlzP6UfzsyYcWkcAACgF0sTxjMZ450km5M8d519PpDkDStPWmtvr6pHJHl+kicn2ZrkkiQ/l+RVrS3/IOrNU19Y7Fj+fy4AAMCGsDSzqXdd5c89gOM+lORx+3vcstg0dad5E7gBAAD0YylnU2ffzYwZ100dAACgF0s3mzr7Z/PUmHGzqQMAAPRjqWZTZ/+ZTR0AAKB/m/a+C8tsNoxL4wAAAH0Qxkdu89Q7QDd1AACAfgjjI6ebOgAAQP+E8ZHbtEk3dQAAgL4J4yO32a3NAAAAeieMj9xUw3h2aBkHAADohTA+cjPd1LWMAwAA9EIYH7nNJnADAADonTA+ctMt49ulcQAAgF4I4yO3xWzqAAAAvRPGR27zVBi/bcfOAUsCAAAwHsL4yE23jO/QTR0AAKAXwvjIbdm8+y1gzDgAAEA/hPGRm2kZ3yGMAwAA9EEYH7mZMeM7jRkHAADogzA+codNdVM3ZhwAAKAfwvjIbXafcQAAgN4J4yNnzDgAAED/hPGRm20ZN2YcAACgD8L4yB3m1mYAAAC9E8ZHbrpl3ARuAAAA/RDGR256zPhtO3RTBwAA6IMwPnJaxgEAAPonjI/cFmPGAQAAeieMj9wWLeMAAAC9E8ZHbvPMmHFhHAAAoA/C+Mht2TzdMm4CNwAAgD4I4yO3ZZMx4wAAAH0TxkfOmHEAAID+CeMjNz1mfLsx4wAAAL0Qxkduesz4dmPGAQAAeiGMj9z0mHHd1AEAAPohjI/c9JhxE7gBAAD0Qxgfuc2bjRkHAADomzA+crMt48aMAwAA9EEYHzljxgEAAPonjI/cdMv4bTtaWhPIAQAAFk0YH7lNmyq1O49H4zgAAMDiCePksKmu6saNAwAALJ4wTjZPdVU3bhwAAGDxhHFuN24cAACAxRLGmbnXuJZxAACAxRPGmbm92W07jBkHAABYNGGcHLFl99vg1u3COAAAwKIJ4+SwzdNjxoVxAACARRPGyeHTLePCOAAAwMIJ48yGcd3UAQAAFk4YJ4dtNoEbAABAn4RxcvhUGL9FyzgAAMDCCePMdFO/bYf7jAMAACyaMM5My7gx4wAAAIsnjGMCNwAAgJ4J45jADQAAoGfCOFrGAQAAeiaMM9MyfouWcQAAgIUTxskR07OpaxkHAABYuKUJ41V1TlW9uqo+WFXXVlWrqjft5ZizquqdVbWtqm6sqk9X1XOranNf5d4IZrqpaxkHAABYuC1DF2COXpDkgUmuT/LlJPfb085V9aQkb0tyc5I3J9mW5AlJXpHk7CRPWWRhN5LDNteun7WMAwAALN7StIwn+dkkpyc5NslP7WnHqjo2yWuT7EjyyNbav22t/cckD0rykSTnVNVTF1zeDePwzbs7AmgZBwAAWLylCeOttb9prX2+tdb2YfdzkpyU5LzW2semznFzJi3syV4C/TIxmzoAAEC/lqmb+v54dLd89xrbzk9yY5KzquqI1toteztZVV2wzqY9dpXfKKa7qWsZBwAAWLylaRnfT/ftlhev3tBa257ki5l8UXGvPgs1lCO0jAMAAPRqrC3jx3XLa9bZvrL++H05WWvtzLXWdy3mD9m/ovVv+j7jwjgAAMDijbVlfG9W+m3vy/jzQ55bmwEAAPRrrGF8peX7uHW2H7tqv6W29bDds6nfcpswDgAAsGhjDeMXdcvTV2+oqi1JTk2yPcmlfRZqKEdOhfGbbtsxYEkAAADGYaxh/H3d8rFrbHt4kqOSfHhfZlJfBkcctvttcLMwDgAAsHBjDeNvTfLNJE+tqoeurKyqrUl+tXv6miEKNoTplnFhHBJjhvoAABfKSURBVAAAYPGWZjb1qvqRJD/SPb1rt3xYVb2h+/mbrbVfSJLW2rVV9cxMQvn7q+q8JNuSPDGT2569Ncmb+yr70I48XDd1AACAPi1NGE/yoCRPX7XuXtl9r/AvJfmFlQ2ttbdX1SOSPD/Jk5NsTXJJkp9L8qrW2ihmUk+MGQcAAOjb0oTx1tq5Sc7dz2M+lORxiyjPoWQmjN9qNnUAAIBFG+uYcaZsPdyYcQAAgD4J49yum/qIeugDAAAMQhgnh23elC2bKkmyY2fLbTuEcQAAgEUSxkmy6vZm23VVBwAAWCRhnCSrxo3fKowDAAAskjBOErc3AwAA6JMwThJhHAAAoE/COEmSrYftfivcpJs6AADAQgnjJEm2TreMC+MAAAALJYyTJDn6iC27fr5BGAcAAFgoYZwkyR227g7j191824AlAQAAWH7COElmw/j1t2wfsCQAAADLTxgnSXLMEYft+vm6m4VxAACARRLGSbK6m7owDgAAsEjCOEmMGQcAAOiTME4SY8YBAAD6JIyTxJhxAACAPgnjJNFNHQAAoE/COElM4AYAANAnYZwkyR10UwcAAOiNME4S3dQBAAD6JIyTJDn2yMNSNfn52pu3Z/uOncMWCAAAYIkJ4yRJNm+qHH/k7q7q37pR6zgAAMCiCOPscsLRh+/6edsNtw5YEgAAgOUmjLPLiUcfsevnq264ZcCSAAAALDdhnF3uePTubupaxgEAABZHGGeXE6Zaxr8ljAMAACyMMM4uJ06NGb9KGAcAAFgYYZxdTOAGAADQD2GcXU48Zqpl/HphHAAAYFGEcXa58x227vr569fePGBJAAAAlpswzi53P353GP/q1TcNWBIAAIDlJoyzy12P2x3Gr7j25mzfsXPA0gAAACwvYZxdjtiyOXc6ZnJ7s50tufK6WwYuEQAAwHISxpmhqzoAAMDiCePMuNtUV/WvXmMSNwAAgEUQxplx8h2P2vXz5dtuHLAkAAAAy0sYZ8a9Tjp6189fuPL6AUsCAACwvIRxZpx20jG7fv7CN4RxAACARRDGmTHTMv6NG9JaG7A0AAAAy0kYZ8ZJxxyRO2zdkiS5/pbtueJatzcDAACYN2GcGVWVe995d1f1C79+7YClAQAAWE7COLfzXfc4btfPn7r86gFLAgAAsJyEcW7ngfc8ftfPn/7yNQOWBAAAYDkJ49zOd528O4x/6vKrTeIGAAAwZ8I4t3OvOx29axK3q264NZe43zgAAMBcCePczqZNlbNPu9Ou5x+4+BsDlgYAAGD5COOs6eGnn7Tr5/M//80BSwIAALB8hHHW9PDTd7eM/90Xrso1N942YGkAAACWizDOmk6+41H5zu4WZ7fu2Jl3/MPXBi4RAADA8hDGWdePPvgeu35+ywWXD1gSAACA5SKMs64nPuju2bKpkiSf+Ker89HLtg1cIgAAgOUgjLOuOx1zxEzr+Kve+3n3HAcAAJgDYZw9etYjT0tNGsfzwc9/M3/92SuGLRAAAMASEMbZo9NOOiZP/e5v2/X8hX/xmXzjulsGLBEAAMChTxhnr5732PvmxKMPT5Jcce0tefaffDw33bpj4FIBAAAcuoRx9ur4ow7Py//vB+3qrv73l23LM9740Vx3s3uPAwAAHAhhnH3yiNNPyi899n67nn/okqvyxN/+UD795asHLBUAAMChafRhvKpOrqo/rKqvVtUtVXVZVb2yqu44dNk2mn/3iNPyH//FfXc9/+I3b8iTfudD+aW3fTpfuuqGAUsGAABwaNkydAGGVFWnJflwkjsn+Yskn0vyPUl+Jsljq+rs1tpVAxZxw3n2o+6dk+94ZH75z/4hN966I60l53308rz5Y5fn0fe9cx7/wLvlB864S47detjQRQUAANiwRh3Gk/x/mQTx57TWXr2ysqpenuRnk7wkybMGKtuG9aQH3SMPPPn4vPh/fTbv+9yVSZLWkvd+7sq893NXZvOmygPufmy+59QT8l0nH5/T73KHnHqno3P4ltF3xAAAAEiSVGtt6DIMoqruleQLSS5LclprbefUtjsk+VqSSnLn1toB9cGuqgse8pCHPOSCCy6YQ4k3pg9d8s289oOX5v0XfWOP+23ZVDn5jkfmbscdmbsdtzV3O35rTjrmiBx9xJYcc8SWbD18czZVZVMllW7ZPd+0qVKZel6VTVWpSmrq+coxu9dlar/Z55tqcs5d59o0u276HDW1BAAAWHHmmWfm4x//+Mdba2fu77Fjbhl/dLf8q+kgniStteuq6kNJHpPk+5K8t+/CHSrOvvedcva975TLvnlD3vEPX8u7PvO1/ONXr83q73i272y57Kobc9lVNw5T0DmZDvTJ5IuD7r+ZddWtS7ovCCYbZtftOq6641bOMX3+dPutXtcds7JunX1Wrrt63eqyJrcvx8o5d59/6sApq9es9Z3FWl9jrP5yY+191jpXrV6xj9fby3nW2mdfrr/OfrffZ/jXbvWevl+aPy/p/Hmfzt9an2McHO/T+fOaMu2h335C/s33nzp0MeZuzGF8ZSayi9fZ/vlMwvjp2UsYr6r1mr7vt876pXPKnY7Osx917zz7UffO1Tfemo9d9q187EvfysVXXJeLr7guX/7WTUMXcS52tmTnzDcN4+xZAgAAfTls83IOdx1zGD+uW16zzvaV9cf3UJalcvxRh+ef3/8u+ef3v8uudTfeuj1f+dZN+eo1N+fr19yUr159c7bdcGtuuGV7rr9le27evjOttbQu7O7sfp5+vrNNom9beb5zdzBe2b77uNnnO2fOvfscLcnOnau2ZXqf3ccCAADMy5jD+N6sdI7Zawxbb3xA12L+kHkW6lB11OFbcp+73CH3ucsdhi7KAVsJ5zt2Tt4SLbtD+q5lt27lS4PJum77PuzT0qb2272uzayb/XJgep+2a13bfd2Vq7bMrNt1zMp1p7etWjdd1pnX5Hav0Zqv3O3XtL3tsfa5Vpdhn49bveea+xzAedbYb+0y7f21W7tM+3C9ffi3rFUG3y/Nny/tFsGLOm/ep/PnJZ0/71NWu/vxW4cuwkKMOYyvtHwft872Y1ftx8hVVTZXsnmTQUwAAMDBWc7O9/vmom55+jrb79Mt1xtTDgAAAAdkzGH8b7rlY6pq5nXobm12dpKbkvxd3wUDAABguY02jLfWvpDkr5KckuTZqza/KMnRSd54oPcYBwAAgPWMecx4kvz7JB9O8qqq+oEkFyb53iSPyqR7+vMHLBsAAABLarQt48mu1vGHJnlDJiH855OcluRVSR7WWrtquNIBAACwrMbeMp7W2uVJfnLocgAAADAeo24ZBwAAgCEI4wAAANAzYRwAAAB6JowDAABAz4RxAAAA6JkwDgAAAD0TxgEAAKBnwjgAAAD0TBgHAACAngnjAAAA0LNqrQ1dhqVVVVcdeeSRJ5xxxhlDFwUAAIA5u/DCC3PTTTdta62duL/HCuMLVFVfTHJskssGLsqe3K9bfm7QUnCg1N+hTx0e2tTfoU8dHvrU4aFN/R36xl6HpyS5trV26v4eKIyPXFVdkCSttTOHLgv7T/0d+tThoU39HfrU4aFPHR7a1N+hTx0eOGPGAQAAoGfCOAAAAPRMGAcAAICeCeMAAADQM2EcAAAAemY2dQAAAOiZlnEAAADomTAOAAAAPRPGAQAAoGfCOAAAAPRMGAcAAICeCeMAAADQM2EcAAAAeiaMj1BVnVxVf1hVX62qW6rqsqp6ZVXdceiyLaOqOrGqnlFVf15Vl1TVTVV1TVX9bVX926pa8/ewqs6qqndW1baqurGqPl1Vz62qzXu41uOr6v3d+a+vqv9TVU/fS/meXlV/3+1/TXf84w/2373squrHq6p1j2ess8/C66OqNnfvi093761t3fvmrIP9Ny6jqvpnVfW2qvpa9/n3tar6q6p63Br7+h3cYKrqh7v6+nL3fr+0qt5SVQ9bZ3912LOqOqeqXl1VH6yqa7vPyDft5ZgNWU9j/Hzdn/qrqvtU1fOq6n1VdXlV3VpVV1TVX1TVo/ZynYXXRVUdWVUvqqqLqurmqrqyqv60qs7Y91fk0HMgv4Orjn9d7f775t7r7NNLfVTVCTXJKJfV5P/ZX61Jhjl5X/89G15rzWNEjySnJbkiSUvy9iQvTfK+7vnnkpw4dBmX7ZHkWd3r+9Ukf5Lk15L8YZKru/VvTVKrjnlSku1Jrk/yuiS/0dVPS/KWda7z0932byb5nSSvSHJ5t+5l6xzzsm775d3+v5Pkqm7dTw/92m3UR5J7dvV3XfdaPWOI+khSSd4y9fv7G9375fru/fOkoV+rjfRI8oLutfpGktcn+a9Jfj/JR5P8t1X7+h3cYI8kvz71+v5B9/+vtya5NcnOJP9aHQ7/SPLJ7t9+XZILu5/ftIf9N2Q9jfXzdX/qL8l53fZ/TPJ7mfx982fd69OSPGeoukhyRJK/7Y75aPf58d+T3JbkhiTfO/RrvRHqcI1jnzB1bEty76HqI8mJSS7qjnlvJp/5b++eX5HkXkO/1nOpr6EL4NFzhSfv6d7E/2HV+pd363936DIu2yPJo7sPt02r1t81yT91r/uTp9Yfm+TKJLckeejU+q1JPtzt/9RV5zolyc3d/8xOmVp/xySXdMc8bNUxZ3XrL0lyx1Xnuqo73ykH829fxkf3P6H/neQL3f+AbhfG+6qPJP+qO+ZDSbZOrf/u7v1zZZI7DP2abYRHkqd0r9Vfr/WaJDls6me/gxvs0X1e7kjy9SR3XrXtUd3reKk6HP7R1cd9us/KR2bPYW7D1lNG+vm6n/X3E0kevMb6R2TyJdktSe42RF0k+eXumLdk6u+vTL78WfkCYdPeXo9D8bE/dbjquJMy+Yw9L8n7s34Y76U+MvmCpyV5+ar1z+nWv3vo13ou9TV0ATx6rOzkXt2b94trvOHvkMk3WjckOXroso7lkeRXujp59dS6f9Ot+6M19n90t+0Dq9a/uFv/ojWOWfN8Sd7Yrf/JNY5Z93xjfyT5mUxa4R6e5NysHcZ7qY8k53frH7XGMeueb2yPTIZkXdp9vp20D/v7HdxgjyTf270ef7HO9muTXKcON9Yjew9zG7aefL7uvf72cuxfZVVjQ191kUkI/VK3/tQ1jln3fMv22J86TPLnmYTxE7PnML7w+khydJIbM8kmq4P9pkyyTMsStI4bMz4uj+6Wf9Va2zm9obV2XSbfcB2V5Pv6LtiI3dYtt0+tW6mnd6+x//mZfDidVVVH7OMx71q1z8EcM2rduKaXJvmt1tr5e9h14fXR1f9ZmbwfPrgf1xmjs5KcmuSdSb7VjTt+XlX9zDpjjf0Objyfz6Sl7Xuq6k7TG6rq4Zl8ofy/p1arw0PDhqwnn69zsdbfN0k/dXFakm9LcnFr7Yv7eMyoVdVPJPmRJM9qrV21h/36qo+HJTkyyYe6jLJLl2H+qnu6x7kJDgXC+Ljct1tevM72z3fL03soy+hV1ZYkT+ueTv9Pad16aq1tz+TbwC2Z9HTYl2O+lkmL4MlVdVR37aOT3CPJ9d321bwXVunq648zGVrwK3vZvY/6uHeSzZl0zV39x856x4zVd3fLK5J8PMn/yuRLlVcm+XBVfaCqTpra3+/gBtNa25bkeUnukuSzVfX7VfVrVfWnmfxR9tdJ/t3UIerw0LBR68nn60Goqm9P8gOZBLbzp9b3VRf+3t0PXX39Viat52/fy+591cdo6lAYH5fjuuU162xfWX98D2VhEgYekOSdrbX3TK0/kHra12OOW7X0Xth3/ynJg5P8RGvtpr3s20d9qMN9d+du+axMvmn/55m0pD4gk3k0Hp7JOLYVfgc3oNbaK5P8y0zC2TOT/FImcwFcnuQNrbUrp3ZXh4eGjVpP6vYAdS2nf5LJhF3ntta+NbW5r7pQf/uoJnf0+aNMuoM/Zx8OUYdzJowzrbplG7QUI1BVz0ny85nMQvnj+3t4t9yfejrQuvVeSFJV35NJa/hvttY+Mo9TdstF1off591Wbo9USc5prb23tXZ9a+0fk/xoki8necQ6XdbX4ndwAFX1i5nMnv6GTLo9Hp3kzEzmA/iTqvpv+3O6bqkON7aNWk8+X9dQk1vR/XGSs5O8OZNZ0w/EoutC/e32s5lMuPfMVV+cHKi+6mNp6lAYH5fV3xavduyq/ViAqnp2Jt2BPpvJZBXbVu1yIPW0r8dcu4/77+0bydGY6p5+cZIX7uNhfdSH3+d9t/IHxqWttU9Nb+h6Oaz0TPmebul3cIOpqkdmciuc/9la+7nW2qWttRtbax/P5AuVryT5+apa6c6sDg8NG7WefL7upy6IvymT3ip/msmtBlcHpb7qQv3tg6q6T5KXJHl9a+2d+3hYX/UxmjoUxsflom653viK+3TL9cZncJCq6rlJfjvJZzIJ4l9fY7d166kLhqdmMiHKpft4zN0yaUH6cmvtxiRprd2QyR+vx3TbV/Ne2O2YTF7XM5LcXFVt5ZHkP3f7vLZb98rueR/1cUkmt3q6V/e+2JdjxmqlPq5eZ/tKWD9y1f5+BzeOx3fLv1m9oXtN/z6Tv2ke3K1Wh4eGjVpPPl/3Q/ca/Y8kT83k3tE/ttZ44h7rwt+7++Y7MhlO8JPTf9t0f988otvn8926H+me91Ufo6lDYXxcVv6IeUw3RmSXqrpDJt2Kbkryd30XbAyq6nlJXpHkk5kE8SvX2fV93fKxa2x7eCYz3n+4tXbLPh7zQ6v2OZhjxuiWJK9b5/GJbp+/7Z6vdGFfeH109f/hTN4P/2w/rjNG52fyB/19qurwNbY/oFte1i39Dm48K7Npn7TO9pX1t3ZLdXho2JD15PN133WfqW/NpEX8jUl+vLW2Yw+H9FEXX8hkstXTq+rUfTxmjC7L+n/frDQWvaV7flnSa338XSaZ5Owuo+zSZZjHdE9v9wXtIWfoe6t59PvIpDtmS/IfVq1/ebf+d4cu4zI+Mune3JJ8LMkJe9n32CTfyCQEPnRq/dZMPgBbkqeuOubUJDcnuSrJKVPr75jJt5gtycNWHXNWt/6SJHecWn9Kd56bp8/lsWZdnZu17zPeS30k+VfdMR9KsnVq/Xd3758rkxw79Ou0ER6ZdJ9sSX511fofzOS+8VcnOb5b53dwgz2S/F/da/X1JPdYte2Hujq8KcmJ6nDjPLL3+4xv2Hry+bpP9XdEknd0+/xBkk37cM5e6iLJL3fHvGW6XEme1K3/x30p76H+2Fsd7uG492f9+4z3Uh9Jfq/b9pur1j+nW//uoV/fudTR0AXw6LnCJ5PeXNG9id+e5Ncy+SaqZdIl5MShy7hsjyRP717f7Zm0jJ+7xuMnVh3zI93+13f/g/tvmUz2tvJBVmtc5z9027+Z5He6a13erXvZOmX7zW775d3+v9Md35L89NCv3UZ/ZJ0w3ld9ZDKByVu67Rd275PXde+b7UmeNPRrtFEemcyo/vnutTo/k4mF3tK9Trclecqq/f0ObqBHJj35/rp7Xa7NZPbfX0/yPzMJ4i3Jz6jD4R/d6/6G7vHu7nX4wtS6l62x/4arp4z083V/6i/J67vt30jyoqz9980jh6iLTL4o+FB3zEczuYPNf8/k8/6GJN879Gu9EepwD+d4f9YP473UR5ITM8kmLcl7M8ksb++eX5HktKFf67nU19AF8Big0pN7dh+gX8ukS9+XMplQbI8tth4H/Hqf231w7Onx/jWOOzvJOzMZz3pTkn/IZNbLzXu41hOSfCDJdd2H20eTPH0v5Xt6t98N3XEfSPL4oV+3Q+GRPYTxvuojk9s8/Wz3/ripe7+8M8lZQ78+G+2R5IRMegF9sfvsuyrJXyT5vnX29zu4gR5JDkvy3Ey6L17b/dF3ZSb3jX+MOtwYj334f95lh0o9jfHzdX/qL7sD254e5w5VF5nMA/KiTL6IvSWTLw3ekuT+Q7/OG6UO93COlbq9XRjvsz4y+f/2b2WSVW7NJLv8YZKTh36d5/Wo7h8KAAAA9MQEbgAAANAzYRwAAAB6JowDAABAz4RxAAAA6JkwDgAAAD0TxgEAAKBnwjgAAAD0TBgHAACAngnjAAAA0DNhHAAAAHomjAMAAEDPhHEAAADomTAOAAAAPRPGAQAAoGfCOAAAAPRMGAcAAICeCeMAAADQs/8f/ez6zrN5dRsAAAAASUVORK5CYII=\n", 163 | "text/plain": [ 164 | "
" 165 | ] 166 | }, 167 | "metadata": { 168 | "image/png": { 169 | "height": 248, 170 | "width": 497 171 | }, 172 | "needs_background": "light" 173 | }, 174 | "output_type": "display_data" 175 | } 176 | ], 177 | "source": [ 178 | "import matplotlib.pyplot as plt\n", 179 | "%config InlineBackend.figure_format = 'retina'\n", 180 | "\n", 181 | "\n", 182 | "fig, ax = plt.subplots(figsize = (8, 4))\n", 183 | "ax.plot(dist)\n", 184 | "ax.set_ylabel(r'$||V^{n+1} - V^n||$')\n", 185 | "plt.show()" 186 | ] 187 | }, 188 | { 189 | "cell_type": "code", 190 | "execution_count": 529, 191 | "metadata": {}, 192 | "outputs": [ 193 | { 194 | "data": { 195 | "image/png": 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\n", 196 | "text/plain": [ 197 | "
" 198 | ] 199 | }, 200 | "metadata": { 201 | "image/png": { 202 | "height": 316, 203 | "width": 503 204 | }, 205 | "needs_background": "light" 206 | }, 207 | "output_type": "display_data" 208 | } 209 | ], 210 | "source": [ 211 | "fig, ax = plt.subplots(figsize = (8, 5))\n", 212 | "ax.plot(k, v)\n", 213 | "ax.set_ylabel(r'$v(k)$')\n", 214 | "ax.set_xlabel(r'$k$')\n", 215 | "ax.grid()\n", 216 | "plt.show()" 217 | ] 218 | }, 219 | { 220 | "cell_type": "code", 221 | "execution_count": 530, 222 | "metadata": {}, 223 | "outputs": [ 224 | { 225 | "data": { 226 | "image/png": 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\n", 227 | "text/plain": [ 228 | "
" 229 | ] 230 | }, 231 | "metadata": { 232 | "image/png": { 233 | "height": 316, 234 | "width": 727 235 | }, 236 | "needs_background": "light" 237 | }, 238 | "output_type": "display_data" 239 | } 240 | ], 241 | "source": [ 242 | "kdot = k**α - δ*k - c\n", 243 | "fig, ax = plt.subplots(1,2,figsize = (12, 5))\n", 244 | "ax[0].plot(k, c)\n", 245 | "ax[0].set_ylabel(r'$c(k)$')\n", 246 | "ax[0].set_xlabel(r'$k$')\n", 247 | "ax[0].grid()\n", 248 | "\n", 249 | "ax[1].plot(k, kdot)\n", 250 | "ax[1].plot(k, np.zeros(N))\n", 251 | "ax[1].set_ylabel(r'$s(k)$')\n", 252 | "ax[1].set_xlabel(r'$k$')\n", 253 | "ax[1].grid()\n", 254 | "plt.show()" 255 | ] 256 | } 257 | ], 258 | "metadata": { 259 | "kernelspec": { 260 | "display_name": "Python 3", 261 | "language": "python", 262 | "name": "python3" 263 | }, 264 | "language_info": { 265 | "codemirror_mode": { 266 | "name": "ipython", 267 | "version": 3 268 | }, 269 | "file_extension": ".py", 270 | "mimetype": "text/x-python", 271 | "name": "python", 272 | "nbconvert_exporter": "python", 273 | "pygments_lexer": "ipython3", 274 | "version": "3.6.9" 275 | }, 276 | "varInspector": { 277 | "cols": { 278 | "lenName": 16, 279 | "lenType": 16, 280 | "lenVar": 40 281 | }, 282 | "kernels_config": { 283 | "python": { 284 | "delete_cmd_postfix": "", 285 | "delete_cmd_prefix": "del ", 286 | "library": "var_list.py", 287 | "varRefreshCmd": "print(var_dic_list())" 288 | }, 289 | "r": { 290 | "delete_cmd_postfix": ") ", 291 | "delete_cmd_prefix": "rm(", 292 | "library": "var_list.r", 293 | "varRefreshCmd": "cat(var_dic_list()) " 294 | } 295 | }, 296 | "types_to_exclude": [ 297 | "module", 298 | "function", 299 | "builtin_function_or_method", 300 | "instance", 301 | "_Feature" 302 | ], 303 | "window_display": false 304 | } 305 | }, 306 | "nbformat": 4, 307 | "nbformat_minor": 2 308 | } 309 | -------------------------------------------------------------------------------- /Y_butterfly.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jbduarte/Numerical_Continuous_Time/2f42aa8002c28f84242f0838c5f4aeb6978e9889/Y_butterfly.pdf -------------------------------------------------------------------------------- /aiyagari_irfs_A_shock.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jbduarte/Numerical_Continuous_Time/2f42aa8002c28f84242f0838c5f4aeb6978e9889/aiyagari_irfs_A_shock.pdf -------------------------------------------------------------------------------- /distributions_cont_incomeType.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jbduarte/Numerical_Continuous_Time/2f42aa8002c28f84242f0838c5f4aeb6978e9889/distributions_cont_incomeType.pdf -------------------------------------------------------------------------------- /policy_functions.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/jbduarte/Numerical_Continuous_Time/2f42aa8002c28f84242f0838c5f4aeb6978e9889/policy_functions.pdf --------------------------------------------------------------------------------