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chriselrod/quant_econ_julia.ipynb

Created February 12, 2018 00:08
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Quant Econ - Numba and Julia
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quant_econ_julia.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"mainOld (generic function with 2 methods)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Compat, BenchmarkTools\n",
"\n",
"\n",
"function mainNew(verbose = true)\n",
" ## 1. Calibration\n",
"\n",
" α = 1/3 # Elasticity of output w.r.t. capital\n",
" β = 0.95 # Discount factor\n",
"\n",
" # Productivity values\n",
" vProductivity = [0.9792 0.9896 1.0000 1.0106 1.0212]\n",
"\n",
" # Transition matrix\n",
" mTransition = [0.9727 0.0273 0.0000 0.0000 0.0000;\n",
" 0.0041 0.9806 0.0153 0.0000 0.0000;\n",
" 0.0000 0.0082 0.9837 0.0082 0.0000;\n",
" 0.0000 0.0000 0.0153 0.9806 0.0041;\n",
" 0.0000 0.0000 0.0000 0.0273 0.9727]\n",
"\n",
" # 2. Steady State\n",
"\n",
" capitalSteadyState = (α*β)^(1/(1-α))\n",
" outputSteadyState = capitalSteadyState^α\n",
" consumptionSteadyState = outputSteadyState-capitalSteadyState\n",
"\n",
" verbose && println(\"Output = \",outputSteadyState,\" Capital = \",capitalSteadyState,\" Consumption = \",consumptionSteadyState)\n",
"\n",
" # We generate the grid of capital\n",
" vGridCapital = collect(0.5*capitalSteadyState:0.00001:1.5*capitalSteadyState)\n",
" #vGridCapital = 0.5*capitalSteadyState:0.00001:1.5*capitalSteadyState\n",
"\n",
" nGridCapital = length(vGridCapital)\n",
" nGridProductivity = length(vProductivity)\n",
"\n",
" # 3. Required matrices and vectors\n",
"\n",
" mOutput = Matrix{Float64}(uninitialized, nGridCapital, nGridProductivity)\n",
" mValueFunction = fill(0.0, nGridCapital, nGridProductivity)\n",
" mValueFunctionNew = Matrix{Float64}(uninitialized, nGridCapital,nGridProductivity)\n",
" mPolicyFunction = Matrix{Float64}(uninitialized, nGridCapital,nGridProductivity)\n",
" expectedValueFunction = Matrix{Float64}(uninitialized, nGridCapital, nGridProductivity)\n",
"\n",
" # 4. We pre-build output for each point in the grid\n",
"\n",
" @. mOutput = vGridCapital^ α * vProductivity;\n",
"\n",
" # 5. Main iteration\n",
"\n",
" maxDifference = 10.0\n",
" tolerance = 0.0000001\n",
" iteration = 0\n",
"\n",
" while(maxDifference > tolerance)\n",
" #A_mul_Bt! for Julia < 0.7\n",
" A_mul_Bt!(expectedValueFunction, mValueFunction, mTransition)\n",
"# mul!(expectedValueFunction, mValueFunction, mTransition')\n",
"\n",
" @inbounds for nProductivity in 1:nGridProductivity\n",
"\n",
" # We start from previous choice (monotonicity of policy function)\n",
" gridCapitalNextPeriod = 1\n",
"\n",
" for nCapital in 1:nGridCapital\n",
"\n",
" valueHighSoFar = -1000.0\n",
" capitalChoice = vGridCapital[1]\n",
"\n",
" for nCapitalNextPeriod in gridCapitalNextPeriod:nGridCapital\n",
"\n",
" consumption = mOutput[nCapital,nProductivity]-vGridCapital[nCapitalNextPeriod]\n",
" valueProvisional = (1-β)*log(consumption)+β*expectedValueFunction[nCapitalNextPeriod,nProductivity]\n",
"\n",
" if (valueProvisional>valueHighSoFar)\n",
" \t valueHighSoFar = valueProvisional\n",
" \t capitalChoice = vGridCapital[nCapitalNextPeriod]\n",
" \t gridCapitalNextPeriod = nCapitalNextPeriod\n",
" else\n",
" \t break # We break when we have achieved the max\n",
" end\n",
"\n",
" end\n",
"\n",
" mValueFunctionNew[nCapital,nProductivity] = valueHighSoFar\n",
" mPolicyFunction[nCapital,nProductivity] = capitalChoice\n",
"\n",
" end\n",
"\n",
" end\n",
" \n",
" # I can write into expectedValueFunction, because we are about to\n",
" # overwrite it anyway on the start of the next iteration.\n",
" @. expectedValueFunction = abs(mValueFunctionNew-mValueFunction)\n",
" maxDifference = maximum(expectedValueFunction)\n",
" mValueFunction, mValueFunctionNew = mValueFunctionNew, mValueFunction\n",
" \n",
" iteration = iteration+1\n",
" if verbose && (mod(iteration,10)==0 || iteration == 1)\n",
" println(\" Iteration = \", iteration, \" Sup Diff = \", maxDifference)\n",
" end\n",
"\n",
" end\n",
"\n",
" if verbose\n",
" println(\" Iteration = \", iteration, \" Sup Diff = \", maxDifference)\n",
" println(\" \")\n",
" println(\" My check = \", mPolicyFunction[1000,3])\n",
" println(\" My check = \", mValueFunction[1000,3])\n",
" end\n",
" return iteration, maxDifference, mPolicyFunction[1000,3], mValueFunction[1000,3]\n",
"\n",
"end\n",
"\n",
"\n",
"function mainOld(verbose = true)\n",
"\n",
" ## 1. Calibration\n",
"\n",
" α = 1/3 # Elasticity of output w.r.t. capital\n",
" β = 0.95 # Discount factor\n",
"\n",
" # Productivity values\n",
" vProductivity = [0.9792 0.9896 1.0000 1.0106 1.0212]\n",
"\n",
" # Transition matrix\n",
" mTransition = [0.9727 0.0273 0.0000 0.0000 0.0000;\n",
" 0.0041 0.9806 0.0153 0.0000 0.0000;\n",
" 0.0000 0.0082 0.9837 0.0082 0.0000;\n",
" 0.0000 0.0000 0.0153 0.9806 0.0041;\n",
" 0.0000 0.0000 0.0000 0.0273 0.9727]\n",
"\n",
" # 2. Steady State\n",
"\n",
" capitalSteadyState = (α*β)^(1/(1-α))\n",
" outputSteadyState = capitalSteadyState^α\n",
" consumptionSteadyState = outputSteadyState-capitalSteadyState\n",
"\n",
" verbose && println(\"Output = \",outputSteadyState,\" Capital = \",capitalSteadyState,\" Consumption = \",consumptionSteadyState)\n",
"\n",
" # We generate the grid of capital\n",
" vGridCapital = collect(0.5*capitalSteadyState:0.00001:1.5*capitalSteadyState)\n",
"\n",
" nGridCapital = length(vGridCapital)\n",
" nGridProductivity = length(vProductivity)\n",
"\n",
" # 3. Required matrices and vectors\n",
"\n",
" mOutput = zeros(nGridCapital,nGridProductivity)\n",
" mValueFunction = zeros(nGridCapital,nGridProductivity)\n",
" mValueFunctionNew = zeros(nGridCapital,nGridProductivity)\n",
" mPolicyFunction = zeros(nGridCapital,nGridProductivity)\n",
" expectedValueFunction = zeros(nGridCapital,nGridProductivity)\n",
"\n",
" # 4. We pre-build output for each point in the grid\n",
"\n",
" mOutput = (vGridCapital.^α)*vProductivity;\n",
"\n",
" # 5. Main iteration\n",
"\n",
" maxDifference = 10.0\n",
" tolerance = 0.0000001\n",
" iteration = 0\n",
"\n",
" while(maxDifference > tolerance)\n",
" expectedValueFunction = mValueFunction*mTransition';\n",
"\n",
" for nProductivity in 1:nGridProductivity\n",
"\n",
" # We start from previous choice (monotonicity of policy function)\n",
" gridCapitalNextPeriod = 1\n",
"\n",
" for nCapital in 1:nGridCapital\n",
"\n",
" valueHighSoFar = -1000.0\n",
" capitalChoice = vGridCapital[1]\n",
"\n",
" for nCapitalNextPeriod in gridCapitalNextPeriod:nGridCapital\n",
"\n",
" consumption = mOutput[nCapital,nProductivity]-vGridCapital[nCapitalNextPeriod]\n",
" valueProvisional = (1-β)*log(consumption)+β*expectedValueFunction[nCapitalNextPeriod,nProductivity]\n",
"\n",
" if (valueProvisional>valueHighSoFar)\n",
" \t valueHighSoFar = valueProvisional\n",
" \t capitalChoice = vGridCapital[nCapitalNextPeriod]\n",
" \t gridCapitalNextPeriod = nCapitalNextPeriod\n",
" else\n",
" \t break # We break when we have achieved the max\n",
" end\n",
"\n",
" end\n",
"\n",
" mValueFunctionNew[nCapital,nProductivity] = valueHighSoFar\n",
" mPolicyFunction[nCapital,nProductivity] = capitalChoice\n",
"\n",
" end\n",
"\n",
" end\n",
" \n",
" maxDifference = maximum(abs.(mValueFunctionNew-mValueFunction))\n",
" mValueFunction, mValueFunctionNew = mValueFunctionNew, mValueFunction\n",
" \n",
" iteration = iteration+1\n",
" if verbose && (mod(iteration,10)==0 || iteration == 1)\n",
" println(\" Iteration = \", iteration, \" Sup Diff = \", maxDifference)\n",
" end\n",
"\n",
" end\n",
"\n",
"\n",
" if verbose\n",
" println(\" Iteration = \", iteration, \" Sup Diff = \", maxDifference)\n",
" println(\" \")\n",
" println(\" My check = \", mPolicyFunction[1000,3])\n",
" println(\" My check = \", mValueFunction[1000,3])\n",
" end\n",
" return iteration, maxDifference, mPolicyFunction[1000,3], mValueFunction[1000,3]\n",
"\n",
"\n",
"end"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Output = 0.5627314338711378 Capital = 0.178198287392527 Consumption = 0.3845331464786108\n",
" Iteration = 1 Sup Diff = 0.05274159340733661\n",
" Iteration = 10 Sup Diff = 0.031346949265852075\n",
" Iteration = 20 Sup Diff = 0.01870345989335709\n",
" Iteration = 30 Sup Diff = 0.01116551203397076\n",
" Iteration = 40 Sup Diff = 0.00666854170813258\n",
" Iteration = 50 Sup Diff = 0.003984292748717033\n",
" Iteration = 60 Sup Diff = 0.0023813118039327508\n",
" Iteration = 70 Sup Diff = 0.0014236586450983024\n",
" Iteration = 80 Sup Diff = 0.0008513397747205165\n",
" Iteration = 90 Sup Diff = 0.0005092051752288995\n",
" Iteration = 100 Sup Diff = 0.00030462324421465237\n",
" Iteration = 110 Sup Diff = 0.00018226485632300005\n",
" Iteration = 120 Sup Diff = 0.00010906950872624499\n",
" Iteration = 130 Sup Diff = 6.527643736320421e-5\n",
" Iteration = 140 Sup Diff = 3.907108211997912e-5\n",
" Iteration = 150 Sup Diff = 2.3388077119990136e-5\n",
" Iteration = 160 Sup Diff = 1.4008644637186762e-5\n",
" Iteration = 170 Sup Diff = 8.391317202871562e-6\n",
" Iteration = 180 Sup Diff = 5.026474537817016e-6\n",
" Iteration = 190 Sup Diff = 3.010899863653549e-6\n",
" Iteration = 200 Sup Diff = 1.8035522479920019e-6\n",
" Iteration = 210 Sup Diff = 1.080340915837752e-6\n",
" Iteration = 220 Sup Diff = 6.471316943423844e-7\n",
" Iteration = 230 Sup Diff = 3.876361938104367e-7\n",
" Iteration = 240 Sup Diff = 2.3219657907525004e-7\n",
" Iteration = 250 Sup Diff = 1.3908720930544405e-7\n",
" Iteration = 257 Sup Diff = 9.716035664908418e-8\n",
" \n",
" My check = 0.1465491436962635\n",
" My check = -0.9714880021887344\n"
]
},
{
"data": {
"text/plain": [
"(257, 9.716035664908418e-8, 0.1465491436962635, -0.9714880021887344)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mainNew()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Output = 0.5627314338711378 Capital = 0.178198287392527 Consumption = 0.3845331464786108\n",
" Iteration = 1 Sup Diff = 0.05274159340733661\n",
" Iteration = 10 Sup Diff = 0.031346949265852075\n",
" Iteration = 20 Sup Diff = 0.01870345989335709\n",
" Iteration = 30 Sup Diff = 0.01116551203397076\n",
" Iteration = 40 Sup Diff = 0.00666854170813258\n",
" Iteration = 50 Sup Diff = 0.003984292748717033\n",
" Iteration = 60 Sup Diff = 0.0023813118039327508\n",
" Iteration = 70 Sup Diff = 0.0014236586450983024\n",
" Iteration = 80 Sup Diff = 0.0008513397747205165\n",
" Iteration = 90 Sup Diff = 0.0005092051752288995\n",
" Iteration = 100 Sup Diff = 0.00030462324421465237\n",
" Iteration = 110 Sup Diff = 0.00018226485632300005\n",
" Iteration = 120 Sup Diff = 0.00010906950872624499\n",
" Iteration = 130 Sup Diff = 6.527643736320421e-5\n",
" Iteration = 140 Sup Diff = 3.907108211997912e-5\n",
" Iteration = 150 Sup Diff = 2.3388077119990136e-5\n",
" Iteration = 160 Sup Diff = 1.4008644637186762e-5\n",
" Iteration = 170 Sup Diff = 8.391317202871562e-6\n",
" Iteration = 180 Sup Diff = 5.026474537817016e-6\n",
" Iteration = 190 Sup Diff = 3.010899863653549e-6\n",
" Iteration = 200 Sup Diff = 1.8035522479920019e-6\n",
" Iteration = 210 Sup Diff = 1.080340915837752e-6\n",
" Iteration = 220 Sup Diff = 6.471316943423844e-7\n",
" Iteration = 230 Sup Diff = 3.876361938104367e-7\n",
" Iteration = 240 Sup Diff = 2.3219657907525004e-7\n",
" Iteration = 250 Sup Diff = 1.3908720930544405e-7\n",
" Iteration = 257 Sup Diff = 9.716035664908418e-8\n",
" \n",
" My check = 0.1465491436962635\n",
" My check = -0.9714880021887344\n"
]
},
{
"data": {
"text/plain": [
"(257, 9.716035664908418e-8, 0.1465491436962635, -0.9714880021887344)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mainOld()"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: \n",
" memory estimate: 3.54 MiB\n",
" allocs estimate: 15\n",
" --------------\n",
" minimum time: 1.333 s (0.00% GC)\n",
" median time: 1.335 s (0.00% GC)\n",
" mean time: 1.336 s (0.00% GC)\n",
" maximum time: 1.342 s (0.00% GC)\n",
" --------------\n",
" samples: 4\n",
" evals/sample: 1"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@benchmark mainNew(false)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"BenchmarkTools.Trial: \n",
" memory estimate: 528.54 MiB\n",
" allocs estimate: 1563\n",
" --------------\n",
" minimum time: 1.569 s (0.80% GC)\n",
" median time: 1.598 s (0.83% GC)\n",
" mean time: 1.605 s (1.69% GC)\n",
" maximum time: 1.656 s (4.21% GC)\n",
" --------------\n",
" samples: 4\n",
" evals/sample: 1"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@benchmark mainOld(false)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.6.2",
"language": "julia",
"name": "julia-0.6"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.6.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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