{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Occasionally binding constraint model - Solved with ANN (Flux.jl)\n",
"\n",
"This notebook solves the Bianchi (2011) model with occasionally binding collateral constraints using an Artificial Neural Network approach.\n",
"\n",
"**Method**: Fischer-Burmeister complementarity formulation with neural network approximation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Setup: Load Required Packages"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"using Flux\n",
"using Plots\n",
"using ProgressMeter\n",
"using LaTeXStrings\n",
"using Random\n",
"using Statistics\n",
"using Distributions\n",
"using Flux.NNlib\n",
"using CUDA\n",
"using cuDNN"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## GPU Device Selection\n",
"\n",
"Check if CUDA is available for GPU acceleration. The code will automatically fall back to CPU if not."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"if CUDA.has_cuda()\n",
" @info \"CUDA is on\"\n",
" CUDA.allowscalar(false)\n",
" const device = gpu\n",
"else\n",
" @info \"CUDA is off\"\n",
" const device = cpu\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model Calibration\n",
"\n",
"Standard parameters from Bianchi (2011):\n",
"- σ: Risk aversion\n",
"- κ: Borrowing constraint parameter\n",
"- β: Discount factor\n",
"- ω: Weight on traded goods\n",
"- η: Elasticity of substitution"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Model calibrated with σ=2.0, κ=0.2808, β=0.91\n"
]
}
],
"source": [
"# Precision type (Float32 for faster GPU computation)\n",
"const FTYPE = Float32\n",
"\n",
"# Structural parameters\n",
"const σ = FTYPE(2.0) # Inverse of intertemporal elasticity\n",
"const κ = FTYPE(0.2808) # Borrowing constraint parameter\n",
"const β = FTYPE(0.91) # Discount factor\n",
"const ω = FTYPE(0.31) # Weight on traded goods\n",
"const η = FTYPE(0.5) # Elasticity of substitution\n",
"const δ = FTYPE(0.14) # Bond duration\n",
"const τ = FTYPE(0.2) # Tax rate\n",
"\n",
"# Endowments\n",
"const yT = FTYPE(1.0) # Traded goods\n",
"const yN = FTYPE(1.0) # Non-traded goods\n",
"\n",
"# Debt grid\n",
"const l_min, l_max = FTYPE(0.1), FTYPE(0.9)\n",
"const n_l = 300\n",
"const l_grid = collect(range(l_min, l_max, length=n_l))\n",
"\n",
"# Interest rate\n",
"const i_l = FTYPE(0.05)\n",
"\n",
"println(\"Model calibrated with σ=$σ, κ=$κ, β=$β\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Stochastic Shocks\n",
"\n",
"The model includes two shocks:\n",
"1. **ν**: Government default cost\n",
"2. **φ**: Private sector default rate\n",
"\n",
"These are discretized into 25 states with transition matrix Π."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Shocks discretized: 25 states\n"
]
}
],
"source": [
"# Pre-computed transition matrix (25x25)\n",
"const Π = FTYPE.([\n",
" 2.1212e-01 5.3030e-01 0.0000e+00 0.0000e+00 0.0000e+00 1.2121e-01 1.3636e-01 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 1.7268e-02 4.6834e-01 2.5432e-01 5.2329e-04 0.0000e+00 7.8493e-03 1.6431e-01 8.6866e-02 5.2329e-04 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 8.7662e-02 5.5571e-01 8.9786e-02 0.0000e+00 0.0000e+00 3.1087e-02 2.0429e-01 3.1280e-02 1.9309e-04 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 2.4401e-01 4.7631e-01 2.0886e-02 0.0000e+00 0.0000e+00 8.1508e-02 1.6913e-01 8.1508e-03 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 3.9423e-01 3.0769e-01 0.0000e+00 0.0000e+00 9.6154e-03 1.2500e-01 1.6346e-01 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 3.3784e-03 5.0676e-03 0.0000e+00 0.0000e+00 0.0000e+00 3.3615e-01 5.1464e-01 1.0135e-02 0.0000e+00 0.0000e+00 5.0113e-02 7.9392e-02 1.1261e-03 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 3.0430e-04 8.0991e-03 4.0963e-03 2.3408e-05 0.0000e+00 2.0458e-02 5.4219e-01 2.8665e-01 1.1938e-03 0.0000e+00 3.3473e-03 8.6234e-02 4.7213e-02 1.8726e-04 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 1.4610e-03 8.4155e-03 1.3157e-03 1.7087e-05 1.1107e-04 1.0535e-01 6.4296e-01 1.0445e-01 1.2815e-04 5.1262e-05 1.5806e-02 1.0315e-01 1.6771e-02 1.7087e-05 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 2.3579e-05 4.1500e-03 8.2999e-03 4.9517e-04 0.0000e+00 1.1082e-03 2.8830e-01 5.3869e-01 2.2330e-02 0.0000e+00 3.3011e-04 4.7701e-02 8.5640e-02 2.9238e-03 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 7.2765e-03 4.1580e-03 0.0000e+00 0.0000e+00 6.2370e-03 5.0260e-01 3.4719e-01 0.0000e+00 0.0000e+00 5.1975e-04 7.6403e-02 5.5613e-02 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 2.1251e-02 2.8537e-02 4.0478e-04 0.0000e+00 0.0000e+00 3.6733e-01 5.3269e-01 9.1075e-03 0.0000e+00 0.0000e+00 1.4572e-02 2.6108e-02 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 1.3778e-03 3.1569e-02 1.7214e-02 1.0333e-04 0.0000e+00 2.2389e-02 5.7034e-01 3.0483e-01 1.4036e-03 0.0000e+00 1.4208e-03 3.1638e-02 1.7610e-02 1.0333e-04 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 1.2406e-05 6.0946e-03 3.7033e-02 6.1442e-03 1.5508e-05 1.0545e-04 1.1019e-01 6.7863e-01 1.0985e-01 1.3337e-04 3.1016e-06 6.3862e-03 3.9043e-02 6.3613e-03 9.3047e-06 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 9.4763e-05 1.6859e-02 3.1746e-02 1.3611e-03 0.0000e+00 1.5076e-03 3.0492e-01 5.6999e-01 2.3053e-02 0.0000e+00 5.1689e-05 1.7006e-02 3.1780e-02 1.6282e-03 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 8.0727e-04 2.7245e-02 1.9576e-02 0.0000e+00 0.0000e+00 9.0817e-03 5.3966e-01 3.5015e-01 0.0000e+00 0.0000e+00 0.0000e+00 3.1887e-02 2.1594e-02 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 5.8564e-02 8.0663e-02 2.2099e-03 0.0000e+00 0.0000e+00 3.4088e-01 4.9558e-01 9.3923e-03 0.0000e+00 0.0000e+00 4.4199e-03 8.2873e-03 0.0000e+00 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 3.3449e-03 8.5006e-02 4.7474e-02 2.5375e-04 0.0000e+00 2.0992e-02 5.3746e-01 2.9186e-01 1.4994e-03 0.0000e+00 2.5375e-04 7.6125e-03 4.1753e-03 6.9204e-05 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 2.5060e-05 1.6982e-02 1.0494e-01 1.6581e-02 4.1767e-05 1.4201e-04 1.0634e-01 6.3816e-01 1.0536e-01 1.2530e-04 0.0000e+00 1.3532e-03 8.5288e-03 1.4117e-03 8.3534e-06;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 2.0451e-04 4.5219e-02 8.4735e-02 3.7948e-03 0.0000e+00 1.7270e-03 2.8756e-01 5.4286e-01 2.3041e-02 0.0000e+00 4.5446e-05 3.4539e-03 7.0896e-03 2.7268e-04;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 9.3781e-02 4.8144e-02 0.0000e+00 0.0000e+00 1.2036e-02 5.0752e-01 3.2297e-01 0.0000e+00 0.0000e+00 0.0000e+00 9.0271e-03 6.5196e-03;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 2.0000e-01 1.1667e-01 0.0000e+00 0.0000e+00 0.0000e+00 2.1667e-01 4.5000e-01 1.6667e-02 0.0000e+00 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 8.3420e-03 1.6788e-01 9.2284e-02 1.0428e-03 0.0000e+00 1.4599e-02 4.5203e-01 2.6173e-01 2.0855e-03 0.0000e+00;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 2.7276e-02 1.8443e-01 2.8902e-02 1.8064e-04 0.0000e+00 9.2666e-02 5.7225e-01 9.4111e-02 1.8064e-04;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 8.6089e-02 1.8058e-01 6.8241e-03 0.0000e+00 1.0499e-03 2.6772e-01 4.3832e-01 1.9423e-02;\n",
" 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 0.0000e+00 1.3793e-01 9.1954e-02 0.0000e+00 0.0000e+00 1.1494e-02 4.9425e-01 2.6437e-01;\n",
"])\n",
"\n",
"# Shock grid (25 x 2): [ν, φ]\n",
"const S = FTYPE.([\n",
" -1.1021e-03 3.3916e-03;\n",
" -1.1021e-03 8.4394e-03;\n",
" -1.1021e-03 2.1000e-02;\n",
" -1.1021e-03 5.2255e-02;\n",
" -1.1021e-03 1.3003e-01;\n",
" 9.0945e-01 3.3916e-03;\n",
" 9.0945e-01 8.4394e-03;\n",
" 9.0945e-01 2.1000e-02;\n",
" 9.0945e-01 5.2255e-02;\n",
" 9.0945e-01 1.3003e-01;\n",
" 1.8200e+00 3.3916e-03;\n",
" 1.8200e+00 8.4394e-03;\n",
" 1.8200e+00 2.1000e-02;\n",
" 1.8200e+00 5.2255e-02;\n",
" 1.8200e+00 1.3003e-01;\n",
" 2.7306e+00 3.3916e-03;\n",
" 2.7306e+00 8.4394e-03;\n",
" 2.7306e+00 2.1000e-02;\n",
" 2.7306e+00 5.2255e-02;\n",
" 2.7306e+00 1.3003e-01;\n",
" 3.6411e+00 3.3916e-03;\n",
" 3.6411e+00 8.4394e-03;\n",
" 3.6411e+00 2.1000e-02;\n",
" 3.6411e+00 5.2255e-02;\n",
" 3.6411e+00 1.3003e-01;\n",
"])\n",
"\n",
"const ν_grid = S[:,1] # Government default cost\n",
"const ϕ_grid = S[:,2] # Private default rate\n",
"const n_s = size(S,1) # Number of states (25)\n",
"\n",
"println(\"Shocks discretized: $n_s states\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Economic Functions\n",
"\n",
"Key equilibrium conditions:\n",
"- Marginal utility of traded consumption\n",
"- Non-traded goods price (from intratemporal FOC)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"price_nt (generic function with 1 method)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Marginal utility of traded consumption\n",
"∂u∂cT(ct, yn; ω_p=ω, η_p=η, σ_p=σ) = ct > 0 ? \n",
" ω_p * ct^(-1/η_p) * (ω_p*ct^((η_p-1)/η_p) + (1-ω_p)*yn^((η_p-1)/η_p))^((1-σ_p*η_p)/(η_p-1)) : \n",
" FTYPE(999_999.0)\n",
"\n",
"# Price of non-traded goods (from intratemporal optimality)\n",
"price_nt(ct, yn; ω_p=ω, η_p=η) = (1-ω_p)/ω_p * (max(ct, FTYPE(1e-9)) / yn)^(1/η_p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Neural Network Architecture\n",
"\n",
"**Input**: 3D state (l, ν, φ) \n",
"**Output**: Policy l' ∈ [l_min, l_max] \n",
"**Architecture**: 3 → 256 → 128 → 1 with ReLU activations"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"const state_dim = 3\n",
"const policy_dim = 1\n",
"const Q1 = 256\n",
"const Q2 = 128\n",
"activation_f = relu\n",
"const T_sigmoid = FTYPE(1.0)\n",
"\n",
"# Build network: maps normalized state to policy\n",
"model = Chain(\n",
" Dense(state_dim, Q1, activation_f),\n",
" Dense(Q1, Q2, activation_f),\n",
" Dense(Q2, policy_dim),\n",
" x -> l_min .+ (l_max - l_min) .* Flux.sigmoid(x ./ T_sigmoid)\n",
")\n",
"\n",
"println(\"Network created with $(sum(length, Flux.params(model))) parameters\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Training Setup\n",
"\n",
"**Optimizer**: AdaBelief with two-stage learning rate \n",
"**Epochs**: 50,000 (warmup at 30,000) \n",
"**Batch size**: 32"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(layers = ((weight = \u001b[32mLeaf(AdaBelief(eta=0.001, beta=(0.9, 0.999), epsilon=1.0e-16), \u001b[39m(Float32[0.0 0.0 0.0; 0.0 0.0 0.0; … ; 0.0 0.0 0.0; 0.0 0.0 0.0], Float32[0.0 0.0 0.0; 0.0 0.0 0.0; … ; 0.0 0.0 0.0; 0.0 0.0 0.0], (0.9, 0.999))\u001b[32m)\u001b[39m, bias = \u001b[32mLeaf(AdaBelief(eta=0.001, beta=(0.9, 0.999), epsilon=1.0e-16), \u001b[39m(Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], (0.9, 0.999))\u001b[32m)\u001b[39m, σ = ()), (weight = \u001b[32mLeaf(AdaBelief(eta=0.001, beta=(0.9, 0.999), epsilon=1.0e-16), \u001b[39m(Float32[0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], Float32[0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; … ; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0], (0.9, 0.999))\u001b[32m)\u001b[39m, bias = \u001b[32mLeaf(AdaBelief(eta=0.001, beta=(0.9, 0.999), epsilon=1.0e-16), \u001b[39m(Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], Float32[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], (0.9, 0.999))\u001b[32m)\u001b[39m, σ = ()), (weight = \u001b[32mLeaf(AdaBelief(eta=0.001, beta=(0.9, 0.999), epsilon=1.0e-16), \u001b[39m(Float32[0.0 0.0 … 0.0 0.0], Float32[0.0 0.0 … 0.0 0.0], (0.9, 0.999))\u001b[32m)\u001b[39m, bias = \u001b[32mLeaf(AdaBelief(eta=0.001, beta=(0.9, 0.999), epsilon=1.0e-16), \u001b[39m(Float32[0.0], Float32[0.0], (0.9, 0.999))\u001b[32m)\u001b[39m, σ = ()), ()),)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"const initial_learning_rate = FTYPE(1e-3)\n",
"const final_learning_rate = FTYPE(1e-6)\n",
"const epochs_warmup = 30000\n",
"const epochs = 50000\n",
"const batch_size = 32\n",
"\n",
"opt = AdaBelief(initial_learning_rate)\n",
"st = Flux.setup(opt, model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## State Normalization\n",
"\n",
"Normalize shocks but keep debt in original scale for better training."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"sample_states (generic function with 1 method)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"const shock_mean = mean(S, dims=1)'\n",
"const shock_std = std(S, dims=1)'\n",
"\n",
"function normalize_state(batch)\n",
" l = batch[1:1, :]\n",
" shocks = batch[2:3, :]\n",
" normalized_shocks = (shocks .- shock_mean) ./ (2 .* shock_std)\n",
" return vcat(l, normalized_shocks)\n",
"end\n",
"\n",
"function sample_states(batch_size::Int)\n",
" # Sample debt uniformly\n",
" loans = rand(FTYPE, 1, batch_size) .* (l_max - l_min) .+ l_min\n",
" # Sample shocks\n",
" shock_indices = rand(1:n_s, batch_size)\n",
" shocks_ν = S[shock_indices, 1]'\n",
" shocks_ϕ = S[shock_indices, 2]'\n",
" return vcat(loans, shocks_ν, shocks_ϕ), shock_indices\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Loss Function: Fischer-Burmeister\n",
"\n",
"The FB function handles complementarity: \n",
"FB(a, b) = a + b - √(a² + b²) \n",
"\n",
"Where:\n",
"- a = Euler equation residual\n",
"- b = Constraint slack\n",
"\n",
"At optimum, FB = 0 whether constraint binds or not."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"ann_loss (generic function with 1 method)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"const huber_delta = FTYPE(0.1)\n",
"\n",
"function huber_loss(x, δ)\n",
" abs_x = abs.(x)\n",
" return Flux.mean(ifelse.(abs_x .< δ, FTYPE(0.5) .* x.^2, δ .* (abs_x .- FTYPE(0.5) * δ)))\n",
"end\n",
"\n",
"function ann_loss(m, batch::AbstractMatrix, shock_indices::Vector{Int})\n",
" current_batch_size = size(batch, 2)\n",
" normalized_batch = normalize_state(batch)\n",
" l, ν, ϕ = batch[1:1, :], batch[2:2, :], batch[3:3, :]\n",
"\n",
" # Current policy\n",
" lp = m(normalized_batch)\n",
" ct = yT*(1-τ) .- l .* (FTYPE(1.0) .- ϕ) .+ lp ./ (FTYPE(1.0) + i_l)\n",
" pn = price_nt.(ct, yN)\n",
"\n",
" # Vectorized expectation: evaluate ALL future states at once\n",
" lp_expanded = repeat(lp, inner=(1, n_s))\n",
" S_tiled = repeat(S', 1, current_batch_size)\n",
" state_prime_unnormalized = vcat(lp_expanded, S_tiled)\n",
" lpp = m(normalize_state(state_prime_unnormalized))\n",
" ϕ_p_tiled = state_prime_unnormalized[3:3, :]\n",
" ct_prime = yT*(1-τ) .- lp_expanded .* (FTYPE(1.0) .- ϕ_p_tiled) .+ lpp ./ (FTYPE(1.0) + i_l)\n",
" future_marg_utils = ∂u∂cT.(ct_prime, yN)\n",
" \n",
" # Compute expectations\n",
" future_marg_utils_reshaped = reshape(future_marg_utils, n_s, current_batch_size)\n",
" E_λp = Π' * future_marg_utils_reshaped\n",
" cartesian_indices = CartesianIndex.(shock_indices, 1:current_batch_size)\n",
" E_λp_final = E_λp[cartesian_indices]'\n",
"\n",
" # Fischer-Burmeister residual\n",
" λ = ∂u∂cT.(ct, yN)\n",
" borr_const = κ .* (pn .* yN .+ yT*(1-τ))\n",
" epsilon = FTYPE(1e-9)\n",
" a_norm = FTYPE(1.0) .- (β .* E_λp_final .* (FTYPE(1.0) + i_l)) ./ (λ .+ epsilon)\n",
" b_norm = FTYPE(1.0) .- lp ./ (borr_const .+ epsilon)\n",
" fb_residual = a_norm .+ b_norm .- sqrt.(a_norm.^2 .+ b_norm.^2)\n",
" \n",
" return huber_loss(fb_residual, huber_delta)\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Multiplier Recovery Function\n",
"\n",
"After training, we can recover the Kuhn-Tucker multiplier μ to see where the constraint binds."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"recover_multiplier (generic function with 1 method)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"function recover_multiplier(m, batch::AbstractMatrix, shock_indices::Vector{Int})\n",
" current_batch_size = size(batch, 2)\n",
" normalized_batch = normalize_state(batch)\n",
" l, ν, ϕ = batch[1:1, :], batch[2:2, :], batch[3:3, :]\n",
" lp = m(normalized_batch)\n",
" ct = yT*(1-τ) .- l .* (FTYPE(1.0) .- ϕ) .+ lp ./ (FTYPE(1.0) + i_l)\n",
"\n",
" # Same vectorized expectation as in loss\n",
" lp_expanded = repeat(lp, inner=(1, n_s))\n",
" S_tiled = repeat(S', 1, current_batch_size)\n",
" state_prime_unnormalized = vcat(lp_expanded, S_tiled)\n",
" lpp = m(normalize_state(state_prime_unnormalized))\n",
" ϕ_p_tiled = state_prime_unnormalized[3:3, :]\n",
" ct_prime = yT*(1-τ) .- lp_expanded .* (FTYPE(1.0) .- ϕ_p_tiled) .+ lpp ./ (FTYPE(1.0) + i_l)\n",
" future_marg_utils = ∂u∂cT.(ct_prime, yN)\n",
" future_marg_utils_reshaped = reshape(future_marg_utils, n_s, current_batch_size)\n",
" E_λp = Π' * future_marg_utils_reshaped\n",
" cartesian_indices = CartesianIndex.(shock_indices, 1:current_batch_size)\n",
" E_λp_final = E_λp[cartesian_indices]'\n",
"\n",
" # Multiplier from Euler equation\n",
" λ = ∂u∂cT.(ct, yN)\n",
" μ = λ ./ (FTYPE(1.0) + i_l) .- β .* E_λp_final\n",
" return μ\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Training Loop\n",
"\n",
"Train for 50,000 epochs with learning rate decay at epoch 30,000."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"println(\"--- Starting ANN Training ---\")\n",
"losses = FTYPE[]\n",
"p_bar = Progress(epochs; desc=\"Training Policy ANN:\")\n",
"\n",
"for epoch in 1:epochs\n",
" # Switch to lower learning rate at warmup point\n",
" if epoch == epochs_warmup\n",
" println(\"\\n--- Switched to final learning rate: $(final_learning_rate) ---\")\n",
" global opt = ADAM(final_learning_rate)\n",
" global st = Flux.setup(opt, model)\n",
" end\n",
" \n",
" # Sample batch and compute loss\n",
" batch, shock_indices = sample_states(batch_size)\n",
" loss, grads = Flux.withgradient(m -> ann_loss(m, batch, shock_indices), model)\n",
" Flux.update!(st, model, grads[1])\n",
" push!(losses, loss)\n",
"\n",
" ProgressMeter.next!(p_bar; showvalues=[(:epoch, epoch), (:loss, loss)])\n",
"end\n",
"\n",
"println(\"--- Training Complete ---\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Visualize Results\n",
"\n",
"Plot:\n",
"1. Training loss convergence\n",
"2. Learned policy function\n",
"3. Kuhn-Tucker multiplier"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Loss plot\n",
"p1 = plot(losses,\n",
" label=\"Training Loss\",\n",
" xlabel=\"Epoch\",\n",
" ylabel=\"Loss (log scale)\",\n",
" title=\"ANN Training Progress\",\n",
" yaxis=:log10,\n",
" legend=:topright)\n",
"\n",
"# Prepare plotting grid (at lowest shocks)\n",
"println(\"Plotting learned policy function...\")\n",
"plot_l_grid = l_grid\n",
"plot_ν_grid = fill(ν_grid[1], n_l)\n",
"plot_ϕ_grid = fill(ϕ_grid[1], n_l)\n",
"plot_grid_unnormalized = vcat(plot_l_grid', plot_ν_grid', plot_ϕ_grid')\n",
"plot_shock_indices = fill(1, n_l)\n",
"\n",
"learned_policy = model(normalize_state(plot_grid_unnormalized))\n",
"\n",
"# Policy plot\n",
"p2 = plot(l_grid, learned_policy',\n",
" label=\"Learned Policy l'(l)\",\n",
" xlabel=\"Current Loans (l)\",\n",
" ylabel=\"Next Period's Loans (l')\",\n",
" title=\"Policy Function (at lowest shocks)\",\n",
" linewidth=2,\n",
" legend=:topleft)\n",
"plot!(l_grid, l_grid,\n",
" linestyle=:dash,\n",
" color=:black,\n",
" label=\"45-degree line\")\n",
"\n",
"# Multiplier plot\n",
"println(\"Recovering and plotting KT multiplier...\")\n",
"recovered_mu = recover_multiplier(model, plot_grid_unnormalized, plot_shock_indices)\n",
"\n",
"p3 = plot(l_grid, recovered_mu',\n",
" label=\"Multiplier μ(l)\",\n",
" xlabel=\"Current Loans (l)\",\n",
" ylabel=\"KT Multiplier (μ)\",\n",
" title=\"Recovered KT Multiplier (at lowest shocks)\",\n",
" linewidth=2,\n",
" legend=:topleft)\n",
"plot!(l_grid, zeros(FTYPE, n_l),\n",
" linestyle=:dash,\n",
" color=:black,\n",
" label=\"\")\n",
"\n",
"# Combine plots\n",
"plt = plot(p1, p2, p3, layout=(1,3), size=(1100, 600))\n",
"display(plt)\n",
"\n",
"# Save figure\n",
"# savefig(plt, \"Collateral_Constraint_ANN_Results.png\")\n",
"# println(\"Figure saved as Collateral_Constraint_ANN_Results.png\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Interpretation\n",
"\n",
"**Policy Function**: Shows characteristic kink where borrowing constraint starts to bind\n",
"\n",
"**Multiplier μ**: \n",
"- μ = 0: Constraint not binding (interior solution)\n",
"- μ > 0: Constraint binds (household wants to borrow more)\n",
"\n",
"The kink location indicates the threshold debt level where sudden stops occur."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.11.2",
"language": "julia",
"name": "julia-1.11"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.11.2"
}
},
"nbformat": 4,
"nbformat_minor": 4
}