demo_notebooks/growth_sequential_demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dae963a0",
   "metadata": {},
   "source": [
    "**Note**: This notebook should take around **a minute** to run.\n",
    "\n",
    "For a more comprehensive and detailed treatment of this problem, please refer to the [GitHub repository](https://github.com/HighDimensionalEconLab/transversality)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad24e909",
   "metadata": {},
   "source": [
    "# The Economic Problem:\n",
    "\n",
    "Consider the following problem:\n",
    "\n",
    "$\\begin{align}\n",
    "\\quad & \\max_{\\{c_t\\}_{t=0}^\\infty } \\sum \\beta^t u(c_t)\\\\\n",
    "\\quad & \\text{s.t.}\\quad  k_{t+1} = f(k_t) + (1-\\delta) k_t -c_t\\\\\n",
    "\\quad & k_{t+1} \\geq 0\\\\\n",
    "\\quad & k_0 \\quad \\text{is given},\n",
    "\\end{align}$\n",
    "\n",
    "where $u(\\cdot)$ is the utility function, $f(\\cdot)$ is the prduction function, $\\beta$ is the discount factor, and $k_0$ is the initial condition for capital.\n",
    "\n",
    "#### First Order Condition\n",
    "\n",
    "The Euler equation can be written as:\n",
    "\n",
    "$\\begin{align}\n",
    "\\quad & u'(c_t) = \\beta u'(c_{t+1})\\big[f'(k_{t+1})+(1-\\delta)\\big]\n",
    "\\end{align}$\n",
    "\n",
    "To pin down the optimal solution a transversality condition is required, described as:\n",
    "\n",
    "$\\begin{align}\n",
    "\\quad & \\lim_{T\\rightarrow \\infty} \\beta^t u'(c_T)k_{T+1} = 0\n",
    "\\end{align}$\n",
    "\n",
    "#### The System of Equations Describing the Optimal Solution:\n",
    "\n",
    "The optimal solution can be written as a **root** of the following system of equations:\n",
    "\n",
    "$\\begin{align}\n",
    "\\quad & \\beta u'\\big(c(t+1)\\big)\\bigg[f'\\big(k(t+1)\\big)+(1-\\delta)\\bigg] - u'\\big(c(t)\\big) = 0 \\\\\n",
    "\\quad & f\\big(k(t)\\big) + (1-\\delta) k(t) -c(t) - k(t+1)  = 0\\\\\n",
    "\\quad & k(0)-k_0 = 0.\n",
    "\\end{align}$\n",
    "\n",
    "#### Note on the Transversality Condition:\n",
    "\n",
    "One of the main contributions of this paper is that one can ignore the transversality condition and completely rely on the implicit bias in deep learning to obtain the optimal solution.\n",
    "\n",
    "\n",
    "\n",
    "In this example we focus on the case of:\n",
    " 1. $u(c) = \\frac{c^{1-\\sigma}}{1-\\sigma}$, and $f(k) = k^\\alpha$,\n",
    "\n",
    " 2.  $\\sigma = 1$, $\\beta = 0.9$, $\\alpha = \\frac{1}{3}$, and $\\delta = 0.1$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ec32d74",
   "metadata": {},
   "source": [
    "#### Importing Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0be8994c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "from torch.utils.data import DataLoader\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f559ba55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<torch._C.Generator at 0x2326b94a0b0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.manual_seed(123) # fixing the seed"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c326069",
   "metadata": {},
   "source": [
    "#### Setting Up the Economic Parameters \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "196b6caf",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 1.0/3.0\n",
    "beta = 0.9\n",
    "delta = 0.1\n",
    "k_0 = 1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dc5db0e",
   "metadata": {},
   "source": [
    "#### Setting Up the Grid ($\\mathcal{X}_{\\text{train}}$) and the DataLoader\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3605c936",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_t_max = 29\n",
    "time_grid = torch.arange(0.0, train_t_max , 1.0)\n",
    "time_grid = time_grid.unsqueeze(dim =1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "31126853",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_loader = DataLoader(time_grid, batch_size=len(time_grid), shuffle = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58bffd2a",
   "metadata": {},
   "source": [
    "#### Setting up the Neural Network\n",
    "This is an approximation for capital $\\hat{k}:\\mathbb{R}_+ \\rightarrow \\mathbb{R}_+$.\n",
    "\n",
    "$\\hat{k}(\\cdot)$ takes time as an input. The positivity of capital is going to be implemented by using a `Softplus` output layer. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9b14524b",
   "metadata": {},
   "outputs": [],
   "source": [
    "class K_hat_NN(nn.Module):\n",
    "    def __init__(self,\n",
    "                 dim_hidden = 128,):\n",
    "        super().__init__()\n",
    "        \n",
    "        self.dim_hidden= dim_hidden\n",
    "        \n",
    "        self.k_hat = nn.Sequential(\n",
    "            nn.Linear(1, dim_hidden, bias=True),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(dim_hidden, dim_hidden, bias=True),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(dim_hidden, dim_hidden, bias=True),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(dim_hidden, dim_hidden, bias=True),\n",
    "            nn.Tanh(),\n",
    "            nn.Linear(dim_hidden, 1),\n",
    "            nn.Softplus(beta=1.0) #To make sure capital stays positive\n",
    "        )\n",
    "\n",
    "    def forward(self, x):\n",
    "        return self.k_hat(x)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c7bfac7",
   "metadata": {},
   "source": [
    "#### Initializing the Neural Network and Defining the Optimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9f802a33",
   "metadata": {},
   "outputs": [],
   "source": [
    "k_hat= K_hat_NN()\n",
    "learning_rate = 1e-3\n",
    "optimizer = torch.optim.Adam(k_hat.parameters(), lr=learning_rate) #Adam Optimizer \n",
    "scheduler = torch.optim.lr_scheduler.StepLR(optimizer, step_size=200, gamma=0.9) #dampening the learning rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "66c43887",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_epochs = 1001 # step of optimization\n",
    "print_epoch_frequency = 100 # how often printing the results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1ddca0c",
   "metadata": {},
   "source": [
    "### Implementing the Economics\n",
    "Here, we implement the economic conditions in the form of residuals to be minimized. Specifically:\n",
    "\n",
    "1. The Euler residuals: the difference between the left-hand and right-hand sides of the Euler equation (i.e., equation 7).\n",
    "\n",
    "2. The initial condition residual: the difference between the approximate capital at time zero and the initial condition for capital (i.e., equation 9).\n",
    "\n",
    "**Note**: the feasibility condition (i.e, equation 8) is used to construct consumption. Therefore, by construction it always holds."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff8f317b",
   "metadata": {},
   "source": [
    "#### Defining the Marginal Utility, Production, and Marginal Product of Capital Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "85a6f5d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(k): # Production function\n",
    "    return k**alpha\n",
    "\n",
    "def df_k(k): # Marinal product of capital\n",
    "    return  alpha*(k**(alpha -1))\n",
    "\n",
    "def du_c(c): # Mariginal utility\n",
    "    return c**(-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df116b86",
   "metadata": {},
   "source": [
    "#### Defining the Residuals Function to be Used in the Optimization\n",
    "This funtion defines the Euler and the intial condition residuals "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "eaf07748",
   "metadata": {},
   "outputs": [],
   "source": [
    "def residuals(batch):\n",
    "    t = batch\n",
    "    time_zero = torch.zeros([1,1]) # t = 0 \n",
    "    t_p1 = t+1 # t+1\n",
    "    t_p2 = t+2 # t+2\n",
    "    k_t = k_hat(t) # k(t), k_hat is the neural network\n",
    "    k_tp1 = k_hat(t_p1) # k(t+1)\n",
    "    k_tp2 = k_hat(t_p2) # k(t+2)\n",
    "    c_t = f(k_t) + (1 - delta) * k_t - k_tp1 # Feasibility condition at t (eq. 8)\n",
    "    c_tp1 = f(k_tp1) + (1 - delta) * k_tp1 - k_tp2 # Feasibility condition at t+1 (eq. 8)\n",
    "    \n",
    "    Euler_residual =  (du_c(c_t) / du_c(c_tp1)) - beta * (1 - delta + df_k(k_tp1)) # Euler residuals (eq. 7)\n",
    "    initial_condition_residual = k_hat(time_zero)-k_0 # Intial condition residulas (eq. 9)\n",
    "    \n",
    "    return Euler_residual, initial_condition_residual\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "350f4ed0",
   "metadata": {},
   "source": [
    "#### Training Loop (Optimization Process)\n",
    "\n",
    "Here, we minimize the mean squared of Euler residuals and the initial condition residuals:\n",
    "\n",
    "$\\min_{\\theta}\\bigg( \\frac{1}{2} \\frac{1}{|\\mathcal{X}_{\\text{train}}|} \\sum_{t\\in \\mathcal{X}_{\\text{train}}} \\bigg[\\frac{u'(c;\\hat{k}(t;\\theta))}{u'(c;\\hat{k}(t+1;\\theta))}- \\beta\\big[1-\\delta+f'\\big(\\hat{k}(t+1;\\theta)\\big)\\big] \\bigg]^2+\\frac{1}{2}\\big[\\hat{k}(0;\\theta)-k_0)\\big]^2\\bigg)$\n",
    "\n",
    "where $\\theta$ is the coefficients of the neural network, and the optimization id done with gradient-based optimizers such as `Gradient Descent (GD)` and `Adam`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7f4f2c52",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch = 0, loss = 5.64e-02\n",
      "epoch = 100, loss = 5.70e-06\n",
      "epoch = 200, loss = 2.94e-07\n",
      "epoch = 300, loss = 2.18e-07\n",
      "epoch = 400, loss = 1.74e-07\n",
      "epoch = 500, loss = 1.40e-07\n",
      "epoch = 600, loss = 1.12e-07\n",
      "epoch = 700, loss = 9.10e-08\n",
      "epoch = 800, loss = 7.42e-08\n",
      "epoch = 900, loss = 6.20e-08\n",
      "epoch = 1000, loss = 5.22e-08\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(num_epochs):\n",
    "    for batch in data_loader:\n",
    "        \n",
    "        optimizer.zero_grad() # Resetting the gradients (with respect to NN coefficients)\n",
    "        \n",
    "        Euler_res, initial_condition_res = residuals(batch) # Constructing the Euler and initial condition residuals\n",
    "        \n",
    "        Euler_loss = Euler_res.pow(2).mean() # Calculating the mean squared (over the grid points) of Euler residuals\n",
    "        initial_condition_loss = initial_condition_res.pow(2).mean() #Calculating the squared of initial condition residuals\n",
    "        \n",
    "        loss = 0.5*Euler_loss + 0.5*initial_condition_loss # A convex combination of mean squared of Euler and initial condition residulas\n",
    "        \n",
    "        loss.backward() # Calculating the gradients (with respect to NN coefficients)\n",
    "        optimizer.step() # Using the gradients to minimize the loss function\n",
    "        \n",
    "    scheduler.step() # Dampening the learning rate\n",
    "    \n",
    "    if epoch % print_epoch_frequency == 0:\n",
    "        print(f\"epoch = {epoch}, loss = {loss.detach().numpy():.2e}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27604ac5",
   "metadata": {},
   "source": [
    "### Plotting the Results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30306ecf",
   "metadata": {},
   "source": [
    "#### Calculating the Steady-State for Capital and Consumption\n",
    "The steady-state for capital and consumption are used to test the convergence to the optimal solution "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6bdac4b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "base = ((1.0/beta)-1.0+ delta)/alpha\n",
    "exponent = 1.0/(alpha-1)\n",
    "\n",
    "k_star = base**exponent\n",
    "c_star = f(k_star)-delta*k_star"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "079a3256",
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating the test data\n",
    "test_T = 50\n",
    "time_grid_test = torch.arange(0.0, test_T , 1.0)\n",
    "time_grid_test = time_grid_test.unsqueeze(dim =1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e725238",
   "metadata": {},
   "source": [
    "#### Calculating the Approximate Capital and Consumption Path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7a23891b",
   "metadata": {},
   "outputs": [],
   "source": [
    "k_hat_path = k_hat(time_grid_test).detach() # \\hat{k}(t)\n",
    "k_hat_path_tp1 = k_hat(time_grid_test+1).detach() # \\hat{k}(t+1)\n",
    "\n",
    "c_hat_path = f(k_hat_path) + (1-delta)*k_hat_path - k_hat_path_tp1 # \\hat{c}(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45c88413",
   "metadata": {},
   "source": [
    "#### Calculating the Euler and Initial Condition Residuals\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ed5dc57c",
   "metadata": {},
   "outputs": [],
   "source": [
    "Euler_res_test, initial_condiotions_res_test = residuals(time_grid_test)\n",
    "Euler_res_test = Euler_res_test.detach()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecd7ee4c",
   "metadata": {},
   "source": [
    "#### Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55e1907c",
   "metadata": {},
   "source": [
    "#### Plot Settings\n",
    "such as font, font size and image size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "54f9f8b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "fontsize= 14\n",
    "ticksize = 14\n",
    "figsize = (14, 4.5)\n",
    "params = {'font.family':'serif',\n",
    "    \"figure.figsize\":figsize,\n",
    "    'figure.dpi': 80,\n",
    "    'figure.edgecolor': 'k',\n",
    "    'font.size': fontsize,\n",
    "    'axes.labelsize': fontsize,\n",
    "    'axes.titlesize': fontsize,\n",
    "    'xtick.labelsize': ticksize,\n",
    "    'ytick.labelsize': ticksize\n",
    "}\n",
    "plt.rcParams.update(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "47476cba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x232720ed970>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1120x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(1, 2 , 1)\n",
    "\n",
    "plt.plot(time_grid_test,k_hat_path, color='k',  label = r\"$\\hat{k}(t)$\")\n",
    "plt.axhline(y=k_star, linestyle='--',color='k', label=\"k Steady-State\")\n",
    "plt.xlabel(r\"Time(t)\")\n",
    "plt.axvline(x= train_t_max , color='k', linestyle=':', label = \"Interpolation vs Extrapolation\")\n",
    "plt.title(r\"Approximate Capital Path\")\n",
    "plt.ylim([k_0-0.1,k_star*(1+0.35) ])\n",
    "plt.legend(loc='best')\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "\n",
    "plt.plot(time_grid_test,c_hat_path, color='b',  label = r\"$\\hat{c}(t)$\")\n",
    "plt.axhline(y=c_star, linestyle='--',color='b', label=\"c Steady-State\")\n",
    "plt.xlabel(r\"Time(t)\")\n",
    "plt.axvline(x= train_t_max , color='b', linestyle=':', label = \"Interpolation vs Extrapolation\")\n",
    "plt.title(r\"Approximate Consumption Path\")\n",
    "plt.ylim([c_hat_path[0]-0.1,c_star*(1+0.25) ])\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "61beb014",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1120x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(time_grid_test,Euler_res_test**2, color='k',  label = r\"Euler Residuals$^2$\")\n",
    "plt.xlabel(r\"Time(t)\")\n",
    "plt.axvline(x= train_t_max , color='k', linestyle=':', label = \"Interpolation vs Extrapolation\")\n",
    "plt.title(r\"Euler Residuals Squared\")\n",
    "plt.legend(loc='lower left')\n",
    "plt.yscale('log')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2d0a289e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d1737cbb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a94b7bd6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}