Code/Python/ApndxBalancedGrowthcNrmAndCov.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Balanced Growth in Mean Normalized $c$ And $\\text{cov}(c_{t},\\mathbf{p}_{t})$\n",
    "### By William Du (with modifications by Chris Carroll)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display, Math, Latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "from HARK.ConsumptionSaving.ConsIndShockModel import IndShockConsumerType\n",
    "from HARK import __version__ as HARKversion\n",
    "from HARK.utilities import (\n",
    "    plot_funcs, find_gui, make_figs)\n",
    "formatter=\"{:.4f}\"\n",
    "def makeFig(figure_name, target_dir=\"../../Figures\"):\n",
    "    print('')\n",
    "    make_figs(figure_name, saveFigs, drawFigs, target_dir)\n",
    "    print('')\n",
    "    \n",
    "# Whether to save the figures to Figures_dir\n",
    "saveFigs = True\n",
    "\n",
    "# Whether to draw the figures\n",
    "drawFigs = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "Harmenberg_Dict={\n",
    "    # Parameters shared with the perfect foresight model\n",
    "    \"CRRA\":2,                             # Coefficient of relative risk aversion\n",
    "    \"Rfree\": 1.02**.25,                  # Interest factor on assets\n",
    "    \"DiscFac\": 0.9935,                    # Intertemporal discount factor\n",
    "    \"LivPrb\" : [1.00],                    # Survival probability\n",
    "    \"PermGroFac\" :[1.00],                 # Permanent income growth factor\n",
    "\n",
    "    # Parameters that specify the income distribution over the lifecycle\n",
    "   \n",
    "    \"PermShkStd\" :  [.06],     # Standard deviation of log permanent shocks to income\n",
    "    \"PermShkCount\" : 5,                    # Number of points in discrete approximation to permanent income shocks\n",
    "    \"TranShkStd\" : [.3],                   # Standard deviation of log transitory shocks to income\n",
    "    \"TranShkCount\" : 5,                    # Number of points in discrete approximation to transitory income shocks\n",
    "    \"UnempPrb\" : 0.07,                     # Probability of unemployment while working\n",
    "    \"IncUnemp\" : 0.3,      # Unemployment benefits replacement rate\n",
    "    \"UnempPrbRet\" : 0.0005,                # Probability of \"unemployment\" while retired\n",
    "    \"IncUnempRet\" : 0.0,                   # \"Unemployment\" benefits when retired\n",
    "    \"T_retire\" : 0,                        # Period of retirement (0 --> no retirement)\n",
    "    \"tax_rate\" : 0.18,      # Flat income tax rate (legacy parameter, will be removed in future)\n",
    "\n",
    "    # Parameters for constructing the \"assets above minimum\" grid\n",
    "    \"aXtraMin\" : 0.001,                    # Minimum end-of-period \"assets above minimum\" value\n",
    "    \"aXtraMax\" : 500,                       # Maximum end-of-period \"assets above minimum\" value\n",
    "    \"aXtraCount\" : 90,                     # Number of points in the base grid of \"assets above minimum\"\n",
    "    \"aXtraNestFac\" : 4,                    # Exponential nesting factor when constructing \"assets above minimum\" grid\n",
    "    \"aXtraExtra\" : [None],                 # Additional values to add to aXtraGrid\n",
    "\n",
    "    # A few other parameters\n",
    "    \"BoroCnstArt\" : 0.0,                   # Artificial borrowing constraint; imposed minimum level of end-of period assets\n",
    "    \"vFuncBool\" : False,                    # Whether to calculate the value function during solution\n",
    "    \"CubicBool\" : False,                   # Preference shocks currently only compatible with linear cFunc\n",
    "    \"T_cycle\" : 1,                         # Number of periods in the cycle for this agent type\n",
    "\n",
    "    # Parameters only used in simulation\n",
    "    \"AgentCount\" : 4000000,                 # Number of agents of this type\n",
    "    \"T_sim\" : 2000,                         # Number of periods to simulate\n",
    "    \"aNrmInitMean\" : np.log(1.25)-(.5**2)/2,# Mean of log initial assets\n",
    "    \"aNrmInitStd\"  : .5,                   # Standard deviation of log initial assets\n",
    "    \"pLvlInitMean\" : 0,                    # Mean of log initial permanent income\n",
    "    \"pLvlInitStd\"  : 0,                    # Standard deviation of log initial permanent income\n",
    "    \"PermGroFacAgg\" : 1.0,                 # Aggregate permanent income growth factor\n",
    "    \"T_age\" : None,                        # Age after which simulated agents are automatically killed\n",
    "\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true,
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPFRaw                 = 0.999727 \n",
      "GPFNrm                 = 1.002960 \n",
      "GPFAggLivPrb           = 0.999727 \n",
      "Thorn = APF            = 1.019722 \n",
      "PermGroFacAdj          = 1.016712 \n",
      "uInvEpShkuInv          = 0.996777 \n",
      "VAF                    = 0.990298 \n",
      "WRPF                   = 0.257772 \n",
      "DiscFacGPFNrmMax       = 0.987645 \n",
      "DiscFacGPFAggLivPrbMax = 0.994043 \n"
     ]
    }
   ],
   "source": [
    "fast = IndShockConsumerType(**Harmenberg_Dict, verbose = 1 )\n",
    "fast.cycles = 0\n",
    "fast.Rfree = 1.2**.25\n",
    "fast.PermGroFac = [1.02]\n",
    "fast.tolerance = fast.tolerance/100\n",
    "\n",
    "fast.track_vars = ['cNrm','pLvl'] \n",
    "fast.solve(verbose=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculate Patience Conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPFRaw                 = 0.999727 \n",
      "GPFNrm                 = 1.002960 \n",
      "GPFAggLivPrb           = 0.999727 \n",
      "Thorn = APF            = 1.019722 \n",
      "PermGroFacAdj          = 1.016712 \n",
      "uInvEpShkuInv          = 0.996777 \n",
      "VAF                    = 0.990298 \n",
      "WRPF                   = 0.257772 \n",
      "DiscFacGPFNrmMax       = 0.987645 \n",
      "DiscFacGPFAggLivPrbMax = 0.994043 \n"
     ]
    }
   ],
   "source": [
    "fast.check_conditions(verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "done\n"
     ]
    }
   ],
   "source": [
    "# Simulate a population\n",
    "fast.initialize_sim()\n",
    "fast.simulate()\n",
    "print('done')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# Compute paths of cNrm, pLvl, cLvl, and cov(cNrm,pLvl)\n",
    "\n",
    "cLvl_avg_lst = [] # Path of mean consumption level\n",
    "pLvl_avg_lst = [] # Path of mean consumption level\n",
    "cNrm_avg_lst = [] # Path of mean consumption normed\n",
    "cNrm_pLvl_cov_lst =[]\n",
    "\n",
    "for i in range (fast.T_sim):\n",
    "    cNrm_avg_now = np.mean(fast.history['cNrm'][i]) # mean cNrm\n",
    "    pLvl_avg_now = np.mean(fast.history['pLvl'][i]) # mean pLvl\n",
    "    cLvl_avg_now = np.mean(fast.history['cNrm'][i]*fast.history['pLvl'][i]) # mean cLvl\n",
    "    cNrm_avg_lst.append(cNrm_avg_now)\n",
    "    pLvl_avg_lst.append(pLvl_avg_now)\n",
    "    cLvl_avg_lst.append(cLvl_avg_now)\n",
    "    cNrm_pLvl_cov_now = np.cov(fast.history['cNrm'][i],fast.history['pLvl'][i])[1][0] # off diag is cov\n",
    "    cNrm_pLvl_cov_lst.append(cNrm_pLvl_cov_now)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot of $\\log \\mathbb{M}[p_{t}]\\mathbf{P}_{t}$ \n",
    "\n",
    "If the sample were arbitrarily large, we would have $\\mathbb{M}[p_{t}]=1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Saving figure logpLvl in ../../Figures\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "groFac_pLvl_cum: 1.01999\n"
     ]
    }
   ],
   "source": [
    "start_plots_at_period=1000\n",
    "num_periods=len(pLvl_avg_lst[start_plots_at_period:])\n",
    "\n",
    "groFac_pLvl_cum=(pLvl_avg_lst[-1]/pLvl_avg_lst[start_plots_at_period])**(1/num_periods)\n",
    "plt.plot(np.log(pLvl_avg_lst[start_plots_at_period:]))\n",
    "plt.title('log of mean(pLvl)')\n",
    "makeFig('logpLvl') \n",
    "\n",
    "print('groFac_pLvl_cum: '+formatter.format(groFac_pLvl_cum))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot of $\\log \\mathbf{\\mathfrak{c}}_{t} (=\\log \\mathbb{M}[c_{t}])$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Saving figure logcNrm in ../../Figures\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "mean cNrm growth: 1.00289\n"
     ]
    }
   ],
   "source": [
    "groFac_cNrm_cum=(cNrm_avg_lst[-1]/cNrm_avg_lst[start_plots_at_period])**(1/num_periods)\n",
    "plt.plot(np.log(cNrm_avg_lst[start_plots_at_period:]))\n",
    "plt.title('log of cNrm_avg')\n",
    "makeFig('logcNrm') \n",
    "\n",
    "print('mean cNrm growth: '+formatter.format(groFac_cNrm_cum))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot of $\\log \\mathbf{C}_{t}$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Saving figure logcLvl in ../../Figures\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "mean cLvl growth: 1.02030\n",
      "mean cLvl growth/mean pLvl growth: 1.00031\n"
     ]
    }
   ],
   "source": [
    "groFac_cLvl_cum=(cLvl_avg_lst[-1]/cLvl_avg_lst[start_plots_at_period])**(1/num_periods)\n",
    "\n",
    "plt.plot(np.log(cLvl_avg_lst[start_plots_at_period:]))\n",
    "plt.title('log_cLvl_avg')\n",
    "makeFig('logcLvl') \n",
    "\n",
    "print('mean cLvl growth: '+formatter.format(groFac_cLvl_cum))\n",
    "print('mean cLvl growth/mean pLvl growth: '+\n",
    "      formatter.format(groFac_cLvl_cum/groFac_pLvl_cum)\n",
    "     )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot of $\\text{cov}_{t}(c_{t},\\mathbf{p}_{t})(=\\text{cov}_{t}(c_{t},p_{t})\\mathbf{P}_{t})$ over time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Saving figure logcov in ../../Figures\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "mean growth: 1.02314\n"
     ]
    }
   ],
   "source": [
    "#start_plots_at_period=1000\n",
    "#num_periods=len(cNrm_pLvl_cov_lst[start_plots_at_period:])\n",
    "\n",
    "groFac_cvar_cum=(cNrm_pLvl_cov_lst[-1]/cNrm_pLvl_cov_lst[start_plots_at_period])**(1/num_periods)\n",
    "\n",
    "plt.plot(np.log(np.abs(cNrm_pLvl_cov_lst[start_plots_at_period:])))\n",
    "plt.title('log of (negative of) covariance between cNrm and pLvl')\n",
    "makeFig('logcov') \n",
    "\n",
    "print('mean growth: '+formatter.format(groFac_cvar_cum))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Relation between cLvl growth, cov growth, and cNrm growth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "\n",
       "mean($\\pmb{\\mathfrak{c}}_{t+1}/\\pmb{\\mathfrak{c}}_{t}$) = 1.0203"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cumulative cLvl growth: 1.0203\n",
      "cumulative pLvl growth: 1.0200\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "\n",
       "mean($\\mathbb{M}[c_{t+1}]/\\mathbb{M}[c_{t}]$) = 1.0029"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cumulative cNrm growth: 1.0029\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "\n",
       "mean(cov$_{t+1}(c_{t+1},\\mathbf{p}_{t+1}) / $cov$_{t}(c_{t}, \\mathbf{p}_{t})$) = 1.0029"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cumulative cvar growth: 1.0231\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\mathbb{M}(\\Omega_{\\pmb{\\mathfrak{c}}}) = $1.0029"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\mathbb{M}(\\Omega_{cov}) = $1.0232"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\mathbb{M}(\\Omega_{cov}/\\Omega_{\\pmb{\\mathfrak{c}}}) = $1.0202"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\mathbb{M}(\\mathbf{p}_{t+1}/\\mathbf{p}_{t}) = $1.0200"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "groFac_cLvl_avg = []\n",
    "groFac_pLvl_avg = []\n",
    "groFac_cNrm_avg = []\n",
    "groFac_cvar_avg = []\n",
    "\n",
    "for i in range(len(cLvl_avg_lst) -1):\n",
    "    groFac_cLvl_avg.append(cLvl_avg_lst[i+1]/cLvl_avg_lst[i])\n",
    "    groFac_pLvl_avg.append(pLvl_avg_lst[i+1]/pLvl_avg_lst[i])\n",
    "    groFac_cNrm_avg.append(cNrm_avg_lst[i+1]/cNrm_avg_lst[i])\n",
    "    groFac_cvar_avg.append(cNrm_pLvl_cov_lst[i+1]/cNrm_pLvl_cov_lst[i])\n",
    "    \n",
    "# start_plots_at_period=500\n",
    "# num_periods=len(groFac_cLvl_avg[start_plots_at_period:])\n",
    "plt.plot(groFac_cLvl_avg[start_plots_at_period:])\n",
    "plt.plot(np.mean(groFac_cLvl_avg[start_plots_at_period:])*np.ones(num_periods))\n",
    "plt.title(r'$\\mathbb{M}[{c}_{t+1}\\mathbf{p}_{t+1}]/\\mathbb{M}[c_{t} \\mathbf{p}_{t}]$')\n",
    "plt.show()\n",
    "display(Latex(r\"\"\"\n",
    "mean($\\pmb{\\mathfrak{c}}_{t+1}/\\pmb{\\mathfrak{c}}_{t}$) = \"\"\"+\n",
    "      formatter.format(np.mean(groFac_cLvl_avg[start_plots_at_period:]))))\n",
    "print('cumulative cLvl growth: '+formatter.format(groFac_cLvl_cum))\n",
    "print('cumulative pLvl growth: '+formatter.format(groFac_pLvl_cum))\n",
    "\n",
    "plt.plot(groFac_cNrm_avg[start_plots_at_period:])\n",
    "plt.plot(np.mean(groFac_cNrm_avg[start_plots_at_period:])*np.ones(num_periods))\n",
    "plt.title(r'$\\mathbb{M}[{c}_{t+1}]/\\mathbb{M}[c_{t}]$')\n",
    "plt.show()\n",
    "\n",
    "display(Latex(r\"\"\"\n",
    "mean($\\mathbb{M}[c_{t+1}]/\\mathbb{M}[c_{t}]$) = \"\"\"+\n",
    "      formatter.format(np.mean(groFac_cNrm_avg[start_plots_at_period:]))))\n",
    "print('cumulative cNrm growth: '+formatter.format(groFac_cNrm_cum))\n",
    "\n",
    "plt.plot(groFac_cvar_avg[start_plots_at_period:])\n",
    "plt.plot(np.mean(groFac_cvar_avg[start_plots_at_period:])*np.ones(num_periods))\n",
    "plt.title(r'cov$_{t+1}(c_{t+1},\\mathbf{p}_{t+1}) / $cov$_{t}(c_{t}, \\mathbf{p}_{t})$')\n",
    "plt.show()\n",
    "\n",
    "display(Latex(r\"\"\"\n",
    "mean(cov$_{t+1}(c_{t+1},\\mathbf{p}_{t+1}) / $cov$_{t}(c_{t}, \\mathbf{p}_{t})$) = \"\"\"+\n",
    "      formatter.format(np.mean(groFac_cNrm_avg[start_plots_at_period:]))))\n",
    "print('cumulative cvar growth: '+formatter.format(groFac_cvar_cum))\n",
    "\n",
    "omega_cNrm = np.mean(groFac_cNrm_avg[start_plots_at_period:])\n",
    "omega_cLvl = np.mean(groFac_cLvl_avg[start_plots_at_period:])\n",
    "omega_pLvl = np.mean(groFac_pLvl_avg[start_plots_at_period:])\n",
    "omega_cvar = np.mean(groFac_cvar_avg[start_plots_at_period:])\n",
    "\n",
    "display(Latex(\"\"\"$\\mathbb{M}(\\Omega_{\\pmb{\\mathfrak{c}}}) = $\"\"\" + formatter.format(omega_cNrm)))\n",
    "display(Latex(\"\"\"$\\mathbb{M}(\\Omega_{cov}) = $\"\"\" + formatter.format(omega_cvar)))\n",
    "display(Latex(\"\"\"$\\mathbb{M}(\\Omega_{cov}/\\Omega_{\\pmb{\\mathfrak{c}}}) = $\"\"\" + formatter.format(omega_cvar/omega_cNrm)))\n",
    "display(Latex(\"\"\"$\\mathbb{M}(\\mathbf{p}_{t+1}/\\mathbf{p}_{t}) = $\"\"\"+formatter.format(omega_pLvl)))"
   ]
  }
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