Generator: BufferStockTheory-make/notebooks_byname
" ] }, { "cell_type": "markdown", "id": "f1b0c985", "metadata": {}, "source": [ "The [TractableBufferStock](http://llorracc.github.io/TractableBufferStock/) model is a (relatively) simple framework that captures all of the qualitative, and many of the quantitative features of optimal consumption in the presence of labor income uncertainty." ] }, { "cell_type": "code", "execution_count": 1, "id": "68713f7a", "metadata": {}, "outputs": [], "source": [ "# This cell has a bit of (uninteresting) initial setup.\n", "# Import the model from the toolkit\n", "from HARK.ConsumptionSaving.TractableBufferStockModel import TractableConsumerType\n", "import ipywidgets as widgets\n", "from ipywidgets import interact, fixed\n", "import matplotlib.pyplot as plt\n", "\n", "import numpy as np\n", "\n", "\n", "def mystr(number):\n", " return \"{:.3f}\".format(number)" ] }, { "cell_type": "markdown", "id": "5fd7b32f", "metadata": {}, "source": [ "The key assumption behind the model's tractability is that there is only a single, stark form of uncertainty: So long as an employed consumer remains employed, that consumer's labor income $P$ will rise at a constant rate $\\Gamma$:\n", "\\begin{align}\n", "P_{t+1} &= \\Gamma P_{t}\n", "\\end{align}\n", "\n", "But, between any period and the next, there is constant hazard $p$ that the consumer will transition to the \"unemployed\" state. Unemployment is irreversible, like retirement or disability. When unemployed, the consumer receives a fixed amount of income (for simplicity, zero). (See the [linked handout](http://www.econ2.jhu.edu/people/ccarroll/public/LectureNotes/Consumption/TractableBufferStock/) for details of the model).\n", "\n", "Defining $G$ as the growth rate of aggregate wages/productivity, we assume that idiosyncratic wages grow by $\\Gamma = G/(1-\\mho)$ where $(1-\\mho)^{-1}$ is the growth rate of idiosyncratic productivity ('on-the-job learning', say). (This assumption about the relation between idiosyncratic income growth and idiosyncratic risk means that an increase in $\\mho$ is a mean-preserving spread in human wealth; again see [the lecture notes](http://www.econ2.jhu.edu/people/ccarroll/public/LectureNotes/Consumption/TractableBufferStock/)).\n", "\n", "Under CRRA utility $u(C) = \\frac{C^{1-\\rho}}{1-\\rho}$, the problem can be normalized by $P$. Using lower case for normalized varibles (e.g., $c = C/P$), the normalized problem can be expressed by the Bellman equation:\n", "\n", "\\begin{eqnarray*}\n", "v_t({m}_t) &=& \\max_{{c}_t} ~ U({c}_t) + \\beta \\Gamma^{1-\\rho} \\overbrace{\\mathbb{E}[v_{t+1}^{\\bullet}]}^{=p v_{t+1}^{u}+(1-p)v_{t+1}^{e}} \\\\\n", "& s.t. & \\\\\n", "{m}_{t+1} &=& (m_{t}-c_{t})\\mathcal{R} + \\mathbb{1}_{t+1},\n", "\\end{eqnarray*}\n", "where $\\mathcal{R} = R/\\Gamma$, and $\\mathbb{1}_{t+1} = 1$ if the consumer is employed (and zero if unemployed).\n", "\n", "Under plausible parameter values the model has a target level of $\\hat{m} = M/P$ (market resources to permanent income) with an analytical solution that exhibits plausible relationships among all of the parameters.\n", "\n", "Defining $\\gamma = \\log \\Gamma$ and $r = \\log R$, the handout shows that an approximation of the target is given by the formula:\n", "\n", "\\begin{align}\n", "\\hat{m} & \\approx 1 + \\left(\\frac{1}{(\\gamma-r)+(1+(\\gamma/\\mho)(1-(\\gamma/\\mho)(\\rho-1)/2))}\\right)\n", "\\end{align}\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "0e98e2c5", "metadata": {}, "outputs": [], "source": [ "# Define a parameter dictionary and representation of the agents for the tractable buffer stock model\n", "TBS_dictionary = {\n", " \"UnempPrb\": 0.00625, # Prob of becoming unemployed; working life of 1/UnempProb = 160 qtrs\n", " \"DiscFac\": 0.975, # Intertemporal discount factor\n", " \"Rfree\": 1.01, # Risk-free interest factor on assets\n", " \"PermGroFac\": 1.0025, # Permanent income growth factor (uncompensated)\n", " \"CRRA\": 2.5,\n", "} # Coefficient of relative risk aversion\n", "MyTBStype = TractableConsumerType(**TBS_dictionary)" ] }, { "cell_type": "markdown", "id": "78a70893", "metadata": {}, "source": [ "## Target Wealth\n", "\n", "Whether the model exhibits a \"target\" or \"stable\" level of the wealth-to-permanent-income ratio for employed consumers depends on whether the 'Growth Impatience Condition' (the GIC) holds:\n", "\n", "\\begin{align}\\label{eq:GIC}\n", " \\left(\\frac{(R \\beta (1-\\mho))^{1/\\rho}}{\\Gamma}\\right) & < 1\n", "\\\\ \\left(\\frac{(R \\beta (1-\\mho))^{1/\\rho}}{G (1-\\mho)}\\right) &< 1\n", "\\\\ \\left(\\frac{(R \\beta)^{1/\\rho}}{G} (1-\\mho)^{-\\rho}\\right) &< 1\n", "\\end{align}\n", "and recall (from [PerfForesightCRRA](https://www.econ2.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA/)) that the perfect foresight 'Growth Impatience Factor' is\n", "\\begin{align}\\label{eq:PFGIC}\n", "\\left(\\frac{(R \\beta)^{1/\\rho}}{G}\\right) &< 1\n", "\\end{align}\n", "so since $\\mho > 0$, uncertainty makes it harder to be 'impatient.' To understand this, think of someone who, in the perfect foresight model, was 'poised': Exactly on the knife edge between patience and impatience. Now add a precautionary saving motive; that person will now (to some degree) be pushed off the knife edge in the direction of 'patience.' So, in the presence of uncertainty, the conditions on parameters other than $\\mho$ must be stronger in order to guarantee 'impatience' in the sense of wanting to spend enough for your wealth to decline _despite_ the extra precautionary motive." ] }, { "cell_type": "code", "execution_count": 3, "id": "9cb33696", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "16df5d4048e44289ad28fb59f500053b", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=0.975, continuous_update=False, description='$\\\\beta$', max=0.99, min=…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Define a function that plots the employed consumption function and sustainable consumption function\n", "# for given parameter values\n", "\n", "\n", "def makeTBSplot(\n", " DiscFac,\n", " CRRA,\n", " Rfree,\n", " PermGroFac,\n", " UnempPrb,\n", " mMax,\n", " mMin,\n", " cMin,\n", " cMax,\n", " plot_emp,\n", " plot_ret,\n", " plot_mSS,\n", " show_targ,\n", "):\n", " MyTBStype.DiscFac = DiscFac\n", " MyTBStype.CRRA = CRRA\n", " MyTBStype.Rfree = Rfree\n", " MyTBStype.PermGroFac = PermGroFac\n", " MyTBStype.UnempPrb = UnempPrb\n", "\n", " try:\n", " MyTBStype.solve()\n", " except:\n", " print(\n", " \"Unable to solve; parameter values may be too close to their limiting values\"\n", " )\n", "\n", " plt.xlabel(\"Market resources ${m}_t$\")\n", " plt.ylabel(\"Consumption ${c}_t$\")\n", " plt.ylim([cMin, cMax])\n", " plt.xlim([mMin, mMax])\n", "\n", " m = np.linspace(mMin, mMax, num=100, endpoint=True)\n", " if plot_emp:\n", " c = MyTBStype.solution[0].cFunc(m)\n", " c[m == 0.0] = 0.0\n", " plt.plot(m, c, \"-b\")\n", "\n", " if plot_mSS:\n", " plt.plot(\n", " [mMin, mMax],\n", " [\n", " (\n", " MyTBStype.PermGroFacCmp / MyTBStype.Rfree\n", " + mMin * (1.0 - MyTBStype.PermGroFacCmp / MyTBStype.Rfree)\n", " ),\n", " (\n", " MyTBStype.PermGroFacCmp / MyTBStype.Rfree\n", " + mMax * (1.0 - MyTBStype.PermGroFacCmp / MyTBStype.Rfree)\n", " ),\n", " ],\n", " \"--k\",\n", " )\n", "\n", " if plot_ret:\n", " c = MyTBStype.solution[0].cFunc_U(m)\n", " plt.plot(m, c, \"-g\")\n", "\n", " if show_targ:\n", " mTarg = MyTBStype.mTarg\n", " cTarg = MyTBStype.cTarg\n", " # + mystr(mTarg) + '\\n$\\hat{c}^* = $ ' + mystr(cTarg)\n", " targ_label = r\"$\\left(\\frac{1}{(\\gamma-r)+(1+(\\gamma/\\mho)(1-(\\gamma/\\mho)(\\rho-1)/2))}\\right) $\"\n", " plt.annotate(\n", " targ_label,\n", " xy=(0.0, 0.0),\n", " xytext=(0.2, 0.1),\n", " textcoords=\"axes fraction\",\n", " fontsize=18,\n", " )\n", " plt.plot(mTarg, cTarg, \"ro\")\n", " plt.annotate(\n", " \"↙️ m target\",\n", " (mTarg, cTarg),\n", " xytext=(0.25, 0.2),\n", " ha=\"left\",\n", " textcoords=\"offset points\",\n", " )\n", "\n", " plt.show()\n", " return None\n", "\n", "\n", "# Define widgets to control various aspects of the plot\n", "\n", "# Define a slider for the discount factor\n", "DiscFac_widget = widgets.FloatSlider(\n", " min=0.9,\n", " max=0.99,\n", " step=0.0002,\n", " value=TBS_dictionary[\"DiscFac\"], # Default value\n", " continuous_update=False,\n", " readout_format=\".4f\",\n", " description=\"$\\\\beta$\",\n", ")\n", "\n", "# Define a slider for relative risk aversion\n", "CRRA_widget = widgets.FloatSlider(\n", " min=1.0,\n", " max=5.0,\n", " step=0.01,\n", " value=TBS_dictionary[\"CRRA\"], # Default value\n", " continuous_update=False,\n", " readout_format=\".2f\",\n", " description=\"$\\\\rho$\",\n", ")\n", "\n", "# Define a slider for the interest factor\n", "Rfree_widget = widgets.FloatSlider(\n", " min=1.01,\n", " max=1.04,\n", " step=0.0001,\n", " value=TBS_dictionary[\"Rfree\"], # Default value\n", " continuous_update=False,\n", " readout_format=\".4f\",\n", " description=\"$R$\",\n", ")\n", "\n", "\n", "# Define a slider for permanent income growth\n", "PermGroFac_widget = widgets.FloatSlider(\n", " min=1.00,\n", " max=1.015,\n", " step=0.0002,\n", " value=TBS_dictionary[\"PermGroFac\"], # Default value\n", " continuous_update=False,\n", " readout_format=\".4f\",\n", " description=\"$G$\",\n", ")\n", "\n", "# Define a slider for unemployment (or retirement) probability\n", "UnempPrb_widget = widgets.FloatSlider(\n", " min=0.000001,\n", " max=TBS_dictionary[\"UnempPrb\"] * 2, # Go up to twice the default value\n", " step=0.00001,\n", " value=TBS_dictionary[\"UnempPrb\"],\n", " continuous_update=False,\n", " readout_format=\".5f\",\n", " description=\"$\\\\mho$\",\n", ")\n", "\n", "# Define a text box for the lower bound of {m}_t\n", "mMin_widget = widgets.FloatText(\n", " value=0.0, step=0.1, description=\"$m$ min\", disabled=False\n", ")\n", "\n", "# Define a text box for the upper bound of {m}_t\n", "mMax_widget = widgets.FloatText(\n", " value=50.0, step=0.1, description=\"$m$ max\", disabled=False\n", ")\n", "\n", "# Define a text box for the lower bound of {c}_t\n", "cMin_widget = widgets.FloatText(\n", " value=0.0, step=0.1, description=\"$c$ min\", disabled=False\n", ")\n", "\n", "# Define a text box for the upper bound of {c}_t\n", "cMax_widget = widgets.FloatText(\n", " value=1.5, step=0.1, description=\"$c$ max\", disabled=False\n", ")\n", "\n", "# Define a check box for whether to plot the employed consumption function\n", "plot_emp_widget = widgets.Checkbox(\n", " value=True, description=\"Plot employed $c$ function\", disabled=False\n", ")\n", "\n", "# Define a check box for whether to plot the retired consumption function\n", "plot_ret_widget = widgets.Checkbox(\n", " value=False, description=\"Plot retired $c$ function\", disabled=False\n", ")\n", "\n", "# Define a check box for whether to plot the sustainable consumption line\n", "plot_mSS_widget = widgets.Checkbox(\n", " value=True, description=\"Plot sustainable $c$ line\", disabled=False\n", ")\n", "\n", "# Define a check box for whether to show the target annotation\n", "show_targ_widget = widgets.Checkbox(\n", " value=True, description=\"Show target $(m,c)$\", disabled=False\n", ")\n", "\n", "# Make an interactive plot of the tractable buffer stock solution\n", "\n", "# To make some of the widgets not appear, replace X_widget with fixed(desired_fixed_value) in the arguments below.\n", "interact(\n", " makeTBSplot,\n", " DiscFac=DiscFac_widget,\n", " CRRA=CRRA_widget,\n", " # We can fix a parameter using the fixed() operator\n", " Rfree=fixed(TBS_dictionary[\"Rfree\"]),\n", " # Rfree = Rfree_widget, # This is the line which, when uncommented, would make Rfree a slider\n", " PermGroFac=PermGroFac_widget,\n", " UnempPrb=UnempPrb_widget,\n", " mMin=mMin_widget,\n", " mMax=mMax_widget,\n", " cMin=cMin_widget,\n", " cMax=cMax_widget,\n", " show_targ=show_targ_widget,\n", " plot_emp=plot_emp_widget,\n", " plot_ret=plot_ret_widget,\n", " plot_mSS=plot_mSS_widget,\n", ");" ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "ExecuteTime,collapsed,jupyter,code_folding,tags,-autoscroll", "encoding": "# -*- 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\n", 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