{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# A Gentle Introduction to HARK: The Perfect Foresight Model\n", "\n", "[![badge](https://img.shields.io/badge/Launch%20using%20-Econ--ARK-blue)](https://econ-ark.org/materials/gentle-intro-to-hark-perfforesightcrra#launch)\n", "\n", "This notebook provides a simple, hands-on tutorial for first time HARK users (and maybe first time Python users) who have a basic knowledge of the theory of intertemporal choice (roughly at the level of first year PhD students - see [PerfForesightCRRA](http://www.econ2.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA/) for a full exposition of the consumption theory).\n", "\n", "It does not go \"into the weeds\" - we have hidden some code cells that do boring things that you don't need to digest on your first experience with HARK. Our aim is to convey a feel for how the toolkit works.\n", "\n", "For the benfit of readers for whom this is your first experience with Python, we have put important Python concepts in **boldface**.\n", "\n", "For those for whom this is the first time they have used a Jupyter notebook, we have put Jupyter instructions in _italics_. Only cursory definitions (if any) are provided here. If you want to learn more, there are many online Python and Jupyter tutorials." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# This cell has just a bit of initial setup. You can click the triangle to the left to expand it.\n", "# Click the \"Run\" button immediately above the notebook in order to execute the contents of any cell\n", "# WARNING: Each cell in the notebook relies upon results generated by previous cells\n", "# The most common problem beginners have is to execute a cell before all its predecessors\n", "# If you do this, you can restart the kernel (see the \"Kernel\" menu above) and start over\n", "from HARK.utilities import plot_funcs\n", "\n", "from copy import deepcopy\n", "\n", "\n", "def mystr(number):\n", " return \"{:.4f}\".format(number)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Your First HARK Model: Perfect Foresight\n", "\n", "We are studying a consumer with constant relative risk aversion utility $U(C) = \\frac{C^{1-\\rho}}{1-\\rho}$ who has perfect foresight about everything except the (stochastic) date of death; death occurs with probability $\\mathsf{D}$, implying a \"survival probability\" $(1-\\mathsf{D}) < 1$. Permanent labor income $P_t$ grows from period to period by a factor $\\Gamma_t$. At the beginning of each period $t$, the consumer has some amount of market resources $M_t$ (which includes both market wealth and currrent income - think of it as bank balances after you have received your paycheck). The consumer must choose how much of those resources to consume $C_t$ and how much to retain in a riskless asset $A_t$ which will earn return factor $R$. The agent receives a flow of utility $U(C_t)$ from consumption and geometrically discounts future utility flows by factor $\\beta$. Between periods, the agent dies with probability $\\mathsf{D}_t$, ending his problem. (This means that the possibility of death is merely another reason to discount the future more -- you might not be there to enjoy it!)\n", "\n", "The agent's problem can be written in Bellman form as:\n", "\n", "\\begin{eqnarray*}\n", "V_t(M_t,P_t) &=& \\max_{C_t} U(C_t) + \\beta (1-\\mathsf{D}_{t+1}) V_{t+1}(M_{t+1},P_{t+1}), \\\\\n", "& s.t. & \\\\\n", "%A_t &=& M_t - C_t, \\\\\n", "M_{t+1} &=& R (M_{t}-C_{t}) + Y_{t+1}, \\\\\n", "P_{t+1} &=& \\Gamma_{t+1} P_t, \\\\\n", "\\end{eqnarray*}\n", "\n", "A particular perfect foresight agent's problem can be characterized by values of risk aversion $\\rho$, discount factor $\\beta$, and return factor $R$, along with sequences of income growth factors $\\{ \\Gamma_t \\}$ and death probabilities $\\{\\mathsf{D}_t\\}$. To keep things simple, let's forget about \"sequences\" of income growth and mortality, and just think about an _infinite horizon_ consumer with constant income growth and survival probability.\n", "\n", "## Representing Agents in HARK\n", "\n", "HARK represents agents solving this type of problem as **instances** of the **class** $\\texttt{PerfForesightConsumerType}$, a **subclass** of $\\texttt{AgentType}$. To make agents of this class, we must import the class itself into our workspace. (Run the cell below in order to do this)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from HARK.ConsumptionSaving.ConsIndShockModel import PerfForesightConsumerType" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $\\texttt{PerfForesightConsumerType}$ class contains within itself the python code that constructs the solution for the perfect foresight model we are studying here, as specifically articulated in [these lecture notes](http://www.econ2.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA/).\n", "\n", "To create an instance of $\\texttt{PerfForesightConsumerType}$, we simply 'call the class'; that is, we invoke it in a way that looks like the way other programming languages evaluate a function, passing as arguments the specific parameter values we want it to have. In the hidden cell below, we define a **dictionary** named $\\texttt{PF_dictionary}$ with these parameter values:\n", "\n", "| Param | Description | Code | Value |\n", "| :---: | --- | --- | --- |\n", "| $\\rho$ | Relative risk aversion | $\\texttt{CRRA}$ | 2.5 |\n", "| $\\beta$ | Discount factor | $\\texttt{DiscFac}$ | 0.96 |\n", "| $R$ | Risk free interest factor | $\\texttt{Rfree}$ | 1.03 |\n", "| $1- \\mathsf{D}$ | Survival probability | $\\texttt{LivPrb}$ | 0.98 |\n", "| $\\Gamma$ | Income growth factor | $\\texttt{PermGroFac}$ | 1.01 |\n", "\n", "\n", "For now, don't worry about the specifics of dictionaries. All you need to know is that a dictionary lets us pass many arguments wrapped up in one simple data structure." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# This cell defines a parameter dictionary. You can expand it if you want to see what that looks like.\n", "PF_dictionary = {\n", " \"CRRA\": 2.5,\n", " \"DiscFac\": 0.96,\n", " \"Rfree\": 1.03,\n", " \"LivPrb\": [0.98],\n", " \"PermGroFac\": [1.01],\n", " \"T_cycle\": 1,\n", " \"cycles\": 0,\n", "}\n", "\n", "# To those curious enough to open this hidden cell, you might notice that we defined\n", "# a few extra parameters in that dictionary: T_cycle, cycles, and AgentCount. Don't\n", "# worry about these for now." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's make an **object** named $\\texttt{PFexample}$ which is an **instance** of the $\\texttt{PerfForesightConsumerType}$ class. The object $\\texttt{PFexample}$ will bundle together the abstract mathematical description of the solution embodied in $\\texttt{PerfForesightConsumerType}$, and the specific set of parameter values defined in $\\texttt{PF\\_dictionary}$. Such a bundle is created passing $\\texttt{PF\\_dictionary}$ to the class $\\texttt{PerfForesightConsumerType}$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "PFexample = PerfForesightConsumerType(**PF_dictionary)\n", "# the asterisks ** basically say \"here come some arguments\" to PerfForesightConsumerType" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In $\\texttt{PFexample}$, we now have _defined_ the problem of a particular infinite horizon perfect foresight consumer who knows how to solve this problem.\n", "\n", "## Solving an Agent's Problem\n", "\n", "To tell the agent actually to solve the problem, we call the agent's $\\texttt{solve}$ **method**. (A **method** is essentially a function that an object runs that affects the object's own internal characteristics -- in this case, the method adds the consumption function to the contents of $\\texttt{PFexample}$.)\n", "\n", "The cell below calls the $\\texttt{solve}$ method for $\\texttt{PFexample}$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "PFexample.solve()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Running the $\\texttt{solve}$ method creates the **attribute** of $\\texttt{PFexample}$ named $\\texttt{solution}.$ In fact, every subclass of $\\texttt{AgentType}$ works the same way: The class definition contains the abstract algorithm that knows how to solve the model, but to obtain the particular solution for a specific instance (paramterization/configuration), that instance must be instructed to $\\texttt{solve()}$ its problem.\n", "\n", "The $\\texttt{solution}$ attribute is always a _list_ of solutions to a sequence of single period solutions of the problem. In the case of an infinite horizon model like the one here, there is just one element in that list -- the solution to all periods of the infinite horizon problem. (In a life cycle model, there would be a list of solutions, one for each age). The consumption function stored as the first element (element 0) of the solution list can be retrieved by:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "PFexample.solution[0].cFunc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One of the results proven in the associated [the lecture notes](http://www.econ2.jhu.edu/people/ccarroll/public/lecturenotes/consumption/PerfForesightCRRA/) is that, for the specific problem defined above, there is a solution in which the _ratio_ $c = C/P$ is a linear function of the _ratio_ of market resources to permanent income, $m = M/P$.\n", "\n", "This is why $\\texttt{cFunc}$ can be represented by a linear interpolation. It can be plotted using the command below:\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mPlotTop = 10\n", "plot_funcs(PFexample.solution[0].cFunc, 0.0, mPlotTop)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The figure illustrates one of the surprising features of the perfect foresight model: A person with zero money should be spending at a rate more than double their income ($\\texttt{cFunc}(0.) \\approx 2.08$). What gives?\n", "\n", "The answer is that we have not incorporated any constraint that would prevent the agent from borrowing against the entire PDV of future earnings -- human wealth.\n", "\n", "How much is that? An equivalent question is: What's the minimum value of $m_t$ where the consumption function is defined (that is, where the consumer has a positive expected _total wealth_ (the sum of human and nonuman wealth)? Let's check:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This agent's human wealth is 50.49994992551661 times his current income level.\n", "This agent's consumption function is defined down to m_t = -50.49994992551661\n" ] } ], "source": [ "humanWealth = PFexample.solution[0].hNrm\n", "mMinimum = PFexample.solution[0].mNrmMin\n", "print(\n", " \"This agent's human wealth is \"\n", " + str(humanWealth)\n", " + \" times his current income level.\"\n", ")\n", "print(\"This agent's consumption function is defined down to m_t = \" + str(mMinimum))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yikes! Let's take a look at the bottom of the consumption function. In the cell below, set the bounds of the $\\texttt{plot\\_funcs}$ function to display down to the lowest defined value of the consumption function." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# YOUR FIRST HANDS-ON EXERCISE!\n", "# Fill in the value for \"mPlotBottom\" to plot the consumption function from the point where it is zero.\n", "mPlotBottom = 0.0 # You should replace 0.0 with the correct answer\n", "plot_funcs(PFexample.solution[0].cFunc, mPlotBottom, mPlotTop)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Changing Agent Parameters\n", "\n", "Suppose you wanted to change one (or more) of the parameters of the agent's problem and see what that does. We want to compare consumption functions before and after we change parameters, so let's make a new instance of $\\texttt{PerfForesightConsumerType}$ by copying $\\texttt{PFexample}$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "NewExample = deepcopy(PFexample)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In Python, you can set an **attribute** of an object just like any other variable. For example, we could make the new agent less patient:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "NewExample.DiscFac = 0.90\n", "NewExample.solve()\n", "mPlotBottom = NewExample.solution[0].mNrmMin\n", "plot_funcs(\n", " [NewExample.solution[0].cFunc, PFexample.solution[0].cFunc], mPlotBottom, mPlotTop\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(Note that you can pass a list of functions to $\\texttt{plot\\_funcs}$ as the first argument rather than just a single function. Lists are written inside of [square brackets].)\n", "\n", "Let's try to deal with the \"problem\" of massive human wealth by making another consumer who has essentially no future income. We can almost eliminate human wealth by making the permanent income growth factor $\\textit{very}$ small.\n", "\n", "In $\\texttt{PFexample}$, the agent's income grew by 1 percent per period-- his $\\texttt{PermGroFac}$ took the value 1.01. What if our new agent had a growth factor of 0.01 -- his income _shrinks_ by 99 percent each period? In the cell below, set $\\texttt{NewExample}$'s discount factor back to its original value, then set its $\\texttt{PermGroFac}$ attribute so that the growth factor is 0.01 each period.\n", "\n", "Important: Recall that the model at the top of this document said that an agent's problem is characterized by a sequence of income growth factors, but we tabled that concept. Because $\\texttt{PerfForesightConsumerType}$ treats $\\texttt{PermGroFac}$ as a _time-varying_ attribute, it must be specified as a **list** (with a single element in this case)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Revert NewExample's discount factor and make his future income minuscule\n", "# your lines here!\n", "\n", "# Compare the old and new consumption functions\n", "plot_funcs([PFexample.solution[0].cFunc, NewExample.solution[0].cFunc], 0.0, 10.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now $\\texttt{NewExample}$'s consumption function has the same slope (MPC) as $\\texttt{PFexample}$, but it emanates from (almost) zero-- he has basically no future income to borrow against!\n", "\n", "If you'd like, use the cell above to alter $\\texttt{NewExample}$'s other attributes (relative risk aversion, etc) and see how the consumption function changes. However, keep in mind that _no solution exists_ for some combinations of parameters. HARK should let you know if this is the case if you try to solve such a model.\n", "\n", "Linear consumption functions are pretty boring, and you'd be justified in feeling unimpressed if all HARK could do was plot some lines. Let's look at [another model](./Gentle-Intro-To-HARK-Buffer-Stock-Model.ipynb) that adds two important layers of complexity: income shocks and (artificial) borrowing constraints." ] } ], "metadata": { "jupytext": { "cell_metadata_json": true, "formats": "ipynb,py:percent", "notebook_metadata_filter": "all" }, "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }