problem_sets/midterm_practice_problems.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Midterm Practice Problems\n",
        "\n",
        "Jesse Perla, UBC"
      ],
      "id": "39ca19a3-c293-401e-8e92-3c2a683016f2"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Student Name/Number: (doubleclick to edit)"
      ],
      "id": "42d8b56b-7498-44fa-97da-4923453253b9"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Instructions\n",
        "\n",
        "The following are example directions for an exam.\n",
        "\n",
        "-   Ensure you modify the field above with your **name and student\n",
        "    number above immediately**\n",
        "-   The exam has **XXXXX questions**, each with multiple parts for a\n",
        "    total of **XXXXX points**. You may not finish the exam, so best to\n",
        "    do your best answering all questions to the extent possible and not\n",
        "    get stuck on any one question.\n",
        "-   This exam is **closed book** and accessing the internet **is not\n",
        "    permitted**\n",
        "    -   See the **formula “sheet”** embedded at the end of this notebook\n",
        "        for reference\n",
        "    -   You can the internal help as required (see the Jupyterhub menu,\n",
        "        use `Settings/Show Contextual Help`)\n",
        "-   **Execute the file** to begin, which will also check your setup. To\n",
        "    do this in Jupyter, in the menu go `> Run > Run All Cells` or the\n",
        "    equivalent buttons\n",
        "-   Edit this file directly, and in-place as an `ipynb` file, which we\n",
        "    will automatically download at the end of the exam time directly. In\n",
        "    particular\n",
        "    -   **DO NOT** rename this file with your name. It is automatically\n",
        "        associated with your canvas account\n",
        "    -   **DO NOT** save-as the file, move it, or export to pdf or html\n",
        "    -   **DO NOT** add any additional packages\n",
        "-   **Save** the notebook as you are working\n",
        "    -   We will only grade what is saved at the end of the exam in this\n",
        "        exact file, and it is your responsibility to ensure the file is\n",
        "        saved\n",
        "    -   We will **not** execute the notebook, so ensure all code,\n",
        "        figures, etc. are ready as-is upon saving for submission\n",
        "-   Ensure you **edit the results in the code blocks or markup blocks\n",
        "    indicated** as we will not grade anything outside of those\n",
        "    -   You will not be judged on code quality directly, but code\n",
        "        clarity may be required for us to ensure you understood the\n",
        "        problem directly\n",
        "    -   If a question requires math, you can try to put latex inside of\n",
        "        the cells but will not be judged on whether you write latex\n",
        "        vs. math in text that doesn’t quite match latex. But it should\n",
        "        be clear"
      ],
      "id": "604336e1-f14a-4045-afd0-614acc493b4e"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Packages available\n",
        "# DO NOT MODIFY OR ADD PACKAGES\n",
        "using Distributions, Plots, LaTeXStrings, LinearAlgebra, Statistics, Random"
      ],
      "id": "66d87697"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Take the followign functions from our previous lectures"
      ],
      "id": "369bd322-fb5c-4938-8ba0-fd2313757947"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "simple_regression (generic function with 1 method)"
            ]
          }
        }
      ],
      "source": [
        "# DO NOT MODIFY\n",
        "function lorenz(v)  # assumed sorted vector\n",
        "    S = cumsum(v)  # cumulative sums: [v[1], v[1] + v[2], ... ]\n",
        "    F = (1:length(v)) / length(v)\n",
        "    L = S ./ S[end]\n",
        "    return (; F, L) # returns named tuple\n",
        "end\n",
        "# Assumes that v is sorted!\n",
        "gini(v) = (2 * sum(i * y for (i,y) in enumerate(v))/sum(v)\n",
        "           - (length(v) + 1))/length(v)\n",
        "\n",
        "function simple_regression(x, y)\n",
        "  x_bar = mean(x)\n",
        "  y_bar = mean(y)\n",
        "  a = sum((x .- x_bar).*(y .- y_bar)) / sum((x .- x_bar).^2)\n",
        "  b = y_bar - a * x_bar\n",
        "  return (;a, b)\n",
        "end           "
      ],
      "id": "6e7b8cd1"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Short Question 1\n",
        "\n",
        "With a CDF of a distribution $F(x)$ with an accompanying counter-cdf\n",
        "$1-F(x)$, what is the definition of a power-law tail? For a stochastic\n",
        "process $X_t$, what features of that stochastic process might lead to a\n",
        "power-law tail in the stationary distribution?"
      ],
      "id": "138fe61e-fe96-414e-a380-899e2ff3d3a2"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "fa771dfc-3b2e-4380-a150-98f6e8005f94"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Short Question 2\n",
        "\n",
        "If you are trying to understand wealth inequality, what features of the\n",
        "distribution are ideal to examine using (a) Lorenz Curves; (b) Gini\n",
        "Coefficients; and (c) Power Law Tails"
      ],
      "id": "91276ad4-df5e-4c8e-91e4-55b6f6aaea34"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "89cb9ec0-5450-4ab5-84d4-bb8531201a06"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Short Question 3\n",
        "\n",
        "If I calculate a log-log plot of a distribution to examine whether it\n",
        "has heavy tails, what should I plot for the x-axis and y-axis? If I did\n",
        "a linear regression and found that the slope was -2, would that\n",
        "necessarily say that the distribution was a power-law distribution? Why\n",
        "or why not?"
      ],
      "id": "2c78fb95-b73b-4c85-b219-90fb0d27d543"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "117c741b-9cbb-4401-8670-c24b34ce7407"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Short Question 4\n",
        "\n",
        "If a log-log plot showed a slope of -1.5 with a clear linear\n",
        "relationship in the right tail, what is the implied power-law exponent?\n",
        "What does this tell us about moments of the underlying distribution?"
      ],
      "id": "0e785d8b-05f1-4f49-9796-11dd1c9b0f08"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "806f00a1-2f3b-4f1f-9d79-f79ec224cf4c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Short Question 5\n",
        "\n",
        "Compare stochastic processes:\n",
        "\n",
        "1.  $X_{t+1} = a_{t+1} X_t + b$\n",
        "2.  $X_{t+1} = X_t + a_{t+1} + b$\n",
        "\n",
        "where in both cases $a_{t+1}$ are IID shocks. Which stochastic process\n",
        "would you expect may have power-law tails in their stationary\n",
        "distribution, and why? What if $b = 0$ in both cases? Provide intuition\n",
        "for the differences."
      ],
      "id": "23ad6868-7c21-45f0-b739-8163e4ae287e"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "093f1a52-3b20-4963-9c61-d70a62401aa1"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Short Question 6\n",
        "\n",
        "Take the following figure showing the Lorenz Curves for data from two\n",
        "different distributions. What can you infer about the inequality in the\n",
        "two distributions? What would you expect the Gini coefficients to be for\n",
        "the two distributions?"
      ],
      "id": "629bcc31-2aa3-4e2d-bb07-1eff4ea3ff84"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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\" />"
            ]
          }
        }
      ],
      "source": [],
      "id": "58372705"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "01ac857b-ebb5-4291-b685-e749d70f303e"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Short Question 7\n",
        "\n",
        "Given a mapping $F : \\mathbb{R}^N \\to \\mathbb{R}^N$ what is the\n",
        "definition of a fixed point $x^*$ of this mapping? Does it always exist?"
      ],
      "id": "d279c7b2-171c-45fd-934e-a1f7dd8bfafe"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "d8ce9763-af51-430e-9f8f-28edf18c3d10"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Short Question 8\n",
        "\n",
        "Explain the importance of the fixed factor of production, land, in the\n",
        "Malthusian growth model"
      ],
      "id": "ea5877a6-0c19-461e-8de6-2f8fdd0eb916"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "d0615fb4-e724-4922-8cd7-264b4a7ff8e6"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Short Question 9\n",
        "\n",
        "An asset pays off a deterministic stream of income,\n",
        "$\\{y_{t+j}\\}_{j=0}^{\\infty}$, and a risk-neutral agent prices this using\n",
        "a discount factor $0 < \\beta < 1$. The PDV of the income is then\n",
        "$p_t = \\sum_{j = 0}^{\\infty}\\beta^j y_{t+j}$\n",
        "\n",
        "The agent prices this asset using the recursive formulation\n",
        "\n",
        "$$\n",
        "p_t = y_t + \\beta p_{t+1}\n",
        "$$\n",
        "\n",
        "Briefly interpret this recursive equation from the agent’s perspective."
      ],
      "id": "d216f644-50e7-4314-affa-ce910cb01f06"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "d44f79dd-a4c9-4fa3-9c7f-639e8bcba074"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Question 0\n",
        "\n",
        "Consider for some $X_t \\sim F$ IID draws from a distribution the log-log\n",
        "plot using the empirical CDF. The dotted line plots the linear\n",
        "regression with this data, with the intercept and slope shown on the\n",
        "legend."
      ],
      "id": "7b2e87a8-3904-4b98-8bdd-acc7c410fa69"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<img 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\" />"
            ]
          }
        }
      ],
      "source": [],
      "id": "6bd19a8b"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Consider the log-log plot of 100 IID draws from a different distribution\n",
        "$Y_t \\sim F$."
      ],
      "id": "8652bf1c-da29-4496-ae66-553a9ee67697"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "<img 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\" />"
            ]
          }
        }
      ],
      "source": [],
      "id": "9200ff04"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Compare the $X_t$ and $Y_t$ log-log plots. What can you infer about\n",
        "these distributions?"
      ],
      "id": "d44bf9c7-70d9-47dc-821d-d0e720302e47"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "0116237f-fa80-433c-898e-19ed0af1ff8a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now consider the log-log plot of draws from a third distribution\n",
        "$Z_t \\sim F$\n",
        "\n",
        "The log-log plot of the $Z_t$ draws"
      ],
      "id": "65cc3b42-e7cc-4010-9af3-a7c57271af44"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
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\" />"
            ]
          }
        }
      ],
      "source": [],
      "id": "50aa57f5"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "What can you infer about this distribution compared to the other two?"
      ],
      "id": "43be9851-d249-4ac6-b03d-d8c0fe83beaa"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "40feee08-0008-4197-b565-f71f1012cd1a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Question 1\n",
        "\n",
        "Following the notes on [AR(1)\n",
        "processes](https://jlperla.github.io/undergrad_computational_macro/slides/stochastic_dynamics.html#/title-slide)\n",
        "rather than plotting the distribution as normal instead lets see what\n",
        "the stationary distribution looks like with simulation.\n",
        "\n",
        "### Part (a)\n",
        "\n",
        "From $X_0 = 1.0$ simulate up to $T=2000$ using the process\n",
        "\n",
        "$$\n",
        "X_t = a X_{t-1} + b + c W_t\n",
        "$$\n",
        "\n",
        "Where $a=0.98, b=0.1, c=0.02$."
      ],
      "id": "4bd1db2f-6dc3-4682-bf02-33087d2f398c"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.02"
            ]
          }
        }
      ],
      "source": [
        "T = 2000\n",
        "X_0 = 1.0\n",
        "a = 0.98\n",
        "b = 0.1\n",
        "c = 0.02\n",
        "# Add code here"
      ],
      "id": "b397d550"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Part (b)\n",
        "\n",
        "On the same graph plot the histogram of those simulated values (i.e.,\n",
        "$\\{X_0, \\ldots X_T\\}$) then plot the density of the stationary\n",
        "distribution calculated in closed from in [those\n",
        "notes](https://jlperla.github.io/undergrad_computational_macro/slides/stochastic_dynamics.html#/ar1-example)\n",
        "(i.e. create a normal distribution with $\\mu^* = b/(1-a)$ and\n",
        "$v^*  = c^2/(1 - a^2)$\n",
        "\n",
        "Hint: `histogram(X, normed=true)` normalizes the empirical draws so they\n",
        "are a proper PMF."
      ],
      "id": "ff6cc263-44a7-42bb-aa48-84aab87d4376"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Add code here"
      ],
      "id": "0656f8c9"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Part (c)\n",
        "\n",
        "Now, do the same plot using the 10th to 500th observations (i.e.,\n",
        "$\\{X_{10}, \\ldots X_{500}\\}$)"
      ],
      "id": "03d9a9a5-3161-4958-a747-91cb5eafbaed"
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Add code here"
      ],
      "id": "6270aa0f"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "And then a separate plot using the rest"
      ],
      "id": "1321cd63-802f-4bde-a701-1af44e5939ce"
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Add code here"
      ],
      "id": "7a03a36a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Compare how these line? Explain why each is better or worse?"
      ],
      "id": "c88696f2-e310-408a-a50b-35c4d6a1f5e8"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "dd9776a3-3b48-4209-8d1b-f2ea424e0c33"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Part (d)\n",
        "\n",
        "Change the `c` parameter to be `0.2`.\n",
        "\n",
        "Now repeat the display of the two histograms (1) split of the 10th to\n",
        "500th ; and (2) the remainder"
      ],
      "id": "d87b4b4c-fb84-41a3-ac4f-65684804d348"
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "0.2"
            ]
          }
        }
      ],
      "source": [
        "T = 2000\n",
        "X_0 = 1.0\n",
        "a = 0.98\n",
        "b = 0.1\n",
        "c = 0.2\n",
        "# Add code here, creating new cells as required"
      ],
      "id": "f32c0249"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Compare this to part (d)? Has the results changed and if so, then why?"
      ],
      "id": "0773961c-d936-4c68-a878-6af3c7f6a855"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "973eebb8-b43c-4a80-95a6-842943a56c06"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Question 2\n",
        "\n",
        "In this problem we will examine wealth dynamics for a simpler setup. Log\n",
        "income, $\\log y_t$ follows an AR(1) process,\n",
        "\n",
        "$$\n",
        "\\log y_{t+1} = \\mu_y + \\rho_y \\log y_t + \\sigma_y \\epsilon_{1,t+1}\n",
        "$$\n",
        "\n",
        "and\n",
        "\n",
        "$$\n",
        "\\log R_{t+1} = \\mu_r + \\sigma_r \\epsilon_{2,t+1}\n",
        "$$\n",
        "\n",
        "where $\\epsilon_{1,t+1} \\sim N(0,1)$ and $\\epsilon_{2,t+1} \\sim N(0,1)$\n",
        "are IID shocks.\n",
        "\n",
        "As in the wealth dynamics problem from before, the evolution of wealth\n",
        "is given by\n",
        "\n",
        "$$\n",
        "w_{t+1} = R_{t+1}s(w_t) + y_{t+1}\n",
        "$$\n",
        "\n",
        "where $s(w_t)$ is the exogenously given savings function from before,\n",
        "\n",
        "$$\n",
        "s(w) =  s_0 w \\cdot \\mathbb 1\\{w \\geq \\hat w\\} = \\begin{cases} s_0 w & w \\geq \\hat{w}\\\\\n",
        "0 & w < \\hat{w}\n",
        "\\end{cases}\n",
        "$$\n",
        "\n",
        "For a constant $s_0 \\in (0,1)$ which is savings rate and $\\hat{w}\\geq 0$\n",
        "is a minimum wealth threshold below which they do not save and instead\n",
        "consumer all of their income (since $w_{t+1} = y_{t+1}$ in that case).\n",
        "\n",
        "Take the following simpler structure for holding the parameters of the\n",
        "model"
      ],
      "id": "c9c15fa3-658e-4c70-92bd-ad3bf24c3c66"
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "simple_wealth_dynamics_model (generic function with 1 method)"
            ]
          }
        }
      ],
      "source": [
        "function simple_wealth_dynamics_model(;\n",
        "                 w_hat=1.0, # savings parameter\n",
        "                 s_0=0.75, # savings parameter\n",
        "                 mu_y=0.1, # labor income parameter\n",
        "                 sigma_y=0.1, # labor income parameter\n",
        "                 rho_y=0.9, # labor income parameter\n",
        "                 mu_r=0.0, # rate of return parameter\n",
        "                 sigma_r=0.2, # rate of return parameter\n",
        "                 )\n",
        "    return (;w_hat, s_0, mu_y, sigma_y, rho_y, mu_r, sigma_r)\n",
        "end"
      ],
      "id": "06a388f9"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "and a modified version of the `simulate_panel` function"
      ],
      "id": "408868a5-b3d9-46b5-ab9d-dc2053d32df0"
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "simulate_panel (generic function with 1 method)"
            ]
          }
        }
      ],
      "source": [
        "function simulate_panel(N, T, p; y_0 = p.mu_y/(1-p.rho_y), w_0 = p.mu_y/(1-p.rho_y))\n",
        "    # Setup initial conditions\n",
        "    w = w_0 * ones(N) # start at same w_0\n",
        "    logy = log.(y_0 * ones(N)) # start at same y_0\n",
        "    logR = zeros(N) # not used in this exact example, but could be generalized\n",
        "    \n",
        "    # Preallocate next period states and R intermediates\n",
        "    w_p = similar(w)\n",
        "    logR_p = similar(w)\n",
        "    logy_p = similar(w)    \n",
        "\n",
        "\n",
        "    # Temporary used in calculations\n",
        "    savings_proportion = similar(w) # include constant and R_{t+1}\n",
        "\n",
        "    for t in 1:T\n",
        "        R_shock = randn(N)\n",
        "        y_shock = randn(N)\n",
        "        @inbounds for i in 1:N\n",
        "            logy_p[i] = p.mu_y + p.rho_y*logy[i] + p.sigma_y*y_shock[i]\n",
        "            logR_p[i] = p.mu_r + p.sigma_r*R_shock[i] # no autocorrelation but could reference logR[i]\n",
        "            savings_proportion[i]  = (w[i] >= p.w_hat) ? p.s_0 * exp(logR_p[i]) : 0.0\n",
        "            w_p[i] = savings_proportion[i]*w[i] + exp(logy_p[i])\n",
        "        end\n",
        "        # Step forward\n",
        "        w .= w_p\n",
        "        logy .= logy_p\n",
        "        logR .= logR_p\n",
        "    end    \n",
        "    sort!(w) # sorts the wealth so we can calculate gini/lorenz        \n",
        "    F, L = lorenz(w)\n",
        "    return (;w, y = exp.(logy_p), F, L, gini = gini(w))\n",
        "end"
      ],
      "id": "2b20169a"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The following code shows a basic simulation,"
      ],
      "id": "64adfe6c-4be5-4e11-a077-9b24eee033bf"
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(res.gini, mean(res.w), mean(res.y)) = (0.1725313965803085, 11.892938704027477, 2.7919856429623664)"
          ]
        }
      ],
      "source": [
        "p = simple_wealth_dynamics_model()# Or simple_wealth_dynamics_model(;w_hat = 2.0) to swap out a single parameter, etc.\n",
        "N = 10_000\n",
        "T = 200\n",
        "w_0 = 10.0\n",
        "\n",
        "res = simulate_panel(N, T, p; w_0) # uses the default y_0 but overrides the w_0 default\n",
        "@show res.gini, mean(res.w), mean(res.y); # show some of the results"
      ],
      "id": "177d3776"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Part (a)\n",
        "\n",
        "Using the above code and default parameter values, simulate the model to\n",
        "see the difference in the gini coefficients where you change the\n",
        "variance on the returns `sigma_r` 10 points between `0.0` to `0.3`.\n",
        "\n",
        "Using your simulations, plot the gini coefficient as a function of\n",
        "`sigma_r` and comment on the results."
      ],
      "id": "3b31c45b-d2c5-4446-8a7c-c902fa35bd18"
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "res.gini = 0.23728529457752828"
          ]
        }
      ],
      "source": [
        "# Modify/add code here, creating new cells as required\n",
        "sigma_r_values = range(0.0, 0.3, 10)\n",
        "N = 10_000\n",
        "T = 200\n",
        "\n",
        "# simple_wealth_dynamics_model(;sigma_r = sigma_r_values[1]) # etc. to create modified models\n",
        "res = simulate_panel(N, T, simple_wealth_dynamics_model(;sigma_r = sigma_r_values[end])) # for example, this swaps the sigma_r with the last value in the range\n",
        "@show res.gini;"
      ],
      "id": "39bf4251"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Can you provide a brief interpretation of the results?"
      ],
      "id": "17337731-b878-4f33-814c-7a84121893f7"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "8f46babb-6979-45db-b558-923e2c484e7e"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Part (b)\n",
        "\n",
        "Now, take the same model and lets shut off all variation on the income\n",
        "process to leave it as a fixed value so $y_{t+1} = y_t$ by setting\n",
        "`sigma_y = 0, rho_y = 1, mu_y = 0` and then initializing all of the\n",
        "agents with the `y_0  = 0.5` and `w_0 = 2.0`\n",
        "\n",
        "Calculate the gini coefficient for the same range of `sigma_r` values as\n",
        "above and plot the results."
      ],
      "id": "e43b7511-8679-412b-8b63-c0a81225c0a2"
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/plain": [
              "2.0"
            ]
          }
        }
      ],
      "source": [
        " # Modify/add code here, creating new cells as required\n",
        "p = simple_wealth_dynamics_model(;sigma_y = 0.0, rho_y = 1.0, mu_y = 0.0)\n",
        "N = 10_000\n",
        "T = 1000\n",
        "y_0 = 5.0\n",
        "w_0 = 2.0\n",
        "# res = simulate_panel(N, T, p; y_0, w_0)  # adapt this, passing in the y_0 and w_0"
      ],
      "id": "7fa991f0"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Can you provide a brief interpretation of the results?"
      ],
      "id": "519a8174-3771-4944-a4c0-088b064d5318"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**(double click to edit your answer)**"
      ],
      "id": "ace7ebc3-27e0-4c34-b6d5-4d884d91c6fc"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Formulas\n",
        "\n",
        "Use the following formulas as needed. Formulas are intentionally\n",
        "provided without complete definitions of each variable or conditions on\n",
        "convergence, which you should study using your notes.\n",
        "\n",
        "**YOU WILL NOT BE EXPECTED TO USE THE MAJORITY OF THESE FORMULAS - BUT\n",
        "SOME MAY HELP PROVIDE INTUITION**\n",
        "\n",
        "## General and Stochastic Process Formulas\n",
        "\n",
        "| Description 1 | Formula 1 | Description 2 | Formula 2 |\n",
        "|----------------|--------------------|----------------|--------------------|\n",
        "| Partial Geometric Series | $\\sum_{t=0}^T c^t = \\frac{1 - c^{T+1}}{1-c}$ | Geometric Series | $\\sum_{t=0}^{\\infty} c^t = \\frac{1}{1 -c }$ |\n",
        "| PDV | $p_t = \\sum_{j = 0}^{\\infty}\\beta^j y_{t+j}$ | Recursive Formulation of PDV | $p_t = y_t + \\beta p_{t+1}$ |\n",
        "| Univariate Linear Difference Equation | $x_{t+1} = a x_t + b$ | Solution | $x_t = b \\frac{1 - a^t}{1 - a} + a^t x_0$ |\n",
        "| Linearity of Normals | $X \\sim \\mathcal{N}(\\mu_X, \\sigma_X^2), Y \\sim \\mathcal{N}(\\mu_Y, \\sigma_Y^2)$ then $a X + b Y \\sim \\mathcal{N}(a \\mu_X + b \\mu_Y, a^2 \\sigma_X^2 + b^2 \\sigma_Y^2)$ | Special Case | $Y \\sim N(\\mu, \\sigma^2)$ then $Y = \\mu + \\sigma X$ for $X \\sim N(0,1)$ |\n",
        "| Partial Sums $X_1,\\ldots$ IID with $\\mu \\equiv \\mathbb{E}(X)$ | $\\bar{X}_n \\equiv \\frac{1}{n} \\sum_{i=1}^n X_i$ | Strong LLN | $\\mathbb{P} \\left( \\lim_{n \\rightarrow \\infty} \\bar{X}_n = \\mu \\right) = 1$ |\n",
        "| AR(1) Process | $X_{t+1} = a X_t + b + c W_{t+1}$ with $W_{t+1} \\sim \\mathcal{N}(0, 1)$ | Stationary Distribution | $X_{\\infty} \\sim \\mathcal{N}(\\frac{b}{1 - a}, \\frac{\\sigma^2_{\\epsilon}}{1 - a^2})$ |\n",
        "| AR(1) Evolution | $X_t \\sim \\mathcal{N}(\\mu_t, v_t)$, then $X_{t+1} \\sim \\mathcal{N}(a \\mu_t + b, a^2 v_t + c^2)$ | Recursively | $\\mu_{t+1} = a \\mu_t + b, v_{t+1} = a^2 v_t + c^2$ |\n",
        "| Mean Ergodic Definition Given Stationary $X_{\\infty}$ | $\\lim_{T\\to\\infty}\\frac{1}{T} \\sum_{t=1}^T X_t = \\mathbb{E}[X_{\\infty}]$ | ARCH (1) | $X_{t+1} = a X_t + \\left(\\beta + \\gamma X_t^2\\right)^{1/2} W_{t+1}$ with $W_{t+1} \\sim \\mathcal{N}(0, 1)$ |\n",
        "\n",
        "## Inequality and Power Law Formulas\n",
        "\n",
        "| Description 1 | Formula 1 | Description 2 | Formula 2 |\n",
        "|----------------|--------------------|----------------|--------------------|\n",
        "| Kesten Process for $a_{t+1}, y_{t+1}$ IID | $X_{t+1} = a_{t+1} X_t + y_{t+1}$ | Key Conditions for Kesten Stationarity | $\\mathbb{E}(\\log a_t) < 0$ and $\\mathbb{E}(y) < \\infty$ |\n",
        "| Counter-CDF | $\\mathbb{P}(X > x) = 1 - \\mathbb{P}(X \\leq x)$ | CCDF With density $f(x)$ and CDF $F(x)$ | $\\int_{x}^{\\infty} f(x) dx = 1 - F(x)$ |\n",
        "| Pareto PDF with $x_m$ minimum and tail parameter $\\alpha$ | $f(x) = \\frac{\\alpha x_m^\\alpha}{x^{\\alpha+1}},\\text{for all } x \\geq x_m$ | CDF and CCDF | $F(x) = 1 - \\left(\\frac{x}{x_m}\\right)^{-\\alpha}$, $1 - F(x)  = \\left(\\frac{x}{x_m}\\right)^{-\\alpha}$ |\n",
        "| Log-Log Plot with CDF $F(x)$ | $\\log(x)$ vs. $\\log(1 - F(x))$ | For Pareto | $\\log(1 - F(x)) = \\alpha \\log(x_m) - \\alpha \\log(x)$ |\n",
        "| Power-law Tail | $\\mathbb{P}(X > x) \\propto x^{-\\alpha}$ for large $x$ | With CCDF | $1 - F(x) \\propto x^{-\\alpha}$ for large $x$ |\n",
        "| Empirical CDF | $\\hat{F}(x) = \\frac{\\text{number of observations } X_n \\leq x}{N}$ | Tail Parameter Regression where $\\alpha \\approx - a$ | $\\log(1 - \\hat{F}(x_i)) = b + a \\log(x_i) + \\epsilon_i$ |\n",
        "| Quantile Function | $x = F^{-1}(p)\\equiv Q(p)$ | Lorenz Curve | $L(p) = \\frac{\\int_{0}^{p} Q(s) ds}{\\int_{0}^{1} Q(s) ds}$ |\n",
        "| CDF with Ordered Data ${v_1, \\ldots v_n}$ | $F(v_i) \\equiv F_i = \\frac{i}{n}$ | Lorenz with Ordered Data | $S_i = \\frac{1}{n}\\sum_{j=1}^i v_j$, $L(v_i) \\equiv L_i = \\frac{S_i}{S_n}$ |\n",
        "| Gini Coefficient | Area between Lorenz Curve and Line of Equality | Gini with Ordered Data | $G = \\frac{2\\sum_{i=1}^n i v_i}{n \\sum_{i=1}^n v_i} - \\frac{n+1}{n}$ |\n",
        "\n",
        "## Solow and Stochastic Growth Formulas\n",
        "\n",
        "| Description 1 | Formula 1 | Description 2 | Formula 2 |\n",
        "|----------------|--------------------|----------------|--------------------|\n",
        "| Production | $Y_t = z_t F(K_t, N_t)$ | Constant Returns to Scale | $F(\\alpha K, \\alpha N) = \\alpha F(K, N) \\quad \\forall \\alpha > 0$ |\n",
        "| Production per Capita | $k_t \\equiv K_t/N_t, f(k_t) \\equiv F(k_t, 1)$ | Scaled Production Function | $f(k_t) = z_t f(k_{t-1})$ |\n",
        "| Marginal Product of Capital | $z_t \\frac{\\partial F(K_t, N_t)}{\\partial K_t}$ | MPK with $f(k) = k^\\alpha$ | $z_t \\frac{\\partial F(K_t, N_t)}{\\partial K_t} = \\alpha z_t  k_t^{\\alpha - 1}$ |\n",
        "| Consumption/Investment | $C_t + X_t = Y_t \\equiv z_t F(K_t, N_t)$ | Capital Accumulation | $K_{t+1} = (1 - \\delta) K_t + X_t$ |\n",
        "| Constant Population Growth | $N_{t+1} = (1+g_N) N_t$ | Per-Capital Evolution | $k_{t+1} = \\frac{1}{1+g_N} \\left[(1-\\delta) k_t + s z_t f(k_t)\\right]$ |\n",
        "| Steady State | $(g_N + \\delta)\\bar{k} = s \\bar{z} f(\\bar{k})$ | Steady State with $f(k) = k^\\alpha$ | $\\bar{k} = \\left(\\frac{s \\bar{z}}{g_N + \\delta}\\right)^{\\frac{1}{1-\\alpha}}$ |\n",
        "| Real Rental Rate of Capital | $r_t = z_t f'(k_t)$ | Real Wages | $w_t = (1-\\alpha) z_t f(k_t)$ |\n",
        "| Stochastic Growth Capital Evolution | $k_{t+1} = (1-\\delta) k_t + s Z_t f(k_t),\\quad \\text{given } k_0$ | Stochastic Growth Productivity Process | $\\log Z_{t+1} = a \\log Z_t + b + c W_{t+1}$ with $W_{t+1} \\sim \\mathcal{N}(0, 1)$ |"
      ],
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