amss2.ipynb

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   "source": [
    "# Fluctuating Interest Rates Deliver Fiscal Insurance"
   ]
  },
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   "source": [
    "## Contents\n",
    "\n",
    "- [Fluctuating Interest Rates Deliver Fiscal Insurance](#Fluctuating-Interest-Rates-Deliver-Fiscal-Insurance)  \n",
    "  - [Overview](#Overview)  \n",
    "  - [Forces at work](#Forces-at-work)  \n",
    "  - [Logical flow of  lecture](#Logical-flow-of--lecture)  \n",
    "  - [Example economy](#Example-economy)  \n",
    "  - [Reverse engineering strategy](#Reverse-engineering-strategy)  \n",
    "  - [Code for reverse engineering](#Code-for-reverse-engineering)  \n",
    "  - [Short simulation for reverse-engineered: initial debt](#Short-simulation-for-reverse-engineered:-initial-debt)  \n",
    "  - [Long simulation](#Long-simulation)  \n",
    "  - [BEGS approximations of  limiting debt and convergence rate](#BEGS-approximations-of--limiting-debt-and-convergence-rate)  "
   ]
  },
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   "source": [
    "**Co-authors: Anmol Bhandari and David Evans**"
   ]
  },
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    "## Overview\n",
    "\n",
    "This lecture extends our investigations of how optimal policies for levying a flat-rate tax on labor income and  issuing government debt depend\n",
    "on whether there are complete  markets for debt\n",
    "\n",
    "A Ramsey allocation and Ramsey policy in the AMSS [[AMSS02]](https://lectures.quantecon.org/py/zreferences.html#amss-2002) model described in [optimal taxation without state-contingent debt](https://lectures.quantecon.org/py/amss.html) generally differs\n",
    "from a Ramsey allocation and Ramsey policy in the  Lucas-Stokey [[LS83]](https://lectures.quantecon.org/py/zreferences.html#lucasstokey1983) model described in [optimal taxation with state-contingent debt](https://lectures.quantecon.org/py/opt_tax_recur.html)\n",
    "\n",
    "This is because the implementability restriction that a competitive equilibrium with a distorting tax  imposes on  allocations in the Lucas-Stokey model is just one among a set of\n",
    "implementability conditions imposed in  the AMSS model\n",
    "\n",
    "These additional constraints require that time $ t $ components of a Ramsey allocation\n",
    "for the AMSS model be **measurable** with respect to time $ t-1 $ information\n",
    "\n",
    "The  measurability constraints imposed by the AMSS model are inherited from the   restriction that  only one-period risk-free bonds\n",
    "can be traded\n",
    "\n",
    "Differences between the  Ramsey allocations in the two models   indicate that at least some of the measurability constraints of the AMSS model of\n",
    "[optimal taxation without state-contingent debt](https://lectures.quantecon.org/py/amss.html) are violated at the Ramsey allocation of a corresponding  [[LS83]](https://lectures.quantecon.org/py/zreferences.html#lucasstokey1983) model with state-contingent debt\n",
    "\n",
    "Another way to say this is that differences between the Ramsey allocations of the two models indicate that some of the measurability constraints of the\n",
    "AMSS model are violated at the  Ramsey allocation of the Lucas-Stokey model\n",
    "\n",
    "Nonzero Lagrange multipliers on those constraints make the Ramsey allocation for the AMSS model differ from the Ramsey allocation for the Lucas-Stokey model\n",
    "\n",
    "This lecture studies a special  AMSS model in which\n",
    "\n",
    "- The exogenous state variable $ s_t $ is governed by  a finite-state Markov chain  \n",
    "- With an arbitrary budget-feasible initial level of government debt, the measurability  constraints  \n",
    "  - bind for many periods, but $ \\ldots $  \n",
    "  - eventually they stop binding evermore, so $ \\ldots $  \n",
    "  - in the tail of the Ramsey plan, the Lagrange multipliers $ \\gamma_t(s^t) $ on the AMSS implementability constraints [(8)](https://lectures.quantecon.org/py/amss.html#equation-ts-gov-wo4)  converge to zero  \n",
    "- After the implementability constraints [(8)](https://lectures.quantecon.org/py/amss.html#equation-ts-gov-wo4) no longer bind in the tail of the AMSS Ramsey plan  \n",
    "  - history dependence of the AMSS state variable $ x_t $ vanishes and  $ x_t $ becomes a time-invariant function of the Markov state $ s_t $  \n",
    "  - the par value of government debt becomes **constant over time** so that $ b_{t+1}(s^t) = \\bar b $ for $ t \\geq T $ for a sufficiently large $ T $  \n",
    "  - $ \\bar b <0 $, so that the tail of the Ramsey plan instructs  the government always to make a constant par value of risk-free one-period loans to the private sector  \n",
    "  - the one-period gross interest rate $ R_t(s^t) $ on risk-free debt  converges to a time-invariant function of the Markov state $ s_t $  \n",
    "- For a **particular** $ b_0 < 0 $ (i.e., a positive level of initial government **loans** to the private sector), the measurability constraints **never** bind  \n",
    "- In this special case  \n",
    "  \n",
    "  - the **par value** $ b_{t+1}(s_t) = \\bar b $  of government debt at time $ t $ and Markov state $ s_t $  is constant across time and states,\n",
    "    but $ \\ldots $  \n",
    "  - the **market value** $ \\frac{\\bar b}{R_t(s_t)} $ of government debt at time $ t $  varies as a time-invariant function of the Markov state $ s_t $  \n",
    "  - fluctuations in the interest rate make gross earnings on government debt $ \\frac{\\bar b}{R_t(s_t)} $ fully insure the gross-of-gross-interest-payments government budget against fluctuations in government expenditures  \n",
    "  - the state variable $ x $ in a recursive representation of a Ramsey plan is a time invariant function of the Markov state for $ t \\geq 0 $  \n",
    "  \n",
    "- In this special case, the Ramsey allocation in the AMSS model agrees with that in a [[LS83]](https://lectures.quantecon.org/py/zreferences.html#lucasstokey1983) model in which\n",
    "  the same amount of state-contingent debt falls due in all states tomorrow  \n",
    "  - it is a situation in which  the Ramsey planner loses nothing from not being  able to  purchase state-contingent debt and being restricted to exchange only risk-free debt  debt  \n",
    "- This outcome emerges only when we initialize government debt at a particular $ b_0 < 0 $  \n",
    "\n",
    "\n",
    "In a nutshell, the reason for this striking outcome is that at a particular level of risk-free government **assets**, fluctuations in the one-period risk-free interest\n",
    "rate provide the government with complete insurance against stochastically varying government expenditures"
   ]
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    "## Forces at work\n",
    "\n",
    "The forces  driving asymptotic  outcomes here are examples of dynamics present in a more general class  incomplete markets models analyzed in [[BEGS17]](https://lectures.quantecon.org/py/zreferences.html#begs1) (BEGS)\n",
    "\n",
    "BEGS provide conditions under which government debt under a Ramsey plan converges to an invariant distribution\n",
    "\n",
    "BEGS  construct approximations to that asymptotically invariant  distribution  of government debt under a  Ramsey plan\n",
    "\n",
    "BEGS also compute an approximation to a Ramsey plan’s rate of convergence  to that limiting invariant distribution\n",
    "\n",
    "We  shall use the BEGS approximating limiting distribution and the approximating  rate of convergence   to help interpret  outcomes here\n",
    "\n",
    "For a long time, the Ramsey plan puts a nontrivial martingale-like component into the par value of  government debt as part of the way that the Ramsey plan imperfectly\n",
    "smooths distortions from the labor tax rate across  time and Markov states\n",
    "\n",
    "But BEGS show that binding implementability constraints slowly push government debt in a direction designed to let the government use fluctuations in equilibrium interest\n",
    "rate  rather than fluctuations in  par values of debt to insure against shocks to government expenditures\n",
    "\n",
    "- This is a **weak** (but unrelenting) force that, starting from an initial debt level, for a long time is dominated by the stochastic martingale-like component of debt\n",
    "  dynamics that the Ramsey planner uses to facilitate imperfect tax-smoothing across time and states  \n",
    "- This weak force slowly drives the par value of government **assets** to a **constant** level at which the government can completely insure against government expenditure shocks while\n",
    "  shutting down the stochastic component of debt dynamics  \n",
    "- At that point, the tail of the par value of government debt becomes a trivial martingale: it is constant over time  "
   ]
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    "## Logical flow of  lecture\n",
    "\n",
    "We present ideas  in the following order\n",
    "\n",
    "- We describe a two-state  AMSS economy and generate a long simulation starting from a positive  initial government debt  \n",
    "- We observe that in a long simulation starting from positive government debt, the par value of  government debt eventually converges to a constant $ \\bar b $  \n",
    "- In fact, the par value of government debt  converges to the same constant level $ \\bar b $ for alternative realizations of the Markov government expenditure process and for alternative settings of initial government\n",
    "  debt $ b_0 $  \n",
    "- We reverse engineer a particular value of initial government debt $ b_0 $ (it turns out to be negative) for which the  continuation debt moves\n",
    "  to $ \\bar b $ immediately  \n",
    "- We note that for this particular initial debt $ b_0 $, the Ramsey allocations  for the AMSS economy and the Lucas-Stokey model are identical  \n",
    "  - we verify that the LS Ramsey planner chooses to purchase **identical** claims to time $ t+1 $ consumption for all Markov states tomorrow for each Markov state today  \n",
    "- We compute the BEGS approximations to check how accurately they describe the dynamics of the long-simulation  "
   ]
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    "### Equations from Lucas-Stokey (1983) model\n",
    "\n",
    "Although we are studying an AMSS [[AMSS02]](https://lectures.quantecon.org/py/zreferences.html#amss-2002) economy,  a Lucas-Stokey [[LS83]](https://lectures.quantecon.org/py/zreferences.html#lucasstokey1983) economy plays\n",
    "an important  role in the reverse-engineering calculation to be described below\n",
    "\n",
    "For that reason, it is helpful  to have readily available some key equations underlying a Ramsey plan for the Lucas-Stokey economy\n",
    "\n",
    "Recall first-order conditions for a Ramsey allocation for the Lucas-Stokey economy\n",
    "\n",
    "For $ t \\geq 1 $, these take the form\n",
    "\n",
    "\n",
    "<a id='equation-ts-barg10a'></a>\n",
    "$$\n",
    "\\begin{aligned}\n",
    "  (1+\\Phi) &u_c(c,1-c-g) + \\Phi \\bigl[c u_{cc}(c,1-c-g) -\n",
    "    (c+g) u_{\\ell c}(c,1-c-g) \\bigr]\n",
    "    \\\\\n",
    "    &= (1+\\Phi) u_{\\ell}(c,1-c-g) + \\Phi \\bigl[c u_{c\\ell}(c,1-c-g) -\n",
    "    (c+g) u_{\\ell \\ell}(c,1-c-g)  \\bigr]\n",
    "\\end{aligned} \\tag{1}\n",
    "$$\n",
    "\n",
    "There is one such equation for each value of the Markov state $ s_t $\n",
    "\n",
    "In addition, given an initial Markov state, the time $ t=0 $ quantities $ c_0 $ and $ b_0 $ satisfy\n",
    "\n",
    "\n",
    "<a id='equation-ts-barg11b'></a>\n",
    "$$\n",
    "\\begin{aligned}\n",
    "      (1+\\Phi) &u_c(c,1-c-g) + \\Phi \\bigl[c u_{cc}(c,1-c-g) -\n",
    "        (c+g) u_{\\ell c}(c,1-c-g) \\bigr]\n",
    "        \\\\\n",
    "        &= (1+\\Phi) u_{\\ell}(c,1-c-g) + \\Phi \\bigl[c u_{c\\ell}(c,1-c-g) -\n",
    "        (c+g) u_{\\ell \\ell}(c,1-c-g)  \\bigr] + \\Phi (u_{cc} - u_{c,\\ell}) b_0\n",
    "\\end{aligned} \\tag{2}\n",
    "$$\n",
    "\n",
    "In addition, the time $ t=0 $ budget constraint is satisfied at $ c_0 $ and initial government debt\n",
    "$ b_0 $:\n",
    "\n",
    "\n",
    "<a id='equation-eqn-amss2-10'></a>\n",
    "$$\n",
    "b_0 + g_0 = \\tau_0 (c_0 + g_0) + \\frac{\\bar b}{R_0} \\tag{3}\n",
    "$$\n",
    "\n",
    "where $ R_0 $ is the gross interest rate for the Markov state $ s_0 $ that is assumed to prevail at time $ t =0 $\n",
    "and $ \\tau_0 $ is the time $ t=0 $ tax rate\n",
    "\n",
    "In equation [(3)](#equation-eqn-amss2-10), it is understood that\n",
    "\n",
    "$$\n",
    "\\begin{gather*}\n",
    "\\tau_0 = 1 - \\frac{u_{l,0}}{u_{c,0}} \\\\\n",
    "R_0^{-1} =  \\beta  \\sum_{s=1}^S \\Pi(s | s_0) \\frac{u_c(s)}{u_{c,0}} \\\\\n",
    "\\end{gather*}\n",
    "$$\n",
    "\n",
    "It is useful to transform  some of the above equations to forms that are more natural for analyzing the\n",
    "case of a CRRA utility specification that we shall use in our example economies"
   ]
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    "### Specification with CRRA Utility\n",
    "\n",
    "As in lectures [optimal taxation without state-contingent debt](https://lectures.quantecon.org/py/amss.html) and [optimal taxation with state-contingent debt](https://lectures.quantecon.org/py/opt_tax_recur.html),\n",
    "we assume that the  representative agent has  utility function\n",
    "\n",
    "$$\n",
    "u(c,n) = {\\frac{c^{1-\\sigma}}{1-\\sigma}} - {\\frac{n^{1+\\gamma}}{1+\\gamma}}\n",
    "$$\n",
    "\n",
    "and set  $ \\sigma = 2 $, $ \\gamma = 2 $, and the  discount factor $ \\beta = 0.9 $\n",
    "\n",
    "We eliminate leisure from the model and continue to assume that\n",
    "\n",
    "$$\n",
    "c_t + g_t = n_t\n",
    "$$\n",
    "\n",
    "The analysis of Lucas and Stokey prevails once we make the following replacements\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "u_\\ell(c, \\ell) &\\sim - u_n(c, n) \\\\\n",
    "u_c(c,\\ell) &\\sim u_c(c,n) \\\\\n",
    "u_{\\ell,\\ell}(c,\\ell) &\\sim u_{nn}(c,n) \\\\\n",
    "u_{c,c}(c,\\ell)& \\sim u_{c,c}(c,n) \\\\\n",
    "u_{c,\\ell} (c,\\ell) &\\sim 0 \\\\\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "With these understandings, equations [(1)](#equation-ts-barg10a) and [(2)](#equation-ts-barg11b) simplify in the case of the CRRA utility function\n",
    "\n",
    "They become\n",
    "\n",
    "\n",
    "<a id='equation-amss2-ts-barg10'></a>\n",
    "$$\n",
    "(1+\\Phi) [u_c(c) + u_n(c+g)] + \\Phi[c u_{cc}(c) + (c+g) u_{nn}(c+g)] = 0 \\tag{4}\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "\n",
    "<a id='equation-amss2-ts-barg11'></a>\n",
    "$$\n",
    "(1+\\Phi) [u_c(c_0) + u_n(c_0+g_0)] + \\Phi[c_0 u_{cc}(c_0) + (c_0+g_0) u_{nn}(c_0+g_0)] - \\Phi u_{cc}(c_0) b_0 = 0 \\tag{5}\n",
    "$$\n",
    "\n",
    "In equation [(4)](#equation-amss2-ts-barg10), it is understood that $ c $ and $ g $ are each functions of the Markov state $ s $\n",
    "\n",
    "The CRRA utility function is represented in the following class"
   ]
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    "import numpy as np\n",
    "\n",
    "\n",
    "class CRRAutility:\n",
    "\n",
    "    def __init__(self,\n",
    "                 β=0.9,\n",
    "                 σ=2,\n",
    "                 γ=2,\n",
    "                 π=0.5*np.ones((2, 2)),\n",
    "                 G=np.array([0.1, 0.2]),\n",
    "                 Θ=np.ones(2),\n",
    "                 transfers=False):\n",
    "\n",
    "        self.β, self.σ, self.γ = β, σ, γ\n",
    "        self.π, self.G, self.Θ, self.transfers = π, G, Θ, transfers\n",
    "\n",
    "    # Utility function\n",
    "    def U(self, c, n):\n",
    "        σ = self.σ\n",
    "        if σ == 1.:\n",
    "            U = np.log(c)\n",
    "        else:\n",
    "            U = (c**(1 - σ) - 1) / (1 - σ)\n",
    "        return U - n**(1 + self.γ) / (1 + self.γ)\n",
    "\n",
    "    # Derivatives of utility function\n",
    "    def Uc(self, c, n):\n",
    "        return c**(-self.σ)\n",
    "\n",
    "    def Ucc(self, c, n):\n",
    "        return -self.σ * c**(-self.σ - 1)\n",
    "\n",
    "    def Un(self, c, n):\n",
    "        return -n**self.γ\n",
    "\n",
    "    def Unn(self, c, n):\n",
    "        return -self.γ * n**(self.γ - 1)"
   ]
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    "## Example economy\n",
    "\n",
    "We set the following parameter values\n",
    "\n",
    "The Markov state $ s_t $ takes two values, namely,  $ 0,1 $\n",
    "\n",
    "The initial Markov state is $ 0 $\n",
    "\n",
    "The Markov transition matrix is $ .5 I $ where $ I $ is a $ 2 \\times 2 $ identity matrix, so the $ s_t $ process is i.i.d.\n",
    "\n",
    "Government expenditures $ g(s) $ equal $ .1 $ in Markov state $ 0 $ and $ .2 $ in Markov state $ 1 $\n",
    "\n",
    "We set preference parameters as follows:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\beta & = .9 \\cr\n",
    "\\sigma & = 2  \\cr\n",
    "\\gamma & = 2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Here are several classes that do most of the work for us\n",
    "\n",
    "The code is  mostly taken or adapted from the earlier lectures [optimal taxation without state-contingent debt](https://lectures.quantecon.org/py/amss.html) and\n",
    "[optimal taxation with state-contingent debt](https://lectures.quantecon.org/py/opt_tax_recur.html)"
   ]
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    "import numpy as np\n",
    "from scipy.optimize import root\n",
    "from quantecon import MarkovChain\n",
    "\n",
    "\n",
    "class SequentialAllocation:\n",
    "\n",
    "    '''\n",
    "    Class that takes CESutility or BGPutility object as input returns\n",
    "    planner's allocation as a function of the multiplier on the\n",
    "    implementability constraint μ.\n",
    "    '''\n",
    "\n",
    "    def __init__(self, model):\n",
    "\n",
    "        # Initialize from model object attributes\n",
    "        self.β, self.π, self.G = model.β, model.π, model.G\n",
    "        self.mc, self.Θ = MarkovChain(self.π), model.Θ\n",
    "        self.S = len(model.π)  # Number of states\n",
    "        self.model = model\n",
    "\n",
    "        # Find the first best allocation\n",
    "        self.find_first_best()\n",
    "\n",
    "    def find_first_best(self):\n",
    "        '''\n",
    "        Find the first best allocation\n",
    "        '''\n",
    "        model = self.model\n",
    "        S, Θ, G = self.S, self.Θ, self.G\n",
    "        Uc, Un = model.Uc, model.Un\n",
    "\n",
    "        def res(z):\n",
    "            c = z[:S]\n",
    "            n = z[S:]\n",
    "            return np.hstack([Θ * Uc(c, n) + Un(c, n), Θ * n - c - G])\n",
    "\n",
    "        res = root(res, 0.5 * np.ones(2 * S))\n",
    "\n",
    "        if not res.success:\n",
    "            raise Exception('Could not find first best')\n",
    "\n",
    "        self.cFB = res.x[:S]\n",
    "        self.nFB = res.x[S:]\n",
    "\n",
    "        # Multiplier on the resource constraint\n",
    "        self.ΞFB = Uc(self.cFB, self.nFB)\n",
    "        self.zFB = np.hstack([self.cFB, self.nFB, self.ΞFB])\n",
    "\n",
    "    def time1_allocation(self, μ):\n",
    "        '''\n",
    "        Computes optimal allocation for time t >= 1 for a given μ\n",
    "        '''\n",
    "        model = self.model\n",
    "        S, Θ, G = self.S, self.Θ, self.G\n",
    "        Uc, Ucc, Un, Unn = model.Uc, model.Ucc, model.Un, model.Unn\n",
    "\n",
    "        def FOC(z):\n",
    "            c = z[:S]\n",
    "            n = z[S:2 * S]\n",
    "            Ξ = z[2 * S:]\n",
    "            return np.hstack([Uc(c, n) - μ * (Ucc(c, n) * c + Uc(c, n)) - Ξ,          # FOC of c\n",
    "                              Un(c, n) - μ * (Unn(c, n) * n + Un(c, n)) + \\\n",
    "                              Θ * Ξ,  # FOC of n\n",
    "                              Θ * n - c - G])\n",
    "\n",
    "        # Find the root of the first order condition\n",
    "        res = root(FOC, self.zFB)\n",
    "        if not res.success:\n",
    "            raise Exception('Could not find LS allocation.')\n",
    "        z = res.x\n",
    "        c, n, Ξ = z[:S], z[S:2 * S], z[2 * S:]\n",
    "\n",
    "        # Compute x\n",
    "        I = Uc(c, n) * c + Un(c, n) * n\n",
    "        x = np.linalg.solve(np.eye(S) - self.β * self.π, I)\n",
    "\n",
    "        return c, n, x, Ξ\n",
    "\n",
    "    def time0_allocation(self, B_, s_0):\n",
    "        '''\n",
    "        Finds the optimal allocation given initial government debt B_ and state s_0\n",
    "        '''\n",
    "        model, π, Θ, G, β = self.model, self.π, self.Θ, self.G, self.β\n",
    "        Uc, Ucc, Un, Unn = model.Uc, model.Ucc, model.Un, model.Unn\n",
    "\n",
    "        # First order conditions of planner's problem\n",
    "        def FOC(z):\n",
    "            μ, c, n, Ξ = z\n",
    "            xprime = self.time1_allocation(μ)[2]\n",
    "            return np.hstack([Uc(c, n) * (c - B_) + Un(c, n) * n + β * π[s_0] @ xprime,\n",
    "                              Uc(c, n) - μ * (Ucc(c, n) *\n",
    "                                               (c - B_) + Uc(c, n)) - Ξ,\n",
    "                              Un(c, n) - μ * (Unn(c, n) * n +\n",
    "                                               Un(c, n)) + Θ[s_0] * Ξ,\n",
    "                              (Θ * n - c - G)[s_0]])\n",
    "\n",
    "        # Find root\n",
    "        res = root(FOC, np.array(\n",
    "            [0, self.cFB[s_0], self.nFB[s_0], self.ΞFB[s_0]]))\n",
    "        if not res.success:\n",
    "            raise Exception('Could not find time 0 LS allocation.')\n",
    "\n",
    "        return res.x\n",
    "\n",
    "    def time1_value(self, μ):\n",
    "        '''\n",
    "        Find the value associated with multiplier μ\n",
    "        '''\n",
    "        c, n, x, Ξ = self.time1_allocation(μ)\n",
    "        U = self.model.U(c, n)\n",
    "        V = np.linalg.solve(np.eye(self.S) - self.β * self.π, U)\n",
    "        return c, n, x, V\n",
    "\n",
    "    def Τ(self, c, n):\n",
    "        '''\n",
    "        Computes Τ given c, n\n",
    "        '''\n",
    "        model = self.model\n",
    "        Uc, Un = model.Uc(c, n), model.Un(c,  n)\n",
    "\n",
    "        return 1 + Un / (self.Θ * Uc)\n",
    "\n",
    "    def simulate(self, B_, s_0, T, sHist=None):\n",
    "        '''\n",
    "        Simulates planners policies for T periods\n",
    "        '''\n",
    "        model, π, β = self.model, self.π, self.β\n",
    "        Uc = model.Uc\n",
    "\n",
    "        if sHist is None:\n",
    "            sHist = self.mc.simulate(T, s_0)\n",
    "\n",
    "        cHist, nHist, Bhist, ΤHist, μHist = np.zeros((5, T))\n",
    "        RHist = np.zeros(T - 1)\n",
    "\n",
    "        # Time 0\n",
    "        μ, cHist[0], nHist[0], _ = self.time0_allocation(B_, s_0)\n",
    "        ΤHist[0] = self.Τ(cHist[0], nHist[0])[s_0]\n",
    "        Bhist[0] = B_\n",
    "        μHist[0] = μ\n",
    "\n",
    "        # Time 1 onward\n",
    "        for t in range(1, T):\n",
    "            c, n, x, Ξ = self.time1_allocation(μ)\n",
    "            Τ = self.Τ(c, n)\n",
    "            u_c = Uc(c, n)\n",
    "            s = sHist[t]\n",
    "            Eu_c = π[sHist[t - 1]] @ u_c\n",
    "            cHist[t], nHist[t], Bhist[t], ΤHist[t] = c[s], n[s], x[s] / \\\n",
    "                u_c[s], Τ[s]\n",
    "            RHist[t - 1] = Uc(cHist[t - 1], nHist[t - 1]) / (β * Eu_c)\n",
    "            μHist[t] = μ\n",
    "\n",
    "        return np.array([cHist, nHist, Bhist, ΤHist, sHist, μHist, RHist])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hide-output": false,
    "html-class": "collapse"
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import fmin_slsqp\n",
    "\n",
    "\n",
    "class RecursiveAllocationAMSS:\n",
    "\n",
    "    def __init__(self, model, μgrid, tol_diff=1e-4, tol=1e-4):\n",
    "\n",
    "        self.β, self.π, self.G = model.β, model.π, model.G\n",
    "        self.mc, self.S = MarkovChain(self.π), len(model.π)  # Number of states\n",
    "        self.Θ, self.model, self.μgrid = model.Θ, model, μgrid\n",
    "        self.tol_diff, self.tol = tol_diff, tol\n",
    "\n",
    "        # Find the first best allocation\n",
    "        self.solve_time1_bellman()\n",
    "        self.T.time_0 = True  # Bellman equation now solves time 0 problem\n",
    "\n",
    "    def solve_time1_bellman(self):\n",
    "        '''\n",
    "        Solve the time  1 Bellman equation for calibration model and\n",
    "        initial grid μgrid0\n",
    "        '''\n",
    "        model, μgrid0 = self.model, self.μgrid\n",
    "        π = model.π\n",
    "        S = len(model.π)\n",
    "\n",
    "        # First get initial fit from Lucas Stokey solution.\n",
    "        # Need to change things to be ex ante\n",
    "        PP = SequentialAllocation(model)\n",
    "        interp = interpolator_factory(2, None)\n",
    "\n",
    "        def incomplete_allocation(μ_, s_):\n",
    "            c, n, x, V = PP.time1_value(μ_)\n",
    "            return c, n, π[s_] @ x, π[s_] @ V\n",
    "        cf, nf, xgrid, Vf, xprimef = [], [], [], [], []\n",
    "        for s_ in range(S):\n",
    "            c, n, x, V = zip(*map(lambda μ: incomplete_allocation(μ, s_), μgrid0))\n",
    "            c, n = np.vstack(c).T, np.vstack(n).T\n",
    "            x, V = np.hstack(x), np.hstack(V)\n",
    "            xprimes = np.vstack([x] * S)\n",
    "            cf.append(interp(x, c))\n",
    "            nf.append(interp(x, n))\n",
    "            Vf.append(interp(x, V))\n",
    "            xgrid.append(x)\n",
    "            xprimef.append(interp(x, xprimes))\n",
    "        cf, nf, xprimef = fun_vstack(cf), fun_vstack(nf), fun_vstack(xprimef)\n",
    "        Vf = fun_hstack(Vf)\n",
    "        policies = [cf, nf, xprimef]\n",
    "\n",
    "        # Create xgrid\n",
    "        x = np.vstack(xgrid).T\n",
    "        xbar = [x.min(0).max(), x.max(0).min()]\n",
    "        xgrid = np.linspace(xbar[0], xbar[1], len(μgrid0))\n",
    "        self.xgrid = xgrid\n",
    "\n",
    "        # Now iterate on Bellman equation\n",
    "        T = BellmanEquation(model, xgrid, policies, tol=self.tol)\n",
    "        diff = 1\n",
    "        while diff > self.tol_diff:\n",
    "            PF = T(Vf)\n",
    "\n",
    "            Vfnew, policies = self.fit_policy_function(PF)\n",
    "            diff = np.abs((Vf(xgrid) - Vfnew(xgrid)) / Vf(xgrid)).max()\n",
    "\n",
    "            print(diff)\n",
    "            Vf = Vfnew\n",
    "\n",
    "        # store value function policies and Bellman Equations\n",
    "        self.Vf = Vf\n",
    "        self.policies = policies\n",
    "        self.T = T\n",
    "\n",
    "    def fit_policy_function(self, PF):\n",
    "        '''\n",
    "        Fits the policy functions\n",
    "        '''\n",
    "        S, xgrid = len(self.π), self.xgrid\n",
    "        interp = interpolator_factory(3, 0)\n",
    "        cf, nf, xprimef, Tf, Vf = [], [], [], [], []\n",
    "        for s_ in range(S):\n",
    "            PFvec = np.vstack([PF(x, s_) for x in self.xgrid]).T\n",
    "            Vf.append(interp(xgrid, PFvec[0, :]))\n",
    "            cf.append(interp(xgrid, PFvec[1:1 + S]))\n",
    "            nf.append(interp(xgrid, PFvec[1 + S:1 + 2 * S]))\n",
    "            xprimef.append(interp(xgrid, PFvec[1 + 2 * S:1 + 3 * S]))\n",
    "            Tf.append(interp(xgrid, PFvec[1 + 3 * S:]))\n",
    "        policies = fun_vstack(cf), fun_vstack(\n",
    "            nf), fun_vstack(xprimef), fun_vstack(Tf)\n",
    "        Vf = fun_hstack(Vf)\n",
    "        return Vf, policies\n",
    "\n",
    "    def Τ(self, c, n):\n",
    "        '''\n",
    "        Computes Τ given c and n\n",
    "        '''\n",
    "        model = self.model\n",
    "        Uc, Un = model.Uc(c, n), model.Un(c, n)\n",
    "\n",
    "        return 1 + Un / (self.Θ * Uc)\n",
    "\n",
    "    def time0_allocation(self, B_, s0):\n",
    "        '''\n",
    "        Finds the optimal allocation given initial government debt B_ and\n",
    "        state s_0\n",
    "        '''\n",
    "        PF = self.T(self.Vf)\n",
    "        z0 = PF(B_, s0)\n",
    "        c0, n0, xprime0, T0 = z0[1:]\n",
    "        return c0, n0, xprime0, T0\n",
    "\n",
    "    def simulate(self, B_, s_0, T, sHist=None):\n",
    "        '''\n",
    "        Simulates planners policies for T periods\n",
    "        '''\n",
    "        model, π = self.model, self.π\n",
    "        Uc = model.Uc\n",
    "        cf, nf, xprimef, Tf = self.policies\n",
    "\n",
    "        if sHist is None:\n",
    "            sHist = simulate_markov(π, s_0, T)\n",
    "\n",
    "        cHist, nHist, Bhist, xHist, ΤHist, THist, μHist = np.zeros((7, T))\n",
    "        # time 0\n",
    "        cHist[0], nHist[0], xHist[0], THist[0] = self.time0_allocation(B_, s_0)\n",
    "        ΤHist[0] = self.Τ(cHist[0], nHist[0])[s_0]\n",
    "        Bhist[0] = B_\n",
    "        μHist[0] = self.Vf[s_0](xHist[0])\n",
    "\n",
    "        # time 1 onward\n",
    "        for t in range(1, T):\n",
    "            s_, x, s = sHist[t - 1], xHist[t - 1], sHist[t]\n",
    "            c, n, xprime, T = cf[s_, :](x), nf[s_, :](\n",
    "                x), xprimef[s_, :](x), Tf[s_, :](x)\n",
    "\n",
    "            Τ = self.Τ(c, n)[s]\n",
    "            u_c = Uc(c, n)\n",
    "            Eu_c = π[s_, :] @ u_c\n",
    "\n",
    "            μHist[t] = self.Vf[s](xprime[s])\n",
    "\n",
    "            cHist[t], nHist[t], Bhist[t], ΤHist[t] = c[s], n[s], x / Eu_c, Τ\n",
    "            xHist[t], THist[t] = xprime[s], T[s]\n",
    "        return np.array([cHist, nHist, Bhist, ΤHist, THist, μHist, sHist, xHist])\n",
    "\n",
    "\n",
    "class BellmanEquation:\n",
    "    '''\n",
    "    Bellman equation for the continuation of the Lucas-Stokey Problem\n",
    "    '''\n",
    "\n",
    "    def __init__(self, model, xgrid, policies0, tol, maxiter=1000):\n",
    "\n",
    "        self.β, self.π, self.G = model.β, model.π, model.G\n",
    "        self.S = len(model.π)  # Number of states\n",
    "        self.Θ, self.model, self.tol = model.Θ, model, tol\n",
    "        self.maxiter = maxiter\n",
    "\n",
    "        self.xbar = [min(xgrid), max(xgrid)]\n",
    "        self.time_0 = False\n",
    "\n",
    "        self.z0 = {}\n",
    "        cf, nf, xprimef = policies0\n",
    "\n",
    "        for s_ in range(self.S):\n",
    "            for x in xgrid:\n",
    "                self.z0[x, s_] = np.hstack([cf[s_, :](x),\n",
    "                                            nf[s_, :](x),\n",
    "                                            xprimef[s_, :](x),\n",
    "                                            np.zeros(self.S)])\n",
    "\n",
    "        self.find_first_best()\n",
    "\n",
    "    def find_first_best(self):\n",
    "        '''\n",
    "        Find the first best allocation\n",
    "        '''\n",
    "        model = self.model\n",
    "        S, Θ, Uc, Un, G = self.S, self.Θ, model.Uc, model.Un, self.G\n",
    "\n",
    "        def res(z):\n",
    "            c = z[:S]\n",
    "            n = z[S:]\n",
    "            return np.hstack([Θ * Uc(c, n) + Un(c, n), Θ * n - c - G])\n",
    "\n",
    "        res = root(res, 0.5 * np.ones(2 * S))\n",
    "        if not res.success:\n",
    "            raise Exception('Could not find first best')\n",
    "\n",
    "        self.cFB = res.x[:S]\n",
    "        self.nFB = res.x[S:]\n",
    "        IFB = Uc(self.cFB, self.nFB) * self.cFB + \\\n",
    "            Un(self.cFB, self.nFB) * self.nFB\n",
    "\n",
    "        self.xFB = np.linalg.solve(np.eye(S) - self.β * self.π, IFB)\n",
    "\n",
    "        self.zFB = {}\n",
    "        for s in range(S):\n",
    "            self.zFB[s] = np.hstack(\n",
    "                [self.cFB[s], self.nFB[s], self.π[s] @ self.xFB, 0.])\n",
    "\n",
    "    def __call__(self, Vf):\n",
    "        '''\n",
    "        Given continuation value function next period return value function this\n",
    "        period return T(V) and optimal policies\n",
    "        '''\n",
    "        if not self.time_0:\n",
    "            def PF(x, s): return self.get_policies_time1(x, s, Vf)\n",
    "        else:\n",
    "            def PF(B_, s0): return self.get_policies_time0(B_, s0, Vf)\n",
    "        return PF\n",
    "\n",
    "    def get_policies_time1(self, x, s_, Vf):\n",
    "        '''\n",
    "        Finds the optimal policies \n",
    "        '''\n",
    "        model, β, Θ, G, S, π = self.model, self.β, self.Θ, self.G, self.S, self.π\n",
    "        U, Uc, Un = model.U, model.Uc, model.Un\n",
    "\n",
    "        def objf(z):\n",
    "            c, n, xprime = z[:S], z[S:2 * S], z[2 * S:3 * S]\n",
    "\n",
    "            Vprime = np.empty(S)\n",
    "            for s in range(S):\n",
    "                Vprime[s] = Vf[s](xprime[s])\n",
    "\n",
    "            return -π[s_] @ (U(c, n) + β * Vprime)\n",
    "\n",
    "        def cons(z):\n",
    "            c, n, xprime, T = z[:S], z[S:2 * S], z[2 * S:3 * S], z[3 * S:]\n",
    "            u_c = Uc(c, n)\n",
    "            Eu_c = π[s_] @ u_c\n",
    "            return np.hstack([\n",
    "                x * u_c / Eu_c - u_c * (c - T) - Un(c, n) * n - β * xprime,\n",
    "                Θ * n - c - G])\n",
    "\n",
    "        if model.transfers:\n",
    "            bounds = [(0., 100)] * S + [(0., 100)] * S + \\\n",
    "                [self.xbar] * S + [(0., 100.)] * S\n",
    "        else:\n",
    "            bounds = [(0., 100)] * S + [(0., 100)] * S + \\\n",
    "                [self.xbar] * S + [(0., 0.)] * S\n",
    "        out, fx, _, imode, smode = fmin_slsqp(objf, self.z0[x, s_],\n",
    "                                              f_eqcons=cons, bounds=bounds,\n",
    "                                              full_output=True, iprint=0,\n",
    "                                              acc=self.tol, iter=self.maxiter)\n",
    "\n",
    "        if imode > 0:\n",
    "            raise Exception(smode)\n",
    "\n",
    "        self.z0[x, s_] = out\n",
    "        return np.hstack([-fx, out])\n",
    "\n",
    "    def get_policies_time0(self, B_, s0, Vf):\n",
    "        '''\n",
    "        Finds the optimal policies \n",
    "        '''\n",
    "        model, β, Θ, G = self.model, self.β, self.Θ, self.G\n",
    "        U, Uc, Un = model.U, model.Uc, model.Un\n",
    "\n",
    "        def objf(z):\n",
    "            c, n, xprime = z[:-1]\n",
    "\n",
    "            return -(U(c, n) + β * Vf[s0](xprime))\n",
    "\n",
    "        def cons(z):\n",
    "            c, n, xprime, T = z\n",
    "            return np.hstack([\n",
    "                -Uc(c, n) * (c - B_ - T) - Un(c, n) * n - β * xprime,\n",
    "                (Θ * n - c - G)[s0]])\n",
    "\n",
    "        if model.transfers:\n",
    "            bounds = [(0., 100), (0., 100), self.xbar, (0., 100.)]\n",
    "        else:\n",
    "            bounds = [(0., 100), (0., 100), self.xbar, (0., 0.)]\n",
    "        out, fx, _, imode, smode = fmin_slsqp(objf, self.zFB[s0], f_eqcons=cons,\n",
    "                                              bounds=bounds, full_output=True, iprint=0)\n",
    "\n",
    "        if imode > 0:\n",
    "            raise Exception(smode)\n",
    "\n",
    "        return np.hstack([-fx, out])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hide-output": false,
    "html-class": "collapse"
   },
   "outputs": [],
   "source": [
    "from scipy.interpolate import UnivariateSpline\n",
    "\n",
    "\n",
    "class interpolate_wrapper:\n",
    "\n",
    "    def __init__(self, F):\n",
    "        self.F = F\n",
    "\n",
    "    def __getitem__(self, index):\n",
    "        return interpolate_wrapper(np.asarray(self.F[index]))\n",
    "\n",
    "    def reshape(self, *args):\n",
    "        self.F = self.F.reshape(*args)\n",
    "        return self\n",
    "\n",
    "    def transpose(self):\n",
    "        self.F = self.F.transpose()\n",
    "\n",
    "    def __len__(self):\n",
    "        return len(self.F)\n",
    "\n",
    "    def __call__(self, xvec):\n",
    "        x = np.atleast_1d(xvec)\n",
    "        shape = self.F.shape\n",
    "        if len(x) == 1:\n",
    "            fhat = np.hstack([f(x) for f in self.F.flatten()])\n",
    "            return fhat.reshape(shape)\n",
    "        else:\n",
    "            fhat = np.vstack([f(x) for f in self.F.flatten()])\n",
    "            return fhat.reshape(np.hstack((shape, len(x))))\n",
    "\n",
    "\n",
    "class interpolator_factory:\n",
    "\n",
    "    def __init__(self, k, s):\n",
    "        self.k, self.s = k, s\n",
    "\n",
    "    def __call__(self, xgrid, Fs):\n",
    "        shape, m = Fs.shape[:-1], Fs.shape[-1]\n",
    "        Fs = Fs.reshape((-1, m))\n",
    "        F = []\n",
    "        xgrid = np.sort(xgrid)  # Sort xgrid\n",
    "        for Fhat in Fs:\n",
    "            F.append(UnivariateSpline(xgrid, Fhat, k=self.k, s=self.s))\n",
    "        return interpolate_wrapper(np.array(F).reshape(shape))\n",
    "\n",
    "\n",
    "def fun_vstack(fun_list):\n",
    "\n",
    "    Fs = [IW.F for IW in fun_list]\n",
    "    return interpolate_wrapper(np.vstack(Fs))\n",
    "\n",
    "\n",
    "def fun_hstack(fun_list):\n",
    "\n",
    "    Fs = [IW.F for IW in fun_list]\n",
    "    return interpolate_wrapper(np.hstack(Fs))\n",
    "\n",
    "\n",
    "def simulate_markov(π, s_0, T):\n",
    "\n",
    "    sHist = np.empty(T, dtype=int)\n",
    "    sHist[0] = s_0\n",
    "    S = len(π)\n",
    "    for t in range(1, T):\n",
    "        sHist[t] = np.random.choice(np.arange(S), p=π[sHist[t - 1]])\n",
    "\n",
    "    return sHist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reverse engineering strategy\n",
    "\n",
    "We can reverse engineer a value $ b_0 $ of initial debt due   that renders the AMSS measurability constraints not binding from time $ t =0 $ onward\n",
    "\n",
    "We accomplish this by recognizing that if the AMSS measurability constraints never bind, then the AMSS allocation and Ramsey plan is equivalent\n",
    "with that for a Lucas-Stokey economy in which for each period $ t \\geq 0 $, the government promises to pay the **same** state-contingent\n",
    "amount  $ \\bar b $ in each state tomorrow\n",
    "\n",
    "This insight tells us to find a $ b_0 $ and other fundamentals for the Lucas-Stokey [[LS83]](https://lectures.quantecon.org/py/zreferences.html#lucasstokey1983) model that make the Ramsey planner\n",
    "want to borrow the same value $ \\bar b $ next period for all states and all dates\n",
    "\n",
    "We accomplish this by using various equations for the Lucas-Stokey [[LS83]](https://lectures.quantecon.org/py/zreferences.html#lucasstokey1983) model\n",
    "presented in [optimal taxation with state-contingent debt](https://lectures.quantecon.org/py/opt_tax_recur.html)\n",
    "\n",
    "We use the following steps\n",
    "\n",
    "**Step 1:**  Pick an initial $ \\Phi $\n",
    "\n",
    "**Step 2:** Given that $ \\Phi $, jointly solve two versions of equation [(4)](#equation-amss2-ts-barg10) for $ c(s), s=1, 2 $ associated with the two values\n",
    "for $ g(s), s=1,2 $\n",
    "\n",
    "**Step 3:**  Solve the following equation for $ \\vec x $\n",
    "\n",
    "\n",
    "<a id='equation-lsa-xsola'></a>\n",
    "$$\n",
    "\\vec x= (I - \\beta \\Pi )^{-1} [ \\vec u_c (\\vec n-\\vec g) - \\vec u_l \\vec n] \\tag{6}\n",
    "$$\n",
    "\n",
    "**Step 4:** After solving for $ \\vec x $, we can find $ b(s_t|s^{t-1}) $ in Markov\n",
    "state $ s_t=s $ from $ b(s) = {\\frac{x(s)}{u_c(s)}} $ or the matrix equation\n",
    "\n",
    "\n",
    "<a id='equation-amss2-lsa-bsol'></a>\n",
    "$$\n",
    "\\vec b = {\\frac{ \\vec x }{\\vec u_c}} \\tag{7}\n",
    "$$\n",
    "\n",
    "**Step 5:** Compute $ J(\\Phi) = (b(1) - b(2))^2 $\n",
    "\n",
    "**Step 6:** Put steps 2 through 6 in a function minimizer and find a $ \\Phi $ that minimizes $ J(\\Phi) $\n",
    "\n",
    "**Step 7:** At the value of $ \\Phi $ and the value of $ \\bar b $ that emerged from step 6, solve equations\n",
    "[(5)](#equation-amss2-ts-barg11) and [(3)](#equation-eqn-amss2-10) jointly for $ c_0, b_0 $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code for reverse engineering\n",
    "\n",
    "Here is code to do the calculations for us"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 24\n",
      "         Function evaluations: 48\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import fsolve, fmin\n",
    "\n",
    "u = CRRAutility()\n",
    "\n",
    "def min_Φ(Φ):\n",
    "\n",
    "    g1, g2 = u.G  # Government spending in s=0 and s=1\n",
    "\n",
    "    # Solve Φ(c)\n",
    "    def equations(unknowns, Φ):\n",
    "        c1, c2 = unknowns\n",
    "        # First argument of .Uc and second argument of .Un are redundant\n",
    "\n",
    "        # Set up simultaneous equations\n",
    "        eq = lambda c, g: (1 + Φ) * (u.Uc(c, 1) - -u.Un(1, c + g)) + \\\n",
    "                            Φ * ((c + g) * u.Unn(1, c + g) + c * u.Ucc(c, 1))\n",
    "\n",
    "        # Return equation evaluated at s=1 and s=2\n",
    "        return np.array([eq(c1, g1), eq(c2, g2)]).flatten()\n",
    "\n",
    "    global c1                 # Update c1 globally\n",
    "    global c2                 # Update c2 globally\n",
    "\n",
    "    c1, c2 = fsolve(equations, np.ones(2), args=(Φ))\n",
    "\n",
    "    uc = u.Uc(np.array([c1, c2]), 1)                                   # uc(n - g)\n",
    "    ul = -u.Un(1, np.array([c1 + g1, c2 + g2])) * [c1 + g1, c2 + g2]   # ul(n) = -un(c + g)\n",
    "    x = np.linalg.solve(np.eye((2)) - u.β * u.π, uc * [c1, c2] - ul)   # solve for x\n",
    "\n",
    "    global b                 # Update b globally\n",
    "    b = x / uc\n",
    "    loss = (b[0] - b[1])**2\n",
    "\n",
    "    return loss\n",
    "\n",
    "Φ_star = fmin(min_Φ, .1, ftol=1e-14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To recover and print out $ \\bar b $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0757576567504166"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_bar = b[0]\n",
    "b_bar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To complete the reverse engineering exercise by jointly determining $ c_0, b_0 $,  we\n",
    "set up a function that returns two simultaneous equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "def solve_cb(unknowns, Φ, b_bar, s=1):\n",
    "\n",
    "    c0, b0 = unknowns\n",
    "\n",
    "    g0 = u.G[s-1]\n",
    "\n",
    "    R_0 = u.β * u.π[s] @ [u.Uc(c1, 1) / u.Uc(c0, 1), u.Uc(c2, 1) / u.Uc(c0, 1)]\n",
    "    R_0 = 1 / R_0\n",
    "\n",
    "    τ_0 = 1 + u.Un(1, c0 + g0) / u.Uc(c0, 1)\n",
    "\n",
    "    eq1 = τ_0 * (c0 + g0) + b_bar / R_0 - b0 - g0\n",
    "    eq2 = (1 + Φ) * (u.Uc(c0, 1)  + u.Un(1, c0 + g0)) + \\\n",
    "            Φ * (c0 * u.Ucc(c0, 1) + (c0 + g0) * u.Unn(1, c0 + g0)) - \\\n",
    "            Φ * u.Ucc(c0, 1) * b0\n",
    "\n",
    "    return np.array([eq1, eq2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To solve the equations for $ c_0, b_0 $, we use SciPy’s fsolve function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9344994030900681, -1.0386984075517638)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c0, b0 = fsolve(solve_cb, [1., -1.], args=(Φ_star, b[0], 1), xtol=1.0e-12)\n",
    "c0, b0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, we have reverse engineered an initial $ b0 = -1.038698407551764 $ that ought to render the AMSS measurability constraints slack"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Short simulation for reverse-engineered: initial debt\n",
    "\n",
    "The following graph shows simulations of outcomes for both a Lucas-Stokey economy and for an AMSS economy starting from initial government\n",
    "debt equal to $ b_0 = -1.038698407551764 $\n",
    "\n",
    "These graphs report outcomes for both the Lucas-Stokey economy with complete markets and the AMSS economy with one-period risk-free debt only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hide-output": false
   },
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      "/home/quantecon/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:231: RuntimeWarning: invalid value encountered in true_divide\n",
      "/home/quantecon/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:231: RuntimeWarning: invalid value encountered in multiply\n"
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\n",
      "text/plain": [
       "<Figure size 1008x720 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "μ_grid = np.linspace(-0.09, 0.1, 100)\n",
    "\n",
    "log_example = CRRAutility()\n",
    "\n",
    "log_example.transfers = True                        # Government can use transfers\n",
    "log_sequential = SequentialAllocation(log_example)  # Solve sequential problem\n",
    "log_bellman = RecursiveAllocationAMSS(log_example, μ_grid, tol_diff=1e-10, tol=1e-12)\n",
    "\n",
    "T = 20\n",
    "sHist = np.array([0, 0, 0, 0, 0, 0, 0, 0, 1, 1,\n",
    "                  0, 0, 0, 1, 1, 1, 1, 1, 1, 0])\n",
    "\n",
    "\n",
    "sim_seq = log_sequential.simulate(-1.03869841, 0, T, sHist)\n",
    "sim_bel = log_bellman.simulate(-1.03869841, 0, T, sHist)\n",
    "\n",
    "titles = ['Consumption', 'Labor Supply', 'Government Debt',\n",
    "          'Tax Rate', 'Government Spending', 'Output']\n",
    "\n",
    "# Government spending paths\n",
    "sim_seq[4] = log_example.G[sHist]\n",
    "sim_bel[4] = log_example.G[sHist]\n",
    "\n",
    "# Output paths\n",
    "sim_seq[5] = log_example.Θ[sHist] * sim_seq[1]\n",
    "sim_bel[5] = log_example.Θ[sHist] * sim_bel[1]\n",
    "\n",
    "fig, axes = plt.subplots(3, 2, figsize=(14, 10))\n",
    "\n",
    "for ax, title, seq, bel in zip(axes.flatten(), titles, sim_seq, sim_bel):\n",
    "    ax.plot(seq, '-ok', bel, '-^b')\n",
    "    ax.set(title=title)\n",
    "    ax.grid()\n",
    "\n",
    "axes[0, 0].legend(('Complete Markets', 'Incomplete Markets'))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Ramsey allocations and Ramsey outcomes are **identical** for the Lucas-Stokey and AMSS economies\n",
    "\n",
    "This outcome confirms the success of our reverse-engineering exercises\n",
    "\n",
    "Notice how for $ t \\geq 1 $, the tax rate is a constant - so is the par value of government debt\n",
    "\n",
    "However, output and labor supply are both nontrivial time-invariant functions of the Markov state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Long simulation\n",
    "\n",
    "The following graph shows the par value of government debt and the flat rate tax on labor income  for a long simulation for our sample economy\n",
    "\n",
    "For the **same** realization of a government expenditure path, the graph reports outcomes for two economies\n",
    "\n",
    "- the gray lines are for the Lucas-Stokey economy with complete markets  \n",
    "- the blue lines are for the AMSS economy with risk-free one-period debt only  \n",
    "\n",
    "\n",
    "For both economies, initial government debt due at time $ 0 $ is $ b_0 = .5 $\n",
    "\n",
    "For the Lucas-Stokey complete markets economy, the government debt plotted is $ b_{t+1}(s_{t+1}) $\n",
    "\n",
    "- Notice that this is a time-invariant function of the Markov state from the beginning  \n",
    "\n",
    "\n",
    "For the AMSS incomplete markets economy, the government debt plotted is $ b_{t+1}(s^t) $\n",
    "\n",
    "- Notice that this is a martingale-like random process that eventually seems to converge to a constant $ \\bar b \\approx - 1.07 $  \n",
    "- Notice that the limiting value $ \\bar b < 0 $ so that asymptotically the government makes a constant level of risk-free loans to the public  \n",
    "- In the simulation displayed as well as  other simulations we have run, the par value of government debt converges to about $ 1.07 $ afters between 1400 to 2000 periods  \n",
    "\n",
    "\n",
    "For the AMSS incomplete markets economy, the marginal tax rate on labor income  $ \\tau_t $ converges to a constant\n",
    "\n",
    "- labor supply and output each converge to time-invariant functions of the Markov state  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = 2000  # Set T to 200 periods\n",
    "\n",
    "sim_seq_long = log_sequential.simulate(0.5, 0, T)\n",
    "sHist_long = sim_seq_long[-3]\n",
    "sim_bel_long = log_bellman.simulate(0.5, 0, T, sHist_long)\n",
    "\n",
    "titles = ['Government Debt', 'Tax Rate']\n",
    "\n",
    "fig, axes = plt.subplots(2, 1, figsize=(14, 10))\n",
    "\n",
    "for ax, title, id in zip(axes.flatten(), titles, [2, 3]):\n",
    "    ax.plot(sim_seq_long[id], '-k', sim_bel_long[id], '-.b', alpha=0.5)\n",
    "    ax.set(title=title)\n",
    "    ax.grid()\n",
    "\n",
    "axes[0].legend(('Complete Markets', 'Incomplete Markets'))\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Remarks about long simulation\n",
    "\n",
    "As remarked above, after $ b_{t+1}(s^t) $ has converged to a constant, the measurablility constraints in the AMSS model cease to bind\n",
    "\n",
    "- the associated Lagrange multipliers on those implementability constraints converge to zero  \n",
    "\n",
    "\n",
    "This leads us to seek an initial value of government debt $ b_0 $ that renders the measurability constraints slack from time $ t=0 $ onward\n",
    "\n",
    "- a tell-tale sign of this situation is that the Ramsey planner in a corresponding Lucas-Stokey economy would instruct the government to issue a\n",
    "  constant level of government debt $ b_{t+1}(s_{t+1}) $ across the two Markov states  \n",
    "\n",
    "\n",
    "We  now describe how to find such an initial level of government debt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BEGS approximations of  limiting debt and convergence rate\n",
    "\n",
    "It is useful to link the outcome of our reverse engineering exercise to limiting approximations constructed by [[BEGS17]](https://lectures.quantecon.org/py/zreferences.html#begs1)\n",
    "\n",
    "[[BEGS17]](https://lectures.quantecon.org/py/zreferences.html#begs1) used a slightly different notation to represent a generalization of the AMSS model\n",
    "\n",
    "We’ll introduce a version of their notation so that readers can quickly relate notation that appears in their key formulas to the notation\n",
    "that we have used\n",
    "\n",
    "BEGS work with objects $ B_t, {\\mathcal B}_t, {\\mathcal R}_t, {\\mathcal X}_t $ that are related to our notation by\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "{\\mathcal R}_t & = \\frac{u_{c,t}}{u_{c,t-1}} R_{t-1}  = \\frac{u_{c,t}}{ \\beta E_{t-1} u_{c,t}} \\\\\n",
    "B_t & = \\frac{b_{t+1}(s^t)}{R_t(s^t)} \\\\\n",
    "b_t(s^{t-1}) & = {\\mathcal R}_{t-1} B_{t-1} \\\\\n",
    "{\\mathcal B}_t & = u_{c,t} B_t = (\\beta E_t u_{c,t+1}) b_{t+1}(s^t) \\\\\n",
    "{\\mathcal X}_t & = u_{c,t} [g_t - \\tau_t n_t]\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "In terms of their notation, equation (44) of [[BEGS17]](https://lectures.quantecon.org/py/zreferences.html#begs1) expresses the time $ t $ state $ s $ government budget constraint as\n",
    "\n",
    "\n",
    "<a id='equation-eq-fiscal-risk'></a>\n",
    "$$\n",
    "{\\mathcal B}(s) = {\\mathcal R}_\\tau(s, s_{-}) {\\mathcal B}_{-} + {\\mathcal X}_{\\tau(s)} (s) \\tag{8}\n",
    "$$\n",
    "\n",
    "where the dependence on $ \\tau $ is to remind us that these objects depend on the tax rate and $ s_{-} $ is last period’s Markov state\n",
    "\n",
    "BEGS interpret random variations in the right side of [(8)](#equation-eq-fiscal-risk) as a measure of **fiscal risk** composed of\n",
    "\n",
    "- interest-rate-driven fluctuations in time $ t $ effective payments due on the government portfolio, namely,\n",
    "  $ {\\mathcal R}_\\tau(s, s_{-}) {\\mathcal B}_{-} $,  and  \n",
    "- fluctuations in the effective government deficit $ {\\mathcal X}_t $  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Asymptotic mean\n",
    "\n",
    "BEGS give conditions under which the ergodic mean of $ {\\mathcal B}_t $ is\n",
    "\n",
    "\n",
    "<a id='equation-prelim-formula'></a>\n",
    "$$\n",
    "{\\mathcal B}^* = - \\frac{\\rm cov^{\\infty}(\\mathcal R, \\mathcal X)}{\\rm var^{\\infty}(\\mathcal R)} \\tag{9}\n",
    "$$\n",
    "\n",
    "where the superscript $ \\infty $ denotes a moment taken with respect to an ergodic distribution\n",
    "\n",
    "Formula [(9)](#equation-prelim-formula) presents $ {\\mathcal B}^* $ as a regression coefficient of $ {\\mathcal X}_t $ on $ {\\mathcal R}_t $ in the ergodic\n",
    "distribution\n",
    "\n",
    "This regression coefficient emerges as the minimizer for a variance-minimization problem:\n",
    "\n",
    "\n",
    "<a id='equation-eq-criterion-fiscal'></a>\n",
    "$$\n",
    "{\\mathcal B}^* = {\\rm argmin}_{\\mathcal B}  {\\rm var} ({\\mathcal R} {\\mathcal B} + {\\mathcal X}) \\tag{10}\n",
    "$$\n",
    "\n",
    "The minimand in criterion [(10)](#equation-eq-criterion-fiscal) is the  measure of fiscal risk associated with a given tax-debt policy that appears on the right side\n",
    "of equation [(8)](#equation-eq-fiscal-risk)\n",
    "\n",
    "Expressing formula [(9)](#equation-prelim-formula) in terms of  our notation tells us that $ \\bar b $ should approximately equal\n",
    "\n",
    "\n",
    "<a id='equation-key-formula'></a>\n",
    "$$\n",
    "\\hat b = \\frac{\\mathcal B^*}{\\beta E_t u_{c,t+1}} \\tag{11}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rate of convergence\n",
    "\n",
    "BEGS also derive the following  approximation to the rate of convergence to $ {\\mathcal B}^{*} $ from an arbitrary initial condition\n",
    "\n",
    "> \n",
    "<a id='equation-rate-of-convergence'></a>\n",
    "$$\n",
    "\\frac{ E_t  ( {\\mathcal B}_{t+1} - {\\mathcal B}^{*} )} { ( {\\mathcal B}_{t} - {\\mathcal B}^{*} )} \\approx \\frac{1}{1 + \\beta^2 {\\rm var} ({\\mathcal R} )} \\tag{12}\n",
    "$$\n",
    "\n",
    "\n",
    "(See the equation above equation (47) in [[BEGS17]](https://lectures.quantecon.org/py/zreferences.html#begs1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Formulas and code details\n",
    "\n",
    "For our example, we describe some code that we use to compute the steady state mean and the rate of convergence to it\n",
    "\n",
    "The  values of $ \\pi(s) $ are .5, .5\n",
    "\n",
    "We can then construct $ {\\mathcal X}(s), {\\mathcal R}(s), u_c(s) $ for our two states using  the definitions above\n",
    "\n",
    "We can then construct $ \\beta E_{t-1} u_c = \\beta \\sum_s u_c(s) \\pi(s) $, $ {\\rm cov}({\\mathcal R}(s), \\mathcal{X}(s)) $ and\n",
    "$ {\\rm var}({\\mathcal R}(s)) $ to be plugged into formula [(11)](#equation-key-formula)\n",
    "\n",
    "We also want to  compute $ {\\rm var}({\\mathcal X}) $\n",
    "\n",
    "To compute the variances and covariance, we use the following standard formulas\n",
    "\n",
    "Temporarily let $ x(s), s =1,2 $ be an arbitrary random variables\n",
    "\n",
    "Then we define\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mu_x & = \\sum_s x(s) \\pi(s) \\\\\n",
    "{\\rm var}(x) &= \\left(\\sum_s \\sum_s x(s)^2 \\pi(s) \\right) - \\mu_x^2 \\\\\n",
    "{\\rm cov}(x,y)  & = \\left(\\sum_s x(s) y(s) \\pi(s) \\right) - \\mu_x \\mu_y\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "After we compute these moments, we  compute the BEGS approximation to the asymptotic mean $ \\hat b $ in formula [(11)](#equation-key-formula)\n",
    "\n",
    "After that, we move on to compute $ {\\mathcal B}^* $ in formula [(9)](#equation-prelim-formula)\n",
    "\n",
    "We’ll also evaluate  the BEGS criterion [(8)](#equation-eq-fiscal-risk) at the limiting value $ {\\mathcal B}^* $\n",
    "\n",
    "\n",
    "<a id='equation-eqn-jcriterion'></a>\n",
    "$$\n",
    "J ( {\\mathcal B}^*)=  {\\rm var}(\\mathcal{R}) \\left( {\\mathcal B}^* \\right)^2 + 2 {\\mathcal B}^* {\\rm cov}(\\mathcal{R},\\mathcal{X}) + {\\rm var}(\\mathcal X) \\tag{13}\n",
    "$$\n",
    "\n",
    "Here are some functions that we’ll use to compute key objects that we want"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "def mean(x):\n",
    "    '''Returns mean for x given initial state'''\n",
    "    x = np.array(x)\n",
    "    return x @ u.π[s]\n",
    "\n",
    "def variance(x):\n",
    "    x = np.array(x)\n",
    "    return x**2 @ u.π[s] - mean(x)**2\n",
    "\n",
    "def covariance(x, y):\n",
    "    x, y = np.array(x), np.array(y)\n",
    "    return x * y @ u.π[s] - mean(x) * mean(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let’s form the two random variables $ {\\mathcal R}, {\\mathcal X} $ appearing in the BEGS approximating formulas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R, X = [1.055169547122964, 1.1670526750992583], [0.06357685646224803, 0.19251010100512958]\n"
     ]
    }
   ],
   "source": [
    "u = CRRAutility()\n",
    "\n",
    "s = 0\n",
    "c = [0.940580824225584, 0.8943592757759343]  # Vector for c\n",
    "g = u.G       # Vector for g\n",
    "n = c + g     # Total population\n",
    "τ = lambda s: 1 + u.Un(1, n[s]) / u.Uc(c[s], 1)\n",
    "\n",
    "R_s = lambda s: u.Uc(c[s], n[s]) / (u.β * (u.Uc(c[0], n[0]) * u.π[0, 0] + \\\n",
    "                u.Uc(c[1], n[1]) * u.π[1, 0]))\n",
    "X_s = lambda s: u.Uc(c[s], n[s]) * (g[s] - τ(s) * n[s])\n",
    "\n",
    "R = [R_s(0), R_s(1)]\n",
    "X = [X_s(0), X_s(1)]\n",
    "\n",
    "print(f\"R, X = {R}, {X}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let’s compute the ingredient of the approximating limit and the approximating rate of convergence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0757585378303758"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bstar = -covariance(R, X) / variance(R)\n",
    "div = u.β * (u.Uc(c[0], n[0]) * u.π[s, 0] + u.Uc(c[1], n[1]) * u.π[s, 1])\n",
    "bhat = bstar / div\n",
    "bhat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print out $ \\hat b $ and $ \\bar b $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.0757585378303758, -1.0757576567504166)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bhat, b_bar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we have"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-8.810799592140484e-07"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bhat - b_bar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These outcomes show that $ \\hat b $ does a remarkably good job of approximating $ \\bar b $\n",
    "\n",
    "Next, let’s compute the BEGS fiscal criterion that $ \\hat b $ is minimizing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-9.020562075079397e-17"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Jmin = variance(R) * bstar**2 + 2 * bstar * covariance(R, X) + variance(X)\n",
    "Jmin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is *machine zero*, a verification that $ \\hat b $ succeeds in minimizing the nonnegative fiscal cost criterion $ J ( {\\mathcal B}^*) $ defined in\n",
    "BEGS and in equation [(13)](#equation-eqn-jcriterion) above\n",
    "\n",
    "Let’s push our luck and compute the mean reversion speed in the formula above equation (47) in [[BEGS17]](https://lectures.quantecon.org/py/zreferences.html#begs1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean reversion speed = 0.9974715478249827\n"
     ]
    }
   ],
   "source": [
    "den2 = 1 + (u.β**2) * variance(R)\n",
    "speedrever = 1/den2\n",
    "print(f'Mean reversion speed = {speedrever}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let’s compute the implied mean time to get to within .01 of the limit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time to get within .01 of limit = 1819.0360880098472\n"
     ]
    }
   ],
   "source": [
    "ttime = np.log(.01) / np.log(speedrever)\n",
    "print(f\"Time to get within .01 of limit = {ttime}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The slow rate of convergence and the implied time of getting within one percent of the limiting value do a good job of approximating\n",
    "our long simulation above"
   ]
  }
 ],
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