"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Default Risk and Income Fluctuations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Contents\n",
"\n",
"- [Default Risk and Income Fluctuations](#Default-Risk-and-Income-Fluctuations) \n",
" - [Overview](#Overview) \n",
" - [Structure](#Structure) \n",
" - [Equilibrium](#Equilibrium) \n",
" - [Computation](#Computation) \n",
" - [Results](#Results) \n",
" - [Exercises](#Exercises) \n",
" - [Solutions](#Solutions) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Overview\n",
"\n",
"This lecture computes versions of Arellano’s [[Are08]](../zreferences.html#arellano2008default) model of sovereign default.\n",
"\n",
"The model describes interactions among default risk, output, and an equilibrium interest rate that includes a premium for endogenous default risk.\n",
"\n",
"The decision maker is a government of a small open economy that borrows from risk-neutral foreign creditors.\n",
"\n",
"The foreign lenders must be compensated for default risk.\n",
"\n",
"The government borrows and lends abroad in order to smooth the consumption of its citizens.\n",
"\n",
"The government repays its debt only if it wants to, but declining to pay has adverse consequences.\n",
"\n",
"The interest rate on government debt adjusts in response to the state-dependent default probability chosen by government.\n",
"\n",
"The model yields outcomes that help interpret sovereign default experiences, including\n",
"\n",
"- countercyclical interest rates on sovereign debt \n",
"- countercyclical trade balances \n",
"- high volatility of consumption relative to output \n",
"\n",
"\n",
"Notably, long recessions caused by bad draws in the income process increase the government’s incentive to default.\n",
"\n",
"This can lead to\n",
"\n",
"- spikes in interest rates \n",
"- temporary losses of access to international credit markets \n",
"- large drops in output, consumption, and welfare \n",
"- large capital outflows during recessions \n",
"\n",
"\n",
"Such dynamics are consistent with experiences of many countries."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Structure\n",
"\n",
"In this section we describe the main features of the model."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Output, Consumption and Debt\n",
"\n",
"A small open economy is endowed with an exogenous stochastically fluctuating potential output stream $ \\{y_t\\} $.\n",
"\n",
"Potential output is realized only in periods in which the government honors its sovereign debt.\n",
"\n",
"The output good can be traded or consumed.\n",
"\n",
"The sequence $ \\{y_t\\} $ is described by a Markov process with stochastic density kernel $ p(y, y') $.\n",
"\n",
"Households within the country are identical and rank stochastic consumption streams according to\n",
"\n",
"\n",
"\n",
"$$\n",
"\\mathbb E \\sum_{t=0}^{\\infty} \\beta^t u(c_t) \\tag{1}\n",
"$$\n",
"\n",
"Here\n",
"\n",
"- $ 0 < \\beta < 1 $ is a time discount factor. \n",
"- $ u $ is an increasing and strictly concave utility function. \n",
"\n",
"\n",
"Consumption sequences enjoyed by households are affected by the government’s decision to borrow or lend internationally.\n",
"\n",
"The government is benevolent in the sense that its aim is to maximize [(1)](#equation-utility).\n",
"\n",
"The government is the only domestic actor with access to foreign credit.\n",
"\n",
"Because household are averse to consumption fluctuations, the government will try to smooth consumption by borrowing from (and lending to) foreign creditors."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Asset Markets\n",
"\n",
"The only credit instrument available to the government is a one-period bond traded in international credit markets.\n",
"\n",
"The bond market has the following features\n",
"\n",
"- The bond matures in one period and is not state contingent. \n",
"- A purchase of a bond with face value $ B' $ is a claim to $ B' $ units of the\n",
" consumption good next period. \n",
"- To purchase $ B' $ next period costs $ q B' $ now, or, what is equivalent. \n",
"- For selling $ -B' $ units of next period goods the seller earns $ - q B' $ of today’s goods \n",
" \n",
" - if $ B' < 0 $, then $ -q B' $ units of the good are received in the current period, for a promise to repay $ -B' $ units next period \n",
" - there is an equilibrium price function $ q(B', y) $ that makes $ q $ depend on both $ B' $ and $ y $ \n",
" \n",
"\n",
"\n",
"Earnings on the government portfolio are distributed (or, if negative, taxed) lump sum to households.\n",
"\n",
"When the government is not excluded from financial markets, the one-period national budget constraint is\n",
"\n",
"\n",
"\n",
"$$\n",
"c = y + B - q(B', y) B' \\tag{2}\n",
"$$\n",
"\n",
"Here and below, a prime denotes a next period value or a claim maturing next period.\n",
"\n",
"To rule out Ponzi schemes, we also require that $ B \\geq -Z $ in every period.\n",
"\n",
"- $ Z $ is chosen to be sufficiently large that the constraint never binds in equilibrium. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Financial Markets\n",
"\n",
"Foreign creditors\n",
"\n",
"- are risk neutral \n",
"- know the domestic output stochastic process $ \\{y_t\\} $ and observe $ y_t, y_{t-1}, \\ldots, $ at time $ t $ \n",
"- can borrow or lend without limit in an international credit market at a constant international interest rate $ r $ \n",
"- receive full payment if the government chooses to pay \n",
"- receive zero if the government defaults on its one-period debt due \n",
"\n",
"\n",
"When a government is expected to default next period with probability $ \\delta $, the expected value of a promise to pay one unit of consumption next period is $ 1 - \\delta $.\n",
"\n",
"Therefore, the discounted expected value of a promise to pay $ B $ next period is\n",
"\n",
"\n",
"\n",
"$$\n",
"q = \\frac{1 - \\delta}{1 + r} \\tag{3}\n",
"$$\n",
"\n",
"Next we turn to how the government in effect chooses the default probability $ \\delta $."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Government’s decisions\n",
"\n",
"At each point in time $ t $, the government chooses between\n",
"\n",
"1. defaulting \n",
"1. meeting its current obligations and purchasing or selling an optimal quantity of one-period sovereign debt \n",
"\n",
"\n",
"Defaulting means declining to repay all of its current obligations.\n",
"\n",
"If the government defaults in the current period, then consumption equals current output.\n",
"\n",
"But a sovereign default has two consequences:\n",
"\n",
"1. Output immediately falls from $ y $ to $ h(y) $, where $ 0 \\leq h(y) \\leq y $ \n",
" \n",
" - it returns to $ y $ only after the country regains access to international credit markets. \n",
" \n",
"1. The country loses access to foreign credit markets. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Reentering international credit market\n",
"\n",
"While in a state of default, the economy regains access to\n",
"foreign credit in each subsequent period with probability\n",
"$ \\theta $."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Equilibrium\n",
"\n",
"Informally, an equilibrium is a sequence of interest rates on its sovereign debt, a stochastic sequence of government default decisions and an implied flow of household consumption such that\n",
"\n",
"1. Consumption and assets satisfy the national budget constraint. \n",
"1. The government maximizes household utility taking into account \n",
" - the resource constraint \n",
" - the effect of its choices on the price of bonds \n",
" - consequences of defaulting now for future net output and future borrowing and lending opportunities \n",
"1. The interest rate on the government’s debt includes a risk-premium sufficient to make foreign creditors expect on average to earn the constant risk-free international interest rate. \n",
"\n",
"\n",
"To express these ideas more precisely, consider first the choices of the\n",
"government, which\n",
"\n",
"1. enters a period with initial assets $ B $, or what is the same thing, initial debt to be repaid now of $ -B $ \n",
"1. observes current output $ y $, and \n",
"1. chooses either \n",
" \n",
" 1. to default, or \n",
" 1. to pay $ -B $ and set next period’s debt due to $ -B' $ \n",
" \n",
"\n",
"\n",
"In a recursive formulation,\n",
"\n",
"- state variables for the government comprise the pair $ (B, y) $ \n",
"- $ v(B, y) $ is the optimum value of the government’s problem when at the beginning of a period it faces the choice of whether to honor or default \n",
"- $ v_c(B, y) $ is the value of choosing to pay obligations falling due \n",
"- $ v_d(y) $ is the value of choosing to default \n",
"\n",
"\n",
"$ v_d(y) $ does not depend on $ B $ because, when access to credit is eventually regained, net foreign assets equal $ 0 $.\n",
"\n",
"Expressed recursively, the value of defaulting is\n",
"\n",
"$$\n",
"v_d(y) = u(h(y)) +\n",
" \\beta \\int \\left\\{\n",
" \\theta v(0, y') + (1 - \\theta) v_d(y')\n",
" \\right\\}\n",
" p(y, y') dy'\n",
"$$\n",
"\n",
"The value of paying is\n",
"\n",
"$$\n",
"v_c(B, y) = \\max_{B' \\geq -Z}\n",
" \\left\\{\n",
" u(y - q(B', y) B' + B) +\n",
" \\beta \\int v(B', y') p(y, y') dy'\n",
" \\right\\}\n",
"$$\n",
"\n",
"The three value functions are linked by\n",
"\n",
"$$\n",
"v(B, y) = \\max\\{ v_c(B, y), v_d(y) \\}\n",
"$$\n",
"\n",
"The government chooses to default when\n",
"\n",
"$$\n",
"v_c(B, y) < v_d(y)\n",
"$$\n",
"\n",
"and hence given $ B' $ the probability of default next period is\n",
"\n",
"\n",
"\n",
"$$\n",
"\\delta(B', y) := \\int \\mathbb 1\\{v_c(B', y') < v_d(y') \\} p(y, y') dy' \\tag{4}\n",
"$$\n",
"\n",
"Given zero profits for foreign creditors in equilibrium, we can combine [(3)](#equation-epc) and [(4)](#equation-delta) to pin down\n",
"the bond price function:\n",
"\n",
"\n",
"\n",
"$$\n",
"q(B', y) = \\frac{1 - \\delta(B', y)}{1 + r} \\tag{5}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Definition of equilibrium\n",
"\n",
"An *equilibrium* is\n",
"\n",
"- a pricing function $ q(B',y) $, \n",
"- a triple of value functions $ (v_c(B, y), v_d(y), v(B,y)) $, \n",
"- a decision rule telling the government when to default and when to pay as a function of the state $ (B, y) $, and \n",
"- an asset accumulation rule that, conditional on choosing not to default, maps $ (B,y) $ into $ B' $ \n",
"\n",
"\n",
"such that\n",
"\n",
"- The three Bellman equations for $ (v_c(B, y), v_d(y), v(B,y)) $ are satisfied. \n",
"- Given the price function $ q(B',y) $, the default decision rule and the asset accumulation decision rule attain the optimal value function $ v(B,y) $, and \n",
"- The price function $ q(B',y) $ satisfies equation [(5)](#equation-bondprice). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Computation\n",
"\n",
"Let’s now compute an equilibrium of Arellano’s model.\n",
"\n",
"The equilibrium objects are the value function $ v(B, y) $, the associated default decision rule, and the pricing function $ q(B', y) $.\n",
"\n",
"We’ll use our code to replicate Arellano’s results.\n",
"\n",
"After that we’ll perform some additional simulations.\n",
"\n",
"It uses a slightly modified version of the algorithm recommended by Arellano.\n",
"\n",
"- The appendix to [[Are08]](../zreferences.html#arellano2008default) recommends\n",
" value function iteration until convergence, updating the price, and then repeating. \n",
"- Instead, we update the bond price at every value function iteration step. \n",
"\n",
"\n",
"The second approach is faster and the two different procedures deliver very similar results.\n",
"\n",
"Here is a more detailed description of our algorithm:\n",
"\n",
"1. Guess a value function $ v(B, y) $ and price function $ q(B', y) $. \n",
"1. At each pair $ (B, y) $, \n",
" - update the value of defaulting $ v_d(y) $ \n",
" - update the value of continuing $ v_c(B, y) $ \n",
"1. Update the value function v(B, y), the default rule, the implied ex ante default probability, and the price function. \n",
"1. Check for convergence. If converged, stop. If not, go to step 2. \n",
"\n",
"\n",
"We use simple discretization on a grid of asset holdings and income levels.\n",
"\n",
"The output process is discretized using [Tauchen’s quadrature method](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/markov/markov_approx.jl).\n",
"\n",
"The code can be found below:\n",
"\n",
"(Results and discussion follow the code)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Setup"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"hide-output": true
},
"outputs": [],
"source": [
"using InstantiateFromURL\n",
"# optionally add arguments to force installation: instantiate = true, precompile = true\n",
"github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.8.0\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"hide-output": true
},
"outputs": [],
"source": [
"using LinearAlgebra, Statistics\n",
"using Parameters, QuantEcon, DataFrames, Plots, Random"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"hide-output": false
},
"outputs": [],
"source": [
"function ArellanoEconomy(;β = .953,\n",
" γ = 2.,\n",
" r = 0.017,\n",
" ρ = 0.945,\n",
" η = 0.025,\n",
" θ = 0.282,\n",
" ny = 21,\n",
" nB = 251)\n",
"\n",
" # create grids\n",
" Bgrid = collect(range(-.4, .4, length = nB))\n",
" mc = tauchen(ny, ρ, η)\n",
" Π = mc.p\n",
" ygrid = exp.(mc.state_values)\n",
" ydefgrid = min.(.969 * mean(ygrid), ygrid)\n",
"\n",
" # define value functions\n",
" # notice ordered different than Python to take\n",
" # advantage of column major layout of Julia)\n",
" vf = zeros(nB, ny)\n",
" vd = zeros(1, ny)\n",
" vc = zeros(nB, ny)\n",
" policy = zeros(nB, ny)\n",
" q = ones(nB, ny) .* (1 / (1 + r))\n",
" defprob = zeros(nB, ny)\n",
"\n",
" return (β = β, γ = γ, r = r, ρ = ρ, η = η, θ = θ, ny = ny,\n",
" nB = nB, ygrid = ygrid, ydefgrid = ydefgrid,\n",
" Bgrid = Bgrid, Π = Π, vf = vf, vd = vd, vc = vc,\n",
" policy = policy, q = q, defprob = defprob)\n",
"end\n",
"\n",
"u(ae, c) = c^(1 - ae.γ) / (1 - ae.γ)\n",
"\n",
"function one_step_update!(ae,\n",
" EV,\n",
" EVd,\n",
" EVc)\n",
"\n",
" # unpack stuff\n",
" @unpack β, γ, r, ρ, η, θ, ny, nB = ae\n",
" @unpack ygrid, ydefgrid, Bgrid, Π, vf, vd, vc, policy, q, defprob = ae\n",
" zero_ind = searchsortedfirst(Bgrid, 0.)\n",
"\n",
" for iy in 1:ny\n",
" y = ae.ygrid[iy]\n",
" ydef = ae.ydefgrid[iy]\n",
"\n",
" # value of being in default with income y\n",
" defval = u(ae, ydef) + β * (θ * EVc[zero_ind, iy] + (1-θ) * EVd[1, iy])\n",
" ae.vd[1, iy] = defval\n",
"\n",
" for ib in 1:nB\n",
" B = ae.Bgrid[ib]\n",
"\n",
" current_max = -1e14\n",
" pol_ind = 0\n",
" for ib_next=1:nB\n",
" c = max(y - ae.q[ib_next, iy]*Bgrid[ib_next] + B, 1e-14)\n",
" m = u(ae, c) + β * EV[ib_next, iy]\n",
"\n",
" if m > current_max\n",
" current_max = m\n",
" pol_ind = ib_next\n",
" end\n",
"\n",
" end\n",
"\n",
" # update value and policy functions\n",
" ae.vc[ib, iy] = current_max\n",
" ae.policy[ib, iy] = pol_ind\n",
" ae.vf[ib, iy] = defval > current_max ? defval : current_max\n",
" end\n",
" end\n",
"end\n",
"\n",
"function compute_prices!(ae)\n",
" # unpack parameters\n",
" @unpack β, γ, r, ρ, η, θ, ny, nB = ae\n",
"\n",
" # create default values with a matching size\n",
" vd_compat = repeat(ae.vd, nB)\n",
" default_states = vd_compat .> ae.vc\n",
"\n",
" # update default probabilities and prices\n",
" copyto!(ae.defprob, default_states * ae.Π')\n",
" copyto!(ae.q, (1 .- ae.defprob) / (1 + r))\n",
" return\n",
"end\n",
"\n",
"function vfi!(ae; tol = 1e-8, maxit = 10000)\n",
"\n",
" # unpack stuff\n",
" @unpack β, γ, r, ρ, η, θ, ny, nB = ae\n",
" @unpack ygrid, ydefgrid, Bgrid, Π, vf, vd, vc, policy, q, defprob = ae\n",
" Πt = Π'\n",
"\n",
" # Iteration stuff\n",
" it = 0\n",
" dist = 10.\n",
"\n",
" # allocate memory for update\n",
" V_upd = similar(ae.vf)\n",
"\n",
" while dist > tol && it < maxit\n",
" it += 1\n",
"\n",
" # compute expectations for this iterations\n",
" # (we need Π' because of order value function dimensions)\n",
" copyto!(V_upd, ae.vf)\n",
" EV = ae.vf * Πt\n",
" EVd = ae.vd * Πt\n",
" EVc = ae.vc * Πt\n",
"\n",
" # update value function\n",
" one_step_update!(ae, EV, EVd, EVc)\n",
"\n",
" # update prices\n",
" compute_prices!(ae)\n",
"\n",
" dist = maximum(abs(x - y) for (x, y) in zip(V_upd, ae.vf))\n",
"\n",
" if it % 25 == 0\n",
" println(\"Finished iteration $(it) with dist of $(dist)\")\n",
" end\n",
" end\n",
"end\n",
"\n",
"function QuantEcon.simulate(ae,\n",
" capT = 5000;\n",
" y_init = mean(ae.ygrid),\n",
" B_init = mean(ae.Bgrid),\n",
" )\n",
"\n",
" # get initial indices\n",
" zero_index = searchsortedfirst(ae.Bgrid, 0.)\n",
" y_init_ind = searchsortedfirst(ae.ygrid, y_init)\n",
" B_init_ind = searchsortedfirst(ae.Bgrid, B_init)\n",
"\n",
" # create a QE MarkovChain\n",
" mc = MarkovChain(ae.Π)\n",
" y_sim_indices = simulate(mc, capT + 1; init = y_init_ind)\n",
"\n",
" # allocate and fill output\n",
" y_sim_val = zeros(capT+1)\n",
" B_sim_val, q_sim_val = similar(y_sim_val), similar(y_sim_val)\n",
" B_sim_indices = fill(0, capT + 1)\n",
" default_status = fill(false, capT + 1)\n",
" B_sim_indices[1], default_status[1] = B_init_ind, false\n",
" y_sim_val[1], B_sim_val[1] = ae.ygrid[y_init_ind], ae.Bgrid[B_init_ind]\n",
"\n",
" for t in 1:capT\n",
" # get today's indexes\n",
" yi, Bi = y_sim_indices[t], B_sim_indices[t]\n",
" defstat = default_status[t]\n",
"\n",
" # if you are not in default\n",
" if !defstat\n",
" default_today = ae.vc[Bi, yi] < ae.vd[yi]\n",
"\n",
" if default_today\n",
" # default values\n",
" default_status[t] = true\n",
" default_status[t + 1] = true\n",
" y_sim_val[t] = ae.ydefgrid[y_sim_indices[t]]\n",
" B_sim_indices[t + 1] = zero_index\n",
" B_sim_val[t+1] = 0.\n",
" q_sim_val[t] = ae.q[zero_index, y_sim_indices[t]]\n",
" else\n",
" default_status[t] = false\n",
" y_sim_val[t] = ae.ygrid[y_sim_indices[t]]\n",
" B_sim_indices[t + 1] = ae.policy[Bi, yi]\n",
" B_sim_val[t + 1] = ae.Bgrid[B_sim_indices[t + 1]]\n",
" q_sim_val[t] = ae.q[B_sim_indices[t + 1], y_sim_indices[t]]\n",
" end\n",
"\n",
" # if you are in default\n",
" else\n",
" B_sim_indices[t + 1] = zero_index\n",
" B_sim_val[t+1] = 0.\n",
" y_sim_val[t] = ae.ydefgrid[y_sim_indices[t]]\n",
" q_sim_val[t] = ae.q[zero_index, y_sim_indices[t]]\n",
"\n",
" # with probability θ exit default status\n",
" default_status[t + 1] = rand() ≥ ae.θ\n",
" end\n",
" end\n",
"\n",
" return (y_sim_val[1:capT], B_sim_val[1:capT], q_sim_val[1:capT],\n",
" default_status[1:capT])\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Results\n",
"\n",
"Let’s start by trying to replicate the results obtained in [[Are08]](../zreferences.html#arellano2008default).\n",
"\n",
"In what follows, all results are computed using Arellano’s parameter values.\n",
"\n",
"The values can be seen in the function ArellanoEconomy shown above.\n",
"\n",
"- For example, r=0.017 matches the average quarterly rate on a 5 year US treasury\n",
" over the period 1983–2001. \n",
"\n",
"\n",
"Details on how to compute the figures are reported as solutions to the exercises.\n",
"\n",
"The first figure shows the bond price schedule and replicates Figure 3 of Arellano, where $ y_L $ and $ Y_H $ are particular below average and above average values of output $ y $\n",
"\n",
"\n",
"\n",
" \n",
"- $ y_L $ is 5% below the mean of the $ y $ grid values \n",
"- $ y_H $ is 5% above the mean of the $ y $ grid values \n",
"\n",
"\n",
"The grid used to compute this figure was relatively coarse (ny, nB = 21, 251) in order to match Arrelano’s findings.\n",
"\n",
"Here’s the same relationships computed on a finer grid (ny, nB = 51, 551)\n",
"\n",
"\n",
"\n",
" \n",
"In either case, the figure shows that\n",
"\n",
"- Higher levels of debt (larger $ -B' $) induce larger discounts on the face value, which correspond to higher interest rates. \n",
"- Lower income also causes more discounting, as foreign creditors anticipate greater likelihood of default. \n",
"\n",
"\n",
"The next figure plots value functions and replicates the right hand panel of Figure 4 of [[Are08]](../zreferences.html#arellano2008default)\n",
"\n",
"\n",
"\n",
" \n",
"We can use the results of the computation to study the default probability\n",
"$ \\delta(B', y) $ defined in [(4)](#equation-delta).\n",
"\n",
"The next plot shows these default probabilities over $ (B', y) $ as a heat\n",
"map\n",
"\n",
"\n",
"\n",
" \n",
"As anticipated, the probability that the government chooses to default in the\n",
"following period increases with indebtedness and falls with income.\n",
"\n",
"Next let’s run a time series simulation of $ \\{y_t\\} $, $ \\{B_t\\} $ and $ q(B_{t+1}, y_t) $.\n",
"\n",
"The grey vertical bars correspond to periods when the economy is excluded from financial markets because of a past default\n",
"\n",
"\n",
"\n",
" \n",
"One notable feature of the simulated data is the nonlinear response of interest rates.\n",
"\n",
"Periods of relative stability are followed by sharp spikes in the discount rate on government debt."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercises\n",
"\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exercise 1\n",
"\n",
"To the extent that you can, replicate the figures shown above\n",
"\n",
"- Use the parameter values listed as defaults in the function ArellanoEconomy. \n",
"- The time series will of course vary depending on the shock draws. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Solutions"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"hide-output": false
},
"outputs": [],
"source": [
"using DataFrames, Plots\n",
"gr(fmt=:png);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compute the value function, policy and equilibrium prices"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"hide-output": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 25 with dist of 0.3424484168091375\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 50 with dist of 0.09820394074288075\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 75 with dist of 0.02915866229151476\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 100 with dist of 0.008729266837651295\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 125 with dist of 0.002618400938121823\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 150 with dist of 0.0007857709211727126\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 175 with dist of 0.00023583246008485048\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 200 with dist of 7.078195654131036e-5\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 225 with dist of 2.1244388765495614e-5\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 250 with dist of 6.376267926100354e-6\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 275 with dist of 1.913766855210497e-6\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 300 with dist of 5.743961786208729e-7\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 325 with dist of 1.723987352875156e-7\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 350 with dist of 5.174360495630026e-8\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Finished iteration 375 with dist of 1.5530289942944364e-8\n"
]
}
],
"source": [
"ae = ArellanoEconomy(β = .953, # time discount rate\n",
" γ = 2., # risk aversion\n",
" r = 0.017, # international interest rate\n",
" ρ = .945, # persistence in output\n",
" η = 0.025, # st dev of output shock\n",
" θ = 0.282, # prob of regaining access\n",
" ny = 21, # number of points in y grid\n",
" nB = 251) # number of points in B grid\n",
"\n",
"# now solve the model on the grid.\n",
"vfi!(ae)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compute the bond price schedule as seen in figure 3 of Arellano (2008)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"hide-output": false
},
"outputs": [
{
"data": {
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"
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# create \"Y High\" and \"Y Low\" values as 5% devs from mean\n",
"high, low = 1.05 * mean(ae.ygrid), 0.95 * mean(ae.ygrid)\n",
"iy_high, iy_low = map(x -> searchsortedfirst(ae.ygrid, x), (high, low))\n",
"\n",
"# extract a suitable plot grid\n",
"x = zeros(0)\n",
"q_low = zeros(0)\n",
"q_high = zeros(0)\n",
"for i in 1:ae.nB\n",
" b = ae.Bgrid[i]\n",
" if -0.35 ≤ b ≤ 0 # to match fig 3 of Arellano\n",
" push!(x, b)\n",
" push!(q_low, ae.q[i, iy_low])\n",
" push!(q_high, ae.q[i, iy_high])\n",
" end\n",
"end\n",
"\n",
"# generate plot\n",
"plot(x, q_low, label = \"Low\")\n",
"plot!(x, q_high, label = \"High\")\n",
"plot!(title = \"Bond price schedule q(y, B')\",\n",
" xlabel = \"B'\", ylabel = \"q\", legend_title = \"y\", legend = :topleft)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Draw a plot of the value functions"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"hide-output": false
},
"outputs": [
{
"data": {
"image/png": 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EISGETJw4US6X67sKXfP39//666/1XQUAdDcsqyzPk2ckyjMT1TV3hJ6DxD5BZjNWcnqZ6buyZ4QgJISQ6OjoEydOCIVCfReiO2lpaceOHdN3FQDQbbAKWp6TIs9MlGfeoMRGYt+hptNWCFx99djtoaN0+w/QUUaOHCmRdOIQPl0NRVEIQgBok7rmrjwjQZ6ZqCzJFjh7i3yCjMfN41n11nddHQlBCAAAf8YwiuIseUaCIvemuu6eyDvQKPh5i2WbOnXATz1CEAIAACEtW76kJ3BNLUS+w0xnru52LV+eAYIQAMCg/T7mS0aCurJU6DlQ5BtkOv0VrrG5vuvSHQQhAIDBYVVKRd4tOiNBnpFI8Xgi36Emzy8Wug/oAS1fnoEhfmYAAMOkqa/RnvwpC27z+7qLfIKs13zGs3XQd116hiAEAOjRHprtSDIwxGLheo6kl74r6yoQhAAAPRCroOXZyfLMRDojkWtsJvIJMp22XOjsTTgcfZfW5SAIAQB6DvX9yt+7/RVnCZy9Rb5DjScs4Fna6buuLg1BCADQzf3R7U+ekcBIG0Q+Qd1owOuuAEGoByUlJRKJxNrauuXC8vJyHo9nZ4c/3ACgXRi5VJGVTGcmyDNvcM2sxT5B5vPXChz79fhufx0OQagHb775Znp6el5eHvXH/9eamhp3d/d//OMfH3zwgX5rA4AuTl1zV54RT2ckqEpzBa6+Yt9hplNe5ppZt/1OeAwEoR6sWbNm0qRJV65cGTNmjHbJnj17NBrN8uXL9VsYAHRRDKMozpRnJNDpCSzdKPIZ2itkhqhfACUwoKkCOg+CUA8mTJjg4eHx448/aoOQZdndu3dPnTq1T5+uO4MzAOje7xc/M+LlWUlcc2ux71CLhe8IHDxw8bNjIQj1gKKolStXbtq0qbq62traOioqKjc3d/v27fquCwC6BO2ED3RGvLIkR+jWX+w7zHTqcq6Zlb7r6rEQhPqxfPnyDz/88MCBA+vWrQsLC3N0dBw/fry+iwIA/WEYZUkWnZ4gz4hnZH9c/HxlECUQ6buyng9BqB+WlpZz5swJCwtbsmTJiRMnPvjgAy6Xq++iAEDXtN3e6YwEeUYC18xK7DPUfME6gYMnLn7qEoJQb9asWRMeHr58+XKGYdBMBsCgaOru0RkJ8vR4ZXGWwMVH5DvUdNJiroWNvusyUAhCvQkODg4ICPjll19mzZrVu3ePmu4ZAB6BZZXlefL0BDojXlNfI/IJMgqehG7vXQGCUJ8WLlyYkpKyatUqfRcCAJ2FVSkVuTfp9Hh5RgIl7iXuP8x89msCJ4z52YUgCPUpNjbWzc0NzWQAeh6mqV7b8kWRl8Z3cBf5DrUOncOzstd3XfAICEL9UKvVFy9ePHHixNdff83BH4YAPYWqskSeHk+nx6vvlYv6BYgHhpjPX4cJj7o4BKEeFBQUuLu7E0ImT56M66IA3R6jURfers9PlWfEE4YR9R9mOnmpwK2/Yc723h3h30kP+vbtm5SUZG5u7urqqu9aAOAZMXKZIiuJTo+TZydzzG2N/EdYLv+Qb++i77rgqek6CO/cucMwTJ8+fZrHm2ZZtqioyMTExMqqXeMmyOXy8vLy3r17GxkZdWalnUgoFA4ePPgJK+Tk5FRXV48cOVJnJQFAO2nq7tHp8fL0eGVJjsCtv7j/MONpK5R8cfc9IoHu7k5dvnzZyckpICBg+PDh/fr1S0pKIoSUlZUNGDDg+eef9/LyWrduXcv1t27dSrWQm5tLCPntt9+cnJxmzZrl6Oh49OhRnRWvYydPnvz888/1XQUA/IFlVeX5Deciqra8XvXl31Tl+UYjp/b++JDVyo+Mgp/nmljouz74S3QXhObm5idPnqysrCwpKZk9e/Yrr7xCCNm0adPw4cNzcnIyMzMPHTp0/fr1lm9ZunQp+wdPT0+GYVauXLlt27a0tLT//ve/r776qlQq1Vn9XUFaWtr58+fv3r1LCKFp+vbt29rld+/ezcrK0j4uKyvTrgAAfxGrVsmzk+uP7bj70eL74ZtZlcJs1mv2Hx82n/+22G84Zn7oMXQXhIMGDRo4cCAhhKKoSZMmlZaWqtXqY8eOrV69mhBiY2Mze/bsw4cPt3rXgwcPmh/HxsY2Nja+9NJLhJBRo0b16dPn7NmzOqtfvxiGeemllxYuXHjw4MGAgIDw8HCWZYcNG1ZXV0cIWbdu3dChQ1UqFSFk2bJlsbGx+q4XoBtjZE2y5Mv3939294P5jRcOcS3trF/fbLfhR9NpK4Suvuj/1/Pop7HM/v37J0+efO/ePZqmte0nCSHu7u4XL15suVpkZOTp06cVCsXKlSv/85//lJSUuLi4NI/J6e7uXlxc3GrLLMveunVLJPrfMLW9evXy9PR82gqvV7LnK5infdezCbHjTOjTxriCx44dS01NTU1NFYlEcXFxkyZNmj59emBg4LVr16ZPn379+vWBAwcmJSUNGjQoPj4+MjJSN5UD9CSa2nvy7CQ6I0FZkC5w6y/2HWo2czUuexqCzg1CmUymPaUTiUTm5ubahWFhYZcuXUpMTKyvryeEiMW/Dy8kkUgaGhqa3ztnzpxVq1YZGRnl5+dPmjSpb9++RkZGzStr129sbGy1R4ZhVq9e3bJnnr+//86dOx+ujWVZmUz2uMq5HCLg6GjQW2479hMXFzdt2jRtwAcHB5uYmGRkZISGhl66dMnNzc3Z2fmFF164dOmSTCbr169fO5sdMQzT1NT0F4tvP6lUSmEcYV2RyWQqlQojubeNZdV3CtXZN1RZN9imB7x+gwUBY4QvvknxBSwhNCGkHb8RhmHkcjnLsp1fLhDylAcTiUTSZl/tzg3C48ePf/LJJ4SQ8ePHa9MoPDz8448/joqKsrW1FQqFhJC6ujpra2tCSG1trZ2dXfN7+/btq33g7u6+Zs2aixcvvvrqq9orgVq1tbW2trat9sjlcuPj4yUSSZu1sSxLUVSvXo/u6BpsQwXbdKGjtkql0n5dWnw+X6VShYaGrlq1ys3NLTQ0NDQ09K233pLJZKGhoe3cJofDedzH7wwsy+pydwaOw+EIhUIE4eOwGrUiL1V+O47OiKeEYnH/YJN5bwmcvJ5tzgeGYbhcLlqN6kyHH0w6NwiXLFmyZMmS5qfHjx9/7733Ll686OHhQQgxMzNzdnZOSEiYOnUqISQ+Pn7IkCGP3E51dbWxsbG/v39ubm59fb2ZmZlarU5KSvrwww87tf6uY+DAgbt27dKGd15eXmVlpY+Pj5mZWVlZWURExNatWwcMGJCfn3///v0vvvhC38UCdFEM3STPSpLfjpPnJPNsncR+wdavb+ZZ99F3XaBnurtHeOnSpQULFmzYsCEzMzMzM5MQMmvWrL/97W/vv/++hYVFenr6lStXvv32W0JIYGDg1q1bo6OjfXx8bG1t4+Pjv/nmm59++snV1XXChAmrV69+55139u7d6+zsPHz4cJ3Vr2MpKSmzZ8/WPjY1Nf3uu+9+/PHHadOmDRs2bO/evf/4xz+0p9EhISHR0dFDhw6lKGrEiBE///xzSEiIXgsH6HI09TV0erz8dqyyJFvoPkDUP9hs9hpOLzN91wVdhe6CkGGYZcuWVVZWVlZWapfMmDHjrbfeYll2w4YNVlZW58+ft7e3J4QEBQWZmZmZmZnt3r27rq7O2dn5zJkzo0ePJoQcOHDgn//859q1a728vE6fPq2z4nVs1qxZ/fr1a34qFAqFQuH169d/+eWXioqKQ4cODR06VPvSv//976qqKj6fTwj55z//+fLLL+P6DICW6m4xfTtOfjtWXVsl8h1qNGKq5Yp/os8DPIzqYTd4JRJJTU1NO+8RSqVS7YXm9r+rx7h27dqmTZuuXbumsz02NjYaGxvrbHcGTiaTGeg9QoZRFGXIb8fRt+MIISK/YHH/4M7u88AwDE3T+BtUZzr8YIKxRgGg22NVSmVRBp0eT9+6xpEYi3yHmS98R+ji82yNX8DQIAgBoLtipA3yjAT6dpwi7xbf0VPsN9xm7XauuY2+64JuBkEIAN2MpvYefTuWTo9TleUL+wWI/Ueaz38bc/7BM0MQAkD3oLpTRN+OpW/Haurvi/sPNR49S+g5iOIL9F0XdHsIwq6osrKyoaGheWQ4hmGSkpIGDhz47bffhoaG+vn5tVr/zp0727dv37x5s84rBehkLKssz5dnJMhSrhC1StR/mNn0V4TuAwjH8NoBQadBEHZFBw4cuHr16pkzZ7RPZTLZ0KFDi4qKcnNzAwMDH16/trY2IiICQQg9BqtSKnJv0rdj6fR4rpm12G+45cv/wJy30EkQhN3Jli1bBAIBIUStVufk5PTp08fIyEgulzevUFBQwOPxnJyc9FcjwLNj5FJ55g06LUaRncLv6yb2G24yYSHXAo1foHMhCLuTSZMmvfPOO56ens8//7yDg0NjY6O3t/edO3d27Nih0WgWLFhQWlpaWFg4Y8aM7777Tt/FArQXI22QZybKbkUrC9L5jp5i36Fms17jmpjruy4wFAjCR1PdKVKW5uhmX3x7V4Fj64miUlJSXnzxRe1jjUbT8qW1a9euWLFi06ZNGo1m0qRJ2oVVVVWLFi2aPHlyTU2Ns7Pzxo0bHRwcdFA8wDNT19yl02LotBj1vXKR9xCjoPGWSzdQAlHb7wToUAjCR9M01CqLs3SzL47YiDwUhH369Fm0aJH2sVwuP3HihPYxy7LR0dHaQVm5XO68efPCw8MJIaamppMnTyaEWFlZubq6FhcXIwiha1KVF9C3Y+i0WEbaIPILNpm0SOjhT3FxLAK9wX++RxN5DRZ5DdZjAba2ti+88IL2catZA1tOydT8oOXwTjweTztbPUBXwbKKokw6LUaeFkM4XLH/CPO5bz7ztEcAHQtB2M1QFOXn53flypUFCxYQQqKiovRdEcBjsRq1IvcWfTtWfjuOY2IhHjDccuVH/N7O+q4L4E8QhN3P559/vnDhwpSUlKqqquzsbIxkDV0Nq1TIs27QabHyrBs8W0fxgOHWb23lWdq1/U4AfUAQdkXjxo3z9vZufioUCrdv325pafnmm2/6+fm5uLjExcVdu3Zt8uTJ2dnZcXFx9vb2LTsRbtq0ycvLSx+Fg0FjZE3yjAQ6LUaRd0vg5CX2H2k6YyUaf0LXh2mYut80TOXl5dXV1b6+vtnZ2XPmzPn000+b25e2H6Zh6tl0OQ2TpqFOnh5Hp8Uoi7OEngPFfiNEvkMNauRPTMOkY5iGCYhMJlu/fn1xcbGVldWbb77ZPJE9gC5pau/RadfptBhVZYnIe4hR8POWyz/EtLfQHSEIux9PT8/ffvtN31WAgVLfK6dTr9NpMeq6e+L+wcbj5wk9B6HzA3Rr+O8LAG1TVRTQaTF0agwjl4oHjDCdsVLo2r9Tp30H0BkEIQA8BssqS3LotOt0agyhiHjACPN5awVO/dD5D3oYBCEA/BnDKArTtYOfcUQSsf9Iy+Wb+H3c9F0WQGdBEAIAIdrO73mpdFoMnRbLNbOS+I+0XvM5zxYD9UHPhyAEMGisWqXIvUnfiqYzEnjW9uIBI23WbkPndzAoCEIAQ8SqlPLsJDr1ujwzkW/nLB4YYjJ5KdfMSt91AegBgvB3ly5dah7A2hDcvn1b3yWAHrBKuTzzBp16XZ6VxHfwEPuPNJ2OwV/A0CEICSHkk08++eabb/Rdha4FBQXpuwTQEVZB0xkJ9K1oRe5NgbO32H+k2ezXOL1M9V0XQJeAIdYMaCAo/cIQa7qkHWKNUtLy9AQ6NVqRnyZw7S8eGCLuH2xQg5/pBoZY0zEMsQYAbWBkTcqUq9KMeFVRhtDDXzzwOfNF6zkiHKYBHg1BCNBDMLJG+nYsfeu6siiD5+YnCRht9fJGSijWd10AXR2CEKB7Y2RN9O1Y+la0sihT2G+QJGic5csbaQ0rFAopncw+AdDdIQgBuiVG1kSnx9G3rikLM4X9AoyCxlsu+wclEP3+skym1+oAuhMEIUB38sf53zVlUUNdEN8AACAASURBVKawX4BkyDjLl1vkHwA8PQQhQDfw5+ufAUZBEyyXbUL+AXQIBCFA1/VQ/v35+icAdAQEIUCXw9BN8ttxst/v/w1C/gF0KgQhQFfByKXytFjZrWhlYYbQc6AkMBT3/wB0AEEIoGeMXCZPj5fdvKYsuC309JcEjrVcugH9/wB0BkEIoB+sSqnITZHdipZnJApcfCQDQywWv8sRtT06IAB0LAQhgE6xSoU8M1F285oiJ0Xg6isZ9JzZ7Ncw/hmAHiEIAXSBVavkWUn0zavyrCSBUz/xoOfM576J8a8BugIEIUAnYjVqRc5N2c2r8owEfh9XyaBRZrNf4xiZ6LsuAPgfBCFAJ2BZRVEmfeuaLOUqz9xaEhhqOm0518RC32UBwCMgCAE6jjb/Uq7Qqde55jbigFG273zDNbPWd1kA8CQIQoAOoCzLo29elaVc5YiNJAGjrd/6imfZW99FAUC7IAgBnp26ukKWHCVLjiIsKwkYZbX6U76do76LAoCngyAEeGqaB/dlN6/SyVc0D2rEg0ZZLH5X4NhP30UBwDNCEAK0FyOX0anXZUmXVRUFYr9g02nLhe4DCIej77oA4C9BEAK0gdWoFdlJ0qTLiuwUoceAXiOninyCKL5A33UBQMdAEAI8lrI4S5Z0SXYrmm/rKAkca/7S3zlidIEH6GkQhACtqe/flSVdliVdJhyuUeBY23XfcM1t9F0UAHQWBCHA7xi5lL4VLUv8TXWvXBIwymLJewIHT30XBQCdTtdBeOfOndraWjc3N7H4f7PMFBQUaDQaT88/HXRompbL5S2XmJmZSaVSlUqlfcrhcExNTXVQM/RsrEatyEmRJV2SZyULPQcZh74o9AqkuPgbEcBQ6O7XXl5eHhoa+uDBAxsbm7Kysq+++mrZsmVyuXzGjBm5ubl8Pt/Ozu7MmTPGxsba9bds2bJ161btY4VCQQh58ODB4sWLL1y4IBQKCSG2trZZWVk6qx96GpZVFmfKkqNkt6J51n2NAseavfg3jIINYIAolmV1s6fq6uqMjIzRo0cTQi5cuDB16tTKysrDhw+Hh4dHR0dzudyJEyeOHTt2w4YND793zZo1NE3v27dv5syZ06ZNW758+eP2IpFIampqJJK2J3VjWVYqlfbqhQOfjjQ2Njb/laNfqrvFsuQoOuUKJRBJBo8RB4zmWdrpu6gOJpPJhEIhl8vVdyEGgWEYmqaNjDCXlo50+MFEd2eE1tbW2hQkhISEhGg0mnv37h05cmTZsmV8Pp8QsmLFin//+98PByFN05GRkSdPntQ+VavVVVVVtra2OqscegZN7T1ZSpQsOYqRyyQBoyxX/JPfx1XfRQGA/unnRsjevXs9PT09PDxKSkpcXX8/GLm6upaUlDy88vHjxy0sLEJCQrRP33vvvQ8//FCpVH722WerV69utTLLsnFxcSKRqHmJqalp//79O+dzQDfASBtkt67RyVGqqjLxwBCzOW8IXXwJRem7LgDoKjo3CBUKRUVFBSGEx+M5Ov4+BuP169c//PDDs2fPcrlcqVTaHFpisbipqYllWerPB6k9e/a88sor2oXbt293cHCgKOrq1auTJ0/29/cPDg5uuTLDMBs2bOC0GOzDz8/vq6++erg2lmVlMpnOrgxDU1OTTvenUqqybyhTozXFWfx+g/jDpwrdB1JcnpIQpY4r0QeappVKJS6N6gbDMHK5nGEYfRdiKJ7qYCKRSNr8IXRuEObl5S1cuJAQYmlpefnyZUJIYmLi7NmzDx8+HBQURAixtbWtra3VrlxbW2tnZ9cqBYuKimJiYg4ePKh92pymo0aNGjduXFRUVKsg5HK5V65caec9Qg6Hg3uEuqSLe4QMI8+9KUu+LE9PEDh7mQSOFS/fRAnFbb+xZ+FyubhHqDMMw/B4PNwj1KXudI+wf//+qampzU9v3bo1Y8aMXbt2jR8/XrskICAgLi5uxowZhJDY2NiAgIBWW9i1a9fEiRPt7e0f3nhlZSW6T0AzZVmuLOkyffMq19xWMniM6fRXuMbm+i4KALoB3d0jLCsrCw0NDQkJuXv3blhYGCFkypQpb7zxxsSJEwcOHCgUCr/88ssjR44QQl5++eUBAwa8/fbbDMOEh4dv375duwWZTPb++++PGzdOIBAcP368qKjoxRdf1Fn90DWp71fKkqNkyZcJw0gGj7H+2xaedR99FwUA3YnuglClUmlzKzk5WbskJCRk6NChkZGRYWFhDMPs2rUrNDSUEDJkyBAnJydCSElJybRp06ZOnapdn8/nm5iY7Nq1S6PReHl5JScno+2owWJkTfSta7KkS6p7FZKAURYL1gmcvPRdFAB0S7rrR6gb6EfYZXVI1x9WrZJn3pAl/abISxN5D5YEhoq8BhMO7oS1hn6EuoR+hDrWjfsRAvwVyuIs2Y1LslvX+PYukiHjzBe8wxG1/ecOAECbEITQpWlq70mTLslu/EY4HKMh42zX7+SaWeu7KADoURCE0BWxCppOvS698ZvqTpEkYLTF4ncFjv30XRQA9EwIQuhKWFZRkC5LvECnxwlc+vcKmS7yHYqJIACgU+EQA12Cpvae9MZFWeJvlEBoNHSC6fQVnF5m+i4KAAwCghD0iVUp6bQYacIFVUWBJGC0xcsbBQ4e+i4KAAwLghD0Q1WeL40/L7t5VeDg0Sv4eZFfMMXj67soADBECELQKYZukiVHSePPsbRMMnQCWoECgN4hCEEnWFZdlFmbdlWekSjyDjSbvlLo4Y+5kACgK0AQQudimuqlCRel8edYDtd4xBSzWWs4ki4xTz0AgBaCEDoHyyrybjXFnlXk3hT7jbBYuF5h2aeXDqZhAgB4SghC6GCaxjpZwgVp/DlKJOkVPNl83lrtWGiKxkZ9lwYA8AgIQuggLKvIT22KPavISREPGGmxZIPA0VPfNQEAtA1BCH8VI2uUJV5sij1LcXlGI6aaz30Lw2EDQDeCIIRnpyzNkcacoW/HinyCLOavFbj46rsiAICnhiCEp8aqlLKUKOn1MwzdaDR8it30VzhGJvouCgDgGSEI4Smoa+5KY36RJl4UOPuYTF4i8hqMvoAA0N0hCKEdWFaeldQUfUpZlmc0dILNum94Frb6rgkAoGMgCOFJGLpJlnCh6fppjti4V8g0y+UfUHyBvosCAOhICEJ4NFVlaVP0SfrmVZH3EItF7wmcvfRdEQBAp0AQwp+xrDwzsfHqCXVlidHwybbv/8g1Mdd3TQAAnQhBCL9jFbQ04UJT9CmO2KjXcy+IBz2HqeEBwBC090in0WhSUlLS0tKqq6v5fL6NjU1QUFC/fv06tTjQDfX9yqboU7Ibv4k8B1ksfEfg7K3vigAAdKftIMzKyvr2228PHjxYV1fX6iUnJ6cVK1asWrXK1hZtCLslRWFG05X/KgpuGw2bZLv+W66Zlb4rAgDQNYpl2ce9Vl1dvXHjxr1797q7u8+aNWv48OH9+vWzsLBQq9X3799PTU29fv36Tz/9JJVK33333ffee08g0H97QolEUlNTI5G0PcQXy7JSqbRXr146qKqrYTVqOvV605X/MrS016iZRkHjKIGos3fa2NhojNkndEUmkwmFQi6Xq+9CDALDMDRNGxkZ6bsQQ9HhB5MnnRGeO3fu7t270dHRwcHBrV6ytbX18fGZP3/+9u3bT58+/dFHH82dO9fTE4Msd3WMXCqN/bUp+hTPqrfJxAUin6HoEQ8ABu5JZ4QqlYrP57dnKyzLajQaHk//bStwRvg4mrp7TVdPSBMvirwDjcfM5vd113EBOCPUJZwR6hLOCHVMp2eEzSnIsizDMNofFcuyp06dSklJcXR0nDZtmo2NDSGEoqiukILwSKqKgsbLx+XZyUZB423f/ZZrZq3vigAAupA20kuj0bz//vu7du1qamqaPn16eHj4smXLjh49qn3V2to6MTHR2dm508uEZ6LIvdl4+biqsqTXcy+YzfkbZkcCAHhYG0F44MCBLVu2jBo1ysXF5cSJE4sWLfrtt9927doVGBiYlJT09ttvf/rppz/++KNuau1w9MVDigfV+q6iEzAMI5dpaqsovsB4zGzx4DHoEQgA8DhtHB8PHz48fvz4CxcuEEIWLlw4fvz4999/f8WKFYQQf3//goKC5rPD7ojv5idk1PquohNQFEdsxOllxu/tjLYwAABP1kYQlpWVLVq0SPv4ueeeoyiqf//+za/6+fl9+eWXnVhdJ+O5+okNprEMAAA8EufJL9M03dwCUyAQ8Pl8oVDY/KpQKFQqlZ1YHQAAQCdrIwgBAAB6tif1IySEODs7C4VCR0dH7dPLly/3799f22WCEHLv3r20tLQnb0HH0I+wy0I/Ql1CP0JdQj9CHdNpP0JCiKOjY0VFRWFhofaps7NzU1NTU1NT8wqurq4dWA0AAICOtRGE165d000dAAAAevHs9wi1fe2//fZbmqY7sCAAAABdevYgZBhm8+bNr7/+uoeHR/ftUw8AAAbu2YOQx+MVFBQkJia+9dZbsbGxHVgTAACAzjz7yFsURbm6urq6ug4ZMqQDCwIAANCl9p4Rzpo1Kzw8XC6Xd2o1AAAAOtbeIGxqalqyZEmfPn3Wrl2bnZ3dqTUBAADoTHuD8MKFC5mZmStXrjxw4IC3t3dgYGBYWJhMJuvU4gAAADrbUzSW8fb2/ve//11RUXH06FFzc/NXX321T58+r776anp6eufVBwAA0KmeutWoSCSaM2fOqVOn3n777fr6+rCwsAEDBkybNi0jI6Mz6gMAAOhUTx2E6enpf//73+3t7bdv3z59+vQzZ86EhYXl5uYGBwffuXOnM0oEAADoPO3tPkHT9NGjR8PCwmJjY+3s7F5//fVVq1Y1D8Y9f/78vn37Xr16df78+Z1WKgAAQMdrbxD6+fkVFBSMHj06MjJy5syZAoGg5atGRkZeXl5qdU+c7R0AAHq09gbhwoUL586d6+Pj87gV4uLiOqgkAAAA3XnSPcKrV68eO3aMYRhCyEcfffS4FKRpeuvWreXl5W3uTKPRZGVlpaWltRqnu7GxUSqVPry+UqlMTk5ungRKq66u7saNG9XV1W3uDgAAoE1PCkKhUPjaa6/179//iy++yM/Pb/WqRqNJSUl55513XFxcfvjhB6FQ+OQ9RUdH29vbz5w5c9myZU5OTufOnSOEbNu2zcHBwcTE5LXXXmu1fl5enqen5+uvv/7cc8+tWLFCO/3viRMn3N3d161b5+XltWvXrqf+uAAAAH/Wxgz19fX1mzdv/vHHH+/fv29tbe3p6WlhYaFWq2tqajIzM6VSqZub29q1a1etWsXn85+8p7y8PJZlPT09CSE7d+78/PPPy8vLk5KShEJhREREZWXl/v37W64/d+7cvn37fvnll/X19X5+fvv373/uueecnJy+++676dOn37hxY+zYsRUVFSYmJi3fhRnquyzMUK9LmKFelzBDvY7peoZ6MzOzzz///J///Ofp06evXr2ampqal5fH4/FsbW3/9re/jRs3bsyYMRxOu/pgeHh4ND8ODg6uqanRaDSBgYGEEB6vdRlKpfLnn3++deuWtoZZs2YdO3aMy+Wq1eqpU6cSQoYMGeLm5nb27Nl58+Y91QcGAABoqV2NZbSd6OfMmdNRe/3++++nT5/+hD9XKysrVSqVi4uL9qmLi8vFixdLS0udnZ2bc9fFxaWkpKTVG1mWjYqKanmd1tzcfPDgwR1VOQAA9DBtBOEnn3wyZcqUQYMGPdvWHzx4UFFRQQgxMjJycnLSLvzhhx8uXLgQHx//hDfKZDKKopo7aYhEIqlUKpPJWnbbEIvFDw92qp0uuGXE+vr69uvX7+FdsCyLsVJ1SSqVUhSl7yoMhUwmU6lUuDSqGwzDyOXyJ99mgg70VAcTiUTS5mXLNoJw165dH3zwwcCBA5ctW7Zw4UJLS8t27lsrOjr6X//6FyEkMDBw586dhJADBw588sknUVFRdnZ2T3ijra0ty7K1tbXW1taEkPv379vZ2dnZ2dXW1javU1NTExIS0uqNXC733Llz7bxHSFEU7hHqDMuy+LZ1hsPh4B6hzjAMw+VycY9QZzr8YNJGTsbGxm7bto1hmDfffNPe3n7atGnHjh1rf8f5qVOnJiQkJCQkaFPw+PHjGzZsOH/+vLu7+5PfaG5u7u7uHhMTo30aExMzZMiQQYMG5efn19TUEEKUSmViYiLmBAYAgL+ojVajzZKTkw8cOHDw4MH79+/37t17zpw5r7zyip+fX/v3dO3atdDQ0Ndee83X11e7ZNGiRYWFhbGxsSdOnKirq1u2bJm/v7+RkdHYsWPLysp279791Vdfbdu2LT09fcuWLdnZ2VZWVnPnzm1qanrzzTcPHDhQWlp67dq1VntBq9EuC61GdQmtRnUJrUZ1rMMPJu0ddHvw4MHbt28vKyuLiIjw9fXdsWOHv79/SEjI3r1727kFsVi8bt06sVhc+AeNRvPgwYPCwsIBAwaMGjWqsLDw/v375ubmixYt4nK5a9as2bhx4+7duwsKCq5evWplZUUI2bNnz5AhQ3bu3Glvb3/y5Mln/NAAAAB/aO8ZYSulpaXbtm3btm0by7Jd6hYxzgi7LJwR6hLOCHUJZ4Q6put+hA/TaDTnz5/ft2/fqVOnWJYdMGBAB1YDAACgY08RhNnZ2ZGRkfv27SspKTE1NV26dOnixYtHjhzZecUBAAB0traD8MGDBydPngwPD7906RJFUcHBwRs3bly0aFF7Lj8CAAB0cW0E4erVq/fv3y+Xy11cXP7v//7v5Zdfbp6MFwAAoAdoIwivXLkybdq0VatWhYaGYlgQAADoedoIwps3b4rFYt2UAgAAoHtt9CNECgIAQM/W3g71AAAAPRKCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBqCEAAADBpP3wUAAAC0S52CnCxhTAh3lnFHbhZnhAAA0KU9UJIDeczU82qXI6pfylgRl+3Y7eOMEAAAuqJGFTlVwhwtYq/eZcb05ix050SO5fTik8ZGpmN3hCAEAIAuRKomp0uYo0Xs5TvMqN6cl1yo8NF8E34n7hFBCAAA+idTk7NlzNFC9kIFM9KWesmVs/c5vqlAF7tGEAIAgN7INeRcOXO0kP21jBlqQ73kyvl+JN9CqNMaEIQAAKBrGpbEVbHh+cyxIsbHjJrjwtk6jG8r1k8xCEIAANARbf4dK2KOFDLuJtQcF07GbH5viZ6rQhACAEDn0rDkWiUbWcD8XMy4m1BzXTnJL/D6GFH6rut3CEIAAOgUDEtiq9gjhczxIqavETXXjZP0As+xV1fJv2YIQgAA6GAJ99gjhcyxItZCSOa6cq5P47mZdLn8a4YgBACAjnHrPnukkDlSyIq45CVX6sLzXG+zrpt/zXQdhDU1NdnZ2WZmZj4+PhzO7wO8qVSqsrIyOzs7ieRP90xpms7IyGAYxtfX18jIiBBSVVUllUq1r3K5XCcnJx3XDwAArWTVs0cKmcgCVsWQua7UifHcARbdIP+a6TQI33777f379/v4+Ny5c8fU1PTcuXM2NjbPPfdcYmKiSqU6c+bMpEmTmlc+ffr00qVLXVxceDxeUVFRZGTk2LFjV69eHRMTY2xsTAixsbGJi4vTZf0AANCssJGNLGCPFDJ1CjLHlTowmhtk3Z3yr5lOB92eM2dOeXl5dHR0bm6upaXl5s2bCSEfffTRnTt3HB0dW63s4eGRnp6enJyckJCwfv36N954Q7v83//+d0FBQUFBAVIQAED3KqTs9nRm5Gl10Al1dj375VBu8Tzel0O7awoSHZ8RBgcHax9wudwBAwbU1NQQQsaMGfPIlb28vJofDxo06D//+Y/2cUNDQ1ZWlouLi0gk6uR6AQDgd/docryIiSxkMuvYF5w5/xfAHWNPcbtr9v2JfhrL1NTUREZGhoWFtXP9HTt2zJkzR/t427ZtYWFhJSUlmzZt2rBhQ6s1WZY9e/asUPi/8XksLCyaA7jVmgzDMEwHj2IOj4NvW5e03zZF9YijVJfH/EHfhXSKOgU5UcoeKWBu1JApDtR6P874PkTAIYSwhGWZDp4QqV2e6ttubozyBJ0ehHl5eQ0NDYQQZ2dnS0tLQghN03PmzJk2bdqUKVPas4WPP/64oKBg//79hJDdu3dbWFgQQm7evDlq1Kjg4ODRo0e3XJlhmLCwsJaf3Nvb29/f/+HNsixL03R7viPoEDRNc7lcfVdhKGQymUajwReuGwzDyOXyHvZnh0xDnSmnjpdyr9+jxtixS1w0B4czYh4hhKjlRK3X2p7qYCKRSNo8znd6EP7www9JSUmEkPXr10+ZMkWhUMyaNcve3n7nzp3tefuWLVsOHjx49epVU1NTQog2BQkhgwYNCg0NvX79eqsg5HK5J06caNX69JFYlqUoqlevXk/7ieDZsCyLb1tnOByOUChEEOoGwzBcLlfbsr27U2jIhQrmWCF7qpTpb04t8eAcHsfp1CmQnkGHH0w6PQi3bNnS/FilUr300ktGRkb79+9vz0/066+/3rlz55UrV+zs7Fq9xLJscXHxxIkTO7hcAADDo2bIpTtsZCFzqoTxt6DmuXG2BvMtdTsFhB7p9B7hG2+8ceXKlfXr13/55ZeEEEdHx/nz54eHh9+5c+fBgwfHjh1LTU19+eWXd+zYUVhYOGfOnLfeemvNmjWRkZHat69evfqNN94YN26cQCD46aefampqXnrpJV3WDwDQkzAsialiIwuZ40WMqzE1z5XzaSDPXtKjrvG2h06DMDAw0NzcvKmpSftUe52zoaGhrq5u1apVhJC6ujqNRjNixAgvLy8LC4t3331Xu1C7vkAgGDhw4OXLlzUazcCBA3/44YfmK6UAANB+yTXs4QLmaCFrLiTz3Djx03kuxgaXf80oltVHo59OI5FIampq2nmPUCqV4q6VzjQ2NmpHQgAdkMlkuEeoMwzD0DTdLe4RFjWyRwvZvbmMXENmOFFLPTgBVt0v/zr8YIKxRgEAerjSJjaykD1cwFTLyUsuVPho7pBu2/m9MyAIAQB6pmo5OVbIHC5ksuvZ2c6cbcO4IXYUBwn4EAQhAECPQqvJL2XMgTzm2l32ud7U3305M5w4AnSZfjwEIQBAT9CyC+AQa2qxO+fwGE6vLtYFsGtCEAIAdGMally6wx4uYE6VMAMtqQVunO3BfHOD6QLYIRCEAADdUvw9bRcIxrEXNd+N81kgv3fb7eXhERCEAADdiXYW3EMFLI8iL7lSV6fyPE3RAOYvQRACAHQD5VL2pyL2WBFT3ERmO1N7Qrgj7ZB/HQNBCADQdd1XkGOFzKECJquene3M+TQQXSA6HoIQAKDLkanJyRLmUAETXck+78BZP4AzsS+6QHQWBCEAQFehZsjFCvZQAfNLKRNsSy1wQxcIXUAQAgDoGUtI/D32UD5ztIhxM6YWuHO+HMq3Eeu7LIOBIAQA0JusevZQAXMonxVyyQI3Ttx0nqsBzwKhLwhCAABduyNjjxWyx4qYokbyogu1fxSagOoTghAAQEceKMl/i5mD+czN++wMJ87Hg7mje6MJqP4hCAEAOpeSIb+WMQfz2QsVzJjenDXenCmOHBEmi+wyEIQAAJ2CJeR6JXuogDlexPiaUwvdOD+MxCigXRGCEACgg2XUsQfzmUMFrDGfLHLnpMzkORjhAmjXhSAEAOgYd2XkcAETkc9Uy8l8N+rUBO4AC+RfN4AgBAD4S2g1+bmMc6RUHVfFTnbgfDSYM9mBw0UCdh8IQgCAZ6FmyIUK9mA+c7aMGWnDXdqPcywUTWC6JQQhAMDTuVHNRuQzRwoZdxNqkTtn+zCumKGNjAT6rgueEYIQAKBdihrZg/lsRD7DErLInRM3nediTBFCGIahaX0XB38BghAA4EnqFORoEROex+Q3sC+5cg6M5gZZ4wZgj4IgBAB4BCVDzpYxB/LYqDvMJAfO+/7cSX0pHiZC6okQhAAA/8MSElfFRuQzx4oYP3NqsQdn3yi+CSZC6tEQhAAAhBBS0MCG5zMR+ayQQxZ7oBe8AUEQAoBBq1OQI4VMRD6T38DOd+McHcsNsEL+GRYEIQAYIg1Lou6wB/KYX8qYEbbUm/05Lzhx+LgFaJAQhABgWBKr2fA85kgh42NOLXbnfDOcb4oegIYNQQgABqG0iY3IZ8PzGYYli905N17gOfXCJVAgBEEIAD0brSa/lDEH8hjtQKDfBHND+1AIQGgJQQgAPRDDkkvaW4ClzKjenGWenOOhHCEGAoVHQRACQI+SWc8eyGMO5rO9JWSJB2frML6VSN81QdeGIASAnuC+ghzKZ8LzmbsystCdOv8818cMV0ChXRCEANCNKRnyaxmzP4+NusNMceR8GsgNtac4SEB4GghCAOiWkmrYA3lMZAHjY04txUBo8BcgCAGgO7krIwcLmP25DK0hSzw4iTN4zsY4AYS/BEEIAN2AXENOljAH8pi4e+xMJ863I7gj7dALAjoGghAAurT4e+z+POZYIRNgRS3x4BwL5Uhw3IIOhf9QANAVVUjZiHx2Xx7DsmSpJ+fWLF5fzAUBnQNBCABdiPYS6L5cJrGafdGFszuEO9wW+QedC0EIAF1CYjW7L5c5WsgMtqKWenL+O44jxvEJdAL/0QBAnyppEpHP7M1hVCxZ6sG5OQvT4YKuIQgBQA+UDPmllNmby8RUsTOdOD+M5I5AK1DQEwQhAOhUWi27J5c5XMB4m1HLPTmRYzlGOA6BXuE/IADoYRSvTQAAEJxJREFUQq2CHCpg9uUy92jysicVN53nio7w0DUgCAGgEzEsuVjB7s1lzpUzUxw4nw/BWKDQ5SAIAaBTFDaye3OZ/bmsjZgs9+R8N4JvLtR3TQCPgiAEgI5Eq8nxYmZPDpNRxy5055yZyPWzwAkgdGk6DUKNRpOamlpbW+vp6eno6Ni8vLKyUqlUtlxCCHnw4MH9+/ebnzo4OPD5fEJIWVlZZmamm5ubu7u7zioHgDYl1bC7c5ijhcwwG+p1H850J46Ao++aANpBd0H44MEDT09PGxsbBweHuLi4lStXfvHFFxcvXlyyZElNTY29vX1JSUnL9ffs2fPpp586Oztrn/73v/91dHSMiIh46623QkJC4uLi3n333bfffltn9QPAI9UrydFC5vsspkZOFrhTKTN5Tr1wCgjdCcWyrG72RNN0Tk7OwIEDCSH5+fne3t5paWkmJiYNDQ0lJSWvvvpqqyDcunVramrqvn37mpcolUoHB4dDhw6FhoZmZGQEBQWVlZVZWFi0fJdEIqmpqZFIJG3Ww7KsVCrt1atXx3w8aEtjY6OxsbG+qzAUMplMKBRyudzO2wXDkt/usLtzmIsVzDRHznJPznO9DbQjIMMwNE0bGRnpuxBD0eEHE91duRCLxdoUJIS4uLhIJJL6+vo+ffp4e3tzOI8uQyaT3bx5s7KyUvv0+vXrXC537NixhBBfX19vb++zZ8/qpngAaFbaxH6UwrgeUf/jhmZMb6poLn//KO4oQ01B6AH001hm9+7ddnZ2AQEBT14tNjZ25cqVeXl5o0ePPnz4cFlZmaOjI/XHz83Jyam8vLzVW1iW/emnn4TC/7VOs7KyGj169MMbZ1mWYRiGYf7SJ4F2w7etS9pvm+rQbFIy5FQpuzuHSblP5rtSP4+j/H9vBWPo/7DMH/RdiKF4qm/7cSdaLXVuECoUihs3bhBCKIoaMWKEduHVq1c3bdp05syZlnH1sFdeeWXt2rWEkPr6+nHjxn3++ecODg483v8KFggEcrm81bsYhjl27FjL1fr16zds2LCHt8+yrFwub7kmdCqFQqFt7gQ6IJfLWZbtqEujOQ3UvgLO4SLK15Rd6sYcHsmKuNq9dMjmuz2GYeRyeadeiIaWnupgIhKJ2szCzo2B+vr6Tz/9lBDC4XDOnDlDCImLi3vppZciIyOHDBny5Pc2XwI2MzNbvHjxL7/8MmTIkJbtSKurqx8+1eNyuZGRke28R8iybHvWhA6h0WjwbevSX79HKFOTo4XMrhymqJG87EnFz+BgLJhH0p5847+3znT4waRzg9DW1vbXX39tfpqSkjJz5sw9e/Zo7/O1X25uro2NzZAhQwoLC+/cuWNvb0/TdEJCwldffdXRJQMASalhf8xhjhYyI2w57w7gTHbg8NARAnou3V0YrKmpCQ0NDQwMTE9PT09PJ4RMnz7d0tJy7969eXl5DQ0Nmzdv7t2795IlS6ysrA4dOnTixAl3d3cbG5v4+Pi9e/deu3atd+/eCxYsmDdv3htvvBERETFy5MgBAwborH6AHq9BRQ7lM7tymFoFWdGPc3s2z16CU0Do+XQXhFwu9/3333/kSx4eHi1feu+999zc3CZNmnT58uW0tDQnJ6fbt2+7ubkRQn744Yfvvvvu7NmzwcHBf//733VUOkBPF3+P/TGb+bmEGWfP+WwIdxyGAwVDort+hLqBfoRdFvoR6lI7+xHWK0lEPvNjNkNryCv9OC97cGzEuimwR0E/Qh3r8IMJ2kwCGKLYKjYsmzlZwjzvwNkWzB2NXoBgwBCEAAbkgZJE5DM/ZDMKDVnpxdkylG8l0ndNAPqGIAQwCDeq2R+ymf8WMxP6cLbjFBCgBQQhQE8mVZPDBcz3WUydgqz04mS/yMddQIBWEIQAPVNmPRuWozlUwITYcT4J5E7og4agAI+GIAToUZQM+bmY2ZnBK2gkr/QjqbN4fY0QgABPgiAE6CEqpOwP2cyuHMbbjFrtoZntxhXyMfolQNsQhADdXtRd9ttMJuoOs8Cdc3kyz8uMksmUGBQNoJ0QhADdVZOKROQzOzIZQsjrPpy9z/F7YXoPgKeHIATofvIb2G8zmQN5zKjenG+Gc8f0xl1AgGeHIAToNlhCLlawX6drbtSwyz05KTN5jr0QgQB/FYIQoBuQqkl4HvN1BiPkkjd8OMfHcURoBwPQQRCEAF1acSP7bRazN5d5zo7z3QjuKFwFBehoCEKArohWk/MVzIE89tpdZpkn58YMnjNmhwfoHAYdhDOu8G/WqfRdhaFgWSFF4dtuL6WGDLWh5rpywkfzjQz6ZwrQ6Qz6F3ZwpFooxhRiOtLU1ITZH9tPyCUSg/51AuiOQf/UevHYXkJ9F2EweErWGN82AHQ9GHwCAAAMGoIQAAAMmuEGoUKhqK2t1XcVBqSyspJlWX1XYSjq6+tpmtZ3FYZCLpfX1dXpuwoDcvfu3Y7doOEGYVRU1IoVK/RdhQHx9/fHoVln1q1b99NPP+m7CkNx/vz5NWvW6LsKA+Lt7a3RaDpwg4YbhAAAAARBCAAABo7qYbdtvL29XVxcOJy2A76urq6ioqJ///9v795Cotr+OIDv493KK85ImqmppXjL+zUf1FKKwi5GkZSSmWClUkEJGqQJ0sUwDOmoTxVomjXZRckHJZsMg5RkvONlGifHUVMzxxlnnYeh/R/ynE5H/7h17+/nae9ZC/aX5WL/nH1Z47ECqYCiqLdv3wYHB//OnwaWr6ury8LCgs/nMx2EE+RyuVQqdXd3ZzoIV7x58yYsLOyPP35rraU7d+44Ojr+ug/bCmFfX59IJGI6BQAArAoRERGmpqa/7sO2QggAAPCf4DoVAABwGgohAABwGrfWGp2bm7t7925XV5e7u3tqaqqBgcFPHebn54uKijw8PGJjYxlJyDIdHR1lZWVKpfLo0aOhoaH053K5vKampr29XV9ff8+ePZGRkQyGZAGJRFJcXDw+Ph4TExMXF6fd9K9zHpagpqamvr7e0tIyLS3NxsaG/lwkEgkEgoGBAWtr66SkJHt7ewZDssarV68EAoGpqWlqaqqDg8PiDjU1NYODgxkZGUs+BLe+ESYkJLx48SI8PLy6ujo5OXlxh7y8vPz8/JqampXPxj79/f1hYWGWlpbbtm3bvXt3c3Mz3VRYWPjq1att27bx+fz4+Ph79+4xmHOtm52dDQ0NHR8fDwwMPHfu3J9//qnd+q9zHv6r0tLS9PT0gICAiYmJ0NDQ2dlZuiklJUUikfj6+spkMk9Pz56eHgZzskNVVdXx48d9fHwWFhZCQkIWLwfW1taWmpp65cqVZR2GcEZ3d7eRkdHExAQhZHR01NDQcHBwULtDW1ubv79/WlpaSkoKQxlZJTMzMzExUbOdl5cXFxdHNymVSnq7qKgoODh4pcOxSHl5eUBAgGb7yZMnzs7OarVas7t4zg8NDTEWlBXUarWLi8vjx481u4GBgeXl5XSr9sTeuXPntWvXVjof6/j7+9MjvGvXrps3b2q3KpXKoKCg4uJiU1PT5RyFQ98IhULh9u3bzc3NKYri8Xhubm7v3r2jW1UqVUpKSklJib6+PnMZWaW5uZm+5hkZGan9jVBP73/X5CcnJy0sLFY6HIv8NM69vb1fvnzR7AqFQh8fn3+a87AEMpmsp6fnNye2paXlSudjF4VC8eHDh38abYqiCgoKIiMjfX19l3kgDhVCqVRqZWVF7/L5fO2VWwsKCiIiIvz8/JiIxk7aA87j8cbGxubn53/q09vbe+vWraysrBVPxx7a42xiYmJkZERP7F/PeViCkZERAwMDMzMzzS6Px5NIJIu7lZWVyWSyhISElU3HNpqV+rVPI9qj3dnZWVFRkZ2dvfwDsfxhGaFQWFlZSVGUm5uboaGhUqmkmxQKhZGRkWa7s7Pz/v37ra2tzKRkkRs3bnz+/JmiqOTkZO0Bn5+f19PT0/5/maIosVgcGxubm5sbHh7OQFa2MDQ0pP/DIISoVCp6Yv9izsPSGBkZqVQqtVqtWSNpfn7e2Nj4pz61tbVZWVn19fUbNmxgIiN7aKar9mmEHm21Wp2cnFxYWLh4/JeA5YXQwsJCs+6RnZ3d9PS0WCymm8Risa2trWZbIBBIpVIvLy+KouRyOSFkYGCgrq6OkcxrmpOTk+ZCnImJia2tLT3gw8PDNjY22uurSaXS6Ojo06dPnzlzhpmsbKE9zhKJZGFhgX6O0dbWdnh4mO6pPedhaTZu3EgIkUgkmzZton5MbO0OdXV1J0+efPbsmbe3N0MZ2YPH4xkYGIjFYs1ZRXu0xWJxS0tLSkoKRVEKhWJmZsbJyen58+eurq5LOdJybjCuLZOTk+vXr//48SMhpKWlxczMbGZmRiaT1dbWTkxM9P2QlJR05MiR4eFhpvOuebdv396xY8fCwgIh5MSJE+np6YSQ9+/fd3R0jI6Ouru75+bmMp2RDRoaGjZt2jQ1NUUIuX79elRUFCGks7NTKBT+NOfNzc2/ffvGcNy1Lzo6uqCggBAyPT1tZ2fX0NBACBEIBHK5vKmpic/nNzY2Mp2RPQ4ePHj58mVCyNzcnJubW1VVFSHk5cuXw8PD9Em7urp6w4YNfX19CoViaUfhUCEkhBQWFlpbWx8+fJjP55eUlBBCXr9+bWxsrN0nIyMDT43+X0xPT/v5+QUHB8fExDg6OorFYkLIgQMHLly4cPbsWX19fb8fYmNjmQ67hqnV6kOHDrm6uu7fv5/H47W0tBBCcnJyYmJiyN/NeVimlpYWHo+3f/9+Nze3Q4cOaZ7R1dPTa2pqcnBw4PF49MTOz89nOuya9+nTJ2tr63379nl5ecXExGiey7Wysnr69CndRygULvOpUc6tNdrT09PZ2enu7r5lyxaKomZnZ4eGhrS/TWsujWo/YgBLplQqm5ubFQpFRESE5lK+WCw2MDDQ0dGZmpqiu+nq6uLV4+UghLS2tkqlUs2LmxRFyWSy79+/b968mVo052H5xsfH3759a21t7e/vr/kNBJFIZG9vPzY2plKp6G6mpqY4kyzf169fm5ubLSwsgoKCNLdXuru7bWxs6FuwCoViZGTkb9+1/02cK4QAAADaOPT6BAAAwGIohAAAwGkohAAAwGkohAAAwGkohAAAwGkohAAAwGksX2INgDsEAkFmZia9y+fzvby8zp8/v3XrVgZTAax+KIQALDEzM9Pf33/q1CknJyeKokZGRh48ePDo0aPW1la8Sg/wCyiEAKxy5MgR+vfb4uPjw8PDKysrL126xGwqgNUM9wgBWMvZ2ZmiKO3V7ABgMRRCAHaSyWTZ2dm6urp79+5lOgvAqoZLowCsEhUVRW+bm5tXVVWFhIQwmAdg9UMhBGCVnJwcDw8PiqJkMlllZWViYqJAIIiIiGA6F8DqhV+fAGCJhw8fHjt2rKGhgX5YRqVSeXp66ujodHR0MJsNYDXDPUIA1tLT0/P29haJRLOzs0xnAVi9UAgBWEulUrW3t69bt87Q0JDpLACrF+4RArBKY2OjXC6nKGpqaqqiokIkEl28eFFXV5fpXACrFwohAKtcvXpVs2FmZubi4lJaWpqUlMRsJIBVDg/LAAAAp+EeIQAAcBoKIQAAcBoKIQAAcBoKIQAAcBoKIQAAcBoKIQAAcBoKIQAAcBoKIQAAcBoKIQAAcBoKIQAAcNpfBr5eqKleeocAAAAASUVORK5CYII="
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(ae.Bgrid, ae.vf[:, iy_low], label = \"Low\")\n",
"plot!(ae.Bgrid, ae.vf[:, iy_high], label = \"High\")\n",
"plot!(xlabel = \"B\", ylabel = \"V(y,B)\", title = \"Value functions\",\n",
" legend_title=\"y\", legend = :topleft)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Draw a heat map for default probability"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"hide-output": false
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"heatmap(ae.Bgrid[1:end-1],\n",
" ae.ygrid[2:end],\n",
" reshape(clamp.(vec(ae.defprob[1:end - 1, 1:end - 1]), 0, 1), 250, 20)')\n",
"plot!(xlabel = \"B'\", ylabel = \"y\", title = \"Probability of default\",\n",
" legend = :topleft)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot a time series of major variables simulated from the model"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"hide-output": false
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Random\n",
"# set random seed for consistent result\n",
"Random.seed!(348938)\n",
"\n",
"# simulate\n",
"T = 250\n",
"y_vec, B_vec, q_vec, default_vec = simulate(ae, T)\n",
"\n",
"# find starting and ending periods of recessions\n",
"defs = findall(default_vec)\n",
"def_breaks = diff(defs) .> 1\n",
"def_start = defs[[true; def_breaks]]\n",
"def_end = defs[[def_breaks; true]]\n",
"\n",
"y_vals = [y_vec, B_vec, q_vec]\n",
"titles = [\"Output\", \"Foreign assets\", \"Bond price\"]\n",
"\n",
"plots = plot(layout = (3, 1), size = (700, 800))\n",
"\n",
"# Plot the three variables, and for each each variable shading the period(s) of default\n",
"# in grey\n",
"for i in 1:3\n",
" plot!(plots[i], 1:T, y_vals[i], title = titles[i], xlabel = \"time\", label = \"\", lw = 2)\n",
" for j in 1:length(def_start)\n",
" plot!(plots[i], [def_start[j], def_end[j]], fill(maximum(y_vals[i]), 2),\n",
" fillrange = [extrema(y_vals[i])...], fcolor = :grey, falpha = 0.3, label = \"\")\n",
" end\n",
"end\n",
"\n",
"plot(plots)"
]
}
],
"metadata": {
"date": 1591310624.7583747,
"download_nb": 1,
"download_nb_path": "https://julia.quantecon.org/",
"filename": "arellano.rst",
"filename_with_path": "multi_agent_models/arellano",
"kernelspec": {
"display_name": "Julia 1.4.2",
"language": "julia",
"name": "julia-1.4"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.4.2"
},
"title": "Default Risk and Income Fluctuations"
},
"nbformat": 4,
"nbformat_minor": 2
}