{ "cells": [ { "cell_type": "markdown", "id": "12f921cc-4f63-40f4-8224-4f516c69d9c0", "metadata": {}, "source": [ "# 2. New Keynesian Model and Tractable Heterogeneity" ] }, { "cell_type": "markdown", "id": "38deb1ae-c30f-41d1-a899-7c84807a8f7b", "metadata": {}, "source": [ "DING Minjie, Spring 2025" ] }, { "cell_type": "markdown", "id": "bf178bea-4622-4bfc-a200-92b5ed121719", "metadata": {}, "source": [ "__________________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "f975f0c4-236a-4e36-9268-6401dccbf02a", "metadata": {}, "source": [ "In this tutorial, we will talk about model setting and dynare coding of New Keynesian model, then extend it to two-agent model.\n", "\n", "1. Household\n", "2. Final goods firms\n", "3. Intermediate goods firms\n", "4. Policy and market clearing\n", "5. Equilibrium and steady state\n", "6. Dynare code for NK model\n", "7. Two-agent New Keynesian model" ] }, { "cell_type": "markdown", "id": "204dbe76-cae8-4c2a-aec8-da2eda3ccda9", "metadata": {}, "source": [ "____________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "8f57b3e7-a8e6-4f36-be71-20927ba5e468", "metadata": {}, "source": [ "In classical models, money is neutral both in the short term and long term, and monetary policy cannot affect the real economy. \n", "\n", "Howeverempiricalnd evidencshows e that monetary policdoes y has impact on the real economy.\n", "\n", "The idea of New Keynesian Model is to introduce some short-run frictions to induce short-run non-neutrality of money." ] }, { "cell_type": "markdown", "id": "b97e409d-f7ad-4520-9a44-7dfd59d3be40", "metadata": {}, "source": [ "There are two key elements of New Keynesian models:\n", "\n", "* Monopolistic competition. Instead of perfect competition, we assume there is imperfect competition, firms are not price taker any more. Prices are set by firms to maximize their profit.\n", "\n", "* Nominal rigidities. Firms cannot freely adjust prices. They are subject to some constraints on the frequency with which they can adjust the prices (Calvo-type sticky price), or they may face some costs of adjusting prices (Rotemberg sticky price)." ] }, { "cell_type": "markdown", "id": "7ab60554-7602-4e95-860a-a272a481c3b3", "metadata": {}, "source": [ "In other words, we can say that:\n", "\n", "$$\n", "New \\space Keynesian \\space Model = RBC \\space Model + Monopolistic \\space Competition + Sticky \\space Price\n", "$$" ] }, { "cell_type": "markdown", "id": "5fe9f343-0bfb-455d-bc0b-a0bb3123dfe4", "metadata": {}, "source": [ "________________________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "10a849ba-da81-47dd-a4ba-2982343d9de6", "metadata": {}, "source": [ "# 1. Household" ] }, { "cell_type": "markdown", "id": "1a9926cd-f579-4a36-ab25-f548527dcd89", "metadata": {}, "source": [ "The representative household solves the following optimization problem:\n", "\n", "$$\n", "\\max _{\\{c_{t}, i_{t}, h_{t}, k_{t}, b_{t}\\}_{t=0}^{\\infty}} E_{0} \\sum_{t=0}^{\\infty} \\beta^{t}\\left(\\frac{c_{t}^{1-\\sigma}}{1-\\sigma}-\\kappa_{L} \\frac{h_{t}^{1+\\varphi}}{1+\\varphi}\\right)\n", "$$" ] }, { "cell_type": "markdown", "id": "bf2262b6-402e-4345-aa3a-5bf00093f7ec", "metadata": {}, "source": [ "$$\n", "\\text{s.t.}\n", "\\left\\{\n", "\\begin{array}{l}\n", "p_{t}c_{t}+p_{t}i_{t}+b_{t}=r_{t}^{k}p_{t} k_{t-1}+r_{t-1} b_{t-1}+ p_{t}w_{t} h_{t}-p_{t}t_{t}+ p_{t}\\Gamma_{t} \\\\\n", "k_{t}=(1-\\delta) k_{t-1}+\\left[1-\\frac{\\kappa_{I}}{2}\\left(\\frac{i_{t}}{i_{t-1}}-1\\right)^{2}\\right] i_{t}\n", "\\end{array}\n", "\\right.\n", "$$" ] }, { "cell_type": "markdown", "id": "68bdb8b8-e0c1-4c3c-990e-9ef2a9ade061", "metadata": {}, "source": [ "where:\n", "* $c_t$ is consumption\n", "* $h_t$ is labor, or you can take it as hours for working\n", "* $i_t$ is investment in new capital, which produce rental rate of $r_t^k$\n", "* $b_{t}$ is the amount of a one-period nominal risk-free bond paying a nominal gross interest rate $r_{t}$\n", "* $\\Gamma_t$ is profit\n", "* $t_t$ is tax\n", "* $p_{t}$ is the price level\n", "* $\\sigma$ is coefficient of relative risk aversion or intertemporal elasticity of substitution (IES)\n", "* $\\phi$ is labor supply elasticity or disutility parameter, or the reciprocal of Frisch elasticity of labor supply\n", "* $\\kappa_L$ is disutility of labor\n", "* $\\kappa_I$ is adjustment cost of investment" ] }, { "cell_type": "markdown", "id": "c7f25180-115b-4d9c-b2a6-b5b4ecd8c4ae", "metadata": {}, "source": [ "Compared with RBC model, we introduce $p_t$ here, now the budget constraint is expressed in nominal terms" ] }, { "cell_type": "markdown", "id": "408a4a20-d5d2-4a7b-bd9c-7666665bd67d", "metadata": {}, "source": [ "The Lagrangian function as follows:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\mathcal{L}= & \\mathbb{E}_{0}\\left\\{\\sum_{t=0}^{\\infty} \\beta^{t} \\left\\{\\left(\\frac{c_{t}^{1-\\sigma}}{1-\\sigma}-\\kappa_{L} \\frac{h_{t}^{1+\\varphi}}{1+\\varphi}\\right)-\\lambda_{t}\\left(c_{t}+i_{t}+\\frac{b_{t}}{p_{t}}-r_{t}^{k} k_{t-1}-r_{t-1} \\frac{b_{t-1}}{p_{t}}-w_{t} h_{t}+t_{t}-\\Gamma_{t}\\right)\\right.\\right. \\\\\n", "& \\left.\\left.-q_{t} \\lambda_{t}\\left\\{k_{t}-(1-\\delta) k_{t-1}-\\left[1-\\frac{\\kappa_{I}}{2}\\left(\\frac{i_{t}}{i_{t-1}}-1\\right)^{2}\\right] i_{t}\\right\\}\\right\\}\\right\\} .\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "id": "00efcf36-bd93-40f4-9c89-b5d9cd27f5a7", "metadata": {}, "source": [ "First order conditions (foc) with respect to (wrt) consumption:\n", "\n", "$$\n", "\\frac{\\partial \\mathcal L}{\\partial c_t}=0 \\to \\space c_{t}^{-\\sigma}=\\lambda_{t} \\tag{1}\n", "$$" ] }, { "cell_type": "markdown", "id": "b50558b8-cf47-49d7-97f0-e6fa4d711f86", "metadata": {}, "source": [ "Foc wrt labor:\n", "\n", "$$\n", "\\frac{\\partial \\mathcal L}{\\partial h_t}=0 \\to \\space \\kappa_{L} h_{t}^{\\varphi}=\\lambda_{t} w_{t} \\tag{2}\n", "$$" ] }, { "cell_type": "markdown", "id": "d597e7f9-e905-47bd-b809-dc784e8a9196", "metadata": {}, "source": [ "Foc wrt bonds:\n", "\n", "$$\n", "\\frac{\\partial \\mathcal L}{\\partial b_t}=0 \\to \\space \\lambda_{t}=\\beta \\mathbb{E}_{t}\\left(\\lambda_{t+1} \\frac{r_{t}}{\\frac{p_{t+1}}{p_t}}\\right)=\\beta \\mathbb{E}_{t}\\left(\\lambda_{t+1} \\frac{r_{t}}{\\pi_{t+1}}\\right) \\tag{3}\n", "$$" ] }, { "cell_type": "markdown", "id": "bd4d7656-35cd-4f20-81b0-b3e8d7d722a6", "metadata": {}, "source": [ "\n", "Foc wrt capital:\n", "\n", "$$\n", "\\begin{align*}\n", "\\frac{\\partial \\mathcal L}{\\partial k_t} &=0 \\to \\space \\\\\n", "0 & =-q_{t} \\lambda_{t}+\\beta \\mathbb{E}_{t}\\left[\\lambda_{t+1} r_{t+1}^{k}+q_{t+1} \\lambda_{t+1}(1-\\delta)\\right] \\to \\\\\n", "q_{t} & =\\beta \\mathbb{E}_{t}\\left\\{\\frac{\\lambda_{t+1}}{\\lambda_{t}}\\left[r_{t+1}^{k}+(1-\\delta) q_{t+1}\\right]\\right\\} \\tag{4}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "d576ad32-b1a6-4825-864c-1766e2abf9aa", "metadata": {}, "source": [ "Foc wrt investment:\n", "\n", "$$\n", "\\begin{align*}\n", "0= & -\\lambda_{t}+q_{t} \\lambda_{t}\\left[1-\\kappa_{I}\\left(\\frac{i_{t}}{i_{t-1}}\\right)\\left(\\frac{i_{t}}{i_{t-1}}-1\\right)-\\frac{\\kappa_{I}}{2}\\left(\\frac{i_{t}}{i_{t-1}}-1\\right)^{2}\\right]+ \\beta \\mathbb{E}_{t}\\left\\{q_{t+1} \\lambda_{t+1}\\left[\\kappa_{I}\\left(\\frac{i_{t+1}}{i_{t}}\\right)^{2}\\left(\\frac{i_{t+1}}{i_{t}}-1\\right)\\right]\\right\\} \\to \\\\\n", "1= & q_{t}\\left[1-\\frac{\\kappa_{I}}{2}\\left(\\frac{i_{t}}{i_{t-1}}-1\\right)^{2}-\\kappa_{I}\\left(\\frac{i_{t}}{i_{t-1}}\\right)\\left(\\frac{i_{t}}{i_{t-1}}-1\\right)\\right]+\\kappa_{I} \\beta \\mathbb{E}_{t}\\left\\{q_{t+1} \\frac{\\lambda_{t+1}}{\\lambda_{t}}\\left[\\left(\\frac{i_{t+1}}{i_{t}}\\right)^{2}\\left(\\frac{i_{t+1}}{i_{t}}-1\\right)\\right]\\right\\} \\tag{5}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "f0c79e95-b997-4347-bebd-a06c5e4675ba", "metadata": {}, "source": [ "The real interest rate $r_{t}^{r}$ is defined as follows:\n", "\n", "$$\n", "r_{t}^{r} \\equiv \\frac{r_{t}}{\\mathbb{E}_{t}\\left[\\pi_{t+1}\\right]} \\tag{6}\n", "$$" ] }, { "cell_type": "markdown", "id": "e9b88a85-798e-4141-a18a-3f5bc09d957b", "metadata": {}, "source": [ "And remember law of motion of capital is:\n", "$$\n", "k_{t}=(1-\\delta) k_{t-1}+\\left[1-\\frac{\\kappa_{I}}{2}\\left(\\frac{i_{t}}{i_{t-1}}-1\\right)^{2}\\right] i_{t} \\tag{7}\n", "$$" ] }, { "cell_type": "markdown", "id": "aaf44bda-6436-4fbf-977f-7189e59a3855", "metadata": {}, "source": [ "**The 7 equations above is equilibrium conditions from households side.**\n", "\n", "You may wonder why we neglect budget constraint condition, the reason is that it is essentially same with market clearing condition. We only need one of them. " ] }, { "cell_type": "markdown", "id": "3d05bf89-f7c9-4b05-ba04-98ccb81dd343", "metadata": {}, "source": [ "The **Dynare** code of this 7 equations is: " ] }, { "cell_type": "markdown", "id": "20a662e2-147b-48a7-a9f8-24f667ea0931", "metadata": {}, "source": [ "\n", "\n", "%% Household side\n", "\n", "% 1. FOC to C
\n", "lambda=c^-sigma; \n", "\n", "% 2. FOC to labor
\n", "kappaL*h^(phi)=w*lambda; \n", "\n", "% 3. FOC to bonds
\n", "1=beta*lambda(1)/lambda*r/pi(1);\n", "\n", "% 4. FOC to capital
\n", "1=beta*lambda(1)/lambda*(rk(1)+(1-delta)*q(1))/q;\n", "\n", "% 5. FOC to investment
\n", "1=q*(1-kappaI/2*(i/i(-1)-1)^2-kappaI*(i/i(-1)-1)*i/i(-1))+kappaI*beta*lambda(1)/lambda*q(1)*(i(1)/i-1)*(i(1)/i)^2; \n", "\n", "% 6. Definition of real interest rate
\n", "rr=r/pi(1);\n", " \n", "% 7. Law of motion of capital
\n", "k=(1-delta)*k(-1)+(1-kappaI/2*(i/i(-1)-1)^2)*i;\n", "\n", " " ] }, { "cell_type": "markdown", "id": "9a9c3c7c-3c4d-408c-8161-6552d537789d", "metadata": {}, "source": [ "_____________________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "349a04bc-f7b6-4ac1-b5a0-ef8a55afd97a", "metadata": {}, "source": [ "# 2. Final Goods Firms" ] }, { "cell_type": "markdown", "id": "caedfaf0-901c-4701-a0ce-da66ccd3e258", "metadata": {}, "source": [ "The representative final-good firm produce goods following CES aggregator:\n", "\n", "$$\n", "y_{t}=\\left[\\int_{0}^{1} y_{t}(i)^{\\frac{\\varepsilon-1}{\\varepsilon}} d i\\right]^{\\frac{\\varepsilon}{\\varepsilon-1}}\n", "$$\n", "\n", "where $y_{t}(i)$ is an intermediate input produced by the intermediate firm $i$, whose price is $p_{t}(i)$. \n", "\n", "The problem of the final-good firm is the following:\n" ] }, { "cell_type": "markdown", "id": "6fcce8fe-838c-40ff-b17d-cbd94b4fa578", "metadata": {}, "source": [ "$$\n", "\\max _{y_{t},\\left\\{y_{t}(i)\\right\\}_{i \\in[0,1]}} p_{t} y_{t}-\\int_{0}^{1} p_{t}(i) y_{t}(i) d i\n", "$$\n", "\n", "$$\n", "\\text { s.t } y_{t}=\\left[\\int_{0}^{1} y_{t}(i)^{\\frac{\\varepsilon-1}{\\varepsilon}} d i\\right]^{\\frac{\\varepsilon}{\\varepsilon-1}}\n", "$$\n" ] }, { "cell_type": "markdown", "id": "80489054-2d16-42ea-8a57-81e290f60e44", "metadata": {}, "source": [ "\n", "Plug the constraint in the objective function:\n", "\n", "$$\n", "\\max _{\\left\\{y_{t}(i)\\right\\}_{i \\in[0,1]}} p_{t}\\left[\\int_{0}^{1} y_{t}(i)^{\\frac{\\varepsilon-1}{\\varepsilon}} d i\\right]^{\\frac{\\varepsilon}{\\varepsilon-1}}-\\int_{0}^{1} p_{t}(i) y_{t}(i) d i\n", "$$\n", "\n", "Foc wrt the generic input $i$:\n", "\n", "$$\r\n", "p_{t}\\left[\\int_{0}^{1} y_{t}(i)^{\\frac{\\varepsilon-1}{\\varepsilon}} d i\\right]^{\\frac{1}{\\varepsilon-1}} y_{t}(i)^{-\\frac{1}{\\varepsilon}} = p_{t}(i) \r\n", "$$\r\n", "\r\n", "$$\r\n", "p_{t} y_{t}^{\\frac{1}{\\varepsilon}} y_{t}(i)^{-\\frac{1}{\\varepsilon}} = p_{t}(i) \r\n", "$$\r\n", "\r\n", "$$\r\n", "y_{t}(i) = y_{t}\\left(\\frac{p_{t}(i)}{p_{t}}\\right)^{-\\varepsilon} \r\n", "$$" ] }, { "cell_type": "markdown", "id": "441aeb92-381b-49a4-af26-efaab013f7f4", "metadata": {}, "source": [ "Since final goods firms produce identical goods, and they are in perfectly competitive market, then their profit is zero. So, we have:\n", "\n", "$$\n", " p_{t}\\left[\\int_{0}^{1} y_{t}(i)^{\\frac{\\varepsilon-1}{\\varepsilon}} d i\\right]^{\\frac{\\varepsilon}{\\varepsilon-1}} - \\int_{0}^{1} p_{t}(i) y_{t}(i) d i = 0\n", "$$" ] }, { "cell_type": "markdown", "id": "37f75322-382b-447f-b38d-1275f2835698", "metadata": {}, "source": [ "Rearrange and we get: \n", "\n", "$$\n", " p_{t}=\\left[\\int_{0}^{1} p_{t}(i)^{1-\\varepsilon} d i\\right]^{\\frac{1}{1-\\varepsilon}} \n", "$$\n", "\n" ] }, { "cell_type": "markdown", "id": "5f9b9ac7-be60-4e01-a5d3-d463b0ca8bad", "metadata": {}, "source": [ "There is no direct equilibiurm condition from final goods firms, so we will not give **Dynare** code in this section. \n", "\n", "NK model introduces final goods firms, mainly to get these two equations: \n", "\n", "$$\n", "y_{t}(i) =y_{t}\\left(\\frac{p_{t}(i)}{p_{t}}\\right)^{-\\varepsilon} \n", "$$\n", "\n", "$$\n", "p_{t}=\\left[\\int_{0}^{1} p_{t}(i)^{1-\\varepsilon} d i\\right]^{\\frac{1}{1-\\varepsilon}} \n", "$$" ] }, { "cell_type": "markdown", "id": "06403d85-403f-4c6d-9b97-50a12fd760d8", "metadata": {}, "source": [ "With these two equations, we can solve optimal equations for intermediate goods firms." ] }, { "cell_type": "markdown", "id": "ed452744-af0d-48dc-97f6-cb40130993f3", "metadata": {}, "source": [ "Personally, I think this is the most counter-intuitive part of New Keynesian Model. How could it be that all final goods firms are perfectly competitive, and all intermediate goods firms are monopoly firms? \n", "\n", "Even in final goods industry like retail industry, there are monopoly firms such as Walmart. And for intermediate goods industry like plastic industry, it's a perfectly competitive market in China. So, NK model seems to be an unplausible and factitious model, from this perspective. \n", "\n", "Let's think the other way. There are always fully competitive firms and monopoly firms. Then we name monopoly firms as intermediate goods firms, even though they are not in intermediate goods industry. We name price takers as final goods firms, even though they are not in final goods industries. Under this definition, monopoly firms have power to export price change to fully competitive firms, even though monopoly firms are final goods firms. \n", "\n", "For example, Walmart is in final goods industry, but also monopoly firm. Under setting of NK model, we should name it as intermediate goods firms. And with its market power, Walmart can export price change to its suppliers. \n", "\n", "In this way, I convince myself that the fundamental model of monetary economics is plausible. " ] }, { "cell_type": "markdown", "id": "f0ed9025-d37b-4e8e-8316-43248b53034a", "metadata": {}, "source": [ "________________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "414e7a65-92d6-45de-a1b0-e4ea6d274337", "metadata": {}, "source": [ "# 3. Intermediate Goods Firms" ] }, { "cell_type": "markdown", "id": "c49342b4-efa6-4f54-9b1c-672b3b12490a", "metadata": {}, "source": [ "There is a continuum of firms of measure unity, indexed by $i$, producing a differentiated input through the following Cobb-Douglas function:\n", "\n", "$$\n", "y_{t}(i)=a_{t}\\left(k_{t-1}(i)\\right)^{\\alpha}\\left(h_{t}(i)\\right)^{1-\\alpha} \\tag{8}\n", "$$\n", "\n", "where $a_{t}$ is the total factor productivity, which follows an autoregressive process:\n", "\n", "$$\n", "\\log \\left(a_{t}\\right)=\\left(1-\\rho_{a}\\right) \\log (\\bar{a})+\\rho_{a} \\log \\left(a_{t-1}\\right)+v_{t}^{a} \n", "$$\n", "\n", "and $v_{t}^{a} \\sim N\\left(0, \\sigma_{a}^{2}\\right)$ is a technology shock." ] }, { "cell_type": "markdown", "id": "f354702d-b2a0-4db9-abd3-c813e6caef65", "metadata": {}, "source": [ "Firms set the price of their own good subject to the demand of the final good firm. In addition, firms pay quadratic adjustment costs $A C_{t}(i)$ in nominal terms according to Rotemberg (1982), whenever they adjust prices with respect to the inflation target $\\bar{\\pi}$.\n", "\n", "\\begin{equation*}\n", "A C_{t}(i)=\\frac{\\kappa_{P}}{2}\\left(\\frac{p_{t}(i)}{p_{t-1}(i)}-\\bar{\\pi}\\right)^{2} p_{t} y_{t}\n", "\\end{equation*}" ] }, { "cell_type": "markdown", "id": "52a1fe24-fcd2-4e7d-9dd6-3b8685ae6f08", "metadata": {}, "source": [ "\n", "The profit maximization problem of the generic firm $i$, expressed in terms of the domestic price index, is the following:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\max _{\\left\\{p_{t}(i), h_{t}(i), k_{t-1}(i), y_{t}(i)\\right\\}_{t=0}^{\\infty}} \\mathbb{E}_{0}\\left\\{\\sum_{t=0}^{\\infty} \\beta^{t} \\frac{\\lambda_{t}}{\\lambda_{0}}\\left[\\frac{p_{t}(i)}{p_{t}} y_{t}(i)-w_{t} h_{t}(i)-r_{t}^{k} k_{t-1}(i)-\\frac{\\kappa_{P}}{2}\\left(\\frac{p_{t}(i)}{p_{t-1}(i)}-\\bar{\\pi}\\right)^{2} y_{t}\\right]\\right\\} \\\\\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "id": "dab317ce-a071-4623-97b4-9658d9e88658", "metadata": {}, "source": [ "$$\n", "s.t.\\left\\{\\begin{array}{l}\n", "y_{t}(i)=y_{t}\\left(\\frac{p_{t}(i)}{p_{t}}\\right)^{-\\varepsilon} \\\\\n", "y_{t}(i)=a_{t}\\left(k_{t-1}(i)\\right)^{\\alpha}\\left(h_{t}(i)\\right)^{1-\\alpha}\n", "\\end{array}\\right.\n", "$$" ] }, { "cell_type": "markdown", "id": "9b507b71-63ba-4ebd-be92-32c11764260c", "metadata": {}, "source": [ "\n", "Eliminate one constraint and write the lagrangian as follows:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\mathcal{L}^{I}= & \\mathbb{E}_{0}\\left\\{\\sum _ { t = 0 } ^ { \\infty } \\beta ^ { t } \\frac { \\lambda _ { t } } { \\lambda _ { 0 } } \\left[\\left(\\frac{p_{t}(i)}{p_{t}}\\right)^{1-\\varepsilon} y_{t}-w_{t} h_{t}(i)-r_{t}^{k} k_{t-1}(i)-\\frac{\\kappa_{P}}{2}\\left(\\frac{p_{t}(i)}{p_{t-1}(i)}-\\bar{\\pi}\\right)^{2} y_{t}+\\right.\\right. \\\\\n", "& \\left.\\left.+m c_{t}(i)\\left[a_{t}\\left(k_{t-1}(i)\\right)^{\\alpha}\\left(h_{t}(i)\\right)^{1-\\alpha}-y_{t}\\left(\\frac{p_{t}(i)}{p_{t}}\\right)^{-\\varepsilon}\\right]\\right]\\right\\}\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "id": "b439c72c-1d96-4426-abfe-3ee5fff99597", "metadata": {}, "source": [ "where $m c_{t}(i)$ is the lagrangian multiplier, which can be interpreted as the real marginal cost of producing an additional unit of output. " ] }, { "cell_type": "markdown", "id": "c0ae4fbf-aca0-465f-b603-c9cc632bce5d", "metadata": {}, "source": [ "Foc wrt capital:\n", "\n", "$$\n", "r_{t}^{k}* k_{t-1}(i) = m c_{t}(i) \\space \\alpha \\space a_{t}\\left(k_{t-1}(i)\\right)^{\\alpha}\\left(h_{t}(i)\\right)^{1-\\alpha}\n", "$$" ] }, { "cell_type": "markdown", "id": "f4416757-361b-406b-ad56-d633fbc8b696", "metadata": {}, "source": [ "Foc wrt to labor:\n", "\n", "$$\n", "w_{t} * h_t(i) =m c_{t}(i)(1-\\alpha) a_{t}\\left(k_{t-1}(i)\\right)^{\\alpha}\\left(h_{t}(i)\\right)^{1-\\alpha}\n", "$$" ] }, { "cell_type": "markdown", "id": "a74458b1-1368-4a4a-b5d5-0dc4781bc4ad", "metadata": {}, "source": [ "Foc wrt to $p_{t}(i)$ :\n", "\n", "$$\n", "\\begin{aligned}\n", "(1-\\varepsilon)\\left(\\frac{p_{t}(i)}{p_{t}}\\right)^{-\\varepsilon} \\frac{y_{t}}{p_{t}}-\\frac{\\kappa_{P}}{p_{t-1}(i)} \\left(\\frac{p_{t}(i)}{p_{t-1}(i)}-\\bar{\\pi}\\right) y_{t}+\\varepsilon m c_{t}(i) \\frac{y_{t}}{p_{t}}\\left(\\frac{p_{t}(i)}{p_{t}}\\right)^{-\\varepsilon-1}+ \\beta \\mathbb{E}_{t}\\left[\\frac{\\lambda_{t+1}}{\\lambda_{t}} \\kappa_{P} \\frac{p_{t+1}(i)}{p_{t}(i)^{2}}\\left(\\frac{p_{t+1}(i)}{p_{t}(i)}-\\bar{\\pi}\\right)^{} y_{t+1}\\right]=0\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "id": "407eda80-1eb8-43ae-9307-1125b378a657", "metadata": {}, "source": [ "In a symmetric equilibrium, firms choose the same price, same inputs and same output. Using the production function it turns out:\n", "\n", "$$\r\n", "r_{t}^{k} = m c_{t} \\alpha \\frac{y_{t}}{k_{t-1}} \\tag{9}\r\n", "$$\r\n", "\r\n", "$$\r\n", "w_{t} = m c_{t}(1-\\alpha) \\frac{y_{t}}{h_{t}} \\tag{10}\r\n", "$$" ] }, { "cell_type": "markdown", "id": "83b9f57c-4efe-40e5-99ac-13ac0dbfb3c0", "metadata": {}, "source": [ "\n", "\n", "\n", "Rearrange the pricing condition:\n", "\n", "$$\n", " (1-\\varepsilon) \\frac{y_{t}}{p_{t}}-\\frac{\\kappa_{P}}{p_{t-1}}\\left(\\frac{p_{t}}{p_{t-1}}-\\bar{\\pi}\\right) y_{t}+\\varepsilon m c_{t} \\frac{y_{t}}{p_{t}}+\\beta \\mathbb{E}_{t}\\left[\\frac{\\lambda_{t+1}}{\\lambda_{t}} \\kappa_{P} \\frac{p_{t+1}}{p_{t}^{2}}\\left(\\frac{p_{t+1}}{p_{t}}-\\bar{\\pi}\\right) y_{t+1}\\right]=0 \n", "$$\n", "\n", "$$\n", " (\\varepsilon-1)+\\kappa_{P} \\frac{p_{t}}{p_{t-1}}\\left(\\frac{p_{t}}{p_{t-1}}-\\bar{\\pi}\\right)-\\varepsilon m c_{t}-\\beta \\mathbb{E}_{t}\\left[\\frac{\\lambda_{t+1}}{\\lambda_{t}} \\kappa_{P} \\frac{p_{t+1}}{p_{t}}\\left(\\frac{p_{t+1}}{p_{t}}-\\bar{\\pi}\\right) \\frac{y_{t+1}}{y_{t}}\\right]=0 \n", "$$\n", "\n", "$$\n", " \\frac{p_{t}}{p_{t-1}}\\left(\\frac{p_{t}}{p_{t-1}}-\\bar{\\pi}\\right)=\\beta \\mathbb{E}_{t}\\left[\\frac{\\lambda_{t+1}}{\\lambda_{t}} \\frac{p_{t+1}}{p_{t}}\\left(\\frac{p_{t+1}}{p_{t}}-\\bar{\\pi}\\right) \\frac{y_{t+1}}{y_{t}}\\right]+\\frac{1}{\\kappa_{P}}\\left(1-\\varepsilon+\\varepsilon m c_{t}\\right) \n", "$$\n", "\n", "$$\n", " \\pi_{t}\\left(\\pi_{t}-\\bar{\\pi}\\right)=\\beta \\mathbb{E}_{t}\\left[\\frac{\\lambda_{t+1}}{\\lambda_{t}} \\pi_{t+1}\\left(\\pi_{t+1}-\\bar{\\pi}\\right) \\frac{y_{t+1}}{y_{t}}\\right]+\\frac{\\varepsilon}{\\kappa_{P}}\\left(m c_{t}-\\frac{\\varepsilon-1}{\\varepsilon}\\right), \\tag{11}\n", "$$" ] }, { "cell_type": "markdown", "id": "c6218dd5-f0af-4331-889e-bd9828f43f9d", "metadata": {}, "source": [ "And profit from monopoly firms are:\n", "\n", "$$\n", "\\Gamma_{t}^{I}=y_{t}\\left[1-m c_{t}-\\frac{\\kappa_{P}}{2}\\left(\\pi_{t}-\\bar{\\pi}\\right)^{2}\\right] \\tag{}\n", "$$\n", "\n", "As compared to profit from fully competitive firms are zero:\n", "\n", "$$\n", "\\Gamma_{t}^{C}=0 \\tag{}\n", "$$" ] }, { "cell_type": "markdown", "id": "44e064fb-32fc-4058-b615-688e51c96aba", "metadata": {}, "source": [ "Now we have 4 more equilibrium conditions from firms side. And write them in **Dynare** code." ] }, { "cell_type": "markdown", "id": "01c30531-6145-4243-9465-cb2a73305569", "metadata": {}, "source": [ "\n", "\n", "%% Firms side\n", "\n", "% 9. Production function
\n", "y=a*k(-1)^alpha*h^(1-alpha);\n", "\n", "% 10. FOC to capital
\n", "alpha*mc*y=rk*k(-1);\n", "\n", "% 11. FOC to wage
\n", "(1-alpha)*mc*y=w*h;\n", "\n", "% 12. FOC to price(i)
\n", "(pi-steady_state(pi))*pi=beta*(lambda(1)/lambda*y(1)/y*pi(1)*(pi(1)-steady_state(pi)))+epsilon/kappaP*(mc-(epsilon-1)/epsilon);\n", "\n", "" ] }, { "cell_type": "markdown", "id": "b3334dea-80b7-4853-a136-91a61c328016", "metadata": {}, "source": [ "________________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "d9ee7230-31e6-4aa2-b29c-750ddac6c99f", "metadata": {}, "source": [ "# 4. Policy and Market Clearing" ] }, { "cell_type": "markdown", "id": "9d3ef2d4-a260-45a3-8481-e91247731373", "metadata": {}, "source": [ "Clearing in the good market implies:\n", "\n", "$$\n", "y_{t}=c_{t}+i_{t}+g_{t}+\\frac{\\kappa_{P}}{2}\\left(\\pi_{t}-\\bar{\\pi}\\right)^{2} y_{t} \\tag{12}\n", "$$\n", "\n", "Clearing in the bond market implies:\n", "\n", "$$\n", "b_{t}=0\n", "$$" ] }, { "cell_type": "markdown", "id": "19ae5408-86da-4322-8f7d-ec687be32d53", "metadata": {}, "source": [ "The monetary authority sets the nominal interest rate according to the following Taylor rule:\n", "\n", "$$\n", "\\frac{r_{t}}{r}=\\left(\\frac{r_{t-1}}{r}\\right)^{\\rho_{r}}\\left[\\left(\\frac{\\pi_{t}}{\\bar{\\pi}}\\right)^{\\phi_{\\pi}}\\left(\\frac{y_{t}}{y}\\right)^{\\phi_{y}}\\right]^{1-\\rho_{r}} \\exp \\left(v_{t}^{m}\\right) \\tag{13}\n", "$$\n", "\n", "where $v_{t}^{m} \\sim N\\left(0, \\sigma_{m}^{2}\\right)$ is a monetary policy shock." ] }, { "cell_type": "markdown", "id": "e910f860-d69d-482f-93f5-f2e2f58a3db6", "metadata": {}, "source": [ "Remember that, the total factor productivity $a_{t}$ follows an autoregressive process:\n", "\n", "$$\n", "\\log \\left(a_{t}\\right)=\\left(1-\\rho_{a}\\right) \\log (\\bar{a})+\\rho_{a} \\log \\left(a_{t-1}\\right)+v_{t}^{a} \\tag{14}\n", "$$\n", "\n", "and $v_{t}^{a} \\sim N\\left(0, \\sigma_{a}^{2}\\right)$ is a technology shock." ] }, { "cell_type": "markdown", "id": "77741146-1fe8-44a8-869f-7dc93612a205", "metadata": {}, "source": [ "Moreover, the government finances public expenditure $g_{t}$ by raising lump-sum taxes:\n", "\n", "$$\n", "g_{t}=t_{t}\n", "$$\n", "\n", "where $g_{t}$ follows an autoregressive process:\n", "\n", "$$\n", "\\log \\left(g_{t}\\right)=\\left(1-\\rho_{g}\\right) \\log (\\bar{g})+\\rho_{g} \\log \\left(g_{t-1}\\right)+v_{t}^{g} \\tag{15}\n", "$$\n", "\n", "and $v_{t}^{g} \\sim N\\left(0, \\sigma_{g}^{2}\\right)$ is a public spending shock." ] }, { "cell_type": "markdown", "id": "ecaef7a0-8d9b-42f8-8a91-ceb5a10c9b85", "metadata": {}, "source": [ "We have the last 4 equiblirium conditions and write them down in **Dynare**." ] }, { "cell_type": "markdown", "id": "9b3339d8-d059-4608-98da-8fb0e4a8410c", "metadata": {}, "source": [ "\n", "\n", "% 12. Market clearing
\n", "y=c+i+g+(kappaP/2*(pi-piss)^2)*y;\n", "\n", "% 13. Monetary policy
\n", "r/(rss)=((pi/steady_state(pi))^(phipi)*(y)^(phiy))^(1-rhom)*(r(-1)/rss)^(rhom)*exp(vm);\n", "\n", "% 14. 15. Shocks
\n", "log(a)=(1-rhoa)*log(ass)+rhoa*log(a(-1))+va;
\n", "log(g)=(1-rhog)*log(gss)+rhog*log(g(-1))+vg; \n", "\n", "" ] }, { "cell_type": "markdown", "id": "22c987bb-4962-4fbe-b563-080e5173db0a", "metadata": {}, "source": [ "_______________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "1d86d8e8-c82e-4538-820e-41b900d7e670", "metadata": {}, "source": [ "# 5. Equilibrium and Steady State Solution" ] }, { "cell_type": "markdown", "id": "7bcfef00-b68f-40b4-827d-c785aaffd93b", "metadata": {}, "source": [ "The equilibrium conditions of the model are the following:\n", "\n", "$$\n", "\\begin{align*}\n", "\\lambda_{t}= & c_{t}^{-\\sigma} \\tag{1} \\\\\n", "\\kappa_{L} h_{t}^{\\varphi}= & \\lambda_{t} w_{t} \\tag{2} \\\\\n", "1= & \\beta \\mathbb{E}_{t}\\left(\\frac{\\lambda_{t+1}}{\\lambda_{t}} \\frac{r_{t}}{\\pi_{t+1}}\\right) \\tag{3} \\\\\n", "1= & \\beta \\mathbb{E}_{t}\\left\\{\\frac{\\lambda_{t+1}}{\\lambda_{t}} \\frac{\\left[r_{t+1}^{k}+(1-\\delta) q_{t+1}\\right]}{q_{t}}\\right\\} \\tag{4} \\\\\n", "1= & q_{t}\\left[1-\\frac{\\kappa_{I}}{2}\\left(\\frac{i_{t}}{i_{t-1}}-1\\right)^{2}-\\kappa_{I}\\left(\\frac{i_{t}}{i_{t-1}}\\right)\\left(\\frac{i_{t}}{i_{t-1}}-1\\right)\\right] +\\kappa_{I} \\beta \\mathbb{E}_{t}\\left\\{q_{t+1} \\frac{\\lambda_{t+1}}{\\lambda_{t}}\\left[\\left(\\frac{i_{t+1}}{i_{t}}\\right)^{2}\\left(\\frac{i_{t+1}}{i_{t}}-1\\right)\\right]\\right\\} \\tag{5} \\\\\n", "k_{t}= & (1-\\delta) k_{t-1}+\\left[1-\\frac{\\kappa_{I}}{2}\\left(\\frac{i_{t}}{i_{t-1}}-1\\right)^{2}\\right] i_{t} \\tag{6} \\\\\n", "r_{t}^{r} = & \\frac{r_{t}}{\\mathbb{E}_{t}\\left[\\pi_{t+1}\\right]} \\tag{7} \\\\\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "bcfff05d-24d5-4151-8ffa-1cdcafe1293f", "metadata": {}, "source": [ "$$\n", "\\begin{align*}\n", "y_{t} & =a_{t} k_{t-1}^{\\alpha} h_{t}^{1-\\alpha} \\tag{8} \\\\\n", "(1-\\alpha) m c_{t} y_{t} & =w_{t} h_{t} \\tag{9} \\\\\n", "\\alpha m c_{t} y_{t} & =r_{t}^{k} k_{t-1} \\tag{10} \\\\\n", "\\pi_{t}\\left(\\pi_{t}-\\bar{\\pi}\\right) & =\\beta \\mathbb{E}_{t}\\left[\\frac{\\lambda_{t+1}}{\\lambda_{t}} \\pi_{t+1}\\left(\\pi_{t+1}-\\bar{\\pi}\\right) \\frac{y_{t+1}}{y_{t}}\\right]+\\frac{\\varepsilon}{\\kappa_{P}}\\left(m c_{t}-\\frac{\\varepsilon-1}{\\varepsilon}\\right) \\tag{11} \\\\\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "f7e8b0bb-6c2b-40b7-aa01-dcf0b375ef63", "metadata": {}, "source": [ "$$\n", "\\begin{align*}\n", "y_{t} & =c_{t}+i_{t}+g_{t}+\\frac{\\kappa_{P}}{2}\\left(\\pi_{t}-\\bar{\\pi}\\right)^{2} y_{t} \\tag{12} \\\\\n", "\\frac{r_{t}}{r} & =\\left(\\frac{r_{t-1}}{r}\\right)^{\\rho_{r}}\\left[\\left(\\frac{\\pi_{t}}{\\bar{\\pi}}\\right)^{\\phi_{\\pi}}\\left(\\frac{y_{t}}{y}\\right)^{\\phi^{y}}\\right]^{1-\\rho_{r}} \\exp \\left(v_{t}^{m}\\right) \\tag{13} \\\\\n", "\\log \\left(a_{t}\\right) & =\\left(1-\\rho_{a}\\right) \\log (\\bar{a})+\\rho_{a} \\log \\left(a_{t-1}\\right)+v_{t}^{a} \\tag{14} \\\\\n", "\\log \\left(g_{t}\\right) & =\\left(1-\\rho_{g}\\right) \\log (\\bar{g})+\\rho_{g} \\log \\left(g_{t-1}\\right)+v_{t}^{g} \\tag{15}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "ca62939b-5df1-4e75-8564-2481a1a729c4", "metadata": {}, "source": [ "Compared to traditional RBC model, there are 3 additional equations: the definition of the real interest rate (7), the Phillips curve (11), and the Taylor rule (13). The 3 additional variables are $r_{t}$, $m c_{t}$, and $\\pi_{t}$. Notice that the price level $p_{t}$, together with inflation $\\pi_{t} \\equiv \\frac{p_{t}}{p_{t}-1}$ are not included in the set of equilibrium conditions because it would introduce a unit root in the model.\n" ] }, { "cell_type": "markdown", "id": "c871d024-d078-4be7-befd-a17b522ba327", "metadata": {}, "source": [ "In steady state, we can easily get:\n", "\n", "$$\n", "a = \\bar{a}\n", "$$\n", "\n", "$$\n", "g = \\bar{g}\n", "$$\n", "\n", "$$\n", "\\pi = \\bar{\\pi}\n", "$$\n", "\n", "$$\n", "r = \\frac{\\bar{\\pi}}{\\beta}\n", "$$\n", "\n", "$$\n", "r^r = \\frac{1}{\\beta}\n", "$$\n", "\n", "$$\n", "q = 1\n", "$$\n", "\n", "$$\n", "r^k = \\frac{1}{\\beta} - (1-\\delta)\n", "$$\n", "\n", "$$\n", "mc = \\frac{\\epsilon - 1}{\\epsilon}\n", "$$" ] }, { "cell_type": "markdown", "id": "5e68cdde-dfb1-43f4-832a-b5ccacca1c6c", "metadata": {}, "source": [ "Assume we know $y$, then from equation (9) and (10), we can get:\n", "\n", "$$\n", "w = \\frac{\\epsilon-1}{\\epsilon} \\frac{(1-\\alpha) y}{h}\n", "$$\n", "\n", "$$\n", "k = \\frac{\\epsilon-1}{\\epsilon} \\frac{\\alpha y}{r^k}\n", "$$" ] }, { "cell_type": "markdown", "id": "2432360c-d287-4b2f-aa12-a61087b02448", "metadata": {}, "source": [ "Then from equation (6), we have:\n", "\n", "$$\n", "i = \\delta k \n", "$$" ] }, { "cell_type": "markdown", "id": "666dbd0c-887a-4ba8-a693-6042773fd879", "metadata": {}, "source": [ "From equation (12), we have:\n", "\n", "$$\n", "c = y - i - \\bar{g}\n", "$$" ] }, { "cell_type": "markdown", "id": "0b430403-ad72-4326-8ce3-9414e5355861", "metadata": {}, "source": [ "Based on equation (1) and (2), we choose a $\\kappa_L$ so that $h=\\frac{1}{3}$\n", "\n", "$$\n", "\\kappa_L = \\frac{w}{c^\\sigma h^\\phi}\n", "$$" ] }, { "cell_type": "markdown", "id": "1b2223e0-0757-4ef8-bff4-5b1898ad9567", "metadata": {}, "source": [ "And we choose a $\\bar{a}$ so that $y = 1$\n", "\n", "$$\n", "y = \\bar{a} k^\\alpha h^{1-\\alpha}\n", "$$" ] }, { "cell_type": "markdown", "id": "52d22b35-28b2-4fc3-b45c-d505884c2ae5", "metadata": {}, "source": [ "___________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "97180e83-3828-4483-a250-cb865027f90a", "metadata": {}, "source": [ "# 6. Dynare code for NK model" ] }, { "cell_type": "markdown", "id": "ff886ba2-d4c2-4bdd-8958-3f5aa12cc1b3", "metadata": {}, "source": [ "Let's see all **Dynare** code." ] }, { "cell_type": "markdown", "id": "58160d06-570a-4bc3-a7e3-e741265d6125", "metadata": {}, "source": [ "Firstly, the variable part. " ] }, { "cell_type": "markdown", "id": "d116e196-2989-4d6f-b53c-b6e158949065", "metadata": {}, "source": [ "\n", "\n", "var c, rk, rr, w, h, y, k, q, i, lambda, r, pi, mc, g, a, \n", "clog, wlog, hlog, klog, ilog;\n", "\n", "varexo va, vg, vm; \n", "\n", "% c consumption
\n", "% rk rental rate of capital
\n", "% rr real interest rate
\n", "% w real wage
\n", "% h hours
\n", "% y output
\n", "% k capital
\n", "% q Tobin Q
\n", "% i investment
\n", "% lambda marginal utility of consumption
\n", "% r nominal interest rate
\n", "% pi inflation
\n", "% mc net marginal cost
\n", "% g public spending
\n", "% a exogenous TFP
\n", "% va productivity shock
\n", "% vg public spending shock
\n", "% vm monetary policy shock
\n", "" ] }, { "cell_type": "markdown", "id": "781a2804-2ef1-4ee5-b54b-f2943d44b9cd", "metadata": {}, "source": [ "Then, parameters part." ] }, { "cell_type": "markdown", "id": "1cbfe98f-50e5-40f0-a5e8-ba4611de87f3", "metadata": {}, "source": [ "\n", "\n", "parameters beta, alpha, delta, sigma, phi, kappaL, epsilon, gss,
\n", "ass, piss, rss, kappaI, kappaP, phipi, phiy, rhoa, rhog, rhom;
\n", "\n", "beta = 0.99; % discount factor
\n", "alpha = 0.33; % capital share
\n", "delta = 0.025; % depreciation rate
\n", "sigma = 2; % relative risk aversion
\n", "phi = 1; % labor elasticity
\n", "kappaL = 13.7; % disutility of labor
\n", "epsilon = 6; % product elasticity
\n", "gss = 0.2; % steady state public spending
\n", "ass = 1.06; % steady state TFP
\n", "piss = 1; % steady state inflation
\n", "rss = 1.01; % steady state interest rate
\n", "kappaI = 2.48; % adjustment cost
\n", "kappaP = 28; % inflation cost
\n", "phipi = 1.5; % Tylor rule coefficient of inflaton
\n", "phiy = 0.125; % Tylor rule coefficient of output
\n", "rhoa = 0.9; % persistence of TFP
\n", "rhog = 0.9; % persistence of public spending
\n", "rhom = 0.8; % persistence of monetary policy shock
\n", "\n", "" ] }, { "cell_type": "markdown", "id": "2d8b06b7-8a27-499a-aafa-60383afd41a9", "metadata": {}, "source": [ "And model part:" ] }, { "cell_type": "markdown", "id": "5650779e-ec76-4f81-b332-cda56e4a8a8e", "metadata": {}, "source": [ "\n", "\n", "model;\n", "\n", "%% Households
\n", "lambda=c^-sigma; % equation 1
\n", "kappaL*h^(phi)=w*lambda; % equation 2
\n", "1=beta*lambda(1)/lambda*r/pi(1); % equation 3
\n", "1=beta*lambda(1)/lambda*(rk(1)+(1-delta)*q(1))/q; % equation 4
\n", "1=q*(1-kappaI/2*(i/i(-1)-1)^2-kappaI*(i/i(-1)-1)*i/i(-1))+kappaI*beta*lambda(1)/lambda*q(1)*(i(1)/i-1)*(i(1)/i)^2; %equation 5
\n", "k=(1-delta)*k(-1)+(1-kappaI/2*(i/i(-1)-1)^2)*i; % equation 6
\n", "\n", "%% Firms
\n", "y=a*k(-1)^alpha*h^(1-alpha); % equation 8
\n", "(1-alpha)*mc*y=w*h; % equation 9
\n", "alpha*mc*y=rk*k(-1); % equation 10
\n", "(pi-steady_state(pi))*pi=beta*(lambda(1)/lambda*y(1)/y*pi(1)*(pi(1)-steady_state(pi)))+epsilon/kappaP*(mc-(epsilon-1)/epsilon); % equation 11
\n", "\n", "%% Market clearing
\n", "y=c+i+g+(kappaP/2*(pi-piss)^2)*y; % equation 12
\n", "\n", "%% Policy
\n", "r/(rss)=((pi/steady_state(pi))^(phipi)*(y)^(phiy))^(1-rhom)*
\n", "(r(-1)/rss)^(rhom)*exp(vm); % equation 13
\n", "\n", "%% Shocks
\n", "log(a)=(1-rhoa)*log(ass)+rhoa*log(a(-1))+va; % equation 14
\n", "log(g)=(1-rhog)*log(gss)+rhog*log(g(-1))+vg; % equation 15
\n", "\n", "%% Auxiliary variables
\n", "rr=r/pi(1); % equation 7
\n", "clog=log(c);
\n", "wlog=log(w);
\n", "hlog=log(h);
\n", "klog=log(k);
\n", "ilog=log(i);
\n", "\n", "end;\n", "" ] }, { "cell_type": "markdown", "id": "4bdf6e7a-9dd6-4bd3-9087-5aaf3d702a1b", "metadata": {}, "source": [ "Set the initial value, which is usually the steady state value." ] }, { "cell_type": "markdown", "id": "3140e0dd-f31f-40ce-9223-e02297f48262", "metadata": {}, "source": [ "\n", "\n", "initval;
\n", "\n", "pi=1; \n", "y=1; \n", "h=1/3; \n", "rr=1/beta; \n", "r=pi/beta; \n", "q=1; \n", "rk=1/beta-(1-delta); \n", "mc=(epsilon-1)/epsilon; \n", "k=alpha*mc*y/rk; \n", "w=(1-alpha)*mc*y/h; \n", "i=delta*k;
\n", "g=gss;
\n", "a=ass;
\n", "c=y-i-g; \n", "lambda=c^(-sigma); \n", "clog=log(c);
\n", "wlog=log(w);
\n", "hlog=log(h);
\n", "klog=log(k);
\n", "ilog=log(i);
\n", "\n", "end;\n", "" ] }, { "cell_type": "markdown", "id": "d31f2da4-b6c5-445f-8932-a285b8dd36cd", "metadata": {}, "source": [ "The remaining part." ] }, { "cell_type": "markdown", "id": "fd044ef1-b8dc-4d1d-b2d0-fc948c5a7a54", "metadata": {}, "source": [ "\n", "\n", "steady;
\n", "\n", "%% Shocks
\n", "shocks;
\n", "var va; stderr 0.01;
\n", "var vg; stderr 0.01;
\n", "var vm; stderr 0.0025;
\n", "end;
\n", "\n", "%% IRFs
\n", "stoch_simul(irf=40,order=1, hp_filter=1600,pruning,noprint)
\n", "y
\n", "clog
\n", "ilog
\n", "hlog
\n", "klog
\n", "wlog
\n", "q
\n", "pi
\n", "r;
\n", "" ] }, { "cell_type": "code", "execution_count": null, "id": "0bb10c7a-28b0-4b11-a822-fdf7856aaf7c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
ans = 'C:\\Users\\ading\\A_TA_Notes'
" ], "text/plain": [ "ans = 'C:\\Users\\ading\\A_TA_Notes'" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cd\"C:\\Users\\ading\\A_TA_Notes\"\n", "pwd" ] }, { "cell_type": "code", "execution_count": null, "id": "b90b96c2-4a9c-4bc4-b92b-0d644271fb94", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Starting Dynare (version 6.2).\n", "Calling Dynare with arguments: none\n", "Starting preprocessing of the model file ... \n", "Found 20 equation(s). \n", "Evaluating expressions... \n", "Computing static model derivatives (order 1). \n", "Normalizing the static model... \n", "Finding the optimal block decomposition of the static model... \n", "6 block(s) found: \n", " 5 recursive block(s) and 1 simultaneous block(s). \n", " the largest simultaneous block has 10 equation(s) \n", " and 10 feedback variable(s). \n", "Computing dynamic model derivatives (order 1). \n", "Normalizing the dynamic model... \n", "Finding the optimal block decomposition of the dynamic model... \n", "4 block(s) found: \n", " 3 recursive block(s) and 1 simultaneous block(s). \n", " the largest simultaneous block has 12 equation(s) \n", " and 12 feedback variable(s). \n", "Preprocessing completed. \n", "Preprocessing time: 0h00m00s.\n", "\n", "STEADY-STATE RESULTS:\n", "\n", "c \t\t 0.606219\n", "rk \t\t 0.035101\n", "rr \t\t 1.0101\n", "w \t\t 1.6788\n", "h \t\t 0.333441\n", "y \t\t 1.00259\n", "k \t\t 7.85482\n", "q \t\t 1\n", "i \t\t 0.196371\n", "lambda \t\t 2.72108\n", "r \t\t 1.01033\n", "pi \t\t 1.00022\n", "mc \t\t 0.833333\n", "g \t\t 0.2\n", "a \t\t 1.06\n", "clog \t\t -0.500514\n", "wlog \t\t 0.518078\n", "hlog \t\t -1.09829\n", "klog \t\t 2.06113\n", "ilog \t\t -1.62775\n" ] }, { "data": { "image/png": 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" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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R7AAAAHSCYKcYtn9ADYqLi2/evKl0FYCqsR8WGkKwAzxXaWnp2LFjT58+rXQhgAbwORyaQLADPFRxcfHYsWMrKiqULgQA4DIEO8DjmM3mNWvWJCQkBAUFKV0LoHYcNgNtIdgpg5kCCqqoqNi6dWtKSsrGjRuVrgUA4Eo+ShcAQG7+/v55eXmtW7cuKytr5LfwUQQANIFgB3gcg8FgMBgas2RISEhhYaG764E6hYSEKF2C8vhIA80h2AF6Zjab7U+PaNOmjVPfTqrzZNL/feIdoC0EOwXwERCyyc7Onjdvnu1hfn6+n5+fgvUAANyKYAfoWXR0dHp6uu2hr6+vgsUA2sKHcGgRwQ7Qs+Dg4ODgYKWrAADIhMudyI1b00BzaFoA0AqCnTLYtg/NoWnhUdgPC41iVyzgudq0acN5rwCgJ2yxAwAA0AmCHQAAgE4Q7JqluLj45s2bjV+egzYAQP2Yq6FdBLumKy0tHTt27OnTp5UuBAAAQAiCXZMVFxePHTvW/mZNAAAAyiLYOc1sNq9ZsyYhISEoKEjpWgAALsZ+WGgawc5pFRUVW7duTUlJ2bhxo9K1AAAA/B+uY+c0f3//vLy81q1bl5WVKV0LVC0kJETpEgAAnoUtdk4zGAytW7dWugpoANf+BQDIjC12DTGbzfanR7Rp06Y5r8ZxGwDgQmaz+dSpU4GBgY888oirXpOJGlpHsGtIdnb2vHnzbA/z8/P9/PwUrAcAIISorKxcuHDh3r17LRaLEKJDhw5LliyJiopSui5AeQS7hkRHR6enp9se+vr6KlgMAECyYMGCQ4cOpaenDx48+O9///uvfvWrKVOm7Nu3Lzg4WOnSAIUR7BoSHBzMNAEPx54pqI3ZbN63b9/rr78eFxcnhOjQocPKlSsHDBiwf//+iRMnNueVpW4HNI1gBwDQkqqqqhUrVkRERNhGHnzwQSFEeXm5S16fjzHQNIIdAEBLAgIChg4daj+SlZUlhIiJiVGoIkBFCHZN16ZNm8Zfz4L9WQDgDmfOnDGZTPHx8ZGRkUrXAiiPYAcAUK+GLzt18uTJpKQko9G4fPly2UsD1IhgBwBQrwYuO7Vr16758+dHR0ebTKbmX4uK/SrQB4IdAEC97nXZqbVr15pMptGjRy9atEih0gA1ItgBANSr3stObdu2zWQypaSkJCUlKVIVoFoEOwCAlly/fn3JkiVdunQJCgratWuXbbxjx47210ABPBPBTg4cugEArnL8+HGz2VxSUjJnzhz78VGjRjU52DFLQzcIdgAALUlISEhISFC6CkClvJQuAAAAAK5BsAMAANAJgh0AwKNxgB30hGAH4J5Y4QGAthDsAAAAdIJg53Zs84A6mc3mY8eOXbx4UelCAAAuw+VOAI9TWVm5cOHCvXv3WiwWIUSHDh2WLFkSFRWldF2AAvjsDZ1hix3gcRYsWPD555+np6cXFBQcOnSoY8eOU6ZMKS0tVbouAEBzEewAz2I2m/ft2zd58uS4uDgvL68OHTqsXLmyqqpq//79SpcGAGgudsUCnqWqqmrFihX2d1568MEHhRDl5eXKFQUAcA2CHeBZAgIChg4daj+SlZUlhIiJiVGoIkAxHGAH/SHYAR7tzJkzJpMpPj4+MjJS6VqgLiEhIUqXAMBpBDtAz8xmc0VFhe1hmzZt7J89efJkUlKS0Whcvny57KVB7QoLCwXxDtAagh2gZ9nZ2fPmzbM9zM/P9/Pzk77etWvX/Pnzo6OjTSaTbRAAoGkEO0DPoqOj09PTbQ99fX2lL9auXWsymUaPHr1o0SKFSgMUxgF20CWCnXsxcUBZwcHBwcHBDoPbtm0zmUwpKSlJSUmKVAXIQJp+AU9DsAM8y/Xr15csWdKlS5egoKBdu3bZxjt27Gh/DRQAgBYR7ADPcvz4cbPZXFJSMmfOHPvxUaNGEeygJ1artUWLFi1atGCfCTwKwQ7wLAkJCQkJCY1ZsqioSHAgAXSK42SgV9xSDAAAQCcIdgAAADpBsAMA6JPRaBT1nR7LCbPQMYIdAMATcYAddIlgBwAAoBMEOwAAAJ0g2AEAdEva32p/UB0XOoG+EezciOkDAADIiWAHAPAUfN6G7hHsAAAAdIJgBwDQM9thdmyugycg2AEAAOgEwQ4A4CnYXAfdI9gBqAc7rQBAi3yULgAAAPfiIwo8B1vsAAAAdIJgBwAAoBMEuyYym83Hjh27ePGi0oUAAAD8C8fYOa2ysnLhwoV79+61WCxCiA4dOixZsiQqKsphsaKiIsGBHQAAQEZssXPaggULPv/88/T09IKCgkOHDnXs2HHKlCmlpaVK1wUAADwdwc45ZrN53759kydPjouL8/Ly6tChw8qVK6uqqvbv3690aQAAwNOxK9Y5VVVVK1asiIiIsI08+OCDQojy8nLligJcz2q1hoSEKF0FAMA5BDvnBAQEDB061H4kKytLCBETE6NQRQAAAP9CsGuWM2fOmEym+Pj4yMhIpWuBurC5CwAgP4JdQ8xmc0VFhe1hmzZt7J89efJkUlKS0Whcvny57KVB7QoLCwXxDgAgL4JdQ7Kzs+fNm2d7mJ+f7+fnJ329a9eu+fPnR0dHm0wm2yAAAICCCHYNiY6OTk9Ptz309fWVvli7dq3JZBo9evSiRYsUKg0AAMARwa4hwcHBwcHBDoPbtm0zmUwpKSlJSUmKVAUAAFAvgp1zrl+/vmTJki5dugQFBe3atcs23rFjR/troADqV15efv78+bCwsICAAKVrAZquvLz8m2++6du3r9KFAKpAsHPO8ePHzWZzSUnJnDlz7MdHjRplH+xatGghuJ8Y1Kq6unr+/Pm7d++WHj711FNvv/028Q4a9eabb+bl5Z0/f17pQgBVINg5JyEhISEhQekqgGb57W9/m5OT8/vf//6xxx7Lz89PTk6eP3/+6tWrla4LcNonn3xy8OBBg8GgdCGAWnBLMcCz1NbWfvTRR+PGjXvssceEEBERES+//HJOTo7FYlG6NMA533777eLFi7k+PGCPYKcrXDUN9+Xt7X3mzJlJkybZRu7cuePlpZapgB5GI1ksltmzZw8dOjQ2NlbpWv4NPQxlqWU2h56oYV5TQw2qZTAYHnjgAYvFUl5evm3btqysrKSkJPVkOzVQQ/+ooQY1y8zMLCsrmzt3rtKFqJQa+kcNNXigFhzg7yY0NMRP959Qp7/85S8TJ04UQnTt2jUzM/Phhx92WIAehlBrD589e3bUqFHbt2+PiIjYtm3bkiVL6j15gh6GUGsPuw8nT7iLp3US1KmB2+KFhYWdPXv24sWLv/nNb55//vlPP/3UIdvRw1CDuj1cVVU1c+bM5OTk+15kih6GB2LnC6Bn2dnZUXYqKyttT7Vp08bX1zc0NDQjI6OioiIrK0vBOoF7qdvDK1euvH37dnh4+OHDhw8fPnzx4kWr1Xr48GFiHCDYYgfoW93b4pWVlZ08eTI8PDwoKEgabNu2bevWrW/cuKFQjUBD6vbwlStXysrKpkyZYr/Y5MmTR4wYsWzZMtkLBNSFYAfoWd3b4lVWVk6bNi01NVU6wE4Icf369du3b3fq1EmB+oD7qdvD69ats786zwcffLB8+fL8/HxOAAIEu2IBTxMcHBwXF7d27drDhw8LIYqLi5OTk//jP/7jhRdeULo0oFG8vb0Ndnx8fIQQBoPB29tb6dIA5bHFDvA4K1asWLBgweTJk6WHPXv2zMrKCgwMVLYqAEDzcbkTwENVV1fn5+d369atbdu2StcCAHANgh0AAIBOcIydHhQXF9+8edNhsLa29tixY3XHXc5sNh87duzixYt1n5KtBiFEeXn5kSNHysvLlS1DquT06dPK1qA59LCghzWOHhb0sEpYoXHXrl3r27fvgQMH7AczMzNDQ0ONRqPRaHz11Vd//PFHd7z17du3Z82a1b17d+mNYmNjjx49KnMNVqv1zp07s2bNMv5k+vTp9u8lWxk2U6dO7dmzp/2I/DVoCz1MD2sdPUwPqwfBTtuKiooGDhxoNBrtJ5Tdu3cbjcaPP/64trb23LlzAwcOTE5Odse7v/HGG3379s3Nza2trS0tLU1MTOzdu/e1a9fkrMFqtaalpfXu3TsvL89qtZ4+fToqKmr69OnSU3KWIfn444+NRqP9hCJ/DdpCD1vpYY2jh630sJoQ7LTq7t27q1ev7tmz5y9/+UuHCeXZZ5+dNGmS7WF2drbRaCwpKXF5Ad27d8/MzLSNfP/990ajcePGjbLVYLVaa2pqQkNDV65caRvJyMjo3r17bW2tnGVILl26FBERMXHiRPsJReYaNIQeltDD2kUPS+hhVeEYO62qqKjYunVrSkrKxo0b7cerq6uLiori4uJsI0OGDBFCHDlyxLUFVFVVrVixYtiwYbaRBx98UAhRXl4uWw1CCG9v7zNnzkyaNMk2cufOHek6pXKWIYSwWCyzZ88eOnRobGysbVDmGrSFHpbQw9pFD0voYVXhOnZa5e/vn5eX17p167KyMvvxEydOCCHat29vGzEYDL6+vgUFBa4tICAgYOjQofYj0s1GY2JiZKvB9uIGg8FisVRUVOzZsycrKyspKcnLy0vmMjIzM8vKyubOnbtz507boMw1aAs9bP/i9LAW0cP2L04PqwTBTqukv6K649KddqRLsdv4+PjcvXvXrfWcOXPGZDLFx8dHRkZKtzSQuYYvv/xSukdW165dExIShLy/irNnz5pMpu3bt/v5+dmPK/W/QxPoYQf0sObQww7oYTVgVyxc4OTJkxMmTDAajcuXL1eqhrCwsLNnz+7cufOBBx54/vnnr169KttbV1VVzZw5Mzk5OSIiQrY3hWvRw/Sw1tHD9LCEYKc3vr6+Qoiamhr7wZqampYtW7rpHXft2vXKK6/07dv3vffekz4nyV+DEKJNmza+vr6hoaEZGRkVFRVZWVmylbFy5crbt2+Hh4cfPnz48OHDFy9etFqthw8fLiwsVORXoXX0MD2sdfQwPawgdsXqTb9+/YQQt27dso2Yzebq6upevXq54+3Wrl1rMplGjx69aNEiRWooKys7efJkeHh4UFCQNNK2bdvWrVvfuHFDtjKuXLlSVlY2ZcoU+8HJkyePGDHinXfekacGPaGH6WGto4fpYQWxxU5vDAZDjx49cnJybCP79+8XQvTv39/l77Vt2zaTyZSSkmI/m8hcQ2Vl5bRp0/bs2WMbuX79+u3btzt16iRbGevWrTtv51e/+pXBYDh//vySJUvk/FXoBj1MD2sdPUwPK0nhy62g2X744Yd6L4y5efPm2trar776auDAgVOnTnX5+5aWlvbs2fPpp5/e+e9Onz4tWw2SqVOnRkRE/PnPf7ZarUVFRSNGjIiKirpx44bMZdhkZWXVvTCmzDVoCz1MD2sdPUwPqwfBTvPqTihWqzUjI8N275SJEye6494pn376qbE+8+bNk60Gye3bt9944w1bAQkJCd98843tWdnKsHGYUBSpQVvoYXpY6+hhelg9WlitVqU3GsItpBundOnSJSAgwBNqqK6uzs/P79atW9u2bRUs417UUIPmqOGXRg+rqgbNUcMvjR5WVQ0yINgBAADoBCdPAAAA6ATBDgAAQCcIdgAAADpBsAMAANAJgh0AAIBOEOwAAAB0gmAHAACgEwQ7AAAAnSDYAQAA6ATBDgAAQCcIdgAAADpBsAMAANAJgh0AAIBOEOwAAAB0gmAHAACgEwQ7AAAAnSDYAQAA6ATBTlcKCwuHDx/es2fPPn36rF27VulygKZbuHDh5MmTla4CADSGYKcfFotl0qRJ8fHxf/vb3/bt27d9+/adO3e68PVNJtP06dMbeHbmzJkufDt4skOHDm3fvt0dr5yRkXGvNqaHoQ90socj2OnHlStX+vfvP23aNCFEcHBwVFTUkSNHXPj6Bw4c2Lx5cwPPvv/++y58O3ismzdvLly4cOLEie548dzc3Hu1MT0MfaCTPRzBTj86deq0YsUKLy8vIcR333136tSpyMhIpYsCnDb5y3+MAAAgAElEQVR37twJEyZ07txZ6UIAQHsIdjr04osvxsbG/vznPx8zZoyb3sJisVgslkYuWVNT0/zXgYfIysqqrq5OTExUupB/oYGhDw13sqCZdYRgpzrFxcU3b950GKytrT127JjDeHFx8eGflJWV2caXLl2alZVVVlY2Y8YMl5f3+eef9+7d29vb22AwxMTEfPPNN/da8osvvoiJiTEYDAaDoX379gsWLLh7967t2b179/bo0UN6nYSEhA8++KBdu3a5ubkuLxjya3IPX7x4cf369cuWLZOtVJPJ1K5du9dee63uUzQwVCU+Pr537962h+Xl5e3atYuJibGNFBUVtWvXbt26dQ7f2HAnC5pZf6xQk2vXrvXt2/fAgQP2g5mZmaGhoUaj0Wg0vvrqqz/++KM0vmDBgp4/OXr0qMNLHT161Gg03rlzx1W1PfPMMz4+Pq1atXr99dc//PDDuXPnCiE6d+5se7Zt27a2hf/0pz95eXl17tw5MzNzx44dEyZMEEIMHjxYelY6qyM8PHzbtm3btm3r06dPq1athBD79u1zVbVQSnN6eMqUKSNGjEhLS0tLSxs3btzgwYPT0tJc2MNWq/W5557z9/eXvk5PTxdCvPrqq9JD+x6mgaE2b731lhCisLBQevjhhx8KIby8vGx/TatWrRJCXLx4sfGdbKWZ9YhgpyJFRUUDBw40Go32K8Xdu3cbjcaPP/64trb23LlzAwcOTE5Orvfb8/Pzp0+fbnt4+vRplwc7IcT7779vG0lOThZCfPXVV9Y6wa5jx45BQUE3btywjaSlpQkhNm3aZLVaH3744a5du96+fVt6qqqqKjQ0lKlEB5rZw3/4wx/m/eSFF16IjY2dN2+em4KddD2gSZMm2Z6y72EaGGpz/PhxIcTatWulh4mJiV27dhVC7NixQxoZPHhweHi41ZlOttLMesSuWFUwm81r1qxJSEgICgpyeGrDhg2DBg0aOXKkl5dXWFhYampqbm7upUuX6r5IcHBwXl7eJ598Ir3ghg0bIiMjfX19XVinl5fXCy+8YHv46KOPCiGuXbvmsNiJEycuX76cmJgYGBhoG5w1a5aXl9eePXtOnDhx9erVCRMm+Pn5SU+1atVKyojQLpf08Pjx49/+SUJCQrdu3d5++23X9rBk/fr1ycnJycnJGzZsqPssDQwV6t+/f1BQkG0P6YEDB8aMGePn55eTkyOEuHv37uHDh4cNG2b/LQ13srQAzaw/BDv3Ki0traysrDt+4cIF+4cVFRVbt25NSUnZuHGj/Xh1dXVRUVFcXJxtZMiQIUKIeq9jEhgYuGbNmt/97ndRUVH9+vWrqqpavXq1a36Mn/j5+Uln3Ursv7b37bffCiH69evn8L0BAQEXLlyQnjUajfbPduzY0bWlwlXk7GF5VFRUTJkyRQhRWFhY7wI0MNRp+PDhf/zjHy0Wy9dff/2///u/jz/++NNPP52XlyeE2Lt3r8ViGT58uP3yDXeybQGaWWcIdu5VWVn5xhtvOKwX33rrrf/93/+1H/H398/Lyxs/frzDt584cUII0b59e9uIwWDw9fUtKCio9+0ee+yxL7/8ct++fadOndq8eXPbtm1d82M0iY+PT91BzrrSHJl72GbkyJH1bk5ziblz586dO/fgwYO///3v77UMDQy1ee655+7cuZOXl5eTk+Pj4xMbGxsfH3/hwoXvvvtu7969Dz30UP/+/et+F53saQh27tWtW7fXX389NTXVtl586623YmJi7DdgCCEMBkPr1q3rfrv0t+fwZ+nj4+NwTpODtm3bGgyG5pbeDNJa/Ouvv7YfrKmpKS8vDw0N7dKlixDi/Pnz9s9evnxZzgrReIr0sFv5+/svXrz417/+ddeuXWfOnFlaWuqwAA0MdXr66adbtmyZm5v75z//+cknn/Ty8ho8eLAQ4uDBg3v37v3lL3/psHzDnSyEoJl1iWDndiEhITNmzJDWiwsXLoyJiXniiSeULsq9YmJiAgMDt2zZYr/y3rhxo8ViGTBgQGRkpNFofO+992yXaKmsrOTOtmqmyx5u2bLlpk2bKioq6l4zjwaGOnl5eSUkJOzfv/+zzz6LjY0VQnTv3j0oKCgtLe27774bMWKEw/INd7IQgmbWJYKdHKT14lNPPRUREeHUGlE6bNzhqpI1NTUtW7Z0cYku5eXltWzZsqKiovj4+D/+8Y9nz55duXLl66+/3r17d+k2nRkZGZcvXx4wYMC6devWr18fHR1d9wwMqIoue3jgwIGTJk2qu0OWBoZqPfvss6dPn66srJS21Qkhnnzyya+//trPz+/xxx93WPi+nSxoZj0i2MkkKysrMTExJyen3uPQ70U66PXWrVu2EbPZXF1d3atXL9eX6FKvvPLKtm3bSkpKhg4d2rt379mzZ48ZMyYvL0+6QlJ8fPzBgwcDAwNnzJgxa9as2NhYOa9Ji6bRZQ+vWrXqoYcemjlz5tWrV+3HaWCo09ChQ728vAICAmx3jJQuRDVixIh6z2ZruJMFzaxLSl9vxSPMmzcvNzfXarUWFRUlJyfbrhhU1w8//OBwDbARI0ZMnTrV9jA7O9toNJaUlLi1YBe6ePHi4cOHq6ur7Qd/+OEHh8WkE3jz8/NlLA1O8NgepoGhD/V2spVm1iOCndvNmTNHWiNKSkpKpkyZcq/1Yt2VonRx182bN9fW1n711VcDBw60X0dqlI+Pz/Dhw+1H+vTp4+/vX1tbq1RJHqimpubo0aPff//9fZekhx3QwCrR+B7GvdDM+kOwc68vv/zSfo0oKSkpsb9/g726K0Wr1ZqRkWG7HdPEiRNtN5DRLum2NmPGjNm0aVN6evovfvELIUR6errSdXmQe93jqy56uC4aWA0a38NoAM2sPwQ7baipqcnPz9fTzLVo0aLQ0NCWLVu2atVq0KBB2dnZSlfkQRp/jy8X0lkP08DKUqSH9Ypm1pkWVqtVseP7tKy2tvavf/1rt27dlL0IMNAEw4YNe+ihh2yX/929e3dqaupnn33WuXNnZQsDGokeBu6Fs2KbYv369eHh4YmJiQMGDBg/fnx5ebnSFQGNpcJ7fAFOoYeBBhDsnLZnz55Vq1alpaUVFBTs2LGjuLh47ty5ShfVKC3UR+lfiSdq8j2+AJWgh4EG1HMLOTRsw4YNgwYNGjlypBAiLCwsNTU1NTX10qVLDrsAQkJCFCpQFBUVKfXWztJWtnO4VXYj3etO80px4h5fmvq/AzcJMRrpYWibhx1yRrBzjrQL4KWXXrKNDBkyJDU19ciRI3WP7ZBtNmxkPFLh8ZTaCnZNSMxNy4IqocgaPSQkRG0xwtMp9xm1+Vzbw9qar2CjujWfmxHsnNP4XQCFRUWyfVhsbNeqb1bS/d+bCleJar7Hl1DfBk6okJw9rJUwp8LP7Sqh4N4zpRDsnNP4XQBu3drhMNfwJ61e6ptTVH6PL+C+5OnhupGOmRaawMkTGuNwzoF00RoF64HmGAyGHj165OTk2Eb2798vhOjfv79yRQFOkKGH606zzLTQCoKdcxTcjWUf6Zho0BwTJkw4ePDgli1bLBbL2bNnly9fHhcXxwXAoCHu6+G6M23zXxOQE7tinaPUbiz7icatbwRPMGzYsKtXry5btmzx4sVCiJiYmKVLlypdFOAEGXqYyRYaRbBzjm0XQEJCgjTi7t1YDnsE3PQu8DTJyclJSUnnzp3r0qVLQECA0uUATnNHD0vzLTMtNI1dsU6TczcWewTgPt7e3n369CHVQbtc28NaOQEWaBhb7Jwm224sdr8CgDyYb6EbBLumkGE3FrMMAMiM+RY6QLBrImkXgJtenFQHALJhJyz0hGPs1ItUBwDuxgdp6AzBTnU4LQsAZMaUC90g2KkLewQAAECTEexUhD0CACAnPktDfwh2qkOqAwA5MetCTwh2asGhdQAAoJkIdgAAT8R+WOgSwU4V2FwHAIpg4oXOEOwAAAB0gmCnPHYHAIDMmHihV9xSTC3YHQBVYbUHT8DEC/1hi53CWH0CAABXIdipAp8aAUA2fKKGjhHslMTkAtWSPmzQotAxPlFDlwh2ymNyAQAALkGwAwAA0AmCnWLYyQUAAFyLYKcw9sMCgJy40w/0jWAHoCFsWgYADSHYAaif0WhUugQAgHMIdspgXwAAAHA5gh0AAIBOEOwAAAB0gmCnAPbDAtAE/Z06w/QL3SPYAbgnbizmmVr8ROlCADiNYAcAEKK+PMeWLUBzfJQuwOOwIwCAqtTdMscEBWgXwQ4APBSRDtAfgh0AeBbyHKBjBDsA8BQOkc7T8hxHwsATEOxkxbQCzbFardIB9fStdrGJDvAcBDsA0C0P30QHeCCCHQDoDXkO8FgEOwDQDyId4OEIdgCgB0Q6AIJgBwCaRp5rJM5dg4fglmLyYVqBRnHHWHWqe/svphcAbLEDAI1hKx2AeyHYAYBmEOkANIxgBwAa4LDXVcFKAKgZwQ4AVI1IB6DxOHlCJpw5AU3j/AlF2J8ewbkRzcEMDM/BFjsAUB220gFoGoIdAKgIkQ5AcxDsAEAViHQAmo9j7AAPZTabjx07dvHiRaULgT6PpautrT127NjNmzebs2TjXwSAhC12TWQ2m0+dOhUYGPjII4/cd2GO24WqVFZWLly4cO/evRaLRQjRoUOHJUuWREVFNfxdVqtVyh90sgvpdSvd+vXrV69eXVNTI4R49NFH33333YCAAGeXbPhF+vTpU1VVZf9SmzZtGjBggJt+IkAr2GLntMrKytTU1PDw8MTExGeeeWbw4MHHjh1TuijACQsWLPj888/T09MLCgoOHTrUsWPHKVOmlJaWKl2XZ6l7QzAFi3GtPXv2rFq1Ki0traCgYMeOHcXFxXPnznV2yYZf5LvvvquqqnrllVd+a6dbt25y/HiAylnhpDfeeKNv3765ubm1tbWlpaWJiYm9e/e+du2aw2JGo9H2Nb9qj2XfBipx9+7d7t27Z2Zm2ka+//57o9G4ceNGhyXrFk8nu4qGJuEm9PCzzz47adIk28Ps7Gyj0VhSUuLUkg2/yIEDB4xG440bNxpZvCZ+1XAHFU7C7sYWO+eYzeZ9+/ZNnjw5Li7Oy8urQ4cOK1eurKqq2r9/v9KlAY1SVVW1YsWKYcOG2UYefPBBIUR5eblyRXkQXR5OZ6+6urqoqCguLs42MmTIECHEkSNHGr/kfV/k66+/9vf3DwwMdNvPAWgVwc45rBShdQEBAUOHDu3QoYNtJCsrSwgRExOjXFEeQfeRTnLixAkhRPv27W0jBoPB19e3oKCg8Uve90WKi4sffvjhxMTEHj169OjR46WXXrp06ZLbfiZASwh2zmGlCJ05c+aMyWSKj4+PjIys+2xISIj9Qyv3n2gqLUa6kJAQhwZoDOmMHB+ffzszz8fH5+7du41f8r4vcubMmZKSkv/6r//KzMxctGjRlStXXnjhhX/84x/1/hTO/gjQDc/8v89Zsc3S8EpRwimxHksNc4rZbK6oqLA9bNOmjf2zJ0+eTEpKMhqNy5cvr/fbCwsL3VufB9DuGRLS//2G27jhBnOft95666GHHgoLC5MeRkREPPPMM5s2bXrzzTcdlqSHPVlhYaEa5mGZEewa0syVIjycGuaU7OzsefPm2R7m5+f7+flJX+/atWv+/PnR0dEmk8k2CBfSbqRrvLoN5uvrK4SQrlFiU1NT07JlS4fvbWDJ+77IE088Yf/UI4880rVr18uXL9dbJJ+u4VEIdg1hpQiti46OTk9Ptz2U1pdCiLVr15pMptGjRy9atEih0nTOft+rspW4Vd0G69evnxDi1q1btkGz2VxdXd2rVy+H721gyYZfpKys7Pz58927d3c4ecLLi4OLAIJdg1gpQuuCg4ODg4MdBrdt22YymVJSUpKSkhSpSt88YUOdTd0G8/b27tGjR05OTkJCgjQiXTSgf//+Dt9rMBjutWQDTwkhfvjhh4kTJ06bNm369OnSs6WlpSUlJUOHDnXTjwloCJ9vGhIcHPyEHW9vb2G3UiTVQYuuX7++ZMmSLl26BAUF7bKTn5/fmG/n/IkGeMh5r/c1YcKEgwcPbtmyxWKxnD17dvny5XFxcZ07dxZCHDly5LXXXjt//vx9l2zgqUceeeTxxx/ftGnToUOHhBDFxcWvvfZaYGDgSy+9pNwPDagFW+yc47BStI137NgxIiJCwcKARjp+/LjZbC4pKZkzZ479+KhRo+jh5vCoDXUNGzZs2NWrV5ctW7Z48WIhRExMzNKlS6Wnrl+/npubO3r06Psu2cBTQojf/va3v/nNb5KTk6XzZ/v167dmzZp73bUM8Cjc9tE5O3furHvWlRBi1KhRb7/9tv1ISEiIdDYWx+16MlsbaNG9iqelHeg70jW5h2tra8+dO9elS5f75q0Glmz4Rcxm8/nz57t27frAAw80UDwd68k0PQk3DVvsnJOQkGA75gMAPOQkiSbw9vbu06dPM5ds+EUMBgObmQEHBDv34pMioFf63lAHQKM4eQKAczh/QmjzThIAPAFb7ADACWyoA6BmBDsAaCyOqAOgcuyKBYBGIdUBUD+CHQCnedphdg5XHla2GABoALtiAaAhRDpN49IE8DQEOwCoH+dJANAcgh0A1IMNdQC0iGPs3IhdANAxfR9mR6oDoFFssQOA/8PuVwCaRrADgH9hQx0ArWNXLAAIQaoDoAsEOwBNpJvD7LhMHQDdYFcsAI9GpAOgJ2yxA+C5SHUAdIZgB6C5tLg3lt2vAHSJYAeg6TQaiewjnUZ/BACoF8HOXYqKioRmV3uAjrGhznMwD8MDEewAuIBW9saS6gDoG8EOQLNoJSFxUB0AT8DlTgDoH5EOgIdgix2A5lL5lYpJdQA8B8EOgJ6R6gB4FHbFAtAn+y2IpDoAHoItdgBcQG17Y7lSHQDPRLADoDfsfgXgsQh2biGtV1ipAPIj1QHwZAQ7AK6h+N5YrlQHAJw8AUAPiHQAINhiB8CFlNpoR6pDXeo5lQeQE8HOLaxWq9FoVLoKwCOQ6tAAugKehmAHwJXk3GjHQXUA4IBgB8At3J3tuFIdANRFsAPgYjLELDbUAUC9CHYA3MUdG+3Y/QoADSDYAXA9N0Uudr8CQMMIdgDcyFUb7dhQB2dxdQJ4JoIdALewxa/mZzs21AFAIxHsALhL87MdG+oAwCkEOwBu1ORs5xDpSHUA0BjcKxaAe1mtVimiSf+9b0Szj4DkOQBwCsEOgNvZsp24R7yruz2PSAcATUCwAyAHh32yDeyZJdIBQJMR7ADI6l43kyXPAUDzEewAKIAYBwDuwFmxAAAAOkGwAwAA0AmCXbOUl5efPn1a6SqApqOHoYja2tpjx47dvHmz+UsWFxc35nUAD0Gwa5Y333xz3LhxSlcBNB09DPmtX78+PDw8MTFxwIAB48ePLy8vb/KSpaWlY8eO5cMJYEOwa7pPPvnk4MGDSlcBNB09DPnt2bNn1apVaWlpBQUFO3bsKC4unjt3btOWLC4uHjt2bEVFhSyFA9pAsGuib7/9dvHixTExMUoXAjQRPQxFbNiwYdCgQSNHjvTy8goLC0tNTc3Nzb106ZJTS5rN5jVr1iQkJAQFBcn+EwCqRrBrCovFMnv27KFDh8bGxipdy78JCQlRugRoAz0MRVRXVxcVFcXFxdlGhgwZIoQ4cuSIU0tWVFRs3bo1JSVl48aNctTtDHoYyiLYNUVmZmZZWdm9dh9ADfOaGmpQM3q4YWroHzXU4HInTpwQQrRv3942YjAYfH19CwoKnFrS398/Ly9v/PjxchStTWroHzXU4IG4QLHTzp49azKZtm/f7ufn1/CSivS0Sv6Q1FCGGmooLCxUuoR60MONoYYy1FCDa3vYYrEIIXx8/m3V4+Pjc/fuXaeWNBgMBoOhMe9ID1ODpyHYNcRsNtsfltumTZuqqqqZM2cmJydHREQ0/L3qXKPD09DDUFDd9pO5AHoYHohg15Ds7Ox58+bZHubn569ater27dvh4eGHDx8WQly8eNFqtR4+fPhnP/sZn0ugQvQwFFS3/Xx9fYUQNTU19ovV1NS0bNnS4XsbvyQAewS7hkRHR6enp9se+vr6XrlypaysbMqUKfaLTZ48ecSIEcuWLZO9QOA+6GEoqG779evXTwhx69Yt26DZbK6uru7Vq5fD9zZ+SQD2CHYNCQ4ODg4Oth9Zt26ddOSH5IMPPli+fHl+fr6XF6ehQI3oYSiobvt5e3v36NEjJycnISFBGtm/f78Qon///g7fazAYGrkkAHtM5c7x9vY22JEO7DUYDN7e3kqXBjQKPQxlTZgw4eDBg1u2bLFYLGfPnl2+fHlcXFznzp2FEEeOHHnttdfOnz9/3yUB3Atb7AAA8hk2bNjVq1eXLVu2ePFiIURMTMzSpUulp65fv56bmzt69Oj7LgngXlpYrValawAAeJba2tpz58516dIlICDAVUsCEAQ7AAAA3eAYOz0oLi6+efOmw2Btbe2xY8fqjruc2Ww+duzYxYsX6z4lWw1CiPLy8iNHjpSXlytbhlTJ6dOnla1Bc+hhQQ9rHD0s6GGVsELjrl271rdv3wMHDtgPZmZmhoaGGo1Go9H46quv/vjjj+5469u3b8+aNat79+7SG8XGxh49elTmGqxW6507d2bNmmX8yfTp0+3fS7YybKZOndqzZ0/7Eflr0BZ6mB7WOnqYHlYPgp22FRUVDRw40Gg02k8ou3fvNhqNH3/8sXRsysCBA5OTk93x7m+88Ubfvn1zc3Nra2tLS0sTExN79+597do1OWuwWq1paWm9e/fOy8uzWq2nT5+OioqaPn269JScZUg+/vhjo9FoP6HIX4O20MNWeljj6GErPawmBDutunv37urVq3v27PnLX/7SYUJ59tlnJ02aZHuYnZ1tNBpLSkpcXkD37t0zMzNtI99//73RaNy4caNsNVit1pqamtDQ0JUrV9pGMjIyunfvXltbK2cZkkuXLkVEREycONF+QpG5Bg2hhyX0sHbRwxJ6WFU4xk6rKioqtm7dmpKSsnHjRvvx6urqoqKiuLg428iQIUOEEEeOHHFtAVVVVStWrBg2bJht5MEHHxRClJeXy1aDEMLb2/vMmTOTJk2yjdy5c0e61q6cZQghLBbL7Nmzhw4dGhsbaxuUuQZtoYcl9LB20cMSelhVuI6dVvn7++fl5bVu3bqsrMx+/MSJE0KI9u3b20YMBoOvr29BQYFrCwgICBg6dKj9SFZWlhAiJiZGthpsL24wGCwWS0VFxZ49e7KyspKSkry8vGQuIzMzs6ysbO7cuTt37rQNylyDttDD9i9OD2sRPWz/4vSwShDstEr6K6o7Lt0tSrqdgI2Pj8/du3fdWs+ZM2dMJlN8fHxkZKR0d3mZa/jyyy8nTpwohOjatat0DyI5fxVnz541mUzbt2/38/OzH1fqf4cm0MMO6GHNoYcd0MNqwK5YuMDJkycnTJhgNBqXL1+uVA1hYWFnz57duXPnAw888Pzzz1+9elW2t66qqpo5c2ZycnJERIRsbwrXoofpYa2jh+lhCcFOb3x9fYUQNTU19oM1NTUtW7Z00zvu2rXrlVde6du373vvvSd9TpK/BiFEmzZtfH19Q0NDMzIyKioqsrKyZCtj5cqVt2/fDg8PP3z48OHDhy9evGi1Wg8fPlxYWKjIr0Lr6GF6WOvoYXpYQeyK1Zt+/foJIW7dumUbMZvN1dXVvXr1csfbrV271mQyjR49etGiRYrUUFZWdvLkyfDw8KCgIGmkbdu2rVu3vnHjhmxlXLlypaysbMqUKfaDkydPHjFixDvvvCNPDXpCD9PDWkcP08MKYoud3hgMhh49euTk5NhG9u/fL4To37+/y99r27ZtJpMpJSXFfjaRuYbKyspp06bt2bPHNnL9+vXbt2936tRJtjLWrVt33s6vfvUrg8Fw/vz5JUuWyPmr0A16mB7WOnqYHlaSwpdbQbP98MMP9V4Yc/PmzbW1tV999dXAgQOnTp3q8vctLS3t2bPn008/vfPfnT59WrYaJFOnTo2IiPjzn/9stVqLiopGjBgRFRV148YNmcuwycrKqnthTJlr0BZ6mB7WOnqYHlYPgp3m1Z1QrFZrRkaG7d4pEydOdMe9Uz799FNjfebNmydbDZLbt2+/8cYbtgISEhK++eYb27OylWHjMKEoUoO20MP0sNbRw/SwerSwWq1KbzSEW0g3TunSpUtAQIAn1FBdXZ2fn9+tW7e2bdsqWMa9qKEGzVHDL40eVlUNmqOGXxo9rKoaZECwAwAA0AlOngAAANAJgh0AAIBOEOwAAAB0gmAHAACgEwQ7AAAAnSDYAQAA6ATBDgAAQCcIdgAAADpBsAMAANAJgh0AAIBOEOwAAAB0gmAHAACgEwQ7AAAAnSDYAQAA6ATBDgAAQCcIdgAAADpBsAMAANAJgp2uFBYWDh8+vGfPnn369Fm7dq3S5QBOo4ehGwsXLpw8ebLSVcDjEOz0w2KxTJo0KT4+/m9/+9u+ffu2b9++c+dOpYsCnKDyHs7IyJg+fbrSVUAbDh06tH37dqWrgCci2OnHlStX+vfvP23aNCFEcHBwVFTUkSNHlC4KcILKezg3N3fz5s1KVwENuHnz5sKFCydOnKh0IfBEBDv96NSp04oVK7y8vIQQ33333alTpyIjI5UuCnCCynt4zpw5H374odJVQAPmzp07YcKEzp07K10IPBHBTodefPHF2NjYn//852PGjFGwDIvFouC7Q9PU0MM1NTUOI1FRUc8++6wixUBDsrKyqqurExMTlS7k/zAbexSCneoUFxffvHnTYbC2tvbYsWMO48XFxYd/UlZWZhtfunRpVlZWWVnZjBkz5Ki4jr179/bs2dPb29tgMIwbN27Xrl3t2rXLy8tTpBjIT7s9PHbs2LFjx+7evfs///M/DQaDr6/v9OnTy8vLpWfHjRvXqVMnOeuBUnA7I18AABveSURBVJrcwxcvXly/fv2yZctkLPaexo4dO27cuHXr1vn6+rZu3Zpj/jyFFWpy7dq1vn37HjhwwH4wMzMzNDTUaDQajcZXX331xx9/lMYXLFjQ8ydHjx51eKmjR48ajcY7d+7IVPpPsrOzhRCPPvpodnb2zp07+/btGxQUJITIycmRuRIoQtM9/MwzzwQHB/v4+CxZsmTfvn2LFi2Smll69rnnnvP395etGCilOT08ZcqUESNGpKWlpaWljRs3bvDgwWlpafLPw5Jnnnmme/fuPj4+zz//fHR0dH5+viJlQGYEOxUpKioaOHCg0Wi0n1B2795tNBo//vjj2trac+fODRw4MDk5ud5vz8/Pnz59uu3h6dOnFQl2Xbt2ffjhh6uqqqSH//znPzt27Eiw8xBa7+FnnnlGCJGZmWkbkTa97Nixw0qw8wzN7OE//OEP837ywgsvxMbGzps3T8FgJ4TYuHGjIu8OpbArVhXMZvOaNWsSEhKkjVv2NmzYMGjQoJEjR3p5eYWFhaWmpubm5l66dKnuiwQHB+fl5X3yySfSC27YsCEyMtLX11eOH+AnX3/99TfffDNmzJhWrVpJI/7+/uPHj5ezBihCNz3cqlWrSZMm2R5OnTpVCCGVBH1zSQ+PHz/+7Z8kJCR069bt7bfflrmH7Xl5eb3yyitKvTsUQbBzr9LS0srKyrrjFy5csH9YUVGxdevWlJSUjRs32o9XV1cXFRXFxcXZRoYMGSKEqPcaEIGBgWvWrPnd734XFRXVr1+/qqqq1atXu+bHaLSioiIhRO/eve0Hw8LCZC4DLuRpPRwdHS2dlivx9/f38/P78ccfZS4DLiRnD6uNn5+fj4+P0lVAVvz/dq/Kysq333575cqVfn5+tsG33norNjY2NDTUNuLv75+Xl9e6dWv748eFECdOnBBCtG/f3jYiHdBdUFBQ79s99thjX3755c2bNwMCAgwGg4t/mKayX01Cczyth1u3bi3/m8KtZO5hm5EjR44cOdI1PwPQaKxx3atbt26vv/56amqq7fPiW2+9FRMTY//hTwhhMBjqXZ1I56g7fN7y8fG5e/duA2/atm1bpVJd165dhRDnzp2zH/z+++8VKQYu4Wk9fOrUKfuHlZWVlZWV/+///T9FioFLKNLDgFIIdm4XEhIyY8YMaU5ZuHBhTEzME088oXRR7hIaGtq1a9ePPvrozp07tsH33ntPwZLQfB7Vw//4xz/sL80j7ZVju4vWeVQPw8MR7OQgzSlPPfVURESEU7OJdMitw4VSa2pqWrZs6eISXScjI+Py5ctPPvlkbm7usWPHXnjhhaNHjypdFJrLo3p45MiRWVlZZ86cMZlMs2fPfuyxx55//nmli0JzeVQPw5MR7GSSlZWVmJiYk5NT7zG899KvXz8hxK1bt2wjZrO5urq6V69eri/RRZ588sk9e/Z88803TzzxRHR0dEFBwcKFC5UuCi7gIT3s7+8/Y8aMV199NSIiIiUlZdSoUdKlGaEDHtLD8HAEOznMnz8/NjZ24sSJDsd53JfBYOjRo0dOTo5tZP/+/UKI/v37u6VQF3n22WevX7/+1VdfFRcX5+fn//znP1e6IjSXR/Xw/Pnzb9++fejQoX/+859ZWVlt2rSRxnfu3PnPf/5T2drQZB7Vw5J9+/bRsR6IYOd2b7755uDBg6WjdLt16zZr1qw33nij8XPKhAkTDh48uGXLFovFcvbs2eXLl8fFxWni3tLh4eHSuRTQOg/s4ZYtW8bGxtqfRAlN88Aehsci2LnXkSNHnnjiCftzrzp37jx79uxPP/20ka8wbNiw//mf/1m2bFmPHj1GjRrVvXv3pUuXuqdYeJZ6b3xZFz0MraOH4VFaWK1WpWvA/Un3senSpUtAQIDStTjtwIEDJpPpnXfe6dOnj9K14F/Wr1+/evVq6XjwRx999N1333V3a2mih3/961+fO3dux44dShcCNdJEDwMEO8Dj7NmzZ9asWe+8887zzz9/4cKFqVOnhoeHZ2RkKF0XAKC5CHaAxxk2bNhDDz20YcMG6eHu3btTU1M/++wzjhkCAK3jGDs1anEPStcFPVD8xpf3am91kud3AgCuwr1im6i2tvavf/1rt27d2rZtW+8CISEhzr5mUVFRwwvYr2aMRqOzrw9FFBYWKl3Cv3HixpfuiTUa20fg8dkuxGhUWw83kjRhMlVCow3cZAS7pmjkgedONZPDtoG6u8gdFnBIgdLyISEhntbBKteEfO9ujb/xZfPX6PVu8Wr48A9V9TBb7IQQWo9F8reTqnoYKpyE3Y1dsU7bs2fPqlWr0tLSCgoKduzYUVxcPHfu3Ga+pm39Yf1J3WWs/67uK7Ro0aKoqIj9R1ADhz5soHUdqGqNaAUHYTtPVT0MD0Swc9qGDRsGDRo0cuRILy+vsLCw1NTU3NzcS5cuNf+VnZpDG558OWAI9yLDjS8b80EFAOAOBDvnuOPAc2kt2MyVXyM/ZHPwONx640v7niHPAYD8CHbOafyB54VFRaJFi8b8s0qHkzduYade0yX/XFuYx/1THxlufMlWOgBQCsHOOU4deC6s1ob/tRBC+nffJRX8ZyuSf034p05uuvGlS7Y9AwCag7NilafyFaHKy1M5dZ6QNWzYsKtXry5btmzx4sVCiJiYmObf+JK99gCgBgQ758hw4Dkgg+Tk5KSkJJff+JKPAVAPq9UqHfRJW8KjEOyc48IDz9lvBWV5e3v36dPHJS9FMwOASnCMnXNkOPAc0BZ2wgKAehDsnOamA88BLeLiJgCgKuyKdZpLDjxnIwf0hFQHACpBsGsKVx14zuoQAAC4EMGuiVx44DmgUWx4BgC14Rg7AM3ChmcAUA+CnQK4NgQAAHAHgh2ApmA/LACoEMEOQNOx4RkAVIVgJzf2wwIAADch2AFwGvthAUCdCHYAmogNzwCgNgQ7AAAAnSDYAQAA6ATBTlacOQEdoI2hFUajUXBIKDwMwQ4AAEAnCHYAAAA6QbADAADQCYIdACdwgB0AqBnBDgAAQCcIdgAAADpBsJMP+7AAAIBbEewAAAB0gmAHAFC74uLimzdvOgzW1tYeO3as7jjgyQh2ABqLwwmgiNLS0rFjx54+fdp+cP369eHh4YmJiQMGDBg/fnx5eblS5QGqQrADAKhXcXHx2LFjKyoq7Af37NmzatWqtLS0goKCHTt2FBcXz507V6kKAVUh2AEA1MhsNq9ZsyYhISEoKMjhqQ0bNgwaNGjkyJFeXl5hYWGpqam5ubmXLl1SpE5AVQh2AAA1qqio2Lp1a0pKysaNG+3Hq6uri4qK4uLibCNDhgwRQhw5ckTuEgH18VG6AAAA6uHv75+Xl9e6deuysjL78RMnTggh2rdvbxsxGAy+vr4FBQVylwioD8FOJhx1DgBOMRgMBoOh7rjFYhFC+Pj82/rLx8fn7t27MlUGqBi7YgE0Ch9OoEVSx0rdC3gCgh0AQEt8fX2FEDU1NfaDNTU1LVu2VKgiQEUIdgAALenXr58Q4tatW7YRs9lcXV3dq1cv5YoC1IJgBwDQEoPB0KNHj5ycHNvI/v37hRD9+/dXrihALQh2TWQ2m48dO3bx4kWlCwEAjzNhwoSDBw9u2bLFYrGcPXt2+fLlcXFxnTt3VrouQHmcFeu0ysrKhQsX7t27Vzozq0OHDkuWLImKilK6LgDwFMOGDbt69eqyZcsWL14shIiJiVm6dKnSRQGqQLBz2oIFCw4dOpSenj548OC///3vv/rVr6ZMmbJv377g4OB7fQunE0Lr6GEoqE2bNoWFhQ6DycnJSUlJ586d69KlS0BAgCKFASrErljnmM3mffv2TZ48OS4uzsvLq0OHDitXrqyqqpKO8AAAyMbb27tPnz6kOsAeW+ycU1VVtWLFioiICNvIgw8+KIQoLy9XrigAAAAhCHbOCggIGDp0qP1IVlaWECImJkahigAAAP6FXbHNcubMGZPJFB8fHxkZqXQtUJ2QkBClSwAAeBaCXUPMZnOZHYdnT548OWHCBKPRuHz5ckXKg8rVPdwbAAC3YldsQ7Kzs+fNm2d7mJ+f7+fnJ329a9eu+fPnR0dHm0wm2yCgS5wSCwBaQbBrSHR0dHp6uu2hdINCIcTatWtNJtPo0aMXLVqkUGkAAACOCHYNCQ4Ornt1um3btplMppSUlKSkpMa8CFs7AACAPAh2zrl+/fqSJUu6dOkSFBS0a9cu23jHjh3tr4ECAAAgP4Kdc44fP242m0tKSubMmWM/PmrUKIIdAKiQ1Wpt0aJFixYt2HMCT0Cwc05CQkJCQoLSVQAuYDabT506FRgY+MgjjyhdCwDANQh2gMeprKxcuHDh3r17LRaLEKJDhw5LliyJiopSui4AQHNxHTvA4yxYsODzzz9PT08v+P/t3X9MVXX8x/EPF653MmUy549izYZ6EVEUdCbliKFtGTZGP/yjLG2i/DD/QM1A6g/n0iXCuk6QcsvW0LFpIbHmljq7ttScA0IWcREwErc0vcagK1wu5/vH6Xu+Nyy/8eOec8/nPh/jj84HuOe167vry3vOPael5fz587NmzcrNze3u7jY6FwBgrCh2QGjxer1ff/315s2bV65cabFYHn/88dLSUo/Hc/r0aaOjAQDGikOxQGjxeDwHDhzw/6zPlClThBA9PT3GhQIAjA+KHRBaoqKiMjIy/FeqqqqEEKmpqQYlAgCMGw7FAiGtsbHR4XCsWrVq6dKlRmdB0ImLizM6AoCRodgBMvN6vW4/w7579erVjRs32u32kpKSf3sEbp0SylpbW42OAGBkOBQLyKy2tra4uFjbbGhoiIyMVP/71KlT7733XkpKisPh0BYBAKZGsQNklpKScujQIW3TZrOp/1FRUeFwONauXbtnzx6DogEAxh/FDpBZTExMTEzMsMVjx445HI5t27bl5OQYkgoAECAUOyC03Lp1a9++fbGxsTNmzDh16pS2PmvWLO53DABmR7ELLE48R7D54YcfvF5vR0fHu+++67/+6quvUuwAwOwodkBoycrKysrKMjoFACAguNwJAEBy6mET9RAKIDeKHQAAgCQodgAAAJKg2AEAAEiCYgcAACAJih2Af8X1egDAXLjcCQDAfBYvXuzxePxXjh49+vTTTxuVBwgSFDsAgMncuXPH4/Fs2LAhPj5eW5w7d66BkYAgQbEDAJhMY2OjECI7O3vatGn/8VcURQkLCwsLC+PUAsiNc+wAACbz888/T5o06b+3OiB0UOwAACbT1tb2xBNPrF+/Pj4+Pj4+ft26dZ2dnUaHAoICxQ4AYDKNjY0dHR1PPfVUZWXlnj17urq6Xnvttd9++83oXIDxOMcOAGAy77///mOPPbZgwQJ1Mykp6YUXXjh69GhhYaGxwQDDUewAACbz3HPP+W/Onj17zpw5v/zyi1F5gODBoVgAgJm43e7vvvvuzp07w9YtFv5GAyh2gcRV+wFg3N27dy87O7u6ulpb6e7u7ujoSEhIePQvqq/G6iszICuKHQDATGbPnp2enn706NHz588LIdra2rZs2TJt2rR169YZHQ0wHsUOwD9zuVyCt5wRlD788MP09PT8/Py4uLg1a9ZERkYeO3YsKirK6FyA8fjwxJj09PRcv349OTnZ6CAAEEKioqIOHDiwb9++5ubmOXPmTJ482ehEQLCg2I1JYWHhhQsXmpubjQ4CACHHarUmJSUZnQIILhyKHb2TJ0+eO3fO6BQAAAB/odiN0o0bN/bu3Zuammp0EAAAgL9Q7EZjaGho586dGRkZaWlpRmcBAAD4C8VuNCorK91ud1FRkdFBELzi4uLi4uKMTgHgb7iUHaTHhydGrKmpyeFwVFdXR0ZGGp0Fwau1tVUIQbcDAOiJYvcoXq+3t7dX24yOjvZ4PAUFBfn5+XwUCwAABBuK3aPU1tYWFxdrmw0NDWVlZX19fYmJiU6nUwjR3t6uKIrT6Zw5cybvzQAAAGNR7B4lJSXl0KFD2qbNZuvq6nK73bm5uf4/tnnz5szMzP379+seEAAA4P9Q7B4lJiYmJibGf+Xw4cNDQ0Pa5vHjx0tKShoaGiwWPoYCAAAMRrEbmfDw8PDwcG0zIiJCCGG1Wo1LBASE+rFBbhQLAObC+0wAgBDCFU8gN4rdmLz++uv/dqNYl8sleMMDAADoiGIHAAAgCYodAACAJCh2AAAAkqDYAfgHiqLY7XajUwABwecnIDGKHQAAgCQodgAAAJKg2AEAQg5HYyErih0AAIAkKHYAAACSoNgBAEIXR2MhGYodACAUcctHSIliBwAAIAmKHQAAgCQodgCAEMVFTyAfih0AAIAkKHYBof77jzNzASBwfD7f5cuX7969O/aH4k07SCPC6AAAAIzYxx9/fPDgwcHBQSHEM88889FHH0VFRY3icRRFodVBJrxjB4S0np6e+vp6o1MAI1NXV1dWVrZ79+6WlpYvvviira2tqKho1I/GmXaQCcUOCGmFhYVvvvmm0SmAkfnkk0+effbZV155xWKxLFiw4J133jl79mxnZ+cYHzbYul3YSBgdFsGCYgeErpMnT547d87oFMDI9Pf3u1yulStXaiurV68WQly8eHHUj6mdEj3uDWlE5WwsXW0sO5LD+P7BmRfn2AEh6saNG3v37k1NTb106ZLRWYARuHLlihBi+vTp2orVarXZbC0tLWN52DGebBeIYjGiT+DRbHgGVLxjJ5W4uDijI8AchoaGdu7cmZGRkZaWZnSWv2GG8f8aGhoSQkRE/O2NiYiIiIGBgWE/2epyibCw//6lCKGebTeKL/V3x/fL8AByfIUa3rELIEP+iuLvRfwXlZWVbre7qKiopqbmET/GDMPU4uz2UfyWy+Ua3e7so9odAq3V6AA6o9gFBFewQzBrampyOBzV1dWRkZGP+LHW1lB7PYQ52Gw2IYR6oRPN4ODghAkThv3kGGf4EYf2eJFH0KLYATLzer29vb3aZnR0tMfjKSgoyM/PT0pKMjAYMGpLliwRQty/f19b8Xq9/f39CxcuHN8d0d5gRhQ7QGa1tbXFxcXaZkNDQ1lZWV9fX2JiotPpFEK0t7criuJ0OmfOnMkxUJiC1WqNj48/c+ZMVlaWunL69GkhxLJlywzNBQSFMP5FAkisu7v7p59+0jbT09Pz8vLUSjdMZmbm/v37dYwGjF5dXd2OHTt27dr1xhtvNDc3b9myZeHChRUVFUbnAoxHsQNCi8/nUz9UqDp+/HhJSUlDQ4PFYgkPDzcwGDAiFRUV5eXl6pl2qamppaWlo7ulGCAZDsUCoSU8PNy/wKnXjLBarcYlAkYjPz8/Jyfn2rVrsbGxVDpAQ7EDAJhSeHj44sWLjU4BBBcOxQIAAEiCO08AAABIgmIng7a2trt37w5b9Pl8ly9ffnh93Hm93suXL7e3tz/8Ld0yCCF6enouXrzY09NjbAw1SX19vbEZTIcZFsywyTHDghkOEgpM7ubNm8nJyd98843/YmVl5fz58+12u91uf+utt/74449A7Lqvr2/Hjh3z5s1Td5SWlnbp0iWdMyiK8uDBgx07dtj/19atW/33pVsMTV5eXkJCgv+K/hnMhRlmhs2OGWaGgwfFztxcLteKFSvsdrv/C8pXX31lt9tPnDjh8/muXbu2YsWK/Pz8QOx9+/btycnJZ8+e9fl83d3d69evX7Ro0c2bN/XMoCjK7t27Fy1adOHCBUVR6uvrly9fvnXrVvVbesZQnThxwm63+7+g6J/BXJhhhRk2OWZYYYaDCcXOrAYGBg4ePJiQkPDyyy8Pe0FZs2bNpk2btM3a2lq73d7R0THuAebNm1dZWamt/P7773a7/ciRI7plUBRlcHBw/vz5paWl2kp5efm8efN8Pp+eMVSdnZ1JSUnZ2dn+Lyg6ZzARZljFDJsXM6xihoMK59iZVW9v7+eff75t27YjR474r/f397tcrpUrV2orq1evFkJcvHhxfAN4PJ4DBw68+OKL2sqUKVOEED09PbplEEKEh4c3NjZu2rRJW3nw4IHFYhE6PhWqoaGhnTt3ZmRkpKWlaYs6ZzAXZljFDJsXM6xihoMK17Ezq0mTJl24cGHixIlut9t//cqVK0KI6dOnaytWq9Vms7W0tIxvgKioqIyMDP+VqqoqIURqaqpuGbQHt1qtQ0NDvb29dXV1VVVVOTk5FotF5xiVlZVut7uoqKimpkZb1DmDuTDD/g/ODJsRM+z/4MxwkKDYmZX6f9HD6+rdotTbCWgiIiIGBgYCmqexsdHhcKxatWrp0qXqrUh1zvD9999nZ2cLIebMmaPeGlzPp6KpqcnhcFRXV0dGRvqvG/XHYQrM8DDMsOkww8Mww8GAQ7EYB1evXt24caPdbi8pKTEqw4IFC5qammpqaiZPnvzSSy/9+uuvuu3a4/EUFBTk5+cnJSXptlOML2aYGTY7ZpgZVlHsZGOz2YQQ6o2xNYODgxMmTAjQHk+dOrVhw4bk5ORPP/1U/XeS/hmEENHR0Tabbf78+eXl5b29vVVVVbrFKC0t7evrS0xMdDqdTqezvb1dURSn09na2mrIU2F2zDAzbHbMMDNsIA7FymbJkiVCiPv372srXq+3v79/4cKFgdhdRUWFw+FYu3btnj17DMngdruvXr2amJg4Y8YMdWXq1KkTJ068ffu2bjG6urrcbndubq7/4ubNmzMzMz/44AN9MsiEGWaGzY4ZZoYNxDt2srFarfHx8WfOnNFWTp8+LYRYtmzZuO/r2LFjDodj27Zt/q8mOmf4888/33777bq6Om3l1q1bfX19Tz75pG4xDh8+3Oxn165dVqu1ubl53759ej4V0mCGmWGzY4aZYSMZfLkVjNm9e/f+8cKYn332mc/n+/HHH1esWJGXlzfu++3u7k5ISHj++edr/q6+vl63DKq8vLykpKRvv/1WURSXy5WZmbl8+fLbt2/rHENTVVX18IUxdc5gLswwM2x2zDAzHDwodqb38AuKoijl5eXavVOys7MDce+UL7/80v5PiouLdcug6uvr2759uxYgKyvr+vXr2nd1i6EZ9oJiSAZzYYaZYbNjhpnh4BGmKIrRbxoiINQbp8TGxkZFRYVChv7+/oaGhrlz506dOtXAGP8mGDKYTjA8acxwUGUwnWB40pjhoMqgA4odAACAJPjwBAAAgCQodgAAAJKg2AEAAEiCYgcAACAJih0AAIAkKHYAAACSoNgBAABIgmIHAAAgCYodAACAJCh2AAAAkqDYAQAASIJiBwAAIAmKHQAAgCQodgAAAJKg2AEAAEiCYgcAACAJih0AAIAkKHYAAACSoNgBAABIgmIHAAAgCYodAACAJCh2AAAAkqDYAQAASIJiBwAAIAmKHQAAgCQodgAAAJKg2AEAAEiCYgcAACAJih0AAIAkKHYAAACSoNgBAABIgmIHAAAgCYodAACAJCh2AAAAkqDYAQAASIJiBwAAIAmKHQAAgCQodgAAAJKg2AEAAEiCYgcAACAJih0AAIAkKHYAAACSoNgBAABIgmIHAAAgCYodAACAJP4HQea+9H9QTYUAAAAASUVORK5CYII=" }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Total computing time : 0h00m09s\n" ] } ], "source": [ "dynare newkeynesian.mod" ] }, { "cell_type": "markdown", "id": "7de2d274-fd53-4eb7-9349-b4195a7b01d1", "metadata": {}, "source": [ "________________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "308dea48-f1c5-48bf-99d9-7d1c36eb4229", "metadata": {}, "source": [ "# 6. Two Agent New Keynesian Model" ] }, { "cell_type": "markdown", "id": "24832adc-a3b5-46f0-adaf-e67b1fe8d55b", "metadata": {}, "source": [ "Now we introduce two types of households, which differ in the access to financial markets. \n", "\n", "* household who can invest in bonds, this household is labeled as \"Ricardian\" or \"Non hand to mouth\".\n", "* household who does not have access to financial markets and just consumes disposable income, this household is typically labeled as \"hand to mouth\" or \"rule-of-thumb\", or \"non-ricardian\".\n", "\n" ] }, { "cell_type": "markdown", "id": "24e8f8f7-9266-440e-84df-b41f50ed88d8", "metadata": {}, "source": [ "Suppose percentage of hand-to-mouth household (HtM household) is $\\eta$, percentage of ricardian household is $1-\\eta$." ] }, { "cell_type": "markdown", "id": "159bf66d-ed30-40dd-b77a-ecd3045fd044", "metadata": {}, "source": [ "**changes 1: HtM household**" ] }, { "cell_type": "markdown", "id": "9db416b0-1599-497d-86ac-f1714733ae3c", "metadata": {}, "source": [ "Since HtM household does not have access to financial market, their behavior has nothing to do with social investment $i_t$, bonds $b_t$ and monopoly profit $\\Gamma_t$. So, the behavior of ricardian households is the same as that in traditional New Keynesian model above. And for HtM households, they solve the following problem." ] }, { "cell_type": "markdown", "id": "ff5a770f-4250-4faf-a14e-195c82672136", "metadata": {}, "source": [ "$$\n", "\\begin{gathered}\n", "\\max _{\\left\\{c_{t}^{r}, h_{t}^{r}\\right\\}_{t=0}^{\\infty}} \\mathbb{E}_{0} \\sum_{t=0}^{\\infty} \\beta^{t}\\left(\\frac{c_{t}^{r(1-\\sigma)}}{1-\\sigma}-\\kappa_{L} \\frac{h_{t}^{r(1+\\varphi)}}{1+\\varphi}\\right) \\\\\n", "\\text { s.t. } c_{t}^{r}=w_{t} h_{t}^{r}-t_{t}^{r}\n", "\\end{gathered}\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "id": "9bfd3b00-eceb-4b76-9c1e-4945637b7492", "metadata": {}, "source": [ "Foc with respect to labor:\n", "\n", "$$\n", "\\begin{align*}\n", "\\kappa_{L}\\left(h_{t}^{r}\\right)^{\\varphi}\\left(c_{t}^{r}\\right)^{\\sigma}=w_{t} \\tag{16}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "d6a66b06-4fcb-4009-b41f-9376bc59b1f2", "metadata": {}, "source": [ "Also, from budget constraint:\n", "\n", "$$\n", "\\begin{align*}\n", "c_{t}^{r}=w_{t} h_{t}^{r}-t_{t}^{r} \\tag{17}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "94c4fa54-904a-49be-8ea3-f704b4aea9bf", "metadata": {}, "source": [ "**change 2: market clear condition**" ] }, { "cell_type": "markdown", "id": "efb9bad4-6479-4241-b09a-e0e73b4dedd8", "metadata": {}, "source": [ "Now we have two types of household, use superfix \"r\" for ricardian households, use superfix \"h\" for HtM households. " ] }, { "cell_type": "markdown", "id": "8a0491e4-2eb1-4092-acb0-1e10d5cb4373", "metadata": {}, "source": [ "Aggregate Consumption:\n", "\n", "$$\n", "\\begin{align*}\n", "c_{t}=(1-\\eta) c_{t}^{r}+\\eta c_{t}^{h} \\tag{18}\n", "\\end{align*}\n", "$$\n", "\n", "Aggregate Labor:\n", "\n", "$$\n", "\\begin{align*}\n", "h_{t}=(1-\\eta) h_{t}^{r}+\\eta h_{t}^{h} . \\tag{19}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "12a721fb-b591-4171-969e-dd5bf1c190b9", "metadata": {}, "source": [ "Aggregate Capital and Investment:\n", "\n", "$$\n", "\\begin{align*}\n", "k_{t} & =(1-\\eta) k_{t}^{o} \\tag{}\\\\\n", "i_{t} & =(1-\\eta) i_{t}^{o} \\tag{}\n", "\\end{align*}\n", "$$\n", "\n", "Aggregate Public Bonds (in Real Terms):\n", "\n", "$$\n", "\\begin{equation*}\n", "d_{t}=(1-\\eta) \\frac{b_{t}}{p_{t}} \\tag{}\n", "\\end{equation*}\n", "$$\n", "\n", "Aggregate capital and investment and aggregate public bonds can introduced into equilibrium condition system.\n", "\n", "When introduced, we add one variable and one equation, since aggregate capital, investment and bonds only cover ricardian households.\n", "\n", "We can also ignore these variables, and delete them from equilibrium system. There is no difference essentially. " ] }, { "cell_type": "markdown", "id": "c1a87286-0e7d-4c6c-8553-6dda75e43f1a", "metadata": {}, "source": [ "Finally, the clearing in the good market implies:\n", "\n", "$$\n", "\\begin{align*}\n", "y_{t}=c_{t}+i_{t}+g_{t}+\\frac{\\kappa_{P}}{2}\\left(\\pi_{t}-\\bar{\\pi}\\right)^{2} y_{t} \\tag{12}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "a718a346-32d7-46ac-8d8b-c3959b1ff2a3", "metadata": {}, "source": [ "Again, this equation is essentially same as budget constraint for ricardian households, so we delete one of them. Here budget constraint is deleted. " ] }, { "cell_type": "markdown", "id": "d0a3f66a-408a-4126-9e44-c73f3b447dfa", "metadata": {}, "source": [ "**change 3: tax policy**" ] }, { "cell_type": "markdown", "id": "0ff55e2c-9986-45ca-a297-5b0a9f75383a", "metadata": {}, "source": [ "The government finances public expenditure $ g_{t} $ by raising lump-sum taxes and public debt $ d_{t} $:\n", "\n", "$$\n", "\\begin{equation*}\n", "g_{t}+\\frac{r_{t-1}}{\\pi_{t}} d_{t-1}=(1-\\eta) t_{t}^{r}+\\eta t_{t}^{h}+d_{t} \\tag{20}\n", "\\end{equation*}\n", "$$\n", "\n", "where $ g_{t} $ follows an autoregressive process:\n", "\n", "$$\n", "\\begin{equation*}\n", "\\log \\left(g_{t}\\right)=\\left(1-\\rho_{g}\\right) \\log (\\bar{g})+\\rho_{g} \\log \\left(g_{t-1}\\right)+v_{t}^{g} \\tag{15}\n", "\\end{equation*}\n", "$$\n", "\n", "and $ v_{t}^{g} \\sim N\\left(0, \\sigma_{g}^{2}\\right) $ is a public spending shock. " ] }, { "cell_type": "markdown", "id": "1959ad71-8899-43a1-8ee0-becb2830ffeb", "metadata": {}, "source": [ "Lump-sum taxes are set according to the following rules:\n", "\n", "$$\n", "\\begin{align*}\n", "& t_{t}^{h}-\\bar{t}^{h}=\\phi_{d}\\left(d_{t-1}-\\bar{d}\\right)+\\phi_{g}\\left(g_{t-1}-\\bar{g}\\right) \\tag{21}\\\\\n", "& t_{t}^{r}-\\bar{t}^{r}=\\phi_{d}\\left(d_{t-1}-\\bar{d}\\right)+\\phi_{g}\\left(g_{t-1}-\\bar{g}\\right) \\tag{22}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "id": "27af0dd0-405f-443e-a5f1-b93ce30d3399", "metadata": {}, "source": [ "Finally, we get an equilibrium system of 22 equations. The first 15 equations are almost the same as those in traditional New Keynesian model, except that superfix should be added for ricardian households only when talking about consumption and labor. " ] }, { "cell_type": "markdown", "id": "c168b97f-e325-4033-b7e5-06dc4a34adcf", "metadata": {}, "source": [ "The newly added 7 equations are:\n", "\n", "$$\n", "\\begin{align*}\n", "\\kappa_{L}\\left(h_{t}^{r}\\right)^{\\varphi}\\left(c_{t}^{r}\\right)^{\\sigma}=w_{t} \\tag{16}\n", "\\end{align*}\n", "$$\n", "\n", "$$\n", "\\begin{align*}\n", "c_{t}^{r}=w_{t} h_{t}^{r}-t_{t}^{r} \\tag{17}\n", "\\end{align*}\n", "$$\n", "\n", "$$\n", "\\begin{align*}\n", "c_{t}=(1-\\eta) c_{t}^{r}+\\eta c_{t}^{h} \\tag{18}\n", "\\end{align*}\n", "$$\n", "\n", "$$\n", "\\begin{align*}\n", "h_{t}=(1-\\eta) h_{t}^{r}+\\eta h_{t}^{h} . \\tag{19}\n", "\\end{align*}\n", "$$\n", "\n", "$$\n", "\\begin{equation*}\n", "g_{t}+\\frac{r_{t-1}}{\\pi_{t}} d_{t-1}=(1-\\eta) t_{t}^{r}+\\eta t_{t}^{h}+d_{t} \\tag{20}\n", "\\end{equation*}\n", "$$\n", "\n", "$$\n", "\\begin{align*}\n", "& t_{t}^{h}-\\bar{t}^{h}=\\phi_{d}\\left(d_{t-1}-\\bar{d}\\right)+\\phi_{g}\\left(g_{t-1}-\\bar{g}\\right) \\tag{21}\\\\\n", "& t_{t}^{r}-\\bar{t}^{r}=\\phi_{d}\\left(d_{t-1}-\\bar{d}\\right)+\\phi_{g}\\left(g_{t-1}-\\bar{g}\\right) \\tag{22}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "id": "a9f81aca-bc1c-4200-9294-be7fdd04b07d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Starting Dynare (version 6.2).\n", "Calling Dynare with arguments: none\n", "Starting preprocessing of the model file ... \n", "WARNING: twoagent.mod:13.1-48.1: Symbol c_r declared twice. \n", "Found 31 equation(s). \n", "Evaluating expressions... \n", "Computing static model derivatives (order 1). \n", "Normalizing the static model... \n", "Normalization failed with cutoff, trying symbolic normalization... \n", "Finding the optimal block decomposition of the static model... \n", "6 block(s) found: \n", " 5 recursive block(s) and 1 simultaneous block(s). \n", " the largest simultaneous block has 17 equation(s) \n", " and 17 feedback variable(s). \n", "Computing dynamic model derivatives (order 1). \n", "Normalizing the dynamic model... \n", "Finding the optimal block decomposition of the dynamic model... \n", "4 block(s) found: \n", " 3 recursive block(s) and 1 simultaneous block(s). \n", " the largest simultaneous block has 19 equation(s) \n", " and 18 feedback variable(s). \n", "Preprocessing completed. \n", "Preprocessing time: 0h00m00s.\n", "\n", "STEADY-STATE RESULTS:\n", "\n", "c \t\t 0.602158\n", "rk \t\t 0.035101\n", "rr \t\t 1.0101\n", "w \t\t 1.66667\n", "h \t\t 0.333333\n", "y \t\t 1\n", "k \t\t 7.91367\n", "q \t\t 1\n", "i \t\t 0.197842\n", "lambda \t\t 1.66069\n", "r \t\t 1.0101\n", "pi \t\t 1\n", "mc \t\t 0.833333\n", "g \t\t 0.2\n", "a \t\t 1.04381\n", "c_h \t\t 0.602158\n", "c_r \t\t 0.602158\n", "h_h \t\t 0.333333\n", "h_r \t\t 0.333333\n", "t_r \t\t -0.0466027\n", "t_o \t\t 0.527411\n", "d \t\t 4\n", "clog \t\t -0.507235\n", "wlog \t\t 0.510826\n", "hlog \t\t -1.09861\n", "klog \t\t 2.06859\n", "ilog \t\t -1.62029\n", "c_h_log \t\t -0.507235\n", "c_r_log \t\t -0.507235\n", "h_h_log \t\t -1.09861\n", "h_r_log \t\t -1.09861\n", "\n", "EIGENVALUES:\n", " Modulus Real Imaginary\n", " 0.1366 0.1366 0\n", " 0.534 0.534 0\n", " 0.8595 0.8595 0\n", " 0.9 0.9 0\n", " 0.9 0.9 0\n", " 0.9383 0.9383 0\n", " 1.071 1.071 0\n", " 1.09 1.047 0.3041\n", " 1.09 1.047 -0.3041\n", " 1.238 1.238 0\n", " 2.536e+16 2.536e+16 0\n", " 8.51e+18 8.51e+18 0\n", "\n", "There are 6 eigenvalue(s) larger than 1 in modulus for 6 forward-looking variable(s)\n", "The rank condition is verified.\n", "\n" ] }, { "data": { "image/png": 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gaa2eP8l20D+CnS/19fVCiK+//vo//uM/lCSXlJQ0Y8aMXbt2TZ482fOZNputpKREiVzKSKg/80wrOqcciEm8A0yGbAed4+QJXzp06CCEmDx5sro+N2rUqO9973sffPBBk8/X5kPOYbwIES6sA3ML1tHP5DnoGcHOl549ewoh2rdv7zkYERHh4494XdYyRMh2ACAR34KgWwQ7X+69995u3bodPXpUHfn73/9eWVk5ZMgQiVUp+MoIAP4L0c3ByHbQG4JdC55++un8/PycnByn01leXr5o0aKuXbtOmDBBdl1C8JURgZB4WzzAlNhzAn3i5IkWPP7447du3dq4caPdbhdCxMXFbdu27fvf/77sur6DY3jh28GDB9euXfvVV18JIbp27bp27doHHnhAdlGAdkKUvbgEFXSIFbuWTZky5f333z906NDbb7994MCBvn37yq7oW3xlRIvaeFs8wDRC8QWYPSfQG4KdXywWS9++fbt16ya7kCawVgffdHJbPMDcyHbQCXbFmgFXLUZz/L8tnoJegvmE6LQJFVe2g64Q7EyFaQVe/LwtHoC24GA76AfBziT4yogm+XlbPKBJ3DolUMzAkI5gZx58ZURj/t8WD2ispKTE6Nku1PthVXy7hk7wld1UOD8LXgK9LR6AViPPQQ8IduZEtoOiFbfFA9BqfLuGdAQ7s+HKdvCk59viASbGDAxZCHYmxO4AeAr0tnjqkoMnDesFgkazA+w8MQNDLk6eMCeuRgZVUG6L55ntaCrAN2ZgSESwMzlmFgghpkyZ8q//+q9lZWXf+973/LmBSuOe8Qx2UlZBACNiBob2CHamxbn38KTcFq/Vf9yzhegroEVcfwqycIydmXEiBUKBvoIh6GRpmY8JNEawMznpkxpMyTPbsd0CmsT0CykIdubHdZUQCm63m6U7wDemX2iPYBdGmFwQdGQ7wB98QKAZgl1YYOuL0KG7oEM6OcBOJzUgrBDswgWTC0KHbAf4wA5ZaIlgF0aYXBA6ZDugRXw6oAGCXXgh2yF0yHZAc9hnAs0Q7MIUm16EAtkOeqDP9uN7NbRBsAs7bHoRUjQYdEK3i2R8NBBSBLtwxKYXIUWDAU3SbdaEmRDsAlBZWXnu3DnZVQQH8wtCiltTAD7woUDoEOwC8Nxzz02dOlV2FUHDAR8IKW5NATTGl2qEGsHOX7t37z5x4oTsKkKCjS5Ch2wHeOFLNUKKYOeXTz/9dO3atcnJybILCTI2utAAbQY0iU8EQoFg1zKXy7Vs2bK0tLSUlBTZtQQfG11ogEPuEJDS0tIbN254DTY0NBQWFjYe96Kfm4n5oPPyYGgEu5bl5uZWVFSsWLFCdiGhQrYLkbi4ONkl6AiH3MFP5eXlTz75pNeZaq+88kp8fPy0adNGjRr1s5/9rLKyUlZ5wcIOWYQIwa4FFy5csNvt69evj46Oll1LCPH1MRRKSkpkl6A7ZDv4Vlpa+uSTT1ZVVXkOHjx4cOPGjatXry4uLt6zZ09paamZvmnzWUBwEex8qa2tXbRoUUZGRkJCguxaQo6vj+FAD5fsYbcsmuR0Ol9++eX09PTY2Fivh7Zs2TJmzJhJkyZZLJZBgwYtXbo0Pz//ypUrUuoMIr5RIxQIdr5kZWVVV1fHx8cXFBQUFBSUlZW53e6CggJzr8SwrTUxnVyyh92yaKyqqur1119fvHjx1q1bPcfr6uocDkdqaqo6Mm7cOCHEqVOntC4xBPhGjaCLlF2Arl29erWiomLevHmeg3PmzJk4ceL69etlVRU6brdbmV/atWvHV0nzUS7ZY7VaZRfyXzz7TbB6EfY6dep08uTJjh07VlRUeI6fOXNGCNG1a1d1xGq1RkVFFRcXa11iKDHrIlgIdr5s3rzZ5XKpP7755puZmZlFRUUWi2lXOsl2ZqVesuf06dOya/mW53IF8S7MWa3WJr91KJNwZOR3tlaRkZG3b99u/GQjdpE66yLowvMMNtMGlKCIiIiwelBmFqvVGhERIbu0EGIfmfno/JI9XntmaTyEG3bIhoi5j5tqDsEOTSDbmYwhLtnjucpCvIMqKipKCFFfX+85WF9f3759e0kVhRBtj7Yj2AVgypQply5dkl2FRsh2pmGgS/Z4Lt0J4p0O6GFP1vDhw4UQN2/eVEecTmddXd3gwYPlFRV8xtp9DD0j2KFZZDsTMOIle4h3+qGHPVlWq7V///7Hjx9XR44cOSKEGDFihLyiQoIdsggKgh18IdsZnXEv2UO8g2rmzJknTpzYvn27y+W6cOFCZmZmampqr169ZNcVKrQ62oKzYtECztgyNKNfssfrq4Xaiuy3Civjx4+/du3a+vXr165dK4RITk5+8cUXGz/N4XAIg/cG8y3ajmCHlilzDRdAMSLTXLLHay+VEa9qAT/deeedjVeUMzIy5s6de/Hixd69e8fExEgpTBvMt2gjgh38wlxjUBEREZ5X51Ev2SOvojZpMt4JEl54iIiIGDp0qOwqtMN8i9Yx2Ld2SMSBvdAJ9zfUkXbfkFgVECwc3Iy2INghAGQ7ozPZJXtIeDAr1urQagQ7BIZsBx0i4cGs6GEEimCHgJHtoFskvLBlvvNp2CGL1iHYoTXIdtA5Eh5MwEw5FZoh2KGV1GzHlhJ65iPh0brQP75FI1AEO7QeewpgII0TnmAZz0RMv7hFl8JPBDu0CdkOhkPCMyubzSa7hJBgmkVACHZoKyYdGJTbgzpIwoMOmX49EkFEsEMQkO1gdByKB53jYDv4iWCH4CDbwRzYUQudow/hG8EOQUO2g5mQ8KA3zLHwB8EOwcS8A/PhUDzoBwfboUWRsguA2Xhd345pCGbS+KuLZ7aj26EBt9utTLD0G5rEih1CgqU7mBs7aiERJ1LAB4IdQoVsh3BAwoNE9BgaI9ghhMh2CB8cigctMbuiOQQ7vzidzsLCwrKyMtmFGI/n7MMEhDBBwoMGyHZoEidPtKCmpmbVqlWHDh1yuVxCiG7duq1bty4pKUl2XUbieTgIB/wirHCyBUJKOZFCdhXQF1bsWrBy5co///nPmzZtKi4ufvvtt3v06DFv3rzy8nLZdRkPXy4RzjgUDyHCiRTwQrDzxel0Hj58eM6cOampqRaLpVu3bllZWbW1tUeOHJFdmiGxWxYg4SHoyHbwxK5YX2prazds2JCQkKCO3HHHHUKIyspKeUUZG7tlZXE6nR988EGXLl3uvfde2bVAiGbWsNX/56OBVmBShSDY+RYTE5OWluY5kpeXJ4RITk6WVJFJqMeFcBFjDXCcqM55nWPh9T98OuAPz0mVnglz7IoNwPnz5+12+9ixYxMTE2XXYniee6PMugchLi5OdglCcJyoofg4ndasHxMEi+lnVPiJYOevs2fPzpw502azZWZmyq7FPMx91F1JSYnsEjhO1Kg4FA+tQLaDINj5ad++fdOnTx82bNi2bduio6Nll2Mq4bB0J5FynOj48ePVEY4TNRYSHgLCdAqOsWtZTk6O3W7/6U9/umbNGtm1mBZH3YUIx4mahu9D8QSfGnyD4+3CHMGuBTt27LDb7YsXL547d67sWkzO64RZwYYqBHwfJxoXF6eH3cdokTZn1OrkIFG0AtkunBHsfPn888/XrVvXu3fv2NjYffv2qeM9evTwvAYKgsjzQupMScF19uzZuXPn+jhOlFRnOL4TnmhbyFP6gXhnUGS7sEWw8+W9995zOp2XL19evny55/gTTzxBsAsdlu5CYd++fb/61a9Gjhxpt9s5TtR8mtxRK7hsSngj24Ungp0v6enp6enpsqsIU8S7IOI40bAS0mU8GAvZLgwR7KBrxLu24zjRsMUyHgTZLvwQ7GAAXgfeCTZIfuM4UShYxgtnZLuwQrCDMXjd5Zp45yeOE4WXFpfxBJ8sM+KSUuGDYAcjId4FiuNE4YM/Ic9ms2laE0LG68gWZk6z4s4TMJ4mb6YpsR7ABNweZNeCEOLWFKZHsINREe+AECHkmRvZztwIdjA2r80P99AEgBaR7UyMYAeTYAEPAPynzpnMliZDsIOpNBnvmLMAoEks3ZkPwQ4m1PjwIOIdADTJ61AWucWg7Qh2MDMW8ACgRV5HKsstBm1EsIP5NbeAx/wFGEhDQ0NhYeGNGzdkF2JaLN2ZAxcoRhhp/JWUm2YChvDKK6+89NJL9fX1Qoj777//t7/9bUxMjOyiTIiLGJsAK3YIRz7W8PieCujNwYMHN27cuHr16uLi4j179pSWlq5YsUJ2UWbG0p2hEewQ1pq8CisJD9CVLVu2jBkzZtKkSRaLZdCgQUuXLs3Pz79y5Yrsusys8fVB5dYD/xHsACGaudQ+y3iAdHV1dQ6HIzU1VR0ZN26cEOLUqVPyigoXXFvAiDjGDvDW5NlhXjMah54A2jhz5owQomvXruqI1WqNiooqLi6WV1QY8TzqTv0fJkA9I9gBzfL6tur5kOePzHFA6LhcLiFEZOR3tlaRkZG3b9/2emaJwyFYUgoN7znOOO9ziewCtEewA/ziZ8gT5DxAkjibraQkDLfjWjPWjBcXFxduPcExdkDA3N/l9ShH5gFBFBUVJYRQLnSiqq+vb9++vaSKwh339dE5VuyAtmp8Uq2sSgDzGT58uBDi5s2b6ojT6ayrqxs8eLC8ouB9LDLXBNUPVuyAIPOxmAcgUFartX///sePH1dHjhw5IoQYMWKEvKLwLe7rozcEOwCArs2cOfPEiRPbt293uVwXLlzIzMxMTU3t1auX7LrwLe7cqB8EO79wj0IYHT0M4xo/fvwvfvGL9evX9+/f/4knnujXr9+LL74ouyg0zccl3wl52uAYu5Zxj0IYHT0Mo8vIyJg7d+7Fixd79+5N9+pfc5cR4EJRGmDFrgXcoxBGRw/DHCIiIoYOHUqqMxx/LiDAYl4QEexawD0KYXT0MAA98H1iWbtGtK/QHAh2vnCPwoDExcXJLuG/6KcS6ejhgOinc/RTCYxFP53juxJ3I42f0zjqEfv8QbDzxRD3KNTPxxg6RA8DGqCH286fqOfJd+xTORwOberXD06e8MUQ9ygsEXq5bR+VNFYi++hgejggVNKY9B4OiMSApZ9sZ5pKbDabj0fDMLH5iWAXJIaa+4Am0MMwOG4UCwh2xfrGPQphdPQwAIQVgp0v3KMQRkcPA0BYIdj5wj0KYXT0MACEFYJdC7hHIYyOHgaA8NGOe3q0KCcnJzs7WzlKKTk5OSsri0ufw1joYQAIEwQ7vzQ0NHCPQhgaPQwA4YBgBwAAYBIcY2dIpaWlN27c8BpsaGgoLCxsPB4iTqezsLCwrKys8UMaV1JZWXnq1KnKykrplaj1nDt3Tg+V6Bk97IkeNiJ62BM9rCONb+IBnbt+/fqwYcOOHTvmOZibmztgwACbzWaz2WbMmPH111+HroDq6uolS5b069dPebmUlJTTp09LqeTWrVtLliyxfWPBggWeL6dlJZ7mz58/cOBAzxFZlegWPayihw2KHlbRw3pDsDMYh8MxevRom83mOaEcOHDAZrPt2rVLOY5q9OjRGRkZoavh2WefHTZsWH5+fkNDQ3l5+bRp04YMGXL9+nXtK1m9evWQIUNOnjzpdrvPnTuXlJS0YMEC5SGNK1Ht2rXLZrN5TiiyKtEtetgTPWxE9LAnelhvCHaGcfv27ZdeemngwIGPP/6414Ty6KOPzp49W/1x//79Npvt8uXLISqjX79+ubm56sg//vEPm822detWjSupr68fMGBAVlaWOpKdnd2vX7+GhgaNK1FduXIlISFh1qxZnhOKlEr0iR72Qg8bDj3shR7WIY6xM4yqqqrXX3998eLFW7du9Ryvq6tzOBypqanqyLhx44QQp06dCkUZtbW1GzZsGD9+vDpyxx13CCEqKys1riQiIuL8+fOzZ89WR27dumWxWITm74nC5XItW7YsLS0tJSVFHZRSiW7Rw17oYcOhh73QwzoUKbsA+KtTp04nT57s2LFjRUWF5/iZM2eEEF27dlVHrFZrVFRUcXFxKMqIiYky/SpHAAAgAElEQVRJS0vzHMnLyxNCJCcna1yJ8vutVqvL5aqqqjp48GBeXt7cuXMtFov2lQghcnNzKyoqVqxYsXfvXnVQSiW6RQ83Rg8bCz3cGD2sNwQ7w1A+PI3HXS6XECIy8jv/lJGRkbdv39agqvPnz9vt9rFjxyYmJhYUFEip5N133501a5YQok+fPunp6ULGe3LhwgW73b5z587o6GjPcbn/OnpDDzeHHjYKerg59LB+sCsWrXf27NmZM2fabLbMzEyJZQwaNOjChQt79+79/ve//9hjj127dk3jAmpraxctWpSRkZGQkKDxS6ON6GEFPWxc9LCCHlYR7AwvKipKCKHcLUpVX1/fvn37kL7uvn37pk+fPmzYsG3btilfj2RVcuedd0ZFRQ0YMCA7O7uqqiovL0/jSrKysqqrq+Pj4wsKCgoKCsrKytxud0FBQUlJiaz3xFjoYXrY6Ohhelg/2BVreMOHDxdC3Lx5Ux1xOp11dXWDBw8O3Yvm5OTY7faf/vSna9askVVJRUXF2bNn4+PjY2NjlZHOnTt37Njxiy++0LiSq1evVlRUzJs3z3Nwzpw5EydO/Pd//3ctKzEoepgeNjp6mB7WD1bsDM9qtfbv3//48ePqyJEjR4QQI0aMCNEr7tixw263L1682HM20b6Smpqap59++uDBg+rI559/Xl1d3bNnT40r2bx58yUPv/zlL61W66VLl9atW6f9v44R0cPqCD1sUPSwOkIPyyf5cisI3FdffdXkhTFfe+21hoaGDz/8cPTo0fPnzw/Rq5eXlw8cOPDhhx/e+13nzp3TuBK32z1//vyEhIS//OUvbrfb4XBMnDgxKSnpiy++0L4ST3l5eY0vjCmlEt2ih1X0sEHRwyp6WG8IdsbTeEJxu93Z2dnqzVJmzZoVupul/OEPf7A15fnnn9e4ErfbXV1d/eyzz6o1pKenf/LJJ+qjWlbiyWtCkViJbtHDKnrYoOhhFT2sN+3cbrfsRUMEh3KnlN69e8fExIRVJXV1dUVFRX379u3cubPcSnzQTyV6pp93iR5uTD+V6Jl+3iV6uDH9VBJSBDsAAACT4OQJAAAAkyDYAQAAmATBDgAAwCQIdgAAACZBsAMAADAJgh0AAIBJEOwAAABMgmAHAABgEgQ7AAAAkyDYAQAAmATBDgAAwCQIdgAAACZBsAMAADAJgh0AAIBJEOwAAABMgmAHAABgEgQ7AAAAkyDYGVhJScmECRMGDhw4dOjQnJwc2eUAAaOHYXT0MPSGYGdULpdr9uzZY8eO/dvf/nb48OGdO3fu3bs3FC9kt9sXLFjg49FFixaF4nVhepr1sBAiOzu7uTamh9FqWvZwi+hkKAh2RnX16tURI0Y8/fTTQoju3bsnJSWdOnUqFC907Nix1157zcejb7zxRiheF6anWQ8LIfLz85trY3oYraZlD7eIToaCYGdUPXv23LBhg8ViEUJ8+eWXH3zwQWJiouyigADQwzA6ehg6RLAzvClTpqSkpPzLv/zL5MmTQ/1aLpfL5XL5+cz6+vq2/x6EAy172E80MAKiwx5W+O5kQTObEcFOstLS0hs3bngNNjQ0FBYWeo2XlpYWfKOiokIdf/HFF/Py8ioqKhYuXBi6Ov/85z8PGTIkIiLCarUmJyd/8sknzT3znXfeSU5OtlqtVqu1a9euK1euvH37tvrooUOH+vfvr/ye9PT0N99886677srPzw9d5Qg1o/SwJ7vdftddd/385z9v/BANHIb03MNjx44dMmSI+mNlZeVdd92VnJysjjgcjrvuumvz5s1ef9B3Jwua2cTckOf69evDhg07duyY52Bubu6AAQNsNpvNZpsxY8bXX3+tjK9cuXLgN06fPu31q06fPm2z2W7duhX0Ih955JHIyMgOHTo888wzb7311ooVK4QQvXr1Uh/t3Lmz+uQ//elPFoulV69eubm5e/bsmTlzphDiwQcfVB5VDiuOj4/fsWPHjh07hg4d2qFDByHE4cOHg142tGGIHna73T/5yU86deqk/P+mTZuEEDNmzFB+9OxhGjgM6byHX3jhBSFESUmJ8uNbb70lhLBYLGpJGzduFEKUlZX538lumtnUCHbSOByO0aNH22w2zwnlwIEDNptt165dDQ0NFy9eHD16dEZGRpN/vKioaMGCBeqP586dC12wE0K88cYb6khGRoYQ4sMPP3Q3CnY9evSIjY394osv1JHVq1cLIV599VW3233PPff06dOnurpaeai2tnbAgAFMJcZllB52ewQ75YIUs2fPVh/y7GEaONzov4ffe+89IUROTo7y47Rp0/r06SOE2LNnjzLy4IMPxsfHuwPpZDfNbGrsipXA6XS+/PLL6enpsbGxXg9t2bJlzJgxkyZNslgsgwYNWrp0aX5+/pUrVxr/ku7du588eXL37t3KL9yyZUtiYmJUVFQoCrZYLP/2b/+m/nj//fcLIa5fv+71tDNnznz22WfTpk3r0qWLOrhkyRKLxXLw4MEzZ85cu3Zt5syZ0dHRykMdOnRQMiIMx3A9rHjllVcyMjIyMjK2bNnS+FEaOKwYpYdHjBgRGxur7iE9duzY5MmTo6Ojjx8/LoS4fft2QUHB+PHjPf+I705WnkAzmxjBLpjKy8tramoaj3/00UeeP1ZVVb3++uuLFy/eunWr53hdXZ3D4UhNTVVHxo0bJ4Ro8vz5Ll26vPzyy7/5zW+SkpKGDx9eW1v70ksvBeev0Uh0dLRy2pfC8/89ffrpp0KI4cOHe/3ZmJiYjz76SHnUZrN5PtqjR49gF4s2MWsPKzXPmzdPCFFSUtLkE2hgczBfD0+YMOGPf/yjy+X6+OOP/9//+38//OEPH3744ZMnTwohDh065HK5JkyY4Pl8352sPoFmNqtI2QWYSk1Nza9//eusrCz1a5AQ4oUXXkhJSVFWuRWdOnU6efJkx44dPY+9FUKcOXNGCNG1a1d1xGq1RkVFFRcXN/lyDzzwwLvvvnvjxo2YmBir1Rrkv0xrRUY20VScdWUU5u5h5QjRdevW/e53v5s1a1aTz6GBjc58PfyTn/xk69atJ0+evHjxYmRkZEpKSklJyR/+8Icvv/zy0KFDd99994gRIxr/KTo5bLFiF0x9+/Z95plnli5dqn5ffOGFF5KTkz2//AkhrFZrx44dG/9x5SPn9WmMjIz0OpXJS+fOnXWS6pSp8OOPP/YcrK+vr6ysHDBgQO/evYUQly5d8nz0s88+07JCtMjEPdypU6e1a9f+r//1v/r06bNo0aLy8nKvJ9DA5mC+Hn744Yfbt2+fn5//l7/85Uc/+pHFYnnwwQeFECdOnDh06NDjjz/u9XzfnSyEoJnNjWAXZHFxcQsXLlTmlFWrViUnJz/00EOyi9JIcnJyly5dtm/f7jkDbt261eVyjRo1KjEx0Wazbdu2Tf1+XFNTw60VdcjcPdy+fftXX321qqpq2rRpXg/RwKZhsh62WCzp6elHjhw5evRoSkqKEKJfv36xsbGrV6/+8ssvJ06c6PV8350shKCZzY1gF3zKnPLjH/84ISEhoNlEOeTW62KS9fX17du3D3KJoWGxWNavX+9wOMaOHfvHP/7xwoULWVlZzzzzTL9+/ZTbdGZnZ3/22WejRo3avHnzK6+8MnLkyMZnYEAPzN3Do0ePnj179okTJ373u995jtPAZmKyHn700UfPnTtXU1OjrNUJIX70ox99/PHH0dHRP/zhD72e3GInC5rZ1Ah2IZGXlzdt2rTjx483eQxvc5RjXW/evKmOOJ3Ourq6wYMHB7/E0Jg+ffqOHTsuX76clpY2ZMiQZcuWTZ48+eTJk8oVksaOHXvixIkuXbosXLhwyZIlKSkp69evl10ymmbuHt64cePdd9+9aNGia9eueY7TwGZiph5OS0uzWCwxMTHqLcuUC1FNnDixybPZfHeyoJnNTfb1Vkzo+eefz8/Pd7vdDocjIyNDvVBQY1999ZXX9ZMmTpw4f/589cf9+/fbbLbLly+HtOBQKCsrKygoqKur8xz86quvvJ6mnEFWVFSkYWloGT1MAxsdPaxospPdNLOpEeyCbPny5cpsorh8+fK8efOam1MaTyjKhTFfe+21hoaGDz/8cPTo0Z7zi9FFRkZOmDDBc2To0KGdOnVqaGiQVRIao4ebQwMbBT3cIprZxAh2wfTuu+96ziaKy5cve962wVPjCcXtdmdnZ6u3spk1a5Z63xgTUG5rM3ny5FdffXXTpk333XefEGLTpk2y68K36GEfaGBDoIf9QTObWDu32y1tNzCaodzHpnfv3jExMbJrCbJf//rXb7311ieffGKxWP7H//gfixcv9rq0JszBrD1MA4cPs/awimY2K4IdAACASXBWLAAAgElwSzGDadeuXZPjrLwC/mjuE+SJTxMA42JXbHDExcWF9Pc7HA4/n+l1X2dI19wt5/Um1D0skf8fn8b4QAmD9LAS2fn3QmOGaOAgYsUuaELUOl4LDE0Gcc/nqNsw7SN7XFycTj4/uqpEdgkB0MmbFixNLs75/lzExcV5pUDPH7X8TNHDraOTN00iXXWOHioxVgMHBcFO19Qtk+8tiuej6h9R/kfLTZEePsMK/VQCKfz5OtSkxp3j+av8/DwGBT2M1tFP5+inknBDsNOv1m1FlCdLjHeARK2OdM3RybcmAPATwU6PPDdOrdt4EO8Qbtr+qWkRHyu5XC5XaWlpQ0NDv379Gt8g1e12t2vXrl07DhxHuONyJ/qlXEI6iL9BmfXaXBegOxqkOs/f7/nJ4mOljYMHD95///0TJkxIT08fM2bMX//6V9kVATpFsNOdoG8kGse74P5+QCLPXNX270IBId5pprCwcMmSJRMmTDh//vw777xz7733/uIXv7hx44bsugA9ItjpS+iOzmYjBPORFek88cnSwG9/+9v77rtvxYoVHTt27NKly5o1ayIiIjg2H2gSx9jpUeg2UZ4HCXGEEAxNy3NUW8QnK3Rqa2uLiopeeukldeSee+55//33JZYE6BnBTkc02x4oRxmrL8oWCIajq1SnIt6FwtmzZ4UQXbt2zcnJOXr0aFVV1UMPPfTzn/88JiZGdmmAHhHs9ELjPThsgWBc+kx1Kj5cwVVTUyOEyMnJqaiomDJlSnl5eV5e3vvvv7979+7G58YCINjpi8YbAK8tEJsf6J9RohLr4sFSX18vhPj666//4z/+Q0lySUlJM2bM2LVr1+TJkz2fabPZHA4H7zbCHF93dEHuAdcc+g1DUPvTKJttzqsIig4dOgghJk+erK7PjRo16nvf+94HH3wgtS5Apwh2fmloaCgsLAz12fUSN1dsgWAURkl1Kq8Pl9xijKhnz55CiPbt23sORkREyKkG0D2CXcteeeWV+Pj4adOmjRo16mc/+1llZaXsikKFLRB0y1hrdY3xxanV7r333m7duh09elQd+fvf/15ZWTlkyBCJVQG6RbBrwcGDBzdu3Lh69eri4uI9e/aUlpauWLEiuC+hty0WWyATq6ysPHfunOwqAqa3z0jr8MWp1Z5++un8/PycnByn01leXr5o0aKuXbtOmDBBdl2AHhHsWrBly5YxY8ZMmjTJYrEMGjRo6dKl+fn5V65ckV1XaLFn1qyee+65qVOnyq4iMCZrPz5ZrfD444+vXLny//7f/zto0KAf/vCHVVVV27Zt+/73vy+7LkCPCHa+1NXVORyO1NRUdWTcuHFCiFOnTgXrJfS8FMECg8ns3r37xIkTsqsIjM6vbNI6fLJaYcqUKe+///6hQ4fefvvtAwcO9O3bV3ZFgE4R7Hw5c+aMEKJr167qiNVqjYqKKi4ulleU1lhgMIdPP/107dq1ycnJsgsJgClTnYpPVqAsFkvfvn27desmuxBA17iOnS8ul0sIERn5nXcpMjLy9u3bXs8scThEq6ZmdWpvVYEa+c5GVd+l6o7NJrsCIYRwuVzLli1LS0vr16/f6dOnZZcTGFOmOgUXkgw65fKBvJkIZ6zYBUeczSbc7kD/ayeEsiPWQP8pNRuxcjn/6UNubm5FRUWL5/3ExcVpU48/9HyUQnDpdukuLi5OVy0BwB+s2PkSFRUlvrnuuaq+vt7rikphhdslGc6FCxfsdvvOnTujo6N9P7OkpESbklqkq3yjAX3epkLpB/Nlu8bdpZM3HAgKVux8GT58uBDi5s2b6ojT6ayrqxs8eHDbf7mhU5Fn2XpbZoCn2traRYsWZWRkJCQkyK7FX+Y+tK45nFGhjSbfWyYxmAnBzher1dq/f//jx4+rI0eOHBFCjBgxQl5ReuG5HRLMjHqVlZVVXV0dHx9fUFBQUFBQVlbmdrsLCgr0szjXnLBKdSrd7pY1B8/vDKrGjwKGxq7YFsycOXPJkiXbt29/6qmnLl26lJmZmZqa2qtXL9l16YXnnllh8GVIU7p69WpFRcW8efM8B+fMmTNx4sT169fLqsoHWogzKkKkuZVgDi+ByRDsWjB+/Phr166tX79+7dq1Qojk5OQXX3xRdlG6Q7zTrc2bNysndyvefPPNzMzMoqIi9X7qusKSiUo96o5sFxQt7t8nT8M0CHYty8jImDt37sWLF3v37h0TExOU32nK6ON1hFB4HimlNxEREZ63S1eu3WO1WuVV1DIaRuGZ7QRvi98aX/HE/7mI9xwmQLDzS0RExNChQ2VXYRgs4KEV6JPGWEYKIj/fPd5zGJ0ed8fAHJo8u4J9bXJNmTLl0qVLsqtoAo3hA2fLtkXrvjDwnsO4CHYIrSZPPSPhoUmsjjSHs2Vbpy3vFdkOBkWwkyA8dzl5xTtBwsM3wvMTESgudNdqrW4t3nAYEcEOmmq8gCdIeOGNf/eAEDX8F5S3iLVSGA4nT0COJrdPnv/P+k1Y4Z/bf5y5GZC2vz+cTgFjIdhpje98Xpq78rvXG8Vkakp8HFqHqOGnIL4zXFkQRkGwk4N5oUk+bu/DfbtNjH/K1iFqNEd9Z0L0a3nDoWccYwedcn9X4ye0a54G5fl4dY0rMS7en7bjCLDmNDdvtP3XKv/Duw3dYsUOxtB4jvYxsTLnGggrH23EblmNcYwjdI4VO00ROILI3Ty5r65xJQbFRjG4WEnSEpeegZ6xYicBG7NQ4x1GGGIlSWMccgd9YsUOgNZIHiHCSpLGeLehQwQ7ADAV0oaWOH8FekOwA6Aplus0QNrQEgul0BWCnXbYngHQjFnTRmVl5blz52RX0QTCNHSCYAdAO3y90Zj5st1zzz03depU2VU0zaxhGsZCsAMAMzPTStLu3btPnDghu4oWmOkNhxER7ABohOU6WcyxkvTpp5+uXbs2OTlZdiEt82xy477hMCiCHQCEBUOvJLlcrmXLlqWlpaWkpMiuxS9eYdpwbziMi2AHQAss1+mBcZfucnNzKyoqVqxYIbuQwLB0B+1x5wmNsFUDoBOGu2XChQsX7Hb7zp07o6OjZdcSMK+b+Qo2BAgxVuz84nQ6CwsLy8rKZBcCGBLbM70x0F7C2traRYsWZWRkJCQkyK6l9dgzC82wYteCmpqaVatWHTp0yOVyCSG6deu2bt26pKQk2XUBQJt4rSTpNnZnZWVVV1fHx8cXFBQIIcrKytxud0FBwQ9+8IO4uDjZ1QVGXSsV+n7PYWgEuxasXLny7bff3rRp04MPPvif//mfv/zlL+fNm3f48OHu3bvLLg0wBpbr9Mxzt6zQ5T/T1atXKyoq5s2b5zk4Z86ciRMnrl+/XlZVrcaeWYQawc4Xp9N5+PDhZ555JjU1VQjRrVu3rKysUaNGHTlyZNasWbKrA4Ag0Pky0ubNm5UdJoo333wzMzOzqKjIYjHwoUTEO4QOwc6X2traDRs2eB7YcccddwghKisr5RUFGAkbLUPQ827ZiIiIiIgI9cfIyEghhNVqlVdR0HhFasEnBcFAsPMlJiYmLS3NcyQvL08IEegVMvnEAtA//e+WNR/PSC30l6phRAZeytbe+fPn7Xb72LFjExMTZdcCAzDckd1BRz4wHP1f6G7KlCmXLl2SXUWQcc4sgogVu285nc6qqir1xzvvvNPz0bNnz86dO9dms2VmZmpeGgyppKSEbAcj8lq6gzY48A5BQbD71v79+59//nn1x6KiIvVimPv27fvVr341cuRIu91uxCtkAtojExiaGjJsNpvsWsIL8Q5tRLD71siRIzdt2qT+GBUVpfxPTk6O3W7/6U9/umbNGkmlAUbFNsnQ3G43q85SEO/QagS7b3Xv3r3x1el27Nhht9sXL148d+5cKVUBRsRyHdB2xDu0AsHOl88//3zdunW9e/eOjY3dt2+fOt6jRw//b27DpxFhi7YH2o54h4AQ7Hx57733nE7n5cuXly9f7jn+xBNPGPquhQAAYyHewU8EO1/S09PT09NlVwEYDFsdIESId2gRwQ4AACNpHO8ECQ/f4ALFAIKJVQRAG56XNRZc2RjfINgBAGBUxDt4IdiFFqsXCCtsUQApiHdQEeyAsOB0OgsLC8vKyjR4Lb7JAFIQ7yA4eQIwvZqamlWrVh06dMjlcgkhunXrtm7duqSkJNl1AQgJNdtx8mx4YsUOMLmVK1f++c9/3rRpU3Fx8dtvv92jR4958+aVl5cH/YXYfgC64rmA1+4bckuCBgh2gJk5nc7Dhw/PmTMnNTXVYrF069YtKyurtrb2yJEjsksDoAX2z4YbdsUCZlZbW7thwwbPG6XccccdQojKysrgvhDLdYCeeV76TvCBNTWCHWBmMTExaWlpniN5eXlCiOTkZEkVAZCGeBcOCHZAGDl//rzdbh87dmxiYmIQfy17dswqLi5OdgkIvibPrhAkPLPgGLsQ4ssQdOXs2bMzZ8602WyZmZmh+P20uvmUlJTILgEhxOF3pkSwA8LCvn37pk+fPmzYsG3btkVHR8suB4BeEO9MhmAHmF9OTs7y5cvT09O3bt0a9FTHyjRgAu5vKD9yeRTj4hg7wOR27Nhht9sXL148d+5c2bUA0DtOsDA6gh1gZp9//vm6det69+4dGxu7b98+dbxHjx6e10BpNb7QA6ZEvDMugh1gZu+9957T6bx8+fLy5cs9x5944omgBDsF0z1gSpw/a0QEO8DM0tPT09PTZVcBwNhYwDMQTp4A0EpM7tCS0+ksLCwsKyuTXUj44gQLQ2DFLlTY5gFAUNTU1KxaterQoUMul0sI0a1bt3Xr1iUlJcmuK3yxgKdnrNgBaA2+pkMzK1eu/POf/7xp06bi4uK33367R48e8+bNKy8vl11XuGMBT58IdgBaj+/oCDWn03n48OE5c+akpqZaLJZu3bplZWXV1tYeOXJEdmn4L01e4piEJwu7YgEA+lVbW7thwwbPk7jvuOMOIURlZaW8otAEr1NoBbtoJWHFLgCVlZXnzp2TXQUgH/M1NBMTE5OWltatWzd1JC8vTwiRnJwsryj4wgKeXAS7ADz33HNTp06VXQUAhK/z58/b7faxY8cmJiY2fjQuLk77ktAkryPwhIyEF579QLDz1+7du0+cOCG7CkA+lusgy9mzZ2fOnGmz2TIzM5t8QklJicYloUXNJTwNXjo8+4Fg55dPP/107dq1rPwDgCz79u2bPn36sGHDtm3bFh0dLbscBEz6Al6YINi1zOVyLVu2LC0tLSUlxc8/wpIGAARRTk7O8uXL09PTt27dSqozND3sojU3gl3LcnNzKyoqVqxYIbsQGIwpD+/gSwu0t2PHDrvdvnjx4jVr1siuBUFDwgsRLnfSggsXLtjt9p07d/IdEYEqKSkxZbYDtPT555+vW7eud+/esbGx+/btU8d79OjheQ0UGFdz10kRfIdsFYLdt5xOZ1VVlfrjnXfeWVtbu2jRooyMDKYPQLBcBxnee+89p9N5+fLl5cuXe44/8cQTzMwmQ8ILCoLdt/bv3//888+rPxYVFW3cuLG6ujo+Pr6goEAIUVZW5na7CwoKfvCDH7ASAwAaSE9PT09Pl10FNEXCawuC3bdGjhy5adMm9ceoqKirV69WVFTMmzfP82lz5syZOHHi+vXrNS8QkIkDXwBojITXCgS7b3Xv3r179+6eI5s3b3a5XOqPb775ZmZmZlFRkcXCSScIU0ymALRHwvMfwc6XiIiIiIgI9cfIyEghhNVqlVcRAADhy0fCE4Q8IQTBDoA/OG0CgK40TniCZTwhBNexC8iUKVMuXbrU4tPYBAIAoA23B3VQvSSew+GQWJsUrNgBaAHfVQAYQpPLeOGGYAcAAEwlnBMeu2IB+BKG0yIA07DZbLJL0BrBDkDL2A8LAIZAsAMAADAJgh2AZnHaBAAYC8EOAADAJAh2QcYKB0yDZgYAwyHYAQAAmATBDkATWK4DACMi2AEAAJgEwS6YWOSAOXBRYgAwKIIdgKbxFQUADIdgB+A7WK4DAOMi2AFoAst1AGBEBLug4QA7mABtDACGRrADAAAwCYIdgP/Cch0AGB3BDoAQQjgcDtklAADaimAXHGwUYQ4s1wGAoRHsgomNInSroaGhsLDwxo0bTT7KJU6gf757GICCYAeY3yuvvBIfHz9t2rRRo0b97Gc/q6ys9HqC2+222Wx8M4FutdjDABQEO8DkDh48uHHjxtWrVxcXF+/Zs6e0tHTFihWyiwICQA8D/iPYASa3ZcuWMWPGTJo0yWKxDBo0aOnSpfn5+VeuXJFdF+AvehjwH8EuCLhIhCIuLk52Cf9FP5VIV1dX53A4UlNT1ZFx48YJIU6dOiWvKP3ST+fopxLp6OGA6Kdz9FNJuCHYGR4fHvhw5swZIUTXrl3VEavVGhUVVVxcLK8ob/QwfKCHgYBEyi7ADNxud1xcnMQPtn7mFCrxUlJSIrcAl8slhIiM/M4nPTIy8vbt217PLHE4hKRzY0uEkPXSXqiksRLZ+yLo4YBQSRNlhBmCXXBI334DbSV7+w20FT0MsCsWMLeoqCghRH19vedgfX19+/btJVUEBJ/edPUAACAASURBVIYeBgJCsAPMbPjw4UKImzdvqiNOp7Ourm7w4MHyigICQA8DASHYAWZmtVr79+9//PhxdeTIkSNCiBEjRsgrCggAPQwEhGAHmNzMmTNPnDixfft2l8t14cKFzMzM1NTUXr16ya4L8Bc9DPivHVdfA0wvJycnOztbOUopOTk5KysrJiZGdlFAAOhhwE8EOyAsNDQ0XLx4sXfv3mwOYVD0MOAPgh0AAIBJcIydIZWWlt64ccNrsKGhobCwsPF4iDidzsLCwrKyssYPaVxJZWXlqVOnKisrpVei1nPu3Dk9VKJn9LAnetiI6GFP9LCOuGE0169fHzZs2LFjxzwHc3NzBwwYYLPZbDbbjBkzvv7669AVUF1dvWTJkn79+ikvl5KScvr0aSmV3Lp1a8mSJbZvLFiwwPPltKzE0/z58wcOHOg5IqsS3aKHVfSwQdHDKnpYbwh2BuNwOEaPHm2z2TwnlAMHDthstl27dinHoIwePTojIyN0NTz77LPDhg3Lz89vaGgoLy+fNm3akCFDrl+/rn0lq1evHjJkyMmTJ91u97lz55KSkhYsWKA8pHElql27dtlsNs8JRVYlukUPe6KHjYge9kQP6w3BzjBu37790ksvDRw48PHHH/eaUB599NHZs2erP+7fv99ms12+fDlEZfTr1y83N1cd+cc//mGz2bZu3apxJfX19QMGDMjKylJHsrOz+/Xr19DQoHElqitXriQkJMyaNctzQpFSiT7Rw17oYcOhh73QwzrEMXaGUVVV9frrry9evHjr1q2e43V1dQ6HIzU1VR0ZN26cEOLUqVOhKKO2tnbDhg3jx49XR+644w4hRGVlpcaVREREnD9/fvbs2erIrVu3LBaL0Pw9UbhcrmXLlqWlpaWkpKiDUirRLXrYCz1sOPSwF3pYhyJlFwB/derU6eTJkx07dqyoqPAcP3PmjBCia9eu6ojVao2KiiouLg5FGTExMWlpaZ4jeXl5Qojk5GSNK1F+v9VqdblcVVVVBw8ezMvLmzt3rsVi0b4SIURubm5FRcWKFSv27t2rDkqpRLfo4cboYWOhhxujh/WGYGcYyoen8bjL5RJCREZ+558yMjLy9u3bGlR1/vx5u90+duzYxMTEgoICKZW8++67s2bNEkL06dMnPT1dyHhPLly4YLfbd+7cGR0d7Tku919Hb+jh5tDDRkEPN4ce1g92xaL1zp49O3PmTJvNlpmZKbGMQYMGXbhwYe/evd///vcfe+yxa9euaVxAbW3tokWLMjIyEhISNH5ptBE9rKCHjYseVtDDKoKd4UVFRQkhlDvtqOrr69u3bx/S1923b9/06dOHDRu2bds25euRrEruvPPOqKioAQMGZGdnV1VV5eXlaVxJVlZWdXV1fHx8QUFBQUFBWVmZ2+0uKCgoKSmR9Z4YCz1MDxsdPUwP6we7Yg1v+PDhQoibN2+qI06ns66ubvDgwaF70ZycHLvd/tOf/nTNmjWyKqmoqDh79mx8fHxsbKwy0rlz544dO37xxRcaV3L16tWKiop58+Z5Ds6ZM2fixIn//u//rmUlBkUP08NGRw/Tw/rBip3hWa3W/v37Hz9+XB05cuSIEGLEiBEhesUdO3bY7fbFixd7zibaV1JTU/P0008fPHhQHfn888+rq6t79uypcSWbN2++5OGXv/yl1Wq9dOnSunXrtP/XMSJ6WB2hhw2KHlZH6GH5JF9uBYH76quvmrww5muvvdbQ0PDhhx+OHj16/vz5IXr18vLygQMHPvzww3u/69y5cxpX4na758+fn5CQ8Je//MXtdjscjokTJyYlJX3xxRfaV+IpLy+v8YUxpVSiW/Swih42KHpYRQ/rDcHOeBpPKG63Ozs7W71ZyqxZs0J3s5Q//OEPtqY8//zzGlfidrurq6ufffZZtYb09PRPPvlEfVTLSjx5TSgSK9EtelhFDxsUPayih/Wmndvtlr1oiOBQ7pTSu3fvmJiYsKqkrq6uqKiob9++nTt3lluJD/qpRM/08y7Rw43ppxI908+7RA83pp9KQopgBwAAYBKcPAEAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsDKykpmTBhwsCBA4cOHZqTkyO7HCBg9DCMjh6G3hDsjMrlcs2ePXvs2LF/+9vfDh8+vHPnzr1798ouCgiAUXo4Ozt7wYIFsquAHhmlhxFWCHZGdfXq1REjRjz99NNCiO7duyclJZ06dUp2UUAAjNLD+fn5r732muwqoEdG6WGEFYKdUfXs2XPDhg0Wi0UI8eWXX37wwQeJiYmyiwICYJQeXr58+VtvvSW7CuiRUXoYYaWd2+2WXQPaZMqUKefPn09MTNy+fbvsWoQQwuVyKdMc4Cdd9XB9fX1kZKTsKmAwuuphFbNxeOKfXLLS0tIbN254DTY0NBQWFnqNl5aWFnyjoqJCHX/xxRfz8vIqKioWLlyoRcXNO3To0MCBAyMiIqxW69SpU/ft23fXXXedPHlSblUINRP08JNPPvnkk08eOHDgv//3/261WqOiohYsWFBZWak8OnXq1J49e0opDNowQQ97evLJJ6dOnbp58+aoqKiOHTvu3LlTdkXQlhvyXL9+fdiwYceOHfMczM3NHTBggM1ms9lsM2bM+Prrr5XxlStXDvzG6dOnvX7V6dOnbTbbrVu3NCq9kf379wsh7r///v379+/du3fYsGGxsbFCiOPHj8sqCRowRw8/8sgj3bt3j4yMXLdu3eHDh9esWaM0s/LoT37yk06dOmlfFbRhjh729Mgjj/Tr1y8yMvKxxx4bOXJkUVGR3HqgMYKdNA6HY/To0TabzXNCOXDggM1m27VrV0NDw8WLF0ePHp2RkdHkHy8qKlqwYIH647lz5+ROKH369Lnnnntqa2uVH//5z3/26NGDYGdupunhRx55RAiRm5urjqxfv14IsWfPHjfBztRM08OelH7eunWr3DIgC7tiJXA6nS+//HJ6erqypuVpy5YtY8aMmTRpksViGTRo0NKlS/Pz869cudL4l3Tv3v3kyZO7d+9WfuGWLVsSExOjoqK0+As08vHHH3/yySeTJ0/u0KGDMtKpU6ef/exnUoqBBszXwx06dJg9e7b64/z584UQSm0wJfP1sCeLxTJ9+nTZVUAOgl0wlZeX19TUNB7/6KOPPH+sqqp6/fXXFy9evHXrVs/xuro6h8ORmpqqjowbN04I0eT58126dHn55Zd/85vfJCUlDR8+vLa29qWXXgrOXyNwDodDCDFkyBDPwUGDBkkqB60Xtj08cuRIz8PMO3XqFB0d/fXXX8uqB60Wtj3sKTo6mnOAwhb/8MFUU1Pz61//OisrKzo6Wh184YUXUlJSBgwYoI506tTp5MmTHTt29Dz2Vghx5swZIUTXrl3VEeU47uLi4iZf7oEHHnj33Xdv3LgRExNjtVqD/JdpM87GMqKw7eGOHTtKfHUEUdj2MKBg0xtMffv2feaZZ5YuXap+X3zhhReSk5M9v/wJIaxWa5NbEZfLJYTw+poVGRl5+/ZtHy/auXNn6bNJnz59hBAXL170HPzHP/4hqRy0Xtj28AcffOD5Y01NTU1NzX/7b/9NVj1otbDtYUBBsAuyuLi4hQsXKnPKqlWrkpOTH3roIdlFhdyAAQP69Onz+9///tatW+rgtm3bJJaEVgvPHv773//ueWkeZffcpEmT5FWE1gvPHgYUBLvgU+aUH//4xwkJCQHNJsoht/X19Z6D9fX17du3D3KJIZCdnf3ZZ5/96Ec/ys/PLyws/Ld/+7fTp0/LLgqtFJ49PGnSpLy8vPPnz9vt9mXLlj3wwAOPPfaY7KLQSuHZw4Ag2IVIXl7etGnTjh8/3uQxvM0ZPny4EOLmzZvqiNPprKurGzx4cPBLDLYf/ehHBw8e/OSTTx566KGRI0cWFxevWrVKdlFovXDr4U6dOi1cuHDGjBkJCQmLFy9+4oknlEszwrjCrYcBBcEu+H71q1+lpKTMmjXL6ziPFlmt1v79+x8/flwdOXLkiBBixIgRISk02B599NHPP//8ww8/LC0tLSoq+pd/+RfZFaGVwrOHf/WrX1VXV7/99tv//Oc/8/Ly7rzzTmV87969//znP+XWhkCFZw8rDh8+TMeGM4JdkD333HMPPvigcpRu3759lyxZ8uyzz/o/p8ycOfPEiRPbt293uVwXLlzIzMxMTU3t1atXKEsOsvj4eOVcCuhKk/dHalI493D79u1TUlI8z6aEftDDgF9kXyHZVN599938/HyvwcuXL7/xxhtNPv+rr77yuuK52+3Ozs5Wb2Uza9Ys9VY2hqMcfs6dJ/SgufsjNRaePfzII49wbwmdo4cBPxHs9Ki+vr6oqMjoU8mf/vSnRx55hNsUSuf//ZGCyFg9vGrVqscee0x2FWgWPQz4r53b7Za9aAgghMaPH3/33Xdv2bJF+fHAgQNLly49evQou5ZgFPQw4D+OsQPMLKD7IwE6RA8DASHYAWYW6P2RAL2hh4GAcK/YIGjXrp0QwmazyS4EelRSUiLx1QO4P1K7dppVBQOJs9noYRhbmB1yRrALGrlznx7ExcXp5E3QVSWyS/CX9O23Huiqc3RSiaCHDUU/naOTSuLi4uQXoS12xSJo9PAZVuinEum4P1JA9NM5+qlEOno4IPrpHP1UEm4IdkGgnFncjr0A0B/ujwSjo4eBgBDsADMzwf2REOboYSAgBDvA5Ix7f6R2fpBdI7Rg4h6WXSBMiJMnAJMbP378tWvX1q9fv3btWiFEcnLyiy++KLsob63ewrX4B7kGuwmYuIf9+VP0MALCnSeCQ/lw8mbCi07OCxNCKPdi6t27d0xMTJNP0L7UoGSyNq558JltET3sm+8ObLHB2r5oRw/7pp8G1gwrdkBYiIiIGDp0qOwq/kvjjVmrN05t3HCG4XpJoElCP1foNGUPt/3bSxguWrML2zeCXXDYbDaHw9GuHSuggC9eM7IGnxffL+HPFqJ1W5Hg/tXYkumH4Xq41c0T9L8abawNgh0ALXjO6fr5/hO6vb263YYF+uYb6CLboWbQHg7dAayyBPTmh2EDE+wAhJy6hdDP5tB/ras5uBtFI75vJmPcHm51wUEPdoZ76wyKYAcgtIy7RWyLsPrLmh49DAMh2AEIlfDcHMJM6GEYDhcoBhASbBFhdPQwjIhgFzTcMRZQsUWE0dHDMCiCHYAgY4sIo6OHYVwEOwAhwRYRRkcPw4gIdgCCidvrwejoYRgawQ5A0HCMKYyOHobREewABAeHJcHo6GGYAMEumDgxFmCLCKOjh2FoBDsAQcBhSTA6ehjmQLADAAAwCYIdgLZiqQNGRw/DNAh2AAAAJkGwCwnOn0D4YKkDRkcPw0wIdkHG1AAAAGQh2AFoPZY6YHT0MEyGYAcAAGASBDsArcRSB4yOHob5EOwAAABMgmAXgMrKynPnzrX4NG4sBgAApCDYBeC5556bOnWq7CoAXWAfFoyOHoYpEez8tXv37hMnTsiuAgAAoFkEO798+umna9euTU5Oll0IAABAswh2LXO5XMuWLUtLS0tJSZFdC6AL7MOCLKWlpTdu3Gj776GHYVYEu5bl5uZWVFSsWLFCdiEwmLi4ONklAKZSXl7+5JNP+nMSGxC2CHYtuHDhgt1uX79+fXR0tP9/ihNjIYQoKSmRXQJgHqWlpU8++WRVVZXsQgBdI9j5Ultbu2jRooyMjISEBNm1AHrBPixozOl0vvzyy+np6bGxsUH5hfQwTCxSdgG6lpWVVV1dHR8fX1BQIIQoKytzu90FBQU/+MEP2MsGANqoqqp6/fX/3979x1RV/3EcPxe43sGUeceSDeYo04uC4sAfg2X4A9cycu5aOjdX6lRAlrVQMsPZ1MoSqa4BWjRXDprNpSA5tzANNulmjEvUYkDopl62XHaNXUC83Hu/f9zv93xvF738vPf8uM/H7h+cz72d+97h3fHFOZ9zzqmCggKj0Zieni51OYCsEez8uXnzps1my8vL8x7MyclZs2bNkSNHpKoKAELK5MmTGxoaIiMjbTab1LUAckew8+f48eMul0tc/Oqrr4qLiy0WS1gYp7ARojiHheDTarVarXai1kYPQ90Idv6Eh4eHh4eLixEREYIgjHD/4na7NRqNRqNh9wEAI+RwOLwvj9Dr9RIWAygRwQ4AIBc1NTVFRUXiosViGdUdCQAQ7EZh48aNGzdulLoKQDLcwQeBlpGRUVpaKi7qdLqJXT89DNUj2AEYHWYXIHDi4+Pj4+MD/S30MFSMiwAAAABUgmAHAACgEpyKDSAujAWACaTX63lSH+AfR+wAjAh3/4LS0cMIBQQ7AAAAlSDYAQAAqATBDgAAQCUIdoHlmczBLTEBAEAQEOwADI9Z51A6ehghgmAHAACgEgQ7IIR0dnbevXtX6ioAAIFCsAs4ptlBJqxW64YNG5qbm6UuBAAQKAQ7ICR0dnZu2LDBbreP4b/lzxIoHT2M0EGwA1TO4XB88sknRqMxNjZ2POth1jmUjh5GKCDYASpnt9tPnTpVUFBQUVEhdS0AgMCKkLqAkOB2uzUajUaj4e9FBN/kyZMbGhoiIyNtNpv/TyYmJvKEdYgSExOlLgHAqBHsAJXTarVarXYknyTVwZunH4h3gLIQ7AD1cDgc3pdH6PX68a+T27pC6ehhhBSCHaAeNTU1RUVF4qLFYomKipKwHgBAkBHsgoRpdgiCjIyM0tJScVGn00lYDAAg+Ah2gHrEx8fHx8dLXQUAQDLc7gQAAEAlCHYAAAAqwanYYGOaHaSi1+tHe0MTLieE0tHDCDUcsQse9iwAACCgCHYAAAAqQbADAABQCYLdiDgcDrPZ3NXVNc71eM7GeuZ8AAAATCwunhhGX1/f22+//e2337pcLkEQ4uLiDh8+nJ6eLnVdAAAAvjhiN4z9+/dfvny5tLS0ra3typUrCQkJeXl5Vqt1nKvloB0AAJhwBDt/HA7HhQsXcnJysrKywsLC4uLiSkpK+vv7L168OOZ1cm0slIL7REBWxjAlhh5GCOJUrD/9/f1Hjx5NTU0VR6ZOnSoIQk9Pj3RFAUBoYUoMMHIcsfMnOjo6Ozs7Li5OHKmsrBQEITMzc/wr52ys6iUmJkpdAqAGAZoSA6gSwW4UWlpaTCbTypUrFy5cOJ71cF4gRIz2MQ8AhgrElBhAxTgVO1JNTU25ubkGg6G4uFjqWgAgVDAlBhgVjtiNSHV19ebNm9PS0k6ePBkVFTVRq+VsLAD4F9ApMYD6EOyGV15evmfPHqPRWFFRMVGpjrOxADAG/qfEMLEV3kKzHzgVO4yqqiqTyVRQUJCbmyt1LUDwcJ8ISMLhcNjtdnFRr9d7vzvslBjvia30MNrb20Mw2xHs/Onu7j58+PCMGTNiY2Orq6vF8YSEBO8JH+Oh0WjY7wCAR01NTVFRkbhosVjE8yTV1dX79u3LyMgwmUwTOCUGUBmCnT8//fSTw+G4fv36nj17vMfXrVs3/mDndruZYwcA3jIyMkpLS8VFnU7n+aG8vNxkMq1fv/7QoUMSlQYoA8HOH6PRaDQaA/0tHLQDAI/4+Pj4+HifQabEACNHsJMSB+0AwL8gTIkB1IRgBwCQr4BOiQHUh2AnMc9BO87GAsBDBWdKDKAa3McOgC/uEwGlo4cRsgh20vPsephsBwAAxolgBwAAoBIEO1ngoB0AABg/gh0AAIBKEOzkgoN2AABgnAh2skO2AwAAY0OwkxGuzIcccJ8IKB09jFBGsJMjDtoBAIAxINjJC39iAgCAMSPYyQ5XUQAAgLEh2MkX2Q4AAIwKwU6OOCELAADGgGAnU5yQhSS4nBBKRw8jxBHs5ItsBwAARoVgpwBkOwAAMBIEO1kTzyaQ7QAAwLAIdnJHtgMAACNEsFMAsh0AABgJgp0ykO0QBFxOCKWjhwGCnWKQ7QAAgH8EOyUh2wEAAD8IdgpDtgMAAI9CsFMesh0AAHgogp0ieWc74h0AAPAg2I2I0+k0m813796VupD/c7vdHLrDBOro6JC6BADAeEVIXYACfPrpp8eOHRscHBQE4amnnvr444+jo6OlLuq/3G63J9VxkT8mBC0E5fL8cUIPI8RxxG4YtbW1H3744YEDB9ra2r755pvOzs69e/dKXdS/+By64+gdAAAhi2A3jM8++2zp0qUvvvhiWFjY3LlzCwsLL126dOPGDanr8kW8A6BuPT09jY2NPT09UhcCyBrBzp+BgYGOjo6srCxxZNWqVYIgNDY2SleUP0PjHQkPHg6Hw2w2d3V1SV0IMGoDAwOFhYWLFi3asmXLokWLXn31VeId8CgEO3+uXbsmCMK0adPEEa1Wq9Pp2trafD7Z3tEhaDQyebkFwfsleT0h/ZKBvr6+wsLClJSUTZs2Pffcc8uXLzebzVIXBYzCBx98UFdX9/nnn7e3t58+ffrnn3/et2+f1EUBMkWw88flcgmCEBHxr0tMIiIiHjx44PPJRINBcLtl+NIIwtCX5FXJcJsE6CUH+/fvv3z5cmlpaVtb25UrVxISEvLy8qxWq9R1ASPidDq//vrrl19++emnnxYEITU19aWXXqqrq/PsnwH4INipnPt/vAc1/yZVbWOmGZ/AFeYeInDfNUIOh+PChQs5OTlZWVlhYWFxcXElJSX9/f0XL170/hhXVUO2wsPDW1patm/fLo7cv38/LMz3Hy96GPAg2Pmj0+kEQfDc6EQ0ODg4adIkiSoaOz9pY6ICUGJi4qg+L1UyGxq/Jso4CwuE/v7+o0ePrl69WhyZOnWqIAhMUXqo0fZw4MinEjnQarVTpkxxuVw9PT1VVVWVlZW5ublDs53AdpPTFpBDJXKoIfi4j50/CxYsEATh3r174ojD4RgYGJg3b97QDyuogQwGg/fio+5MO4YIFdDjYSKf+kdLQb+p8YuOjs7OzvYeqaysFAQhMzNz6IdDass8inw2gnwqkYmrV69u27ZNEISZM2cajcZHfYztJp8tIJ9KQgrBzh+tVjtnzpy6ujpxJ+I5gbV48WKfT7a3twe7uMALdEqT5yEudWtpaTGZTCtXrly4cKH3OL8LyITD4bDb7eKiXq8Xf547d25ra2tXV9fBgwfXrl179uzZ6dOni+/Sw4AHp2KHsXXr1u+///7LL790uVytra3FxcVZWVlPPPGE1HUFQ+BOWcr2xKXSORwOmxefd5uamrZu3WowGIqLiyUpDxhWTU1Nupe+vj7xLb1er9PpkpKSysrK7Ha759gzAB8csRvG6tWrb926deTIkffee08QhMzMzPfff1/qooCHq6mpKSoqEhctFktUVJTn5+rq6n379mVkZJhMJnEQkJuMjIzS0lJxUafT2Wy2pqamlJSU2NhYz2BMTExkZOSdO3ckqhGQNQ0HTkbC6XT++uuvM2bMkM9TYoGhrFbr77//Li6uWLEiPDxcEITy8nKTybR+/fpDhw5JVx0wFlardcWKFYWFhZ4JdoIgdHd3L1++PD8//7XXXpO2NkCGCHaAylVVVR08eLCgoCA3N1fqWoCxyM/PN5vNH3300dKlSzs7OwsLC//888/z588/9thjUpcGyA7BDlCz7u7uZ555Zvr06T6pLiEhITU1VaqqgFHp6+vbv39/bW2tZzE5Obm4uPjJJ5+UtipAngh2gJqdO3fuzTffHDq+bt26d955J/j1AGM2MDBgsVhmzZoVExMjdS2AfBHsAAAAVILbnQAAAKgEwU6ROjs779696zPodDrNZvPQ8QBxOBxms7mrq2voW0GupKenp7Gx8aHPyApyJWI9zc3NcqhEzuhhb/SwEtHD3uhhGQn0TWgx4W7fvp2Wlvbdd995D544cSIpKclgMBgMhi1btvzzzz+BK6C3t3f37t2zZ8/2fN2yZct+/PFHSSq5f//+7t27Df+zc+dO768LZiXeduzYkZyc7D0iVSWyRQ+L6GGFoodF9LDcEOwUpqOjY8mSJQaDwXuHcv78eYPBcObMGc/99pYsWZKfnx+4Gnbt2pWWlnbp0iWn02m1Wjdt2jR//vzbt28Hv5IDBw7Mnz+/oaHB7XY3Nzenp6fv3LnT81aQKxGdOXPGYDB471CkqkS26GFv9LAS0cPe6GG5IdgpxoMHD44dO5acnPzCCy/47FCef/757du3i4s1NTUGg+H69esBKmP27NknTpwQR/766y+DwVBRURHkSgYHB5OSkkpKSsSRsrKy2bNnO53OIFciunHjRmpq6rZt27x3KJJUIk/0sA96WHHoYR/0sAwxx04x7Hb7qVOnCgoKKioqvMcHBgY6OjqysrLEkVWrVgmC0NjYGIgy+vv7jx49unr1anFk6tSpgiD09PQEuZLw8PCWlpbt27eLI/fv3w8LCxOCvk08XC7XG2+8kZ2dvWzZMnFQkkpkix72QQ8rDj3sgx6WIZ4VqxiTJ09uaGiIjIz0ebj7tWvXBEGYNm2aOKLVanU6XVtbWyDKiI6Ozs7O9h7xPIo7MzMzyJV41q/Val0ul91ur62trayszM3NDQsLC34lgiCcOHHCZrPt3bv33Llz4qAklcgWPTwUPaws9PBQ9LDcEOwUw/M/z9Bxl8slCEJExL9+lREREQ8ePAhCVS0tLSaTaeXKlQsXLqyvr5ekkqtXr3oeIjlz5kyj0ShIsU1aW1tNJtPp06ejoqK8x6X97cgNPfwo9LBS0MOPQg/LB6diMXZNTU1bt241GAzFxcUSljF37tzW1tZz585NmTJl7dq1t27dCnIB/f39r7/+en5+Pg/pUhx62IMeVi562IMeFhHsFE+n0wmCMDg46D04ODg4adKkgH5vdXX15s2b09LSTp486fnzSKpK9Hq9TqdLSkoq3Be43wAAAx1JREFUKyuz2+2VlZVBrqSkpKS3tzclJaW+vr6+vr6rq8vtdtfX17e3t0u1TZSFHqaHlY4epoflg1OxirdgwQJBEO7duyeOOByOgYGBefPmBe5Ly8vLTSbT+vXrDx06JFUlNputqakpJSUlNjbWMxITExMZGXnnzp0gV3Lz5k2bzZaXl+c9mJOTs2bNmnfffTeYlSgUPUwPKx09TA/LB0fsFE+r1c6ZM6eurk4cuXjxoiAIixcvDtA3VlVVmUymgoIC771J8Cvp6+t75ZVXamtrxZHu7u7e3t7HH388yJUcP378Ny9vvfWWVqv97bffDh8+HPzfjhLRw+IIPaxQ9LA4Qg9LT+LbrWD0/v7774feGPOLL75wOp2//PLLkiVLduzYEaBvt1qtycnJzz777Ll/a25uDnIlbrd7x44dqampP/zwg9vt7ujoWLNmTXp6+p07d4JfibfKysqhN8aUpBLZoodF9LBC0cMielhuCHbKM3SH4na7y8rKxIelbNu2LXAPSzl79qzhYYqKioJcidvt7u3t3bVrl1iD0Wj8448/xHeDWYk3nx2KhJXIFj0soocVih4W0cNyo3G73VIfNMTE8DwpZcaMGdHR0SFVycDAgMVimTVrVkxMjLSV+CGfSuRMPluJHh5KPpXImXy2Ej08lHwqCSiCHQAAgEpw8QQAAIBKEOwAAABUgmAHAACgEgQ7AAAAlSDYAQAAqATBDgAAQCUIdgAAACpBsAMAAFAJgh0AAIBKEOwAAABUgmAHAACgEgQ7AAAAlSDYAQAAqATBDgAAQCUIdgAAACpBsAMAAFAJgh0AAIBKEOwAAABUgmAHAACgEgQ7AAAAlSDYAQAAqATBDgAAQCUIdgAAACpBsAMAAFAJgh0AAIBKEOwAAABUgmAHAACgEgQ7AAAAlSDYAQAAqATBDgAAQCUIdgAAACpBsAMAAFAJgh0AAIBKEOwAAABUgmAHAACgEgQ7AAAAlSDYAQAAqATBDgAAQCUIdgAAACpBsAMAAFAJgh0AAIBKEOwAAABUgmAHAACgEgQ7AAAAlSDYAQAAqMR/AGJxpjX9uGZbAAAAAElFTkSuQmCC" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "Total computing time : 0h00m08s\n", "Note: 1 warning(s) encountered in the preprocessor\n" ] } ], "source": [ "dynare twoagent.mod" ] }, { "cell_type": "markdown", "id": "19125cd4-822e-4863-9884-beed3bc3611a", "metadata": {}, "source": [ "With two agent New Keynesian model, we can check policy effect on different types of households.\n", "\n", "For example, when there is positive monetary policy shock, or an increase in interest rate, consumption of HtM households decreases more than that of ricardian households, due to no access to financial market. And HtM households have to work for more hours to compensate for this shock." ] }, { "cell_type": "markdown", "id": "bd217c5e-76e0-4f2f-a648-a1f047adb3e4", "metadata": {}, "source": [ "Some literature explores three-agent New Keynesian model, which is similar to two-agent model." ] }, { "cell_type": "markdown", "id": "e9fbe34a-6a00-4dd0-8dd0-bfd465af48e8", "metadata": {}, "source": [ "________________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "865243dc-8808-4ead-b330-4f5e16347fa9", "metadata": {}, "source": [ "# Reference" ] }, { "cell_type": "markdown", "id": "304abffe-e923-439a-90ba-905b1963308f", "metadata": {}, "source": [ "1. Valerio Nispi Landi, Note on NK Model and TANK Model, 2021" ] }, { "cell_type": "markdown", "id": "9f685f5f-9c89-468a-aeaf-8abf93cc1087", "metadata": {}, "source": [ "2. Gali, Monetary Policy, Inflation, and the Business Cycle, 2015" ] }, { "cell_type": "markdown", "id": "e794badf-4e69-45ff-8ae1-3a1e090c88de", "metadata": {}, "source": [ "3. Gali, Lopez, Valles, Understanding the Effects of Government Spending on Consumption, Journal of the European Economic Association, 2007" ] } ], "metadata": { "kernelspec": { "display_name": "MATLAB Kernel", "language": "matlab", "name": "jupyter_matlab_kernel" }, "language_info": { "file_extension": ".m", "mimetype": "text/x-matlab", "name": "matlab" } }, "nbformat": 4, "nbformat_minor": 5 }