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+# FBS-NK
+
+# by [William Du]
+
+## Description
+
+This repository corresponds to the Final assignment of the course Advanced Macroeconomics II at Johns Hopkins University, by Professor Christopher D. Carroll.
+
+## Location of main files:
+
+  1. A Jupyter notebook delineating the model and the current results using HARK can be found at code/python/FBS-NK-model.ipynb.
+
+  2. The code that generates all the figures and results in the previous document can be found at code/python/Jacobian-SS.py
+
+  3. reproduce.sh: produces all results.  
+
+## Package/data requirements
+
+The following packages and data files are required for executing the <tt>REMARK</tt> notebook:
+ 
+- econ-ark == 0.11.0
+
+- numpy == 1.20.2
+
+- matplotlib == 3.4.1
+
+- scipy==1.6.2
+
diff --git a/REMARKs/FBS-NK/code/python/FBS-NK-model.ipynb b/REMARKs/FBS-NK/code/python/FBS-NK-model.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# FBS-NK Model One Asset"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Summary of Model\n",
+    "\n",
+    "HANK model with Friedman Buffer Stock income process and  wage and price stickiness a la calvo.\n",
+    "\n",
+    "The model is heavily drawn from Auclert et al. 2020 ( Adrien Auclert & Matthew Rognlie & Ludwig Straub, 2020. \"Micro Jumps, Macro Humps: Monetary Policy and Business Cycles in an Estimated HANK Model,\" NBER Working Papers 26647, National Bureau of Economic Research, Inc. ) \n",
+    "\n",
+    "Latest version of the paper can be found at https://aauclert.people.stanford.edu/research \n",
+    "\n",
+    "\n",
+    "\n",
+    "### Model Organization:\n",
+    "\n",
+    "Households\n",
+    "\n",
+    "Financial Intermediary / Mutual fund\n",
+    "\n",
+    "Firms\n",
+    "- Final Goods Producer\n",
+    "- Intermediate Goods Producers\n",
+    "\n",
+    "Labor Market\n",
+    "- Competitive Labor Packer\n",
+    "- Labor unions\n",
+    "\n",
+    "Government\n",
+    "\n",
+    "Central Bank\n",
+    "\n",
+    "\n",
+    "### Indexation notation\n",
+    "\n",
+    "Households are indexed by $i \\in [0,1]$.\n",
+    "\n",
+    "Firms are indexed by $j \\in [0,1]$.\n",
+    "\n",
+    "Labor types are indexed by $g \\in [0,1]$.\n",
+    "\n",
+    "nb.: Neither firm nor labor heterogeneity matters for anything in the aggregate.  They are necessary to allow, respectively, sticky prices and sticky wages, but otherwise have little role"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Households\n",
+    "\n",
+    "$$\n",
+    "\\max_{\\{c_{it+s}\\}_{s=0}^{\\infty}} \\mathrm{E_{t}}\\left[\\sum_{s=0}^{\\infty} (\\not D \\beta_{i})^{t+s} U\\left(\\mathbf{c_{i t+s}, n_{i t+s}}\\right)\\right]\n",
+    "$$\n",
+    "\n",
+    "Where $U\\left(\\mathbf{c_{i t}, n_{i t}}\\right) = \\mathbf{\\frac{c_{i t}^{1-\\rho}}{1 -\\rho} - \\frac{n_{it}^{1+\\varphi}}{1+\\varphi}}$ \n",
+    "\n",
+    "Households will decide $\\mathbf{c_{it}}$ but $\\mathbf{n_{it}}$ will be decided by bargaining between a \"union\" and employers (per ARS)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Budget Constraint\n",
+    "\n",
+    "$$ \\pmb{\\mathrm{m}}_{i t} = \\pmb{\\mathrm{z}}_{i t}  + (1+\\mathit{r}^{a}_{t})\\pmb{\\mathrm{a}}_{i t-1}$$\n",
+    "\n",
+    "$$ \\pmb{\\mathrm{c}}_{i t}  + \\pmb{\\mathrm{a}}_{i t}= \\pmb{\\mathrm{z}}_{i t}  + (1+\\mathit{r}^{a}_{t}) \\pmb{\\mathrm{a}}_{i t-1}  $$ \n",
+    "\n",
+    "$$\\pmb{\\mathrm{a}}_{it} \\geq 0$$\n",
+    "\n",
+    "where \n",
+    "\n",
+    "$\\pmb{\\mathrm{m}}_{it}$ is cash on hand.\n",
+    "\n",
+    "$\\pmb{\\mathrm{a}}_{it}$ value of mutual fund share holdings.\n",
+    "\n",
+    "$\\pmb{\\mathrm{z}}_{it}$ is labor income.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Labor Income\n",
+    "\n",
+    "Labor income composed of permanent component $\\mathit{p}$ and transitory component $\\xi$. \n",
+    "\n",
+    "\n",
+    "$$\\pmb{\\mathrm{z}}_{it} = \\pmb{\\mathrm{p}}_{it} \\xi_{it}$$\n",
+    "\n",
+    "$$\\pmb{\\mathrm{p}}_{it}=\\pmb{\\mathrm{p}}_{i t-1} \\psi_{it}$$\n",
+    "\n",
+    "$$ (\\psi_{it} , \\xi_{it}) = \\begin{cases}\n",
+    "      (x^{u}_{it}, \\mathit{u}) & \\ \\text{with probability }\\mho_{t} \\\\\n",
+    "      \\left(x^{e}_{it}, \\frac{(1-\\tau_{t})w_{t}N_{t} \\theta_{it}}{1-\\mho_{t}} \\right)  &  \\ \\text{with probability } 1- \\mho_{t} \\\\\n",
+    "    \\end{cases}\\\\\n",
+    "$$\n",
+    "\n",
+    "WLOG assume unemployed individuals lie within $i \\in [0, \\mho]$\n",
+    "\n",
+    "where \n",
+    "\n",
+    "$ log(x^{e}_{it}) \\sim N\\left( -\\frac{\\sigma_{\\psi}^2}{2} ,  \\sigma_{\\psi}^2 \\right) , \\quad \\forall i \\in [\\mho, 1]$\n",
+    " \n",
+    "\n",
+    "$log(x^{u}_{it}) \\sim N\\left( log(1-k)-\\frac{{L\\sigma_{\\psi}}^2}{2}, L\\sigma_{\\psi}^2 \\right), \\quad \\forall i \\in [0,\\mho], \\ k \\in (0,1),\\ L >1 $\n",
+    "\n",
+    "\n",
+    "$ log(\\theta_{it}) \\sim N\\left(-\\frac{\\sigma_{\\theta}^2}{2}, \\sigma_{\\theta}^2 \\right), \\quad \\forall i \\in [\\mho,1]$ \n",
+    "\n",
+    "The idea here is that if/when $(\\psi_{it} , \\xi_{it})= (x^{u}_{it} , \\mathit{u})$ (an individual becomes unemployed), he receives a negative first moment shocks and a positive second moment shock to his permanent income. Markov chain specification for employment is avoided to avoid an additional state variable.\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Law of motion for the Distribution Function\n",
+    "\n",
+    "$$ \\Phi_{t+1}(\\mathbf{a},\\mathit{p},\\xi) = H\\left(\\Phi_{t}(\\mathbf{a},\\mathit{p}, \\xi)\\right)$$\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Financial Intermediary / Mutual Fund\n",
+    "\n",
+    "Beginning of  period outstanding value of assets must equal value of the portfolio of shares and bonds.\n",
+    "\n",
+    "$$(1+r^{a}_{t}) A_{t-1} =  B_{t-1} + \\int_{0}^{1} (q^{s}_{jt}+ D_{jt})\\mathit{v}_{jt-1} \\, dj +(1+i_{t-1}) \\frac{M_{t-1}}{P_{t}}$$\n",
+    "\n",
+    " Portfolio-Investment Constraint: End of the period t value of newly issued assets equals value of newly purchased shares and bonds. \n",
+    "\n",
+    "$$A_{t} = \\frac{M_{t}}{P_{t}} +q^{b}_{t} B_{t} + \\int_{0}^{1} q^{s}_{jt}\\mathit{v}_{jt}\\,dj$$\n",
+    "\n",
+    "### Mutual Fund's Problem\n",
+    "\n",
+    "$$\\max_{\\{B_{t}, M_{t} , \\mathit{v}_{jt} \\}} \\mathrm{E}_{t}\\left[1+r^{a}_{t+1} \\right] = \\mathrm{E}\\left[ \\frac{ B_{t} + \\int_{0}^{1} (q^{s}_{jt+1}+ D_{jt+1})\\mathit{v}_{jt} \\, dj +(1+i_{t}) \\frac{M_{t}}{P_{t+1}}}{\\frac{M_{t}}{P_{t}} +q^{b}_{t} B_{t} + \\int_{0}^{1} q^{s}_{jt}\\mathit{v}_{jt}\\,dj} \\right]$$\n",
+    "\n",
+    " \n",
+    "### FOC: Asset Pricing Equations/ No Arbitrage\n",
+    "\n",
+    "$$ \\mathrm{E}_{t}\\left[1+r^{a}_{t+1}\\right]= \\frac{1}{q^{b}_{t}}  =\\frac{\\mathrm{E}_{t}\\left[q^{s}_{jt+1} + D_{jt+1} \\right]}{q^{s}_{jt}} = (1+i_{t}) \\mathrm{E}_{t}\\left[\\frac{P_{t}}{P_{t+1}}\\right] \\equiv 1 +r_{t}$$\n",
+    "\n",
+    "where \n",
+    "\n",
+    "$A_{t} = \\int_{0}^{1} a_{it} \\, di$ is the value of assets at the end of period t.\n",
+    "\n",
+    "$r_{t}$ is the ex-ante real interest rate.\n",
+    "\n",
+    "$i_{t}$ is the nominal interest rate on reserves $M_{t}$.\n",
+    "\n",
+    "$B_{t}$ are zero coupon government bonds. Assume $B_{t} =0, \\forall t$\n",
+    "\n",
+    "$q^{b}_{t}$ is the price of a government bond in period $t$.\n",
+    "\n",
+    "$ \\mathit{v}_{jt}$ is the portfolio share of firm $j$ stocks where $\\int_{0}^{1} \\mathit{v}_{jt}\\,dj =1$\n",
+    "\n",
+    "$ q^{s}_{jt}$ is the stock price of intermediate firm $j$.\n",
+    "\n",
+    "$D_{jt} = Y_{jt} -  \\frac{W_{t}}{P_{jt}} N_{jt}$ is the dividend of intermediate firm $j$.\n",
+    "\n",
+    "$M_{t}$ are nominal reserves at the central bank. Assume $M_{t} = 0 , \\forall t$\n",
+    "\n",
+    "\n",
+    "### Aggregate Stock Market Price\n",
+    "\n",
+    "Define $q^{s}_{t} = \\int_{0}^{1} q^{s}_{jt}\\,dj$ to be the price of the aggregate stock market.\n",
+    "\n",
+    "and $D_{t} = \\int_{0}^{1} D_{jt} \\,dj$ is the aggregate dividend.\n",
+    "\n",
+    "Then $$q^{s}_{t} = \\frac{\\mathrm{E}_{t}\\left[q^{s}_{t+1} +D_{t+1}\\right]}{1+r_{t}}$$. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Household Bellman Equation\n",
+    "\n",
+    "\n",
+    "For household i's dynamic program is\n",
+    "\n",
+    "$$ V(\\pmb{\\mathrm{m}}_{it},\\pmb{\\mathrm{p}}_{it})=\\max_{\\{ \\pmb{\\mathrm{c}}_{it}\\}} { U( \\pmb{\\mathrm{c}}_{it}, n_{it}) + \\beta_{i} \\not D \\mathrm{E}_{t}[V( \\pmb{\\mathrm{m}}_{it+1} , \\pmb{\\mathrm{p}}_{it+1})]}$$\n",
+    "\n",
+    "subject to $$ \\pmb{\\mathrm{m}}_{i t} = \\pmb{\\mathrm{z}}_{i t}  + (1+\\mathit{r}^{a}_{t})\\pmb{\\mathrm{a}}_{i t-1}$$\n",
+    "\n",
+    "$$ \\pmb{\\mathrm{c}}_{i t}  + \\pmb{\\mathrm{a}}_{i t}= \\pmb{\\mathrm{z}}_{i t}  + (1+\\mathit{r}^{a}_{t}) \\pmb{\\mathrm{a}}_{i t-1}  $$ \n",
+    "\n",
+    "$$\\pmb{\\mathrm{a}}_{it} \\geq 0$$\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Normalized Bellman Equation \n",
+    "\n",
+    "\n",
+    "Here non boldface variables are normalized by permanent income $\\mathit{p_{it}}$. \n",
+    "\n",
+    "e.g. $x_{it} = \\frac{\\mathbf{x_{it}}}{\\pmb{\\mathrm{p}}_{it}}$\n",
+    "\n",
+    "$$ V(m_{it}) = \\max_{\\{c_{it}\\}} { U(c_{it}, n_{it}) + \\beta_{i}\\not D \\mathrm{E}_{t}[\\psi_{it+1}^{1-\\rho} V(m_{it+1})]}$$\n",
+    "\n",
+    " subject to $$m_{i t} =  \\xi_{it}  + (1+r^{a}_{t}) \\frac{a_{i t-1}}{\\psi_{it-1}}$$\n",
+    "\n",
+    "$$ c_{i t}  + a_{i t}= \\xi_{it}  + (1+r^{a}_{t}) \\frac{a_{i t-1}}{\\psi_{it-1}} $$\n",
+    "\n",
+    "$$ a_{it} \\geq 0 $$\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Euler Equation\n",
+    "\n",
+    "For household i, \n",
+    "\n",
+    "$$ U_{c}(c_{it},n_{it}) =  R^{a}_{t} \\not D \\beta_{i}  \\mathrm{E}_{t}\\left[ \\psi_{it+1}^{-\\rho} U_{c}(c_{it+1},n_{it+1})\\right]$$\n",
+    "\n",
+    "where $R^{a}_{t} = 1+r^{a}_{t}$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Firms"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Final Good Producer\n",
+    "\n",
+    "\n",
+    "\n",
+    "Perfectly Competitive Final Good Producer aggregates goods with CES technology\n",
+    "\n",
+    "$$ Y_{t} = \\left(\\int_{0}^{1} Y_{jt}^{\\frac{\\epsilon_{p}-1}{\\epsilon_{p}}}\\, dj\\right)^{\\frac{\\epsilon_{p}}{\\epsilon_{p}-1}}$$\n",
+    "\n",
+    "Final Good Producer Profit maximzation Problem\n",
+    "\n",
+    "$$ \\max_{Y_{jt}} P_{t} \\left(\\int_{0}^{1} Y_{jt}^{\\frac{\\epsilon_{p}-1}{\\epsilon_{p}}}\\, dj\\right)^{\\frac{\\epsilon_{p}}{\\epsilon_{p}-1}} - \\int_{0}^{1} P_{jt} Y_{jt} ,\\ dj $$\n",
+    "\n",
+    "\n",
+    "This leads to demand\n",
+    "\n",
+    "$$ Y_{jt} = \\left(\\frac {P_{jt}}{P_{t}}\\right)^{- \\epsilon_{p}} Y_{t}$$\n",
+    "\n",
+    "Plugging this demand into $ P_{t}Y_{t} = \\int_{0}^{1} P_{jt} Y_{jt} ,\\ dj$ , we obtain\n",
+    "\n",
+    "Price index $$P_{t} = \\left(\\int_{0}^{1} P_{jt}^{1-\\epsilon_{p}}\\,dj \\right )^{\\frac{1}{1-\\epsilon_{p}}}$$\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Intermediate Good Producers\n",
+    "\n",
+    "Continuum of $j \\in [0,1]$ monopolistically competitive intermediate good producers\n",
+    "\n",
+    "Probabiliy of resetting price $1-\\lambda_{P}$ each period\n",
+    "\n",
+    "$$Y_{jt} = Z_{t}  N_{jt}$$\n",
+    "\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " ### Firm Maximization Problem\n",
+    " \n",
+    " \n",
+    " Firm $j$ chooses $P_{jt}$ to maximize its dividend $D_{jt}$ and its stock price $q^{s}_{jt} $\n",
+    " \n",
+    " $$\\max_{\\{P_{jt}\\}} \\overbrace{\\frac{(P_{jt} - MC_{t})Y_{jt}}{P_{t}}}^{=D_{jt}} + q^{s}_{jt}\\left(P_{jt}\\right) $$\n",
+    " \n",
+    "Given $q^{s}_{jt}\\left(P_{jt}\\right) = \\frac{\\mathrm{E}_{t}\\left[q^{s}_{jt+1} +D_{jt+1}\\left(P_{jt}\\right)\\right]}{1+r_{t}}$, this is equivalent to: \n",
+    " \n",
+    " $$\\max_{\\{P_{jt}\\}} \\mathrm{E}_{t}\\left[\\sum_{s=0}^{\\infty} (\\lambda_{P}) ^{s} M_{t,t+s} \\left[ \\frac{(P_{jt} - MC_{t+s})Y_{jt+s}}{P_{t+s}}\\right]\\right]$$\n",
+    " \n",
+    "subject to $$Y_{jt} = \\left(\\frac {P_{jt}}{P_{t}}\\right)^{- \\epsilon_{p}} Y_{t}$$\n",
+    " \n",
+    "where $ \\lambda_{P}$ is the  probability a firm cannot change its price,  $M_{t, t+s} = \\prod_{k=t}^{t+s-1} \\frac{1}{1+r_{k}}$ is the stochastic discount factor and $MC_{t} = \\frac{W_{t}}{A_{t}}$ is the marginal cost\n",
+    "\n",
+    "### The optimal price :\n",
+    "For firm $j$\n",
+    "\n",
+    "$$ P_{jt}^{*} = \\frac{\\epsilon_{p}}{\\epsilon_{p}-1} \\frac{\\sum_{s=0}^{\\infty}\\lambda_{p}^{s} \\mathrm{E}_{t}\\left[M_{t,t+s} \\frac{Y_{t+s}}{P_{t+s}^{1-\\epsilon_{p}}} MC_{t+s}\\right]}{\\sum_{s=0}^{\\infty}\\lambda_{p}^{s} \\mathrm{E}_{t}\\left[M_{t,t+s} \\frac{Y_{t+s}}{P_{t+s}^{1-\\epsilon_{p}}}\\right]}$$\n",
+    "\n",
+    "\n",
+    "Taking logs , optimal price can be expressed as \n",
+    "\n",
+    "$$ p_{t}^{*} = ln\\left(\\frac{\\epsilon_{p}}{\\epsilon_{p}-1}\\right) + \\left(1 - \\frac{\\lambda_{p}}{1+r^{*}}\\right) \\sum_{s=0}^{\\infty} \\lambda_{p}^{s} \\mathrm{E}_{t} \\left [ M_{t,t+s} [w_{t+s} - a_{t+s}]\\right]$$\n",
+    "\n",
+    "where the variables above are logged and $r^{*}$ is the steady state interest rate. \n",
+    "\n",
+    "\n",
+    " ## Phillips Curve:\n",
+    "\n",
+    "$$ \\pi_{t} = \\frac{\\mathrm{E}_{t}[\\pi_{t+1}]}{1+r^{*}} + \\lambda (\\mu_{t}-\\mu)$$\n",
+    "\n",
+    "where $r^{*}$ is the natural rate of interest in the steady state, $\\lambda = \\frac{(1-\\lambda_{p})(1-\\frac{\\lambda_{p}}{1+r^{*}})}{\\lambda_{p}}$,  $ \\mu_{t} = log(P_{t}) - log(W_{t}) + log(A_{t})$ and $\\mu = \\frac{\\epsilon_{p}}{1-\\epsilon_{p}}$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Labor Market\n",
+    "\n",
+    "Continuum of $g \\in [0,1]$ labor unions that supply $N_{gt}$ to a competitve labor packer\n",
+    "\n",
+    "Household $i$ provides $n_{igt}$ hour of labor to labor union $g \\in [0,1]$ and assume $n_{igt} = n_{gt}$\n",
+    " \n",
+    "\n",
+    "$$n_{it} \\equiv \\int_{0}^{1} n_{igt}\\,dg$$\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "Assume WLOG  households $i \\in [0 ,\\mho]$ are unemployed, let\n",
+    "\n",
+    "\n",
+    "$$N_{gt} = \\int_{\\mho_{t}}^{1} n_{igt}\\,di = (1-\\mho_{t}) \\mathit{n}_{gt}$$ \n",
+    "\n",
+    "Labor supply $N_{gt}$ is the aggregation of labor supplied by each employed household.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Competitve Labor  Packer\n",
+    "\n",
+    "Perfectly Competitive Labor Packer purchases labor from Labor Unions and  aggregates Labor using CES technology and sells $N_{t}$ to firms at price $W_{t}$\n",
+    "\n",
+    "\n",
+    "$$ N_{t} = \\left(\\int_{0}^{1} N_{gt}^{\\frac{\\epsilon_{w}-1}{\\epsilon_{w}}}\\,dg\\right)^{\\frac{\\epsilon_{w}}{\\epsilon_{w}-1}}$$\n",
+    "\n",
+    "The Competitve Labor Packer's profit maximizing Problem \n",
+    "\n",
+    "$$ \\max_{n_{jgt}} W_{t} \\left(\\int_{0}^{1} N_{jgt}^{\\frac{\\epsilon_{w}-1}{\\epsilon_{w}}} \\, dg \\right)^ {\\frac{\\epsilon_{w}}{\\epsilon_{w}-1}} - \\int_{0}^{1} W_{gt}N_{jgt}\\, dj $$\n",
+    "\n",
+    "\n",
+    "### Competitive Labor Packer Demand for labor types\n",
+    "\n",
+    "$$ N_{gt} = \\left(\\frac{W_{gt}}{W_{t}}\\right)^{-\\epsilon_{w}} N_{t} $$\n",
+    "\n",
+    "Wage index follows\n",
+    "$$ W_{t} = \\left(\\int_{0}^{1} W_{gt}^{1-\\epsilon_{w}}\\,dg\\right)^{\\frac{1}{1-\\epsilon_{w}}}$$\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Labor Union Maximization Problem\n",
+    "\n",
+    "Labor Union $g$ will set a wage to maximize expected lifetime utility. It may only adjust its price given it is chosen by the calvo fairy. \n",
+    "\n",
+    "$$ \\max_{\\{W_{gt}\\}} \\mathrm{E_{t}}\\left[\\sum_{s=0}^{\\infty} (\\not D \\lambda_{w})^{s} \\int_{0}^{1} \\beta_{i}^{t+s} U\\left (c(W_{t+s}), n_{i t+s}) \\, d \\Phi_{it+s} \\right)\\right] $$\n",
+    "\n",
+    "subject to the following three constraints $$ N_{gt} = \\left(\\frac{W_{gt}}{W_{t}}\\right)^{-\\epsilon_{w}} N_{t} $$\n",
+    "\n",
+    "$$ W_{t} = \\left(\\int_{0}^{1} W_{gt}^{1-\\epsilon_{w}}\\,dg\\right)^{\\frac{1}{1-\\epsilon_{w}}}$$\n",
+    "\n",
+    "where $\\lambda_{w}$ probability labor union cannot adjust its wage and $\\Phi_{it+s}$ is the distribution of  liquid assets, transitory and permanent shocks over households at period $t+s$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Optimal Wage\n",
+    "\n",
+    "$$ W_{t}^{*} = \\frac{\\epsilon_{w}}{\\epsilon_{w}-1} \\frac{\\mathrm{E}_{t} \\left[\\sum_{s=0}^{\\infty} (\\not D \\lambda_{w})^{s} N_{t+s} MV_{t+s} W_{t+s}^{\\epsilon_{w}} \\right]} {\\mathrm{E}_{t} \\left[ \\sum_{s=0}^{\\infty} (\\not D \\lambda_{w})^{s} \\frac{(1-\\tau_{t+s})}{P_{t+s}} N_{t+s}  MU_{t+s} W_{t+s}^{\\epsilon_{w}}\\right]}$$\n",
+    "\n",
+    "where $MU_{t+s} = \\int_{0}^{1}  \\beta_{i}^{t+s} \\theta_{it} U_{c} \\left(c_{i t+s}, n_{i t+s} \\right) \\  d \\Phi_{it+s} $\n",
+    "\n",
+    "$ \\quad \\quad MV_{t+s} = - \\int_{0}^{1}  \\beta_{i}^{t+s} U_{n} \\left(c_{i t+s}, n_{i t+s} \\right) \\ d \\Phi_{it+s} $\n",
+    "\n",
+    "Taking the log of both sides and isolating for $w$\n",
+    "\n",
+    "$$ w_{t}^{*} = w - \\tau - p - mrs + (1 - \\not D \\lambda_{w}) \\mathrm{E}_{t}\\left[\\sum_{s=0}^{\\infty} ( \\not D \\lambda_{w})^{s} ( mrs_{t+s} + p_{t+s} + \\tau_{t+s})\\right]$$\n",
+    "\n",
+    "$$ w_{t}^{*} = ln\\left(\\frac{\\epsilon_{w}}{\\epsilon_{w}-1}\\right) + (1 - \\not D \\lambda_{w}) \\mathrm{E}_{t}\\left[\\sum_{s=0}^{\\infty} ( \\not D \\lambda_{w})^{s} ( mrs_{t+s} + p_{t+s} + \\tau_{t+s})\\right]$$\n",
+    "\n",
+    "where $w , \\tau, p$ are logged steady state values, $mrs_{t+s} = log \\left(- \\frac{\\int_{0}^{1}  \\beta_{i}^{t+s} U_{n} \\left(c_{i t+s}, n_{i t+s} \\right) \\ d \\Phi_{it+s} ) }{\\int_{0}^{1}  \\beta_{i}^{t+s} \\theta_{it} U_{c} \\left(c_{i t+s}, n_{i t+s} \\right) \\  d \\Phi_{it+s} )} \\right)$\n",
+    "\n",
+    "Note $w- \\tau - p - mrs$ is the markup of the wage over the flexible equilibrium level."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Wage Phillips Curve\n",
+    "\n",
+    "Optimal Wage can be rewritten as \n",
+    "\n",
+    "$$ w_{t}^{*} = \\not D \\lambda_{w} \\mathrm{E}_{t} w_{t+1}^{*} + (1-\\not D \\lambda_{w})(\\mu_{w} + mrs_{t} + p_{t} + \\tau_{t})$$\n",
+    "\n",
+    "where $\\mu_{w} = ln\\left(\\frac{\\epsilon_{w}}{\\epsilon_{w}-1}\\right)$\n",
+    "\n",
+    "Then. using the approximation $w_{t} = \\lambda_{w} w_{t-1} + (1 -\\lambda_{w}) w_{t}^{*}$\n",
+    "\n",
+    "$$ \\pi_{t}^{w} =  \\not D  \\mathrm{E}_{t} \\left[ \\pi_{t+1}^{w}\\right] + \\frac{(1-\\lambda_{w})}{\\lambda_{w}} (1-\\not D \\lambda_{w}) (\\mu_{w} +mrs_{t} + p_{t}- w_{t} + \\tau_{t})$$\n",
+    "\n",
+    "\n",
+    "$$ \\pi_{t}^{w} =  \\not D  \\mathrm{E}_{t} \\left[ \\pi_{t+1}^{w}\\right] + \\frac{(1-\\lambda_{w})}{\\lambda_{w}} (1-\\not D \\lambda_{w}) (\\mu^{w} - \\mu_{t}^{w})$$\n",
+    "\n",
+    "where $\\mu_{t}^{w} = w_{t} - p_{t} - \\tau_{t} - mrs_{t}$\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Central Bank / Monetary Policy\n",
+    "\n",
+    "The central bank follows the taylor rule: \n",
+    "\n",
+    "$$i_{t} = r_{t}^{*} +\\phi \\pi_{t} + \\phi_{y} (Y_{t} - Y_{ss}) + v_{t}$$\n",
+    "\n",
+    "where $v_{t} = \\rho_{v} v_{t-1} +\\varepsilon_{t}$\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Government \n",
+    "\n",
+    "\n",
+    "The government follows the balanced budget\n",
+    "\n",
+    "\n",
+    "\n",
+    "$$ q^{b}_{t} B_{t} + G_{t} + (1-k)\\mathit{u} \\mho_{t} =  B_{t-1} +  \\tau_{t} w_{t} N_{t} $$ \n",
+    "\n",
+    "here (1-k) is needed to clear the market. Only $(1-\\mho)$ of households have labor income that is taxable\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Equilibrium\n",
+    "\n",
+    "An equilibrium in this economy is a sequence of:\n",
+    "\n",
+    "- Policy Functions $\\left( \\mathcal{A}_{t}(m) , \\mathcal{C}_{t}(m) \\right )_{t=0}^{\\infty}$ \n",
+    "\n",
+    "- Value functions $ \\left( V_{t}(m) \\right)_{t=0}^{\\infty}$\n",
+    "\n",
+    "- Distributions $ \\left(\\Phi_{t}(m) \\right)_{t=0}^{\\infty}$\n",
+    "\n",
+    "- Prices $ \\left( r^{a}_{t}, i_{t}, q^{s}_{t}, q^{b}_{t}, P_{t}, W_{t} , w_{t} , \\pi_{t}, \\pi^{w}_{t} \\right) _{t=0}^{\\infty}$\n",
+    "\n",
+    "- Aggregates $ \\left(C_{t}, Y_{t} , N_{t},D_{t} , A_{t},M_{t},  G_{t} , B_{t}, \\tau_{t} \\right)_{t=0}^{\\infty}$\n",
+    "\n",
+    "Such that:\n",
+    "\n",
+    "$ \\left( \\mathcal{A}_{t}(m) , \\mathcal{C}_{t}(m), V_{t}(m)\\right)_{t=0}^{\\infty}$  solves the household's maximization problem given $  \\left( w_{t}, N_{t},  r^{a}_{t}, \\tau_{t}, \\Phi_{t-1}(m)\\right)_{t=0}^{\\infty}$.\n",
+    "\n",
+    "The Mutual Fund, Final Goods producer, intermediate goods producers, labor packer, and labor unions maximize their objective function.\n",
+    "\n",
+    "The government budget constraint holds.\n",
+    "\n",
+    "The nominal interest rate is set according to the central bank's Taylor rule.\n",
+    "\n",
+    "\n",
+    "$ \\Phi_{t+1}(m) = H(\\Phi_{t}(m))$ holds.\n",
+    "\n",
+    "\n",
+    "Markets clear:\n",
+    "\n",
+    " $$ A_t = \\int_{0}^{1} \\mathcal{A}(m)\\, d\\Phi_{t}(m)$$\n",
+    " \n",
+    " $$ Y_t = C_{t} +G_{t} $$\n",
+    " \n",
+    " where $C_{t} = \\int_{0}^{1} \\mathcal{C}(m)\\, d\\Phi_{t}(m)$\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "attachments": {
+    "Presentation2.png": {
+     "image/png": 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"
+    }
+   },
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Steady State Distribution of Cash On Hand\n",
+    "\n",
+    "![Presentation2.png](attachment:Presentation2.png)"
+   ]
+  },
+  {
+   "attachments": {
+    "Aggregate_assets.png": {
+     "image/png": 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"
+    }
+   },
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Aggregate Assets\n",
+    "\n",
+    "![Aggregate_assets.png](attachment:Aggregate_assets.png)"
+   ]
+  },
+  {
+   "attachments": {
+    "Asset_jacobians.png": {
+     "image/png": 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"
+    }
+   },
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Asset Jacobians\n",
+    "\n",
+    "![Asset_jacobians.png](attachment:Asset_jacobians.png)"
+   ]
+  },
+  {
+   "attachments": {
+    "Aggregate_Consumption.png": {
+     "image/png": 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"
+    }
+   },
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Aggregate Consumption\n",
+    "\n",
+    "![Aggregate_Consumption.png](attachment:Aggregate_Consumption.png)"
+   ]
+  },
+  {
+   "attachments": {
+    "Consumption_jacobians.png": {
+     "image/png": 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"
+    }
+   },
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Consumption Jacobians\n",
+    "\n",
+    "![Consumption_jacobians.png](attachment:Consumption_jacobians.png)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/REMARKs/FBS-NK/code/python/Jacobian-SS.py b/REMARKs/FBS-NK/code/python/Jacobian-SS.py
new file mode 100644
index 00000000..3ab714e3
--- /dev/null
+++ b/REMARKs/FBS-NK/code/python/Jacobian-SS.py
@@ -0,0 +1,868 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Sat Apr 24 00:51:38 2021
+
+@author: William Du
+
+python 3.8.8
+
+
+"""
+import numpy as np
+import matplotlib.pyplot as plt
+from copy import copy, deepcopy
+from timeit import timeit
+from HARK.distribution import DiscreteDistribution,combine_indep_dstns, Lognormal, MeanOneLogNormal, Uniform, calc_expectation
+from HARK.utilities import get_percentiles, get_lorenz_shares, calc_subpop_avg
+from HARK import Market, make_one_period_oo_solver
+
+import HARK.ConsumptionSaving.ConsIndShockModel as ConsIndShockModel
+from HARK.ConsumptionSaving.ConsIndShockModel import (
+    ConsIndShockSolver,
+    IndShockConsumerType,
+    PerfForesightConsumerType,
+)
+from HARK.distribution import Uniform
+from HARK.ConsumptionSaving.ConsAggShockModel import CobbDouglasEconomy, AggShockConsumerType
+from HARK import MetricObject, Market, AgentType
+from scipy.optimize import brentq, minimize_scalar
+import matplotlib.pyplot as plt
+from scipy.io import loadmat
+
+from HARK.utilities import plot_funcs_der, plot_funcs
+
+
+##############################################################################
+
+
+
+##############################################################################
+##############################################################################
+
+
+
+
+    
+
+
+
+
+
+##############################################################################
+
+
+class FBSNK_agent(IndShockConsumerType):
+    
+   
+    time_inv_ = IndShockConsumerType.time_inv_  + ["mu_u",
+                                                   "L",
+                                                   "SSPmu",
+                                                   "wage",
+                                                   "N",
+                                                   "B",
+                                                 
+                                                   "s",
+                                                   "dx",
+                                                   "T_sim",
+                                                   "jac",
+                                                   "jacW",
+                                                   "PermShkStd",
+                                                   "Ghost",
+                                                   
+                                                    "PermShkCount",
+                                                    "TranShkCount",
+                                                    "TranShkStd",
+                                                    "tax_rate",
+                                                    "UnempPrb",
+                                                    "IncUnemp",
+                                                    "G",
+                                                                               
+                    
+                                                  ]
+    
+    
+
+    
+    def __init__(self, cycles= 200, **kwds):
+        
+        IndShockConsumerType.__init__(self, cycles = 200, **kwds)
+        
+     
+    
+    
+
+    def  update_income_process(self):
+        
+        self.wage = 1/(self.SSPmu) #calculate SS wage
+        self.N = (self.mu_u*(self.IncUnemp*self.UnempPrb ) + self.G )/ (self.wage*self.tax_rate)#calculate SS labor supply from Budget Constraint
+        
+
+        
+        
+        
+        PermShkDstn_U = Lognormal(np.log(self.mu_u) - (self.L*(self.PermShkStd[0])**2)/2 , self.L*self.PermShkStd[0] , 123).approx(self.PermShkCount) #Permanent Shock Distribution faced when unemployed
+        PermShkDstn_E = MeanOneLogNormal( self.PermShkStd[0] , 123).approx(self.PermShkCount) #Permanent Shock Distribution faced when employed
+        
+        
+        pmf_P = np.concatenate(((1-self.UnempPrb)*PermShkDstn_E.pmf ,self.UnempPrb*PermShkDstn_U.pmf)) 
+        X_P = np.concatenate((PermShkDstn_E.X, PermShkDstn_U.X))
+        PermShkDstn = [DiscreteDistribution(pmf_P, X_P)]
+        self.PermShkDstn = PermShkDstn 
+        
+        TranShkDstn_E = MeanOneLogNormal( self.TranShkStd[0],123).approx(self.TranShkCount)#Transitory Shock Distribution faced when employed
+        TranShkDstn_E.X = (TranShkDstn_E.X *(1-self.tax_rate)*self.wage*self.N)/(1-self.UnempPrb)**2 #NEED TO FIX THIS SQUARE TERM #add wage, tax rate and labor supply
+        
+        lng = len(TranShkDstn_E.X )
+        TranShkDstn_U = DiscreteDistribution(np.ones(lng)/lng, self.IncUnemp*np.ones(lng)) #Transitory Shock Distribution faced when unemployed
+        
+        IncShkDstn_E = combine_indep_dstns(PermShkDstn_E, TranShkDstn_E) # Income Distribution faced when Employed
+        IncShkDstn_U = combine_indep_dstns(PermShkDstn_U,TranShkDstn_U) # Income Distribution faced when Unemployed
+        
+        #Combine Outcomes of both distributions
+        X_0 = np.concatenate((IncShkDstn_E.X[0],IncShkDstn_U.X[0]))
+        X_1=np.concatenate((IncShkDstn_E.X[1],IncShkDstn_U.X[1]))
+        X_I = [X_0,X_1] #discrete distribution takes in a list of arrays
+        
+        #Combine pmf Arrays
+        pmf_I = np.concatenate(((1-self.UnempPrb)*IncShkDstn_E.pmf, self.UnempPrb*IncShkDstn_U.pmf))
+        
+        IncShkDstn = [DiscreteDistribution(pmf_I, X_I)]
+        self.IncShkDstnN = IncShkDstn
+
+        self.IncShkDstn = IncShkDstn
+        self.add_to_time_vary('IncShkDstn')
+        
+        
+        
+        
+        PermShkDstn_Uw = Lognormal(np.log(self.mu_u) - (self.L*(self.PermShkStd[0])**2)/2 , self.L*self.PermShkStd[0] , 123).approx(self.PermShkCount) #Permanent Shock Distribution faced when unemployed
+        PermShkDstn_Ew = MeanOneLogNormal( self.PermShkStd[0] , 123).approx(self.PermShkCount) #Permanent Shock Distribution faced when employed
+        
+        TranShkDstn_Ew = MeanOneLogNormal( self.TranShkStd[0],123).approx(self.TranShkCount)#Transitory Shock Distribution faced when employed
+        TranShkDstn_Ew.X = (TranShkDstn_Ew.X *(1-self.tax_rate)*(self.wage+self.dx)*self.N)/(1-self.UnempPrb)**2 #add wage, tax rate and labor supply
+        
+        lng = len(TranShkDstn_Ew.X )
+        TranShkDstn_Uw = DiscreteDistribution(np.ones(lng)/lng, self.IncUnemp*np.ones(lng)) #Transitory Shock Distribution faced when unemployed
+        
+        IncShkDstn_Ew = combine_indep_dstns(PermShkDstn_Ew, TranShkDstn_Ew) # Income Distribution faced when Employed
+        IncShkDstn_Uw = combine_indep_dstns(PermShkDstn_Uw,TranShkDstn_Uw)  # Income Distribution faced when Unemployed
+        
+        #Combine Outcomes of both distributions
+        X_0 = np.concatenate((IncShkDstn_Ew.X[0],IncShkDstn_Uw.X[0]))
+        X_1=np.concatenate((IncShkDstn_Ew.X[1],IncShkDstn_Uw.X[1]))
+        X_I = [X_0,X_1] #discrete distribution takes in a list of arrays
+        
+        #Combine pmf Arrays
+        pmf_I = np.concatenate(((1-self.UnempPrb)*IncShkDstn_Ew.pmf, self.UnempPrb*IncShkDstn_Uw.pmf))
+        
+        IncShkDstnW = [DiscreteDistribution(pmf_I, X_I)]
+        
+        self.IncShkDstnW = IncShkDstnW
+        self.add_to_time_vary('IncShkDstnW')
+        
+ 
+    
+    def get_Rfree(self):
+        """
+        Returns an array of size self.AgentCount with self.Rfree in every entry.
+        Parameters
+        ----------
+        None
+        Returns
+        -------
+        RfreeNow : np.array
+             Array of size self.AgentCount with risk free interest rate for each agent.
+        """
+    
+        
+        if self.jac==True or self.Ghost == True:
+            RfreeNow = self.Rfree[self.t_sim - 1]* np.ones(self.AgentCount)
+        else:
+           
+            RfreeNow = 1.05**.25 * np.ones(self.AgentCount)
+            
+        return RfreeNow
+    
+    def transition(self):
+        
+        
+        pLvlPrev = self.state_prev['pLvl']
+        aNrmPrev = self.state_prev['aNrm']
+        RfreeNow = self.get_Rfree()
+
+        # Calculate new states: normalized market resources and permanent income level
+        pLvlNow = pLvlPrev*self.shocks['PermShk']  # Updated permanent income level
+        # Updated aggregate permanent productivity level
+        PlvlAggNow = self.state_prev['PlvlAgg']*self.PermShkAggNow
+        # "Effective" interest factor on normalized assets
+        ReffNow = RfreeNow/self.shocks['PermShk']
+        bNrmNow = ReffNow*aNrmPrev         # Bank balances before labor income
+        mNrmNow = bNrmNow + self.shocks['TranShk']  # Market resources after income
+        
+        
+        if self.jac == True or self.jacW == True or self.Ghost==True:
+        
+            if self.t_sim == 0:
+                
+                for i in range(num_consumer_types):
+                    if  self.DiscFac == consumers_ss[i].DiscFac:
+
+                        mNrmNow = consumers_ss[i].history['mNrm'][self.T_sim-1,:]
+                        pLvlNow = consumers_ss[i].history['pLvl'][self.T_sim-1,:]
+                        print(self.DiscFac)
+    
+
+        return pLvlNow, PlvlAggNow, bNrmNow, mNrmNow, None
+    
+    
+    
+    
+FBSDict={
+    # Parameters shared with the perfect foresight model
+    "CRRA":2,                           # Coefficient of relative risk aversion
+    "Rfree": 1.05**.25,                       # Interest factor on assets
+    "DiscFac": 0.978,                     # Intertemporal discount factor
+    "LivPrb" : [.98],  #.9725                  # Survival probability
+    "PermGroFac" :[1.00],                 # Permanent income growth factor
+
+    # Parameters that specify the income distribution over the lifecycle
+   
+    "PermShkStd" :  [(0.01*4/11)**0.5],    # Standard deviation of log permanent shocks to income
+    "PermShkCount" : 5,                    # Number of points in discrete approximation to permanent income shocks
+    "TranShkStd" : [.2],        # Standard deviation of log transitory shocks to income
+    "TranShkCount" : 5,                    # Number of points in discrete approximation to transitory income shocks
+    "UnempPrb" : 0.05,                     # Probability of unemployment while working
+    "IncUnemp" : 0.08,                      # Unemployment benefits replacement rate
+    "UnempPrbRet" : 0.0005,                # Probability of "unemployment" while retired
+    "IncUnempRet" : 0.0,                   # "Unemployment" benefits when retired
+    "T_retire" : 0,                        # Period of retirement (0 --> no retirement)
+    "tax_rate" : 0.1,                      # Flat income tax rate (legacy parameter, will be removed in future)
+
+    # Parameters for constructing the "assets above minimum" grid
+    "aXtraMin" : 0.001,                    # Minimum end-of-period "assets above minimum" value
+    "aXtraMax" : 20,                       # Maximum end-of-period "assets above minimum" value
+    "aXtraCount" : 48,                     # Number of points in the base grid of "assets above minimum"
+    "aXtraNestFac" : 3,                    # Exponential nesting factor when constructing "assets above minimum" grid
+    "aXtraExtra" : [None],                 # Additional values to add to aXtraGrid
+
+    # A few other parameters
+    "BoroCnstArt" : 0.0,                   # Artificial borrowing constraint; imposed minimum level of end-of period assets
+    "vFuncBool" : True,                    # Whether to calculate the value function during solution
+    "CubicBool" : False,                   # Preference shocks currently only compatible with linear cFunc
+    "T_cycle" : 1,                         # Number of periods in the cycle for this agent type
+
+    # Parameters only used in simulation
+    "AgentCount" : 150000,                  # Number of agents of this type
+    "T_sim" : 500,                         # Number of periods to simulate
+    "aNrmInitMean" : np.log(.27)-(.5**2)/2,                 # Mean of log initial assets
+    "aNrmInitStd"  : 0.3,                  # Standard deviation of log initial assets
+    "pLvlInitMean" : 0.0,                  # Mean of log initial permanent income
+    "pLvlInitStd"  : 0.0,                  # Standard deviation of log initial permanent income
+    "PermGroFacAgg" : 1.0,                 # Aggregate permanent income growth factor
+    "T_age" : None,                        # Age after which simulated agents are automatically killed
+    
+    # new parameters
+     "mu_u"       : .9 ,
+     "L"          : 1.1, 
+     "s"          : 1,
+     "dx"         : .1,                  #Deviation from steady state
+     "jac"        : True,
+     "jacW"       : True, 
+     "Ghost"      : False, 
+     
+    #New Economy Parameters
+     "SSWmu " : 1.025 ,                      # Wage Markup from sequence space jacobian appendix
+     "SSPmu" :  1.025,                       # Price Markup from sequence space jacobian appendix
+     "calvo price stickiness":  .926,      # Auclert et al 2020
+     "calvo wage stickiness": .899,        # Auclert et al 2020
+     "B" : 0,                               # Net Bond Supply
+     "G" : .01
+     }
+
+
+    
+###############################################################################
+
+
+
+###############################################################################
+
+ss_agent = FBSNK_agent(**FBSDict)
+ss_agent.cycles = 0
+ss_agent.jac = False
+ss_agent.jacW = False
+ss_agent.dx = 0
+ss_agent.T_sim = 1400
+ss_agent.track_vars = ['aNrm','mNrm','cNrm','pLvl']
+
+target = .27704816263570453
+
+NumAgents = 150000
+
+tolerance = .001
+
+completed_loops=0
+
+go = True
+
+num_consumer_types = 7     # number of types 
+
+
+'''
+example = FBSNK_agent(**IdiosyncDict)
+example.cycles = 0
+example.jac = False
+example.jacW = False
+example.dx = 0
+example.T_sim = 1400
+example.track_vars = ['aNrm','mNrm','cNrm','pLvl']
+example.DiscFac = .986
+
+example.solve()
+example.initialize_sim()
+example.simulate()
+
+'''
+
+#center = .977 for Rfree 1.04**.25 and target 0.34505832912738216
+center =.9681
+#center =.7
+
+while go:
+    
+    discFacDispersion = 0.0049
+    bottomDiscFac     = center - discFacDispersion
+    topDiscFac        = center + discFacDispersion
+    
+    #tail_N = 3
+    #param_dist = Lognormal(mu=np.log(center)-0.5*spread**2,sigma=spread,tail_N=tail_N,tail_bound=[0.0,0.9], tail_order=np.e).approx(N=param_count-tail_N)
+    
+    #DiscFac_dist =Lognormal(mu=np.log(center)-0.5*discFacDispersion**2,sigma=discFacDispersion).approx(N=num_consumer_types-3,tail_N=3, tail_bound=[0,0.9])
+    DiscFac_dist  = Uniform(bot=bottomDiscFac,top=topDiscFac,seed=606).approx(N=num_consumer_types)
+    DiscFac_list  = DiscFac_dist.X
+    
+    consumers_ss = [] 
+    
+    # now create types with different disc factors
+    for i in range(num_consumer_types):
+        consumers_ss.append(deepcopy(ss_agent))
+        
+    for i in range(num_consumer_types):
+        consumers_ss[i].DiscFac    = DiscFac_list[i]
+        consumers_ss[i].AgentCount = int(NumAgents*DiscFac_dist.pmf[i])
+    
+    
+
+    list_pLvl=[]
+    list_aNrm =[]
+    list_aLvl=[]
+    litc=[]
+    # simulate and keep track mNrm and MPCnow
+    for i in range(num_consumer_types):
+        consumers_ss[i].solve()
+        consumers_ss[i].initialize_sim()
+        consumers_ss[i].simulate()
+        
+        list_pLvl.append(consumers_ss[i].state_now['pLvl'])
+        list_aNrm.append(consumers_ss[i].state_now['aNrm'])
+        litc.append((consumers_ss[i].state_now['mNrm'] - consumers_ss[i].state_now['aNrm'])*consumers_ss[i].state_now['pLvl'])
+        list_aLvl.append(consumers_ss[i].state_now['aLvl'])
+        
+        print('one consumer solved and simulated')
+    
+    pLvl = np.concatenate(list_pLvl)
+    aNrm = np.concatenate(list_aNrm)
+    c = np.concatenate(litc)
+    a = np.concatenate(list_aLvl)
+    AggA = np.mean(np.array(a))
+    AggC = np.mean(np.array(c))
+
+    
+    
+    if AggA - target > 0 :
+        
+       center = center - .0001
+        
+    elif AggA - target < 0: 
+        center = center + .0001
+        
+    else:
+        break
+    
+    
+    print('Assets')
+    print(AggA)
+    print('consumption')
+    print(AggC)
+    print('center')
+    print(center)
+    
+    distance = abs(AggA - target) 
+    
+    completed_loops += 1
+    
+    print('Completed loops')
+    print(completed_loops)
+    
+    go = distance >= tolerance and completed_loops < 1
+        
+print("Done Computing Steady State")
+
+
+###############################################################################
+###############################################################################
+
+
+
+funcs=[]
+list_mLvl = []
+list_mNrm = []
+list_aNrm = []
+for i in range(num_consumer_types):
+    list_mLvl.append(consumers_ss[i].state_now['mNrm']*consumers_ss[i].state_now['pLvl'] )
+    list_mNrm.append(consumers_ss[i].state_now['mNrm'])
+    list_aNrm.append(consumers_ss[i].state_now['aNrm'])
+    funcs.append(consumers_ss[i].solution[0].cFunc)
+
+mNrm = np.concatenate(list_mNrm)   
+mLvl = np.concatenate(list_mLvl)
+aNrm = np.concatenate(list_aNrm)
+
+
+
+x = np.linspace(0, 1.4, 1000, endpoint=True)
+
+y=[]
+for i in range(num_consumer_types):
+    y.append(funcs[i](x))
+
+
+h = np.histogram(mNrm, bins=np.linspace(0,1.4,num=1000))
+
+fig = plt.figure()
+ax1 = fig.add_subplot(111)
+plt.xlabel('Cash on Hand')
+plt.xlim(0,1.4)
+ax1.plot(x, y[0], 'k' )
+
+ax1.plot(x, y[1], 'm' )
+ax1.plot(x, y[2], 'darkorange' )
+ax1.plot(x, y[3], 'forestgreen' )
+ax1.plot(x, y[4], 'deepskyblue' )
+ax1.plot(x, y[5], 'r' )
+ax1.plot(x, y[6], 'darkslategrey' )
+
+
+ax1.set_ylim((0,.23))
+ax1.set_ylabel('Consumption', color='k')
+
+
+ax2= ax1.twinx()
+ax2.hist(mNrm, bins=np.linspace(0,1.4,num=1000),color = 'darkviolet')
+#ax2.hist(example.state_now['mNrm'],bins=np.linspace(0,1.4,num=1000),color= 'orange' )
+ax2.set_ylim((0,1600))
+ax2.set_ylabel('Number of Households', color='k')
+#plt.savefig("Presentation.png", dpi=150)
+
+
+
+################################################################################
+################################################################################
+
+
+class FBSNK2(FBSNK_agent):
+    
+    
+    
+     def update_solution_terminal(self):
+        """
+        Update the terminal period solution.  This method should be run when a
+        new AgentType is created or when CRRA changes.
+        Parameters
+        ----------
+        none
+        Returns
+        -------
+        none
+        """
+        
+        for i in range(num_consumer_types):
+            if self.DiscFac == DiscFac_list[i]:
+                self.solution_terminal.cFunc = deepcopy(consumers_ss[i].solution[0].cFunc)
+                self.solution_terminal.vFunc = deepcopy(consumers_ss[i].solution[0].vFunc)
+                self.solution_terminal.vPfunc = deepcopy(consumers_ss[i].solution[0].vPfunc)
+                self.solution_terminal.vPPfunc =  deepcopy(consumers_ss[i].solution[0].vPPfunc)
+        
+
+###############################################################################
+
+params = deepcopy(FBSDict)
+
+
+params['T_cycle']= 200
+params['LivPrb']= params['T_cycle']*[.98]
+params['PermGroFac']=params['T_cycle']*[1]
+params['PermShkStd'] = params['T_cycle']*[(0.01*4/11)**0.5]
+params['TranShkStd']= params['T_cycle']*[.2]
+listRfree = params['T_cycle']*[ss_agent.Rfree]
+params['Rfree'] = listRfree
+
+###############################################################################
+
+
+ghost_agent = FBSNK2(**params)
+ghost_agent.pseudo_terminal = False
+ghost_agent.IncShkDstn = params['T_cycle']*ghost_agent.IncShkDstn
+ghost_agent.del_from_time_inv('Rfree')
+ghost_agent.add_to_time_vary('Rfree')
+
+ghost_agent.T_sim = params['T_cycle']
+ghost_agent.cycles = 1
+ghost_agent.track_vars = ['aNrm','mNrm','cNrm','pLvl','aLvl']
+ghost_agent.dx = 0
+ghost_agent.jac = False
+ghost_agent.jacW = False
+ghost_agent.Ghost = True
+
+
+ghosts= [] 
+
+for i in range(num_consumer_types):
+    ghosts.append(deepcopy(ghost_agent))
+
+# now create types with different disc factors
+for i in range(num_consumer_types):
+        ghosts[i].DiscFac   = DiscFac_list[i]
+        ghosts[i].AgentCount = int(NumAgents*DiscFac_dist.pmf[i])
+        #ghosts[i].solution_terminal = deepcopy(consumers_ss[i].solution[0]) ### Should it have a Deepcopy?
+        #ghosts[i].cFunc_terminal_ = deepcopy(consumers_ss[i].solution[0].cFunc)
+
+        
+##############################################################################
+     
+     
+listA_g = []
+listH_Ag= []
+listC_g = []
+listH_g = []
+listH_Mg =[]
+listM_g = []
+    
+for k in range(num_consumer_types):
+    ghosts[k].solve()
+    ghosts[k].initialize_sim()
+    ghosts[k].simulate()
+
+    listH_g.append([ghosts[k].history['cNrm'], ghosts[k].history['pLvl']])
+    listH_Ag.append(ghosts[k].history['aLvl'])
+    listH_Mg.append(ghosts[k].history['mNrm'])
+    
+for j in range(ghost_agent.T_sim):
+
+    litc_g=[]
+    lita_g=[]
+    litm_g=[]
+    for n in range(num_consumer_types):
+        litc_g.append(listH_g[n][0][j,:]*listH_g[n][1][j,:])
+        lita_g.append(listH_Ag[n][j,:])
+        litm_g.append(listH_Mg[n][j,:]*listH_g[n][1][j,:])
+        
+    Ag=np.concatenate(lita_g)
+    Ag=np.mean(np.array(Ag))
+    
+    Cg = np.concatenate(litc_g)
+    Cg = np.mean(np.array(Cg))
+
+    Mg = np.concatenate(litm_g)
+    Mg = np.mean(np.array(Mg))
+
+    listM_g.append(Mg)
+    listA_g.append(Ag)
+    listC_g.append(Cg)
+        
+M_dx0 = np.array(listM_g)
+A_dx0 = np.array(listA_g)
+C_dx0 = np.array(listC_g)
+
+plt.plot(C_dx0, label = 'Consumption Steady State')
+plt.legend()
+plt.show()
+
+
+###############################################################################
+###############################################################################
+
+
+jac_agent = FBSNK2(**params)
+jac_agent.pseudo_terminal = False
+jac_agent.dx = 0.1
+jac_agent.jac = True
+jac_agent.jacW = False
+jac_agent.IncShkDstn = params['T_cycle']*jac_agent.IncShkDstn
+jac_agent.del_from_time_inv('Rfree')
+jac_agent.add_to_time_vary('Rfree')
+jac_agent.T_sim = params['T_cycle']
+jac_agent.cycles = 1
+jac_agent.track_vars = ['aNrm','mNrm','cNrm','pLvl','aLvl']
+
+
+consumers = [] 
+
+# now create types with different disc factors
+
+for i in range(num_consumer_types):
+    consumers.append(deepcopy(jac_agent))
+
+
+for i in range(num_consumer_types):
+        consumers[i].DiscFac    = DiscFac_list[i]
+        consumers[i].AgentCount = int(NumAgents*DiscFac_dist.pmf[i])
+        #consumers[i].solution_terminal = deepcopy(consumers_ss[i].solution[0]) ### Should it have a Deepcopy?
+        #consumers[i].cFunc_terminal_ = deepcopy(consumers_ss[i].solution[0].cFunc)
+
+
+###############################################################################
+###############################################################################
+
+
+testSet= [1,15,40,100]
+
+Mega_list =[]
+CHist = []
+AHist = []
+MHist = []
+#for i in range(jac_agent.T_sim):
+for i in testSet:
+        
+        listH_C = []
+        listH_A = []
+        listH_M = []
+        listC = []
+        listA = []
+        listM = []
+        for k in range(num_consumer_types):
+            
+            consumers[k].s = i 
+            #consumers[k].IncShkDstn = (i-1)*ss_agent.IncShkDstn + jac_agent.IncShkDstnW + (params['T_cycle'] - i)*ss_agent.IncShkDstn
+            consumers[k].Rfree = (i- 1)*[ss_agent.Rfree] + [ss_agent.Rfree + jac_agent.dx] + (params['T_cycle']- i)*[ss_agent.Rfree]
+
+
+            consumers[k].solve()
+            consumers[k].initialize_sim()
+            consumers[k].simulate()
+            
+            listH_C.append([consumers[k].history['cNrm'],consumers[k].history['pLvl']])
+            listH_M.append(consumers[k].history['mNrm'])
+            #listA.append([consumers[k].history['aNrm'],consumers[k].history['pLvl']])
+            listH_A.append(consumers[k].history['aLvl'])
+
+            
+        for j in range(jac_agent.T_sim):
+            
+            litc_jac= []
+            lita_jac =[]
+            litm_jac =[]
+            for n in range(num_consumer_types):
+                litc_jac.append(listH_C[n][0][j,:]*listH_C[n][1][j,:])
+                lita_jac.append(listH_A[n][j,:])
+                litm_jac.append(listH_M[n][j,:]*listH_C[n][1][j,:])
+
+            
+            c = np.concatenate(litc_jac)
+            c = np.mean(np.array(c))
+            listC.append(c)
+            
+            a = np.concatenate(lita_jac)
+            a = np.mean(np.array(a))
+            listA.append(a)
+            
+            
+            m = np.concatenate(litm_jac)
+            m = np.mean(np.array(m))
+            listM.append(m)
+            
+
+        
+        AHist.append(np.array(listA))
+        MHist.append(np.array(listM))
+        CHist.append(np.array(listC))
+        #Mega_list.append(np.array(listC)- C_dx0)  # Elements of this list are arrays. The index of the element +1 represents the 
+                                                  # Derivative with respect to a shock to the interest rate in period s.
+                                                  # The ith element of the arrays in this list is the time t deviation in consumption to a shock in the interest rate in period s
+        print(i)
+
+###############################################################################
+###############################################################################
+
+
+
+
+'''
+plt.plot(M_dx0, label = 'm steady state')
+plt.plot(MHist[1], label = '15')
+plt.plot(MHist[3], label = '100')
+plt.plot(MHist[2], label = '40')
+plt.legend()
+plt.show()
+
+plt.plot(MHist[1] - M_dx0, label = '15')
+plt.plot(MHist[3] - M_dx0, label = '100')
+plt.plot(MHist[2] - M_dx0, label = '40')
+plt.plot(np.zeros(jac_agent.T_sim), 'k')
+plt.legend()
+plt.show()
+'''
+
+
+plt.plot(A_dx0, label = 'Asset steady state')
+plt.plot(AHist[2], label = '40')
+plt.plot(AHist[3], label = '100')
+plt.plot(AHist[0], label = '15')
+plt.plot(AHist[0], label = '1')
+plt.ylim([.240,.33])
+plt.xlabel("Period")
+plt.ylabel("Aggregate Assets")
+plt.title("Aggregate Assets")
+plt.legend()
+plt.show()
+
+
+
+plt.plot((AHist[0][1:]- A_dx0[1:])/(jac_agent.dx), label = '1')
+plt.plot((AHist[1][1:]- A_dx0[1:])/(jac_agent.dx), label = '15')
+plt.plot((AHist[2][1:] - A_dx0[1:])/(jac_agent.dx), label = '40')
+plt.plot((AHist[3][1:] - A_dx0[1:])/(jac_agent.dx), label = '100')
+plt.plot(np.zeros(jac_agent.T_sim), 'k')
+plt.xlabel("Period")
+plt.ylabel("dA / dr")
+plt.ylim([-.2,.6])
+plt.title("Asset Jacobians")
+plt.legend()
+plt.show()
+#plt.savefig("Rfree_jacobian.jpg", dpi=150)
+
+
+plt.plot(C_dx0 , label = 'Steady State')
+plt.plot(CHist[1], label = '15')
+plt.plot(CHist[3], label = '100')
+plt.plot(CHist[2], label = '40')
+plt.title("Aggregate Consumption")
+plt.ylabel("Aggregate Consumption")
+plt.xlabel("Period")
+
+plt.ylim([0.12,.1350])
+plt.legend()
+#plt.savefig("May3rdWage.jpg", dpi=150)
+plt.show()
+
+
+
+
+
+plt.plot((CHist[0][1:]- C_dx0[1:])/(jac_agent.dx), label = '1')
+plt.plot((CHist[3][1:]- C_dx0[1:])/(jac_agent.dx), label = '100')
+plt.plot((CHist[1][1:]- C_dx0[1:])/(jac_agent.dx), label = '15')
+plt.plot((CHist[2][1:] - C_dx0[1:])/(jac_agent.dx), label = '40')
+plt.plot(np.zeros(jac_agent.T_sim), 'k')
+plt.ylim([-.04,.04])
+plt.ylabel("dC / dr")
+
+plt.xlabel("Period")
+plt.title("Consumption Jacobians")
+plt.legend()
+#plt.savefig("wage_jacobian.jpg", dpi=150)
+plt.show()
+
+
+# =============================================================================
+# 
+# G=.01
+# t=.1
+# Inc = .08
+# mho=.05
+# 
+# w = (1/1.025)
+# N = (.9*(Inc*mho)+G)/ (w*t) 
+# r = (1.05)**.25 -1
+# print(N)
+# 
+# N1 = (.9*(.08*.05)+.01)/ (w*t) 
+# 
+# 
+# q = ((1-w)*N)/r
+# 
+# print(N)
+# print(N1-N)
+# print(q)
+# 
+# =============================================================================
+
+'''
+funcs=[]
+list_mLvl = []
+list_mNrm = []
+for i in range(num_consumer_types):
+    list_mLvl.append(consumers_ss[i].state_now['mNrm']*consumers_ss[i].state_now['pLvl'] )
+    list_mNrm.append(consumers_ss[i].state_now['mNrm'])
+    funcs.append(consumers_ss[i].solution[0].cFunc)
+
+mNrm = np.concatenate(list_mNrm)   
+mLvl = np.concatenate(list_mLvl)
+plot_funcs(funcs,0,1.4)
+plt.hist(mNrm, bins=np.linspace(0,1.4,num=1000))
+plt.show()
+
+plt.hist(mLvl, bins=np.linspace(0,1.2,num=1000))
+plt.show()
+
+
+
+x = np.linspace(0, 1.4, 1000, endpoint=True)
+
+y=[]
+for i in range(num_consumer_types):
+    y.append(funcs[i](x))
+
+
+h = np.histogram(mNrm, bins=np.linspace(0,1.4,num=1000))
+
+fig = plt.figure()
+ax1 = fig.add_subplot(111)
+plt.xlabel('Cash on Hand')
+ax1.plot(x, y[0], 'm' )
+
+
+ax1.plot(x, y[1], 'k' )
+ax1.plot(x, y[2], 'darkorange' )
+ax1.plot(x, y[3], 'forestgreen' )
+ax1.plot(x, y[4], 'deepskyblue' )
+ax1.plot(x, y[5], 'r' )
+ax1.plot(x, y[6], 'darkslategrey' )
+ax1.set_ylim((0,.23))
+ax1.set_ylabel('Consumption', color='k')
+
+
+ax2= ax1.twinx()
+ax2.hist(mNrm, bins=np.linspace(0,1.4,num=1000),color= 'darkviolet')
+ax2.set_ylim((0,1600))
+ax2.set_ylabel('Number of Households', color='k')
+#plt.savefig("Presentation.png", dpi=150)
+
+
+sigma=.3
+mean=np.log(.4)-(sigma**2)/2
+
+print(np.exp(mean + (sigma**2)/2))
+print((np.exp(sigma)-1)*np.exp(2*mean+sigma**2))
+
+'''
+
+
+
+
+
+
+
+
+
+
diff --git a/REMARKs/FBS-NK/reproduce.sh b/REMARKs/FBS-NK/reproduce.sh
new file mode 100644
index 00000000..e0caf24a
--- /dev/null
+++ b/REMARKs/FBS-NK/reproduce.sh
@@ -0,0 +1,8 @@
+#!/bin/bash
+# install the versioned required packages
+python3 -m pip install --quiet -r requirements.txt
+
+# navigate to code/ and execute the python file to create figures
+cd ./code/python
+jupyter notebook FBS-NK-model.ipynb
+ipython Jacobian-SS.py
\ No newline at end of file
diff --git a/REMARKs/FBS-NK/requirements.txt b/REMARKs/FBS-NK/requirements.txt
new file mode 100644
index 00000000..7c47d329
--- /dev/null
+++ b/REMARKs/FBS-NK/requirements.txt
@@ -0,0 +1,8 @@
+ 
+econ-ark == 0.11.0
+
+numpy == 1.20.2
+
+matplotlib == 3.4.1
+
+scipy==1.6.2
\ No newline at end of file