Merge pull request #12 from wmutschl/Guerrieri-Iacoviello

Add Guerrieri and Iacoviello 2015 RBC and NK model with occbin

Guerrieri_Iacoviello_2015/Guerrieri_Iacoviello_2015_nk.mod

@@ -0,0 +1,203 @@
+/*
+ * This file replicates the IRFs in figure 5 of the NK model with a 
+ * constraint on nominal interest rates illustrated in:
+ * Guerrieri and Iacoviello (2015): "OccBin: A toolkit for solving dynamic 
+ *   models with occastionally binding constraints easily", Journal of
+ *   Monetary Economics 70, pp.22-38.
+ *
+ * Notes:
+ *  - This mod file uses Dynare's occbin toolkit which is based on the one
+ *    by Guerrieri and Iacoviello (2015)
+ *  - The model equations are taken from the appendix as the equations in 
+ *    the printed version have some typos, e.g. missing paranthesis in eq. (24).
+ *    Moreover, in the original replication files the model equations were
+ *    simplified to reduce the model size for the global solution method;
+ *    however, for this replication this is not important so we stick with
+ *    the full version as outlined in the appendix.
+ *  - The authors do not provide a calibrated value for PSI. Looking at 
+ *    the original replication files it looks like PSI is an endogenous
+ *    parameter that makes sure that in steady-state y=1. This is implemented
+ *    in the steady-state model block in this mod file.
+ *  - The value for the shock is not clear.
+ *    In the paper it is claimed that the size is equal to 4 standard 
+ *    deviations and the standard deviation is given in table 3 as 0.005.
+ *    However, a positive shock of size 4*0.005=0.02 brings \beta_6 up to 
+ *    1.000514 (and not to 1.019 as claimed in Fig. 5) and a negative shock
+ *    of this size brings \beta_6 down to 0.987486 (and not to 0.969 as 
+ *    claimed in Fig. 5). In the replication files a value of 0.024 is used;
+ *    however, the positive shock of this size brings \beta_6 up to 1.001817
+ *    and a negative shock down to 0.986183. The printed figure, however,
+ *    looks closest to a value of 5*0.005=0.025, which is chosen below.
+ *    Of course one can change the size below.
+ *  - The reporting variables are different in the replication files than
+ *    in the published paper. This implementation focuses on the figure
+ *    in the published paper.
+ * 
+ * This implementation was written by Willi Mutschler (@wmutschl).
+ *
+ * If you spot mistakes, email me at [email protected]
+ *
+ * Please note that the following copyright notice only applies to this Dynare 
+ * implementation of the model.
+ */
+
+/*
+ * Copyright © 2022 Willi Mutschler
+ *
+ * This is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * It is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * For a copy of the GNU General Public License,
+ * see <https://www.gnu.org/licenses/>.
+ */
+
+var
+  bet        ${\beta}$              (long_name='time-varying discount factor')
+  c          ${C}$                  (long_name='consumption')
+  y          ${Y}$                  (long_name='output')
+  l          ${L}$                  (long_name='labor')
+  w          ${w}$                  (long_name='wage')
+  mc         ${mc}$                 (long_name='marginal cost')  
+  r          ${R}$                  (long_name='nominal interest rate')
+  g          ${G}$                  (long_name='government spending')
+  pie        ${\Pi}$                (long_name='inflation')
+  pie_star   ${\Pi^*}$              (long_name='reset price')
+  x1         ${x1}$                 (long_name='aux. sum 1 recursive price setting')
+  x2         ${x2}$                 (long_name='aux. sum 1 recursive price setting')
+  v          ${v}$                  (long_name='price dispersion')
+  pie_an     ${\pi^{ann}}$          (long_name='annualized inflation (in percentage point deviation from steady-state)')
+  r_an       ${R^{ann}}$            (long_name='annualized nominal interest rate (in level percent deviation from ZLB)')
+  yhat       ${\hat{y}}$            (long_name='output (in percentage deviation from steady-state)')
+;
+
+varexo
+  epsi       ${\epsilon}$           (long_name='discount factor shock')
+;
+
+parameters
+  BETA       ${\beta}$              (long_name='steady-state discount factor')
+  THETA      ${\theta}$             (long_name='Calvo parameter')
+  PHI_Y      ${\phi_y}$             (long_name='response to output, Mon. Pol. Rule')
+  PHI_PI     ${\phi_\pi}$           (long_name='response to inflation, Mon. Pol. Rule')
+  RHO        ${\rho}$               (long_name='persistence of discount rate shock')
+  EPSILON    ${\varepsilon}$        (long_name='elasticity of substitution across goods')
+  G_Y        ${s_g}$                (long_name='steady-state ratio of G/Y')
+  PI         ${\Pi}$                (long_name='steady-state inflation')
+  PHI        ${\phi}$               (long_name='labor supply elasticity')
+  PSI        ${\psi}$               (long_name='utility weight leisure (endogenous)')
+  ZLB        ${ZLB}$                (long_name='value of zero lower bound')
+;
+
+BETA    = 0.994;
+THETA   = 0.90;
+PHI_Y   = 0.25;
+PHI_PI  = 2.5;
+RHO     = 0.8;
+EPSILON = 6;
+G_Y     = 0.20;
+PI      = 1.005;
+PHI     = 1;
+ZLB     = 1;
+% note that PSI is calibrated in the steady_state model block such that y=1;
+
+model;
+[name='(A.2): consumption Euler equation']
+c^(-1) = bet*c(+1)^(-1)*r/pie(+1);
+[name='(A.3): marginal costs / labor demand']
+mc = w;
+[name='(A.4): labor supply']
+w = PSI*l^PHI*c;
+[name='(A.5): optimal price setting']
+EPSILON*x1 = (EPSILON-1)*x2;
+[name='(A.6): optimal price setting auxiliary recursion 1']
+x1 = mc*y/c + THETA*bet*pie(+1)^EPSILON*x1(+1);
+[name='(A.7): optimal price setting auxiliary recursion 2']
+x2/pie_star = y/c + THETA*bet*pie(+1)^(EPSILON-1)*x2(+1)/pie_star(+1);
+[name='(A.8): monetary policy rule',relax='zlb']
+r = steady_state(r)*(pie/PI)^PHI_PI*(y/steady_state(y))^PHI_Y;
+[name='(A.8): monetary policy rule',bind='zlb']
+r = ZLB;
+[name='(A.10): government spending']
+g = G_Y*y;
+[name='(A.11): law of motion for optimal reset price']
+1 = THETA*pie^(EPSILON-1) + (1-THETA)*pie_star^(1-EPSILON);
+[name='(A.12): law of motion for price dispersion']
+v = THETA*pie^EPSILON*v(-1) + (1-THETA)*pie_star^(-EPSILON);
+[name='(A.13): aggregate demand']
+y = c + g;
+[name='(A.14): aggregate supply']
+y = l/v;
+[name='(A.15): law of motion discount factor']
+log(bet) = (1-RHO)*log(BETA) + RHO*log(bet(-1)) + epsi;
+
+[name='reporting: annualized nominal interest rate (in level percent deviation from ZLB)']
+r_an = 400*(r-ZLB);
+[name='reporting: reporting: annualized inflation (in percentage point deviation from steady-state)']
+pie_an = 400*(pie-steady_state(pie));
+[name='reporting: output (in percentage deviation from steady-state)']
+yhat = 100*(y/steady_state(y)-1);
+end;
+
+
+steady_state_model;
+bet = BETA;
+pie = PI;
+pie_star = ((1-THETA*pie^(EPSILON-1))/(1-THETA))^(1/(1-EPSILON));
+mc = (EPSILON-1)/EPSILON * pie_star * (1-bet*THETA*pie^EPSILON) / (1-bet*THETA*pie^(EPSILON-1)) ;
+v = (1-THETA)*pie_star^(-EPSILON)/(1-THETA*pie^EPSILON);
+r = pie/BETA;
+w = mc;
+y_c = 1/(1-G_Y);
+x2 = pie_star*y_c / (1-THETA*bet*pie^(EPSILON-1));
+x1 = (EPSILON-1)/EPSILON*x2;
+% calibrate PSI such that y=1 in steady-state
+y = 1;
+l = v*y;
+c = (1-G_Y)*y;
+g = G_Y*y;
+PSI = w/(l^PHI*c); % note that this is an endogenous parameter updated during steady-state computations
+r_an = 400*(r-ZLB);
+pie_an = 0;
+yhat = 0;
+end;
+steady;
+
+occbin_constraints;
+name 'zlb'; bind r <=  ZLB; relax r > ZLB;
+end;
+
+% shock size: see notes on top
+@#define SHOCKSIZE = 5*0.005
+
+% replicate left column of Fig. 5 (increase in discount factor)
+shocks(surprise,overwrite);
+var epsi; periods 6; values @{SHOCKSIZE};
+end;
+
+occbin_setup(simul_periods=30,simul_check_ahead_periods=200);
+occbin_solver;
+% the figure only plots simulations for periods 6 to 15
+oo_.occbin.simul.piecewise = oo_.occbin.simul.piecewise(6:15,:);
+oo_.occbin.simul.linear = oo_.occbin.simul.linear(6:15,:);
+occbin_graph r_an v pie_an yhat;
+fprintf('positive shock of size %f brings beta up to %f\n',options_.occbin.simul.SHOCKS(6,1),oo_.occbin.simul.piecewise(6,ismember(M_.endo_names,'bet')));
+
+% replicate left column of Fig. 5 (decrease in discount factor)
+shocks(surprise,overwrite);
+var epsi; periods 6; values -@{SHOCKSIZE};
+end;
+occbin_setup(simul_periods=30,simul_check_ahead_periods=200);
+occbin_solver;
+% the figure only plots simulations for periods 6 to 15
+oo_.occbin.simul.piecewise = oo_.occbin.simul.piecewise(6:15,:);
+oo_.occbin.simul.linear = oo_.occbin.simul.linear(6:15,:); % 
+occbin_graph r_an v pie_an yhat;
+fprintf('negative shock of size %f brings beta down to %f\n',options_.occbin.simul.SHOCKS(6,1),oo_.occbin.simul.piecewise(6,ismember(M_.endo_names,'bet')));
+

Guerrieri_Iacoviello_2015/Guerrieri_Iacoviello_2015_rbc.mod

@@ -0,0 +1,122 @@
+/*
+ * This file replicates the IRFs in figure 3 of the RBC model with a 
+ * constraint on investment illustrated in:
+ * Guerrieri and Iacoviello (2015): "OccBin: A toolkit for solving dynamic 
+ *   models with occastionally binding constraints easily", Journal of
+ *   Monetary Economics 70, pp.22-38.
+ *
+ * Notes:
+ *  - This mod file uses Dynare's occbin toolkit which is based on the one
+ *    by Guerrieri and Iacoviello (2015)
+ *  - The consumption Euler equation (11) in the paper has a typo at the 
+ *    end as it should be \lambda_{t+1}; this is correct in the Appendix
+ * 
+ * This implementation was written by Willi Mutschler (@wmutschl).
+ *
+ * If you spot mistakes, email me at [email protected]
+ *
+ * Please note that the following copyright notice only applies to this Dynare 
+ * implementation of the model.
+ */
+
+/*
+ * Copyright © 2022 Willi Mutschler
+ *
+ * This is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * It is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * For a copy of the GNU General Public License,
+ * see <https://www.gnu.org/licenses/>.
+ */
+
+var
+  a        $A$            (long_name='technology')
+  c        $C$            (long_name='consumption')
+  iv       $I$            (long_name='investment')
+  k        $K$            (long_name='capital')
+  lam      $\lambda$      (long_name='Lagrange multiplier on investment constraint')  
+  chat     ${\hat{c}}$    (long_name='consumption (percent dev from ss)')
+  ivhat    ${\hat{i}}$    (long_name='investment (percent dev from ss)')
+  khat     ${\hat{k}}$    (long_name='capital (percent dev from ss)')  
+;
+
+varexo
+  epsi     $\epsi$        (long_name='negative TFP shock')
+;
+
+parameters
+  ALPHA    $\alpha$       (long_name='bias towards capital in production')
+  DELTA    $\delta$       (long_name='depreciation rate')
+  BETA     $\beta$        (long_name='discount factor')
+  GAMMA    $\gamma$       (long_name='risk aversion')
+  RHO      $\rho$         (long_name='persistence technology')
+  PHI      $\phi$         (long_name='fraction parameter for lower bound on investment')
+;
+
+ALPHA = 0.33;
+DELTA = 0.1;
+BETA  = 0.96;
+GAMMA = 2;
+RHO   = 0.9;
+PHI   = 0.975;
+
+model;
+[name='consumption Euler equation, eq. (11), eq. (A.1)']
+c^(-GAMMA) - lam = BETA*( c(+1)^(-GAMMA)*(1-DELTA+ALPHA*a(+1)*k^(ALPHA-1)) -(1-DELTA)*lam(+1) ); // note that there is a small typo in the paper, but not in the appendix
+[name='resource constraint, eq. (7)']
+c + iv = a*k(-1)^(ALPHA);
+[name='capital accumulation, eq. (8)']
+k = (1-DELTA)*k(-1) + iv;
+[name='law of motion for technology, eq. (10)']
+log(a) = RHO*log(a(-1)) + epsi;
+[name='reporting: investment percent deviation from steady-state']
+ivhat = 100*(iv/steady_state(iv)-1);
+[name='reporting: consumption percent deviation from steady-state']
+chat = 100*(c/steady_state(c)-1);
+[name='reporting: capital percent deviation from steady-state']
+khat = 100*(k/steady_state(k)-1);
+
+[name='investment constraint',relax='irr']
+lam = 0;
+[name='investment constraint',bind='irr']
+iv = PHI*steady_state(iv);
+end;
+
+steady_state_model;
+a   = 1;
+k   = ((1/BETA-1+DELTA)/ALPHA)^(1/(ALPHA-1));
+c   = -DELTA*k + k^ALPHA;
+iv  = DELTA*k;
+lam = 0;
+khat  = 0;
+ivhat = 0;
+chat  = 0;
+end;
+steady;
+
+occbin_constraints;
+name 'irr'; bind iv < PHI*steady_state(iv); relax lam <= 0;
+end;
+
+% replicate left column of Fig. 3
+shocks(surprise,overwrite);
+var epsi; periods 1; values -0.04;
+end;
+occbin_setup;
+occbin_solver(simul_periods=50,simul_check_ahead_periods=100);
+occbin_graph ivhat chat khat;
+
+% replicate right column of Fig. 3
+shocks(surprise,overwrite);
+var epsi; periods 1; values 0.04;
+end;
+occbin_setup;
+occbin_solver(simul_periods=100);
+occbin_graph ivhat chat khat;

README.md

@@ -238,6 +238,18 @@ It provides a replication code for the main results of the original paper for th
 
 This mod-file shows how to use the loglinear and logdata options of Dynare.
 
+## Guerrieri_Iacoviello_2015
+Replicates the RBC model with a constraint on investment (irreversible investment)
+and the New Keynesian model with a constraint on the nominal interest rate (zero-lower-bound)
+studied in Guerrieri, Luca and Iacoviello, Matteo (2015): 
+"OccBin: A toolkit for solving dynamic models with occastionally binding
+constraints easily", Journal of Monetary Economics 70, pp.22-38.
+
+It provides replication codes for the IRFs in figures 3 and 5.
+
+The mod files show how to use Dynare's occbin toolbox for stochastic 
+simulations with occasionally binding constraints.
+
 ## Ghironi_Melitz_2005.mod
 
 This file replicates the Baseline model under Financial Autarky of

run_all_files.m

@@ -43,6 +43,9 @@
 dynare Gali_Monacelli_2005
 cd('../Ghironi_Melitz_2005')
 dynare Ghironi_Melitz_2005.mod
+cd('../Guerrieri_Iacoviello_2015')
+dynare Guerrieri_Iacoviello_2015_rbc
+dynare Guerrieri_Iacoviello_2015_nk
 cd('../Hansen_1985')
 dynare Hansen_1985.mod
 cd('../Jermann_Quadrini_2012/Jermann_Quadrini_2012_RBC')