diff --git a/doc/manual/source/examples.rst b/doc/manual/source/examples.rst
index 7a367d82b803d49a010d64f01f5d547b8cab2fd3..f5acea2b497ec5112cc8e4d93e3a5e9026bd9406 100644
--- a/doc/manual/source/examples.rst
+++ b/doc/manual/source/examples.rst
@@ -79,3 +79,10 @@ description, please refer to the comments inside the files themselves.
File demonstrating how to conduct optimal policy experiments in a
simple New Keynesian model under commitment (Ramsey) with a user-defined
conditional steady state file
+
+``rbc_irf_matching.mod``
+
+ Baseline RBC model with government spending shocks estimated via impulse response function (IRF) matching.
+ Both Frequentist (Maximum Likelihood) and Bayesian (Slice Sampling) approaches are presented.
+ Additionally, it is shown how to estimate an AR(2)-process
+ by working with the roots of the autoregressive process instead of the coefficients
diff --git a/examples/rbc_irf_matching.mod b/examples/rbc_irf_matching.mod
new file mode 100644
index 0000000000000000000000000000000000000000..27aecaa5322b2c6b0608bfe797b5ba814324c61f
--- /dev/null
+++ b/examples/rbc_irf_matching.mod
@@ -0,0 +1,265 @@
+/*
+ * This file presents a baseline RBC model with government spending shocks where the persistence of the
+ * government spending shock is estimated via impulse response function (IRF) matching.
+ *
+ * Notes:
+ * - The empirical IRFs were estimated using the Blanchard/Perotti (2002) approach, see
+ * https://github.com/JohannesPfeifer/DSGE_mod/blob/master/RBC_IRF_matching/get_empirical_IRFs.m
+ * - They are given in the csv file rbc_irf_matching_data.csv, the first two columns contain
+ * the empirical IRFs of G and Y, while the third and fourth column contain the corresponding
+ * variances of the IRFs from a bootstrap approach.
+ * Importantly: this mod file does not show how to get the empirical IRFs from a SVAR model,
+ * but takes these as "data".
+ * - Of course the RBC model is not capable of generating the consumption increase
+ * after a government spending shock. For that reason, this mod-file only targets the IRFs for G and Y.
+ * - The weighting matrix uses a diagonal matrix with the inverse of the pointwise IRF variances on the main diagonal.
+ * - The empirical IRFs and model IRFs use an impulse size of 1 percent. Thus, there is no uncertainty about the
+ * initial impact. The IRF matching therefore only targets the G-response starting in the second period.
+ * - Note that for the current model, the number of IRFs exceeds the number of VAR parameters. Therefore,
+ * the distribution of the estimator will be non-standard, see Guerron-Quintana/Inoue/Kilian (2016),
+ * http://dx.doi.org/10.1016/j.jeconom.2016.09.009
+ * - The mod-file also shows how to estimate an AR(2)-process by working with the roots of the autoregressive
+ * process instead of the coefficients. This allows for easily restricting the process to the stability region and
+ * would allow specifying e.g. a beta prior for both roots as was done in Born/Peter/Pfeifer (2013), Fiscal news
+ * and macroeconomic volatility, https://doi.org/10.1016/j.jedc.2013.06.011
+ *
+ * Please note that the following copyright notice only applies to this Dynare
+ * implementation of the model.
+ */
+
+/*
+ * Copyright (C) 2016-17 Johannes Pfeifer,
+ * Copyright (C) 2024 Dynare Team
+ *
+ * This file is part of Dynare.
+ *
+ * Dynare 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.
+ *
+ * Dynare 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.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with Dynare. If not, see <https://www.gnu.org/licenses/>.
+ */
+
+%----------------------------------------------------------------
+% define variables
+%----------------------------------------------------------------
+@#define IRF_periods=80
+
+var y ${y}$ (long_name='output')
+ c ${c}$ (long_name='consumption')
+ k ${k}$ (long_name='capital')
+ l ${l}$ (long_name='hours')
+ z ${z}$ (long_name='TFP')
+ ghat ${\hat g}$ (long_name='government spending')
+ r ${r}$ (long_name='annualized interest rate')
+ w ${w}$ (long_name='real wage')
+ invest ${i}$ (long_name='investment')
+ log_y ${\log(y)}$ (long_name='log output')
+ log_k ${\log(k)}$ (long_name='log capital stock')
+ log_c ${\log(c)}$ (long_name='log consumption')
+ log_l ${\log(l)}$ (long_name='log labor')
+ log_w ${\log(w)}$ (long_name='log real wage')
+ log_invest ${\log(i)}$ (long_name='log investment')
+;
+
+varexo eps_z ${\varepsilon_z}$ (long_name='TFP shock')
+ eps_g ${\varepsilon_g}$ (long_name='government spending shock')
+;
+
+%----------------------------------------------------------------
+% define parameters
+%----------------------------------------------------------------
+
+parameters
+ beta ${\beta}$ (long_name='discount factor')
+ psi ${\psi}$ (long_name='labor disutility parameter')
+ sigma ${\sigma}$ (long_name='risk aversion')
+ delta ${\delta}$ (long_name='depreciation rate')
+ alpha ${\alpha}$ (long_name='capital share')
+ rhoz ${\rho_z}$ (long_name='persistence TFP shock')
+ root_g_1 ${\rho_g}$ (long_name='first root of AR(2) G process')
+ root_g_2 ${\rho_g}$ (long_name='second root of AR(2) G process')
+ gammax ${\gamma_x}$ (long_name='composite growth rate')
+ gshare ${\frac{G}{Y}}$ (long_name='government spending share')
+ n ${n}$ (long_name='population growth')
+ x ${x}$ (long_name='technology growth (per capita output growth)')
+ i_y ${\frac{I}{Y}}$ (long_name='investment-output ratio')
+ k_y ${\frac{K}{Y}}$ (long_name='capital-output ratio')
+ g_ss ${\bar G}$ (long_name='government spending in steady state')
+ l_ss ${\bar L}$ (long_name='labor in steady state')
+;
+
+%----------------------------------------------------------------
+% model equations
+%----------------------------------------------------------------
+model;
+# rho_g_1= (root_g_1+root_g_2);
+# rho_g_2= - root_g_1*root_g_2;
+[name='Euler equation']
+c^(-sigma)=beta/gammax*c(+1)^(-sigma)*
+ (alpha*exp(z(+1))*(k/l(+1))^(alpha-1)+(1-delta));
+[name='Labor FOC']
+psi*c^sigma*1/(1-l)=w;
+[name='Law of motion capital']
+gammax*k=(1-delta)*k(-1)+invest;
+[name='resource constraint']
+y=invest+c+g_ss*exp(ghat);
+[name='production function']
+y=exp(z)*k(-1)^alpha*l^(1-alpha);
+[name='real wage/firm FOC labor']
+w=(1-alpha)*y/l;
+[name='annualized real interst rate/firm FOC capital']
+r=4*alpha*y/k(-1);
+[name='exogenous TFP process']
+z=rhoz*z(-1)+eps_z;
+[name='government spending process']
+ghat=rho_g_1*ghat(-1)+rho_g_2*ghat(-2)+eps_g;
+[name='Definition log output']
+log_y = log(y);
+[name='Definition log capital']
+log_k = log(k);
+[name='Definition log consumption']
+log_c = log(c);
+[name='Definition log hours']
+log_l = log(l);
+[name='Definition log wage']
+log_w = log(w);
+[name='Definition log investment']
+log_invest = log(invest);
+end;
+
+%----------------------------------------------------------------
+% set steady state values
+%---------------------------------------------------------------
+
+steady_state_model;
+ gammax = (1+n)*(1+x);
+ delta = i_y/k_y-x-n-n*x;
+ beta = (1+x)*(1+n)/(alpha/k_y+(1-delta));
+ l = l_ss;
+ k = ((1/beta*(1+n)*(1+x)-(1-delta))/alpha)^(1/(alpha-1))*l;
+ invest = (x+n+delta+n*x)*k;
+ y = k^alpha*l^(1-alpha);
+ g = gshare*y;
+ g_ss = g;
+ c = (1-gshare)*k^(alpha)*l^(1-alpha)-invest;
+ psi = (1-alpha)*(k/l)^alpha*(1-l)/c^sigma;
+ w = (1-alpha)*y/l;
+ r = 4*alpha*y/k;
+ log_y = log(y);
+ log_k = log(k);
+ log_c = log(c);
+ log_l = log(l);
+ log_w = log(w);
+ log_invest = log(invest);
+ z = 0;
+ ghat =0;
+end;
+
+%----------------------------------------------------------------
+% calibration
+%----------------------------------------------------------------
+sigma = 1;
+alpha = 0.33;
+i_y = 0.25;
+k_y = 10.4;
+x = 0.0055;
+n = 0.0027;
+rhoz = 0.97;
+root_g_1 = 0.9602;
+root_g_2 = 0;
+gshare = 0.2038;
+l_ss = 1/3;
+
+shocks;
+var eps_g = 1;
+end;
+steady;
+check;
+
+varobs ghat log_y y; // you need to specify observables
+
+%----------------------------------------------------------------
+% IRF matching example 1:
+% - different ways to MANUALLY enter values and weights
+% - Maximum likelihood estimation
+%----------------------------------------------------------------
+estimated_params;
+root_g_1 , 0.90 , 0, 1;
+root_g_2 , 0.10 , 0, 1;
+end;
+
+xx = [1.007,1.117,1.092];
+ww = [51,52];
+
+matched_irfs;
+var log_y ; varexo eps_g ; periods 1, 2 ; values 0.20, 0.17 ; weights 360, 140 ;
+var ghat ; varexo eps_g ; periods 2 3:5 ; values 1.01, (xx) ; weights 50, 20 ;
+var y ; varexo eps_g ; periods 10:11 ; values (log(1.05)) ; weights (ww) ;
+end;
+
+method_of_moments(mom_method = irf_matching, mode_compute = 5, additional_optimizer_steps=[4]);
+
+
+%----------------------------------------------------------------
+% IRF matching example 2
+% - use all IRFs given in MATLAB objects
+% - use Bayesian Slice sampler
+%----------------------------------------------------------------
+estimated_params(overwrite);
+root_g_1 , 0.50 , 0, 1, beta_pdf , 0.50 , 0.20;
+root_g_2 , 0.10 , 0, 1, beta_pdf , 0.50 , 0.20;
+end;
+
+% get data
+irfs_data = importdata('rbc_irf_matching_data.csv');
+irfs_ghat_eps_g = irfs_data.data(2:80,1); % start in t=2 due to identification restrictions in SVAR
+irfs_log_y_eps_g = irfs_data.data(1:80,2);
+weights_ghat_eps_g = 1./irfs_data.data(2:80,3);
+weights_log_y_eps_g = 1./irfs_data.data(1:80,4);
+
+matched_irfs(overwrite);
+var ghat ; varexo eps_g; periods 2:80; values (irfs_ghat_eps_g); weights (weights_ghat_eps_g);
+var log_y; varexo eps_g; periods 1:80; values (irfs_log_y_eps_g); weights (weights_log_y_eps_g);
+end;
+
+method_of_moments(mom_method = irf_matching
+ ,order = 1
+ ,mh_nblocks = 2, mh_replic = 50
+ ,posterior_sampling_method = 'slice'
+ ,plot_priors = 1
+ );
+
+%----------------------------------------------------------------
+% IRF matching example 3:
+% - use anonymous function to access IRFs more flexibly
+% - showcase how to use irf_matching_file
+% - find posterior mode
+%----------------------------------------------------------------
+
+% get data
+irfs_data = importdata('rbc_irf_matching_data.csv');
+
+% use anonymous function (or MATLAB function) to have more flexibility, but inputs can only be numerical
+% we also take 100 just for illustration that you can do any required transformation in an irf_matching_file
+irfs_vals = @(j) 100.*(irfs_data.data(2:80,j));
+irfs_weights = @(j) 1./(irfs_data.data(2:80,j));
+
+matched_irfs(overwrite);
+var ghat ; varexo eps_g; periods 2:80; values (irfs_vals(1)); weights (irfs_weights(3));
+var log_y; varexo eps_g; periods 2:80; values (irfs_vals(2)); weights (irfs_weights(4));
+end;
+
+% we use the irf_matching_file to transform variable y to log(y) so the model
+% variable aligns with the variable from the given empirical SVAR
+method_of_moments(mom_method = irf_matching
+ ,irf_matching_file = rbc_irf_matching_transformations
+ ,mh_replic = 0,plot_priors = 0
+ );
\ No newline at end of file
diff --git a/examples/rbc_irf_matching_data.csv b/examples/rbc_irf_matching_data.csv
new file mode 100644
index 0000000000000000000000000000000000000000..91647e6e15123fd59309037c2d4a3de6db69e66e
--- /dev/null
+++ b/examples/rbc_irf_matching_data.csv
@@ -0,0 +1,81 @@
+G,Y,var_G,var_Y
+1,0.208070478344545,1.12054105855257e-33,0.0027602236508546
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diff --git a/examples/rbc_irf_matching_transformations.m b/examples/rbc_irf_matching_transformations.m
new file mode 100644
index 0000000000000000000000000000000000000000..f29572090255563d30450f86c66dbb64a5013333
--- /dev/null
+++ b/examples/rbc_irf_matching_transformations.m
@@ -0,0 +1,50 @@
+function [modelIrf, error_indicator] = rbc_irf_matching_transformations(modelIrf, M_, options_mom_, ys_)
+% -------------------------------------------------------------------------
+% This file manipulates model IRFs to be consistent with empirical IRFS
+% -------------------------------------------------------------------------
+% INPUTS
+% - modelIrf: [options_mom_.irf by M_.endo_nbr by M_.exo_nbr]
+% array of IRFs for all model variables and all shocks
+% - M_: [structure] Dynare model structure
+% - options_mom_: [structure] Dynare options structure
+% - ys_: [double] steady state values of all endogenous variables
+% -------------------------------------------------------------------------
+% OUTPUTS
+% - modelIrf: [options_mom_.irf by M_.endo_nbr by M_.exo_nbr]
+% modified array of IRFs for all model variables and all shocks
+% - error_indicator: [boolean] indicator of success (0) or failure (1)
+% -------------------------------------------------------------------------
+% This function is called by
+% - mom.run
+% -------------------------------------------------------------------------
+
+% Copyright © 2024 Dynare Team
+%
+% This file is part of Dynare.
+%
+% Dynare 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.
+%
+% Dynare 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.
+%
+% You should have received a copy of the GNU General Public License
+% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
+
+% initialize error indicator
+error_indicator = 0;
+
+% get indices of variables
+idx_ghat = find(ismember(M_.endo_names,'ghat'));
+idx_log_y = find(ismember(M_.endo_names,'log_y'));
+idx_eps_g = find(ismember(M_.exo_names,'eps_g'));
+
+% manipulate the model IRFs to match the empirical IRFs (e.g. cumsum, common scaling, trends, ratios, etc.)
+modelIrf(:,idx_ghat,idx_eps_g) = 100.*modelIrf(:,idx_ghat,idx_eps_g);
+modelIrf(:,idx_log_y,idx_eps_g) = 100.*modelIrf(:,idx_log_y,idx_eps_g);
+
+end
\ No newline at end of file