A. Appendix
A.5. Dynare and MATLAB Code
68 A.4.11. The Job Creation Condition
Equation 5.2-7 states
π
π(ππ‘)= πΈπ‘π½ππ,π‘+1 ππ,π‘ π½π‘+1. Taking logs results in
ln(π ) β ln(π(ππ‘)) = ln(π½) + ln(ππ,π‘+1) β ln(ππ,π‘) + ln (π½π‘+1) Linearization yields
ln(π ) β [ln(π(π)) + 1
π(π)πβ²(π)π (ππ‘β π π )]
= ln(π½) + ln(ππ) + 1
ππ(ππ,π‘+1β ππ) β [ln(ππ) + 1
ππ(ππ,π‘β ππ)] + ln(π½) +1
π½(π½π‘+1β π½).
Dropping steady-state terms and using the elasticity of the job filling rate with respect to the labor market tightness, defined as β π =ππ(π)
ππ π
π(π), the function can be simplified to
ππΜπ‘ = πΜπ,π‘+1β πΜπ,π‘+ π½Μπ‘+1. A.4.11
69
%%%%%%%%%%%%%
%% CEE part%%
%%%%%%%%%%%%%
% * indicates that the variable was present in the 13 variable system from the original CEE
%paper var
pi % inflation *
s % real marginal cost for intermediate goods firms in the CEE model qbar % transaction money / m1 *
q % real transaction money r % nominal interest rate * m2 % total money supply / m2 * mu % money growth rate
psi % marginal utility of consumption * c % consumption *
wbar % wage *
% w % real wage (now determined in the DMP model via Nash bargaining) p_ki % marginal product of capital in marginal utility terms *
% l % labor * (now determined in the DMP model part) h % habit formation *
kbar % capital stock * k % capital services * i % capital investment * y % output
u % capacity utilization rk % return to capital
z % TFP shock in the intermediate goods production sector (not part of CEE)
%%%%%%%%%%%%%
%% DMP part%%
%%%%%%%%%%%%%
l % aggregate labor input (produced by the DMP model firms)
% r % nominal interest rate (already defined in the CEE part)
pw % price paid by intermediate goods firms for the aggregate labor input mc % marginal costs for DMP model firms
% psi % stochastic discount factor term (already from CEE) w % real wage determined by Nash bargaining
% wc % Calvo wage un % unemployment
n % employment (as measured in the data and determined in DMP model) a % labor augmenting technology
v % vacancies
m % matching function theta % labor market tightness
j % value of a job (=value of a firm)
;
varexo epsilon_TFP, epsilon, eR; % eR is from the Taylor rule, epsilon from AR1 shock parameters
%%%%%%%%%%%%%%
%% CEE part %%
%%%%%%%%%%%%%%
R % steady-state nominal interest rate beta % discount rate
alph % labor share of production delt % capital depreciation rate
% b_w % simplifying parameter (defined below) redundant xi_p % price stickiness
% xi_w % wage stickiness (redundant)
lam_w % household labor market power (only needed for DMP model steady-state MC) mubar % steady-state money growth rate
mbar % steady-state m2 qbar_ss % steady-state m1
% wbar_ss % steady-state wage (redundant)
% lbar % steady-state labor supply b % habit parameter 1
chi % habit parameter 2 (see Appendix of Cleveland Fed Working Paper version) sig_c % simplifying parameter (defined below)
sig_a % relates capacity utilization to return on capital sig_q % relates cash holding and the interest rate
e_CEE % price elasticity for MC and markup in CEE model (markup=e/(e-1)) MC_CEE % steady-state marginal cost (1/markup)
K_Y % steady-state capital-output ratio K_H % steady-state capital-labor ratio Y_H % steady-state output-labor ratio C_Y % steady-state consumption output ratio
70
kappa_v_Y % steady-state total vacancy cost output ratio (from DMP model) rho_r % interest rate smoothing policy parameter
rho_pi % Taylor rule inflation response rho_y % Taylor rule output response
eta_k % investment adjustment cost parameter: (kappa in CEE: 1/eta_k is the elasticity of % investment with respect to a 1% in the current price of installed capital)
%%%%%%%%%%%%%
%% DMP part%%
%%%%%%%%%%%%%
A, % steady-state technology
delta_l, % AR1 shock to technology parameter (labor augmenting technology) delta_TFP % AR1 TFP shock
sigma_l, % AR1 shock sd (labor augmenting) sigma_TFP % AR1 TFP shock sd
e_DMP, % elasticity for steady-state MC in DMP model firms MC_DMP, % S.S. MC
L, % steady-state output of the aggregate labor input used in intermediate goods production
W % steady-state wage
THETA % steady-state labor market tightness qTHETA % steady-state job filling rate
% beta % discount factor (identical to CEE: depends on Households) xi % matching function elasticity parameter
rho % job separation rate kappa % costs per vacancy
Q % average vacancy filling rate eta % bargaining power of worker N % steady-state employment level U % steady-state unemployment level M % steady-state job matches
V % steady-state number of vacancies o % outside option
J % Value of a firm at steady-state
;
%---%
% PARAMETER values %
%---%
%%%%%%%%%%%%%
%% CEE part%%
%%%%%%%%%%%%%
% 1) PREFERENCES
% (intertemporal elasticity of sub. in C = 1)
b = 0.65; % degree of habit persistence (CEE: both models)
% b = 0.8; % CET
% b = 0.803; % GST
beta = 1.03^(-1/4); % subjective discount factor (CEE: both models, corresponds to 0.9926)
% beta = 0.9968; % CET
% beta = 0.99; % GST R = 1/beta; % steady-state nominal rate
% psi0 =1; % marginal disutility of hours
chi = 0.0; % habit parameter 2 (only specified because it is modelled like that % in CEE: but technically useless)
% 2) TECHNOLOGY
alph = 0.36; % share of capital (CEE: both models) use this also for_alpha1.mod
% alph = 0.26; % CET
% alph = 0.33; % GST
delt = 0.025; % depreciation rate (identical in all models)
% 3) CALVO PARAMETERS
% xi_w = 0.64; % on wages (only for CEE Benchmark model)
% xi_w = 0.000000001; % for fully flex model: if set to zero, the Wage Phillips Equation is % undefined: this shortcut allows sufficiently close results without deriving a new WPC) xi_p = 0.60; % on prices (both CEE: the reestimated model parameters are not % displayed in the paper by CEE because the degree of wage rigidity is driven to unity)
% xi_p = 0.79; % CET
% xi_p = 0.575; % GST
% 4) INDEXATION
lam_w = 1.05; % household labor market power (only needed for DMP model steady-state MC lam_f = 1.2; % firm market power (CEE BM)
% lam_f = 1.45; % CEE working paper
% lam_f = 1.36; % CET
% lam_f = 1.351; % GST
71
% 5) ELASTICITIES OF SUBSTITUTIONS
e_CEE = -lam_f/(1-lam_f); % price-elasticity of demand for a differentiated % good [calculated from lam_f=e_CEE/(e_CEE-1)]
MC_CEE = (e_CEE-1)/e_CEE; % marginal cost
% 6) OTHER CALIBRATIONS
% lbar = 1; % steady-state labor supplied by households [now
% determined in DMP model (only left here to show the old parameters as well]
sig_a = 0.01; % capital utilization adjustment parameter (both CEE)
% sig_a = 0.03; % CET
% sig_a = 5.76; % GST
mubar = 1.017; % steady state money growth rate, calibrated post WW2 % (just in CEE model, not part of the utility function in the other models) qbar_ss = mubar*(1-0.36/(beta*(1-alph)));% steady-state M1
mbar = (1/0.44)*qbar_ss; % steady-state M2
sig_q = 10.62; % relates cash holding and the interest rate (9.966 % according to the working paper)
eta_k = 2.48; % investment adjustment cost parameter: (kappa in CEE: 1/eta_k is the % elasticity of investment with respect to a 1% in the current price of installed capital)
% eta_k = 3.57; % CEE flex wage
% eta_k = 17.49 % CET
% eta_k = 1.179 % GST
% eta_k = 4.4; % lower investment adjustment cost: NKSM_low_I.mod
%%%%%%%%%%%%%
%% DMP part%%
%%%%%%%%%%%%%
e_DMP = -lam_w/(1-lam_w); % elasticity for steady-state MC in DMP model firms MC_DMP = (e_DMP-1)/e_DMP; % marginal cost at steady-state
delta_l = 0.97; % AR1 shock to technology parameter (labor augmenting) sigma_l = 0.07; % A1 shock sd (labor augmenting)
delta_TFP = 0.95; % AR1 TFP shock parameter sigma_TFP = 0.04; % AR1 TFP shock sd
xi = 0.55; % matching function elasticity parameter: CET
% xi = 0.5; % GST rho = 0.1; % job separation rate: CET
% rho = 0.105; % GST
Q = 0.7; % average vacancy filling rate: CET
% Q = 0.4517; % GST (also used for AK_CET_Vacancies: all other values like in CET eta = 0.44; % workers bargaining power: Hosios (1990) efficiency condition % for firms bargaining power says xi=eta: here the CET value is used
% eta = 0.589; % GST
%eta = 0.35; % for CET_barg1.mod
%eta=0.25; % for CET_barg2.mod
%eta = 0.589; % for CET_barg3.mod o = 0.965; % outside option: HM setup
% o = 0.982; % GST
%---%
% STEADY-STATE RATIOS and VALUES %
%---%
%%%%%%%%%%%%%
%% DMP part%%
%%%%%%%%%%%%%
N= 0.945; % steady-state employment: CET
% N= 0.94 % GST U = 1-N; % steady-state unemployment
M = rho*N; % steady-state matching: from N=(1-rho)N+M at the steady state V = M/Q; % steady-state vacancies
THETA = U/V; % steady-state labor market tightness qTHETA = M/V; % steady-state job filling rate kappa = 0.30; % costs per vacancy: CET
% kappa = 0.2093; % GST
W = eta*MC_DMP*A+(1-eta)*o+eta*k*THETA; % steady-state wage rate
L=N; % stead state aggregate labor input: since L=A*N with A=1 in steady-state J=(MC_DMP*A-W)/(1-(1-rho)*beta); % steady-state value of a job
%%%%%%%%%%%%%
%% CEE part%%
%%%%%%%%%%%%%
% underscore denotes a ratio
% 2) ENDOGENOUS VALUES (using A=1 at steady-state)
rk_bar = (1/beta-1+delt); % steady-state capital rental rate
K_H = MC_CEE^(1/(alph*(1-alph)))*(rk_bar/alph)^(1/(alph-1)); % capital-labor ratio Y_H = (K_H)^alph; % output-labor ratio
K_Y = K_H/Y_H; % capital-output ratio
72
C_Y = 1-delt*K_Y; % consumption output ratio I_Y = delt*K_Y; % investment over output K= (K_H)^(1/alph)/N % steady-state capital kappa_v_Y =(kappa*V)/(K^alph*L^(1-alph)); % steady-state total vacancy cost/ output ratio //wbar_ss = (1-alph)/alph*(K_H)*rk_bar;
% wbar_ss = MC_CEE^(1/(1-alph))*(1-alph)*alph^(alph/(1-alph))*rk_bar^(alph/(alph-1))/R;
% steady-state wage (redundant: determined in DMP model)
%---%
% Simplifying Parameters %
%---%
% b_w = (2*lam_w - 1)/((1-xi_w)*(1-beta*xi_w));
sig_c = (1-chi)/(1-chi-b)*(1-beta*chi)/(1-beta*chi-beta*b);
%---%
% MONETARY RULE %
%---%
rho_pi = 1.5; % monetary rule parameter (on inflation) as used by CEE
% rho_pi = 1.36; % CET
% rho_pi = 1.99; % GST
rho_y = 0.5; % monetary rule parameter (on output) as used by CEE
% rho_y = 0.01; % CET
% rho_y = 0.019; % GST
rho_r = 0.8; % monetary rule parameter (on lagged interest rate) as used by CEE
% rho_r = 0.82; % CET
% rho_r = 0.7; % GST
%---%
% Investment Shocks %
%---%
A = 1; % steady-state technology (normalized to 1)
delta_l = 0.97; % AR1 shock to technology parameter (labor augmenting) sigma_l = 0.7; % A1 shock sd (labor augmenting)
delta_TFP = 0.95; % AR1 TFP shock parameter sigma_TFP = 0.4; % AR1 TFP shock sd
model(linear);
%%%%%%%%%%%%%
%% CEE part%%
%%%%%%%%%%%%%
% A.3.1 Inflation Phillips curve
pi = (1/(1+beta))*pi(-1) + (beta/(1+beta))*pi(+1) + ((1-beta*xi_p)*(1-xi_p)/((1+beta)*xi_p))*s;
% A.3.2. Money demand
q = (-1/sig_q)*(R/(R-1)*r + psi);
% A.3.3 Wage Phillips curve
%0 = w(-1) - ((b_w*(1+beta*xi_w^2)-lam_w)/(b_w*xi_w))*w + beta*w(+1) + (beta*(pi(+1) - pi)
% - (pi - pi(-1))) + ((1-lam_w)/(b_w*xi_w))*(psi-l);
% A.3.4 Household intertemporal Euler equation 0 = psi(+1) + r(+1) - pi(+1) - psi;
% A.3.5 Capital Euler equation
0 = -p_ki - psi + psi(+1) + (1-beta*(1-delt))*(rk(+1)) + beta*(1-delt)*p_ki(+1);
% A.3.6 Aggregate resource constraint (without variable capital utilization)
1/beta - (1-delt))*(K_Y/C_Y)*u + c + delt*(K_Y/C_Y)*i = (alph/C_Y)*k + ((1-alph)/C_Y)*l;
% A.3.7 Loan market clearing
0 = mubar*mbar*(mu + m2) - qbar_ss*q - W*L*(pw + l);
% A.3.8 Relation between money growth and the inflation rate 0 = mu(-1) + m2(-1) - pi - m2;
% A.3.9 Definition of habit formation h = chi*h(-1) + (1-chi)*c(-1);
% A.3.10 Consumption Euler equation
0 = -beta*chi*psi(+1) + sig_c*(c - h*b/(1-chi)) - (b+chi)*beta*sig_c*(c(+1) - h(+1)*b/(1-chi)) + psi;
% A.3.11 Investment Euler equation
p_ki = eta_k*(i - i(-1) - beta*(i(+1) - i));
% A.3.12 Capital accumulation equation kbar = (1-delt)*kbar(-1) + delt*i;
73
% A.3.13 FOC for capital utilization u -(1/sig_a)*rk = 0;
% A.3.14 Definition of capacity utilization u = k - kbar(-1);
% A.3.15 Return on capital rk = pw + r + l - k;
% A.3.16 Taylor rule
r = (1-rho_r)*(rho_pi*pi + rho_y*y) +rho_r*r(-1) - eR;
% r = (1-rho_r)*(rho_pi*pi(+1) + rho_y*y) +rho_r*r(-1) - eR; % this is the CEE variant; also % use it for _Taylor.mod files
% A.3.17 Definition of real marginal cost s = alph*rk + (1-alph)*(pw + r);
% A.3.18 Cobb-Douglas production function
y = z+alph*k + (1-alph)*l; % including the TFP shock, denoted by z
% Definition of further variables (compare CEE)
% A.3.19 Real Wage qbar = q - pi;
A.3.20 Real Cash Balances wbar = w - pi;
%%%%%%%%%%%%%%
%% DMP part %%
%%%%%%%%%%%%%%
% A.4.1 Aggregate resource constraint (with variable capital utilization)
(1/beta - (1-delt))*(K_Y/C_Y)*u + c + delt*(K_Y/C_Y)*i +(kappa_v_Y/C_Y)*v= (alph/C_Y)*k + ((1-alph)/C_Y)*(n+a);
% A. 4.2 AR1 technology shock
0 = a - delta_l*a(-1) - epsilon; % labor augmenting (delete this for CEE variant) 0=z-delta_TFP*z(-1) - epsilon_TFP; % TFP shock (keep this for CEE as well)
% A.4.3 price charged for aggregate labor input equals marginal costs: competitive firms pw=mc;
% A.4.4 The DMP production fct: aggregate labor input used in intermediate goods production l=a+n;
% A.4.6 unemployment equation 0 = (N/U)*n+un;
% A.4.7 matching function m = (1-xi)*v+xi*un;
% A.4.8 labor market tightness theta = v-un;
% A.4.9 wage equation W*w = eta*MC_DMP*A*(a+mc)+eta*kappa*THETA*theta;
% A.4.10 marginal cost equation(value of a job equation) J*j=MC_DMP*A*(mc+a)-(W*w)+(1-rho)*beta*J*(j(+1)+psi(+1)-psi);
% A.4.11 job creation condition
xi*theta =psi(+1)-psi+j(+1);
end;
steady;
check;
shocks;
var eR; stderr 0.6;
var epsilon = sigma_l^2;
var epsilon_TFP= sigma_TFP^2;
end;
% stoch_simul(irf=25,nocorr,hp_filter=1600); % default: displays IRFs of the variables stoch_simul(irf=25,nocorr,nodisplay,hp_filter=1600);% used for the matlab function that % combines the IRFs automatically
74 The MATLAB code only needs to be copied into a new script and saved as a regular MATLAB file (with the ending .m). Once the Dynare files are saved accordingly, the MATLAB file produces all the figures used in this thesis.
%%% Alexander Koll, Johannes Kepler University Linz, May 2015 %%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Unemployment, the business cycle and monetary policy %%%
%%% Augmenting a medium sized New Keynesian DSGE model
%%% with labor market dynamic
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% this file produces all the Impulse Response Functions used throughout this thesis
% before running, make sure the files of all models are saved in the working directory
% with the names as written after each Dynare command below
% make sure the workspace in MATLAB is cleared to ensure no existing data interferes with the simulation
clear
% close all % only needed in case the graphs cannot be opened
% close all open % like above clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%
%%% the following part contains all the model names that need to be saved %%% in the working
%%%directory of MATLAB
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%
dynare CEE2005_flexW.mod noclearall load('CEE2005_flexW_results.mat', 'oo_') irf1=oo_.irfs;
save irf1 oo_1=oo_
load irf1
dynare CEE2005_timing.mod noclearall load('CEE2005_timing_results.mat', 'oo_') irf2=oo_.irfs;
oo_2=oo_
save irf2 load irf2
dynare AK_CEE.mod noclearall load('AK_CEE_results.mat', 'oo_') irf3=oo_.irfs;
oo_3=oo_
save irf3 load irf3
unemp3=un_eR*U % this is needed to obtain percentage point deviations save irf3
load irf3
dynare AK_CET.mod noclearall load('AK_CET_results.mat', 'oo_') irf4=oo_.irfs;
oo_4=oo_
save irf4 load irf4 unemp4=un_eR*U save irf4 load irf4
dynare AK_GST.mod noclearall load('AK_GST_results.mat', 'oo_') irf5=oo_.irfs;
oo_5=oo_
save irf5 load irf5 unemp5=un_eR*U save irf5 load irf5
%%% lower investment adjustment costs dynare NKSM_low_I.mod noclearall load('NKSM_low_I_results.mat', 'oo_') irf6=oo_.irfs;
oo_6=oo_
75
save irf6 load irf6 unemp6=un_eR*U save irf6 load irf6
%%% impact of the steady-state vacancy filling rate dynare AK_CET_Vacancies.mod noclearall
load('AK_CET_Vacancies_results.mat', 'oo_') irf7=oo_.irfs;
oo_7=oo_
save irf7 load irf7 unemp7=un_eR*U save irf7 load irf7
%%% impact of different Taylor rules
dynare CEE2005_timing_Taylor.mod noclearall load('CEE2005_timing_Taylor_results.mat', 'oo_') irf8=oo_.irfs;
oo_8=oo_
save irf8 load irf8
%%% impact of the capital share on the models performance dynare CET_alpha1.mod noclearall
load('CET_alpha1_results.mat', 'oo_') irf9=oo_.irfs;
oo_9=oo_
save irf9 load irf9 unemp9=un_eR*U save irf9 load irf9
dynare CET_alpha2.mod noclearall load('CET_alpha2_results.mat', 'oo_') irf10=oo_.irfs;
oo_10=oo_
save irf10 load irf10 unemp10=un_eR*U save irf10 load irf10
%%% impact of the worker bargaining power in the CET parameterization dynare CET_barg1.mod noclearall
load('CET_barg1_results.mat', 'oo_') irf11=oo_.irfs;
oo_11=oo_
save irf11 load irf11 unemp11=un_eR*U save irf11 load irf11
dynare CET_barg2.mod noclearall load('CET_barg2_results.mat', 'oo_') irf12=oo_.irfs;
oo_12=oo_
save irf12 load irf12 unemp12=un_eR*U save irf12 load irf12
dynare CET_barg3.mod noclearall load('CET_barg3_results.mat', 'oo_') irf13=oo_.irfs;
oo_13=oo_
save irf13 load irf13 unemp13=un_eR*U save irf13 load irf13
76
% for TFP shocks
dynare AK_CET_TFP.mod noclearall load('AK_CET_TFP_results.mat', 'oo_') irf14=oo_.irfs;
oo_14=oo_
save irf14 load irf14
unemp14=un_epsilon_TFP*U save irf14
load irf14
dynare AK_CEE_TFP.mod noclearall load('AK_CEE_TFP_results.mat', 'oo_') irf15=oo_.irfs;
oo_15=oo_
save irf15 load irf15
unemp15=un_epsilon_TFP*U save irf5
load irf15
dynare AK_GST_TFP.mod noclearall load('AK_GST_TFP_results.mat', 'oo_') irf16=oo_.irfs;
oo_16=oo_
save irf16 load irf16
unemp16=un_epsilon_TFP*U save irf16
load irf16
%%%%%%%% commands that produce the graphs from this thesis %%%%%%
set(gcf,'Position',[400 50 800 700])
%% this code sets the size of %the plots in a way that ensures readability
%%% Taylor rules: section 6.2 of this thesis plot(oo_2.irfs.pi_eR,'k--');hold
all;plot(oo_8.irfs.pi_eR,'Color',[0.6,0.5,0.8],'marker','+');hold off;title('Response of Inflation to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend1=legend('Benchmark CEE','Benchmark CEE with Taylor Rule from CET','Location','Best');
set(legend1,'FontSize',17)
savefig('Response of Inflation to a MP shock for Different Taylor rules')
plot(oo_2.irfs.y_eR,'k--');hold
all;plot(oo_8.irfs.y_eR,'Color',[0.6,0.5,0.8],'marker','+');hold off;title('Response of Output to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend2=legend('Benchmark CEE','Benchmark CEE with Taylor Rule from CET','Location','Best');
set(legend2,'FontSize',17)
savefig('Response of Output to a MP shock for Different Taylor rules')
plot(oo_2.irfs.r_eR,'k--');hold
all;plot(oo_8.irfs.r_eR,'Color',[0.6,0.5,0.8],'marker','+');hold off;title('Response of the Interest Rate to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize',
17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17) legend3=legend('Benchmark CEE','Benchmark CEE with Taylor Rule from CET','Location','southeast');
set(legend3,'FontSize',17)
savefig('Response of the Interest Rate to a MP shock for Different Taylor rules')
%%% IRFs of shocks to Monetary Policy: section 6.3 of this thesis plot(oo_1.irfs.pi_eR,'b:');hold
all;plot(oo_2.irfs.pi_eR,'k--');plot(oo_3.irfs.pi_eR,'r');plot(oo_4.irfs.pi_eR,'c');plot(oo_5.irfs.pi_eR,'m'); hold off;title('Response of Inflation to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17) legend4=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CEE Parameters','NKSM CET Parameters','NKSM GST Parameters','Location','Best')
set(legend4,'FontSize',17)
axis([0 20 -0.4 0.6]) % this sets the axis limits for the various plots, the first two entries %relate to the size of the x axes
savefig('Response of Inflation to a MP shock')
plot(oo_1.irfs.w_eR,'b:');hold
all;plot(oo_2.irfs.w_eR,'k--');plot(oo_3.irfs.w_eR,'r');plot(oo_4.irfs.w_eR,'c');plot(oo_5.irfs.w_eR,'m');hold
77
off;title('Response of Wages to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend4=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CEE Parameters','NKSM CET Parameters','NKSM GST Parameters','Location','Best')
set(legend4,'FontSize',17) axis([0 25 -0.4 1.6])
savefig('Response of Wages to a MP shock')
plot(oo_1.irfs.y_eR,'b:');hold
all;plot(oo_2.irfs.y_eR,'k--');plot(oo_3.irfs.y_eR,'r');plot(oo_4.irfs.y_eR,'c');plot(oo_5.irfs.y_eR,'m');hold
off;title('Response of Output to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend5=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CEE Parameters','NKSM CET Parameters','NKSM GST Parameters','Location','Best')
set(legend5,'FontSize',17) axis([0 20 -0.5 1])
savefig('Response of Output to a MP shock')
plot(unemp3,'r');hold all;plot(unemp4,'c');plot(unemp5,'m');hold off;title('Response of Unemployment to a MP Shock', 'FontSize', 20);ylabel('Percentage Point Deviation from the Unshocked Path', 'FontSize', 17)
legend6=legend('NKSM CEE Parameters','NKSM CET Parameters','NKSM GST Parameters','Location','Best');xlabel('Quarters', 'FontSize', 17) set(legend6,'FontSize',17)
axis([0 15 -0.25 0.2])
savefig('Response of Unemployment to a MP Shock')
plot(oo_1.irfs.r_eR,'b:');hold
all;plot(oo_2.irfs.r_eR,'k--');plot(oo_3.irfs.r_eR,'r');plot(oo_4.irfs.r_eR,'c');plot(oo_5.irfs.r_eR,'m');hold
off;title('Response of the Interest Rate to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize',17)
legend7=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CEE Parameters','NKSM CET Parameters','NKSM GST Parameters','Location','Best')
set(legend7,'FontSize',17) axis([0 25 -0.7 0.2])
savefig('Response of the Interest Rate to a MP shock')
plot(oo_1.irfs.i_eR,'b:');hold
all;plot(oo_2.irfs.i_eR,'k--');plot(oo_3.irfs.i_eR,'r');plot(oo_4.irfs.i_eR,'c');plot(oo_5.irfs.i_eR,'m');hold off;title('Response of Investment to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17) legend8=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CEE Parameters','NKSM CET Parameters','NKSM GST Parameters','Location','Best')
set(legend8,'FontSize',17) axis([0 25 -1 2])
savefig('Response of Investment to a MP shock')
plot(oo_1.irfs.c_eR,'b:');hold
all;plot(oo_2.irfs.c_eR,'k--');plot(oo_3.irfs.c_eR,'r');plot(oo_4.irfs.c_eR,'c');plot(oo_5.irfs.c_eR,'m');hold off;title('Response of Consumption to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17) legend9=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CEE Parameters','NKSM CET Parameters','NKSM GST Parameters','Location','Best')
set(legend9,'FontSize',17) axis([0 25 -0.1 0.3])
savefig('Response of Consumption to a MP shock')
plot(oo_1.irfs.u_eR,'b:');hold
all;plot(oo_2.irfs.u_eR,'k--');plot(oo_3.irfs.u_eR,'r');plot(oo_4.irfs.u_eR,'c');plot(oo_5.irfs.u_eR,'m');hold
off;title('Response of Capital Utilization to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend10=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CEE Parameters','NKSM CET Parameters','NKSM GST Parameters','Location','Best')
set(legend10,'FontSize',17) axis([0 20 -0.6 1])
savefig('Response of Capital Utilization to a MP shock')
%%% Impulse Response Functions for a variant of the NKSM CET (lower investment adj. costs) and the BM CEE Model:
%%% Figure 6.3.8 and Figure 6.3.9 plot(oo_2.irfs.y_eR,'k--');hold
all;plot(oo_6.irfs.y_eR,'Color',[0.6,0.5,0.8],'marker','+');hold off;title('Response of Output to a MP Shock', 'FontSize', 20);ylabel('Percent Deviation from the Unshocked Path',
'FontSize', 17)
legend11=legend('Benchmark CEE','NKSM Lower Investment Adj.
Costs','Location','Best');xlabel('Quarters', 'FontSize', 17)
78
set(legend11,'FontSize',17)
savefig('Response of Output to Lower Investment Adjustment Cost')
plot(oo_2.irfs.r_eR,'k--');hold all;plot(oo_6.irfs.r_eR,'Color',[0.6,0.5,0.8],'marker','+');
hold off;title('Response of the Interest Rate to a MP Shock', 'FontSize',
20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend12=legend('Benchmark CEE','NKSM Lower Investment Adj. Costs','Location','Best') set(legend12,'FontSize',17)
savefig ('Response of the Interest Rate to Lower Investment Adjustment Cost')
plot(oo_2.irfs.i_eR,'k--');hold all;plot(oo_6.irfs.i_eR,'Color',[0.6,0.5,0.8],'marker','+');
hold off;title('Response of Investment to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17) legend13=legend('Benchmark CEE','NKSM Lower Investment Adj. Costs','Location','Best') set(legend13,'FontSize',17)
savefig ('Response of Investment to Lower Investment Adjustment Cost')
plot(oo_2.irfs.c_eR,'k--');hold all;plot(oo_6.irfs.c_eR,'Color',[0.6,0.5,0.8],'marker','+');
hold off;title('Response of Consumption to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17) legend14=legend('Benchmark CEE','NKSM Lower Investment Adj. Costs','Location','Best') set(legend14,'FontSize',17)
savefig ('Response of Consumption to Lower Investment Adjustment Cost')
plot(unemp4,'c');hold all;plot(unemp6,'Color',[0.6,0.5,0.8],'marker','+'); hold off;title('Response of Unemployment to a MP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend15=legend('NKSM CET Parameters','NKSM Lower Investment Adj. Costs','Location','Best') set(legend15,'FontSize',17)
axis([0 22 -0.25 0.1])
savefig('Response of Unemployment to Lower Investment Adjustment Cost')
%%% IRFs for different capital shares in the NKSM CET parameterization
%%% not provided in this thesis
plot(unemp4,'c'); hold on ;plot(unemp9,'m');plot(unemp10,'b');hold off;title('Response of Unemployment to Different Capital Shares', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percentage Point Deviation from the Unshocked Path', 'FontSize', 17)
legend16=legend('NKSM CET Parameters','NKSM CET \alpha=0.36','NKSM CET
\alpha=0.2','Location','Best') set(legend16,'FontSize',17)
savefig('Response of Unemployment to Different Capital Shares')
plot(oo_4.irfs.y_eR,'c'); hold on ;plot(oo_9.irfs.y_eR,'m');plot(oo_10.irfs.y_eR,'b');hold off;title('Response of Output to Different Capital Shares', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 20)
legend17=legend('NKSM CET Parameters','NKSM CET \alpha=0.36','NKSM CET
\alpha=0.2','Location','Best') set(legend17,'FontSize',17)
savefig('Response of Output to Different Capital Shares')
plot(oo_4.irfs.pi_eR,'c'); hold on ;plot(oo_9.irfs.pi_eR,'m');plot(oo_10.irfs.pi_eR,'b');hold off;title('Response of Inflation to Different Capital Shares', 'FontSize',
20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend18=legend('NKSM CET Parameters','NKSM CET \alpha=0.36','NKSM CET
\alpha=0.2','Location','Best') set(legend18,'FontSize',17)
savefig('Response of Inflation to Different Capital Shares')
%%% produces graphs for different vacancy filling rates
%%% Figure 6.4.1
plot(unemp4,'c'); hold on ;plot(unemp7,'Color',[0.6,0.5,0.8],'marker','+');hold off;title('Response of Unemployment to Different Vacancy Filling Rates', 'FontSize',
20);xlabel('Quarters', 'FontSize', 17);ylabel('Percentage Point Deviation from the Unshocked Path', 'FontSize', 17)
legend19=legend('NKSM CET Parameters','NKSM CET with Vacancy Filling Rate of GST','Location','Best')
set(legend19,'FontSize',17)
savefig('Response of Unemployment to Different Vacancy Filling Rates')
plot(oo_4.irfs.y_eR,'c'); hold on
;plot(oo_7.irfs.y_eR,'Color',[0.6,0.5,0.8],'marker','+');hold off;title('Response of Output to Different Vacancy Filling Rates', 'FontSize', 20);xlabel('Quarters', 'FontSize',
17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
79
legend20=legend('NKSM CET Parameters','NKSM CET with Vacancy Filling Rate of GST','Location','Best')
set(legend20,'FontSize',17)
savefig('Response of Output to Different Vacancy Filling Rates')
plot(oo_4.irfs.pi_eR,'c'); hold on
;plot(oo_7.irfs.pi_eR,'Color',[0.6,0.5,0.8],'marker','+');hold off;title('Response of
Inflation to Different Vacancy Filling Rates', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend21=legend('NKSM CET Parameters','NKSM CET with Vacancy Filling Rate of GST','Location','Best')
set(legend21,'FontSize',17)
savefig('Response of Inflation to Different Vacancy Filling Rates')
%%% IRFs for different values of the worker bargaining power (eta) plot(unemp4,'c'); hold on
;plot(unemp11,'r');plot(unemp12,'Color',[0.6,0.5,0.8]);plot(unemp13,'m');hold off;title('Response of Unemployment to Changes in Bargaining Power', 'FontSize',
20);xlabel('Quarters', 'FontSize', 17);ylabel('Percentage Point Deviation from the Unshocked Path', 'FontSize', 17)
legend22=legend('NKSM CET Parameters','NKSM CET \eta=0.35','NKSM CET \eta=0.25','NKSM CET
\eta=0.589 (GST)','Location','Best') set(legend22,'FontSize',17)
savefig('Response of Unemployment to Different Values of the Worker Bargaining Power')
plot(oo_4.irfs.y_eR,'c'); hold on
;plot(oo_11.irfs.y_eR,'r');plot(oo_12.irfs.y_eR,'Color',[0.6,0.5,0.8]);plot(oo_13.irfs.y_eR,'m ');hold off;title('Response of Output to Changes in Bargaining Power', 'FontSize',
20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 20)
legend23=legend('NKSM CET Parameters','NKSM CET \eta=0.35','NKSM CET \eta=0.25','NKSM CET
\eta=0.589 (GST)','Location','Best') set(legend23,'FontSize',17)
savefig('Response of Output to Different Values of the Worker Bargaining Power')
plot(oo_4.irfs.pi_eR,'c'); hold on
;plot(oo_11.irfs.pi_eR,'r');plot(oo_12.irfs.pi_eR,'Color',[0.6,0.5,0.8]);plot(oo_13.irfs.pi_eR ,'m');hold off;title('Response of Inflation to Changes in Bargaining Power', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend24=legend('NKSM CET Parameters','NKSM CET \eta=0.35','NKSM CET \eta=0.25','NKSM CET
\eta=0.589 (GST)','Location','Best') set(legend24,'FontSize',17)
savefig('Response of Inflation to Different Values of the Worker Bargaining Power')
plot(oo_4.irfs.w_eR,'c'); hold on
;plot(oo_11.irfs.w_eR,'r');plot(oo_12.irfs.w_eR,'Color',[0.6,0.5,0.8]);plot(oo_13.irfs.w_eR,'m ');hold off;title('Response of Wages to Changes in Bargaining Power', 'FontSize',
20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend24=legend('NKSM CET Parameters','NKSM CET \eta=0.35','NKSM CET \eta=0.25','NKSM CET
\eta=0.589 (GST)','Location','Best') set(legend24,'FontSize',17)
savefig('Response of Wages to Different Values of the Worker Bargaining Power')
%%% IRFs for TFP shock (with identical Taylor rules as used by CEE)
plot(oo_1.irfs.r_epsilon_TFP,'b:');hold
all;plot(oo_2.irfs.r_epsilon_TFP,'k--');plot(oo_14.irfs.r_epsilon_TFP,'c');plot(oo_15.irfs.r_epsilon_TFP,'r');plot(oo_16.irfs.r_eps ilon_TFP,'m'); hold off;title('Response of the Interest Rate to a TFP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend25=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CET Parameters','NKSM CEE Parameters','NKSM GST Parameters','Location','Best');
set(legend25,'FontSize',17)
savefig('Response of the Interest Rate to a TFP shock Taylor')
plot(oo_1.irfs.y_epsilon_TFP,'b:');hold
all;plot(oo_2.irfs.y_epsilon_TFP,'k--');plot(oo_14.irfs.y_epsilon_TFP,'c');plot(oo_15.irfs.y_epsilon_TFP,'r');plot(oo_16.irfs.y_eps ilon_TFP,'m');hold off;title('Response of Output to a TFP Shock', 'FontSize',
20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend26=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CET Parameters','NKSM CEE Parameters','NKSM GST Parameters','Location','Best')
set(legend26,'FontSize',17)
savefig('Response of Output to a TFP shock Taylor')
80
plot(unemp14,'c');hold all;plot(unemp15,'r');plot(unemp16,'m');hold off;title('Response of Unemployment to a TFP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize',
17);ylabel('Percentage Point Deviation from Unshocked Path', 'FontSize', 17) legend27=legend('NKSM CET Parameters','NKSM CEE Parameters','NKSM GST
Parameters','Location','Best') set(legend27,'FontSize',17)
savefig('Response of Unemployment to a TFP Shock Taylor')
plot(oo_1.irfs.i_epsilon_TFP,'b:');hold
all;plot(oo_2.irfs.i_epsilon_TFP,'k--');plot(oo_14.irfs.i_epsilon_TFP,'c');plot(oo_15.irfs.i_epsilon_TFP,'r');plot(oo_16.irfs.i_eps ilon_TFP,'m');hold off;title('Response of Investment to a TFP Shock', 'FontSize',
20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend28=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CET Parameters','NKSM CEE Parameters','NKSM GST Parameters','Location','Best')
set(legend28,'FontSize',17)
savefig('Response of Investment to a TFP shock Taylor')
plot(oo_1.irfs.pi_epsilon_TFP,'b:');hold
all;plot(oo_2.irfs.pi_epsilon_TFP,'k--');plot(oo_14.irfs.pi_epsilon_TFP,'c');plot(oo_15.irfs.pi_epsilon_TFP,'r');plot(oo_16.irfs.pi_
epsilon_TFP,'m');hold off;title('Response of Inflation to a TFP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend29=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CET Parameters','NKSM CEE Parameters','NKSM GST Parameters','Location','Best')
set(legend29,'FontSize',17)
savefig('Response of Inflation to a TFP shock Taylor')
plot(oo_1.irfs.y_epsilon_TFP,'b:');hold
all;plot(oo_2.irfs.y_epsilon_TFP,'k--');plot(oo_14.irfs.y_epsilon_TFP,'c');plot(oo_15.irfs.y_epsilon_TFP,'r');plot(oo_16.irfs.y_eps ilon_TFP,'m');hold off;title('Response of Output to a TFP Shock', 'FontSize',
20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend26=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CET Parameters','NKSM CEE Parameters','NKSM GST Parameters','Location','Best')
set(legend26,'FontSize',17) axis([0 15 -0.2 0.8])
savefig('Response of Output to a TFP shock Taylor 2')
plot(unemp14,'c');hold all;plot(unemp15,'r');plot(unemp16,'m');hold off;title('Response of Unemployment to a TFP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize',
17);ylabel('Percentage Point Deviation from the Unshocked Path', 'FontSize', 17) legend27=legend('NKSM CET Parameters','NKSM CEE Parameters','NKSM GST
Parameters','Location','Best') set(legend27,'FontSize',17) axis([0 15 -0.2 0.2])
savefig('Response of Unemployment to a TFP Shock Taylor 2')
plot(oo_1.irfs.pi_epsilon_TFP,'b:');hold
all;plot(oo_2.irfs.pi_epsilon_TFP,'k--');plot(oo_14.irfs.pi_epsilon_TFP,'c');plot(oo_15.irfs.pi_epsilon_TFP,'r');plot(oo_16.irfs.pi_
epsilon_TFP,'m');hold off;title('Response of Inflation to a TFP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend29=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CET Parameters','NKSM CEE Parameters','NKSM GST Parameters','Location','Best')
set(legend29,'FontSize',17) axis([0 15 -0.8 0.2])
savefig('Response of Inflation to a TFP shock Taylor 2')
plot(oo_1.irfs.r_epsilon_TFP,'b:');hold
all;plot(oo_2.irfs.r_epsilon_TFP,'k--');plot(oo_14.irfs.r_epsilon_TFP,'c');plot(oo_15.irfs.r_epsilon_TFP,'r');plot(oo_16.irfs.r_eps ilon_TFP,'m'); hold off;title('Response of the Interest Rate to a TFP Shock', 'FontSize', 20);xlabel('Quarters', 'FontSize', 17);ylabel('Percent Deviation from the Unshocked Path', 'FontSize', 17)
legend25=legend('Benchmark Flexible Wage','Benchmark CEE','NKSM CET Parameters','NKSM CEE Parameters','NKSM GST Parameters','Location','Best')
set(legend25,'FontSize',17) axis([0 15 -0.4 0.2])
savefig('Response of the Interest Rate to a TFP shock Taylor 2')
81 B. List of Figures
Figure 3.1-1 Model and VAR based Impulse Responses (CEE 2005) ... 6
Figure 3.3-1 The Model Economy ... 7
Figure 3.6-1 Habit Formation in the Utility Function ... 12
Figure 4-1 Dice-DFH Mean Vacancy Duration Measure ... 20
Figure 6.2-1 Impact of different Taylor Rules ... 33
Figure 6.2-2 Impact of different Taylor Rules on the Interest Rate ... 33
Figure 6.3-1 Impulse Response of Inflation for Flexible and Sticky Wages ... 34
Figure 6.3-2 Response of Wages to a Monetary Policy Shock ... 35
Figure 6.3-3 Response of Output to a Monetary Policy Shock ... 35
Figure 6.3-4 Response of Unemployment to a Monetary Policy Shock ... 36
Figure 6.3-5 Response of Capital Utilization to a Monetary Policy Shock ... 37
Figure 6.3-6 Impulse Response Functions of Several Variables to a Monetary Policy Shock ... 38
Figure 6.3-7 Impulse Response Functions for a variant of the NKSM CET and the BM CEE Model ... 39
Figure 6.3-8 Impulse Response of Unemployment to a MP shock with lower Investment Adustment Costs ... 39
Figure 6.4-1 Impulse Responses of the NKSM CET Model with Different Vacancy Filling Rates ... 41
Figure 6.4-2 Impulse Responses of the NKSM CET Model to Changes in Worker Bargaining Power ... 42
Figure 6.5-1 Impulse Response Functions to a TFP Shock in the NKSM CET Model ... 44
Figure 6.5-2 Impulse Response Functions to a Neutral Technology Shock in the Cristiano et al. (2013) Model 44 Figure 6.5-3 Impulse Response of Output, Unemployment and Inflation to a TFP Shock ... 46
Figure 6.5-4 Impulse Responses of the Interest Rate to a TFP Shock ... 47
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