Difference between revisions of "Kooma"
From Testiwiki
Jump to: navigation, search
(Kooma code) |
(No difference)
|
Latest revision as of 15:14, 27 April 2017
This page is a method.
The page identifier is Op_en7789 |
|---|
| Moderator:Jouni (see all) |
|
Give your opinion to the peer rating of the content of this page. |
| Upload data
|
Kooma is a dynamic economic model used by the Ministry of Finance of Finland. The model is described here (original published code as pdf(!))
%% Kooma-model file.
% Valtiovarainministeriö
% Kansantalousosasto
% Mika Kuismanen & Mikko Sariola &
% Samuli Pietiläinen September 2013
%----------------------------------
% Meri Obstbaum November 2013
% adds frictional labour market
%linear
!transition_variables
%Households
'Private consumption' cp
'Transitory UIP shock process (risk premium)' i_e
% Ricardian Households
'Consumption of forward looking households' cp_fl
'Marginal utility of consumption' muc
'Shadow value of consumption' iso_lambda
'Capital-labour ratio in production' k
'Effective capital' K
'Physical capital' Kp
'Capacity utilisation rate' nu
'Investment' ip
'Rental rate on capital k' yint_roc
'Real value of installed capital - Tobin Q' tobin_q
'Nominal interest rate' i
'Price of domestic wholesale good' pyint
'Consumer price' p
'CPI inflation' pie_p
'Producer price inflation' pie_yint
'Real price of K-L product' preal_kl
'Price of K-L product in terms of the CPI' pyint_kl
'Marginal productivity of capital' mpk
'Shock process of household consumption' cp_fl_e
'Shock process of investment adjustment costs' eps_ip
'Shock process of Tobin Q ' eps_tobin_q
'Process of TFP shock' yint_z
'Operating surplus / dividents' D
% Rule of thumb households
'Consumption of hand-to-mouth households' cp_lc
% Labour Market matching
% PRODUCTION
'Output of labour and capital intermediate' yint_kl
'Aggregate output n*yint_kl' yint
% LABOUR MARKET
'number of matches' match
'unemployment' u
'Employment, number of workers' n
'Working hours, per person' h
'Total hours =n*h' total_h
'Vacancies' v
'job destruction rate' rhohat
'firms vacancy-filling probability' qf
'workers job-finding probability' qw
'labour market tightness' theta
'Shock process of labour shock' n_e
% Wage bargaining
'Firm surplus' J
'Worker surplus' H
'Marginal Productivity of Labour' mpl
'Contract wage' w_contract
'Nominal wage' w
'Employers social contribution' tau_sc
'Marginal rate of substitution btw consumption and labour' mrs
'Workers tax on earned income' tau_w
'Value added tax' tau_cp
'Bargaining strenght of workers' etahat
% Job creation and determination of hours worked (per person)
'Vacancy posting cost' kappahat
%Marginal cost of wholesale firm
'price mark-up domestic market' yint_phi
% RETAILERS, final goods producers
%Retailer of investment good
'price of composite investment good' pip
'demand of domestic intermediate investment good' iph
'imported investment good' mi
%Importer price setting: consumption good
'pcp price of imported consumption good' pmc_pcp % PCP pri-
ce equation for imported intermediate input ($)
'lcp price of imported consumption good' pmc_lcp % LCP pri-
ce equation for imported intermediate input (€)
'price of imported consumption good' pmc % aggregate
import price equation of consumption good
%Retailer of consumption good
'price of composite consumption good' pcp
'imported consumption good' mc
%'price of domestic intermediate good' pcph
'demand of domestic intermediate consumption good' cph
%Retailer of export good
'demand for imports used in exports' mex
'demand for domestic goods used in exports' hex
%Importer price setting: export good
'PCP price of imported intermediate good used in exports ($)'
pmex_pcp
'LCP price of imported intermediate good used in exports (€)'
pmex_lcp
'price of composite import good used in exports' pmex
% EXTERNAL SECTOR: Exports, imports
%Total imports
'imports' m
'import price' pm
%%Importer price setting: investment good
'PCP price equation for imported intermediate input ($)' pmi_pcp
'LCP price equation for imported intermediate input (€)' pmi_lcp
'aggregate import price equation of investment good' pmi
% Exports
'marginal cost of exports' mcex
'export market size' xd
'aggregate export price level' px
'LCP export price' px_lcp
'PCP export price' px_pcp
'aggregate exports' x
'LCP export volume' x_lcp
'PCP export volume' x_pcp
'Foreign price level ($) competing with finnish exporters' f_pex
% one foreign price level, $ equal to f_pim
% Some general variables
'exchange rate' e
'foreign price level ($) competing with finnish importers'
f_pim % foreign price level
'Trade balance' tb;
'Foreign bond' BF;
'Foreign interest rate' istar
% Shock processes to imports and exports
'Transitory price shock process to imported consumption goods' pmc_e
'Transitory price shock process to mc of exports' mcex_e
'Transitory price shock process to imported investment goods' pmi_e
'Transitory price shock process to imported goods used in exports'
pmex_e
'Transitory shock process to imported consumption goods' mc_e
'Transitory shock process to imported investment goods' mi_e
'Transitory shock process to imported goods used in exports' mex_e
% Public sector / General government
'General government bonds' BH
'Tax on dividents' tau_d
'Tax on investment/ investment tax credit' tau_ip
'Tax on capital' tau_k
'general government consumption (real)' cg
'transfers to households' ott
% Some reporting variables
'General government income' GG_income
'General government income, VAT' GG_income_VAT
'General government income, tau_W+tau_SC' GG_income_W_SC
'General government income, tau_W' GG_income_W
'General government income, tau_SC' GG_income_SC
'General government income, tau_D' GG_income_D
'price of oil, $' poil
'export price aggegation' px_e
'general government investment (real)' ig
!transition_shocks
'UIP shock (risk premium)' e_i_e
'Transitory shock to investments' e_ip
'Transitory shock to Tobin q' e_eps_q
'Transitory household consumption preference shock' e_cp_fl
'Transitory shock in productivity' e_yint_z
'Labour shock' e_n
'Shock to job destruction rate' e_rhohat
'Shock to vacancy costs' e_kappahat
'Shock to workers negotiation weight' e_etahat
'Shock to average wage process' e_w
'Shock to unemployment rate'e_u
'Price markup shock of intermediate firm' e_yint_phi
'exchange rate shock' e_e
'foreign price shock' e_f_pim
'export demand shock' e_xd
'Price shock to imported consumption goods' e_pmc
'Price shock to MC of exports' e_mcex
'Price shock to imported investment goods' e_pmi
'Price shock to imported goods used in exports' e_pmex
'Shock to aggregate imports' e_m_e
'Shock to imported consumption goods' e_mc_e
'Shock to imported investment goods' e_mi_e
'Shock to imported consumption goods used in exports' e_mex_e
'Shock to wage tax parameter' e_tau_w
'Shock to VAT tax parameter' e_tau_cp
'Shock to capital tax' e_tau_k
'Shock to employers social contributions' e_tau_sc
'Shock to dividend tax' e_tau_d
'Shock to investment tax or subsidy if minus sign' e_tau_ip
'Shock to government transfers' e_ott
'Shock to government consumption' e_cg
'Shock to government investment' e_ig
'Shock to oil price' e_poil
'shock to export price aggregation' e_px
%
!parameters
omega_lc % share of liquidity constrained households,
set =0 with matching
istar_ss % SS foreign interest rate
gamma_sastar % debt elastic interest rate penalty parame-
ter
rho_i_e % AR-coefficient of UIP shock process
tau_cp_ss % SS VAT on consumption
sigma_cp % household risk aversion
varkappa % habit persistence
rho_cp_fl_e % AR coefficient of consumption shock
beta % discount factor
cp_ss % SS consumption
cp_lc_ss % SS consumption of liquidity constraint hou-
seholds
cp_fl_ss % SS consumption of forward-looking house-
holds
ott_ss % SS transfers to households
% Investment and capital
%-----------------------
kappa_i % investment adjustment cost parameter
rho_ip % AR coefficient of investment shock
delta_k % depreciation of capital
gamma_yint % share of capital in intermediate goods pro-
duction
eta_nu % capital utilization rate
yint_roc_ss % SS return on capital
rho_tobin_q % AR coefficient of equity premium shock
rho_z % AR coefficient of transitory technology
shock
% Labour market matching and wage bargaining
%-------------------------------------------
sigma_M % elasticity of matches w.r.t. unemployment
rho % SS job destruction rate
match_ss % SS matches
n_ss % SS employment
u_ss % SS unemployment
pyint_kl_ss % SS price of K-L good, = preal_kl_ss
mpl_ss % SS marginal productivity of labour
h_ss % SS hours worked per person
J_ss % SS firm surplus
w_ss % SS wage
b % unemployment benefit
tau_sc_ss % SS employer's social contribution
k_ss % SS operative capital
tau_w_ss % SS worker's tax on earned income
H_ss % SS worker surplus
mrs_ss % SS marginal rate of substitution
sigma_n % Frish elasticity of labour
qw_ss % SS job-finding probability
eta % SS bargaining power
omega_w % Weight of contract wage
rho_n_e % AR of labour supply shock
rho_rhohat % AR of job destruction shock
rho_kappahat % AR of vacancy cost shock
rho_etahat % AR of shock to workers' negotiation weight
% Wholesale firm
%---------------
rho_yint_phi % AR-coeff. of markup shock%
pyint_ksi % probability of taking the price as given
(calvo)
pyint_ss % SS price of domestic intermediate input
SAMULI
yint_ss % SS production of intermediate firm
%-----------------------------------
f_pim_ss % foreign SS price level ($) for intermediate
import input market.
rhoe % ar coefficient in exchange rate shock
rho_f_pim % ar coefficient in foreign price shock
i_ss % SS nominal interest rate
% importer price setting: investment good
%----------------------------------------
omegai % share of LCP importing firms. (1-omegai) is the
share of pcp firms
gammai_lcp % calvo parameter, share of LCP import firms that are
NOT allowed to change price at period t
gammai_pcp % calvo parameter, share of PCP import firms that are
NOT allowed to change price at period t
% retailer of investment good
thetaip % demand elasticity for domestic and foreign interme-
diate investment good
omegaip % share of domestic intermediate investment good in
production of composite investment good
% Importer price setting: consumption good
%----------------------------------------
omegac % share of LCP importing firms. (1-omegac) is
the share of pcp firms
gammac_lcp % calvo parameter, share of LCP import firms
that are NOT allowed to change price at period t
gammac_pcp % calvo parameter, share of PCP import firms
that are NOT allowed to change price at period t
%Retailer of consumption good
thetacp % demand elasticity for domestic and foreign interme-
diate consumption good
omegacp % share of domestic intermediate consumtion good in
production of composite consumption good
%Exporter
%------------
gammax_pcp % calvo parameter, share of PCP firms that are NOT
allowed to change price at period t,
gammax_lcp % calvo parameter, share of LCP firms that are NOT
allowed to change price at period t
omegax % share of LCP firms in exports
thetax % price elasticity of demand for the export product.
Determined by rhox
x_ss % SS of exports
rhoxd % ar-parameter of foreign market shock
rhostar
thetaex
deltaex
mex_ss
%Importer price setting: export good
%-----------------------------------
mcex_ss % SS marginal cost of exports
pmex_ss % aggregate steady state import price level for goods
used in export production(€)
omegaex % share of LCP importing firms. (1-omegaex) is the
share of pcp firms
gammaex_lcp % calvo parameter, share of LCP import firms that are
NOT allowed to change price at period t
gammaex_pcp % calvo parameter, share of PCP import firms that are
NOT allowed to change price at period t
m_ss % SS imports
mc_ss % SS imported C goods share of total imports
mi_ss % SS imported I goods share of total imports
rho_pmc_e % ar coefficient in imported consumption good price
shock
rho_mcex_e % ar coefficient in mc of exports shock
rho_pmi_e % ar coefficient in imported investment good price
shock
rho_pmex_e % ar coefficient in imported goods used in exports
price shock
rho_mc_e % the following 3 are ar's of import volume shocks
rho_mi_e
rho_mex_e
% Public sector
%--------------
BH_ss % General government bonds in SS
tau_d_ss % Tax on dividents in SS
tau_k_ss % Tax on effective capital in SS
tau_ip_ss % Tax on investments in SS
rho_cg % AR of public spending shock
rho_ig % AR of public investment shock
rho_ott % AR-coeff of transfers to households (ott_e) shock
rho_tau_w
rho_tau_cp
rho_tau_k
rho_tau_sc
rho_tau_d
rho_tau_ip
rho_poil
% Closing the model
%------------------
ip_ss % Investment in SS
cg_ss % Government consumption
ig_ss % Government investment
v_ss % Vacancies in SS
kappa % Vacancy posting cost in SS
K_ss % Effective capital in SS
rho_istar % AR coefficient of foreign interest
D_ss % Dividends in SS
total_h_ss % Total hours worked in SS
% shock magnitude parameters
std_e_rhohat % std error of job destruction shock
std_e_kappahat % std error of vacancy cost shock
std_e_etahat % std error of shock to negotiation weight
std_e_pmc % st. error of the shock
std_e_mcex % st. error of the shock
std_e_pmi % st. error of the shock
std_e_pmex % st. error of the shock
std_e_m_e
std_e_mc_e
std_e_mi_e
std_e_mex_e
std_e_e % st. error of the shock
std_e_f_pim % st. error of the shock
std_e_i_e % st. error of the shock
std_e_xd % st. error of the shock
std_e_px
std_e_n
std_e_ott % St. error of transfers to households (ott_e) shock
std_e_tau_w
std_e_tau_k
std_e_tau_cp
std_e_tau_sc
std_e_tau_d
std_e_tau_ip
std_e_cg
!transition_equations
%% Debt-elastic interest rate
i=istar-gamma_sastar*(BF-yint-pyint)+i_e;
i_e=rho_i_e*i_e{-1}+e_i_e;
poil = rho_poil*poil{-1}+e_poil;
%% Ricardian Households
% Consumption
iso_lambda = iso_lambda{+1}+i-(p{+1}-p); % Euler equation
iso_lambda = muc-(tau_cp_ss)/(1+tau_cp_ss)*tau_cp; % Marginal uti-
lity of wealth
muc = -((sigma_cp)/(1-varkappa))*(cp_fl-varkappa*cp_fl{-1})+cp_fl_e;
% where muc is marginal utility of consumption
% Investment and capital accumulation
nu = eta_nu*yint_roc; % Capital utili-
zation rate
ip = (1/(1+beta))*ip{-
1}+(beta/(1+beta))*ip{+1}+(1/(1+beta))*(1/kappa_i)*tobin_q-
(1/(1+beta))*(beta*eps_ip{+1}-eps_ip); % Investment
Kp = (1-delta_k)*Kp{-1}+delta_k*ip{-1}; % (physical)
Capital accumulation equation
K = nu+Kp{-1}; % Effective ca-
pital
tobin_q = -(i-(p{+1}-p))+((1-delta_k)/(1-
delta_k+yint_roc_ss))*tobin_q{+1}+((yint_roc_ss)/(1-
delta_k+yint_roc_ss))*yint_roc{+1}+eps_tobin_q; % Real value of capital,
Tobin Q
yint_roc = pyint_kl+mpk; % Rental rate
for capital
pyint_kl = pyint-p+preal_kl;
mpk = (1-gamma_yint)*(h-k)+yint_z;
k = K-n; % Capital-Labour
ratio
% shocks
cp_fl_e=rho_cp_fl_e*cp_fl_e{-1}+e_cp_fl; % AR consumption
shock process
eps_ip=rho_ip*eps_ip{-1}+e_ip; % Investment
AR1-Shock
eps_tobin_q = rho_tobin_q*eps_tobin_q{-1}+e_eps_q; %
yint_z=rho_z*yint_z{-1}+e_yint_z; % Technology
shock
%% Rule of thumb households
%Liquidity constrained households consume all their income
cp_lc = ((n_ss*w_ss*h_ss*(1-
tau_w_ss))/((1+tau_cp_ss)*cp_lc_ss))*(w+h) + ((n_ss*(w_ss*h_ss*(1-
tau_w_ss)-b))/((1+tau_cp_ss)*cp_lc_ss))*n +
(ott_ss/((1+tau_cp_ss)*cp_lc_ss))*ott
- (1-((b*(1-n_ss))/((1+tau_cp_ss)*cp_lc_ss)))*p -
(tau_cp_ss/(1+tau_cp_ss))*tau_cp -
((n_ss*w_ss*h_ss*tau_w_ss)/((1+tau_cp_ss)*cp_lc_ss))*tau_w;
% Aggregate consumption
cp = ((omega_lc*cp_lc_ss)/cp_ss)*cp_lc + (((1-
omega_lc)*cp_fl_ss)/cp_ss)*cp_fl;
%% Labour Market matching
% On intermediate firms:
% Matching and employment dynamics
match = sigma_M*u+(1-sigma_M)*v ; % Nr of new mat-
ches in each period
n = (1-rho)*n{-1}+(match_ss/n_ss)*match{-1}-rho*rhohat ; % Total
nr of matches that enter each period = employment
u = -((1-u_ss)/u_ss)*n + e_u ; % unem-
ployment, e_u added to be able to exogenise in conditional forecast
qf = match-v ; % vacancy-
filling probability
qw = match-u ; % job-
finding probability
theta = v-u ; % labour market
tightness
rhohat = rho_rhohat*rhohat{-1}+e_rhohat ; % Shock to
job destruction rate
%rhohat = -7.79*yint_z+e_rhohat ;
%% Wage bargaining
%
% Firm surplus
J = ((pyint_kl_ss*mpl_ss*h_ss)/((1-
gamma_yint)*J_ss))*(pyint_kl+mpl+h)-
((w_ss*h_ss*(1+tau_sc_ss))/J_ss)*(w+h-p)
-((w_ss*h_ss*tau_sc_ss)/J_ss)*tau_sc-
(((yint_roc_ss)*k_ss)/J_ss)*(yint_roc+k)+(beta*(1-
rho))*(J{+1}+iso_lambda{+1}-iso_lambda)
-(beta*rho)*(rhohat{+1});
% where the marginal productivity of labour is
% mpl = gamma_yint*(k-h)+yint_z
mpl = gamma_yint*(k-h)+yint_z ;
% Worker surplus
H = ((w_ss*h_ss*(1-tau_w_ss))/H_ss)*(w+h-p)-
((w_ss*h_ss*tau_w_ss)/H_ss)*tau_w-
((mrs_ss*h_ss*(1+tau_cp_ss))/((1+sigma_n)*H_ss))*(mrs+h)
-((mrs_ss*h_ss*tau_cp_ss)/((1+sigma_n)*H_ss))*tau_cp+(beta*(1-rho-
qw_ss))*(H{+1}+iso_lambda{+1}-iso_lambda)-(beta*rho)*rhohat{+1}-
(beta*qw_ss)*qw;
% where the marginal rate of substitution is
mrs = sigma_n*h+(1-sigma_n)*n_e-muc;
% Negotiated wage
w_contract = ((eta*pyint_kl_ss*mpl_ss)/((1+tau_sc_ss)*(1-
gamma_yint)*w_ss))*(pyint_kl+mpl)-
((eta*yint_roc_ss*k_ss)/(w_ss*h_ss*(1+tau_sc_ss)))*(yint_roc+k)
+(((1-eta)*H_ss*beta*qw_ss)/(w_ss*h_ss*(1-
tau_w_ss)))*(H{+1}+iso_lambda{+1}-iso_lambda+qw)+(((1-
eta)*mrs_ss*(1+tau_cp_ss))/((1-tau_w_ss)*(1+sigma_n)*w_ss))*mrs
-(1-((eta*pyint_kl_ss*mpl_ss)/((1+tau_sc_ss)*(1-gamma_yint)*w_ss))-(((1-
eta)*mrs_ss*(1+tau_cp_ss))/((1-tau_w_ss)*(1+sigma_n)*w_ss)))*h
+((((1-eta)*tau_w_ss)/(1-tau_w_ss))*(1-(H_ss/(w_ss*h_ss*(1-
tau_w_ss)))))*tau_w
+((((1-eta)*tau_w_ss)/(1-tau_w_ss))*((H_ss*beta*(1-rho))/(w_ss*h_ss*(1-
tau_w_ss))))*tau_w{+1}
-
(((eta*tau_sc_ss)/(1+tau_sc_ss))*(1+(J_ss/(w_ss*h_ss*(1+tau_sc_ss)))))*ta
u_sc
+(((eta*tau_sc_ss)/(1+tau_sc_ss))*((J_ss*beta*(1-
rho))/(w_ss*h_ss*(1+tau_sc_ss))))*tau_sc{+1}
+(((1-eta)*mrs_ss*tau_cp_ss)/((1-tau_w_ss)*(1+sigma_n)*w_ss))*tau_cp
+(1/(1-eta))*etahat-((H_ss*beta*(1-rho))/(w_ss*h_ss*(1-
tau_w_ss)))*etahat{+1}+p;
% Average wage
w = omega_w*w_contract + (1-omega_w)*w{-1} + e_w;
% Shock to workers' negotiation weight
etahat = rho_etahat*etahat{-1}+e_etahat;
% Hours supply shock process
n_e=rho_n_e*n_e{-1}+e_n;
%% Job creation and determination of hours worked (per person)
%--------------------------
%
% Comments here
% Vacancy posting / job creation condition (analogous to labour de-
mand in conventional models
kappahat-qf = J{+1}+iso_lambda{+1}-iso_lambda;
% Hours worked xmpl(1-tau_w)=mrs(1+tau_sc)(1+tau_cp)
pyint_kl+mpl = mrs+(tau_w_ss/(1-
tau_w_ss))*tau_w+(tau_sc_ss/(1+tau_sc_ss))*tau_sc+(tau_cp_ss/(1+tau_cp_ss
))*tau_cp;
% Shock to vacancy costs
kappahat = rho_kappahat*kappahat{-1}+e_kappahat;
%
%% Wholesale firm, price setting
%-------------------------------
% New Keynesian Phillips curve
pie_yint = (((1-pyint_ksi)*(1-
(pyint_ksi*beta)))/pyint_ksi)*(preal_kl+yint_phi)+beta*pie_yint{1};
pie_yint = pyint-pyint{-1};
yint_phi = rho_yint_phi*yint_phi{-1}+e_yint_phi;
%% External sector: Imports, Exports
%
% Comments here
%
% Aggregate imports
m = (mex_ss/m_ss)*mex+(mc_ss/m_ss)*mc+(mi_ss/m_ss)*mi+e_m_e;
pm = (mex_ss/m_ss)*pmex+(mc_ss/m_ss)*pmc+(mi_ss/m_ss)*pmi;
% Importer price setting: INVESTMENT good
pmi = omegai*pmi_lcp - omegai*e +(1-omegai)*pmi_pcp + pmi_e; % aggre-
gate
pmi_lcp - pmi_lcp{-1} = (1/(1+beta))*(pmi_lcp{-1} - pmi_lcp{-2}) +
(((1-gammai_lcp)*(1-beta*gammai_lcp))/((1+beta)*gammai_lcp))*(f_pim-e-
pmi_lcp)+(beta/(1+beta))*(pmi_lcp{+1}-pmi_lcp); %LCP
pmi_pcp - pmi_pcp{-1} = (1/(1+beta))*(pmi_pcp{-1} - pmi_pcp{-2}) +
(((1-gammai_pcp)*(1-beta*gammai_pcp))/((1+beta)*gammai_pcp))*(f_pim-
pmi_pcp)+(beta/(1+beta))*(pmi_pcp{+1}-pmi_pcp); %PCP
pmi_e = rho_pmi_e*pmi_e{-1} + e_pmi;
% Importer price setting: CONSUMPTION good
pmc = omegac*pmc_lcp - omegac*e +(1-omegac)*pmc_pcp +0.0463*poil +
pmc_e;
pmc_lcp - pmc_lcp{-1} = (1/(1+beta))*(pmc_lcp{-1} - pmc_lcp{-
2}) + (((1-gammac_lcp)*(1-
beta*gammac_lcp))/((1+beta)*gammac_lcp))*(f_pim-e-
pmc_lcp)+(beta/(1+beta))*(pmc_lcp{+1}-pmc_lcp); %LCP
pmc_pcp - pmc_pcp{-1} = (1/(1+beta))*(pmc_pcp{-1} - pmc_pcp{-
2}) + (((1-gammac_pcp)*(1-
beta*gammac_pcp))/((1+beta)*gammac_pcp))*(f_pim-
pmc_pcp)+(beta/(1+beta))*(pmc_pcp{+1}-pmc_pcp); %PCP
pmc_e = rho_pmc_e*pmc_e{-1} + e_pmc;
% Importer price setting: EXPORT good
pmex = omegaex*pmex_lcp - omegaex*e +(1-omegaex)*pmex_pcp
+0.1043*poil + pmex_e; % aggregate import price equation that com-
bines PCP and LCP price levels
pmex_lcp - pmex_lcp{-1} = (1/(1+beta))*(pmex_lcp{-1} - pmex_lcp{-2})
+ (((1-gammaex_lcp)*(1-beta*gammaex_lcp))/((1+beta)*gammaex_lcp))*(f_pim-
e-pmex_lcp)+(beta/(1+beta))*(pmex_lcp{+1}-pmex_lcp);
pmex_pcp - pmex_pcp{-1} = (1/(1+beta))*(pmex_pcp{-1} - pmex_pcp{-2})
+ (((1-gammaex_pcp)*(1-beta*gammaex_pcp))/((1+beta)*gammaex_pcp))*(f_pim-
pmex_pcp)+(beta/(1+beta))*(pmex_pcp{+1}-pmex_pcp);
pmex_e = rho_pmex_e*pmex_e{-1} + e_pmex; % price shock AR to
imported good used in exports
% Export price setting
px = omegax*px_lcp - omegax*e+(1-omegax)*px_pcp + px_e;
px_lcp - px_lcp{-1} = (1/(1+beta))*(px_lcp{-1} - px_lcp{-2}) + (((1-
gammax_lcp)*(1-beta*gammax_lcp))/((1+beta)*gammax_lcp))*(mcex -e -
px_lcp)+(beta/(1+beta))*(px_lcp{+1}-px_lcp);
px_pcp - px_pcp{-1} = (1/(1+beta))*(px_pcp{-1} - px_pcp{-2}) + (((1-
gammax_pcp)*(1-beta*gammax_pcp))/((1+beta)*gammax_pcp))*(mcex-
px_pcp)+(beta/(1+beta))*(px_pcp{+1}-px_pcp);
%px = omegax*px_lcp +(1-omegax)*px_pcp; % aggregate export price
equation that combines PCP and LCP price levels
px_e = rho_pmex_e*px_e{-1} + e_px;
% Exchange rate shock
e = rhoe*e{-1}+e_e;
f_pim = rho_f_pim*f_pim{-1}+e_f_pim; % foreign price shock
f_pex = f_pim; %
%% Final goods producers
%
% Comments here
% The public consumption-good is in the section on the public sector
% Investment good retailer
iph = thetaip*(pip-pyint)+ip; % demand for domestic
intermediate good in investment-good production
mi = thetaip*(pip-pmi)+ip + mi_e; % demand for foreign
intermediate good in investment-good production
mi_e= rho_mi_e*mi_e{-1} + e_mi_e; % shock to the volume
of imported investment good
pip = omegaip*pyint+(1-omegaip)*pmi; % price of composite
investment good
% Consumption good retailer
cph = thetacp*(pcp-pyint)+cp; % demand for domestic
intermediate good
mc = thetacp*(pcp-pmc)+cp+mc_e; % demand for foreign
intermediate good
mc_e= rho_mc_e*mc_e{-1} + e_mc_e; % shock to the volume
of imported consumption good
pcp = omegacp*pyint+(1-omegacp)*pmc; % price of composite
consumption good = CPI
% Export good retailer: volumes
hex = thetaex*(mcex-pyint)+x; % demand for domes-
tic intermediate good used in exports
mex = thetaex*(mcex-pmex)+x+mex_e; % demand for impor-
ted foreign goods used in export-good production
mex_e= rho_mex_e*mex_e{-1} + e_mex_e; % shock to the volume
of imported export good
% Export good retailer: marginal costs
mcex = ((delta-
ex^thetaex)*(pyint_ss/mcex_ss)^(rhostar/(rhostar+1)))*pyint + (((1-
deltaex)^thetaex)*(pmex_ss/mcex_ss)^(rhostar/(rhostar+1)))*pmex + mcex_e
;% mcex of exports
mcex_e = rho_mcex_e*mcex_e{-1} + e_mcex; % Price shock to mar-
ginal costs of exports
% Export volumes
x_lcp = thetax*(f_pex-px_lcp)+xd; % LCP export demand
equation
x_pcp = thetax*(f_pex-px_pcp-e)+xd; % PCP export demand
equation
% CHECK THESE
% aggr. export demand = aggr. export supply, i.e. the aggregator!
x = omegax*x_lcp+(1-omegax)*x_pcp; % aggregate export
demand, assumes linear combination
xd = rhoxd*xd{-1}+e_xd; % Export demand /
foreign market AR
%% Public sector
%
% General government
% Government budget constraint / Evolution of gvmt REAL debt
BH = i_ss*(BH{-1}+i-pie_p) + (cg_ss/BH_ss)*(pyint+cg) +
((b*u_ss*u)/BH_ss) + ((-cg_ss-ig_ss-ott_ss)/BH_ss)*p +
(ig_ss/BH_ss)*(pyint+ig)
+ (ott_ss/BH_ss)*ott -
(((n_ss*w_ss*h_ss)*(tau_w_ss+tau_sc_ss))/BH_ss)*(n+w+h) -
((n_ss*w_ss*h_ss*tau_w_ss)/BH_ss)*tau_w
- ((n_ss*w_ss*h_ss*tau_sc_ss)/BH_ss)*tau_sc -
((tau_cp_ss*cp_ss)/BH_ss)*(tau_cp+cp) - ((tau_d_ss*D_ss)/BH_ss)*(tau_d+D)
- ((yint_roc_ss*tau_k_ss*K_ss)/BH_ss)*(yint_roc+tau_k+K);
% where dividends to domestic households
(D_ss/yint_ss)*D = yint -
(((1+tau_sc_ss)*w_ss*total_h_ss)/(yint_ss))*(w+total_h) -
((tau_sc_ss*w_ss*total_h_ss)/(yint_ss))*(tau_sc)
-(yint_roc_ss*K_ss/yint_ss)*(yint_roc+K)+(1-
(kappa*v_ss/yint_ss))*pyint_kl-(kappa*v_ss/yint_ss)*(kappahat+v)
+(x_ss/yint_ss)*px-(mcex_ss*x_ss/yint_ss)*mcex+((1-
mcex_ss)*x_ss/yint_ss)*x+(m_ss/yint_ss)*pm-
(f_pim_ss*m_ss/yint_ss)*f_pim+(1-f_pim_ss/yint_ss)*m_ss*m;
% For reporting purposes: General government income
GG_income= (tau_cp_ss*cp_ss)*(tau_cp+p+cp) +
(tau_ip_ss*ip_ss)*(tau_ip+pip+ip) +
(n_ss*w_ss*h_ss*tau_sc_ss)*(tau_sc+n+w+h) +
(n_ss*w_ss*h_ss*tau_w_ss)*(tau_w+n+w+h) +
(yint_roc_ss*tau_k_ss*K_ss)*(yint_roc+tau_k+K) +
(D_ss*tau_d_ss)*(tau_d+D);
GG_income_VAT = (tau_cp_ss*cp_ss)*(tau_cp+p+cp);
GG_income_W_SC = (n_ss*w_ss*h_ss*tau_sc_ss)*(tau_sc+n+w+h) +
(n_ss*w_ss*h_ss*tau_w_ss)*(tau_w+n+w+h);
GG_income_W = (n_ss*w_ss*h_ss*tau_w_ss)*(tau_w+n+w+h);
GG_income_SC = (n_ss*w_ss*h_ss*tau_sc_ss)*(tau_sc+n+w+h);
GG_income_D = (D_ss*tau_d_ss)*(tau_d+D);
% Expenditure
ott = rho_ott*ott{-1}+e_ott;
cg = rho_cg*cg{-1}+e_cg;
% Revenue
ig = rho_ig*ig{-1}+e_ig;
tau_w = rho_tau_w*tau_w{-1} + e_tau_w;
tau_cp = rho_tau_cp*tau_cp{-1} + e_tau_cp;
tau_k = rho_tau_k*tau_k{-1} + e_tau_k;
tau_sc = rho_tau_sc*tau_sc{-1} + e_tau_sc;
tau_d = rho_tau_d*tau_d{-1} + e_tau_d;
tau_ip = rho_tau_ip*tau_ip{-1} + e_tau_ip;
%% Closing the model
%
% Comments here
%
% Trade Balance
tb = yint - cp_ss*cp - ip_ss*ip - cg_ss*cg + ((1-mcex_ss)*x_ss)*x +
((1-f_pim_ss)*m_ss)*m + x_ss*px - (mcex_ss*x_ss)*mcex
+ m_ss*pm - (f_pim_ss*m_ss)*f_pim - cp_ss*p - ip_ss*pip + (1-cg_ss-
(kappa*v_ss))*pyint -(kappa*v_ss)*(kappahat+v) - (yint_roc_ss*K_ss)*nu;
BF = tb + i_ss*istar{-1}+i_ss*(1-gamma_sastar)*BF{-1} +
i_ss*gamma_sastar*f_pim{-1} + i_ss*gamma_sastar*yint{-1};
istar=rho_istar*istar{-1}+i_e;
% Economy wide resource constraint
yint = (omegacp*cp_ss)*cp + (omegacp*cp_ss*thetacp)*p + (ome-
gaip*ip_ss)*ip + (omegaip*ip_ss*thetaip)*pip + (omegaex*x_ss)*x + (omega-
ex*x_ss*thetaex)*px
+ cg_ss*cg - (ome-
gacp*cp_ss*thetacp+omegaip*ip_ss*thetaip+omegaex*x_ss*thetaex)*pyint;
%Production
yint_kl = gamma_yint*k+(1-gamma_yint)*h+yint_z;
yint = n+yint_kl;
total_h=n + h;
p = pcp;
pie_p = p-p{-1};
%% Measurement / Data
%
% Comments here
%
!measurement_variables
'Consumption' cp_
'Output' yint_
'Imports' m_
'Exports' x_
'Private investment' ip_
'Interest rate' i_
'Nominal wage' w_
'Exchange rate' e_
'Consumption good price level' pcp_
'Labour force, total hours' total_h_
'Unemployment' u_
'Operating surplus / Dividents (nominal)' D_
'Import price level' pm_ %%%hankala
'Export price level' px_ %%%hankala
'price of composite investment good' pip_
'Foreign price level ($) competing with finnish importers' f_pim_
%%%hankala
'Foreign price level ($) competing with finnish exporters' f_pex_
%%
'External demand' xd_
'Price of imported consumption good' pmc_
'Price of imported investment good' pmi_
'Price of imported good used in exports' pmex_
'General government consumption (real)' cg_
'Price of oil' poil_
!measurement_shocks
'measurement error on foreign prices competing with importers' m_f_pim
'measurement error on foreign prices competing with exporter' m_f_pex
'measurement error on price of imported consumption good' m_pmc
'measurement error on price of imported investment good' m_pmi
'measurement error on price of imported good used in exports' m_pmex
'measurement error on external demand' m_xd
'measurement error on output' m_yint
!measurement_equations
cp_ = cp;
yint_ = yint;
m_ = m;
x_ = x;
ip_ = ip;
e_ = e;
i_ = i;
w_ = w;
pcp_ = pcp;
total_h_ = total_h;
u_ = u;
D_ = D; %osv
cg_ = cg;
pm_ = pm;
px_ = px;
pip_ = pip; %
f_pim_ = f_pim+m_f_pim;
f_pex_ = f_pex +m_f_pex; %
xd_ = xd+m_xd; %
pmc_ = pmc + m_pmc; %
pmi_ = pmi+ m_pmi; %
pmex_ = pmex+ m_pmex ; %
poil_ = poil;
%%
%% Set parameters
omega_lc = 0.2 ; % share of liquidity constrained households
i_ss=0.03/4 ; % SS nominal interest rate
istar_ss = i_ss ; % SS foreign interest rate
gamma_sastar = 0.01 ; % debt elastic interest rate penalty parameter
rho_i_e = 0.8; % AR-coefficient of UIP shock process
tau_cp_s = 0.11; % " SS VAT on consumption"
sigma_cp = 1.6; % household risk aversion
varkappa = 0.6; % habit persistence
rho_cp_fl_e = 0.8; % AR coefficient of consumption shock
beta = 0.99; % discount factor
BH_ss = 0.6; % SS gvmt debt
% Investment and capital
%
-----------------------
kappa_i = 6.617; % investment adjustment cost parameter
rho_ip= 0.485; % AR coefficient of investment shock
delta_k= 0.025; % depreciation of capital
gamma_yint = 0.33; % share of capital in intermediate goods
production
eta_nu = 0.43; % capital utilization rate
yint_roc_ss = i_ss+delta_k; % SS return on capital
rho_tobin_q = 0.3; % AR coefficient of equity premium shock
rho_z = 0.9 ; % AR coefficient of transitory techno-
logy shock
tau_ip_ss = 0.1; % check this value
tau_k_ss = 0.1; % check this value
tau_d_ss = 0.1; % check this value
% Labour market matching and wage bargaining
%
-------------------------------------------
sigma_n = 10; % Frish elasticity of labour
eta = 0.5; % SS bargaining power
b = 0.3; % unemployment benefit
tau_w_ss = 0.15; % SS worker's tax on earned income 0.30
tau_sc_ss = 0.12; % sotut/palkkasumma, keskiarvo v. 2010-2013.
SS employer's social contribution 0.23
tau_cp_ss = 0.11; % SS Consumption tax
omega_w = 0.3; %0.5 % Ad hoc wage rigidity parameter
sigma_M = 0.6; % Elasticity of mat-
ching w.r.t unemployment (exponent of Cobb-Douglas matching function
rho = 0.06; % SS job destruction
rate
qf_ss = 0.7; % Steady state vacancy
filling rate
u_ss = 0.1; % Steady state unem-
ployment, keskiarvo 1994-2010 = 10.2
n_ss = 1-u_ss; % Steady state emplo-
yment rate
match_ss = rho*n_ss; % Steady state matches are
equal to ss separations
v_ss = match_ss/qf_ss; % Steady state vacancies
theta_ss = v_ss/u_ss; % Labour market tightness;
vacancies per unemployed searching workers
eff_match = match_ss/((u_ss^sigma_M)*(v_ss^(1-sigma_M))); % Efficiency
of matching
qw_ss = match_ss/u_ss; % Steady state job finding
rate, 1994-2010 datan keskiarvo = 0.28
h_ss = 0.33; % SS hours worked per
person
preal_kl_ss = (5-1)/5; % =1/markup =>
implies a markup of 20 %
pyint_kl_ss = P.preal_kl_ss; % SS price of K-L
good, = preal_kl_ss. Equal to marginal cost of wholesale firm
mpk_ss = yint_roc_ss/pyint_kl_ss; % SS marginal producti-
vity of capital
k_ss = gamma_yint*(1/(n_ss*mpk_ss)); % SS capital-labour ratio in
the firm-level production function
K_ss = k_ss*n_ss; % SS aggregate capital
yint_z_ss = 1/((K_ss^(gamma_yint))*((n_ss*h_ss)^(1-gamma_yint))); %
Technology
yint_kl_ss=P.yint_z_ss*(k_ss)^(gamma_yint)*(h_ss)^(1-gamma_yint); %
SS output of K-L good
mpl_ss = yint_z_ss*(1-gamma_yint)*k_ss^(gamma_yint)*(h_ss)^(-gamma_yint);
% SS marginal productivity of labour
mrs_ss = ((1-tau_w_ss)/((1+tau_sc_ss)*(1+tau_cp_ss)))*preal_kl_ss*mpl_ss;
% SS marginal rate of substitution
w_ss = 1.5849;
kappa = 0.0976;
% The resulting Firm and Worker surpluses are
H_ss = (1/1-beta*(1-rho-qw_ss))*(w_ss*h_ss*(1-tau_w_ss)-
(mrs_ss*h_ss*(1+tau_cp_ss))/(1+sigma_n)-b); % SS worker surplus
J_ss = (1/(1-beta*(1-rho)))*(pyint_kl_ss*yint_kl_ss -
(1+tau_sc_ss)*w_ss*h_ss - yint_roc_ss*k_ss); % SS firm
surplus
R_rate = b/(w_ss*h_ss*(1-tau_w_ss));
% Fiscal policy rule parameters
tau_share = 0.5;
w_para = 1;
%% Closing the model
%------------------
ip_ss = 0.172; % Investment in SS
cg_ss = 0.28; % Government consumption
ig_ss = 0.04; % Government investment
yint_ss = yint_kl_ss*n_ss; % Aggregate SS production of intermediate
firm
cp_ss = yint_ss-ip_ss-cg_ss-kappa*v_ss ; % SS consumption
cp_lc_ss = 0.2*cp_ss; % SS consumption of liquidity constrained
households
cp_fl_ss = 0.8*cp_ss; % SS consumption of forward-looking hou-
seholds
D_ss = yint_kl_ss - ((1+tau_sc_ss)*n_ss*w_ss*h_ss) - (yint_roc_ss*K_ss) -
(kappa*v_ss);
ott_ss = (tau_cp_ss*cp_ss) + (tau_ip_ss*ip_ss) +
((tau_w_ss+tau_sc_ss)*n_ss*w_ss*h_ss) + (tau_k_ss*yint_roc_ss*K_ss) +
(tau_d_ss*D_ss) - cg_ss - (1-n_ss)*b - (1-i_ss)*BH_ss;
total_h_ss = n_ss*h_ss; % Total hours worked in SS
%%
% parameter values
rho_istar=0.95; % AR coefficient of foreign interest
rho_n_e=0.37; % AR of labour supply shock
rho_rhohat=0.75; % AR of job destruction shock
rho_kappahat=0.75; % AR of vacancy cost shock
rho_etahat=0.75; % AR of shock to workers' negotiation weight
% Wholesale firm
%---------------
rho_yint_phi=0.80; % AR-coeff. of markup shock
pyint_ksi= 0.75; % probability of taking the price as given (cal-
vo)
pyint_ss=5; % SS price of domestic intermediate input
% These needed to calculate ss prices
%-----------------------------------
f_pim_ss= 1 ; % foreign SS price level ($) for intermediate
import input market.
rhoe= 0.4; % ar coefficient in exchange rate shock
rho_f_pim=0.4 ; % ar coefficient in foreign price shock
rho_f_pex=0.4 ; % ar coefficient in foreign price shock
% importer price setting: investment good
%----------------------------------------
omegai= 0.15; %0.8 ; % share of LCP importing firms. (1-
omegai) is the share of pcp firms
gammai_lcp= 0.4; %0.5 ; % calvo parameter, share of LCP import
firms that are NOT allowed to change price at period t
gammai_pcp=0.5 ; % calvo parameter, share of PCP import firms
that are NOT allowed to change price at period t
%
% retailer of investment good
thetaip=0.22; % demand elasticity for domestic and foreign
intermediate investment good, previously 2.2
omegaip=0.67; % share of domestic intermediate investment
good in production of composite investment good
% Importer price setting: consumption good
%----------------------------------------
omegac=0.15; %0.8; %" share of LCP importing firms. (1-
omegac) is the share of pcp firms
gammac_lcp=0.4; %0.5; %" calvo parameter, share of LCP import
firms that are NOT allowed to change price at period t
gammac_pcp=0.5; %" calvo parameter, share of PCP import firms
that are NOT allowed to change price at period t
%Retailer of consumption good
thetacp=0.45; % demand elasticity for domestic and foreign
intermediate consumption good, previously 4.5
omegacp=0.65; % share of domestic intermediate consumtion
good in production of composite consumption good
% Exporter
%------------
gammax_pcp=0.65; %0.5; % calvo parameter, share of PCP firms
that are NOT allowed to change price at period t,
gammax_lcp=0.65; %0.5; % calvo parameter, share of LCP firms
that are NOT allowed to change price at period t
omegax=0.1; %0.5; % share of LCP firms in exports
thetax=0.5882; % price elasticity of demand for the export
product. Determined by rhox
x_ss=0.39; % SS of exports
rhoxd=0.7346; % ar-parameter of foreign market shock
rhostar=1;
thetaex=0.4545; % phi
deltaex=0.8; % delta
mex_ss=0.22; % SS imports used in export production
%
% Importer price setting: export good
%-----------------------------------
mcex_ss=1; % SS marginal cost of exports
pmex_ss=1; % aggregate steady state import price level for
goods used in export production(€)
omegaex=0.15; % share of LCP importing firms. (1-omegaex)
is the share of pcp firms
gammaex_lcp=0.4; % calvo parameter, share of LCP import firms
that are NOT allowed to change price at period t
gammaex_pcp=0.5; % calvo parameter, share of PCP import firms
that are NOT allowed to change price at period t
%
m_ss=0.39; % SS imports
mc_ss=0.09; % SS imported C goods share of total imports
mi_ss=0.08; % SS imported I goods share of total imports
%
rho_pmc_e=0.7; % ar coefficient in imported consumption good
price shock
rho_mcex_e=0.4; % ar coefficient in mc of exports shock
rho_pmi_e=0.7; % ar coefficient in imported investment good
price shock
rho_pmex_e=0.7; % ar coefficient in imported goods used in ex-
ports price shock
rho_mc_e=0.7; %
rho_mi_e=0.7; %
rho_mex_e=0.7; %
%
% Public sector
%--------------
rho_cg= 0.9; % AR of public spending shock
rho_ig= 0.9; % AR of public investment shock
rho_ott=0.9; % AR-coeff of transfers to households (ott_e)
shock
rho_tau_w=0.9;
rho_tau_cp=0.9;
rho_tau_k=0.9;
rho_tau_sc=0.9;
rho_tau_d=0.9;
rho_tau_ip=0.9;
rho_poil=0.6;
std_e_tau_w= 0.01;
std_e_tau_cp= 0.01;
std_e_tau_k= 0.01;
std_e_tau_sc= 0.01;
std_e_tau_d= 0.01;
std_e_tau_ip= 0.01;
std_e_ott= 0.01;
std_e_cg= 0.01;
|
Retrieved from "http://www.opasnet.org/testiwiki/index.php?title=Kooma&oldid=40535"
