calibration
close all;
clear all;
% ************************************
% "THE ROLE OF MULTINATIONAL PRODUCTION IN A RISKY ENVIRONMENT"
% by NATALIA RAMONDO AND VERONICA RAPPOPORT
% THIS VERSION: DECEMBER 2009.
%
%
%
%
%
%
%
THIS CODE IS FOR THE REVISED VERSION OF THE PAPER FOR JIE.
THE MAIN CHANGE IS THAT WE INCORPORATE CONSUMPTION IN PERIOD 0 AND FIXED
COSTS ARE PAID IN UNITS OF THIS GOOD.
HENCE: the old variable for the price of the capital good is now the MU
of consumption at time zero pk = C(0)^-sigma
The resource constraints need to be adjusted accordingly in order to find
the initial endowment of consumption good in the world, Y0.
% ==============================
% PARAMETERS
sigma = 2;
% risk aversion from BKK
beta = 0.98;
% discount
eta
= 3;
% elasticity of substitution in CES from BrodaWeinstein
gamma = 4;
% pareto shape parameter from HMY
alpha = 0.5;
% labor share in manufacturing from AL
z_min = 1; % normalization in pareto distribution
% Other
a
=
phi_1 =
b
=
phi_3 =
phi_0 =
phi_2 =
useful parameters
1 + gamma
- eta;
eta + alpha - 1;
(1-alpha) / (eta-1);
(alpha^alpha) *((1-alpha)^(1-alpha))* (eta/phi_1) * ((eta-1)/eta)^(alpha);
(alpha^alpha) *((1-alpha)^(1-alpha))* ((eta-1)/eta)^(alpha);
(alpha^alpha) *((1-alpha)^(1-alpha))* ((eta-1)/eta)^(1-alpha);
% ==============================
% ==============================
% LOAD DATA
load size
% This file has the vector with equipped labor L_e (from K-RC, 05), avg. 90s, and
realGDPpc (from PWT, "RGDPL")
% Number of countries = 19
n = length(L_e);
% Variable indicating the index for U.S. (the last country, ordered alphabetically)
d_US = n;
% Rename the labor size variable
L
= L_e;
L
= L/L(d_US); % relative to US
L_w = sum(L);
% world size
% Variable needed due to the scale effect in the Pareto distribution:
% G_i(z) = L_i G(z) where G(z) = 1-z^-gamma
L_ij = repmat(L,1,n)./repmat(L,1,n)'; % this is L_i/L_j
L_Z = L;
% ==============================
% MP shares
load shares
% variable is sh_ij where the diagonal is zero: [0 sh_21 sh_31 .... sh_n1; sh_12 0
sh_32 ... sh_n2; ... ; sh_1n sh_2n ... 0]
Page 1
calibration
% Row is recipient country j
% Column is origin country i
sh_ii = 1 - sum(sh_ij,2);
% dometic share
sh_ij = diag(sh_ii) + sh_ij;
% fill in the diagonal
sh_ii_matrix = repmat(sh_ii,1,n);
% ==============================
load mom_rgdpl_7004
% Matrix of cross-country correlations (CORR) and vector with s.d. (STD_) of log of
RGDPL (H-P filtered, ciclycal component),
% the variable AVG_ is the average of log of RGDPL, no H-P filtered
% All variables are for the period 1970-2004
% This file is the output of the code rgdpl_filtering in the folder "rgdpl
% filtering"
% ==============================
% ==============================
% Calibrating the bilateral cut-offs from i to j, from observed MP shares
% and size.
z_ij = max(z_min*ones(n,n),(L_ij.*sh_ij./(sh_ii_matrix/z_min)).^(-1/a)); % z_ij_bar
Z_ij = gamma/a * repmat(L_Z,1,n)'.* z_ij.^(-a);
%
productivity index for firms from i in j, Z_ij
Z_j = sum(Z_ij,2) ;
% aggregate
productivity index in j, Z_j
clear shares
% ==============================
% Calibrating the process for the country shocks
% We assume log-Normal
% Mean for log A
r_GDPpc = CGDP;
r_GDPpc = r_GDPpc/r_GDPpc(d_US);
A_m = r_GDPpc.* (Z_j/Z_j(d_US)).^-b; % vector Ix1
% VAR-COV Matrix for log A = VAR-COV Matrix for log realGDPpc
D
= STD_; % STD = var^0.5; vector Ix1
SIGMA = (diag(D)*ones(n,n)).*(diag(D)*ones(n,n))'.*CORR; % corr_ij * sd_i * sd_j;
matrix IxI
S
= 500000; % number of draws
log_A
= mvg(log(A_m),SIGMA,S); % matrix IxS from a multivariate-normal
distribution
A = exp(log_A); % the shock in levels, matrix IxS
Pr = (1/S)*ones(S,1); % Recall that draws are already made from a CDF that was
log-normal. Hence, they already have the right frecuency.
% That is why we use a uniform probability across states
% Our measure of weight in the paper
weightBench = (L.*Z_j.^b)/sum(L.*Z_j.^b);
% World average shock as defined in the paper
A_w
= weightBench' * A; % a row vector 1XS
% Consumption risk premium for the calibrated model: u[E(C_i)(1-rho)] = E[u(C_i)]
rhoBench
= 1 - mean(A_w.^(1-sigma))^(1/(1-sigma))/mean(A_w);
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calibration
% Initialize matrices
corr_YYw
= zeros(n,1);
corr_YYw_a = zeros(n,1);
corr_YYw_c1 = zeros(n,1);
corr_YYw_c2 = zeros(n,1);
COR_A_A_w_s = zeros(n,1);
% ==============================
% % ==============================
% CALIBRATION OF THE FIXED COSTS
% FINAL OUTPUT BY COUNTRY AND STATE s
Y
= phi_3 * repmat(L,1,S) .* (repmat(Z_j,1,S).^b) .* A; % matrix of IxS
% WORLD OUPUT BY STATE
Y_w = sum(Y); % vector of 1xS
% Correlation between country output and world output
for i=1:n
aa = corrcoef(Y(i,:)',Y_w);
corr_YYw(i) = aa(1,2);
end
% Arrow-Debreu Prices
qs = beta * Y_w'.^(-sigma).*Pr; % vector of Sx1
Qs = qs/sum(qs);
% vector of Sx1
clear qs
% Expected Value of doing MP from i in j Prof_ij = sum_s q(s)*prof_ij(s) for a
% firm with productivity z_ij -the marginal firm
Prof_ij
= ((1-alpha)/eta)* (z_ij.^(eta-1) ./repmat(Z_j,1,n)) .* repmat(Y*Qs,1,n);
% matrix of IxI where j=row, i=column
clear Qs Y
% Here, we pin down MU of aggregate consumption at time 0:
% pk = C(0)^-sigma. The Normalization is f_{us,1} = 1. Hence, we take the
% expected profits for i=US and j=US (d_US is the index for the US)
pk = Prof_ij(1,d_US);
C0
= pk^(-1/sigma);
% USING ZPC: V_ij =
f_ij = Prof_ij/pk;
Prof_ij * C(0)^sigma =
Prof_ij/pk =f_ij
% Compute the number of multinationals from i to n using the Pareto
G_ij = 1 - (z_min./z_ij).^gamma;
Y_0
= sum(sum(repmat(L_Z,1,n)'.*(1- G_ij).*f_ij)) + C0;
% Correlation between country shocks A_i and A_w^-sigma
for i=1:n
CCC = corrcoef(A(i,:), A_w.^-sigma);
COR_A_A_w_s(i) = CCC(1,2);
end
clear A_w
% ================================
% COUNTERFACTUAL: ECONOMY WITH NO MP -only domestic firms but complete
% financial markets
% Productivity index under autarky
Z_j_a = (gamma/a) *L_Z* (z_min^-a);
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calibration
% Country final outpuf in each state s
Y_a
= phi_3 * repmat(L,1,S).* (repmat(Z_j_a,1,S).^b) .* A; % matrix of IxS
% World output in state s
Y_w_a
= sum(Y_a); % vector Sx1
% Correlation between country output and world output under no MP
for i=1:n
aa = corrcoef(Y_a(i,:)',Y_w_a);
corr_YYw_a(i) = aa(1,2);
end
% Total change in welfare between no MP and the calibrated world with MP
Welfare =(Y_0+beta*(Y_w_a.^(1-sigma)*Pr))/ (Y_0 + beta*(Y_w.^(1-sigma)*Pr));
clear Y_w_a Y_a
% Country weight varphi under no MP
weightAut = (L.*Z_j_a.^b)/sum(L.*Z_j_a.^b); % vector Ix1
A_w_a
= weightAut' * A; % vector Sx1 = (Ix1)' * (IxS)
% Consumption risk premium in a world with no MP
rhoAut = 1 - mean(A_w_a.^(1-sigma))^(1/(1-sigma))/mean(A_w_a);
clear A_w_a
% =========================================================================
% COUNTERFACTUAL: ECONOMY WITH frictionless MP FROM U.S. but NO MP FOR THE REST
% f_(US,j) == 0 and f_(i,j) --> Inf for all i~=US
% Productivity index under this counterfactual for each country except the
% US: Z_ij
Z_ij_c1
= diag(Z_j_a);
% Productivity index for the US abroad: Z_(US,j)
Z_ij_c1(:,d_US) = gamma/a * L_Z(d_US) * z_min^(-a);
% Aggregate productivity index Z_j
Z_j_c1
= sum(Z_ij_c1,2) ;
% Country Output in each s
Y
= phi_3 * repmat(L,1,S) .* (repmat(Z_j_c1,1,S).^b) .* A; % matrix of IxS
% World Otuput in each s
Y_w
= sum(Y); % vector 1xS
% Correlation of country and world output
for i=1:n
aa = corrcoef(Y(i,:)',Y_w);
corr_YYw_c1(i) = aa(1,2);
end
clear Y Y_w
% Country's weight varpi
weight
= (L.*Z_j_c1.^b)/sum(L.*Z_j_c1.^b);
A_w
= weight' * A; % a row vector 1XS
% Consumption risk premium
rho_f_US_out = 1 - mean(A_w.^(1-sigma))^(1/(1-sigma))/mean(A_w);
clear A_w
Page 4
calibration
% =========================================================================
% COUNTERFACTUAL: ECONOMY WITH frictionless MP INTO US but no MP FOR THE REST
% f_(i,US) and f_(i,j) for all i~=US, and j
% Productivity index Z_ij
Z_ij_c2
= diag(Z_j_a);
% Productivity index for US Z_(i,US) -the US is recipient
Z_ij_c2(d_US,:) = gamma/a * L_Z* z_min^(-a); % CAREFUL!! The US is recipient and
that is row=d_US=19
% Aggregate productivity index
Z_j_c2
= sum(Z_ij_c2,2) ; % Ix1
% Country output in state s
Y
= phi_3 * repmat(L,1,S) .* (repmat(Z_j_c2,1,S).^b) .* A; % matrix of IxS
% World output in state s
Y_w = sum(Y); % vector 1xS
% Correlation between country's output and world output
for i=1:n
aa = corrcoef(Y(i,:)',Y_w);
corr_YYw_c2(i) = aa(1,2);
end
clear Y Y_w
% Country's weight varpi
weight = (L.*Z_j_c2.^b)/sum(L.*Z_j_c2.^b);
A_w
= weight' * A; % vector 1XS
% Consumption risk premium
rho_f_US_in = 1 - mean(A_w.^(1-sigma))^(1/(1-sigma))/mean(A_w);
clear A_w
% =================================
% OUTPUT
% ENTRY
f_in
f_in
f_out
f_out
COSTS
= median(f_ij,2);
= f_in/f_in(d_US);
= median(f_ij)';
= f_out/f_out(d_US);
% TECHNOLOGY FLOWS OUTWARD, INWARD, NET
TECH_out = (sum(Z_ij,1)' - diag(Z_ij))./(sum(sum(Z_ij,1))' - sum(diag(Z_ij)));
TECH_in
= (sum(Z_ij,2) - diag(Z_ij))./(sum(sum(Z_ij,1))' - sum(diag(Z_ij)));
TECH_net = TECH_out - TECH_in;
% OUTPUT FOR TABLES IN THE MAIN BODY OF THE PAPER
BENCH
= [weightBench COR_A_A_w_s f_out f_in TECH_out*100 TECH_in*100
TECH_net*100];
results = [(rhoBench/rhoAut-1)*100 (rho_f_US_out/rhoAut-1)*100
(rho_f_US_in/rhoAut-1)*100];
COR_YYw = [corr_YYw corr_YYw_a corr_YYw_c1 corr_YYw_c2];
Page 5
decomposition_RiskEffect
close all;
clear all;
% ================================================
% % COUNTERFACTUAL: ECONOMY with EQUAL SIZE and CALIBRATED SHOCKS PROCESS
% ==============================
% PARAMETERS
sigma = 2;
% risk aversion from BKK
beta = 0.98;
% discount
eta
= 3;
% elasticity of substitution in CES from BrodaWeinstein
gamma = 4;
% pareto shape parameter from HMY
alpha = 0.5;
% labor share in manufacturing from AL
z_min = 1; % normalization in pareto distribution
% Other
a
=
phi_1 =
b
=
phi_3 =
phi_0 =
phi_2 =
useful parameters
1 + gamma
- eta;
eta + alpha - 1;
(1-alpha) / (eta-1);
(alpha^alpha) *((1-alpha)^(1-alpha))* (eta/phi_1) * ((eta-1)/eta)^(alpha);
(alpha^alpha) *((1-alpha)^(1-alpha))* ((eta-1)/eta)^(alpha);
(alpha^alpha) *((1-alpha)^(1-alpha))* ((eta-1)/eta)^(1-alpha);
% ==============================
% ==============================
% LOAD DATA
load size
% This file has the vector with equipped labor L_e (from K-RC, 05), avg. 90s, and
realGDPpc (from PWT, "RGDPL")
% Number of countries = 19
n = length(L_e);
% Variable indicating the index for U.S. (the last country, ordered alphabetically)
d_US = n;
% WE WANT COUNTRIES OF EQUAL SIZE
L_w = sum(L_e/L_e(d_US)); % world size
L = ones(n,1)*L_w/n;
% Variable needed due to the scale effect in the Pareto distribution:
% G_i(z) = L_i G(z) where G(z) = 1-z^-gamma
L_ij = repmat(L,1,n)./repmat(L,1,n)'; % this is L_i/L_j
L_Z = L;
% ==============================
% MP shares
load shares
% variable is sh_ij where the diagonal is zero: [0 sh_21 sh_31 .... sh_n1; sh_12 0
sh_32 ... sh_n2; ... ; sh_1n sh_2n ... 0]
% Row is recipient country j
% Column is origin country i
sh_ii = 1 - sum(sh_ij,2);
% dometic share
sh_ij = diag(sh_ii) + sh_ij;
% fill in the diagonal
sh_ii_matrix = repmat(sh_ii,1,n);
% ==============================
load mom_rgdpl_7004
Page 1
decomposition_RiskEffect
% Matrix of cross-country correlations (CORR) and vector with s.d. (STD_) of log of
RGDPL (H-P filtered, ciclycal component),
% the variable AVG_ is the average of log of RGDPL, no H-P filtered
% All variables are for the period 1970-2004
% This file is the output of the code rgdpl_filtering in the folder "rgdpl
% filtering"
% ==============================
% ==============================
% Calibrating the bilateral cut-offs from i to j, from observed MP shares
% and size.
z_ij = max(z_min*ones(n,n),(L_ij.*sh_ij./(sh_ii_matrix/z_min)).^(-1/a)); % z_ij_bar
Z_ij = gamma/a * repmat(L_Z,1,n)'.* z_ij.^(-a);
%
productivity index for firms from i in j, Z_ij
Z_j = sum(Z_ij,2) ;
% aggregate
productivity index in j, Z_j
clear shares
% ==============================
weight
= (L.*Z_j.^b)/sum(L.*Z_j.^b);
% ==============================
% Calibrating the process for the country shocks
% We assume log-Normal
% Mean for log A
r_GDPpc = CGDP;
r_GDPpc = r_GDPpc/r_GDPpc(d_US);
A_m = r_GDPpc.* (Z_j/Z_j(d_US)).^-b; % vector Ix1
% VAR-COV Matrix for log A = VAR-COV Matrix for log realGDPpc
D
= STD_; % STD = var^0.5; vector Ix1
SIGMA = (diag(D)*ones(n,n)).*(diag(D)*ones(n,n))'.*CORR; % corr_ij * sd_i * sd_j;
matrix IxI
S
= 500000; % number of draws
log_A
= mvg(log(A_m),SIGMA,S); % matrix IxS from a multivariate-normal
distribution
A = exp(log_A); % the shock in levels, matrix IxS
clear log_A
% ECONOMY
Z_j_a
weightAut
A_w
rho
rhoAut
WITH NO MP AND COUNTRIES WITH EQUAL SIZE
= (gamma/a) * (z_min^-a)*L_Z;
= (L.*Z_j_a.^((1-alpha)/(eta-1)))/sum(L.*Z_j_a.^((1-alpha)/(eta-1)));
= weightAut' * A; % a row vector 1XS
= 1 - mean((weight' * A).^(1-sigma))^(1/(1-sigma))/mean(weight' * A);
= 1 - mean(A_w.^(1-sigma))^(1/(1-sigma))/mean(A_w);
RiskEffect = (rho/rhoAut - 1)*100;
Page 2
decomposition_SizeEffect
close all;
clear all;
% =================================================================
% COUNTERFACTUAL: ECONOMY with IID SHOCKS but ASYMMETRIC SIZE
% ==============================
% PARAMETERS
sigma = 2;
% risk aversion from BKK
beta = 0.98;
% discount
eta
= 3;
% elasticity of substitution in CES from BrodaWeinstein
gamma = 4;
% pareto shape parameter from HMY
alpha = 0.5;
% labor share in manufacturing from AL
z_min = 1; % normalization in pareto distribution
% Other
a
=
phi_1 =
b
=
phi_3 =
phi_0 =
phi_2 =
useful parameters
1 + gamma
- eta;
eta + alpha - 1;
(1-alpha) / (eta-1);
(alpha^alpha) *((1-alpha)^(1-alpha))* (eta/phi_1) * ((eta-1)/eta)^(alpha);
(alpha^alpha) *((1-alpha)^(1-alpha))* ((eta-1)/eta)^(alpha);
(alpha^alpha) *((1-alpha)^(1-alpha))* ((eta-1)/eta)^(1-alpha);
% ==============================
% ==============================
% LOAD DATA
load size
% This file has the vector with equipped labor L_e (from K-RC, 05), avg. 90s, and
realGDPpc (from PWT, "RGDPL")
% Number of countries = 19
n = length(L_e);
% Variable indicating the index for U.S. (the last country, ordered alphabetically)
d_US = n;
% Rename the labor size variable
L
= L_e;
L
= L/L(d_US); % relative to US
L_w = sum(L);
% world size
% Variable needed due to the scale effect in the Pareto distribution:
% G_i(z) = L_i G(z) where G(z) = 1-z^-gamma
L_ij = repmat(L,1,n)./repmat(L,1,n)'; % this is L_i/L_j
L_Z = L;
% ==============================
% MP shares
load shares
% variable is sh_ij where the diagonal is zero: [0 sh_21 sh_31 .... sh_n1; sh_12 0
sh_32 ... sh_n2; ... ; sh_1n sh_2n ... 0]
% Row is recipient country j
% Column is origin country i
sh_ii = 1 - sum(sh_ij,2);
% dometic share
sh_ij = diag(sh_ii) + sh_ij;
% fill in the diagonal
sh_ii_matrix = repmat(sh_ii,1,n);
% ==============================
Page 1
decomposition_SizeEffect
load mom_rgdpl_7004
% Matrix of cross-country correlations (CORR) and vector with s.d. (STD_) of log of
RGDPL (H-P filtered, ciclycal component),
% the variable AVG_ is the average of log of RGDPL, no H-P filtered
% All variables are for the period 1970-2004
% This file is the output of the code rgdpl_filtering in the folder "rgdpl
% filtering"
% ==============================
% ==============================
% Calibrating the bilateral cut-offs from i to j, from observed MP shares
% and size.
z_ij = max(z_min*ones(n,n),(L_ij.*sh_ij./(sh_ii_matrix/z_min)).^(-1/a)); % z_ij_bar
Z_ij = gamma/a * repmat(L_Z,1,n)'.* z_ij.^(-a);
%
productivity index for firms from i in j, Z_ij
Z_j = sum(Z_ij,2) ;
% aggregate
productivity index in j, Z_j
clear shares
% ==============================
% Compute the weight of each country under this counterfactual --do not
% change with respect to benchmark
weight = (L.*Z_j.^b)/sum(L.*Z_j.^b);
% Mean for log A
r_GDPpc = CGDP;
r_GDPpc = r_GDPpc/r_GDPpc(d_US);
A_m = r_GDPpc.* (Z_j/Z_j(d_US)).^-b;
% We assume i.i.d shocks with the median observed SD and mean.
A_m = ones(n,1)*median(A_m);
D
= median(STD_)*ones(n,1);
SIGMA = diag(D.^2).*eye(n);
S
= 500000;
log_A = mvg(log(A_m),SIGMA,S);
A
= exp(log_A);
clear log_A
% ECONOMY WITH NO MP AND IID SHOCKS
Z_j_a = (gamma/a) * (z_min^-a)*L_Z;
weightAut = (L.*Z_j_a.^((1-alpha)/(eta-1)))/sum(L.*Z_j_a.^((1-alpha)/(eta-1)));
% Consumption
rho
= 1 % Consumption
rhoAut = 1 -
risk premium with i.i.d. shocks
mean((weight' * A).^(1-sigma))^(1/(1-sigma))/mean(weight' * A);
risk premium with i.i.d. shocks and no MP
mean((weightAut' * A).^(1-sigma))^(1/(1-sigma))/mean(weightAut' * A);
% Change in consumption risk premium
SizeEffect = (rho/rhoAut - 1)*100;
Page 2