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stata_to_tau_to_trade.m
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stata_to_tau_to_trade.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This code runs a gravity regression of the type in Eaton and Kortum (2002) or in Waugh (2010).
% The code calls stata to run a very simple regression using their
% powerfull tools to incoperate various fixed-effects. It then constructs
% trade costs and simmulates an equillibrium.
%
% A note on the organization of tradeshare matrix and tradecost matrix.
% This is always setup so that a row is an importer, and a column is an
% exporter.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear
close all
theta = 4; % Pick a \theta parameter.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This calls the stata program ``gravity_run.do''. Note this is callable on
% its own. But make sure to remove the final line ``exit'' in the code to
% see the output in stata. Note will have to change the directory to find
% stata on your computere.
dos('"C:\Program Files (x86)\Stata13\StataSE-64" do gravity_run.do')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This loads some data and the coeffecients from the regression in stata,
% i.e. the coeff.txt.
load('trade_grav_est_30.mat')
beta = load('coeff.txt', '-ascii')';
% Just some house keeping. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
N = (length(beta)-7)/2;
% This is the number of countries. Why? Stata writes the coeffecients with
% the base set to zero. So there are 2*N fixed effects. Then one can look
% and see that country 1's are all set to zero... So subtract off the parts
% for distance and border, divide by two and you have the number of
% countries
home_home = eye(N);
hh = (home_home(:)~=1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ssd_stata = -beta(N+1:end-7); % Note Stata Code has exporter first, the Ss come off the importer effects
asym_est = beta(1:N) - ssd_stata;
% Then the difference in exporter and importer effects is the assymetric
% component.
% Now convert this into trade cost levels
asym = exp(-(1./theta).*asym_est)-1; % The asymetric component...
dist = exp(-(1./theta).*beta(end-6:end-1,:))-1; % The distance effects
bord = exp(-(1./theta).*beta(end,:))-1; % The boarder effect
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Then what the next set of code does is that it arranging the assymetric component of the
% matrix with the diagonal part removed (which is set to one). This is
% where one can interpert the assymetric componentn differently....
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Option #1: Interpertation of the asymmetric component on the export side,
% this is as in Waugh (2010)....
asym=(asym(:,:)*ones(1,N));
asym = asym(hh);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Option #2: Interpertation of the asymmetric component on the import side,
% this is as in EK(2002)....
% asym= rot90((asym(:,:)*ones(1,N)),1);
% asym = asym(hh);
%
% ssd_stata = beta(1:N);
% % Then in this case the S's are identified off the exporter effects (why,
% % the importer effects are ``tainted'' with the asymetric component).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This is just to construct the distance matrix that is used to put
% together the trade frictions
mdist = .6213711*distance;
mdist_nz = mdist(hh);
for i = 1:length(distance(hh))
ddd = mdist_nz(i);
dmat_nz(i,:) = double([(ddd < 375) (375<=ddd & ddd<750) (750<=ddd& ddd<1500) (1500<=ddd& ddd<3000)...
(3000<=ddd& ddd<6000) (6000<=ddd)]);
end
border_nz = b(hh);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Now reconstruct the trade frictions, tau_stata
tau_stata = zeros(N^2,1);
dist_stata = zeros(N^2,1);
tau_stata(~hh) = 1;
dist_stata(~hh) = 1;
tau_stata(hh) = (1+dmat_nz*dist).*(1+border_nz.*bord).*(1+asym);
tau_stata = reshape(tau_stata,N,N);
% Just distance....
% dist_stata(hh) = (1+dmat_nz*dist).*(1+border_nz.*bord);
% dist_stata = reshape(dist_stata,N,N);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This then double checks that the trade pattern is exactly the same. Note
% that sim_trade_pattern_ek_mex, uses a simmulation approach to construct
% the pattern of trade.
[m_stata, ~] = sim_trade_pattern_ek(exp(ssd_stata),tau_stata,theta,1.5,1);
% This .mex file should run on (at least) Matlab 14a and later.
figure
plot(log(m_stata(:)),log(tradeshare(:)),'b*')
xlabel('Log Trade Shares from Model'); ylabel('Log Trade Shares from Data')