sem_panel.m

面板数据模型的matlab程序（以香烟为例）

function results = sem_panel(y,x,W,T,info)
% PURPOSE: computes spatial error model estimates for spatial panels (N regions*T time periods)
%           y = XB + u,  u = p*W*u + e, using sparse algorithms
% Supply data sorted first by time and then by spatial units, so first region 1,
% region 2, et cetera, in the first year, then region 1, region 2, et
% cetera in the second year, and so on
% sem_panel computes y and x in deviation of the spatial and/or time means
% (see Baltagi, 2001, Econometric Analysis of Panel Data, ch. 2 and ch. 3)
% ---------------------------------------------------
%  USAGE: results = sem_panel(y,x,W,T,info)
%  where: y = dependent variable vector
%         x = independent variables matrix 
%         W = spatial weights matrix (standardized)
%         T = number of points in time
%       info = an (optional) structure variable with input options:
%       info.model = 0 pooled model without fixed effects (default, x may contain an intercept)
%                  = 1 spatial fixed effects (x may not contain an intercept)
%                  = 2 time period fixed effects (x may not contain an intercept)
%                  = 3 spatial and time period fixed effects (x may not contain an intercept)
%       info.rmin  = (optional) minimum value of rho to use in search  
%       info.rmax  = (optional) maximum value of rho to use in search    
%       info.convg = (optional) convergence criterion (default = 1e-4)
%       info.maxit = (optional) maximum # of iterations (default = 500)
%       info.lflag = 0 for full lndet computation (default = 1, fastest)
%                  = 1 for MC lndet approximation (fast for very large problems)
%                  = 2 for Spline lndet approximation (medium speed)
%       info.order = order to use with info.lflag = 1 option (default = 50)
%       info.iter  = iterations to use with info.lflag = 1 option (default = 30)     
%       info.lndet = a matrix returned by sar, sar_g, sarp_g, etc.
%                    containing log-determinant information to save time
% ---------------------------------------------------
%  RETURNS: a structure
%         results.meth  = 'sem' if infomodel=0
%                       = 'semsfe' if info.model=1
%                       = 'semtfe' if info.model=2
%                       = 'semstfe' if info.model=3
%         results.beta  = bhat
%         results.rho   = rho (p above)
%         results.tstat = asymp t-stats (last entry is rho=spatial autocorrelation coefficient)
%         results.yhat  = yhat
%         results.resid = residuals
%         results.sige  = sige = e'(I-p*W)'*(I-p*W)*e/nobs
%         results.rsqr  = rsquared
%         results.rbar  = rbarsquared
%         results.sfe   = spatial fixed effects (if info.model=1 or 3)
%         results.tfe   = time period fixed effects (if info.model=2 or 3)
%         results.con   = intercept (if info.model=3)
%         results.lik   = log likelihood
%         results.nobs  = # of observations
%         results.nvar  = # of explanatory variables in x
%         results.tnvar = nvar + # fixed effects
%         results.y     = y data vector
%         results.iter  = # of iterations taken
%         results.rmax  = 1/max eigenvalue of W (or rmax if input)
%         results.rmin  = 1/min eigenvalue of W (or rmin if input)
%         results.lflag = lflag from input
%         results.liter = info.iter option from input
%         results.order = info.order option from input
%         results.limit = matrix of [rho lower95,logdet approx, upper95] intervals
%                         for the case of lflag = 1
%         results.time1 = time for log determinant calcluation
%         results.time2 = time for eigenvalue calculation
%         results.time3 = time for hessian or information matrix calculation
%         results.time4 = time for optimization
%         results.time  = total time taken         
%         results.lndet = a matrix containing log-determinant information
%                          (for use in later function calls to save time)
%  --------------------------------------------------
%  NOTES: if you use lflag = 1 or 2, info.rmin will be set = -1 
%                                    info.rmax will be set = 1
%         For number of spatial units < 500 you should use lflag = 0 to get exact results
% ---------------------------------------------------
%
% written by: J.Paul Elhorst 11/2004
% University of Groningen
% Department of Economics
% 9700AV Groningen
% the Netherlands
% [e-mail]
%
% REFERENCES: 
% "Specification and Estimation of Spatial Panel Data Models",
% International Regional Science Review, Vol. 26, pp. 244-268.
% Formulas for information matrix are not in this paper, I derived them
% later

% This function is based on James. P LeSage's function SEM

time1 = 0; 
time2 = 0;
time3 = 0;

timet = clock; % start the clock for overall timing

% if we have no options, invoke defaults
if nargin == 4
    info.lflag = 1;
    info.model = 0;
    fprintf(1,'default: pooled model without fixed effects \n');
end;

fields = fieldnames(info);
nf = length(fields);
if nf > 0
    for i=1:nf
        if strcmp(fields{i},'model') model = info.model;
        end
    end
end
if model==0
    results.meth='sem';
elseif model==1
    results.meth='semsfe';
elseif model==2
    results.meth='semtfe';
elseif model==3
    results.meth='semstfe';
else
    error('sem_panel: wrong input number of info.model');
end

% check size of user inputs for comformability
[nobs nvar] = size(x);
[N Ncol] = size(W);
if N ~= Ncol
error('sem: wrong size weight matrix W');
elseif N ~= nobs/T
error('sem: wrong size weight matrix W or matrix x');
end;
[nchk junk] = size(y);
if nchk ~= nobs
error('sar: wrong size vector y or matrix x');
end;

% return the easy stuff
results.y = y;
results.nobs = nobs;
results.nvar = nvar; 

% parse input options
[rmin,rmax,convg,maxit,detval,ldetflag,eflag,order,miter,options] = sem_parse(info); %function of LeSage

% compute eigenvalues or limits
[rmin,rmax,time2] = sem_eigs(eflag,W,rmin,rmax,N); %function of LeSage

results.rmin = rmin;
results.rmax = rmax;
results.lflag = ldetflag;
results.miter = miter;
results.order = order;

% do log-det calculations
[detval,time1] = sem_lndet(ldetflag,W,rmin,rmax,detval,order,miter); % function of LeSage

% demeaning of the y and x variables, depending on (info.)model

if (model==1 | model==3);
meanny=zeros(N,1);
meannx=zeros(N,nvar);
for i=1:N
    ym=zeros(T,1);
    xm=zeros(T,nvar);
    for t=1:T
        ym(t)=y(i+(t-1)*N,1);
        xm(t,:)=x(i+(t-1)*N,:);
    end
    meanny(i)=mean(ym);
    meannx(i,:)=mean(xm);
end
clear ym xm;
end % if statement

if ( model==2 | model==3)
meanty=zeros(T,1);
meantx=zeros(T,nvar);
for i=1:T
    t1=1+(i-1)*N;t2=i*N;
    ym=y([t1:t2],1);
    xm=x([t1:t2],:);
    meanty(i)=mean(ym);
    meantx(i,:)=mean(xm);
end
clear ym xm;
end % if statement
    
en=ones(T,1);
et=ones(N,1);
ent=ones(nobs,1);

if model==1;
    ywith=y-kron(en,meanny);
    xwith=x-kron(en,meannx);
elseif model==2
    ywith=y-kron(et,meanty);
    xwith=x-kron(et,meantx);
elseif model==3
    ywith=y-kron(en,meanny)-kron(et,meanty)+kron(ent,mean(y));
    xwith=x-kron(en,meannx)-kron(et,meantx)+kron(ent,mean(x));
else
    ywith=y; 
    xwith=x;
end % if statement
    
t0 = clock;

for t=1:T
    t1=1+(t-1)*N;t2=t*N;
    Wx([t1:t2],:)= sparse(W)*xwith([t1:t2],:);
    Wy([t1:t2],1)= sparse(W)*ywith([t1:t2],1);
end

options = optimset('MaxIter',maxit);
rho = 0.5;
converge = 1;
criteria = 1e-4;
iter = 1;

while (converge > criteria) & (iter < maxit)

xs = xwith - rho*Wx;
ys = ywith - rho*Wy;
b = (xs'*xs)\(xs'*ys);
e = (ywith - xwith*b);
rold = rho;
[rho,like,exitflag,output] = fminbnd('f_sempanel',rmin,rmax,options,e,W,detval,T);
converge = abs(rold - rho);
iter = iter + 1;
end;


liktmp = like;
time4 = etime(clock,t0);

if exitflag == maxit
fprintf(1,'\n sem: convergence not obtained in %4d iterations \n',output.iterations);
end;
results.iter = output.iterations;

% compute results 
results.beta= b;
results.rho = rho;

if model==1
    results.sfe=meanny-meannx*results.beta; % including intercept