Matlab Code for Final Version

Matlab code for

Moeltner, K., J. S. Shonkwiler, (forthcoming). Correcting for Size Biased Sampling in Random Utility Models. American Journal of Agricultural Economics.

% Main Script

% Fresh Script for jet ski paper for all models after getting Danielle's expanded data set

% this version w/o 7 persons that had >40 trips total.

% load e:\workspace\klaus\lil_tahoe\mlab\worksp\freshto_mlab2.raw;% data=[freshto_mlab2(:,end) freshto_mlab2(:,1:end-1)]; % bring running id back to front% clear freshto_mlab2;% save e:\workspace\klaus\lil_tahoe\mlab\worksp\freshdata2 data;% 'done'% break

load e:\workspace\klaus\lil_tahoe\mlab\worksp\freshdata2;load e:\workspace\klaus\lil_tahoe\mlab\worksp\h_mat1000; % that h_mat can handle up to 5 RCs

% Contents of data:

%1 % id running visitor panel id%2 % site lake index%3 % sur_y survey year%4 % own 1 if own jet ski, 0 if rented%5 % jetonly 1 if jet skiing = sole reason for visit%6 % jetprim 1 if other activities as well, but jet ski=primary%7 % milecost per mile autocost in cents%8 % trips trips this year to the six lakes%9 % dist distance traveled, one way%10 % gender gender, some missing values ("999")%11 % age age, some missing values%12 % educ education level, some missing values%13 % income in dollars,(category midpoint)%14 % sur_site site of interview%15 % food 1 if site has food services%16 % elev lake elevation in feet%17 % size surface area in acres%18 % shore length of shoreline in miles%19 % cantrent 1 if visitor = renter, but lake has no rental%20 % ban 1 = owned jet ski banned at Tahoe%21 % autocost =per-mile cost in $%22 % timecost time cost based on income/(3*2080); for round trip%23 % tc autocost + timecost%24:29 %site intercepts

% scale & explicitly label some variablesfood=data(:,15);elev=data(:,16)./100;% elevation in 1000ft or 100ft (try both)surface=(data(:,17)./639.5)/10; % translation: units of 10 squ. milesshore=data(:,18)./10; % units of 10 miles

1

shape =(10*surface)./(10*shore); % square miles / miles

% declare data to be used here to free memory later during loop

id = max(data(:,1)); % total number of respondentsd = max(data(:,2)); % total number of lakesn = id*d; % total number of observations

y=data(:,8);s=data(:,14); % lake of intercept

% compute new TCdist=data(:,9);own=data(:,4);timecost=data(:,22);tc=2*dist.*(0.4*own+0.3*(1-own))+timecost;

% Open log file [fid]=fopen('e:\workspace\Klaus\lil_tahoe\mlab\logs\freshmix_correctprice_dmcorronly.txt','w');if fid==-1; warning('File could not be opened');else; disp('File opened successfully');end;

header.title='Jet ski models';header.date=date;header.name='Klaus Moeltner';fprintf(fid,'Title:\t%s \n',header.title);fprintf(fid,'Date:\t\t%s \n',header.date);fprintf(fid,'Author:\t%s \n',header.name);fprintf(fid,'*******************************************************\n\n');header.model ='Uncorrected MNL';fprintf(fid,'Model:\t%s \n',header.model);fprintf(fid,'\n');fprintf(fid,'*******************************************************\n\n');jet.obs=n;fprintf(fid,'Number of observations =\t%6.0f \n',jet.obs);fprintf(fid,'\n');

r=1000;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Simple MNL model %

load e:\workspace\klaus\lil_tahoe\mlab\worksp\freshmnlmix40;clear X y;

X =[tc ... % price data(:,19:20) ... % lake restrictions data(:,25) ... % site intercept

2

elev surface]; % lake features



cf = 4; number of fixed coefficientscr = 2; total number of random coefficients, correlated or notc=cf+cr;cr_cov = 0; number of correlated random coefficients - unchanged from first roundcr_nocov = cr-cr_cov;

jet.rep=r;fprintf(fid,'Number of Halton replications =\t%4.0f\n',jet.rep);fprintf(fid,'\n');

% Starting valuesstartmean= [-0.25 ... %price -3.7 -2 ... % lake restrictions -0.9 ... % site intercept -0.05 0.03]'; % lake features jet.beta_in = startmean;fprintf(fid,'Starting mean vector for coefficients =\n\n');fprintf(fid,'%6.2f\n',jet.beta_in);fprintf(fid,'\n');

% declare full VCOV matrix for random coeffcients, with upper left corner for uncorrleated ones

int1 =0.001*ones(cr_nocov,1);int2 = diag(int1); % submatrix for uncorrelated RC'sint3 = zeros(cr_nocov, cr_cov);int4 = [int2 int3]; % creates upper part of full VCOVint5 = zeros(cr_cov, cr_nocov);int6 = 0.001*ones(cr_cov,1);int7 = diag(int6)+0.01 ;% submatrix for correlated coefficientsint8 = [int5 int7];vcov_in = [int4; int8] ;%works fineclear int*;

int =(chol(vcov_in)); %upper triangularvcovsend = nonzeros(int); %yields cr_nocov + (cr_cov*(cr_cov+1))/2 column vector with all non-zero elements%of int. collected as if from a lower Chol, row by rowS=sparse(int); %stores position of nonzero elements of int - useful to reconstruct it in llf

% para_in=[startmean;vcovsend];para_in=x;% para_in=[x(1:c);x(c+2:end)]; % omit Donner for second series of models

3

% Actual Maximization routinex0 = para_in;options=optimset('LargeScale','off','display','iter','TolFun',0.001,'TolX',0.001,'GradObj','off',... 'Hessian','off','DerivativeCheck','off');

tic, [x,fval,exitflag,output,grad,hessian]=... fminunc('jetllf_mnlmix',x0,options,X,y,h_mat,id,d,r,cf,cr,cr_cov,S)...,time=toc;

jet.run_time=time/60;jet.options=options;jet.output=output;jet.fval=fval;jet.exitflag=exitflag;

fprintf(fid,'Optimization Options:\n\n');fprintf(fid,'Large scale algorithm:\t%s\n',jet.options.LargeScale);fprintf(fid,'User supplied gradient:\t%s\n',jet.options.GradObj);fprintf(fid,'User supplied hessian:\t%s\n',jet.options.Hessian);fprintf(fid,'Termination tolerance on function level:\t%6.5f\n',jet.options.TolFun);fprintf(fid,'Termination tolerance on parameters:\t%6.5f\n',jet.options.TolX);fprintf(fid,'\n');fprintf(fid,'Optimization Output:\n\n');fprintf(fid,'Iterations:\t\t\t\t\t\t\t%6.0f\n',jet.output.iterations);fprintf(fid,'Function evaluations:\t\t\t\t\t%6.0f\n',jet.output.funcCount);fprintf(fid,'Infinity norm of gradient at solution:\t\t%6.4f\n',jet.output.firstorderopt);fprintf(fid,'Value of objective function at solution:\t\t%6.4f\n',jet.fval);fprintf(fid,'Algorithm:\t\t\t\t\t\t\t%s\n',jet.output.algorithm);fprintf(fid,'Exit condition (">0" = convergence):\t\t%1.0f\n',jet.exitflag);fprintf(fid,'\n');

% Conventional Hessian

H1=inv(hessian);d1 = diag(H1);jet.hess = H1; %capture, but don't print

results = x;se = sqrt(d1);t_val = results./se;

outmat=[x se t_val]ll=length(x);count=[1:100];jet.out = [count(1:ll);results';se';t_val'];

fprintf(fid,'Output table for jetmodel - simple MNL: \n\n');fprintf(fid,'Label\tCoeff.\ts.e.\t\tt-value\n\n');fprintf(fid,'% 2.0f\t%6.3f\t%6.3f\t%6.3f\n',jet.out);fprintf(fid,'\n');

fprintf(fid,'Elapsed time (in minutes):\t%6.2f\n',jet.run_time);fprintf(fid,'\n');

4

% White-corrected se's

L = L_mnlmix(x,X,y,h_mat,id,d,r,cf,cr,cr_cov,S); % save for later (Vuong test etc.)G = numgrad('L_mnlmix',x,X,y,h_mat,id,d,r,cf,cr,cr_cov,S);

int1=H1*G'*G*H1; % H already invertedint2=diag(int1);se=sqrt(int2);

jet.out2 = [1:length(x); x'; se'; (x./se)'];

fprintf(fid,'White-corrected output for jetmodel - simple MNL: \n\n');fprintf(fid,'Label\tCoeff.\ts.e.\t\tt-value\n\n');fprintf(fid,'% 2.0f\t%6.3f\t%6.3f\t%6.3f\n',jet.out2);fprintf(fid,'\n');

save e:\workspace\klaus\lil_tahoe\mlab\worksp\freshmnlmix40_1000 x X y jet L G H1;clear x jet L G H1;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Corrected MNL model

load e:\workspace\klaus\lil_tahoe\mlab\worksp\freshmnlcorrmix40;clear X y;

X =[tc ... % price data(:,19:20) ... % lake restrictions data(:,25) ... % site intercept elev surface]; % lake features



header.model ='Corrected MNL';fprintf(fid,'Model:\t%s \n',header.model);fprintf(fid,'\n');fprintf(fid,'*******************************************************\n\n');

% Starting values

jet.beta_in = startmean;fprintf(fid,'Starting mean vector for coefficients =\n\n');fprintf(fid,'%6.2f\n',jet.beta_in);fprintf(fid,'\n');


5



% para_in=[startmean;vcovsend];para_in=x;% para_in=[x(1:c);x(c+2:end)]; % omit Donner for second series of models


tic, [x,fval,exitflag,output,grad,hessian]=... fminunc('jetllf_mnlcorrmix',x0,options,X,y,h_mat,s,id,d,r,cf,cr,cr_cov,S)...,time=toc;




H1=inv(hessian);

6

d1 = diag(H1);jet.hess = H1; %capture, but don't print



fprintf(fid,'Output table for jetmodel - corrected MNL: \n\n');fprintf(fid,'Label\tCoeff.\ts.e.\t\tt-value\n\n');fprintf(fid,'% 2.0f\t%6.3f\t%6.3f\t%6.3f\n',jet.out);fprintf(fid,'\n');



L = L_mnlcorrmix(x,X,y,h_mat,s,id,d,r,cf,cr,cr_cov,S); % save for later (Vuong test etc.)G = numgrad('L_mnlcorrmix',x,X,y,h_mat,s,id,d,r,cf,cr,cr_cov,S);



fprintf(fid,'White-corrected output for jetmodel: \n\n');fprintf(fid,'Label\tCoeff.\ts.e.\t\tt-value\n\n');fprintf(fid,'% 2.0f\t%6.3f\t%6.3f\t%6.3f\n',jet.out2);fprintf(fid,'\n');

save e:\workspace\klaus\lil_tahoe\mlab\worksp\freshmnlcorrmix40_1000 x X y jet L G H1;clear x jet L G H1;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Uncorrected DM model

load e:\workspace\klaus\lil_tahoe\mlab\worksp\freshdmmix40;clear X y;



7


header.model ='Uncorrected DM';fprintf(fid,'Model:\t%s \n',header.model);fprintf(fid,'\n');fprintf(fid,'*******************************************************\n\n');

% Starting valuesstartmean= [.8 -.2 -4 -1.4 -0.8 -0.05 -.05]'; % add starting value for sqrt(alpha)





% para_in=[startmean;vcovsend];para_in=[startmean;0.13; 0.1];% para_in=[x(1:c);x(c+2:end)]; % omit Donner for second series of models


tic, [x,fval,exitflag,output,grad,hessian]=... fminunc('jetllf_dmmixfresh',x0,options,X,y,h_mat,id,d,r,cf,cr,cr_cov,S)...,time=toc;

jet.run_time=time/60;jet.options=options;jet.output=output;

8

jet.fval=fval;jet.exitflag=exitflag;









L = L_dmmix(x,X,y,h_mat,id,d,r,cf,cr,cr_cov,S); % save for later (Vuong test etc.)G = numgrad('L_dmmix',x,X,y,h_mat,id,d,r,cf,cr,cr_cov,S);



fprintf(fid,'White-corrected output for jetmodel: \n\n');fprintf(fid,'Label\tCoeff.\ts.e.\t\tt-value\n\n');fprintf(fid,'% 2.0f\t%6.3f\t%6.3f\t%6.3f\n',jet.out2);

9

fprintf(fid,'\n');

save e:\workspace\klaus\lil_tahoe\mlab\worksp\freshdmmix40_1000 x X y jet L G H1;clear x jet L G H1;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Corrected DM model

load e:\workspace\klaus\lil_tahoe\mlab\worksp\freshdmcorrmix40;clear X y;




header.model ='Corrected DM';fprintf(fid,'Model:\t%s \n',header.model);fprintf(fid,'\n');fprintf(fid,'*******************************************************\n\n');


% para_in=[startmean;vcovsend]; % use same stuff from previous modelpara_in=[1 -0.1 -2 -2 -0.7 -0.04 0.03 0.1 0.1]';% para_in=[x(1:c);x(c+2:end)]; % omit Donner for second series of models


tic, [x,fval,exitflag,output,grad,hessian]=... fminunc('jetllf_dmcorrmixfresh',x0,options,X,y,h_mat,s,id,d,r,cf,cr,cr_cov,S)...,time=toc;


fprintf(fid,'Optimization Options:\n\n');fprintf(fid,'Large scale algorithm:\t%s\n',jet.options.LargeScale);

10

fprintf(fid,'User supplied gradient:\t%s\n',jet.options.GradObj);fprintf(fid,'User supplied hessian:\t%s\n',jet.options.Hessian);fprintf(fid,'Termination tolerance on function level:\t%6.5f\n',jet.options.TolFun);fprintf(fid,'Termination tolerance on parameters:\t%6.5f\n',jet.options.TolX);fprintf(fid,'\n');fprintf(fid,'Optimization Output:\n\n');fprintf(fid,'Iterations:\t\t\t\t\t\t\t%6.0f\n',jet.output.iterations);fprintf(fid,'Function evaluations:\t\t\t\t\t%6.0f\n',jet.output.funcCount);fprintf(fid,'Infinity norm of gradient at solution:\t\t%6.4f\n',jet.output.firstorderopt);fprintf(fid,'Value of objective function at solution:\t\t%6.4f\n',jet.fval);fprintf(fid,'Algorithm:\t\t\t\t\t\t\t%s\n',jet.output.algorithm);fprintf(fid,'Exit condition (">0" = convergence):\t\t%1.0f\n',jet.exitflag);fprintf(fid,'\n');








L = L_dmcorrmix(x,X,y,h_mat,s,id,d,r,cf,cr,cr_cov,S); % save for later (Vuong test etc.)G = numgrad('L_dmcorrmix',x,X,y,h_mat,s,id,d,r,cf,cr,cr_cov,S);



fprintf(fid,'White-corrected output: \n\n');fprintf(fid,'Label\tCoeff.\ts.e.\t\tt-value\n\n');fprintf(fid,'% 2.0f\t%6.3f\t%6.3f\t%6.3f\n',jet.out2);fprintf(fid,'\n');

save e:\workspace\klaus\lil_tahoe\mlab\worksp\freshdmcorrmix40_1000 x X y jet L G H1;clear x jet L G H1;

11

st=fclose(fid);

if st==0; disp('File closed successfully');else; warning('Problem with closing file');end;

12

% Log-Likelihood Functions for all 4 Models

function [LL_all] = jetllf_mnlmix(x,X,y,h_mat,id,d,r,cf,cr,cr_cov,S)

% the incoming order of parameters in x is:

% fixed coefficients (alpha=first)% uncorrelated RCs% correlated RCs% Cholesky terms for RCs

% note: The shuffled Halton matrix is arranged in r stacked blocks of id by cr% columns; so the first id rows represent the consecutive list of id% individuals and their associated set of coefficients

n = id*d; % total number of observationsc = cf+cr; % total number of coefficientscr_nocov = cr-cr_cov; % number of uncorrelated random coefficients

b = x(1:c);% vector of coefficient means, including fixed coefficientsb_f = x(1:cf);% subvector of fixed coefficientsb_r = x(cf+1:cf+cr);% subvector of random coefficients

%re-construct chol(vcov_in) based on elements of x

A = zeros(cr,cr);int = full(S);%recreates upper cholesky matrixi=find(int>0 | int<0);A(i) = x(c+1:end); % re-creates upper cholesky in relation to xdel_sub = A'; %get lower choleskyclear int A;

h_mat = h_mat(:,1:cr);% h_mat is now (id x r) by crp_vec=zeros(id,1);

j=1;k=1;

for j=1:r

% draw betas for given rn_mat = (h_mat(k:j*id,1:cr))'; % cr by idint = repmat(b_r,1,id); % blow up random coeff vector to matrix with same dim. as n_matbr_mat = (int + del_sub*n_mat)';%id by crclear int;z=ones(d,1); br_mat=kron(br_mat,z);int = repmat(b_f',n,1);b_mat =[int br_mat];% n by cclear int br_mat;

% compute choice probabilities for given rp1 = exp(sum(X.*b_mat,2)); % exp(XB) with constant-w/in-individuals beta sets; size n by 1

13

f=find(isinf(p1)); p1(f)=1.0e+10;f=find(p1==0);p1(f)=1.0e-10;int = reshape(p1,d,id); int = sum(int); int = repmat(int,d,1); % blow up to d by t*idp2 = reshape(int,n,1); % stacks everything to be compatible with p1;p = p1./p2; % n by 1 vector of choice probabilities for each person, (day), and sitef=find(isinf(p)); p(f)=1.0e+10;f=find(p==0);p(f)=1.0e-10;clear p1 p2 int;

% Compute LLH component simultaneously for all individuals for given r

int1=reshape(y,d,id)'; %id by d like Scott'sint2=reshape(p,d,id)'; %id by d like Scott's

Y=sum(int1,2); % total number of trips per person, id by 1

p_add = exp(gammaln(Y+1)+sum(int1.*log(int2),2)-sum(gammaln(int1+1),2));

p_vec=p_vec+p_add;% f=find(isinf(p_vec)); % p_vec(f)=1.0e+10; % if length(f)>0% error('p_vec violation');% end

j=j+1;k=k+id; % move on to next set of betas

end

p_agg = p_vec/r; % get average of simulated probabilities for each person; id by 1f = find(p_agg==0);p_agg(f)=1.0e-10;% if length(f)>0% error('p_agg violation')% end

LL_all = -sum(log(p_agg));

function [LL_all] = jetllf_mnlcorrmix(x,X,y,h_mat,s,id,d,r,cf,cr,cr_cov,S)

% the incoming order of parameters in x is:

% fixed coefficients (alpha=first)

14

% uncorrelated RCs% correlated RCs% Cholesky terms for RCs

% note: The shuffled Halton matrix is arranged in r stacked blocks of id by cr% columns; so the first id rows represent the consecutive list of id% individuals and their associated set of coefficients

n = id*d; % total number of observationsc = cf+cr; % total number of coefficientscr_nocov = cr-cr_cov; % number of uncorrelated random coefficients

b = x(1:c);% vector of coefficient means, including fixed coefficientsb_f = x(1:cf);% subvector of fixed coefficientsb_r = x(cf+1:cf+cr);% subvector of random coefficients



h_mat = h_mat(:,1:cr);% h_mat is now (id x r) by crp_vec=zeros(id,1);

j=1;k=1;

for j=1:r

% draw betas for given rn_mat = (h_mat(k:j*id,1:cr))'; % cr by idint = repmat(b_r,1,id); % blow up random coeff vector to matrix with same dim. as n_matbr_mat = (int + del_sub*n_mat)';%id by crclear int;z=ones(d,1); br_mat=kron(br_mat,z);int = repmat(b_f',n,1);b_mat =[int br_mat];% n by cclear int br_mat;

% compute choice probabilities for given rp1 = exp(sum(X.*b_mat,2)); % exp(XB) with constant-w/in-individuals beta sets; size n by 1f=find(isinf(p1)); p1(f)=1.0e+10;f=find(p1==0);p1(f)=1.0e-10;int = reshape(p1,d,id); int = sum(int); int = repmat(int,d,1); % blow up to d by t*idp2 = reshape(int,n,1); % stacks everything to be compatible with p1;p = p1./p2; % n by 1 vector of choice probabilities for each person, (day), and site

15

f=find(isinf(p)); p(f)=1.0e+10;f=find(p==0);p(f)=1.0e-10;clear p1 p2 int;


int1=reshape(y,d,id)'; %id by d like Scott'sint2=reshape(p,d,id)'; %id by d like Scott'sint3=reshape(s,d,id)'; % site of interview indicator


p_add=exp(gammaln(Y+1)+sum(int1.*log(int2),2)-sum(gammaln(int1+1),2)+ log(sum(int1.*int3,2))... -log(sum(int2.*int3,2))-log(Y));

p_vec=p_vec+p_add;% f=find(isinf(p_vec)); % p_vec(f)=1.0e+10; % if length(f)>0% error('p_vec violation');% end

j=j+1;k=k+id; % move on to next set of betas

end



function [LL_all] = jetllf_dmmixfresh(x,X,y,h_mat,id,d,r,cf,cr,cr_cov,S)

% this is with fixed alpha, in contrast to jetllf_dm_mix% the incoming order of parameters in x is:

% fixed coefficients, not counting alpha% uncorrelated RCs, not counting alpha% correlated RCs, not counting alpha% mean of log(alpha)% Cholesky terms for RCs, not counting alpha

16

% standard deviation for log(alpha)

% note: The shuffled Halton matrix is arranged in r stacked blocks of id by cr+1% columns; so the first id rows represent the consecutive list of id% individuals and their associated set of coefficients

n = id*d; % total number of observationsc = cf+cr; % total number of coefficients, excluding alphacr_nocov = cr-cr_cov; % number of uncorrelated random coefficients

b = x(2:c+1);% vector of coefficient means, including fixed coefficientsb_f = x(2:cf+1);% subvector of fixed coefficientsb_r = x(cf+2:cf+1+cr);% subvector of random coefficients

a=1/(x(1)^2);



h_mat = h_mat(:,1:cr);p_vec=zeros(id,1);

j=1;k=1;

for j=1:r

% draw betas for given rn_mat = (h_mat(k:j*id,1:cr))'; % cr by idint = repmat(b_r,1,id); % blow up random coeff vector to matrix with same dim. as n_matbr_mat = (int + del_sub*n_mat)';%id by crclear int;z=ones(d,1); %6 by 1br_mat=kron(br_mat,z);int = repmat(b_f',n,1);b_mat =[int br_mat];% n by cclear int br_mat;

% compute choice probabilities for given rp1 = exp(sum(X.*b_mat,2)); % exp(XB) with constant-w/in-individuals beta sets; size n by 1f=find(isinf(p1)); p1(f)=1.0e+10;f=find(p1==0);p1(f)=1.0e-10;int = reshape(p1,d,id); int = sum(int); int = repmat(int,d,1); % blow up to d by t*id

17

p2 = reshape(int,n,1); % stacks everything to be compatible with p1;p = p1./p2; % n by 1 vector of choice probabilities for each person, (day), and siteclear p1 p2 int;


int1=reshape(y,d,id)'; %id by d like Scott'sint2=reshape(p,d,id)'; %id by d like Scott's


p_add = exp(gammaln(Y+1)+gammaln(a)-gammaln(Y+a)+sum(gammaln(int1+a*int2),2)... -sum(gammaln(int1+1),2)-sum(gammaln(a*int2),2));

p_vec=p_vec+p_add;f=find(isinf(p_vec)); p_vec(f)=1.0e+10; % if length(f)>0% error('p_vec violation');% end

j=j+1;k=k+id; % move on to next person

end



function [LL_all] = jetllf_dmcorrmixfresh(x,X,y,h_mat,s,id,d,r,cf,cr,cr_cov,S)

% fixed alpha in contrst to original function% the incoming order of parameters in x is:

% fixed coefficients, not counting alpha% uncorrelated RCs, not counting alpha% correlated RCs, not counting alpha% mean of log(alpha)% Cholesky terms for RCs, not counting alpha% standard deviation for log(alpha)

% note: The shuffled Halton matrix is arranged in r stacked blocks of id by cr+1% columns; so the first id rows represent the consecutive list of id% individuals and their associated set of coefficients

18

n = id*d; % total number of observationsc = cf+cr; % total number of coefficients, excluding alphacr_nocov = cr-cr_cov; % number of uncorrelated random coefficients

b = x(2:c+1);% vector of coefficient means, including fixed coefficientsb_f = x(2:cf+1);% subvector of fixed coefficientsb_r = x(cf+2:cf+1+cr);% subvector of random coefficients

a=1/(x(1)^2);



h_mat = h_mat(:,1:cr);p_vec=zeros(id,1);

j=1;k=1;

for j=1:r

% draw betas for given rn_mat = (h_mat(k:j*id,1:cr))'; % cr by idint = repmat(b_r,1,id); % blow up random coeff vector to matrix with same dim. as n_matbr_mat = (int + del_sub*n_mat)';%id by crclear int;z=ones(d,1); %6 by 1br_mat=kron(br_mat,z);int = repmat(b_f',n,1);b_mat =[int br_mat];% n by cclear int br_mat;

% compute choice probabilities for given rp1 = exp(sum(X.*b_mat,2)); % exp(XB) with constant-w/in-individuals beta sets; size n by 1f=find(isinf(p1)); p1(f)=1.0e+10;f=find(p1==0);p1(f)=1.0e-10;int = reshape(p1,d,id); int = sum(int); int = repmat(int,d,1); % blow up to d by t*idp2 = reshape(int,n,1); % stacks everything to be compatible with p1;p = p1./p2; % n by 1 vector of choice probabilities for each person, (day), and siteclear p1 p2 int;f=find(isinf(p)); p(f)=1.0e+10;f=find(p==0);

19

p(f)=1.0e-10;clear p1 p2 int;


int1=reshape(y,d,id)'; %id by d like Scott'sint2=reshape(p,d,id)'; %id by d like Scott'sint3=reshape(s,d,id)'; % site of interview indicator


p_add=exp(gammaln(Y+1)+gammaln(a)-gammaln(Y+a)+sum(gammaln(int1+a*int2),2)... -sum(gammaln(int1+1),2)-sum(gammaln(a*int2),2)+log(sum(int1.*int3,2))... -log(sum(int2.*int3,2))-log(Y));

f=find(isinf(p_add)); p_add(f)=1.0e+10;f=find(p_add==0);p_add(f)=1.0e-10;

p_vec=p_vec+p_add;f=find(isinf(p_vec)); p_vec(f)=1.0e+10; % if length(f)>0% error('p_vec violation');% end

j=j+1;k=k+id; % move on to next set of id elements of h_mat

end



(note: the L_- functions in the main script are identical to the likelihood functions, except for the last line, which reads

LL =(log(p_agg));

So the LLHF returns the negative sum of individual LLH elements (since "fminunc" mimimizes functions). The L-function returns the entire n by 1 vector of individual LLH elements

20

% Numerical gradient

function[G] = numgrad(FUN,x0,varargin);

% PURPOSE: computes numerical Jacobian matrix%% INPUTS:

% FUN = Handle or name for function that generates a n x 1 vector of % individual LLH components% Note: That function is specific to a given application & should be % generated & saved w/in that application% x0 = k x 1 vector of betas% varargin = all inputs needed for evaluating FUN, other than x0 % % % OUTPUT: G = n x k numerical Jacobian%% Written by:% Klaus Moeltner% Department of Applied Economics & Statistics% University of Nevada, Reno% based on GAUSS' "gradp" command

L0 = feval(FUN,x0,varargin{:}); % n by 1n=length(L0);k = length(x0);

G=zeros(n,k);

% Compute step size (amount of perturbation of x0)

ax0 = abs(x0);dax0 = x0./ax0;dh=(1e-8)*max([ax0 1e-2*ones(k,1)]')'.*dax0; % k x 1xdh = x0+dh;dh = xdh-x0; % apparently increases precision

int1 = diag(dh); % k by k square matrix with xdh on diagonalint2 = repmat(x0,1,k); % k by karg = int2+int1;

i=1;for i=1:k; G(:,i)=feval(FUN,arg(:,i),varargin{:});end

int1=repmat(L0,1,k); % n by kint2=repmat(dh',n,1);G = (G-int1)./int2;

21

% Halton Draws

function[h]=halton(n,q);

% creates a halton sequence a la Feenberg and Skinner% n= length of sequence% q=prime number

phi=zeros(n+11,1);i=1;

while i<n+11; i=i+1; y=1/q; x=1-phi(i-1); while x<=(y+1.e-11) y=y/q; end phi(i)=phi(i-1)+(q+1)*y-1;end

h=phi(12:n+11);

clear i y x phi

% Shuffling of Haltons

function[M]=shuffle(h_mat,n,r,cr)

% Program to reshuffle basic matrix of norminv(Halton) a la Train% for simple cross-sectional setup

% Inputs: h_mat = (n * r) by cr matrix of norminv(Halton)% n = number of individuals% r = number of reps% cr = number of random coefficients

% Output: a matrix M of exact same dimensions (n*r,cr), but reshuffled such that% first individual gets first row of obs for each vector of repetitions, second indiv gets second% row etc.

M = zeros(n,r*cr);

i=1;k=1;for i=1:n;int = h_mat(k:i*r,:); %first r rows of h_matint = reshape(int,1,r*cr);% same as stacking all columns and flipping them into one long rowM(i,:)=int;k=k+r;i=i+1;

22

end

M = reshape(M,n*r,cr);

% works fine - tested it!!% example original matrix; n=4,r=3,cr=3(number of columns)% 1 101 201% 2 102 202% 3 103 203% 4 104 204% 5 105 205% 6 106 206% 7 107 207% 8 108 208% 9 109 209% 10 110 210% 11 111 211% 12 112 212 % after shuffling% 1 101 201% 4 104 204% 7 107 207% 10 110 210% 2 102 202% 5 105 205% 8 108 208% 11 111 211% 3 103 203% 6 106 206% 9 109 209% 12 112 212

23

% Post-Estimation Script

% this script is for Scott's suggested strategy to examine the asymptotic% properties of the differences of means

% Open log file [fid]=fopen('e:\workspace\klaus\lil_tahoe\mlab\logs\welfare_take3.txt','w');if fid==-1; warning('File could not be opened');else; disp('File opened successfully');end;

load e:\workspace\klaus\lil_tahoe\mlab\worksp\freshdata2;


y=data(:,8);s=data(:,14); % lake of interceptsite=data(:,2);

clear data;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% sample counts per site%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

f=find(s==1);g=find(s==0);

f1=find(site==1);f2=find(site==2);f3=find(site==3);f4=find(site==4);f5=find(site==5);f6=find(site==6);

sitef=site(f);f1f=find(sitef==1);f2f=find(sitef==2);f3f=find(sitef==3);f4f=find(sitef==4);f5f=find(sitef==5);f6f=find(sitef==6);

siteg = site(g);f1g = find(siteg==1);f2g = find(siteg==2);f3g = find(siteg==3);f4g = find(siteg==4);f5g = find(siteg==5);f6g = find(siteg==6);

24

load e:\workspace\klaus\lil_tahoe\mlab\worksp\postest5;

trip51 = trip1;trip52 = trip2;trip53 = trip3;trip54 = trip4;trip55 = trip5;trip56 = trip6;

pt51 = pt1;pt52 = pt2;pt53 = pt3;pt54 = pt4;pt55 = pt5;pt56 = pt6;

clear trip1 trip2 trip3 trip4 trip5 trip6 pt1 pt2 pt3 pt4 pt5 pt6;








25






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% trips%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

E=cov([trip51 trip61 trip71 trip81]);M=mean([trip51 trip61 trip71 trip81]);x5=M(1);x6=M(2);x7=M(3);x8=M(4);v5=E(1,1);v6=E(2,2);v7=E(3,3);v8=E(4,4);cov58=E(1,end);cov68=E(2,end);cov78=E(3,end);d58=x5-x8;d68=x6-x8;d78=x7-x8;s58=sqrt((v5+v8-2*cov58)/id);s68=sqrt((v6+v8-2*cov68)/id);s78=sqrt((v7+v8-2*cov78)/id);D1=[d58 s58 d68 s68 d78 s78];

E=cov([trip52 trip62 trip72 trip82]);M=mean([trip52 trip62 trip72 trip82]);x5=M(1);x6=M(2);x7=M(3);x8=M(4);v5=E(1,1);v6=E(2,2);v7=E(3,3);v8=E(4,4);cov58=E(1,end);

26

cov68=E(2,end);cov78=E(3,end);d58=x5-x8;d68=x6-x8;d78=x7-x8;s58=sqrt((v5+v8-2*cov58)/id);s68=sqrt((v6+v8-2*cov68)/id);s78=sqrt((v7+v8-2*cov78)/id);D2=[d58 s58 d68 s68 d78 s78];



E=cov([trip55 trip65 trip75 trip85]);M=mean([trip55 trip65 trip75 trip85]);x5=M(1);x6=M(2);x7=M(3);

27

x8=M(4);v5=E(1,1);v6=E(2,2);v7=E(3,3);v8=E(4,4);cov58=E(1,end);cov68=E(2,end);cov78=E(3,end);d58=x5-x8;d68=x6-x8;d78=x7-x8;s58=sqrt((v5+v8-2*cov58)/id);s68=sqrt((v6+v8-2*cov68)/id);s78=sqrt((v7+v8-2*cov78)/id);D5=[d58 s58 d68 s68 d78 s78];


Dtrips=[D1;D2;D3;D4;D5;D6];Dtrips=[(1:1:6); Dtrips']

fprintf(fid,'trip differences: \n\n');fprintf(fid,'site\td58\t\ts58\t\td68\t\ts68\t\td78\t\ts78\n\n');fprintf(fid,'% 2.0f\t%6.3f\t%6.3f\t%6.3f\t%6.3f\t%6.3f\t%6.3f\n',Dtrips);fprintf(fid,'\n');fprintf(fid,'\n');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% welfare%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

E=cov([pt51 pt61 pt71 pt81]);M=mean([pt51 pt61 pt71 pt81]);x5=M(1);x6=M(2);x7=M(3);x8=M(4);

28

v5=E(1,1);v6=E(2,2);v7=E(3,3);v8=E(4,4);cov58=E(1,end);cov68=E(2,end);cov78=E(3,end);d58=x5-x8;d68=x6-x8;d78=x7-x8;s58=sqrt((v5+v8-2*cov58)/id);s68=sqrt((v6+v8-2*cov68)/id);s78=sqrt((v7+v8-2*cov78)/id);D1=[d58 s58 d68 s68 d78 s78];

E=cov([pt52 pt62 pt72 pt82]);M=mean([pt52 pt62 pt72 pt82]);x5=M(1);x6=M(2);x7=M(3);x8=M(4);v5=E(1,1);v6=E(2,2);v7=E(3,3);v8=E(4,4);cov58=E(1,end);cov68=E(2,end);cov78=E(3,end);d58=x5-x8;d68=x6-x8;d78=x7-x8;s58=sqrt((v5+v8-2*cov58)/id);s68=sqrt((v6+v8-2*cov68)/id);s78=sqrt((v7+v8-2*cov78)/id);D2=[d58 s58 d68 s68 d78 s78];


29



E=cov([pt56 pt66 pt76 pt86]);M=mean([pt56 pt66 pt76 pt86]);x5=M(1);x6=M(2);x7=M(3);x8=M(4);v5=E(1,1);v6=E(2,2);v7=E(3,3);v8=E(4,4);cov58=E(1,end);cov68=E(2,end);cov78=E(3,end);d58=x5-x8;d68=x6-x8;

30

d78=x7-x8;s58=sqrt((v5+v8-2*cov58)/id);s68=sqrt((v6+v8-2*cov68)/id);s78=sqrt((v7+v8-2*cov78)/id);D6=[d58 s58 d68 s68 d78 s78];

Dpt=[D1;D2;D3;D4;D5;D6];Dpt=[(1:1:6); Dpt']

fprintf(fid,'welfare differences: \n\n');fprintf(fid,'site\td58\t\ts58\t\td68\t\ts68\t\td78\t\ts78\n\n');fprintf(fid,'% 2.0f\t%6.3f\t%6.3f\t%6.3f\t%6.3f\t%6.3f\t%6.3f\n',Dpt);fprintf(fid,'\n');fprintf(fid,'\n');

st=fclose(fid);

if st==0; disp('File closed successfully');else; warning('Problem with closing file');end;

31

Matlab Code for Final Version

Documents

Transcript of Matlab Code for Final Version