BLP type Random Coefficients Logit Model

Question

ebdilden 2021-1-22

0
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https://ww2.mathworks.cn/matlabcentral/answers/724503-blp-type-random-coefficients-logit-model

I am working on a project- where I interact my price with a policy dummy zero- one, i.e. Policy_Var= price*policy_dum. So, the variable of interest is not price (I don't have price in the mean utility but price interaction with a zero-one dummy), but it is Policy_Var.

I have a question for you: in calculating elasticities of the RCM model- I know I need to subtract the price effect from mean utility. Since I have Policy_var=price*policy_dum, I need to subtract price and policy_dum from my mean utility- then calculate the mu and individual price sensitivity, alphai's.

I am puzzled about the fact that how can I add these two effects back into my mean utility and re-calculate its exponential? How can I add policy_var back into the mean utility?

I would appreciate your help very much.

global ns cdid cdindex x1 x2 schoolid theti thetj v
 
load ps2
load delta
load theta_final
load schoolid
 
ns = 300;       
               %constant, income, sex, race, momedu, dadedu
 
theta2w=    [  -0.0080       0                 0    0           0    0 ; %constant
               -0.0023       -0.0153           0    -0.1505     0    0 ]; %Policy_Var
           
[theti, thetj, theta2]=find(theta2w);
 
%mval = meanval(theta2);                     %mean utility levels%
mval = delta;                     %mean utility levels%
 
theta2w = full(sparse(theti,thetj,theta2));
policy_price = x1(:,4); %price*LSD
policy_var =x1(:,2); %LSD=1
 
 
 
[n k] = size(x2);
j = size(theta2w,2)-1;
 
 
c_pre = schoolid; 
 
load v
 
%compute the exp of everything but the price effects (will be used below)
mvall = mval - policy_price*theta1(4)-policy_var*theta1(2);
%mvall = mval - policy_cdr2*theta1(4);
 
mu = zeros(n,ns);
for i = 1:ns
    vfull1 = v(cdid,i:ns:k*ns);
    vfull1 = vfull1(:,[1 3:k]);
    dfull1 = demogr(cdid,i:ns:j*ns);
           mu(:,i) = (x2(:,[1 3:k]).*vfull1*theta2w([1 3:k],1))+x2(:,[1 3:k]).*(dfull1*theta2w([1 3:k],2:j+1)')*ones(k-1,1);
           %mu(:,i) = (x2(:,[1 3:k]).*vfull1*theta2w([1 3:k],1)); % this eliminates demographic variables
end
expall = exp(mu + kron(ones(1,ns),mvall));
%clear mu vfull1 dfull1
%compute individual price sensitivity, alphai (will be used below)
v_long = reshape(v(:,ns+1:2*ns)',size(cdindex,1)*ns,1);
 
%clear v
 
%compute individual price sensitivity, alphai (will be used below)
v_long = reshape(v(:,ns+1:2*ns)',size(cdindex,1)*ns,1);
for i=1:j  %this is the case with demographic variables
    d_long(:,i) = reshape(demogr(:,(i-1)*ns+1:i*ns)',size(cdindex,1)*ns,1);  
end %this is the case with demographic variables
 
%Case when alphai is the coefficeint on price plus the nonlinear random taste component of utility   
alphai = theta1(4) + theta1(2)+ [v_long d_long]*theta2w(2,:)' ; %Keep this like that.WHY? Not so sure?
alphai = reshape(alphai,ns,size(cdindex,1))';
 
%%%%%%%
%Question: How to add back policy_price and policy_var back here?
eg = expall.*exp(policy_price*ones(1,ns).*(alphai(cdid,:))); %How to add back policy_var here?