% hw3a.m
% M-file for Homework 3, Q2

% load data
load ps3a.mat
n = length(p);

% part a
x = [ones(n,1) p];
b_a = inv(x'*x)*x'*q

% part b	 	  
z = [ones(n,1) stormy];

pi_1 = inv(z'*z)*z'*p
pi_2 = inv(z'*z)*z'*q
alpha_1 = pi_2(2) / pi_1(2)

% part c - expanded model
Z = [ones(n,1) stormy cold rainy mon tue wed thu];
X = [ones(n,1) p cold rainy mon tue wed thu];
k = size(X,2);

% 2SLS estimate
[alpha,se_1, se_2] = tsls(q,X,Z);
alpha
se_1 
se_2

% end hw3a.m