%Hendrik Wolff  
%ARE 213, January 18, 2006

% "%" is the symbol making a comment!

% The following changes the Directory for Matlab: same as DOS commands
% Exampe, this file is in ..../ARE213/Section/test.m

cd .. % we go to ..../ARE213/
cd data  % changes to ....ARE213/data/
load nls_2006.mat % Here we load data from the subfolder data
cd .. % go back to ..../ARE213/
cd HWOutput 
diary diaryfortest % this automatically creates a diary, useful later analyzing output later and for debugging
cd ..
cd Section % ..../ARE213/Section/ Hence here the file OLS.m and the file test.m are located


% For this problem set you will have to use the data set NLS 2006.MAT which is available
% on the website for the course. There are 929 observations on nine variables in this data set,
% luwe (log weekly wage), educ (years of education), exper (years of experience), age (age
% in years), fed (father’s education in years), med (mothers education in years), kww (a test
% score), iq (an iq score), and white (indicator for white).
% 1. Report the minimum, maximum, mean and standard deviation for all variables.

'Problem 1'
'Report the minimum, maximum, mean and standard deviation for all variables: '

% ***commands ending with ";" surpress output, otherwise result will be printed on screen
data = [luwe educ exper age fed med kww, iq white]; 
% data is a (N x K) Matrix 

mini = min(data) %min(data) goes columnwise over data and picks for each column the min, the result is a 1 x K vector
'In Columns: minimum  maximum  standard deviation '
'In Rows: luwe educ exper age fed med kww iq white'
sum = [mini', max(data)', std(data)']

% 2. Estimate a linear regression model for log wages on education, experience, and experience
% squared. Report the estimates and standard errors. Also report the full
% variance/covariance matrix for all parameters, that is both the regression parameters
% as well as the residual variance.


exper_sq = exper .* exper; % note .* , ./ are cell by cell operators instead of the usual matrix operators
n = length (luwe);
on=ones(n,1);
X = [on educ exper exper_sq];
y = luwe;
Beta = inv(X'*X)*X'*y
eps = y - X * Beta;
[n, k] = size(X);
sig_sq = eps' * eps / (n-k);
var = sig_sq * inv(X'*X);
'Standard Errors of Coefficients'
se = sqrt(diag(var))
'Variance Covariance Matrix for Coefficients'
var
'Variance for residual'
sig_sq
'Variance for variance '
2*sig_sq*sig_sq/n

%Variance-Covariance Matrix of the entire parameter vector of beta and
%sigma2, see below 
% Here an useful alternnative to Problem 2:
% We start with the self defined OLS function
'cross check results with above'
[out,var,rsq,sigs]=ols(luwe,[on,educ,exper,exper.*exper]) % should be self-explanatory when looking at the function ols.m. 

'compute an Confidence Interval for beta2' 
[out(2,1),out(2,1)-1.96*out(2,2),out(2,1)+1.96*out(2,2)]


% 3. Predict the effect on average log earnings of decreasing everybody’s education level by
% one year.


diary off