Query regarding fama macbeth regression

Dear all,

I need to run FamaBeth regressions.

My Y is a T*N matrix, where T is the number of periods and N the number of firms.

My X is also T*N. Hence, I only have one predictor for each regression.

In the first stage of the so-called FamaMacBeth regression, I must run, for each firm, a time series regression of the dependent variable on the predictor. Hence, I am to run N regressions in the first stage. Then, I store the N estimated coefficients in a N*1 vector called "beta".

In the second stage, I must run, for each time period t, a cross-sectional of the dependent variable on the betas found in the first stage. I thus get T coefficients which I store in a T*1 vector called "lambda".

In a third stage, I simply compute the mean of the vector lambda and the standard errors.

The problem is that my matrices Y and X both contain NaNs. Hence, I try to account for them by, for each of the T*N regressions I ran, deleting all rows for which a NaN appears in the relevant subvector of the Y and X matrices (relavant for each regression; as each regression uses different parts of Y and X matrices).

The problem is that I keep on getting these messages

"> In famamacbeth at 37 Warning: Rank deficient, rank = 1, tol = 1.1538e-015. "

for both the estimation of the beta coefficients and the lambda coefficients.

When I run loops separately, I am able to get each coefficient (associated with that loop) without receiving any message, though.. which kind of puzzles me since the regression should be exactly the same.

I am not sure what the problem is, as the code makes perfect sense in my mind! Hope someone can enlighten me!

 function [lambda beta lambdaFinal lambdaStd] = famamacbeth(ymat,xmat)
%preallocate memory
 [T N] = size(ymat);

 alpha1 = NaN(N,1);

 beta = NaN(N,1);

 alpha2 = NaN(T,1);

 lambda = NaN(T,1);

 %first stage

 for n = 1:N  %here I run a time series regression for each firm

 %I extract the relevant column(firm)

    localX = xmat(:,n); 

    localY = ymat(:,n);

 %I get rid of the nans here

    index1 =  isnan(localY);

    index2 = isnan(localX);

    index = index1 + index2;

    index = ~logical(index);

    localX = localX(index);

    localY = localY(index); 

 %I run the regression

    R = numel(localX);

    localX = horzcat(ones(R,1),localX); %add intercept

    alphaBeta = localX\localY;

    alphaBeta = alphaBeta';

    alpha1(n,1) = alphaBeta(1,1);

    beta(n,1) = alphaBeta(1,2);

 end

 %second stage

 Ylocal = ymat';

 for t = 1 : T %here I run a cross-sectional regression for each time period t

    y = Ylocal(:,t); 

    localX = beta;

    index1 =  isnan(y);

    index2 = isnan(localX);

    index = index1 + index2;

    index = ~logical(index);

    localX = localX(index);

    y = y(index); 

    L = numel(localX);

    localX = horzcat(ones(L,1),localX);

    alphaLambda = localX\y;

    alphaLambda = alphaLambda';

    alpha2(t,1) = alphaLambda(1,1);

    lambda(t,1) = alphaLambda(1,2);

 end

 %"third stage"

 lambdaFinal = mean(lambda);

 lambdaStd = sum((lambda-lambdaFinal).^2)/(T^2);

 end