Cluster Standard Errors with fitlm

I have panel data (county, year) and want to run a regression with individual-specific effects that are uncorrelated (a fixed effects regression in economics parlance). Does fitlm automatically cluster the standard errors? If not, is there a way to do this?

[Aditya Patil]

Can you elaborate on what you mean by clustering of standard errors? I assume you are using fitlme, and want the errors for all the inputs to be clustered under some condition?

[Joshua]

Clustered standard errors refers to Cluster Robust Covariance Matrices (see Greene's Econometric Analysis section 11.3.3). The need arises when errors within a group are correlated but the erros between groups are not.

I am using fitlm with a categorical variable. I believe fitlm employs a least squares dummy variable approach.

[Aditya Patil]

Can you have a look at the examples provided in https://www.mathworks.com/help/stats/fitlme.html and let me know if this serves your usage? By providing random effect as (1 + x | g), you should be able to have correlation within group errors, while errors outside group will be uncorrelated.

[Joshua]

Fitlme does not provide the option to cluster errors in estimation of the coefficient variance matrix. Nor does it provide the option to return the estimated data covariance matrix, which could be used to cluster the coefficient standard errors.

I wrote a function that estimates the Cluster Robust Variance matrix based the idea that X is 'augmented' prior to input.

Here is a fixed effects estimation. I apologize that it is not well commented.

%%%SCRIPT

%%GENERATE DUMMY MATRIX

id = unique(ID);

for ii = 1:G

D(:,ii) = (ID == id(ii)); %#ok<SAGROW>

end

%AUGMENT MATRIX

Md = eye(N)-((D*inv(D'*D))*D');

%ESTIMATE COEFFICIENTS

b = (inv(X'*Md*X))*(X'*Md*y);

%FIXED EFFECTS ERROR

efe = Md*y-(Md*X*b);

%COEFFIENT VARIANCE

crobust = (G/(G-1))*((N-1)/(N-G-K)); %correction

Vrobust = CRV(Md*X,efe,ID,crobust);

%FUNCTION

function V = CRV(X,e,ID,c)

if nargin<4

[N,K] = size(X); G = numel(unique(ID)); c = (G/(G-1))*((N-1)/(N-K));

end

if numel(c)>1

error('correction is not a scalar value');

end

%CLUSTER ROBUST VARIANCE MATRIX

g = unique(ID); G = numel(g);

%initialize 'Meat' matrix

M = 0;

for ii = 1:G

selvec = g(ii) == ID;

wi = e(selvec);

M = M+X(selvec,:)'*(wi*wi')*X(selvec,:);

end

V = c*inv(X'*X)*M*inv(X'*X);

Answer 1

[Aditya Patil]

Currently, clustered standard errors is not supported in Statistics and Machine Learning Toolbox. I have brought the request to the notice of concerned developers.