Hi,
I have a trouble with constructing the McElroy's Goodness of Fit statistics for the seemingly unrelated regressions with system wide constraints.
I have three equations, whose vector of explanatory variables are same for all three.By using mksplne command, each equation is characterized by continuous piecewise linear functional form.
I would like to construct the system wide measurement of goodness of fit, following McElroy(1977)'s R^2
Array
Where bz is the vector of estimated coefficients of slope parameters, and Z is corresponding vector of explanatory variables. S^{-1} is the consistent estimator of cross-equation variance-covariance matrix.
A is defined as
Array
where l is a (nx1) column vector of ones and n is the number of observations.
By using the estimated coefficient matrix e(b) (which is partitioned into slope and constant terms) and variance-covariace matrix of residual e(Sigma), i constructed the McElroy's R^2. Matrix calculation is technically operated successfully, but the problem is that the LHS and RHS (in the definition of R^2) does not equate.
When we have a system-wide constraint, should we include (in some ways) the constraint matrix to calculate the R^2?
It would be greatly appreciated if you could give me some tips to untangle this puzzle.
Thanks in advance!
Kensuke
I have a trouble with constructing the McElroy's Goodness of Fit statistics for the seemingly unrelated regressions with system wide constraints.
I have three equations, whose vector of explanatory variables are same for all three.By using mksplne command, each equation is characterized by continuous piecewise linear functional form.
I would like to construct the system wide measurement of goodness of fit, following McElroy(1977)'s R^2
Array
Where bz is the vector of estimated coefficients of slope parameters, and Z is corresponding vector of explanatory variables. S^{-1} is the consistent estimator of cross-equation variance-covariance matrix.
A is defined as
Array
where l is a (nx1) column vector of ones and n is the number of observations.
By using the estimated coefficient matrix e(b) (which is partitioned into slope and constant terms) and variance-covariace matrix of residual e(Sigma), i constructed the McElroy's R^2. Matrix calculation is technically operated successfully, but the problem is that the LHS and RHS (in the definition of R^2) does not equate.
When we have a system-wide constraint, should we include (in some ways) the constraint matrix to calculate the R^2?
It would be greatly appreciated if you could give me some tips to untangle this puzzle.
Thanks in advance!
Kensuke