Calculate the following Wald statistic in Stata

[River Huang]

Hello everyone,

I already have excess return data for ten assets (variables er1, er2, ..., er10) and a market portfolio labeled "vwerm." I am looking to compute the statistic from the following Equation (1). Since this is a just-idenfitied system, indicating that all parameters can be estimated by OLS, and residuals can be obtained accordingly.

I wrote a custom gmmwald.ado script using Claude, but the computed values seem excessively large.

capture program drop gmmwald
program define gmmwald, eclass
    version 12
    syntax varlist [if], flist(string) [nqui]
    
    marksample touse
    local nvar: word count `varlist'
    
    // Store sample size
    qui count if `touse'
    local T = r(N)
    
    // Store all OLS coefficients (both α and β)
    tempname delta
    matrix `delta' = J(2*`nvar', 1, 0)
    
    // Generate residuals first
    local i = 1
    foreach var of varlist `varlist' {
        tempvar res_`i'
        qui reg `var' `flist' if `touse'
        matrix `delta'[2*`i'-1, 1] = e(b)[1,1]  // α
        matrix `delta'[2*`i', 1] = e(b)[1,2]    // β
        qui predict double `res_`i'' if `touse', residuals
        local ++i
    }
    
    // Create DT and ST matrices
    tempname DT ST
    matrix `DT' = J(2*`nvar', 2*`nvar', 0)
    matrix `ST' = J(2*`nvar', 2*`nvar', 0)
    
    tempvar x1 x2
    gen double `x1' = 1 if `touse'
    gen double `x2' = `flist' if `touse'
    
    // Process each observation to build DT
    local xTx11_sum = 0
    local xTx12_sum = 0
    local xTx22_sum = 0
    qui forvalues t = 1/`T' {
        local x1t = `x1'[`t']
        local x2t = `x2'[`t']
        local xTx11_sum = `xTx11_sum' + `x1t'*`x1t'
        local xTx12_sum = `xTx12_sum' + `x1t'*`x2t'
        local xTx22_sum = `xTx22_sum' + `x2t'*`x2t'
    }
    
    // Fill DT matrix (sum of IN⊗xtxt')
    forvalues i = 1/`nvar' {
        forvalues j = 1/`nvar' {
            if `i'==`j' {
                matrix `DT'[2*`i'-1,2*`j'-1] = `xTx11_sum'
                matrix `DT'[2*`i'-1,2*`j'] = `xTx12_sum'
                matrix `DT'[2*`i',2*`j'-1] = `xTx12_sum'
                matrix `DT'[2*`i',2*`j'] = `xTx22_sum'
            }
        }
    }
    
    // Fill ST matrix based on equation (22): sum of êtêt'⊗xtxt'
    forvalues i = 1/`nvar' {
        forvalues j = 1/`nvar' {
            tempvar p11 p12 p21 p22
            gen double `p11' = `res_`i''*`res_`j''*`x1'*`x1' if `touse'
            gen double `p12' = `res_`i''*`res_`j''*`x1'*`x2' if `touse'
            gen double `p21' = `res_`i''*`res_`j''*`x2'*`x1' if `touse'
            gen double `p22' = `res_`i''*`res_`j''*`x2'*`x2' if `touse'
            
            qui sum `p11' if `touse'
            matrix `ST'[2*`i'-1,2*`j'-1] = r(sum)
            qui sum `p12' if `touse'
            matrix `ST'[2*`i'-1,2*`j'] = r(sum)
            qui sum `p21' if `touse'
            matrix `ST'[2*`i',2*`j'-1] = r(sum)
            qui sum `p22' if `touse'
            matrix `ST'[2*`i',2*`j'] = r(sum)
        }
    }
    
    // Now divide both matrices by T
    matrix `DT' = `DT'/`T'
    matrix `ST' = `ST'/`T'
    
    // Create selection matrix R = IN ⊗ (1 0)
    tempname R
    matrix `R' = J(`nvar', 2*`nvar', 0)
    forvalues i = 1/`nvar' {
        forvalues j = 1/`nvar' {
            if `i' == `j' {
                matrix `R'[`i', 2*`j'-1] = 1  // 1 in first column
                matrix `R'[`i', 2*`j'] = 0    // 0 in second column
            }
        }
    }
    
    // Get alpha vector: α = R𝛿
    tempname alpha
    matrix `alpha' = `R'*`delta'
    
    // Calculate test statistic
    tempname DTST DTD RDTDR phi1
    matrix `DTST' = `DT''*syminv(`ST')
    matrix `DTD' = `DTST'*`DT'
    matrix `RDTDR' = `R'*syminv(`DTD')*`R''
    matrix `phi1' = ((`T'-`nvar'-1)/`T')*`alpha''*syminv(`RDTDR')*`alpha'
    
    // Store and display results
    ereturn clear
    ereturn scalar chi2 = `phi1'[1,1]
    ereturn scalar df = `nvar'
    ereturn scalar p = chi2tail(`nvar', `phi1'[1,1])
    ereturn scalar N = `T'
    
    di as txt _n "GMM test of mean-variance efficiency"
    di as txt "Chi2(" as res `nvar' as txt ") = " as res %8.4f `phi1'[1,1]
    di as txt "Prob > chi2 = " as res %8.4f chi2tail(`nvar', `phi1'[1,1])
end

I would greatly appreciate it if any expert could spare some time to help identify and correct the issue. Thank you!

Note that some data can be found here: ado file for gmm wald test? - Statalist 。