I am trying to compute the standard errors of an estimate obtained using the Lubotsky-Wittenberg (2006) methodology for proxy combination. Here it is the list of commands:

gen a=.
gen b=.
gen c=.
gen d=.
gen e=.
gen f=.

reg y x_1 x_2 x_3
replace a = _b[x_1]
replace b = _b[x_2]
replace c = _b[x_3]

ivreg x_1 ( x_1 = y)
replace d = _b[x_1]
ivreg x_2 ( x_1 = y)
replace e = _b[x_1]
ivreg x_3 ( x_1 = y)
replace f = _b[x_1]
qui gen pbhat =a*d + b*e + c*f
sum pbhat

The estimate is "pbhat" that is a linear combination of multivariate regression coefficients and IV regression coefficients. Can you help me in obtaining the standard errors with this procedure?
Thank you in advance.