Maximum Likelihood Estimation in Stata

Hey,

i have a set of data consisting of three variables x1, x2 and x3 with N observations. I want to estimate a relationship between these by using a translog function equal to zero. (i do NOT have a dependent variable y). Thus, the problem is formulated as:

I have tried to implement this in Stata by assuming that the error term is standard normal with mean 0 and stdev 1. By solving the above equation for epsilon and maximizing the log-likelihood one gets:

where is the standard normal density function. I've tried to solve this in stata by using the following program:

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program myprog

version 11

args lnf epsilon

quietly replace `lnf' = log(normalden(`epsilon'))

end

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ml model lf myprog (all independent variables here)

ml maximize

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I get the error message: "could not calculate numerical derivatives -- discontinuous region with missing values encountered"

It probably has something to do with me not specifying any $ML_y1, but I cant get my head around this problem when y=0 in my regression! Does anyone have a clue?