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:
args lnf epsilon
quietly replace `lnf' = log(normalden(`epsilon'))
ml model lf myprog (all independent variables here)
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?