st: Generate new variable with an implicit formulation

[Bob Hammond <robert.g.hammond@vanderbilt.edu>]

I would like to define a new variable based on two current variables, 
but the new variable cannot be expressed as an explicit function of the 
current variables. The relationship is:

x = n*y^(n-1) - (n-1)*y^n

where I have data on x and n and would like to create a new variable, y. 
x and y are restricted to the real numbers on the open interval (0,1) 
and n is restricted to being a positive integer. Under these 
restrictions, the function is well-behaved and provides a unique 
solution, but not an explicit formulation. I can generate y with the 
following loop:

forvalues i=0(0.001)1 {
replace y=`i' if x - n*`i'^(n-1) + (n-1)*`i'^n < 0.0001 & x - 
n*`i'^(n-1) + (n-1)*`i'^n > -0.0001
}

but I am wondering if there is a more efficient and precise way. If this 
type of loop is best, what precision would you recommend for the steps 
of `i’ and the tolerance (the ><0.0001)? (I’m on Intercooled Stata 9 for 
Windows if that matters.) Thanks in advance,

Bob

--
------------------------------------------------------------------------
Bob Hammond
Department of Economics
Vanderbilt University
http://people.vanderbilt.edu/~robert.g.hammond/ 
<http://people.vanderbilt.edu/%7Erobert.g.hammond/>
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