Solving non-linear equations within a loop in Stata

[Sher Afghan Asad]

Cross posted on Stack Overflow.

Hi I am trying to solve 3 non-linear equations using nl command in Stata within a loop. The working program to solve equations for one set of values is as follows;

capture program drop nlcostsolver
program nlcostsolver    
syntax varlist(min=1 max=1) [if], at(name)      

tempname    G S K    
scalar      `G' = `at'[1,1]    
scalar      `S' = `at'[1,2]    
scalar      `K' = `at'[1,3]      

tempvar     yh    

gen         double `yh' = `G'*log(1531.560) - log(`S'+0) + log(`K') + 1 in 1    
replace     `yh' = `G'*log(2015.896) - log(`S'+0.01) + log(`K') in 2    
replace     `yh' = `G'*log(2152.582) - log(`S'+0.10) + log(`K') in 3      

replace     `varlist' = `yh'    
end  

clear  

set         obs 3
generate    y = 0
replace     y = 1 in 1  

scalar      k = exp((log(0.10) - ((log(0.01)*log(2152.582))/log(2015.896))) / (1 - (log(2152.582)/log(2015.896))))
scalar      gamma = exp(log((log(0.01) - log(k))/log(2015.896)))
scalar      s = exp(exp(log(gamma))*log(1531.560) + log(k))  

nl costsolver@ y, parameters(G S K) initial(G gamma S s K k)

The above code gives me the value of parameters (G, S and K) for particular values (1531.560, 2015.896, 2152.582) in the program. However, I have 3 variables (Points0, Points3 and Points0) with 1000 observations each for which I need to calculate values of these parameters. So I need to calculate 1000 set of parameters. I tried looping the program as follows;

gen     G = .
gen     S = .
gen     K = .  

forvalues i = 1/1000 {    

capture program drop nlcostsolver    
program nlcostsolver        
syntax      varlist(min=1 max=1) [if], at(name)          

tempname    G S K        

scalar      `G' = `at'[1,1]        
scalar      `S' = `at'[1,2]        
scalar      `K' = `at'[1,3]          

tempvar     yh        

gen         double `yh' = `G'*log(`Points0[`i']') - log(`S'+0) + log(`K') + 1 in 1        
replace     `yh' = `G'*log(`Points3[`i']') - log(`S'+0.03) + log(`K') in 2        
replace     `yh' = `G'*log(`Points9[`i']') - log(`S'+0.09) + log(`K') in 3          

replace     `varlist' = `yh'              

scalar      k = exp((log(0.09) - ((log(0.03)*log(`Points9[`i']'))/log(`Points3[`i']'))) / (1 - (log(`Points9[`i']')/log(`Points3[`i']'))))        
scalar      gamma = exp(log((log(`p3') - log(k))/log(`Points3[`i']')))        
scalar      s = exp(exp(log(gamma))*log(`Points0[`i']') + log(k))      
end      
preserve        
clear          
set         obs 3        
generate    y = 0        
replace     y = 1 in 1          

nl costsolver @ y, parameters(G S K) initial(G gamma S s K k)    
restore      

replace G = [G]_b[_cons] in `i'    
replace S = [S]_b[_cons] in `i'    
replace K = [K]_b[_cons] in `i' }

However, since I am using program within a loop, the moment I get to end statement in the program the loop breaks. Appreciate your help.

[Jean-Claude Arbaut]

You can't define a program inside a loop. Define the program before the loop. If you need to use an extra parmeter that you can't pass with the nl command, you could use a global macro.

[Sher Afghan Asad]

Hi Jean,

Thanks for your comment. I have realized that programs can't be used inside a loop. However I remain unable to come up with a program that can use values from the variable to generate parameters for each combination of variables value. Sorry I can't see straight away how could using global macros achieve what I want in this case.

It seems to me Stata is not an ideal software for non-linear optimization, maybe I should do this in R then.

[Sher Afghan Asad]

The trick with using globals worked. Thanks for the suggestion Jean!