st: Programming an iterative regression with converging parameters

[pstock@rumms.uni-mannheim.de]

Hello STATA users,

I am new to STATA and have to replicate a paper by Easton, Taylor,  
Shroff, Soughiannis (2002) about the implicit calculation of the  
implied cost of capital r. The problem is that the proxy for the  
dependent variable X_cT is caluclated with r, while r itself is to be  
estimated from the regression coefficients. They note that an initial  
r=0.12 or 12% is used to calculate X_cT. Then it is used as dependent  
variable to run the first regression. From the resulting intercept and  
regression coefficient the r and growth rate g are calculated. The new  
r is used as revised estimate of the implied cost of capital r to  
recalculate X_cT. The regression is run again and the process of  
estimating r from the coefficients, and recalculating X_cT starts all  
over. The logic is simple and straight forward - the programming for a  
rookie is not. Reading about STATA Programming I guess that a loop  
using the while command is needed, with the iterative regression to  
stop when the r from the previous run and the new r are so close as  
not changing matterially. I used r_`j'-r_`i'>0.0001 as indicator to  
continue with the loop, as the "true" condition. Also r must be  
positiv, whereas the forth root can be negative, but is economic  
meaningless. How to program constraints I do not know - sounds like  
MATA-rogramming then. So I tried it first without the constraints.  
Maybe the nl command could work.

Here is my do file, and when executing it I even do not get an error  
message, neither results, not anything:

clear
set memory 50m
use "C:\Users\stock.GESS\Desktop\IBES  
Datensatz\Data_replication_study_1_X_cT.dta"
preserve
generate r_1=0.12
generate X_cT_1=x1+x2+x3+x4+[(1+r_1)^3-1]*d0+[(1+r_1)^2-1]*d0+[(1+r_1)-1]*d0
generate depvar=X_cT_1/B0
local i=1
forvalues i=1/100 {
local j=1
while r_`j'-r_`i'>0.001 {
	replace r_`i'=r_`j'
	replace  
X_cT_`i'=x1+x2+x3+x4+[(1+r_`i')^3-1]*d0+[(1+r_`i')^2-1]*d0+[(1+r_`i')-1]*d0
	replace depvar=X_cT_`i'/B0
	regress depvar indvar
	generate g_`i'=(_b[_cons]+1)^(1/4)-1, replace
	generate r_`j'=(_b[indvar]+(_b[cons]+1))^(1/4)-1, replace
	}
}
save Data_replication_study_1_X_cT_1.dta
describe
summarize
estimates save regression_1, replace
estimates tab

Any suggestions hw to program such a process are highly appreciated.

Kind regards

Pascal Stock

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