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From |
Joerg Luedicke <joerg.luedicke@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Proportional Independent Variables |

Date |
Thu, 28 Feb 2013 00:39:48 -0500 |

When unsure about things like these, it is always a good idea to run a bunch of simulations with fabricated data. Below is some code for checking consistency of OLS estimates, based on the described set up. First, we generate 5 variables containing uniform random variates on the range [0,1), and constrain the variables such that they sum up to one for each observation. Then, we set up a program to feed to Stata's -simulate-, and finally inspect the results. You can change sample size, number of variables, and parameter values in order to closer resemble your problem at hand. The amount of bias looks indeed negligible to me, confirming Nick Cox' impressions. Efficiency might be a different story though... Joerg *-------------------------------------------- // Generate data clear set obs 500 set seed 1234 forval i=1/5 { gen u`i' = runiform() } egen su = rowtotal(u*) gen wu = 1/su forval i=1/5 { gen cnsx`i' = u`i'*wu } keep cnsx* // Set up program for -simulate- program define mysim, rclass cap drop e y gen e = rnormal() gen y = 0.1*cnsx1 + 0.2*cnsx2 + /// 0.3*cnsx3 + 0.4*cnsx4 + e reg y cnsx1 cnsx2 cnsx3 cnsx4 forval i = 1/4 { local b`i' = _b[cnsx`i'] return scalar b`i' = `b`i'' } end // Run simulations simulate b1=r(b1) b2=r(b2) b3=r(b3) b4=r(b4), /// reps(10000) seed(4321) : mysim // Results sum *-------------------------------------------- On Wed, Feb 27, 2013 at 3:40 PM, nick bungy <nickbungystata@hotmail.co.uk> wrote: > Dear Statalist, > > I have a dependent variable that is continuous > and a set of 20 independent variables that are percentage based, with > the condition that the sum of these variables must be 100% across each > observation. The data is across section only. > > I am aware that > interpretting the coefficients from a general OLS fit will be > inaccurate. The increase of one of the 20 variables will have to be > facilitated by a decrease in one or more of the other 19 variables. > > Is > there an approach to get consistent coefficient estimates of these > parameters that consider the influence of a proportionate decrease in > one or more of the other 20 variables? > > Best, > > Nick > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Proportional Independent Variables***From:*Joerg Luedicke <joerg.luedicke@gmail.com>

**References**:**st: Proportional Independent Variables***From:*nick bungy <nickbungystata@hotmail.co.uk>

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