Constrained OLS

[Jared Greathouse]

Hi, is it possible that I can force my independent variables in regress to be positive and add up to 1?

clear *


cls


u "http://fmwww.bc.edu/repec/bocode/s/synth_smoking.dta", clear

keep state year cigsale


frame put state year cigsale, into(scmframe)

cwf scmframe

reshape wide cigsale, i(year) j(state)

// California's ID is 3, so it goes first by convention
order cigsale3, a(year)

tsset year

reg cigsale3 cigsale1-cigsale39 if year < 1989, nocons

predict cf_Cali

line cigsale3 cf_Cali year, xli(1989)

br

I want to illustrate the synthetic control method as simply being a from of constrained OLS, but I've never manually done this in Stata. Easily done in Python, but I was unsure if we could do it here. Precisely, I need for there to be 1: no constant, 2, all the betas should be greater than or = 0, and the sum of the coefficients must add up to 1. I know cnserg exists, but I've never used it and I was wondering if someone else has

[Leonardo Guizzetti]

Working with constraints is too difficult, but you'll find that they only work with linear constraints, no non-linear (including inequalities).

Here's an example using a constraint on the sum of coefficients:

sysuse auto, clear

reg mpg head trunk length

constraint 1 _b[headroom] + _b[trunk] + _b[length] = 1
cnsreg mpg head trunk length, constraint(1)

You'll see there's no guarantee that all coefficients are constrained to be non-negative. To the best of my knowledge, SEM software is more naturally able to impose non-linear constraints of the type you're interested (MPlus is what I'm familiar with), but Stata's sem/gsem are both limited to the linear constraints (as I think are all of the usual estimation commands in Stata).

[Jared Greathouse]

Okay this makes sense! No wonder the real optimizations are done in Mata.