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Re: st: Decreasing Returns to SCALE

From   "Joseph Coveney" <>
To   "Statalist" <>
Subject   Re: st: Decreasing Returns to SCALE
Date   Tue, 20 May 2008 09:19:31 +0900

Altay Turk wrote:

How can I test for decreasing returns to scale?

Suppose I ran the regression:

log_y = a+b(logx)+c(logz)

I'd like to test b+c<1


My guess is that you'd logarithmically transform your variables, perform
ordinary least-squares linear regression, calculate the one-sided 95%
confidence interval of the linear combination of the two slope regression
coefficients and inspect whether the upper confidence limit exceeds one.

Joseph Coveney

clear *
set more off
set seed `=date("2008-05-20", "YMD")'
set obs 25
generate float y = exp(invnormal(uniform()))
generate float x = uniform()
generate float z = uniform()
* Begin here
foreach var of varlist y x z {
   generate float log_`var' = ln(`var')
regress log_y log_x log_z
// Below, is the UCL < 1?
lincom _b[log_x] + _b[log_z], level(90)

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