Constraining slope - regression

Question

I'm a beginner in Stata. I'm trying to run the following regression:
regress logy logI logh logL
but I would like to constrain the slope of logh to be one. Can someone tell me the command for this?

Answer 1

There are at least three ways to do this in Stata.
1) Use constrained linear regression:
. sysuse auto
(1978 Automobile Data)
. constraint 1 mpg = 1
. cnsreg price mpg weight, constraints(1)
Constrained linear regression Number of obs = 74
Root MSE = 2502.5449
( 1) mpg = 1
------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mpg | 1 (constrained)
weight | 2.050071 .3768697 5.44 0.000 1.298795 2.801347
_cons | -46.14764 1174.541 -0.04 0.969 -2387.551 2295.256
------------------------------------------------------------------------------
2) Variable transformation (suggested by whuber in the comment above):
. gen price2 = price - mpg
. reg price2 weight
Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 1, 72) = 29.59
Model | 185318670 1 185318670 Prob > F = 0.0000
Residual | 450916627 72 6262730.93 R-squared = 0.2913
-------------+------------------------------ Adj R-squared = 0.2814
Total | 636235297 73 8715552.01 Root MSE = 2502.5
------------------------------------------------------------------------------
price2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | 2.050071 .3768697 5.44 0.000 1.298795 2.801347
_cons | -46.14764 1174.541 -0.04 0.969 -2387.551 2295.256
------------------------------------------------------------------------------
3) Using a GLM model with an offset:
. glm price weight , family(gaussian) link(identity) offset(mpg)
Iteration 0: log likelihood = -683.04238
Iteration 1: log likelihood = -683.04238
Generalized linear models No. of obs = 74
Optimization : ML Residual df = 72
Scale parameter = 6262731
Deviance = 450916626.9 (1/df) Deviance = 6262731
Pearson = 450916626.9 (1/df) Pearson = 6262731
Variance function: V(u) = 1 [Gaussian]
Link function : g(u) = u [Identity]
AIC = 18.51466
Log likelihood = -683.0423847 BIC = 4.51e+08
------------------------------------------------------------------------------
| OIM
price | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | 2.050071 .3768697 5.44 0.000 1.31142 2.788722
_cons | -46.14764 1174.541 -0.04 0.969 -2348.205 2255.909
mpg | 1 (offset)
------------------------------------------------------------------------------
The glm route could also handle the log transformation of your outcome for you if you change the link and family options appropriately.