# [Limdep Nlogit List] OLS constraints

William Greene wgreene at stern.nyu.edu
Sat Nov 17 23:48:19 EST 2007

```----- Original Message -----
From: "Erik Ferguson" <eferguson at aus.edu>
To: "Limdep and Nlogit Mailing List" <limdep at limdep.itls.usyd.edu.au>
Sent: Saturday, November 17, 2007 6:40:14 AM (GMT-0500) Auto-Detected
Subject: [Limdep Nlogit List] OLS constraints
I have a simple theoretical OLS model of the following form:
Y = a + b*x1 + c*x2
According to the theory, the estimated coefficients of this model should
be constrained as follows:
c = a - b
I have tried to program this model in Limdep in several different ways,
including the CLS command, but it does not seem to want to cooperate.
Is there a problem in constraining the intercept term?
--
Erik Ferguson
Urban Planning Graduate Program
School of Architecture and Design
American University of Sharjah
PO Box 26666
Sharjah, UNITED ARAB EMIRATES

There is no problem. Please see below.
**************************************

--> samp;1-100\$
--> crea;x1=rnn(0,1);x2=rnn(0,1);y=x1+x2+rnn(0,1)\$
--> regr;lhs=y;rhs=one,x1,x2;cls:b(1)-b(2)-b(3)=0\$

+----------------------------------------------------+
| Ordinary    least squares regression               |
| Model was estimated Nov 17, 2007 at 07:47:21AM     |
| LHS=Y        Mean                 =  -.2977003E-01 |
|              Standard deviation   =   1.729971     |
| WTS=none     Number of observs.   =        100     |
| Model size   Parameters           =          3     |
|              Degrees of freedom   =         97     |
| Residuals    Sum of squares       =   106.2195     |
|              Standard error of e  =   1.046445     |
| Fit          R-squared            =   .6414982     |
|              Adjusted R-squared   =   .6341064     |
| Model test   F[  2,    97] (prob) =  86.79 (.0000) |
| Diagnostic   Log likelihood       =  -144.9107     |
|              Restricted(b=0)      =  -196.2018     |
|              Chi-sq [  2]  (prob) = 102.58 (.0000) |
| Info criter. LogAmemiya Prd. Crt. =   .1203559     |
|              Akaike Info. Criter. =   .1203379     |
| Autocorrel   Durbin-Watson Stat.  =  2.0157790     |
|              Rho = cor[e,e(-1)]   =  -.0078895     |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient  | Standard Error |t-ratio |P[|T|>t]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
Constant|    -.01539830       .10469604     -.147   .8834
X1      |     .95953721       .11712426     8.192   .0000   -.02496906
X2      |    1.04648459       .11875324     8.812   .0000    .00916115

+----------------------------------------------------+
| Linearly restricted regression                     |
| Ordinary    least squares regression               |
| Model was estimated Nov 17, 2007 at 07:47:21AM     |
| LHS=Y        Mean                 =  -.2977003E-01 |
|              Standard deviation   =   1.729971     |
| WTS=none     Number of observs.   =        100     |
| Model size   Parameters           =          2     |
|              Degrees of freedom   =         98     |
| Residuals    Sum of squares       =   238.5861     |
|              Standard error of e  =   1.560305     |
| Fit          R-squared            =   .1947475     |
|              Adjusted R-squared   =   .1865307     |
| Model test   F[  1,    98] (prob) =  23.70 (.0000) |
| Diagnostic   Log likelihood       =  -185.3719     |
|              Restricted(b=0)      =  -196.2018     |
|              Chi-sq [  1]  (prob) =  21.66 (.0000) |
| Info criter. LogAmemiya Prd. Crt. =   .9095654     |
|              Akaike Info. Criter. =   .9095600     |
| Autocorrel   Durbin-Watson Stat.  =  1.9275877     |
|              Rho = cor[e,e(-1)]   =   .0362062     |
| Restrictns.  F[  1,    97] (prob) = 120.88 (.0000) |
| Not using OLS or no constant. Rsqd & F may be < 0. |
| Note, with restrictions imposed,  Rsqd may be < 0. |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient  | Standard Error |t-ratio |P[|T|>t]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
Constant|     .62949533       .12930700     4.868   .0000
X1      |     .29922589       .14993092     1.996   .0488   -.02496906
X2      |     .33026944       .14804790     2.231   .0280    .00916115

--> create;z1=x2+1;z2=x1-x2\$
--> regr;lhs=y;rhs=z1,z2\$

+----------------------------------------------------+
| Ordinary    least squares regression               |
| Model was estimated Nov 17, 2007 at 07:48:36AM     |
| LHS=Y        Mean                 =  -.2977003E-01 |
|              Standard deviation   =   1.729971     |
| WTS=none     Number of observs.   =        100     |
| Model size   Parameters           =          2     |
|              Degrees of freedom   =         98     |
| Residuals    Sum of squares       =   238.5861     |
|              Standard error of e  =   1.560305     |
| Fit          R-squared            =   .1947475     |
|              Adjusted R-squared   =   .1865307     |
| Model test   F[  1,    98] (prob) =  23.70 (.0000) |
| Diagnostic   Log likelihood       =  -185.3719     |
|              Restricted(b=0)      =  -196.2018     |
|              Chi-sq [  1]  (prob) =  21.66 (.0000) |
| Info criter. LogAmemiya Prd. Crt. =   .9095654     |
|              Akaike Info. Criter. =   .9095600     |
| Autocorrel   Durbin-Watson Stat.  =  1.9275877     |
|              Rho = cor[e,e(-1)]   =   .0362062     |
| Not using OLS or no constant. Rsqd & F may be < 0. |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient  | Standard Error |t-ratio |P[|T|>t]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
Z1      |     .62949533       .12930700     4.868   .0000   1.00916115
Z2      |     .29922589       .14993092     1.996   .0487   -.03413021

--> wald;fn1=b_z1-b_z2\$

+-----------------------------------------------+
| WALD procedure. Estimates and standard errors |
| for nonlinear functions and joint test of     |
| nonlinear restrictions.                       |
| Wald Statistic             =      4.97659     |
| Prob. from Chi-squared[ 1] =       .02569     |
+-----------------------------------------------+
+--------+--------------+----------------+--------+--------+
|Variable| Coefficient  | Standard Error |b/St.Er.|P[|Z|>z]|
+--------+--------------+----------------+--------+--------+
Fncn(1) |     .33026944       .14804790     2.231   .0257

```