LIML Procedure

@LIML estimates a linear equation using limited information maximum likelihood. This is rarely used as the simpler 2SLS seems to work better in practice. Before using this, you should set the instrument set using INSTRUMENTS.

@LIML depvar start end resids

# list of explanatory variables (in Regression Format)

Parameters

depvar	dependent variable
start, end	range for estimation (by default, maximum range possible given variables)
resids	residuals (optional)

Variables Defined

%CDSTAT	test statistic for overidentification (REAL)
%SIGNIF	the marginal significance level of %CDSTAT (REAL)

Example

* Greene, Econometric Analysis, 7th Edition

* Section 10.6. Estimates of Klein's Model I from page 333.

open data tablef10-3.csv

calendar 1920

data(format=prn,org=columns) 1920:1 1941:1 year c p wp in k1 x wg g tax

set totwage = wp+wg

set trend = (t-1931:1)

* 2SLS

instruments constant trend wg g tax p{1} x{1} k1

linreg(inst,equation=conseq)

linreg(inst,equation=inveq)

linreg(inst,equation=wageeq)

* LIML

@liml c

# constant p{0 1} totwage

@liml in

# constant p{0 1} k1

@liml wp

# constant x x{1} trend

Sample Output

This is for the final @LIML. The LIML specification test has four degrees of freedom because it has eight instruments and four coefficients. This would indicate that at least one of the instruments is likely correlated with the error term.

Linear Regression - Estimation by LIML

Dependent Variable WP

Annual Data From 1921:01 To 1941:01

Usable Observations 21

Degrees of Freedom 17

Centered R^2 0.9873924

R-Bar^2 0.9851675

Uncentered R^2 0.9996491

Mean of Dependent Variable 36.361904762

Std Error of Dependent Variable 6.304401335

Standard Error of Estimate 0.767805151

Sum of Squared Residuals 10.021920736

Regression F(3,17) 443.7968

Significance Level of F 0.0000000

Log Likelihood -22.0304

Durbin-Watson Statistic 2.0015

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant 1.5261866858 1.3208378633 1.15547 0.26388110

2. X 0.4339413995 0.0755074037 5.74700 0.00002371

3. X{1} 0.1513206755 0.0745267767 2.03042 0.05825943

4. TREND 0.1315931213 0.0359954941 3.65582 0.00195681

LIML Specification Test

Chi-Squared(4)= 30.840234 with Significance Level 0.00000330