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Title

lmcovreg3: Breusch-Pagan LM Diagonal Covariance Matrix Test after (3SLS-SURE)

Table of Contents

Syntax

Description

Saved Results

References

*** Examples

Author

Syntax

lmcovreg3

Description

lmcovreg3 computes Breusch-Pagan LM Diagonal Covariance Matrix Test after:

- (3SLS) Three-Stage Least Squares reg3 for systems of simultaneous equations.

- (SUR) Seemingly Unrelated Regression sureg for sets of equations.

- 3SLS or SURE Estimations assume:

1- Independence of the errors in each eqution or no correlations between different periods in the same equation.

2- no correlations between the errors for any of two equtions between two different periods, this is called "Intertemporal Correlation".

3- correlations may be exist between different two equations, but at the same period, and this is called "Contemporaneous Correlation".

4- SURE can be applied when there is correlations between different two equations at the same period, or if the independent variables are differnt from equation to equation.

5- If "Contemporaneous Correlation" does not exist, ordinary least squares (OLS) can be applied separately to each equation, the results are fully efficient and there is no need to estimate SURE.

Breusch-Pagan LM can test whether contemporaneous diagonal covariance matrix is 0. (Independence of the Errors), or correlated if at least one covariance is nonzero.

Ho: no Contemporaneous Correlation: Sig12 = Sig13 = Sig23 = ... = 0.

Ha: Contemporaneous Correlation: at least one Covariance is nonzero.

Saved Results

lmcovreg3 saves the following in r():

r(lmcov) LM Diagonal Covariance Matrix Test
r(lmcovp) LM Diagonal Covariance Matrix Test P-Value
r(lmcovdf) Chi2 Degrees of Freedom

References

Judge, Georege, R. Carter Hill, William . E. Griffiths, Helmut Lutkepohl, & Tsoung-Chao Lee (1988)
"Introduction To The Theory And Practice Of Econometrics",
2nd ed., John Wiley & Sons, Inc., New York, USA; 456-461.

Judge, Georege, W. E. Griffiths, R. Carter Hill, Helmut Lutkepohl, & Tsoung-Chao Lee(1985)
"The Theory and Practice of Econometrics",
2nd ed., John Wiley & Sons, Inc., New York, USA.

Examples

clear all

sysuse lmcovreg3.dta , clear

* (1) SUR Model:

sureg (y1 y2 x1 x2) (y2 y1 x3 x4)

lmcovreg3

return list

* (2) 3SLS Model:

reg3 (y1 y2 x1 x2) (y2 y1 x3 x4) , exog(x1 x2 x3 x4)

lmcovreg3

return list

. clear all
. sysuse lmcovreg3.dta , clear
. sureg (y1 y2 x1 x2) (y2 y1 x3 x4)

* Seemingly unrelated regression

. lmcovreg3
==============================================================================
* Breusch-Pagan LM Diagonal Covariance Matrix Test (sure)
==============================================================================
Ho: Diagonal Disturbance Covariance Matrix (Independent Equations)
Ho: Run OLS - Ha: Run SUR

Lagrange Multiplier Test = 0.00149
Degrees of Freedom = 1.0
P-Value > Chi2(1) = 0.96921
==============================================================================

. reg3 (y1 y2 x1 x2) (y2 y1 x3 x4) , exog(x1 x2 x3 x4)

* Three-stage least-squares regression

. lmcovreg3
==============================================================================
* Breusch-Pagan LM Diagonal Covariance Matrix Test (3sls)
==============================================================================
Ho: Diagonal Disturbance Covariance Matrix (Independent Equations)
Ho: Run OLS - Ha: Run 3SLS

Lagrange Multiplier Test = 0.99968
Degrees of Freedom = 1.0
P-Value > Chi2(1) = 0.31739
==============================================================================

Example of Breusch-Pagan LM Diagonal Covariance Matrix Test

is decribed in: [Judge, et al(1988, p.461)].

clear all
sysuse lmcovreg31.dta, replace
gen ly=ln(y)
gen lq1=ln(q1)
gen lq2=ln(q2)
gen lq3=ln(q3)
gen lp1=ln(p1)
gen lp2=ln(p2)
gen lp3=ln(p3)
sureg (lq1 lp1 ly) (lq2 lp2 ly) (lq3 lp3 ly)
lmcovreg3

lmcovreg3
==============================================================================
* Breusch-Pagan LM Diagonal Covariance Matrix Test (sure)
==============================================================================
Ho: Diagonal Disturbance Covariance Matrix (Independent Equations)
Ho: Run OLS - Ha: Run SUR

Lagrange Multiplier Test = 18.73338
Degrees of Freedom = 3.0
P-Value > Chi2(3) = 0.00031
==============================================================================

Author

Emad Abd Elmessih Shehata
Professor (PhD Economics)
Agricultural Research Center - Agricultural Economics Research Institute - Egypt
Email: emadstat@hotmail.com
WebPage: http://emadstat.110mb.com/stata.htm
WebPage at IDEAS: http://ideas.repec.org/f/psh494.html
WebPage at EconPapers: http://econpapers.repec.org/RAS/psh494.htm

LMCOVREG3 Citation

Shehata, Emad Abd Elmessih (2012)

LMCOVREG3: "Stata Module to Compute Breusch-Pagan Lagrange Multiplier Diagonal Covariance Matrix Test after (3SLS-SURE) Regressions"

http://ideas.repec.org/c/boc/bocode/s457411.html

http://econpapers.repec.org/software/bocbocode/s457411.htm

Online Help:

* Breusch-Pagan Diagonal Covariance Matrix Test:
lmcovnlsur (NL-SUR) Breusch-Pagan Diagonal Covariance Matrix Test
lmcovreg3 (3SLS-SUR) Breusch-Pagan Diagonal Covariance Matrix Test
lmcovsem (SEM-FIML) Breusch-Pagan Diagonal Covariance Matrix Test
lmcovvar (VAR) Breusch-Pagan Diagonal Covariance Matrix Test
lmcovxt Panel Data Breusch-Pagan Diagonal Covariance Matrix Test
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* (1) (3SLS-SUR) * Simultaneous Equations:
lmareg3 (3SLS-SUR) Overall System Autocorrelation Tests
lmhreg3 (3SLS-SUR) Overall System Heteroscedasticity Tests
lmnreg3 (3SLS-SUR) Overall System Non Normality Tests
lmcovreg3 (3SLS-SUR) Breusch-Pagan Diagonal Covariance Matrix
r2reg3 (3SLS-SUR) Overall System R2, F-Test, and Chi2-Test
diagreg3 (3SLS-SUR) Overall System ModeL Selection Diagnostic Criteria
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* (2) (SEM-FIML) * Structural Equation Modeling:
lmasem (SEM-FIML) Overall System Autocorrelation Tests
lmhsem (SEM-FIML) Overall System Heteroscedasticity Tests
lmnsem (SEM-FIML) Overall System Non Normality Tests
lmcovsem (SEM-FIML) Breusch-Pagan Diagonal Covariance Matrix Test
r2sem (SEM-FIML) Overall System R2, F-Test, and Chi2-Test
diagsem (SEM-FIML) Overall System ModeL Selection Diagnostic Criteria
---------------------------------------------------------------------------
* (3) (NL-SUR) * Non Linear Seemingly Unrelated Regression:
lmanlsur (NL-SUR) Overall System Autocorrelation Tests
lmhnlsur (NL-SUR) Overall System Heteroscedasticity Tests
lmnnlsur (NL-SUR) Overall System Non Normality Tests
lmcovnlsur (NL-SUR) Breusch-Pagan Diagonal Covariance Matrix Test
r2nlsur (NL-SUR) Overall System R2, F-Test, and Chi2-Test
diagnlsur (NL-SUR) Overall System ModeL Selection Diagnostic Criteria
---------------------------------------------------------------------------
* (4) (VAR) * Vector Autoregressive Model:
lmavar (VAR) Overall System Autocorrelation Tests
lmhvar (VAR) Overall System Heteroscedasticity Tests
lmnvar (VAR) Overall System Non Normality Tests
lmcovvar (VAR) Breusch-Pagan Diagonal Covariance Matrix Test
r2var (VAR) Overall System R2, F-Test, and Chi2-Test
diagvar (VAR) Overall System ModeL Selection Diagnostic Criteria
---------------------------------------------------------------------------