+-------+ ----+ 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. 4- 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) Lagrange Multiplier LM Test r(lmcovp) Lagrange Multiplier LM 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 Assistant Professor Agricultural Research Center - Agricultural Economics Research Institute - Eg > ypt 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"
Online Help:
lmcovreg3, r2reg3, lmareg3, lmhreg3, lmnreg3. (if installed).