help: lmareg3 dialog:

Title

lmareg3: Overall System Autocorrelation Tests after (3SLS-SURE) Regressions

Syntax

lmareg3

Description

lmareg3 computes overall system autocorrelation, after:

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

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

lmareg3 calculates Harvey and Guilkey autocorrelation LM tests:

- Harvey LM test, see Judge et al(1985, p.494) eq.12.3.45.

- Guilkey LM test, see Judge et al(1985, p.494) eq.12.3.46.

- Durbin-Watson DW test.

1- Harvey Single Equation LM test = N(Rho_i) ~ Chi2(1)
Ho: No Autocorrelation in eq. # : Pij=0

Q
2- Harvey Overall System LM test = N [ Sum(Rho_i) ] ~ Chi2(Q)
i=1

3- Guilkey Overall System LM test = R'[ inv(Sig) # E1'E1 ] R ~ Chi2(Q^2)
Ho: No Autocorrelation in the Overall System: P11 = P22 = PMM = 0

where
N = Number of Observations.
Q = Number of Equations.
Rho_i = Autoregressive Coefficient of eq. i
E1 = Lagged Residuals Matrix [(N-1)xQ].
R = Vector of Rho Coefficients.
Sig = Sigma hat Matrix.

Saved Results

lmareg3 saves the following in r():

Scalars

r(rho_#) Rho Value for eq.#

r(lmh_#) Durbin-Watson Single Equation Test for eq.#

r(lmh_#) Harvey Single Equation LM Test for eq.#

r(lmhp_#) Harvey Single Equation LM Test P-Value for eq.#

r(lmh) Harvey Overall System Autocorrelation LM test

r(lmhp) Harvey Overall System Autocorrelation LM test P-Value

r(lmg) Guilkey Overall System Autocorrelation LM test

r(lmgp) Guilkey Overall System Autocorrelation LM test P-Value

Examples

clear all

sysuse lmareg3.dta , clear

* (1) SUR Model:

sureg (y1 x1 z1) (y2 x2 z2) (y3 x3 z3) (y4 x4 z4)

lmareg3

return list

* (2) 3SLS Model:

reg3 (y1 x1 z1) (y2 x2 z2) (y3 x3 z3) (y4 x4 z4)

lmareg3

return list

* If you want to use dialog box: Press OK to compute lmareg3

db lmareg3

. clear all
. sysuse lmareg3.dta , clear
. reg3 (y1 x1 z1) (y2 x2 z2) (y3 x3 z3) (y4 x4 z4)
. lmhreg3

=================================================
* System Autocorrelation Tests (3sls)
=================================================
*** Single Equation Autocorrelation Tests:
Ho: No Autocorrelation in eq. #: Pij=0

Eq. y1 : Harvey LM Test = 4.8859 Rho = 0.2443 P-Value > Chi2(1) 0.0271
Eq. y2 : Harvey LM Test = 0.0028 Rho = 0.0001 P-Value > Chi2(1) 0.9577
Eq. y3 : Harvey LM Test = 4.9830 Rho = 0.2492 P-Value > Chi2(1) 0.0256
Eq. y4 : Harvey LM Test = 4.4273 Rho = 0.2214 P-Value > Chi2(1) 0.0354
------------------------------------------------------------------------------
Eq. y1 : Durbin-Watson DW Test = 0.9323
Eq. y2 : Durbin-Watson DW Test = 1.9417
Eq. y3 : Durbin-Watson DW Test = 1.0017
Eq. y4 : Durbin-Watson DW Test = 1.0510
------------------------------------------------------------------------------
*** Overall System Autocorrelation Tests:
Ho: No Overall System Autocorrelation: P11 = P22 = PMM = 0

- Harvey LM Test = 14.2991 P-Value > Chi2(4) 0.0064
- Guilkey LM Test = 22.6759 P-Value > Chi2(16) 0.1227
------------------------------------------------------------------------------

References

Guilkey, David K. (1974)
"Alternative Tests for a First-Order Vector Autoregressive Error Specification",
Journal of Econometrics, vol.2(1); 95-104.

Guilkey, David K. (1975)
"A Test for the Presence of First-Order Vector Autoregressive Errors When Lagged Endogenous Variables Are Present",
Econometrica, vol.43, July; 711-117.

Guilkey, David K. Peter Schmidt (1973)
"Estimation of Seemingly Unrelated Regression Equations with First-Order Autoregressive Errors",
{it:Journal of the American Statistical Association, vol. 68, September; 642-647.

Harvey, Andrew C. (1982)
"A Test of Misspecification for Systems of Equations",
Discussion Paper No. A31, London School of. Economics Econometrics Programme, London, England.

Harvey, Andrew C. (1990)
"The Econometric Analysis of Time Series",
2nd Edition, MIT Press Books, The MIT Press, edition 2, volume 1, number 026208189x.

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; 494.

Author

Emad Abd Elmessih Shehata
Assistant Professor
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

lmareg3 Citation

Shehata, Emad Abd Elmessih (2011)

LMAREG3: "Stata Module to Compute Overall System Autocorrelation Tests after (3SLS-SURE) Regressions"

http://ideas.repec.org/c/boc/bocode/s457345.html

http://econpapers.repec.org/software/bocbocode/s457345.htm

Online Help:

lmareg lmareg2 lmareg3 (if installed).