Testing Panel Data Regression Models with Spatial Error Correlation



2.5 LR Test for Ha: λ = ¾2 = 0

We also compute the Likelihood ratio (LR) test for Ha: A = ¾2l = 0.  Estimation of the

unrestricted log-likelihood function is obtained using the method of scoring. The details of
the estimation procedure are available upon request from the authors. Let
A°, A, b and b
denote the unrestricted maximum likelihood estimators and let Bb = INAW and u = yX0b,
then the unrestricted maximum log-likelihood estimator function is given by

NT         1                                    1

Lu =       ln2¼¾° ~n InljTAIN + (BA0IA)-1 j] + (T — 1) ln B —   .l ti§-1^;    (2.21)

2            2                                        2¾°

see Anselin (1988), where §b is obtained from (2.8) with Bb replacing B and Ab replacing A: But
under the null hypothesis
Ha, the variance-covariance matrix reduces to U = u = ¾°IτN
and the restricted maximum likelihood estimator of β is ~~ols , so that ~ = y X,∕~ols
are the OLS residuals and ¾° = U0U=ΝT. Therefore, the restricted maximum log-likelihood
function under
Haa is given by

NT        1

Lr = —in ln 2¼¾° — ..2 u ~∙                                               (2.22)

2            2¾°

Hence, the likelihood ratio test statistic for Haa : A = ¾2p = 0 is given by

LRJ = 2(LuLr);                                                            (2.23)

and this should be asymptotically distributed as a mixture of Â2 given in (2.20) under the
null hypothesis.

2.6 Conditional LM Test for Had: λ = 0 (assuming ¾2 > 0)

When one uses LM2; given by (2.16), to test Hac : A = 0; one implicitly assumes that the
random region effects do not exist. This may lead to incorrect decisions especially when
¾2
is large. To overcome this problem, this section derives a conditional LM test for spatially
uncorrelated disturbances assuming the possible existence of random regional effects. The
null hypothesis for this model is
Had : A = 0 (assuming ¾2p > 0). Under the null hyphothesis,
the variance-covariance matrix reduces to
a = ¾2pJT IN + ¾2°INT . It is the familiar form
of the one-way error component model, see Baltagi(1995), with
-1 = (¾2)-1(Jτ IN) +
(
¾°)-1(Et   IN), where ¾2 = iμ + ¾°; and Et = ItJt. Using derivations analogous

to those for the joint LM-test, see Appendix A.1, we obtain the following LM test for Had vs
H1d,



More intriguing information

1. Beyond Networks? A brief response to ‘Which networks matter in education governance?’
2. SOME ISSUES CONCERNING SPECIFICATION AND INTERPRETATION OF OUTDOOR RECREATION DEMAND MODELS
3. Draft of paper published in:
4. The Clustering of Financial Services in London*
5. The name is absent
6. Behavioural Characteristics and Financial Distress
7. The name is absent
8. Can we design a market for competitive health insurance? CHERE Discussion Paper No 53
9. AGRIBUSINESS EXECUTIVE EDUCATION AND KNOWLEDGE EXCHANGE: NEW MECHANISMS OF KNOWLEDGE MANAGEMENT INVOLVING THE UNIVERSITY, PRIVATE FIRM STAKEHOLDERS AND PUBLIC SECTOR
10. Conflict and Uncertainty: A Dynamic Approach
11. The name is absent
12. Imperfect competition and congestion in the City
13. Constrained School Choice
14. Clinical Teaching and OSCE in Pediatrics
15. The role of statin drugs in combating cardiovascular diseases
16. Estimating the Technology of Cognitive and Noncognitive Skill Formation
17. The name is absent
18. Fertility in Developing Countries
19. The name is absent
20. ROBUST CLASSIFICATION WITH CONTEXT-SENSITIVE FEATURES