1. Econometric Analysis of Panel Data
Hypothesis Testing
Specification Tests
Fixed Effects vs. Random Effects
Heteroscedasticity
Autocorrelation
Serial Autocorrelation
Spatial Autocorrelation
More on Autocorrelation

2. Hypothesis Testing Heteroscedasticity Serial Correlation
Spatial Correlation

3. Hypothesis Testing
Heteroscedasticity

4. Hypothesis Testing Test for Homoscedasticity
If su2=0 (constant effects or pooled model), then
LM Test (Breusch and Pagan, 1980)

5. Hypothesis Testing Test for Homoscedasticity
If su2>0 (random effects), then
LM Tests (Baltagi, Bresson, and Pirott, 2006)

6. Hypothesis Testing Test for Homoscedasticity
Marginal LM Test
See, Montes-Rojas and Sosa-Escudero (2011)

7. Hypothesis Testing Test for Homoscedasticity
Marginal LM Test
Joint LM Test
Sum of the above two marginal test statistics (approximately)
See, Montes-Rojas and Sosa-Escudero (2011)

8. Hypothesis Testing Testing for Homoscedasticity
References
Batagi, B.H., G. Bresson, and A. Priotte, Joint LM Test for Homoscedasticity in a One-Way Error Component Model, Journal of Econometrics, 134, 2006,
Breusch, T. and A. Pagan, “A Simple Test of Heteroscedasticity and Random Coefficient Variations,” Econometrica, 47, 1979,
Montes-Rojas, G. and W. Sosa-Escudero, Robust Tests for Heteroscedasticity in the One-Way Error Components Model, Journal of Econometrics, 2011, forthcoming.

9. Hypothesis Testing Serial Correlation AR(1) in a Random Effects Model
LM Test for Serial Correlation and Random Effects

10. Hypothesis Testing Test for Serial Correlation
LM Test Statistics: Notations Based on OLS residuals of the restricted model (i.e. pooled model with no serial correlation)

11. Hypothesis Testing Test for Serial Correlation
Marginal LM Test Statistic for a Pooled Model
See Breusch and Pagan (1980)
Marginal LM Test Statistic for Serial Correlation
See Breusch and Godfrey (1981)

12. Hypothesis Testing Test for Serial Correlation
Robust LM Test Statistic
See Baltagi and Li (1995)

13. Hypothesis Testing Test for Serial Correlation
Joint LM Test Statistic for Pooled Model with Serial Correlation
See Baltagi and Li (1995)

14. Hypothesis Testing Test for Serial Correlation
LM Test Statistic for a Fixed Effects Model
See Baltagi, Econometric Analysis of Panel Data (2008)

15. Hypothesis Testing Test for Serial Correlation
References
Breusch, T. and A. Pagan, “A Simple Test of Heteroscedasticity and Random Coefficient Variations,” Econometrica, 47, 1979,
Breusch, T. and A. Pagan, “The LM Test and Its Applications to Model Specification in Econometrics,” Review of Economic Studies, 47, 1980,
Breusch, T. and L.G. Godfrey, A Review of Recent Work on Testing for Autocorrelation in Dynamic Simultaneous Models, in D.A. Currie, R. Nobay and D. Peel (eds.), Macroeconomic Analysis, Essays in Macroeconomics and Economics (Croom Helm, London),
Baltagi, B.H. and Q. Li, Testing AR(1) Against MA(1) Disturbances in an Error Components Model, Journal of Econometrics, 68, 1995,

16. Autocorrelation
AR(1)
Assumptions

17. Autocorrelation AR(1) Model Estimation (Paris-Winsten)
Begin with r=0, estimate the model
Transform variables according

18. Autocorrelation
Estimate the transformed model
Iterate until converges

19. Autocorrelation
Notational Complexity with time lags in unbalanced panel data (Unbalanced unequal space panel data) i t
zit
zit-1
z*it 1
z11 .
(1-r2)1/2 z11 2
z12
z12 -rz11 3 4
z14
(1-r2)1/2 z14 5
z15
z15 -rz14
z21
(1-r2)1/2 z21
z24
(1-r2)1/2 z24
z25
z25 -rz24
z33
(1-r2)1/2 z33 i t
zit 1
z11 2
z12 4
z14 5
z15
z21
z24
z25 3
z33

20. Autocorrelation Hypothesis Testing
Modified Durbin-Watson Test Statistic (Bhargava, Franzini, Narendranathan, 1982)
LBI Test Statistic (Baltagi-Wu, 1999)
For unbalanced unequal spaced panel data

21. Example: Investment Demand
Grunfeld and Griliches [1960]
i = 10 firms: GM, CH, GE, WE, US, AF, DM, GY, UN, IBM; t = 20 years:
Iit = Gross investment
Fit = Market value
Cit = Value of the stock of plant and equipment