Econometric Analysis of Panel Data

• Hypothesis Testing– Specification Tests• Fixed Effects vs. Random Effects

– Heteroscedasticity– Autocorrelation• Serial Autocorrelation• Spatial Autocorrelation

• More on Autocorrelation

Hypothesis Testing

• Heteroscedasticity

• Serial Correlation

• Spatial Correlation

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Hypothesis Testing

• Heteroscedasticity'

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Hypothesis TestingTest for Homoscedasticity

• If u2=0 (constant effects or pooled model), then

• LM Test (Breusch and Pagan, 1980)

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Hypothesis TestingTest for Homoscedasticity

• If u2>0 (random effects), then

• LM Tests (Baltagi, Bresson, and Pirott, 2006)

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Hypothesis TestingTest for Homoscedasticity

• Marginal LM Test

• See, Montes-Rojas and Sosa-Escudero (2011)

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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)

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x

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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, 401-417.

– Breusch, T. and A. Pagan, “A Simple Test of Heteroscedasticity and Random Coefficient Variations,” Econometrica, 47, 1979, 1287-1294.

– Montes-Rojas, G. and W. Sosa-Escudero, Robust Tests for Heteroscedasticity in the One-Way Error Components Model, Journal of Econometrics, 2011, forthcoming.

Hypothesis Testing

• Serial Correlation AR(1) in a Random Effects Model

• LM Test for Serial Correlation and Random Effects

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Hypothesis TestingTest for Serial Correlation

• LM Test Statistics: NotationsBased on OLS residuals of the restricted model (i.e. pooled model with no serial correlation)

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Hypothesis TestingTest 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)

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Hypothesis TestingTest for Serial Correlation

• Robust LM Test Statistic

• See Baltagi and Li (1995)

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Hypothesis TestingTest for Serial Correlation

• Joint LM Test Statistic for Pooled Model with Serial Correlation

• See Baltagi and Li (1995)

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Hypothesis TestingTest for Serial Correlation

• LM Test Statistic for a Fixed Effects Model

– See Baltagi, Econometric Analysis of Panel Data (2008)

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residuals of mean deviation regression

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Hypothesis TestingTest for Serial Correlation

• References– Breusch, T. and A. Pagan, “A Simple Test of Heteroscedasticity and

Random Coefficient Variations,” Econometrica, 47, 1979, 1287-1294.– Breusch, T. and A. Pagan, “The LM Test and Its Applications to Model

Specification in Econometrics,” Review of Economic Studies, 47, 1980, 239-254.

– 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), 63-100.

– Baltagi, B.H. and Q. Li, Testing AR(1) Against MA(1) Disturbances in an Error Components Model, Journal of Econometrics, 68, 1995, 133-151.

Autocorrelation

• AR(1)

• Assumptions

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Autocorrelation

• AR(1) Model Estimation (Paris-Winsten)– Begin with =0, estimate the model

– Transform variables according

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Autocorrelation

– Estimate the transformed model

– Iterate until converges

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Autocorrelation• Notational Complexity with time lags in unbalanced panel data

(Unbalanced unequal space panel data)

i t zit zit-1 z*it

1 1 z11 . (1-2)1/2 z11

1 2 z12 z11 z12 -z11

1 3 . . .

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1 5 z15 z14 z15 -z14

2 1 z21 . (1-2)1/2 z21

2 2 . . .

2 3 . . .

2 4 z24 . (1-2)1/2 z24

2 5 z25 z24 z25 -z24

3 1 . . .

3 2 . . .

3 3 z33 . (1-2)1/2 z33

3 4 . z33 .

3 5 . . .

i t zit

1 1 z11

1 2 z12

1 4 z14

1 5 z15

2 1 z21

2 4 z24

2 5 z25

3 3 z33

Autocorrelation

• Hypothesis Testing– Modified Durbin-Watson Test Statistic (Bhargava,

Franzini, Narendranathan, 1982)

– LBI Test Statistic (Baltagi-Wu, 1999)• For unbalanced unequal spaced panel data

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1 1

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i

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Example: Investment Demand

• Grunfeld and Griliches [1960]

– i = 10 firms: GM, CH, GE, WE, US, AF, DM, GY, UN, IBM; t = 20 years: 1935-1954

– Iit = Gross investment

– Fit = Market value

– Cit = Value of the stock of plant and equipment

21 ~ (0, )

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