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**Econometric Analysis of Panel Data**

Hypothesis Testing Specification Tests Fixed Effects vs. Random Effects Heteroscedasticity Autocorrelation Serial Autocorrelation Spatial Autocorrelation More on Autocorrelation

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**Hypothesis Testing Heteroscedasticity Serial Correlation**

Spatial Correlation

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Hypothesis Testing Heteroscedasticity

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**Hypothesis Testing Test for Homoscedasticity**

If su2=0 (constant effects or pooled model), then LM Test (Breusch and Pagan, 1980)

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**Hypothesis Testing Test for Homoscedasticity**

If su2>0 (random effects), then LM Tests (Baltagi, Bresson, and Pirott, 2006)

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**Hypothesis Testing Test 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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**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.

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**Hypothesis Testing Serial Correlation AR(1) in a Random Effects Model**

LM Test for Serial Correlation and Random Effects

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**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)

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**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)

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**Hypothesis Testing Test for Serial Correlation**

Robust LM Test Statistic See Baltagi and Li (1995)

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**Hypothesis Testing Test for Serial Correlation**

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

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**Hypothesis Testing Test for Serial Correlation**

LM Test Statistic for a Fixed Effects Model See Baltagi, Econometric Analysis of Panel Data (2008)

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**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,

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Autocorrelation AR(1) Assumptions

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**Autocorrelation AR(1) Model Estimation (Paris-Winsten)**

Begin with r=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 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

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**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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**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

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