Panel Data Analysis Using GAUSS

1

Kuan-Pin LinPortland State University

Panel Data AnalysisIntroduction

Panel Data Definition Unbalanced Panel

Balanced Panel: Short Panel: Long Panel:

Panel Data Analysis Unobserved Heterogeneity

Cross Section and Time Series Correlation

, ( 1, 2,..., ; 1,..., )it it iy t T i N x,iT T i

,T N

,T N

it it i t ity u v e x

Panel Data AnalysisIntroduction

Model Representation N-first or T-first representation

Pooled Model Fixed Effects Model Random Effects Model

Asymptotic Theory N→∞, or T→∞ N→∞, T→∞ Panel-Robust Inference

Panel Data AnalysisIntroduction

The Model

One-Way (Individual) Effects: Unobserved Heterogeneity Cross Section and Time Series Correlation

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Panel Data Analysis Introduction

N-first Representation

Dummy Variables Representation

T-first Representation'

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Panel Data Analysis Introduction

Notations'

1, 1 2, 1 , 11 1 11'

1, 2 2, 2 , 22 2 22

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Pooled (Constant Effects) Model

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y u e i N t T

u u i

y u e or

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x β

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Fixed Effects Model

ui is fixed, independent of eit, and may be correlated with xit.

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t t t

u i i Nt T

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Fixed Effects Model Fixed Effects Model

Classical Assumptions Strict Exogeneity: Homoschedasticity: No cross section and time series correlation:

Extensions: Panel Robust Variance-Covariance Matrix

( | , ) 0itE e u X2( | , )it eVar e u X

2( | , ) e NTVar e u X I

( | , )Var e u X

Random Effects Model Error Components

ui is random, independent of eit and xit.

Define the error components as it = ui + eit

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it i it

yu e i N t T

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Random Effects Model

Random Effects ModelClassical Assumptions

Strict Exogeneity

X includes a constant term, otherwise E(ui|X)=u.Homoschedasticity

Constant Auto-covariance (within panels)

( | ) 0, ( | ) 0 ( | ) 0it i itE e E u E X X X

2 2 '( | )i e T u T TVar ε X I i i

2 2

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Random Effects Model

Random Effects ModelClassical Assumptions (Continued)

Cross Section Independence

Extensions:Panel Robust Variance-Covariance Matrix

2 2 '( | )( | )i e T u T T

N

VarVar

ε X I i iε X Ω I

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

it i it it itI F C

Example: Output Function Cobb-Douglas Output Function

i = 30 provinces; t = 11 years: 1996-2006 ln(GDP)it = Log real GDP ln(L)it = Log Labor Employment ln(K)it = Log Capital Stock

( ) ( ) ( )it i it it itln GDP ln L ln K

References B. H. Baltagi, Econometric Analysis of Panel Data, 4th

ed., John Wiley, New York, 2008. W. H. Greene, Econometric Analysis, 7th ed., Chapter

11: Models for Panel Data, Prentice Hall, 2011. C. Hsiao, Analysis of Panel Data, 2nd ed., Cambridge

University Press, 2003. J. M. Wooldridge, Econometric Analysis of Cross Section

and Panel Data, The MIT Press, 2002.