Panel Data Analysis Using GAUSS
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Panel Data Analysis Using GAUSS
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Kuan-Pin LinPortland State University
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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
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it it i t ity u v e x
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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
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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'
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Pooled (Constant Effects) Model
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Fixed Effects Model
ui is fixed, independent of eit, and may be correlated with xit.
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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
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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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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)
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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
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ε X I i iε X Ω 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
it i it it itI F C
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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
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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.