Spatial Econometric Analysis Using GAUSS

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Spatial Econometric Analysis Using GAUSS

• 8
• Kuan-Pin LinPortland State University

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Panel Data AnalysisA Review

• Model Representation
• N-first or T-first representation
• Pooled Model
• Fixed Effects Model
• Random Effects Model
• Asymptotic Theory
• N?8, or T?8
• N?8, T?8
• Panel-Robust Inference

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Panel Data AnalysisA Review

• The Model
• One-Way (Individual) Effects
• Unobserved Heterogeneity
• Cross Section and Time Series Correlation

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Panel Data AnalysisA Review

• N-first Representation
• Dummy Variables Representation

• T-first Representation

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Panel Data AnalysisA Review

• 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

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Random Effects Model

• Error Components
• ui is random, independent of eit and xit.
• Define the error components as eit ui eit

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Random Effects Model

• Random Effects Model
• Classical Assumptions
• Strict Exogeneity
• X includes a constant term, otherwise E(uiX)u.
• Homoschedasticity
• Constant Auto-covariance (within panels)

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Random Effects Model

• Random Effects Model
• Classical Assumptions (Continued)
• Cross Section Independence
• Extensions
• Panel Robust Variance-Covariance Matrix

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Fixed Effects Model Estimation

• Within Model Representation

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Fixed Effects Model Estimation

• Model Assumptions

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Fixed Effects Model Estimation OLS

• Within Estimator OLS

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Fixed Effects Model Estimation ML

• Normality Assumption

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Fixed Effects Model Estimation ML

• Log-Likelihood Function
• Since Q is singular and Q0, we maximize

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Fixed Effects Model Estimation ML

• ML Estimator

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Fixed Effects ModelHypothesis Testing

• Pool or Not Pool
• F-Test based on dummy variable model constant or
  zero coefficients for D w.r.t F(N-1,NT-N-K)
• F-test based on fixed effects (unrestricted)
  model vs. pooled (restricted) model

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Fixed Effects ModelHypothesis Testing

• Based on estimated residuals of the fixed effects
  model
• Heteroscedasticity
• Breusch and Pagan (1980)
• Autocorrelation AR(1)
• Breusch and Godfrey (1981)

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Random Effects Model Estimation GLS

• The Model

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Random Effects Model Estimation GLS

• GLS

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Random Effects Model Estimation GLS

• Feasible GLS
• Based on estimated residuals of fixed effects
  model

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Random Effects Model Estimation ML

• Log-Likelihood Function

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Random Effects Model Estimation ML

• where

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Random Effects Model Estimation ML

• ML Estimator

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Random Effects ModelHypothesis Testing

• Pool or Not Pool
• Test for Var(ui) 0, that is
• For balanced panel data, the Lagrange-multiplier
  test statistic (Breusch-Pagan, 1980) is

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Random Effects ModelHypothesis Testing

• Pool or Not Pool (Cont.)

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Random Effects ModelHypothesis Testing

• Fixed Effects vs. Random Effects

Estimator Random Effects E(uiXi) 0 Fixed Effects E(uiXi) / 0
GLS or RE-OLS (Random Effects) Consistent and Efficient Inconsistent
LSDV or FE-OLS (Fixed Effects) Consistent Inefficient Consistent Possibly Efficient
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Random Effects ModelHypothesis Testing

• Fixed effects estimator is consistent under H0
  and H1 Random effects estimator is efficient
  under H0, but it is inconsistent under H1.
• Hausman Test Statistic

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Random Effects ModelHypothesis Testing

• Alternative Hausman Test
• Estimate the random effects model
• F Test that g 0

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Random Effects ModelHypothesis Testing

• Heteroscedasticity

• H0 ?20 ?10
• H0 ?10 ?20
• H0 ?20, ?10

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Random Effects ModelHypothesis Testing

• Heteroscedasticity (Cont.)
• Based on random effects model with
  homoscedasticity

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Random Effects ModelHypothesis Testing

• Heteroscedasticity (Cont.)

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Random Effects ModelHypothesis Testing

• Heteroscedasticity (Cont.)
• Baltagi, B., Bresson, G., Pirotte, A. (2006)
  Joint LM test for homoscedasticity in a one-way
  error component model. Journal of Econometrics,
  134, 401-417.

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Random Effects ModelHypothesis Testing

• Autocorrelation AR(1)
• Based on random effects model with no
  autocorrelation
• LM test statistic is tedious, see
• Baltagi, B., Li, Q. (1995) Testing AR(1) against
  MA(1) disturbances in an error component model.
  Journal of Econometrics, 68, 133-151.

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Random Effects ModelHypothesis Testing

• Joint Test for AR(1) and Random Effects
• Based on OLS residuals
• Marginal Test for AR(1) Random Effects

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Random Effects ModelHypothesis Testing

• Robust LM Tests for AR(1) and Random Effects
• Because

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Panel Data AnalysisAn Example U. S. Productivity

• The Model (Munnell 1988)

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Panel Data AnalysisAn Example U. S. Productivity

• Productivity Data
• 48 Continental U.S. States, 17 Years1970-1986
• STATE State name,
• ST_ABB State abbreviation,
• YR Year, 1970, . . . ,1986,
• PCAP Public capital,
• HWY Highway capital,
• WATER Water utility capital,
• UTIL Utility capital,
• PC Private capital,
• GSP Gross state product,
• EMP Employment,
• UNEMP Unemployment rate

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U. S. ProductivityBaltagi (2008) munnell.1,
munnell.2

• Panel Data Model ln(GSP) b0 b1 ln(Public)
  b2ln(Private) b3ln(Labor)
  b4(Unemp) e

Fixed Effects s.e Random Effects s.e
b1 -0.026 0.029 0.003 0.024
b2 0.292 0.025 0.310 0.020
b3 0.768 0.030 0.731 0.026
b4 -0.005 0.001 -0.006 0.001
b0 2.144 0.137
F(47,764) 75.82 F(47,764) 75.82 LM(1) 4135 LM(1) 4135
Hausman LM(4) 905.1 Hausman LM(4) 905.1 Hausman LM(4) 905.1 Hausman LM(4) 905.1
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Panel Data AnalysisAnother Example China
Provincial Productivity

• Cobb-Douglass Production Function
• ln(GDP) a b ln(L) g
  ln(K) e

Fixed Effects s.e. Random Effects s.e
b 0.30204 0.078 0.4925 0.078
g 0.04236 0.0178 0.0121 0.0176
a 2.6714 0.6254
F(29,298) 158.81 F(29,298) 158.81 LM(1) 771.45 LM(1) 771.45
Hausman LM(2) 48.4 Hausman LM(2) 48.4 Hausman LM(2) 48.4 Hausman LM(2) 48.4
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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, 6th ed.,
  Chapter 9 Models for Panel Data, Prentice Hall,
  2008.
• 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.