Econometric Analysis of Panel Data

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Econometric Analysis of Panel Data

• Panel Data Analysis
• Linear Model
• One-Way Effects
• Two-Way Effects
• Pooled Regression
• Classical Model
• Extensions

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Panel Data Analysis

• Linear Model Representation

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Linear Panel Data Model (1)

• One-Way (Individual) Effects

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Linear Panel Data Model (1)

• One-Way (Time) Effects

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Linear Panel Data Model (1)

• Two-Way Effects

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Linear Panel Data Model (2)

• One-Way (Individual) Effects

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Linear Panel Data Model (2)

• One-Way (Time) Effects

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Linear Panel Data Model (2)

• Two-Way Effects

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Panel Data Analysis

• Between Estimator
• If ,then the pooled or
  population-averaged model is more efficient.

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Panel Data Analysis

• Linear Pooled (Constant Effects) Model

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Pooled Regression Model

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

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Pooled Regression Model

• Extensions
• Weak Exogeneity
• Heteroschedasticity

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Pooled Regression Model

• Extensions
• Time Series Correlation (with cross section
  independence for short panels)

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Pooled Regression Model

• Extensions
• Cross Section Correlation (with time series
  independence for long panels)

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Pooled Regression Model

• Extensions
• Cross Section and Time Series Correlation

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Alternative Pool Regression Models

• Between (Group Means) Estimator
• First-Difference Estimator
• Within (Group Mean Deviations) Estimator

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Pooled Regression OLS

• Classical Model Estimation (OLS)
• Variance estimator is inconsistent
  because of heteroscedasticity and autocorrelation.

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Pooled Regression OLS

• Panel-Robust Variance-Covariance Matrix

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Pooled Regression GLS

• The Model
• Generalized Least Squares (GLS)
• If cross sections are independent (short panels)
• where is the consistent estimator of

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Pooled Regression GLS

• Heteroscedasticity
• Cross Section Correlation
• Time Series Correlation

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Pooled Regression GLS

• Examples of Time Series Correlation
• Equal-Correlation
• AR(1)
• Stationary(1)
• Nonstationary(1)

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Model Extensions

• Time-invariant regressors
• Random regressors
• Lagged dependent variables
• Dynamic models

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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

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Example Investment Demand

• Pooled Model (Population-Averaged Model)
• Classical OLS
• Panel-Robust OLS
• Feasible GLS
• Heteroscedastcity
• Autocorrelation