Speci cation tests and analysis of covariance Linear unobserved e ects panel data models

Speci?cation tests and analysis of covariance
Linear unobserved e⁄ects panel data models
Random coe¢ cients models
Chapter 1. Linear Panel Models and Heterogeneity
Master of Science in Economics - University of Geneva
Christophe Hurlin, UniversitØ d OrlØans
UniversitØ d?OrlØans
January 2010
C. Hurlin Panel Data EconometricsSpeci?cation tests and analysis of covariance
Linear unobserved e⁄ects panel data models
Random coe¢ cients models
Introduction
The outline of the chapter:
1 Speci?cation tests and analysis of covariance
2 Linear unobserved e⁄ects panel data models
3 Fixed or random methods?
4 Fixed-E⁄ects methods: Least Squares dummy variable
approach
5 Random e⁄ects methods
6 Heterogeneous panels: random coe¢ cients models
C. Hurlin Panel Data EconometricsSpeci?cation tests and analysis of covariance
Speci?cation tests
Linear unobserved e⁄ects panel data models
Application: strikes in OECD
Random coe¢ cients models
Speci?cation tests and analysis of covariance
Section 1.
Speci?cation tests and analysis of
covariance
C. Hurlin Panel Data EconometricsSpeci?cation tests and analysis of covariance
Speci?cation tests
Linear unobserved e⁄ects panel data models
Application: strikes in OECD
Random coe¢ cients models
Speci?cation tests and analysis of covariance
A linear model commonly used to assess the e⁄ects of both
quantitative and qualitative factors is postulated as
0y = α +β x +εi,t i,t i,t i,ti,t
where8i = 1, ..,N,8t = 1, ..,T
α and β = (β ,β , ...,β ) are 11 and 1K vectors ofit 1it 2it Kit
parameters that vary across i and t,
x = (x , ...,x ) is a 1K vector of exogenous variables,it 1it Kit
u is the error term.it
C. Hurlin Panel Data EconometricsSpeci?cation tests and analysis of covariance
Speci?cation tests
Linear unobserved e⁄ects panel data models
Application: strikes in OECD
Random coe¢ cients models
Speci?cation tests and analysis of covariance
Three aspects of the estimated regression coe¢ cients can be
tested:
1 the homogeneity of regression slope coe¢ cients
2 they ofion intercept coe¢ cients.
3 the time stability of parameters (slopes and constants). We
will not consider this issue (not speci c to panel data models)
here.
C. Hurlin Panel Data EconometricsSpeci?cation tests and analysis of covariance
Speci?cation tests
Linear unobserved e⁄ects panel data models
Application: strikes in OECD
Random coe¢ cients models
Speci?cation tests and analysis of covariance
We assume that parameters are constant over time, but can vary
across individuals.
0y = α +β x +εi,t i i,t i,ti
Three types of restrictions can be imposed on this model.
Regression slope coe¢ cients are identical, and intercepts are not
(model with individual / unobserved e⁄ects).
0y = α +β x +εi,t i i,t i,t
Regression intercepts are the same, and slope coe¢ cients are not
(unusual).
0y = α+β x +εi,t i,t i,ti
Both slope and intercept coe¢ cients are the same (homogeneous
/ pooled panel).
0y = α+β x +εi,t i,t i,t
C. Hurlin Panel Data EconometricsSpeci?cation tests and analysis of covariance
Speci?cation tests
Linear unobserved e⁄ects panel data models
Application: strikes in OECD
Random coe¢ cients models
Speci?cation tests and analysis of covariance
De nition
An heterogeneous panel data model is a model in which all
parameters (constant and slope coe¢ cients) vary accross
individuals.
De nition
An homogeneous panel data model (or pooled model) is a
model in which all parameters (constant and slope coe¢ cients) are
common
C. Hurlin Panel Data EconometricsSpeci?cation tests and analysis of covariance
Speci?cation tests
Linear unobserved e⁄ects panel data models
Application: strikes in OECD
Random coe¢ cients models
Speci?cation tests and analysis of covariance
Speci?cation Tests
C. Hurlin Panel Data EconometricsSpeci?cation tests and analysis of covariance
Speci?cation tests
Linear unobserved e⁄ects panel data models
Application: strikes in OECD
Random coe¢ cients models
Speci?cation tests and analysis of covariance
Figure: Hsiao (2003)
1TestH:a =ab =b "i˛[1,N]0 i i
1 1
H rejetée H vraie0 0
2TestH : b =b "i˛[1,N] y =a+b'x +e0 i i,t i,t i,t
2 2
H rejetée H vraie0 0
3TestH : a =a"i˛[1,N]0 iy =a +b'x +ei,t i i i,t i,t
3 3
H vraie H rejetée0 0
y =a+b'x +e y =a +b'x +ei,t i,t i,t i,t i i,t i,t
C. Hurlin Panel Data EconometricsSpeci?cation tests and analysis of covariance
Speci?cation tests
Linear unobserved e⁄ects panel data models
Application: strikes in OECD
Random coe¢ cients models
Speci?cation tests and analysis of covariance
Lemma
Under the assumption that the ε are independently normallyit
2distributed over i and t with mean zero and variance σ , F testsε
can be used to test the restrictions postulated
C. Hurlin Panel Data Econometrics