Chapter 5
Dynamic Panel Model
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Objectives
(1) Introduce about Dynamic Panel Model
(2) Fixed and Random Effects Estimation
(3) Instrumental Variable Estimation (IV approach) (Anderson and
Hsiao, 1982)
(4) 2SLS, Generalized Method of Moment (GMM) approach (Arenallo
and Bond, 1985)
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5.1 Introduction
Linear dynamic panel data models include lag dependent variables as
covariates along with the unobserved effects, fixed or random, and
exogenous regressor
Notes: The presence of lagged dependent variable as a regressor
incorporates the entire history of it, and any impact of xit on yit is
conditioned on this history.
We consider a dynamic panel model, in the sense that it contains (at
least) one lagged variables. For simplicity, let us consider
yit = γ1yit-1+β’itxit +αi*+ uit (5.2)
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p p
j t j j t j
j
i
*
it 0 it i t it i it
1 j 1
y ) x u xy
u (5.1
y
yit = γ1yit-1+β’itxit +αi*+ uit (5.2)
Eq. (5.2) requires that |γ | <1
yit = γ1yit-1+αi*+ uit= γ0 + γ1yit-1+ αi + uit (5.3)
Assumptions on random disturbance are the following:
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i
2 2
i i i i it i j
it
2 2
it it it u
i
i
t
t j
it 1
i
s
it 1 0
About ,
E 0, ,V E , ,E x 0, ,E 0
About u ,
E u 0, ,V u E u , ,E u n
E
i
u y
u 0 for
/
j
0
a
/
s
E y
d t
By setting t = 1, 2,… and so on, the autoregressive process can be
expressed in the following way:
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0 0 0
2 0 1 2 0 1 0 1 0 0 2
2
0 0 1 1 1 0 1 1 2
1
1 1
0 1 1 1 1 1 0 1 ,
( 1)
0
.............
1 ... 1 ...
i i i i
i i i i i i i i
t
t
i
i i i i i
t
t t j
it i i i t j
j
y y u
y u u
1 1 1
0 1 1 1 0 1 ,
0 0 0
t t t
j j t j
it i i i t j
j j j
O
y u
r
y
2 2 2
1
1 0 1 1 1 0 1 , 1
0 0 0
t t t
j j t j
it i i i t j
j j j
T r
y y u
he efore