1. Arthur CHARPENTIER - discussion on panel cointegration tests
Discussion of
Decentralisation as a constraint to Leviahan
a panel cointegration analysis
by J. Ashworth, E. Galli & F. Padovano
Arthur Charpentier
arthur.charpentier@univ-rennes1.fr
Public Economics At the Regional and Local level in Europe, May 2008
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2. Arthur CHARPENTIER - discussion on panel cointegration tests
unit root test for panel series
Classical model, Zi,t = αi + φiZi,t−1 + εi,t.
Unit root assumption is H0 : φi = 1 for all i.
∆Zi,t = αi + ρiZi,t + εi,t,
with εi,t i.i.d., with Var(εi,t) = σ2
i .
Null hypothesis, H0 : ρi = 0 for all i.
Levin & Lin (1993) , H1 : ρi = ρ = 0 for at all i.
Im, Pesaran & Shin (1997) , H1 : ρi = 0 for at least one i.
ADF t Test on all series Yi,t, X1,i,t, · · · , XM,i,t.
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3. Arthur CHARPENTIER - discussion on panel cointegration tests
from unit root to cointegration
Two integrated series Z1,t ∼ I(1) and Z2,t ∼ I(1) are cointegrated if
α1Z1,t + α2Z2,t = α
1×2
Zt ∼ I(0)
Two cointegrated series
0 50 100 150 200
−15−10−50
−4−2024
Firstseries
Secondseries
Linear combination of cointegrated series
0 50 100 150 200
−3−2−101234
Among N integrated series Y1,t, · · · , YN,t ∼ I(1), there are r cointegration
relationships if
α
r×N
Y t ∼ I(0)
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4. Arthur CHARPENTIER - discussion on panel cointegration tests
from cointegration to short/long run
• from cointegration to error-correction model.
Consider two cointegrated series, Z1,t and Z2,t such that α Zt is stationary, then
Z1,t
∼I(1)
=
α2
α1
Z2,t
∼I(1)
+ ut
∼I(0)
long-run relationship,
The associated error correction model is
∆Z1,t
∼I(0)
= γ ∆Z2,t
∼I(0)
+ α Zt
∼I(0)
+ηt short-run relationship.
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5. Arthur CHARPENTIER - discussion on panel cointegration tests
panel cointegration tests
• Pedroni (1995, 1999), Kao (1999) and Bai & Ng (2001) extended tests of Engle
& Granger (1987) (for time series)
• Larsen et al. (1998) and Groen & Kleibergen (2003) extended tests of
Johansen (1991), when r is unknown.
Yi,t = αi + β1,iX1,i,t + · · · + βM,iXM,i,t + εi,t.
=⇒ estimation by OLS, for each cross section,
Yi,t = αi + β1,iX1,i,t + · · · + βM,iXM,i,t and εi,t = Yi,t − Yi,t.
=⇒ unit root test on the residual series εi,t, e.g. ADF
εi,t = γiεi,t−1 +
Ki
t=1
γi,k∆εi,t−k + ui,t,
H0 : γi = 1 for all i = 1, · · · , N, against H1 : γi < 1 for all i = 1, · · · , N.
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6. Arthur CHARPENTIER - discussion on panel cointegration tests
comment on the empirical study
Here N = 28 (28 countries) and T = 25 (time period 1976 − 2000).
Recall that given a statistic Z to test H0 against H1,



type 1 error : α = P(reject H0|H0 is true)
type 2 error : β = P(accept H0|H0 is false)



type 1 error : reject unit root when there is
type 2 error : suppose unit root when there is not



type 1 error : accept cointegation when there is not
type 2 error : rejct cointegation when there is
Karaman ¨Orsal (2008) ran monte carlo simulations to study Pedroni’s test, and
studies α (rejection percentage), “tests are inappropriate if time dimension is
much smaller than the cross-section dimension”, here α ≈ 50%.
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7. Arthur CHARPENTIER - discussion on panel cointegration tests
from Karaman ¨Orsal (2008).
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8. Arthur CHARPENTIER - discussion on panel cointegration tests
is it necessary to seek for cointegration ?
Can we conclude that the logarithm of total public expenditures over GDP, i.e.
Yi,t, has a unit root ?
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9. Arthur CHARPENTIER - discussion on panel cointegration tests
is it necessary to seek for cointegration ?
Model (1) is Yi,t = α0 + β1,iX1,i,t + · · · + βM,iXM,i,t + εi,t.
Here are given εi,·’s. Why not plotting αi’s (or αi − α) in
Yi,t = αi + β1,iX1,i,t + · · · + βM,iXM,i,t + εi,t ?
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