Discussion

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

[email protected]

Public Economics At the Regional and Local level in Europe, May 2008

1


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) = σ2i .

Null hypothesis, H0 : ρi = 0 for all i.

Levin & Lin (1993) , H1 : ρi = ρ 6= 0 for at all i.

Im, Pesaran & Shin (1997) , H1 : ρi 6= 0 for at least one i.

ADF t Test on all series Yi,t, X1,i,t, · · · , XM,i,t.

2


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′1×2Zt ∼ I(0)

Two cointegrated series

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4

Firs

t ser

ies

Sec

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serie

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Linear combination of cointegrated series

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Among N integrated series Y1,t, · · · , YN,t ∼ I(1), there are r cointegrationrelationships if

α′r×N

Y t ∼ I(0)

3


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

α1Z2,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.

4


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 ofJohansen (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.

5


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, andstudies α (rejection percentage), “tests are inappropriate if time dimension ismuch smaller than the cross-section dimension”, here α ≈ 50%.

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from Karaman Orsal (2008).

7


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 ?

8


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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