0
Arthur CHARPENTIER - discussion on panel cointegration tests
Discussion of
Decentralisation as a constraint to Leviahan
a ...
Arthur CHARPENTIER - discussion on panel cointegration tests
unit root test for panel series
Classical model, Zi,t = αi + ...
Arthur CHARPENTIER - discussion on panel cointegration tests
from unit root to cointegration
Two integrated series Z1,t ∼ ...
Arthur CHARPENTIER - discussion on panel cointegration tests
from cointegration to short/long run
• from cointegration to ...
Arthur CHARPENTIER - discussion on panel cointegration tests
panel cointegration tests
• Pedroni (1995, 1999), Kao (1999) ...
Arthur CHARPENTIER - discussion on panel cointegration tests
comment on the empirical study
Here N = 28 (28 countries) and...
Arthur CHARPENTIER - discussion on panel cointegration tests
from Karaman ¨Orsal (2008).
7
Arthur CHARPENTIER - discussion on panel cointegration tests
is it necessary to seek for cointegration ?
Can we conclude t...
Arthur CHARPENTIER - discussion on panel cointegration tests
is it necessary to seek for cointegration ?
Model (1) is Yi,t...
Upcoming SlideShare
Loading in...5
×

Discussion

251

Published on

Published in: Technology, Economy & Finance
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
251
On Slideshare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
3
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Transcript of "Discussion"

  1. 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 1
  2. 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. 2
  3. 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) 3
  4. 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. 4
  5. 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. 5
  6. 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%. 6
  7. 7. Arthur CHARPENTIER - discussion on panel cointegration tests from Karaman ¨Orsal (2008). 7
  8. 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 ? 8
  9. 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 ? 9
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×