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- 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. 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. 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. 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. 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. 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. Arthur CHARPENTIER - discussion on panel cointegration tests from Karaman ¨Orsal (2008). 7
- 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. 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

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