PANEL INDEX VAR MODELS: SPECIFICATION, ESTIMATION - Ivie

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Appendix In this appendix we report the expressions of the parameters of the posterior distributions derivedinsection3.1.Theyare: ˆδ t = ˆV t [(Ω −1 ⊗ σ 2 I k ) Ξθ t + X tΩ −1 Y t ] ˆV t =[(Ω −1 ⊗ σ 2 I k )+X tΩ −1 X t ] −1 ẑ 1 = T (1 + k + z 1 ) −1 ˆQ 1 = Q −1 1 + t U tUt/σ 2 + t E tEt ˆθ o = ˆΨ Ψ −1 Pµ +(I − C) Bo −1 t ˜θ t /ξ t ˆΨ = Ψ −1 +(I − C) Bo −1 (I − C) t 1/ξ −1 t ˆµ = ˆΣ µ P Ψ −1 θ o + Σ −1 µ ¯µ ; ˆΣ µ = P Ψ −1 P + Σ −1 µ ẑ 2 = NGKT + z 2 ; ˆQ 2 = Q 2 + t u t (Ω ⊗ I k ) −1 u t ẑ 3 = T + z 3 ˆQ 3 = Q 3 + t θ 1 t − θt−1 ∗1 2 /ξ t ẑ 4i = T + z 4i ; ˆQ 4i = Q −1 4i + t ẑ o =1+z o ; ˆQ o = Q −1 o θ i t − θt−1 ∗i θ i t − θt−1 ∗i −1 /ξ t +(θ o − Pµ)(θ o − Pµ) −1 where notation θ i t refers to the i-th sub vector of θ t . −1 30
References [1] Binder, M, Hsiao, C. and Pesaran H. (2001) Estimation and Inference in Short Panel Vector Autoregressions with Unit Roots and Cointegration, University of Maryland, manuscript. [2] Canova, F. (1993b) ”Modelling and Forecasting Exchange Rates using a Bayesian Time varying coefficient model”, Journal of Economic Dynamics and Control, 17, 233-262. [3] Canova, F. and Ciccarelli, M. (1999) ”Forecasting and Turning Point Prediction in a Bayesian Panel <strong>VAR</strong> Model”, UPF working paper 443, available at www.econ.upf.es. [4] Chamberlin, G. (1983) ”Panel Data” in Griliches, Z. and Intrilligator, M. (eds.) The Handbook of Econometrics, II, North Holland. [5] Chib S. and E. Greenberg (1995), ‘Hierarchical Analysis of SUR Models with Extensions to Correlated Serial Errors and Time-Varying Parameter Models’, Journal of Econometrics, 68, 409—431. [6] Cogley, T. and Sargent, T. (2002) Drift and Volatilities: Monetary Policy and Output in Post WWII US, Stanford University, working paper. [7] Cumba Mendez, G., Kapetanios, G. Smith R., Weale, M. (2001) ”An automatic leading indicator of economic activity in forecasting GDP growth for European countries” Econometric Journal 4(1), 37-57. [8] Forni,M., Hallin,M, Lippi, M. and Reichlin, L. (2000), ”The Generalized Dynamic- Factor Model: identification and estimation”, TheReviewofEconomicsandStatistics, 82(4) 540-54. [9] Gallant, R., Rossi, P. and Tauchen, G. (1993) ”Nonlinear Dynamic Structures”, Econometrica, 61, 871-907. [10] Geweke, J. (2000) Simulation Based Bayesian Inference for Economic Time Series, in Mariano, R. Shuermann, M. Weeks (eds.) Simulation Based Inference in Econometrics: Methods and Applications, Cambridge University Press. [11] Granger, C. (2001) Evaluation of forecasts in Hendry, D. and Ericsson, N. (eds.) Understanding Economic Forecasts, MIT Press. [12] Holtz—Eakin D., W. Newey and H. Rosen (1988), Estimating vector autoregressions with panel data, Econometrica, 56(6) 1371—1395. 31
Page 1 and 2: PANEL INDEX VAR MODELS: SPECIFICATI
Page 3 and 4: 1 Introduction There has been a gro
Page 5 and 6: on predictive Bayes factors, to exa
Page 7 and 8: e represented, for example, as: δ
Page 9 and 10: units. In (11) the variance of the
Page 11 and 12: B o1 | Y T ẑ 3 , ψ −Bo1 ∼ IG
Page 13 and 14: where v t = E t + X t u t has covar
Page 15 and 16: Convergence of the Gibbs sampler ke
Page 17 and 18: using its out-of-sample prediction
Page 19 and 20: Iterating on (23) we have δ t+τ =
Page 21 and 22: to those of these three countries,
Page 23 and 24: Figure 2: Testing interdependencies
Page 25 and 26: Figure 4: Fixed effects Evolution o
Page 27 and 28: inflation is at the upper edge of t
Page 29: 7 Conclusions This paper attempted

PANEL INDEX VAR MODELS: SPECIFICATION, ESTIMATION - Ivie

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