Econ226_IIDF

Econ226_IIDF - 1 II Vector autoregressions A Introduction B...

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Unformatted text preview: 1 II. Vector autoregressions A. Introduction B. Normal-Wishart priors for VAR’s C. Bayesian analysis of structural VAR’s D. Identification using inequality constraints Structural model: B y t b B 1 y t " 1 B 2 y t " 2 C B p y t " p u t E u t u t " m U I n for m for m p u ft one standard deviation shock to Fed policy P t GDP price deflator y 3 t N t nonborrowed reserves y 4 t r t fed funds rate y 6 t 2 P t s u ft t for s 0,1,2,3,4,5 N t s u ft t for s 0,1,2,3,4,5 r t s u ft u for s 0,1,2,3,4,5 VAR (reduced-form) y t n 1 vector y t c o 1 y t " 1 o 2 y t " 2 C o p y t " p / t / t y t " § y t | t " 1 E / t / t U ( ' s y t s / t U ( PP U ( P lower triangular) q s y t s u ft Claim: there exists a unique ) such that q s ' s P ) ) U ) 1 3 In order to satisfy sign constraint, P t s u ft t for s 0,1,2,3,4,5 , we must have e 3 U ' s P ) t for s 0,1,2, 3,4,5 Constraints on signs for nonborrowed reserves and fed funds rate require e 4 U ' s P ) t for s 0,1,2, 3,4,5 e 6 U ' s P ) u for s 0,1,2, 3,4,5 Estimation strategy (Bayesian approach) Use noninformative Normal-Wishart priors (1) Estimate i th equation of VAR by OLS for i 1,2,..., n x t U 1, y t " 1 U , y t " 2 U ,..., y t " p U § + i ! t 1 T x t x t U " 1 ! t 1 T x t y it M ' ! t 1 T x t x t U " 1 + + 1 U , + 2 U ,..., + n U U 4 (2) Calculate residual of i th equation and sum of outer products of residuals: § / it y it " § + i U x t / t / 1 t , / 2 t , ..., / nt U n n S ! t 1 T § / t § / t U (3) For m 1,2,..., 10, 000 , generate an artificial sample of size T of n 1 vectors z t m where z t m ~ N , S " 1 and calculate the n n matrix W m ! t 1 T z t m z t m U (4) Set ( m W m " 1 (5) Generate a draw for + m from a N § + , ( m § M ' distribution (6) Generate ) m L N , I n ) ' m ) m / ¡ ) m U ) m ¢ 1/2 5 (7) Flip signs if initial shocks have wrong sign: ) 1 m ) 2 m ) 3 m ) 4 m ) 5 m ) 6 m ) 1 ' m ) 2 ' m ) 3 ' m...
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Econ226_IIDF - 1 II Vector autoregressions A Introduction B...

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