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Econ226_IVD - IV Markov-switching models A Introduction B...

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1 IV. Markov-switching models A. Introduction B. Bayesian analysis of Markov-switching models C. State-space models with Markov switching D. Panel models with Markov switching y nt ± growth of employment in state n for quarter t y nt ± ) n ² + n s nt ² / nt s nt ± 1 when state n is in recession for quarter t s nt ± 0 for expansion
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2 NBER National Recession: 1980:Q1 - 1980:Q3
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3 NBER National Recession: 1980:Q1 - 1980:Q3 NBER National Recession: 1980:Q1 - 1980:Q3 NBER National Recession: 1980:Q1 - 1980:Q3
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4 NBER National Recession: 1980:Q1 - 1980:Q3 NBER National Recession: 1980:Q1 - 1980:Q3 NBER National Recession: 1980:Q1 - 1980:Q3
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5 NBER National Recession: 1980:Q1 - 1980:Q3 NBER National Recession: 1981:Q3 - 1982:Q4
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6 NBER National Recession: 1981:Q3 - 1982:Q4 NBER National Recession: 1981:Q3 - 1982:Q4 NBER National Recession: 1981:Q3 - 1982:Q4
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7 NBER National Recession: 1981:Q3 - 1982:Q4 NBER National Recession: 1981:Q3 - 1982:Q4 NBER National Recession: 1981:Q3 - 1982:Q4
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8 NBER National Recession: 1981:Q3 - 1982:Q4 NBER National Recession: 1981:Q3 - 1982:Q4
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10
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14 y t ± y 1 t , y 2 t ,..., y Nt   U N ± 48 s t ± s 1 t , s 2 t ,..., s Nt   U ) ± ) 1 , ) 2 ,..., ) N   U + ± + 1 , + 2 ,..., + N   U y t ± ) ² + © s t ² / t / t | s t L N 0 , ( s t    p s t ± h m | s t " 1 ± h n   ± p nm ( s t   ± @ 1 2 0 C 0 0 @ 2 2 C 0 B B B B 0 0 C @ N 2 ± (
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15 Could in principle use identical algorithm to calculate f y 1 ,..., y T | ) , + , ¡ p nm ¢ , ( .    Problem: ¡ p nm ¢ is 2 N 2 N   2 N ± 2.8 10 14 Solution: restrict s t ± £ h 1 , h 2 ,..., h K ¤ K ³³ 2 N aggregate (unobserved) regime z t when z t ± k , s t ± h k y t | z t ± k L N m k , (   for k ± 1,..., K m k ± ) ² + © h k Pr z t ± j | z t "
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