325_Lecture19_April11

325_Lecture19_April11 - MONETARY POLICY IN THE...

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1 M ONETARY P OLICY IN THE I NFINITE- P ERIOD A NALYSIS A PRIL 11, 2011 April 11, 2011 2 B ASICS Introduction ± Extend our infinite-period framework ± Introduce money and short-term bonds into the Chapter 8 framework ± So now three types of assets (stocks, short-term bonds, money) for representative consumer to use for savings purposes ± Will allow us to think further about what the “pricing kernel” is ± Will allow us to think about connection between bond prices and stock prices ± Will allow us to think about issue of monetary neutrality (the main issue in the RBC vs. New Keynesian debate) ± i.e., does money (and thus monetary policy) have important consequences for real (i.e., consumption and real GDP) variables? ± Index time periods by arbitrary indexes t , t +1, t+ 2, etc. ± Important: all of our analysis will be conducted from the perspective of the very beginning of period t ± Sequential Lagrangian analysis (with money in the utility function)
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2 April 11, 2011 3 B ASICS Introduction ± Timeline of events ± Notation ± c t :c o n s u m p t i o n i n p e r i o d t ± P t :n o m i n a l p r i c e o f c o n s u m p t i o n i n p e r i o d t ± Y t o m i n a l i n c o m e i n p e r i o d t (“falls from the sky”) ± a t- 1 :r e a l s t o c k h o l d i n g s a t b e g i n n i n g o f p e r i o d t /end of period t -1 ± M t- 1 o m i n a l m o n e y h o l d i n g s a t b e g i n n i n g o f p e r i o d t /end of period t -1 ± B t- 1 o m i n a l b o n d h o l d i n g s a t b e g i n n i n g o f p e r i o d t /end of period t -1 Now three types of assets consumers can use for savings purposes April 11, 2011 4 B ASICS ± Timeline of events ± Notation ± c t o n s u m p t i o n i n p e r i o d t ± P t o m i n a l p r i c e o f c o n s u m p t i o n i n p e r i o d t ± Y t o m i n a l i n c o m e i n p e r i o d t (“falls from the sky”) ± a t- 1 e a l s t o c k h o l d i n g s a t b e g i n n i n g o f p e r i o d t /end of period t -1 ± M t- 1 o m i n a l m o n e y h o l d i n g s a t b e g i n n i n g o f p e r i o d t /end of period t -1 ± B t- 1 o m i n a l b o n d h o l d i n g s a t b e g i n n i n g o f p e r i o d t /end of period t -1 ± S t o m i n a l p r i c e o f a u n i t o f s t o c k i n p e r i o d t ± D t o m i n a l d i v i d e n d p a i d i n p e r i o d t by each unit of stock held at the start of t ± P b t o m i n a l p r i c e o f a b o n d i n p e r i o d t ± i t o m i n a l i n t e r e s t r a t e o n a b o n d p u r c h a s e d i n t and which pays off in t +1 ± Ⱥ t +1 e t i n f l a t i o n r a t e b e t w e e n p e r i o d t and period t +1 ± y t e a l i n c o m e i n p e r i o d t ( = Y t / P t ) Now three types of assets consumers can use for savings purposes
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3 April 11, 2011 5 B ASICS Introduction ± Timeline of events ± Notation ± c t +1 :c o n s u m p t i o n i n p e r i o d t +1 ± P t +1 :n o m i n a l p r i c e o f c o n s u m p t i o n i n p e r i o d t +1 ± Y t +1 o m i n a l i n c o m e i n p e r i o d t+ 1 (“falls from the sky”) ± a t :r e a l s t o c k h
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325_Lecture19_April11 - MONETARY POLICY IN THE...

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