325_Lecture10_Feb23

325_Lecture10_Feb23 - INFINITE-PERIOD FRAMEWORK FEBRUARY...

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1 I NFINITE- P ERIOD F RAMEWORK F EBRUARY 23, 2011 February 23, 2011 2 B ASICS Introduction ± Modern workhorse macroeconomic frameworks feature an infinite number of periods ± A more realistic (?) view of time ± Especially useful for thinking about asset accumulation and asset pricing ± The intersection of modern macro theory and modern finance theory ± Here, suppose just one real asset ± Call it a “stock” – i.e., a share in the S&P 500 ± (In Chapter 14, two nominal assets: bonds and money) ± 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 ± …so an “infinite future” (period t+ 1, period, t+ 2, period t +3, …) for which to save
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2 February 23, 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 w e a l t h ( 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 ± 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 ± 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 ) 11 1 1 tt t t tt PPP PP S ±± ± §· ² ² ¨¸ ©¹ The “defining features” of stock February 23, 2011 4 B ASICS ± Timeline of events ± Notation ± c t +1 o n s u m p t i o n i n p e r i o d t+ 1 ± P t +1 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 e a l w e a l t h ( 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 +1/end of period t ± S t +1 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 +1 ± D t +1 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 +1 ± Ⱥ t +2 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 +1 and period t +2 ± y t +1 e a l i n c o m e i n p e r i o d t +1 ( = Y t +1 / P t +1) 21 2 2 1 t t PP P ± ± ² ² The “defining features” of stock
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3 February 23, 2011 5 B ASICS Introduction ± Timeline of events ± Notation ± And so on for period t +2, t +3, etc… February 23, 2011 6 S UBJECTIVE D ISCOUNT F ACTOR Macro Fundamentals ± Infinite number of periods a more serious view of time ± Impatience potentially an issue when taking a serious view of time ± Individuals (i.e., consumers) are impatient ± All else equal, would rather have X utils today than identical X utils at some future date ± An introspective statement about the world ± An empirical statement about the world ± Subjective discount factor ± A simple model of consumer impatience ± ǃ (a number between zero and one) measures impatience ± The lower is ǃ
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325_Lecture10_Feb23 - INFINITE-PERIOD FRAMEWORK FEBRUARY...

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