Transcript The Information-Technology Revolution and the Stock Market

The Information-Technology
Revolution and the Stock Market
Jeremy Greenwood and Boyan Jovanic
AER 1999
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A simple model (a la Lucas 1978)
Simple exchange economy: many infinitely lived
agents, and equally many “trees”, each tree yielding
a “dividend” (output that goes to the owner) of dt
at each period t.
The (stock market) price of a tree at time zero:
Po 
2
t  U ' ( yt ) 

d
t 0  
t

U ' ( y 0 ) 
Lucas model – cont.
if d t  1 for all t :
Po 
t U ' (1) 

t 0  

1

U ' (1)  1  
Notice that P0 is also the ratio: stock market
value/output (S/GDP) since output=1.
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An (expected) tech shock
News arrive at t=0 that a fraction x of existing
trees will die at date T, and will be replaced by
equally many better trees, yielding an output of
1+z. Thus output from T on will be:
yt  (1  x )  x(1  z )  1  xz
Output over time is therefore,
for t  T  1
1
yt  
1  xz for t  T
The new trees will not trade in the stock market
until they actually appear at T.
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Two types of trees traded in the
stock market, before T
Type-1 tree – dies at T, liquidation value of
zero; before T its price is,
T t
1 
P1,t 
1 
Type-2 tree – lives forever. It stock market
value:
2 ,t
P
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Type-2 trees
Define,
U ' (1  xz ) 

1

 U ' (1) 
1

T t
P2,t  (1   )


1 
1 
1
1
T t

1   (1   ) 
1 
1 
P2,t  P1,t
T t

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
Stock market value before T
Pt  xP1,t  (1  x ) P2,t 

1
T t
T t

(1   )    (1  x )
1 
Recall that,

P2,t  P1,t
Hence if x goes up, overall market value goes
down.
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Stock market value: comparative statics (for t<T)
Pt
 0,
x
Pt
 0,
z
Pt
 0,
T
Pt
0
t
Pt decreases with x:
(i) more trees are expected to be replaced by trees
that are not yet in the market (type 1);
(ii) higher x increases consumption in the future,
hence lowering U’: alpha down, P2 down.
Pt decreases with z: same as (ii)
Pt increases with T: longer life of present trees,
thus their (present) value goes up (recall beta<1,
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hence if T goes to infinity, max value).
Stock market value after T
At date T new trees pop up and start to be traded.
Output per tree, hence also consumption and
dividends rise permanently to (1 + xz). Hence,
 Pt
* 
Pt  1  xz
1 

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for t  T  1
for t  T
Stock market to output ratio
 Pt

*
Pt  1  xz ,
1 

 Pt
Pt 
 1
yt 
1  
*
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for t  T-1
1

yt  
1  xz for t  T

for t  T-1
for t  T
Stock Market value relative to GDP
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Stock Market Value to GDP Ratio from
GPT HT model
S falls faster than GDP in phase 1,
but starts recovering before phase 2
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Actual S/GDP
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Comments on S/GDP
• Big innovations may at first (and for quite a
while) reduce overall Stock Market Value: the
appearance of the new GPT means that the old
one will soon be obsolete, and these are bad
news!
• In the GJ model cannot trade in the new “trees”
• In HT can trade but the new firms are making
zero profits; the old firms have constant profits
over the first phase, but their horizon is
shrinking!
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1968 Incumbents (“old trees”) vs. all firms
“old tree” firms
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The rise of Nadaq firms
The 1968 incumbents
did badly, entrants did
very well ~ 20 years later
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Winners and Losers in IT
IBM, Burroughs, Honeywell,
NCR, Sperry Rand, DEC,
Data General
Apple, Compaq, Dell, Gateway,
Microsoft, Novel, Oracle, AOL,
Yahoo, etc.
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