Transcript The IS Curve and Aggregation

The IS Curve: Derivation and
Aggregation
CCBS/HKMA May 2004
The IS Curve - Some history
• Developed by Keynes (1936)
• Made famous by Hicks’ IS-LM framework
• Tool for macroeconomists during 1950s to
1970s
• With rational expectations revolution,
approach seemed to fall out of favour
• Recent literature (McCallum, Rotemberg,
Woodford, etc) has resurrected it
The IS curve - a reminder!
• Based on principle investment = saving
• An equilibrium condition since throughout
the curve investment = saving
• In its simplest form it results in a
relationship between output and the rate of
interest
The IS curve - reminder!
• Constructed with expressions for consumption
(C), investment (I), government expenditure (G)
and exports (X) and imports (Z)
• C and Z depend on income (+): key parameters are
marginal propensities
• I depends on the interest rate (-) and income (+):
coefficient on rate is slope of IS curve
• G is exogenous
The IS-LM (&AS) framework
• Derivation of the liquidity = money curve gives us
equilibrium in the money market
• The LM and IS curves lead to the aggregate
demand schedule
• Together with an expression for aggregate supply
based on the labour market, we have a description
of the economy
• Easy, convenient and flexible framework, useful
for policy-makers
IS-LM: Out of favour
• McCallum and Nelson (1997) give 6 ‘failures’:
–
–
–
–
–
–
1. IS-LM analysis presumes a fixed, rigid price level
2. No distinction between real and nominal rates
3. Only 2 assets; money and bonds
4. Only short-run, no steady states
5. Capital stock fixed
6. Not derived using microfoundations => Lucas
Critique
• Rational Expectations revolution: Move away
from IS-LM (although equivalent expressions
were still used!)
IS-(LM): Back in favour!
• From the mid 1990s some authors have claimed
that an IS-looking schedule, together with an
interest rate rule and an aggregate supply schedule
can explain an economy’s dynamics
• LM schedule not needed as interest rate rule pins
money market equilibrium down
• ‘Monetary policy without money’
• Plus this can be useful to policy-makers
IS derivation
• Strongly micro-founded
• Take a Rotemberg-Woodford (1997) or
McCallum-Nelson (1999) framework:
1. Agents are consumers as well as producers
2. Imperfect competition: agents cannot affect
prices; downward sloping demand curves
3. Agents maximise lifetime utility subject to
constraint that all lifetime expenditure =
lifetime resources
IS derivation
• Problem: 

max Et  
 j 0
subject to
j
uC
i
t j


; t  j   y
1
 1


i
i
Ct    ct z   dz 
0

i
t j
; t  j

 1
, 1



i 
i
Et  t ,t  j St  j   Et  t ,t  j pt  j (i) yt  j  Tt  j   Ati
 j 0

 j 0

where

1


1
i
i
S t  Pt Ct , Pt    pt z  dz 
0


1
1




IS derivation
• FOCs
 
i
t 2
Et uc C
;t  2
 E 
i
t 2
t
  t ,t  j   
i
t
j
i
t j
• Define Rt  Et  t ,t 1 
• Then we can write
1
  Et Rt 
i
t
i
t 1

Pt  2

IS derivation
• Assumption: all agents have identical initial
wealth, and can insure against income risk
(ie no precautionary saving!) thus ignore i
superscripts
• log-linear approximation and solving
forward gives expression for interest rates


l
ˆ
ˆ
t  rt   Et Rˆ t  j   t  j 1
j 0

IS derivation
• A log-linear approximation of FOC for C:


l
~E C
ˆ
ˆ


C

E
r
t
t 2
t 2
t t 2
• where σ is elasticity of substitution and C is the
certainty equivalent level of consumption that
guarantees a constant level of marginal utility
• Assumption: aggregate demand given by Y=C+G
IS derivation
• Log-linearise aggregate demand:
~
ˆ
ˆ
Yt  sC Ct  Gt ,
C
sC 
Y
• Use FOC for C to get IS curve
Yˆt   1 Et 2 rˆtl  Gˆ t   ~ sC
~
ˆ
Gt  Gt  sC Et 2Ct
Interpretation
• (Negative) slope of IS curve given by:
elasticity of substitution and share of
consumption in aggregate demand
• Expectations important
• Long-rate enters the IS, not the short rate
• ‘Aggregate block’: IS, long-rate expression
and monetary policy rule (say a Taylor rule)
Useful or useless?
• Difficult to derive yet beautiful. But does it serve
any purpose? Why do we use it?
• A next step is to calibrate the model and check
whether it matches aggregate data
• To do this need to identify exogenous shocks,
estimate structural parameters (or impose
numbers!)
• If one gets a close approximation to the data it is
possible to do policy experiments to examine
impact of monetary policy
Useful or Useless?
• So mechanics not too straight-forward but
nonetheless rich and may serve as a good
benchmark
• Model based on many assumptions and some of
the structural parameters have to imposed
• Model may match time series data, but will the
model hold at all time periods? (eg are the
assumptions made correct?)
• => Lucas’ Critique revisited?
• Furher (1997) argues so
Some of the assumptions made
• Agents can insure themselves against income risk
(no precautionary saving)
• All agents have identical initial wealth (no
considerations about the wealth distribution)
• Agents live forever, no life-cycle considerations
(implications for an ageing economy?)
• Capital markets are perfect ( liquidity constraints)
• Functional form of aggregate demand
• Interest rate rule can be ad hoc
Precautionary saving
• If there is income risk, the level of wealth (and
therefore the capital stock) should be higher
• The consumption rule will be concave leading to
aggregation problems. Using a ‘representative’
agent may not lead to ‘representative’ conclusions
• Evidence on the latter point mixed: Carroll (2001)
argues this is important, Gourinchas (2000) argues
not that quantitatively important
• Carroll points out that the distribution of wealth
important
Life-cycle considerations
• Theory: young dis-save, mid-age save, old
dis-save
• Response to shocks likely to be different
• Implications for capital stock?
• Ignores age composition of the economy
Perfect capital markets
• Not everyone can borrow at a constant interest rate
• Credit supply normally upward sloping
• But it has been noticed that when companies’
balance sheets healthy, these can borrow at more
favourable terms: financial accelerator effect
• This effect can also be found for households
• Effect of financial liberalisation
• Interactions with liquidity constraints?
Aggregate demand
• No role for an external sector
• Is this a good assumption for your
economy?
• What is the role of the government sector?
• This is likely to complicate the model
• If the model becomes more complex, will it
be able to match time series data?
External sector: Svensson
• Svensson includes an external sector; other
approaches see Clarida, Gali and Gertler or
McCallum and Nelson
• See Batini Haldane (1999) for a UK model that
includes the external sector
• What needs to be modified in the previous set up?
• We will need to modify all the expressions (IS,
long-rate expression, policy rule, AS)
• Why?
External sector: Svensson
• Consumption now made up of domestic and foreign goods
(modify utility and price and expenditure aggregators)
• Consumption will depend on the exchange rate (modified
Euler equation)
• Inflation now made of domestic and foreign prices
• Resource constraint now made of domestic and foreign
consumption of domestically produced goods
• Real long rate now depends on inflation that is determined
by domestic and foreign prices
External sector: Svensson
• Thus IS depends on (modified) real rates,
government/shocks and the exchange rate
• Production must serve domestic and foreign markets thus
depends on the exchange rate
• Wages ‘home determined’
• Probability of changing prices exogenous, not determined
by foreign competition
• Problem set as before; yields an expression for inflation as
a function of expectations, the exchange rate, the gap and
future inflation
• Two more equations needed: exchange rate plus an
expression for inflation (and foreign equations!)
Other issues
• Data measurement:
– How do you measure output gap?
– What interest rate do you use?
– What price index to use? GDP deflator, CPI?
•
•
•
•
•
Is there a role for money?
What expression for the exchange rate condition?
What exchange rate data?
Homogeneity in equations
Econometric techniques: IV (endogeneity), GMM
(forward looking variables and RE)
Other issues
• Functional forms:
– Role for habit formation?
– Deviations from Cobb-Douglas production functions?
•
•
•
•
Specific role for labour market and sticky wages?
Role for other transmission mechanism?
Log-linearisation of the model?
Around what steady state?
Conclusions
• Model examined is interesting and can give us
plenty of insights
• Role of expectations and shocks very important
for policy makers
• But before going away to develop a simple model
one needs to think about one’s economy
• Use variables and equations that will give you the
results you want!