Download Exchange rates under sticky prices: The Dornbusch (1976

Exchange rates under sticky prices:
The Dornbusch (1976) overshooting model
(Obstfeld and Rogoff, 1996, chapter 9)
Some stylized facts:
1) Exchange rates (s) are more volatile than prices or relative prices (p/p*)
2,6
2,4
2,2
2
1,8
1,6
1,4
1,2
1
0,45
BP/USD exchange rate
0,4
BP/US relative prices
0,35
0,3
0,25
0,2
1975
1980
1985
1990
1995
2) Exchange rate changes (log[st/st-1]) are more volatile than inflation differentials
(log[pt/pt-1]- log[pt*/p*t-1])
30
15
0
-15
Inflation differential US-UK
Exchange rate changes USD-BP
-30
1975
1980
1985
1990
1995
⇒ The volatility of the real exchange rate (log[s+p*-p]) is similar to that of the
nominal exchange rate
An important note: In the monetary model prices and exchange rates should display close
comovements – unless the shocks in the economy are real (i.e. in competitiveness)...
BUT: REAL EXCHANGE RATES ARE LESS VOLATILE UNDER FIXED
THAN UNDER FLOATING RATES: SO, REAL SHOCKS ARE NOT A
PROBABLE CAUSE OF VARIABILITY!!
We need exchange rates to be more volatile than prices
under a floating rate setup.
A solution is offered by the Dornbusch (1976) sticky price model.
Basic characteristics:
- sticky prices
- no microfoundations (i.e. no current account and welfare issues) included
Building blocks of the Dornbusch (1976) sticky price model.
(small capital letters denote variables in logs – except of the interest rate)
- Uncovered Interest Parity (UIP)
•
S
= st +1 − st = it +1 − i *
S
- Money demand function and monetary sector equilibrium
mt − pt = φy t − ηit +1
- Real exchange rate determination (PPP need not always hold!)
qt = st + p * − pt
- Domestic output determination
y td = y + δ ( st + p * − pt − q )
y = ‘natural’ rate of output
q = ‘equilibrium’ real exchange rate consistent with full employment
Note: A rise in e or p* relative to p that triggers domestic demand can be
justified by:
- shifting demand from foreign tradables to domestic non-tradables
- the country has monopoly power in the tradable sector
- Price level determination: Inflation-expectation augmented Phillips curve:
inflation = excess demand + expected inflation (or productivity growth)
•
P
= pt +1 − pt = ψ ( y td − y ) + ( pt +1 − pt )
P
where pt ≡ ( st + p * − q ) . By the last definition and since p* and
pt +1 − pt = ψ ( y td − y ) + (et +1 − et )
q
are constant:
Conceptual solution of the model
Market clearing:
- Asset market clears always
- Goods market may not clear
Under fully flexible prices, we would have yd = y = y and q= q .
BUT: Under sticky prices, the price level is pre-determined (responds slowly)
⇒ Unanticipated shocks lead to excess demand or supply
Graphical solution of the model
Substituting in the money demand and the price eqs we have (if p* =
mt= m ):
y
= i* and
•
Goods market:
Q
= qt +1 − qt = −ψδ (qt − q ) with ψδ<1
Q
Asset market:
s
(1 − φδ )qt (φδq + m )
S
= st +1 − st = t −
−
S
η
η
η
•
S
Q& = 0
S& = 0
φδq + m
q
q
q& = 0 line: vertical at q , as the adjustment in the goods market is independent of
nominal factors
s& = 0 line: upward sloping if φδ<1
⇒ The system is saddle path stable
Steady-state solution of the system: Q& = 0 and S& = 0
⇒ q =e −m ⇔ p=m
In the steady state, all monetary variables are determined independently of real
variables, i.e. there is full dichotomy between the real and the financial sector of
the economy.
Question: What happens after a monetary policy change (an increase in the money
supply)?
In the long-run (steady-state) a rise in the money supply from m = m ′ will lead to
an analogous rise in the price level and the exchange rate, i.e.
m − m ′ = p − p′ = s − s ′
BUT: in the short-run, prices are sticky.
S& ′ = 0
S
Q& = 0
S& = 0
s0
s′
s
q
q0
q
The rise from m = m ′ moves the S& = 0 locus upwards to S& ′ = 0 .
But: prices are sticky and the price level remains at p .
So, the exchange rate moves (jumps) to point (s0 , q0) on the new saddle path.
In the transition period we have s 0 > s ′
and the exchange rate overshoots its long-run level.
Logic behind overshooting:
The money balance equation states that m − pt = φy t − ηit +1 ⇒ so a rise in
real money balances (m – p), since p is fixed.
m
raises
Proof by contradiction:
1) If s jumped to
δ ( s ′ − s ) = δ (m ′ − m )
s′
(no overshooting), the output would rise by
⇒ Money demand would rise by φδ (m ′ − m ) .
Assuming that φδ<1
⇒ rise in money demand < rise in money supply
⇒ (it < i*) to restore equilibrium, which would imply an appreciation of st via
UIP (contradiction!)
2) If
s
jumped by less than (m ′ − m ) , i.e. ( s ′ − s ) < (m ′ − m ) , then:
it would have to fall and st to appreciate, i.e. move away from the steady state
(contradiction!)
THEREFORE:
3) OVERSHOOTING IS THE ONLY POSSIBILITY, I.E. ( s ′ − s ) > (m ′ − m ) TO
ACCOUNT FOR THE FALL IN i DUE TO THE DISEQUILIBRIUM IN THE
MONEY MARKET AND THE EXPECTED APPRECIATION.
- Note: By the differential equation for the exchange rate, the larger η
(interest rate elasticity of money demand), the larger the fall in i needed to
restore equilibrium, and thus the larger the expected appreciation and
overshooting.
The case for undershooting
- Overshooting depends critically on the condition φδ<1
- If δ (the response of output to exchange rate depreciation) and/or φ (income
elasticity of money demand) are large, then we may have φδ>1 and the
S& = 0 locus may downward sloping
S
Q& = 0
φδq ′ + m
s′
φδq + m
S& ′ = 0
S& = 0
q
q
An unanticipated rise in m raises s by less than proportionately (undershooting)
- Note: In both cases (overshooting and undershooting) the dynamics of real
variables (output, real exchange rate) are the same. The nominal
depreciation implies a real depreciation (with sticky prices), aggregate
demand rises and output is above its steady state value y .
Fiscal policy
The model can be extended to evaluate the effects of fiscal policy. In such a case,
the determination of output is given by:
y td = y + δ ( st + p * − pt − q ) + g
where g = domestic public expenditure. The equation of motion for q is now:
•
Q
= qt +1 − qt = −ψδ (qt − q ) + g
Q
Graphical solution of the model
S
Q& ′ = 0
Q& = 0
S& = 0
s
s′
φδq + m
q′
q
q
Steady-state result of a rise in government expenditure:
- real exchange rate appreciation (the exchange rate falls from s to s ′ )
- exports are reduced by the amount of the rise in government expenditure
The nominal exchange rate s jumps to the new saddle path (reducing exports), and
continues to appreciate; there is no overshooting. The rise in demand triggers the
price mechanism, and as p rises, the real exchange rate continues to appreciate
further towards a new equilibrium, thereby further reducing exports.
- Note: This ‘crowding-out’ result in the composition of output is similar to
that of the Mundell-Fleming model.