LECTURE 25: Dornbusch Overshooting Model
Starting point of the Dornbusch model:
Although adjustment in financial markets is instantaneous, adjustment in goods markets is slow.
Interpretation:
โข prices are sticky:
โ canโt jump at a moment in time
โ but adjust gradually โข in response to excess demand:
โ ๐ = โฮฝ(๐ โ ๐ ).
โข One theoretical rationale:
โ Calvo overlapping contracts.
We saw that 100 or 200 years of data can reject a random walk for Q,
i.e., detect regression to the mean.
Q
Dornbusch overshooting model
PPP holds only in the Long Run, for ๐ . In the SR, S can be pulled away from ๐ .
Consider an increase in real interest rate r i โ ฯ e (e.g., due to sudden M contraction; as in UK or US 1980, or Japan 1990)
Domestic assets more attractive
Appreciation: S
until currency โovervaluedโ relative to ๐ => investors expect future depreciation se .
When se is large enough to offset i - i*, that is the overshooting equilibrium.
Dornbusch Overshooting Model
Financial markets
See table for evidence of
regressive expectations.
interest differential pulls currency above
LR equilibrium.
i โ i* = ๐ ๐ + Regressive expectations
๐ ๐ = -ฮธ (s-๐ )
UIP
We could stop here.
(s-๐ ) = - 1
ฮธ(i โ iโ)
โse = a โ ฯ (s - ๐ ).
Forecasts from survey data show a tendency for appreciation today to induce expectations of depreciation in the future, back toward long-run equilibrium.
Some evidence that expectations are indeed formed regressively:
Dornbusch Overshooting Model
Financial markets
=> Inverse relationship between s & p to satisfy financial market equilibrium.
What determines i & i* ?
LR
SR
Money market equilibrium: The change in m is one-time: Subtract
equations:
โข
]
(s-๐ ) = - 1
ฮธ(i โ iโ)
m - p = ฯy - ฮปi
๐ - ๐ = ฯ๐ฆ - ฮป๐ ๐ = m;
๐ฆ = y; & ๐ = i* m - ๐ = ฯy - ฮปi*
=> (p - ๐ ) = ฮป(i โ iโ) = - ฮป ฮธ (s-๐ ) =
its The
Dornbusch Diagram
In the SR, we need not be on the goods market equilibrium line (PPP),
but we are always on the financial market equilibrium line (inverse proportionality between p and s):
B
C
If ฮธ is high, the line is steep, and there is not much overshooting.
A
PPP holds in LR.
Because P is tied down in the SR, S overshoots its new LR equilibrium.
Experiment: a one-time monetary expansion
- Old p
- New p
? | overshooting |
| |
๐ = ๐ โ1
ฮปฮธ(p-๐ ).
(p - ๐ ) = - ฮปฮธ (๐ โ ๐ ).
(m/p) โ => i โ
Sticky p =>
Excess Demand at C causes P to rise over time until reaching LR equilibrium at B.
In the instantaneous overshooting equilibrium (at C), S rises more-than-proportionately to M to equalize expected returns.
How do we get from SR to LR? I.e., from inherited P, to PPP?
The experiment: a permanent โm
We now know how far s and p have moved along the path from C to B , after t years have elapsed.
[SEE APPENDIX I]
=>
=>
Goods markets
Sticky p
P responds gradually to excess demand:
Solve differential equations for p & s:
= overshooting from a monetary expansion
at point C
Neutrality at point B
LR PPP ๐ = ๐ โ ๐ โ
LR ฮ๐ = ฮ๐ = ฮm.
SR ฮ๐ = (1 +
1
ฮป๐)ฮm.
๐ = - ฮฝ (p - ๐ )
p t = ๐ + (p0 - ๐ ) exp(- ฮฝ t).
๐ = - ฮฝ (s - ๐ )
s t = ๐ + (s0 - ๐ ) exp(- ฮฝ t).
Now consider a special case: rational expectations
The actual speed with which s moves to LR equilibrium:
matches the speed it was expected to move to LR equilibrium:
in the special case: ฮธ = ฮฝ.
In the very special case ฮธ = ฮฝ = โ, we jump to B at the start -- the flexible-price case.
=> Overshooting results from instant adjustment in financial markets combined with slow adjustment in goods markets: ฮฝ < โ.
๐ = - ฮฝ (s - ๐ )
๐ ๐ = - ฮธ (s - ๐ ).
SUMMARY OF FACTORS DETERMINING THE EXCHANGE RATE
(1) LR monetary equilibrium:
(2) Dornbusch overshooting: SR monetary fundamentals pull S away from ๐ , in proportion to the real interest differential.
(3) LR real exchange rate ๐ can change, e.g., Balassa-Samuelson or oil shock.
(4) Speculative bubbles: S can wander away from all fundamentals.
๐ = (๐
๐โ) ๐ =
๐/๐โ
๐ฟ( ,)/๐ฟโ(,)๐ .
How do we get from SR to LR? I.e., from inherited P, to PPP?
Appendix I: (1) Solution to Dornbusch differential equations
at point B
at point C
P responds gradually to excess demand:
Solve differential equation for p:
Use inverse proportion-ality between p & s:
Use it again:
Solve differential equation for s:
Neutrality
= overshooting from a monetary expansion
We now know how far s and p have moved along the path from C to B , after t years have elapsed.
โข Endogenous y (pp. 1171-75 at end of RD 1976 paper)
โข Bubble paths
โข More complicated M supply processes
โ Random walk
โ Expected future change in M
โ Changes in steady-state M growth, gm = ฯ : โข Regressive expectations: ๐ ๐ โก (๐ ๐ - ฯ๐ + ฯโ๐ )
= - ฮธ (q - ๐ ) (1)
โข UIP: i โ i* = ๐ ๐ (2)
โข => (q - ๐ ) = - 1
๐ [(i-ฯ๐) โ (i*-ฯโ๐) ]
(2) Extensions of Dornbusch overshooting model
I.e., real exchange rate depends on real interest differential.
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Appendix II: How well do the models hold up?
(1) Empirical performance of monetary models
At first, the Dornbusch (1976) overshooting model had some good explanatory power. But these were in-sample tests.
In a famous series of papers, Meese & Rogoff (1983) showed all models did very poorly out-of-sample. In particular, the models were โout-performed by the random walk,โ at least at short horizons. I.e., todayโs spot rate is a better forecast of next monthโs spot rate than are observable macro fundamentals.
Later came evidence monetary models were of some help in forecasting exchange rate changes, especially at long horizons. E.g., N. Mark (1995): a basic monetary model beats RW at horizons of 4-16 quarters, not just in-sample, but also out-of-sample.
At short horizons of 1-3 months the random walk has lower prediction error than the monetary models.
At long horizons, the monetary models have lower prediction error than the random walk.
(2) Forecasting
Nelson Mark (AER, 1995): a basic monetary model can beat a Random Walk at horizons of 4 to 16 quarters,
not just with parameters estimated in-sample but also out-of-sample.
Cerra & Saxena (JIE, 2012), too, find it in a 98-currency panel.
Forecasting, continued
Possible Techniques for Predicting the Exchange Rate
Models based on fundamentals โข Monetary Models
โข Monetarist/Lucas model โข Overshooting model
โข Other models based on economic fundamentals โข Portfolio-balance modelโฆ
Models based on pure time series properties โข โTechnical analysisโ (used by many traders)
โข ARIMA, VAR, or other time series techniques (used by econometricians)
Other strategies
โข Use the forward rate; or interest differential; โข random walk (โthe best guess as to future spot rate
is todayโs spot rateโ)