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Uncovered Interest Parity and Monetary Policy Near and Far from the Zero Lower Bound
Menzie ChinnUW‐Madison and
NBER
Yi ZhangUW‐Madison
European Central BankDG‐ResearchMay 26, 2015
MotivationConsider the following relationship, for advanced economy currencies and interest rates
These two combined lead to the Fama Regression
Estimates of β at different horizons
-2.0
-1.6
-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
UIP value = 1
3 mo. 6 mo. 1 yr. 5 yr. 10 yr.
Up to2000
Up to2011
US‐UK Example: Short Horizons
US‐UK Example: Short Horizons
US‐UK Example: Long Horizon
Short Horizon Regressions
Source: Chinn and Quayyum (2013)
Long Horizon Regressions
Source: Chinn and Quayyum (2013)
Long Horizon Regressions
Outline
• The Model• Calibration• Solution, far from Zero Lower Bound• Solution, near Zero Lower Bound• Concluding remarks
The Model
• New Keynesian model in the spirit of Gali (2008) and Walsh (2010)
• Assume small open economy• Key aspect is inclusion of an “error term” in uncovered interest parity
• And expectations hypothesis of term structure• Intuition: A CB Taylor rule means short rates endogenous, long rates less so
• Importance of cost, monetary policy shocks decreased importance at long horizon when ZLB binds
Households
Where Ch and Cf are Dixit-Stiglitz aggregates of home and foreign goods
Production, Price Setting, Real Exchange Rate
Calvo pricing, with 1-omega the fraction of price re-setting firms
Law of one price holds, but not purchasing power parity
Deviation from Uncovered Interest Parity
The key equation that the results center on is a particular deviation from UIP:
The uit term is not a risk premium in the conventional sense; McCallum calls it an “aggregation error”
Monetary Policy Reaction Function
The central bank follows a Taylor rule; because overall inflation depends on home goods and foreign goods, the real exchange rate change enters.
Expectations Hypothesis of the Term Structure
Summary
Summary
Calibration
• Fit to Japanese data• Assume no structural change 1975‐96• RoW constant• Three shocks, ρi=0
Closed Form Solution
c1 = 0.20c2 = 1.95c3 = ‐0.0655
Far from ZLB: UIP shock
Far from ZLB: UIP shock
Far from ZLB: UIP shock
Far from ZLB: NK Phillips Curve shock
Far from ZLB: NK Phillips Curve shock
Far from ZLB: NK Phillips Curve shock
Far from ZLB: MP shock
Far from ZLB: MP shock
Far from ZLB: MP shock
Fama Regression, Short Horizon
Fama Regression, Long Horizon
Since monetary and cost shocks are persistent, they dominate at long horizons, making fraction smaller, and hence making the plim of the coefficient closer to unity
Simulation, Near ZLB
• Method follows Holden and Patz (2012), similar to Erceg and Linde (EJEA, 2014).
• Define “random ZLB” vs. “persistent ZLB”• If the interest rate is at zero, then will likely have adjoining years at zero.
• At ZLB, the cost shock and the MP shock are treated by agents as if they are zero
• That lessens the size of those components, so the bias is less attenuated at long horizons
Simulation Method
“The method endogenously determines when the constraint will bind, and can handle constraints that may bind in multiple disjoint runs, or that may not begin to bind until long after the initial impulse. The general idea is to introduce “shadow price shocks”, which hit the bounded variables every time the constraint is violated, and “push” these variables back to zero. To ensure the solution is consistent with rational expectations, these shocks are expected by agents in advance, so they may be thought of as a kind of endogenous news shock.”
Constrained ZLB
Short Rates in Major Economies
-4
0
4
8
12
16
20
24
1980 1985 1990 1995 2000 2005 2010
CA_A3M UK_A3M JA_A3MUS_A3M SW_A3M EU_A3M
Conclusion• If there is a random shock to the UIP relationship
• The long maturity yield is determined by EHTS• And the central bank responds to exchange rate changes by leaning against the wind
• Then negative(positive) Fama coefficient at short(long) horizons can be explained
• The ZLB can attenuate this distinction as it suppresses negative innovations to monetary, cost shocks