meese rogoff redux

Meese-Rogoff Redux:Micro-Based

Exchange-Rate ForecastingBy MARTIN D. D. EVANS AND RICHARD K. LYONS

SHIEH AND HSIEH

International Economic

INTRODUCTION

• Present a micro-based model

• Compare with standard macro model and random walk

• Longer-horizon forecasting

• R.M & K.R.（1983）benchmark

Meese-Rogoff Redux : Micro-Based Exchange-Rate Forecasting

INTRODUCTION

• Exchange-rate dynamics from expectational surprises

• Result that the micro-based model better

• Macro model will never explain exchange rate

• Not orthogonal to the evolving real economy


MEESE and ROGOFF 1983

S= 𝑎0 + 𝑎1 𝑚 − 𝑚 + 𝑎2 𝑦 − 𝑦 + 𝑎3 𝑟𝑠 − 𝑟𝑠 +

𝑎4 𝜋𝑐 − 𝜋𝑐 + 𝑎5𝑇𝐵 + 𝑎5 𝑇𝐵 + 𝑢

logarithm of the dollar price of foreign currency

logarithm of the ratio of the U.S. money supply to the foreign money supply

logarithm of the ratio of U.S. to foreign real income

short-term interest rate differential

expected long-run inflation differentia

cumulated U.S. and foreign trade balances

𝑟𝑠

𝜋

𝑦

𝑚

𝑠

𝑇𝐵


CONTENTS

1.Forecasting Exchange Rates

2.Forecasting 4 Models

3.Macro

4.Micro

5.Empirical Analysis

6.Conclusions

1.Forecasting Exchange Rates

Why are future changes in exchange rates so hard to forecast ?

𝑆𝑡 = (1 − 𝑏) 𝑖=0∞ 𝑏𝑖𝐸𝑡𝑓𝑡+𝑖 (1)

𝑆𝑡 Log nominal exchange rate

𝑏 Discount factor

𝐸𝑡

𝑓𝑡+𝑖 Current macro fundamentals

Exchange rate

Forecasting Exchange Rates



𝑆𝑡 = (1 − 𝑏) 𝑖=0∞ 𝑏𝑖𝐸𝑡𝑓𝑡+𝑖 (1)

𝑆𝑡 = 𝐸𝑡𝑓𝑡 +𝑏

1 − 𝑏𝐸𝑡∆𝑆𝑡+1

∆S𝑡+1 =1−𝑏

𝑏𝑆𝑡 − 𝐸𝑡𝑓𝑡 + 𝜀𝑡+1 (2)

𝑆𝑡 = E𝑡𝑓𝑡

𝜀𝑡+1 ≡ 1 − 𝑏

𝑖=0

∞

𝑏𝑖 E𝑡+1 − 𝐸𝑡 𝑓𝑡+𝑖+1 (3)


∆𝑓𝑡 = ∅∆𝑓𝑡−1 + 𝑢 (4)

𝑆𝑡 − 𝑓𝑡 = ∅ 𝑆𝑡−1 − 𝑓𝑡−1 +𝑏∅

1 − 𝛽∅𝑢𝑡

𝜀𝑡+1 =1

1 − 𝑏∅𝑢𝑡+1

∆𝑆𝑡+1=1 − 𝑏

𝑏(𝑆𝑡 − 𝑓𝑡 + 𝜀𝑡+1)



1 > ∅ > 0 𝑆𝑡 = E𝑡𝑓𝑡

2.Forecasting 4 Model

Marco or Micro ?

• UIP • Fama

• Micro1 • Micro2

∆𝑺𝒕+𝟏 = 𝒂𝟎 + 𝒂 𝒊𝒕 − 𝒊𝒕∗ + 𝜺𝒕+𝟏 ∆𝑺𝒕+𝟏 = 𝒂𝟎 + 𝒂 𝒊𝒕 − 𝒊𝒕

∗ + 𝜺𝒕+𝟏

∆𝑆𝑡+1 = 𝜌 + 𝑖𝑡 − 𝑖𝑡∗ + 𝜀𝑡+1 ∆𝑆𝑡+1 = 𝜂 0 + 1 − 𝜂 𝑖𝑡 − 𝑖𝑡

∗ + 𝜀𝑡+1

∆𝑺𝒕+𝟏 = 𝒂𝟎 + 𝒂𝑿𝒕𝑨𝑮𝑮 + 𝒆𝒕+𝟏

∆𝑺𝒕+𝟏 = 𝒂𝟎 +

𝒋=𝟏

𝟔

𝒂𝒋𝑿𝒋,𝒕𝑫𝑰𝑺 + 𝒆𝒕+𝟏

𝑎0 = 𝜌 , 𝑎 = 1 𝑎0 = 𝜂0 , 𝑎 = 1 − 𝜂


3.Macro Model

The Money-Income And Taylor model

1.the discount factor b is very close to unity

2. Information about future fundamentals arrives simultaneously

to all agents, who in turn revise their forecasts for fundamentals

in unison

Macro Models


𝑓𝑡 = 𝑚𝑡 −𝑚𝑡∗ − 𝑟 𝑦𝑡 − 𝑦𝑡

∗ + 𝑞𝑡 − 𝛼𝜌𝑡

𝑓𝑡 ≡ 𝑝𝑡 − 𝑝𝑡∗ −

1

𝜑0[𝜌𝑡 + 𝜑1 𝑦𝑡

𝑔− 𝑦𝑡

∗𝑔+ 𝜑2(𝜋𝑡 − 𝜋𝑡

∗)]

∆𝑆𝑡+1 → S𝑡 − 𝑓𝑡

∆𝑆𝑡+1 = 𝑖𝑡 − 𝑖𝑡∗ + 𝜌𝑡 + 𝜀𝑡+1

Macro Models


𝑖𝑡 − 𝑖𝑡∗ + 𝜌𝑡 =

1 − 𝑏

𝑏(𝑆𝑡 − 𝐸𝑡𝑓𝑡)

∆S𝑡+1 =1−𝑏

𝑏𝑆𝑡 − 𝐸𝑡𝑓𝑡 + 𝜀𝑡+1 (2)

∆S𝑡+1 = 𝑖𝑡 − 𝑖𝑡∗ + 𝜌𝑡 + 𝜀𝑡+1 (5) UIP


Macro Models

∆𝑺𝒕+𝟏 = 𝒂𝟎 + 𝒂 𝒊𝒕 − 𝒊𝒕∗ + 𝜺𝒕+𝟏

𝑎0 = 𝜌 , 𝑎 = 1

∆𝑆𝑡+1 = 𝜌 + 𝑖𝑡 − 𝑖𝑡∗ + 𝜀𝑡+1

∆𝑺𝒕+𝟏 = 𝒂𝟎 + 𝒂 𝒊𝒕 − 𝒊𝒕∗ + 𝜺𝒕+𝟏

𝑎0 = 𝜂0 , 𝑎 = 1 − 𝜂

∆𝑆𝑡+1 = 𝜂 0 + 1 − 𝜂 𝑖𝑡 − 𝑖𝑡∗ + 𝜀𝑡+1

UIP Fama


Macro Models

4.Micro Model

Aggregate order flow and Disaggregate order flow

𝑆𝑡 = (1 − 𝑏) 𝑖=0∞ 𝑏𝑖𝐸𝑡𝑓𝑡+𝑖 (1)

𝑆𝑡 Log nominal exchange rate

𝑏 Discount factor

𝐸𝑡𝑚

𝑓𝑡+𝑖 Current macro fundamentals

Expectations conditioned on market-marker’s information at t


A Micro-Based Model

S𝑡 = (1 − 𝑏) 𝑖=0∞ 𝑏𝑖𝐸𝑡

𝑚𝑓𝑡+𝑖 (7)

A Micro-Based Model

S𝑡 = (1 − 𝑏)

𝑖=0

∞

𝑏𝑖𝐸𝑡𝑚𝑓𝑡+𝑖

∆S𝑡+1 =1 − 𝑏

𝑏𝑆𝑡 − 𝐸𝑡

𝑚𝑓𝑡 + 𝜀𝑡+1𝑚

𝜀𝑡+1𝑚 ≡ (1 − 𝑏)

𝑖=0

∞

𝑏𝑖(𝐸𝑡+1𝑚 − 𝐸𝑡

𝑚)𝑓𝑡+𝑖+1


∆𝑆𝑡+1 = 𝑎0 + 𝑎𝑋𝑡𝐴𝐺𝐺 + 𝑒𝑡+1

∆𝑆𝑡+1 = 𝑎0 +

𝑗=1

6

𝑎𝑗𝑋𝑗,𝑡𝐷𝐼𝑆 + 𝑒𝑡+1


A Micro-Based Model

1. 1.Transactions flows must contain information relevant for fundamentals.

2. 2. If there is no delay because market-makers can observe aggregate order flow contemporaneously, then spot rates will be correlated contemporaneously with order flow


A Micro-Based Model

5.Empirical Analysis

Empirical analysis ─ Data

• End-user transaction flows

• Spot rate

• Euro deposit rate


Empirical analysis ─Forecast comparisons• MSE

• Projection stat.

∆ℎ𝑠𝑡+ℎ 𝑡 the forecast of ∆ℎ𝑠𝑡+ℎ ≡ 𝑠𝑡+ℎ - 𝑠𝑡 on day “t”Step1 recursive h-period out of sample forecasts for non-RW model over the forecasting period

S→ T-h (i.e., ∆𝑠𝑡+ℎ 𝑡 for S < t ≤ 𝑇 − ℎ)

Step2 regress the forecasts on the realized value

∆ℎ𝑠𝑡+ℎ 𝑡 = 𝛽0 + 𝛽 ∆𝑠𝑡+ℎ + 𝑤𝑡+ℎ

Null hypothesis : 𝑠𝑡~RW


Empirical analysis ─ Result

• MSE ratio is the ratio of mean squared forecast errors for the non-RW model to the RW model.


6.Conclusions

Conclusions


Conclusions – Future work

• Is the forecasting power here coming from the real economy?

• If the dispersed information framework is the right one,what are the implications for deep issues?

• what degree is the information being revealed in order flow actually macroeconomic information?


Thank you for your listening!

meese rogoff redux

Art & Photos