Topic IIC:

Empirical Analysis: How Well Do the Parity Relations Hold?

International Fixed IncomeInternational Fixed Income

OUTLINE

• Review of Evidence on PPP

• Alternative Exchange Rate Approaches

• Forecasting– Forward Premium Puzzle

I. Recall the Evidence on PPP

• Deviations from purchasing power parity can be substantial in the short run.

• Real exchange rates can take several years to return to equilibrium.

• Real exchange rates are autoregressive autoregressive (that is, they depend on previous levels).

The empirical Record of RPPP in the long run

-4%

-2%

2%

4%

-2% 2% 4% 5%

M ean annual percentage changein the spot exchange rate

S.Africa

Spain

Italy

U.K.

Hong Kong SwedenCanada

France

Denm ark

Norway

Netherlands

Japan

Austria

M alaysia

Belgium

Germ anySingapore

Switzerland

Difference inannual inflation rates

Evidence on RPPP Deviations

RXRs Over the (Very) Long Run: 1900-1990

Implementation Issues

A few problems/questions arise

• The choice of a price index– choices include CPI, PPI, GDP

• The choice of a base year/reference level– chose an “equilibrium” period

...but (I) how do we know?, and (II) what does disequ’m mean?

– some fundamental structural changes might have occurred

• Relative prices might have changed – hence PPP is not expected to hold

PPP: an Exchange Rate Determination Theory

• Causality is

Goods market ==> Currency Market

The adjustment mechanism:

real$ is weak and domestic prices are low

=> export will rise & import will fall

=> a trade surplus will generate a real and nominal $ appreciation

• We completely ignore

– the role of financial transactions

– the forward-looking nature of exchange rates

– the stickiness of prices

Recall the Evidence on the Fisher Relation

-5%

0%

5%

10%

-5% 0% 5% 10% 15%

Difference in 3-monthEurocurrency interest rates (i£i$)

Difference in realized quarterly inflation (£$)

II. Alternative Approaches to Modeling XR Determination

• Main challenge is to relate– Macro variables:

• consumption, savings, taxes, investments, export, import, gvt’ deficit

==> supply and demand of FX

THE FUNDAMENTALSFUNDAMENTALS APPROACH TO XRs DETERMINATION– Financial variables:

• interest rates, asset flows, volatility, risk premiums, stockmarket behavior• central bank policy and intervention

THE ASSETASSET APPROACH TO XRs DETERMINATION• ...and to provide theory(ies) which explain and reconcile

– short, medium and long term behavior of XRs and RXRs– puzzles

The Balance of Payments Approach

• Current Account: (sales and purchases of goods and services)– CA= X - M

X - export of goods and services

M - import of goods and services• As the RXR rises (real appreciation) X__, M__ => CA__• In Equ’m: Y = C + I + G + CA

GNP= consumption+investment+gvt’spend

Open economy: add CA surplus(deficit)• RXR <==> CA(RXR) = Y - C - I - G

...in order to (improve CA) <=> (reduce RXR)

we need to increase Y and/or reduce C and/or reduce I and/or reduce G

• Causality is the big leap of faith

The Asset Approach

• The traditional approach:

XRs adjust to eliminate trade imbalances

==> Countries with CA surplus will experience an appreciating currency

• Empirical evidence is counterfactual to this theory

consider especially the US during 1980-85 (deficit + appreciation)

• The asset approach treats XRs as a financial asset

– attribute a FORWARD LOOKING role to XRs, consistent w/ other financial theories

– explain large moves relative to fundamental

III. FORECASTING

• What do we (think we) know ?

– Higher interest rates ==> strengthening currency

– Inflation rises ==> currency weakens

…but for given real rates, high inflation <=> high interest rates

– Trade deficit ==> weaker currency

… but recall the experience in the US in the early 80’s and recent opposite experience in FE countries

Merrill’s March98 3mon Forecasts

• 3 out of 5 forecasts in the “right direction”• Mean change is 3.364% • Mean absolute error of forecast 4.102%• HOW DO THESE FORECASTS COMPARE TO MARKET-WIDE AVAILABLE FORECASTS ?(e.g., CURRENT XRs and FORWARD rates)

Currency March 98 June 98 Change (%) June forecast Error(%p.a.)DEM 1.815 1.770 -2.452 1.850 4.514JPY 125.530 139.330 10.993 130.000 -6.696GBP 0.607 0.611 0.543 0.629 2.985FFR 6.083 5.936 -2.423 6.200 4.447CHF 1.467 1.473 0.409 1.500 1.868

STATS - MAE= 3.364 - 4.102

Source: March 5th, 1998 “Currency and Bond Market Trends” biweekly review

Exchange Rate Forecasting

Market-Based Exchange Rate Forecasts

E[Std/f] = S0

d/f - The random walk hypothesis

E[Std/f] = Ft

d/f - The expectations hypothesis

E[Std/f] = S0

d/f [(1+pd)/(1+pf)]t - RPPP

Model-Based Exchange Rate Forecasts

• Technical analysis - uses the past history of exchange rates to predict future exchange rates

• Fundamental analysis - uses macroeconomic data to predict future exchange rate changes

March98 3mon Forward Forecasts

• 3 out of 5 forecasts in the “right direction”• Mean change is 3.364% •Mean absolute error of forecast 3.337%

Currency March 98 June 98 Interest Forward Error(%p.a.)DEM 1.815 1.770 3.490 1.805 1.973JPY 125.530 139.330 0.460 123.930 -11.053GBP 0.607 0.611 7.430 0.610 -0.099FFR 6.083 5.936 3.920 6.058 2.051CHF 1.467 1.473 1.150 1.450 -1.507

STATS - Ius,3m= 5.630 MAE= 3.337

Forward vs. Merrill

• 3 out of 5 forecasts in the “right direction” in both• Forward forecast outperforms

Currency March 98 June 98 Interest Forward Error(%p.a.)DEM 1.815 1.770 3.490 1.805 1.973JPY 125.530 139.330 0.460 123.930 -11.053GBP 0.607 0.611 7.430 0.610 -0.099FFR 6.083 5.936 3.920 6.058 2.051CHF 1.467 1.473 1.150 1.450 -1.507

STATS - Ius,3m= 5.630 MAE= 3.337

Currency March 98 June 98 Change (%) June forecast Error(%p.a.)DEM 1.815 1.770 -2.452 1.850 4.514JPY 125.530 139.330 10.993 130.000 -6.696GBP 0.607 0.611 0.543 0.629 2.985FFR 6.083 5.936 -2.423 6.200 4.447CHF 1.467 1.473 0.409 1.500 1.868

STATS - MAE= 3.364 - 4.102

Merrill vs. Random Walk

• Random Walk MAE is 3.170%• Outperforms both Forward and Merrill’s forecasts...

Currency March 98 June 98 Change (%) June forecast Error(%p.a.)DEM 1.815 1.770 -2.452 1.850 4.514JPY 125.530 139.330 10.993 130.000 -6.696GBP 0.607 0.611 0.543 0.629 2.985FFR 6.083 5.936 -2.423 6.200 4.447CHF 1.467 1.473 0.409 1.500 1.868

STATS - MAE= 3.364 - 4.102Currency March 98 June 98 Change (%) RW forecast Error(%p.a.)DEM 1.815 1.770 -2.452 1.815 2.514JPY 125.530 139.330 10.993 125.530 -9.905GBP 0.607 0.611 0.543 0.607 -0.540FFR 6.083 5.936 -2.423 6.083 2.483CHF 1.467 1.473 0.409 1.467 -0.407

STATS - MAE= 3.364 - 3.170

Forward premiumor discount

Actual change in the spot rate

-15%

-10%

-5%

0%

5%

10%

15%

-1% 0% 1%

1-month forward rates as spot rate predictors:Yen per dollar exchange rates 1970-1995

The Forward Premium Puzzle

• The Expectations hypothesisFFt+1t+1/ S/ Stt= E= Ett[S[St+1t+1] / S] / Stt

• Consider the regressionSSt+1t+1/ S/ Stt

= = + + (F (Ft+1t+1 / S / Stt) + err) + errtt

• Random walk ==> =___, =___, =___=___

• Exp’ Hypothesis==> =___, =___, =___=___

The Forward Premium PuzzleCurrency R2

GBP -.0062 *(.0027)

-1.840 *(0.847)

0.0213

CAD -.0036 *(.0009)

-1.575 *(0.460)

0.0341

FF -.0021(.0031)

-0.674(0.827)

0.0042

DM .0033(.0025)

-0.743(0.805)

0.0041

ITL -.0042(.0039)

-0.073(0.453)

0.0001

JPY .0080 *(.0024)

-1.711 *(0.643)

0.0230

The Forward Premium Puzzle:Long Horizon Evidence

Currency Mean forward Premia Mean Depreciaiton

GBP -3% -2%

CAD -1.7% -1.8%

FF -3% -0.5%

DM 1.7% 2.3%

ITL -6.5% -4.7%

JPY 2.5% 5.3%

Implications and Interpretations

• With a beta=-1.8, on average when i*>i by 1%, then the XR appreciates by 0.88% instead of depreciating by 1%

==> Sell a currency trading at a premium(UIP predicts it should appreciate, but empirically the reverse happens), and buy a currency at a discount