Uncovered Interest Parity with Fundamentals: A Brazilian

Exchange Rate Forecast Model

Uncovered Interest Parity with Fundamentals: A Brazilian

Exchange Rate Forecast Model

Marcelo Kfoury MuinhosPaulo Springer de Freitas

Fabio Araujo

Research Department Central Bank of Brazil

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil 1 - Introduction1 - Introduction

Motivation: The most challenging topic Pass-through UIP, PPP and Random Walk

Objetives of the Paper UIP with a equilibrium exchange

rate that clears the Balance of Payments

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil 2 – UIP and others2 – UIP and others

Survey : JP Morgan Model (2000)

Productivity, terms of trade, and trade openness

Obstfeld and Rogoff (1996) Wadhwani (1999)

),()(_

*ttttkt Zqqiie

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil 3 – BCB X-Models3 – BCB X-Models

Random Walk with Monetary Surprises (RWMS)

UIP with “Rational Expectations”

UIP with “Adaptive Expectations”

tttttt xiieeE *

1

ttttttttt ixiixie )( **

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

4 – The UIP with Fundamentals

4 – The UIP with Fundamentals

IS Curve

Phillips Curve

Taylor Rule

tttttt uaiahaah 131211101 )(

ttttttt hapeaaaa 124*

2221222121 )()1(

tttt haaai 32*

3130 )(

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

4 – The UIP with Fundamentals

4 – The UIP with Fundamentals

The UIP with Fundamentals

is the exchange rate that should clear BP at t + K.

1* )(

K

njKttjtjtjttntt eExiiEeE

jjj PyQBC ).,(.

BKBSBCBP

Ktt eE

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

4 – The UIP with Fundamentals

4 – The UIP with Fundamentals

Solving the system Balance of payment clears at time

t+K

Linear equations: 11 K - 1

Non-linear trade balance equation

At t+1, taken values at t as given

Deviation from equilibrium

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

5 - Simulations UIP - 12 x 4 periods

5 - Simulations UIP - 12 x 4 periods

Interest Response to Inflation Shock

0.000

0.004

0.008

0.012

0.016

1 7 13

19

25

31

37

43

49

55

61

67

i 4 i 12

Inflation Response to Inflation Shock

0.000

0.004

0.008

0.012

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

pi 4 pi 12

Output Gap Resp to Inflation Shock

-0.003

-0.002

-0.001

0.000

1 7

13

19

25

31

37

43

49

55

61

67

h 4 h 12

Real Exchange Resp to Inflation Shock

-0.040

-0.030

-0.020

-0.010

0.000

1 7

13

19

25

31

37

43

49

55

61

67

73

real exch (4) real exch (12)

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

5 – UIP with and without real exchange

in IS

5 – UIP with and without real exchange

in IS

Interest Response to Inflation Shock

0.000

0.004

0.008

0.012

0.016

1 7 13

19

25

31

37

43

49

55

61

67

73

79

i without real exch i with real exch

Inflation Response to Inflation Shock

0.000

0.004

0.008

0.012

1 6 11

16

21

26

31

36

41

46

51

56

61

66

71

pi without real exch pi with real exch

Output Gap Resp to Inflation Shock

-0.003

-0.002

-0.001

0.000

1 7

13

19

25

31

37

43

49

55

61

67

h without real exch h with real exch

Real Exchange Resp to Inflation Shock

-0.040

-0.030

-0.020

-0.010

0.000

1 7

13

19

25

31

37

43

49

55

61

67

73

real exch without real exch with

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

5 – Random Walk with and without real exch. in

IS

5 – Random Walk with and without real exch. in

ISInterest Response to Inflation Shock

-0.004

0.000

0.004

0.008

0.012

0.016

1 7 13 19 25 31 37 43 49 55 61 67 73 79RW without real exch RW with real exch

Inflation Response to Inflation Shock

-0.004

0.000

0.004

0.008

0.012

1 7 13 19 25 31 37 43 49 55 61 67 73 79

rw without real exch rw with real exch

Output Gap Resp to Inflation Shock

-0.003

-0.002

-0.001

0.000

1 7

13 19 25 31 37 43 49 55 61 67 73 79

rw withouht rw with

Real Exchange Resp to Inflation Shock

-0.090-0.080-0.070-0.060-0.050-0.040-0.030-0.020-0.0100.000

1 7

13 19 25 31 37 43 49 55 61 67 73 79

rw without rw with

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

5 – UIP & RW(resp. to inflation

shock)

5 – UIP & RW(resp. to inflation

shock) Interest Response to Inflation Shock

-0.005

0.000

0.005

0.010

0.015

0.020

1 7 13

19

25

31

37

43

49

55

61

67

73

79

UIP RW

Inflation Response to Inflation Shock

-0.0020.0000.0020.0040.0060.0080.0100.012

1 7 13

19

25

31

37

43

49

55

61

67

73

79

UIP RW

Output Gap Resp to Inflation Shock

-0.003

-0.003

-0.002

-0.002

-0.001

-0.001

0.000

1 7

13

19

25

31

37

43

49

55

61

67

UIP RW

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

5 – UIP & RW(resp. to inflation

shock)

5 – UIP & RW(resp. to inflation

shock) Real Exchange Resp to Inflation Shock

-0.060

-0.050

-0.040

-0.030

-0.020

-0.010

0.000

1 7

13 19 25 31 37 43 49 55 61 67 73 79

UIP RW

Nom Exch Rate Resp to Infl Shock

-0.050

0.000

0.050

0.100

0.150

0.200

1 7 13 19 25 31 37 43 49 55 61 67 73 79UIP RW

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

5 – UIP & RW(resp. to interest rate

shock)

5 – UIP & RW(resp. to interest rate

shock) Interest Response to Interest Shock

-0.004-0.0020.0000.0020.0040.0060.0080.0100.012

1 7 13

19

25

31

37

43

49

55

61

67

73

79

UIP RW

Inflation Response to Interest Shock

-0.001

-0.001

0.000

0.001

0.001

1 7 13

19

25

31

37

43

49

55

61

67

73

79

UIP RW

Output Gap Resp to Interest Shock

-0.005

-0.004

-0.003

-0.002

-0.001

0.000

0.001

1 7

13

19

25

31

37

43

49

55

61

67

73

UIP RW

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

5 – UIP & RW(resp. to interest rate

shock)

5 – UIP & RW(resp. to interest rate

shock) Real Exchange Resp to Interest Shock

-0.010

-0.005

0.000

0.005

0.010

1 7

13

19

25

31

37

43

49

55

61

67

73

79

UIP RW

Nominal Exchange Rate Resp to Interest Shock

-0.025-0.020-0.015-0.010-0.0050.0000.0050.010

1 7 13 19 25 31 37 43 49 55 61 67 73 79

UIP RW

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

5 – UIP & RW(resp. to output gap

shock)

5 – UIP & RW(resp. to output gap

shock) Interest Resp. to Output Gap Shock

-0.002

0.000

0.002

0.004

0.006

0.008

1 7 13

19

25

31

37

43

49

55

61

67

73

79

i uip i rw

Inflation Resp. to Output Gap Shock

-0.002-0.001-0.0010.0000.0010.0010.0020.002

1 7 13

19

25

31

37

43

49

55

61

67

73

79

pi uip pi rw

Output Gap Resp. to Output Gap Shock

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

1 7 13

19

25

31

37

43

49

55

61

67

73

79

h uip h rw

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil

5 – UIP & RW(resp. to output gap

shock)

5 – UIP & RW(resp. to output gap

shock)

Real Exchange Resp to Interest Shock

-0.010

-0.005

0.000

0.005

0.010

1 7

13

19

25

31

37

43

49

55

61

67

73

79

Real Exch. Resp. to Output Gap Shock

-0.020

-0.015

-0.010

-0.005

0.000

1 7 13

19

25

31

37

43

49

55

61

67

73

79

teta uip teta rw

Nom. Exch. Resp. to Output Gap Shock

-0.020-0.0100.0000.0100.0200.0300.0400.0500.060

1 7 13

19

25

31

37

43

49

55

61

67

73

79

e uip e rw

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil 5 – UIP & RW

(resp. to risk shock) 5 – UIP & RW

(resp. to risk shock) Interest Response to Risk Shock

-0.010

-0.005

0.000

0.005

0.010

0.015

1 2 3 4 5 6 7 8 9 10 11 12 13UIP RW

Inflation Response to Risk Shock

-0.006-0.004-0.0020.0000.0020.0040.0060.0080.010

1 2 3 4 5 6 7 8 9 10 11 12 13UIP RW

Output Gap Response to Risk Shock

-0.002

-0.002

-0.001

-0.001

0.000

0.001

0.001

1 2 3 4 5 6 7 8 9 10 11 12 13UIP RW

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil 5 – UIP & RW

(resp. to risk shock) 5 – UIP & RW

(resp. to risk shock)

Nom Exch Rate Resp to Risk Shock

-0.0200.0000.0200.0400.0600.0800.1000.120

1 2 3 4 5 6 7 8 9 10 11 12 13

UIP RW

Real Exch Rate Resp to Risk Shock

-0.020

0.000

0.020

0.040

0.060

0.080

0.100

1 2 3 4 5 6 7 8 9 10 11 12 13

teta uip teta rw

Research Department – Central Bank of Brazil

One Year of Inflation Targeting in Brazil 6 - Conclusion6 - Conclusion

UIP with Fundamentals & RWMS

Expected time to clear the BP

Extensions