The Bank of Israel’s Monetary Model

Prof. Zvi Eckstein

Deputy Governor – Bank of Israel 2008 Outlook of the Local and Global Capital Markets

The Monetary Decision Process

• The Governor makes the monthly interest rate decision on the Monday before the last Wednesday in the month.

• The interest rate is the overnight rate available for all banks (now also to non-bank institutions through REPO)

• The decision-making process is as follows: 1. Weekly meetings of the “narrow forum” (heads of

departments, Deputy Governor and the Governor).2. Sunday before the decision, presentation of main

economic facts and models in a broad forum attended by economists from various departments.

3. Sunday meeting of narrow forum to discuss the Departments’ interest rate recommendations.

4. Monday meeting to discuss the background and main factors in the decision.

The Models in Use

1. A small reduced form model for inflation and interest rate (quarterly) – Research Department. Output: Inflation and interest rate for 2/3 years

2. An approximate DSGE model for inflation, output gap, exchange rate and interest rate (quarterly) – Monetary Department (presented below). Output: Inflation and interest rate for 2/3 years

3. Monthly inflation forecasting econometric models – various.

(Since last year: Monetary Models’ Forum to analyze and develop models with extensive visitor program)

The Quarterly Model

Aggregate Demand Equation

• Households solve an inter-temporal consumption (C) problem:

• This yields the Euler condition (log-linear form):

0

1

t,, 1

Emaxk

ktk

BBC

Cfttt

tct

ftt

ct

tcttt

ftt

ctt

tt X

P

B

P

B

Pi

B

Pi

BCts

11

)1()1( .

)(1E /11tc

ttttt icc )1(

Aggregate Demand Equation (cont.)

• Assume foreign demand for Israel’s exports (xht):

• Assume exogenous demand for government purchases (gh

t) and investment (invht) .

• Aggregate resource constraint (added value form):

t

f

tht q

wyx

1

World

demandReal exchange

rate

)2(

htg

htinv

htx

htct ginvxcy )3(

Aggregate Demand Equation (cont.)

• Aggregate demand equation (1+2+3):

tttxgctttg

tttxtttcf

xcfc

cttt

cttt

invinvgg

yyqqw

w

iyy

/1/1

/1/1

/1/1

)1(

)1(

)(

)(

World demand

Real exchange rate

Real interest rate

Output gap

Government purchases Investment

Consumption

Net-export

Price Friction or “New Keynesian”

• Local producers face “menu costs.” Minimize quadratic loss function:

• The optimal flex-price is derived from profit maximization given the production function:

0

2/1/

2// )()ˆ(min

0

htt

htt

htt

htt

pppcpp

cht

11 )()(

zf

zf wf

t

whtt ZZY

Local inputs

Imported inputs

Deviation of actual price from optimal flex-price

Change in actual price

Price Friction or “New Keynesian” (cont.)

• Yields local price Phillips Curve:

• Overall CPI inflation (πc) is a combination of domestic inflation (πh) and imported inflation (πf) :

• We assume dynamic adjustment of the exchange rate pass-through:

htzftqty

htt

ht ppbyb /1

ft

cf

ht

cf

ct ww )1(

)( ttft ep

Relative price of imported inputs

Output gapLocal inflation

Foreign prices + depreciation rate

Uncovered Interest Rate Parity

• The exchange rate is determined by the following UIP:

erroriiee tttt tt

/1Exogenous

risk premium

Interest rate

spread

NIS/$ exchange

rate

Expected rate

Interest Rate by a “Taylor Rule”

• The model is closed with a forecast-based Taylor-type rule:

13 ])4([)1( tityTt

ctt

Tttit iyEri

Domestic interest rate

Long-run real rate

Inflation target

Year ahead inflation

Inflation target

Output gap

Lagged rate

14

1

33 c

t

ctc

t PP

Model Adjustment

• The model is adjusted to become more compatible with actual dynamics.

• Lags of the dependent variable were augmented.

• Example (local Phillips curve):

• This could be justified by partly adaptive expectations or firms who index their price instead of optimizing.

htzftqty

htlead

httlead

ht ppbyb 1/1 )1(

Relative price of imported inputs

Output gap

Domesticinflation

Expected inflation

Lagged inflation

Estimation

• The models (Aggregate Demand, Phillips Curve & UIP) were estimated by the GMM method (equation by equation).

• Quarterly data from 1992-2006.

• The interest rate reaction function was calibrated.

Estimated Equation’s Fit

-4

-2

0

2

4

6

8

10

12

14

16

92

94

96

98

00

02

04

06

-25

-20

-15

-10

-5

0

5

10

15

20

25

Residual Fitted Actual

-4

-2

0

2

4

6

8

10

12

14

16

92

94

96

98

00

02

04

06

-28

-24

-20

-16

-12

-8

-4

0

4

8

12Phillips Curve IS Curve

Within Sample Dynamic Simulation

-8-6-4-202468

101214

1999 2001 2003 2005 2007

-3

-2

-1

0

1

2

3

4

5

1999 2001 2003 2005 2007-30

-20

-10

0

10

20

30

40

1999 2001 2003 2005 2007

Quarterly CPI Inflation (πc) Change in Interest Rate (Δi) Nominal Depreciation (Δe)

With

out

UIP

Sho

ck

-8-6-4-202468

101214

1999 2001 2003 2005 2007

-3

-2

-1

0

1

2

3

4

5

1999 2001 2003 2005 2007

-30

-20

-10

0

10

20

30

40

1999 2001 2003 2005 2007

Incl

udin

g U

IP S

hock

Using the Model at the Bank of Israel

Using the Model at the BoI

• At the end of December 2006 the BoI’s interest rate was 5.0%. Nominal appreciation was pulling inflation down.

• Using the model’s concepts, we split inflation outcomes into domestic inflation and imported inflation.

• This showed that domestic prices were rising at a high rate of 3.4% while imported prices fell by 5.9% pulling the overall CPI downwards.

Using the Model at the BoI

Nominal Interest Rate

4.44.5

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

6.00

2006:4 2007:2 2007:4 2008:2 2008:4

BoI key rate

% Inflation

1.1

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

2006:4 2007:2 2007:4 2008:2 2008:4

Inflation Target

%

Quarterly inflation

Year on year inflation

Dollar interest rate

•At the end of the month the Governor decided the cut the BoI rate by 0.5 percentage points to 4.5%.

January Interest Rate Decision

Using the Model at the BoI

• At the end of April 2007 the BoI’s interest rate was 4.0%. Nominal appreciation was pulling inflation down.

• Domestic prices were rising at a high rate of 4.0% while imported prices fell by 4.9% pulling the overall CPI downwards.

Using the Model at the BoI

Nominal Interest Rate

3.63.6

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

2007:1 2007:3 2008:1 2008:3 2009:1

BoI key rate

% Inflation

0.8

-2.0

-1.0

0.0

1.0

2.0

3.0

2007:1 2007:3 2008:1 2008:3 2009:1

Inflation Target

%

Quarterly inflation

Year on year inflation

Dollar interest rate

•At the end of the month the Governor decided the cut the BoI rate by 0.25 percentage points to 3.75%.

May Interest Rate Decision

Using the Model at the BoI

• At the end of October 2007 the BoI’s interest rate was 4.0%.

• Nominal appreciation had been picking up again since August.

• On the other hand there were inflationary pressures arising from excess demand and foreign inflation. Domestic prices were rising at a high rate of 4.0%.

Using the Model at the BoI

Nominal Interest Rate

4.04.0

3.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

2007:3 2008:1 2008:3 2009:1 2009:3

BoI key rate

% Inflation

1.2

0.0

1.0

2.0

3.0

4.0

2007:3 2008:1 2008:3 2009:1 2009:3

Inflation Target

%

Quarterly inflation

Year on year inflation

Dollar interest rate

•At the end of the month the Governor decided to leave the interest rate at 4.0%

November Interest Rate Decision

8.4

Interest Rate and Year on Year Inflation Fan Charts

%

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

06Q3

06Q4

07Q1

07Q2

07Q3

07Q4

08Q1

08Q2

08Q3

08Q4

09Q1

09Q2

09Q3

09Q4

10Q1

10Q2

55%

%

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

06Q3

06Q4

07Q1

07Q2

07Q3

07Q4

08Q1

08Q2

08Q3

08Q4

09Q1

09Q2

09Q3

09Q4

10Q1

10Q2

33%

47%

20%

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