1. The Bank of Israel’s New DSGE Model Project
Team:
David Elkayam, Eyal Argov, Emanuel Barnea, Alon Binyamini, Eliezer Borenstein, Irit Rozenshtrom
Updated: 22 October 2009
Prepared for presentation at the Central Bank Macroeconomic Modeling Workshop, Jerusalem - 28/10/2009

2. Contents Overview of the project.
Short description of the New Area Wide Model (NAWM).
4 main deviations from NAWM:
Imports in exports.
UIP condition.
Time varying long-run real interest rate.
Rest of the world model.

3. Project Motivation
From 2005 until today, the main monetary model operated at the Bank of Israel to support interest rate decisions is:
“Open-economy New-Keynesian small DSGE ‘lite’ model”.
Four blocks:
Inflation
Output gap
Exchange rate
Interest-rate
What's missing?
The model is too small – real sector not rich enough, does not cover GDP components, no labor market, no investment-capital dynamics.
Limited amounts of questions you can ask.
Loose ends on theory – ad hoc imported inflation equation, exogenous investment, ad hoc “closing open-economy model”.
HP filtered gaps – hard to present growth forecasts.
In 2008 the BoI Monetary Models Forum initiated the development of a new DSGE model for use in forecasting and policy analysis.

4. The Project Starting point – ECB’s “New Area Wide Model”
Similar (RAMSES, NEMO, TOTEM)
Stages of the project:
Study and replicate the NAWM – done.
Derive analytical solution to steady state – done.
Calibrate version for Israel – done.
Implementing the model for practical use – ongoing
Bayesian estimation of the model – ongoing
Extensions of the model – future work
Financial frictions
Search and matching labor market
Distinction of business sector vs. government output.
בנקודה זו אולי כדאי להרחיב טיפה: יישום KF, תחזיות מותנות, מניפות ופירוק היסטורי.

5. The New Area Wide Model (Christoffel et al
The New Area Wide Model (Christoffel et al. , 2008) – Main Economic Units
Households:
Consume.
Invest in capital stock.
Rent capital services to intermediate goods firms.
Save in domestic or foreign bond
Monopolistic suppliers of labor – subject to Calvo (1983) rigidity in wage setting.
Domestic producers of intermediate goods:
Produce with labor and capital (and technology).
Sell to local final good produces (C, I, G) and foreign importers (X)
In each market: monopolistic competition + Calvo (1983) rigidity in price setting

6. The New Area Wide Model (Christoffel et al
The New Area Wide Model (Christoffel et al. , 2008) – Main Economic Units
Importers of intermediate goods:
Buy foreign output.
Monopolistic competition + Calvo (1983) rigidity in price setting (LCP).
Final good producers (type C, type I):
Aggregate domestic and imported intermediate goods.
Perfect competition.
Central bank: Sets nominal interest rate according to Taylor-type rule in order to meet IT.
Fiscal authority: exogenously sets government consumption and tax rates.
Foreign economy (y*, r*, π*): determined by VAR.

7. Extension I: Imports in Exports
In the NAWM exports are domestically produced (Not like C or I).
Israel:
Export weight in GDP – 36%.
Estimates of import intensiveness in exports are around 30%.
To model the use of imported intermediate goods in the production of exports:
Not enough to model exports like other final goods (C, I) that are produced with domestic and imported intermediate goods. We also want to maintain assumption of Local Currency Pricing.
Solution: Two stage production of exports:
First stage: CES aggregation of domestic and imported intermediate goods (like C and I).
Second stage: Then brand-naming and monopolistic competition with Calvo (1983) price rigidity.

8. Extension I: Imports in Exports Domestic final goods firms
Final export good (before brand-naming) CES production function:
Final export good’s price aggregator (marginal cost of distributors):
Final Export good before brand-naming
Domestic Intermediate goods
Imported Intermediate goods

9. Extension I: Imports in Exports Exporters
Domestic monopolistic exporting firms buy the homogenous export good ( ) at constant marginal cost –
Differentiate it using a simple production function:
Sell it abroad at a marked-up price, , to foreign retail firms. They set their price in foreign currency (LCP), and face a Calvo (1983) problem.

10. Extension I: Imports in Exports Market Clearing Conditions
Two equilibrium conditions defining nominal and real GDP from the supply side:
Nominal GDP:
NAWM:
BoI Model:
Real GDP:
BoI Model problem – H, X, and QX are not the same good!
Solution:

11. Extension I: Imports in Exports Export demand shock
Exports (x)
Output (y)
inflation (πc)
Imports (im)
Nominal interest rate (r)
Nominal exchange rate (S)
Baseline Model
Without IM in X

12. Extension I: Imports in Exports Export demand shock
Exports (x)
Correlation between Δx and Δim:
Observed in data:
Baseline Model:
Model without IM in X: – 0.08
Output (y)
inflation (πc)
Imports (im)
Nominal interest rate (r)
Nominal exchange rate (S)
Baseline Model
Without IM in X

13. Extension II: UIP Modifications General Overview
Three Modifications to the UIP condition:
Incomplete financial markets – external risk premium depends on foreign asset position (Benigno, 2001).
“Modified” UIP – external risk premium depends on expected and lagged nominal exchange rate (Adolfson et al., 2007).
“Modified” UIP compatible with persistent inflation target differentials.

14. Extension II: UIP Modifications The explicit modeling
From the households budget constraint:
Local nominal rate
Local bonds
Foreign bonds
External risk premium
Foreign nominal rate
I. Foreign asset position
“Modified” UIP
External risk premium
II. Expected depreciation
III. Adjusted of inflation target differentials

15. Extension II: UIP Modifications External Risk Premium Shock
Real exchange rate (s)
Output (y)
inflation (πc)
External Risk Premium (ΓB*)
Nominal interest rate (r)
Nominal exchange rate (S)
Baseline Model
Non - “Modified” UIP

16. Extension II: UIP Modifications Permanent 1% increase in foreign price level
Real exchange rate (s)
Output (y)
inflation (πc)
External Risk Premium (ΓB*)
Nominal interest rate (r)
Nominal exchange rate (S)
Baseline Model
Non - “Modified” UIP

17. Year-on-year Inflation and the Inflation Target – Israel and G4, 1992-2009

18. Extension II: UIP Modifications Inflation Target Shock
Annualized Inflation target (4*πTAR)
Output (y)
Inflation – deviation from Tar. (πc-πTAR)
External Risk Premium (ΓB*)
Nominal interest rate (r)
Nominal exchange rate (S)
Baseline Model
“Modified” UIP – not adjusted to IT

19. Extension II: UIP Modifications Inflation Target Shock
Annualized Inflation target (4*πTAR)
Output (y)
Inflation – deviation from Tar. (πc-πTAR)
External Risk Premium (ΓB*)
Nominal interest rate (r)
Nominal exchange rate (S)
Baseline Model
“Modified” UIP – not adjusted to IT

20. Extension III: Time Varying LR Real Rate Motivation
5-10 Years Ahead Forward Real Interest Rates
(Derived from Government Indexed Bonds)
US (Nominal)
Israel US

21. Extension III: Time Varying LR Real Rate
We add to the model:
Financial shock and structure that allow expected long-run (5 to 10 years) interest rates to change over time.
Monetary policy uses long-run interest rates (forward 5 to 10 years ahead) as benchmark rates.
Use data on long-run interest rates in estimation.

22. Extension III: Time Varying LR Real Rate The explicit modeling
From the households budget constraint:
Domestic financial premium:
Local nominal rate
Local bonds
Foreign bonds
External risk premium
Foreign nominal rate
III. Domestic financial risk premium shock
II. Symmetric financial risk-premium shock
I. External financial risk-premium shock

23. Extension III: Time Varying LR Real Rate The explicit modeling
Interest rate rule:
Long-run fwd real-rate:
Short-run real rate:
Smoothing
Long-run
Inflation
Output
Long-run fwd real rate
Inflation target

24. Extension III: Time Varying LR Real Rate The explicit modeling
The observable 5-10 year forward real rate derived from indexed government bonds:
Observed fwd rate
Model predicted fwd rate
Constant
Measurement error
Time varying term premium

25. Extension III: Time Varying LR Real Rate Motivation
5-10 Years Ahead Forward Real Interest Rates
(Derived from Government Indexed Bonds)
Israel
Model derived “pure” fwd real-rate US

26. Extension IV: The Rest of the World Options at Hand
How to model the rest of the world (i*, π*, y*)?
Single-equation AR. Problem: can’t apply structural foreign shocks.
VAR (example - NAWM). Problem: “Well” looking structural shocks depend on identification assumption.
Closed economy NK small model.
Compared to AR: better fit, structural shocks.
Compared to VAR: worse fit, better interpretation of shocks.
Problem: variables relevant to world model may be less relevant to Israeli economy. Solution: bridge equations.

27. Extension IV: The Rest of the World The world Model
IS curve (world output):
Phillips Curve (CPI inflation) :
Taylor rule (CB key rates) :

28. Extension IV: The Rest of the World Observable Variables
i* – G4 effective CB key rates
π* – G4 effective CPI inflation
Δy* - Dilemma:
G4 effective output growth is more adequate for world model.
G4 effective import growth (Δim* ) is more adequate to explain Israeli exports:
Solution: use Δy* and Δim* in observable set. Define bridge equation:

29. Extension IV: The Rest of the World Recap on Foreign Output Transmission Mechanism
IS curve for G4 effective output (Δy* ):
Bridge equation for G4 imports:
Export demand equation

30. Extension IV: The Rest of the World World Import Shock (blue) vs
Extension IV: The Rest of the World World Import Shock (blue) vs. World Demand shock (red)
World: imports (im*), output (y*)
Output (y)
inflation (πc)
World: key-rate (r*), inflation (π*)
Nominal interest rate (r)
Nominal exchange rate (S)
World import shock (Non structural)
World demand shock (structural)

31. Extension IV: The Rest of the World World Import Shock (blue) vs
Extension IV: The Rest of the World World Import Shock (blue) vs. World Demand shock (red)
World: imports (im*), output (y*)
Output (y)
inflation (πc)
World: key-rate (r*), inflation (π*)
Nominal interest rate (r)
Nominal exchange rate (S)
World import shock (Non structural)
World demand shock (structural)

32. The End Thank You

33. Schematic Diagram: Resources and Uses
Private Consumption G
Public consumption I
Investment IM
Imports K
Capital H
Intermediate goods
(Y – Gross Domestic
Product) X
Exports L
Labor

34. Schematic Diagram: PricesPC
Private Consumption PI
Investment PG
Public consumption
PIM
Imports RK
Rent PH
Intermediate goods
(Y – Gross Domestic
Product) PX
Exports W
Wage

35. Schematic Diagram: Production and Inputs
Households Hf
Investment I Hf
Intermediate good Hf
Production Function
Technology
Z, ε
Capital services
Ksf
Adjustment costs
Investment productivity
Labor aggregate Nf
Utilization rate u
Monopolistic Competition
Wage Rigidity (Calvo,1983)
Capital stock Kh Nh Nh Nh Nh Nh

36. Schematic Diagram: From Intermediate Goods to Final Goods
Foreign Demand Y* Xf
Homogenous Export good X
Foreign products X*
Final Local Uses
C, I, G
Export (stage I) QX MC
Calvo Xf Xf
Perfect Competition
Homogenous local intermediate good
H (Y)
Homogenous imported intermediate good IM
Monopolistic Competition
Price Rigidity (Calvo,1983)
Monopolistic Competition
Price Rigidity (Calvo,1983) Hf Hf Hf Hf Hf
IMf
IMf
IMf
IMf
IMf

37. Schematic Diagram: Monetary Transmission Process (signs relate to interest rate hike)
Demands
Factors of production Y
Output
Production costs I
Demand
(-)
(-)
(-)
(-) KD RK
Rent C
(+)
(-)
(-) LD
RM-π
Expected real
interest
Rate (Market) NX W
Wage
(-)
Supply
(-)
(-)
(+)
(-) Ks
(+)
(+) PH
Price of domestic
intermediate goods s
Real Exchange
Rate Ls
(-)
(-) Pc
Consumer Price
Index R
BoI interest
rate
(+) S
Nominal Exchange
Rate
(-)
(-)
PIM
Imports prices
(-)