The Bank of Israel ’ s New DSGE Model Project

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.

5. 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. , 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 ExportsMarket Clearing Conditions • Two equilibrium conditions defining nominal and real GDP from the supply side: • Nominal GDP: • NAWM: • BoI Model: • Real GDP: • NAWM: • BoI Model problem – H, X, and QX are not the same good! Solution:

11. Extension I: Imports in ExportsExport 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 ExportsExport demand shock Exports (x) Correlation between Δx and Δim: Observed in data: 0.50 Baseline Model: 0.38 Modelwithout 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 ModificationsGeneral 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 ModificationsThe 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 RateMotivation 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 Inflation target Long-run fwd real rate

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 RateMotivation 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 WorldOptions 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 WorldThe world Model • IS curve (world output): • Phillips Curve (CPI inflation) : • Taylor rule (CB key rates) :

28. Extension IV: The Rest of the WorldObservable Variables • 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* andΔim* in observable set. Define bridge equation:

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

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

32. The EndThank You

33. Schematic Diagram: Resources and Uses C 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: Prices PC 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 goodHf Production Function Adjustment costs Investment productivity Technology Z, ε Capital services Ksf 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 Demand I (-) (-) (-) (-) 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 (-)