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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

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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.

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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.

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The Project Starting point – ECBs 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.

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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

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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.

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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.

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

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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.

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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: NAWM: BoI Model problem – H, X, and Q X are not the same good! Solution:

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Extension I: Imports in Exports Export demand shock Exports (x) Imports (im) Output (y) Nominal interest rate (r) inflation (π c ) Nominal exchange rate (S) Baseline ModelWithout IM in X

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Extension I: Imports in Exports Export demand shock Exports (x) Imports (im) Output (y) Nominal interest rate (r) inflation (π c ) Nominal exchange rate (S) Correlation between Δx and Δim : Observed in data: 0.50 Baseline Model: 0.38 Model without IM in X: – 0.08 Baseline ModelWithout IM in X

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

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

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Extension II: UIP Modifications External Risk Premium Shock Real exchange rate (s) External Risk Premium (Γ B* ) Output (y) Nominal interest rate (r) inflation (π c ) Nominal exchange rate (S) Baseline ModelNon - Modified UIP

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Extension II: UIP Modifications Permanent 1% increase in foreign price level Real exchange rate (s) External Risk Premium (Γ B* ) Output (y) Nominal interest rate (r) inflation (π c ) Nominal exchange rate (S) Baseline ModelNon - Modified UIP

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

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Extension II: UIP Modifications Inflation Target Shock Annualized Inflation target (4*π TAR ) External Risk Premium (Γ B* ) Nominal interest rate (r) Inflation – deviation from Tar. (π c -π TAR ) Nominal exchange rate (S) Baseline ModelModified UIP – not adjusted to IT Output (y)

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Extension II: UIP Modifications Inflation Target Shock External Risk Premium (Γ B* ) Output (y) Nominal interest rate (r) Inflation – deviation from Tar. (π c -π TAR ) Nominal exchange rate (S) Baseline ModelModified UIP – not adjusted to IT Annualized Inflation target (4*π TAR )

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

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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.

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

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Interest rate rule: Long-run fwd real-rate: Short-run real rate: Inflation Long-run fwd real rate Extension III: Time Varying LR Real Rate The explicit modeling OutputLong-runSmoothing Inflation target

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

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

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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: cant 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.

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

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Extension IV: The Rest of the World Observable 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* and Δim* in observable set. Define bridge equation:

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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

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

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

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The End Thank You

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

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Schematic Diagram: Prices P C Private Consumption P IM Imports P G Public consumption P I Investment P H Intermediate goods (Y – Gross Domestic Product) R K Rent W Wage P X Exports

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Schematic Diagram: Production and Inputs NhNh NhNh NhNh NhNh Monopolistic Competition Wage Rigidity (Calvo,1983) Labor aggregate N f Intermediate good H f NhNh Capital services K s f Technology Z, ε Production Function HfHf HfHf Investment I Capital stock K h Utilization rate u Adjustment costs Investment productivity Households

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Schematic Diagram: From Intermediate Goods to Final Goods HfHf HfHf HfHf HfHf Monopolistic Competition Price Rigidity (Calvo,1983) Homogenous local intermediate good H (Y) Final Local Uses C, I, G HfHf IM f Homogenous imported intermediate good IM IM f XfXf XfXf XfXf Export (stage I) Q X Homogenous Export good X Monopolistic Competition Price Rigidity (Calvo,1983) Foreign products X* Foreign Demand Y* Perfect Competition MC Calvo

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Schematic Diagram: Monetary Transmission Process (signs relate to interest rate hike) LsLs KsKs R BoI interest rate S Nominal Exchange Rate P IM Imports prices Pc Consumer Price Index s Real Exchange Rate R M - π Expected real interest Rate (Market) W Wage LDLD KDKD R K Rent P H Price of domestic intermediate goods I C NX Production costs (-) (+) Y Output Supply (-) (+) (-) Demand Factors of production (-) (+) (-) (+) Demands

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