1. Introduction to a Small Macro Model Jaromir Hurnik Monetary Policy and Business Cycle April 2009

2. “All models are wrong! Some are useful.” George Box George E.P. Box and Norman R. Draper, “Empirical Model-Building and Response Surfaces” (Wiley 1987), pp. 424.

3. Outline  Basic equations  Calibration versus estimation  Forecast uncertainty

4. The Model  A canonical gap model (reduced-form new- Keynesian model) Aggregate demand Aggregate supply Uncovered interest rate parity (simple/extended) Policy rule  Work horse at many central banks Developed countries: Bank of Canada, Reserve Bank of New Zealand Emerging economies: Czech Republic, Ukraine, Romania, Colombia, Peru, Guatemala, Botswana

5. The Model  Distinguishes between the observed value and a trend ( ≈ steady-state values of the system)  Forward-looking Model consistent expectations  Inflation  Exchange rate  Policy analysis Central bank is part of the model  Open structure Expert views may be easily incorporated

6. Schematic Transmission Mechanism Shocks hitting the economy SR interest rate LR interest rates Ex rate Financial shocks: Foreignrates Portfolio changes Demand shocks: Foreign demand Fiscal policy Inflation shocks: Indirect taxes Energy prices Inflation RMCIOutput gap Inflation expectations Transmission Mechanism

7. Aggregate Demand  Relates monetary policy and real economic activity  Depends on Own lagged value Monetary policy  Nominal interest rate – sticky prices - real interest rate  Nominal exchange rate – sticky prices – real exchange rate External developments

8. Aggregate Demand  Real interest rate affects Substitution between consumption today and in the future Investment activity  Real exchange rate Substitution between home and foreign goods

9. Aggregate Demand Russia, 2000Q1 – 2008Q4 Rolling correlation between the real interest rate and output gaps Relatively stable negative relationship between real interest rate and output

10. Aggregate Demand Russia, 2000Q1 – 2008Q4 Rolling correlation between the real exchange rate and output gaps Counter intuitive relationship between real exchange rate and output in the data. Not surprising. Closed economy and appreciation (depreciation) driven by commodity prices.

11. Aggregate Supply  Relates real economic activity and inflation  Monopolistic competition  Sticky prices  Depends on Expectations  Backward- and/or forward-looking Real marginal costs Cost push shocks

12. Aggregate Supply  Output gap approximates domestic inflationary pressure Real marginal cost of domestic producers  Real exchange rate gap approximates external inflationary pressure Real marginal cost of importers

13. Aggregate Supply Russia, 2001Q1 – 2008Q4 Rolling correlation between inflation and real marginal cost Stable relationship. High real marginal cost are followed by higher inflation with a lag of 1-2 quarters

14. Uncovered Interest Rate Parity  Relates domestic and foreign interest rate with the expected change in the exchange rate Domestic interest rate Foreign interest rate Current and expected exchange rate Exchange rate shocks

15. Uncovered Interest Rate Parity Russia, 1991Q1 – 2006Q4 Weak relation- ship between the money market and the exchange rate. Not surprising, because the nominal exchange rate served as the nominal anchor

16. Modified UIP  Extension for a more rigid exchange rate regime Smoothness Interventions where the exchange rate target is defined as

17. Policy Rule  Describes behavior of the central bank Reacts when inflation deviates from the price stability Smoothes its reaction to inflation or the output gap (uncertainty about real-time estimates of output gap) Takes into account real economic activity Policy shocks Neutral nominal rate = trend real rate + model-consistent inflation forecast

18. Policy Rule Russia, 2001Q1 – 2008Q4 Interest rate seems to react to both inflation and output, however with a lag only

19. Policy Rule Digression  The Taylor-type rule can make policy scenarios difficult to compare  One option: replace the rule with a loss function (ála Norges Bank): Min ℓ = var() + *var(y)  Policymaker decides the value of

20. Model Limitations  No explicit modeling of the supply side The choice of the inflation target value does not affect potential output growth  No stock and assets equilibria How to model crises?  No stock-flow consistency… From gaps back to the levels  No explicit modeling of central bank “credibility”

21. Calibration Versus Estimation  Estimation Short data sample Changes in economy Policy regime changes Some parameters are difficult to estimate because of endogeneity of policy actions

22. Endogeneity of policy actions (1)  The AD equation predicts a negative relationship between r and y  Timeline: Expected economic slowdown Policymaker cuts the interest rate The economy still slows down Econometrician observed positive correlation between interest rate and output gap  Do rate cuts slow down the economy?

23. Endogeneity of policy actions (2)  UIP predicts a positive correlation between E(Δs t+1 ) and r-r*  Timeline: Inflation increased Exchange rate depreciated Policymaker hiked the rate to combat inflation Econometrician observed negative correlation between interest rate and exchange rate  Do rate cuts appreciate the currency?

24. Calibration Versus Estimation  Econometricians reduce our forward-looking model into a backward-looking one:  Such model cannot predict future inflation: Ignores reactions of the policymaker to shocks Coefficients often contradict theory  Adaptive expectations of inflation  Inflation ≈ past output gaps:

25. Calibration Versus Estimation  Calibration Parameters set on the basis of model properties Restriction from economic theory Responses to typical shocks Adaptive strategy  Verification Reactions to shocks Residuals In-sample simulation Data versus model-implied correlations

26. Estimating Versus Calibrating Estimated regression Calibrated model time horizon Estimate precision There are instances to use estimated models, but not for long- run forecasts!