Estimating Time Varying Preferences of the FED

1. Estimating Time Varying Preferences of the FED Ümit Özlale Bilkent University, Department of Economics

2. OUTLINE: Introduction • INTRODUCTION • Change in the conduct of monetary policy • Estimated policy rules vs. Optimal policy rules • What’s missing? • What is the contribution of this paper?

3. The U.S. economy since late 1970’s • General consensus: Favorable economic outcomes in the U.S. economy since the late 1970’s. • Little consensus: Role of monetary policy • Several papers, including Clarida et al (2000, QJE) report a change in the conduct of monetary policy, which contributes to overall improvement in the economy

4. Why is there a change in the conduct of monetary policy? • Fed’s preferences have changed over time • References: Romer and Romer(1989, NBER), Favero and Rovelli (2003, JMCB), Ozlale (2003, JEDC), Dennis (2005, JAE) • Variance and nature of shocks changed. • References: Hamilton (1983, JPE), Sims and Zha (2006, AER) • Learning and changing beliefs about the economy • References: Sargent (1999), Taylor (1998), Romer and Romer (2002)

5. Estimated Policy Rules vs. Optimal Policy Rules • To understand the changes in the monetary policy, two main approaches: • Estimate interest rate rules, which started with the celebrated Taylor Rule • Some references: Taylor (1993, Carnegie-Rochester CS), Boivin (2007, JMCB) • Derive optimization based policy rules • Some references: Rotemberg and Woodford (1997, NBER), Rudebusch and Svensson (1998, NBER)

6. Estimated Policy Rules • Advantages: • Capturing the systematic relationship between interest rates and macroeconomic variables • Empirical support • Disadvantages: • Do not satisfy a structural understanding of monetary policy • Unable to address questions about policy formulation process or policy regime change

7. Optimal Policy Rules • Advantages: • Optimization based policy rules • Theoretical strength • Disadvantages: • Cannot adequately explain how interest rates move over time. • Estimate more aggressive responses to shocks than typically observed.

8. Combining optimal rule with the data • Combine the two areas by: • Assuming that monetary policy is set optimally • Estimating the policy function along with the parameters that characterize the economy • References: • Salemi (1995, JBES) uses inverse control • Favero and Rovelli (2003, JMCB) uses GMM • Ozlale (2003, JEDC) uses optimal linear regulator • Dennis (2004, OXBES and 2005, JAE) uses optimal linear regulator

9. Combining optimal rule with the data • Advantages: • Assess whether observed outcomes can be reconciled within optimal policy framework • Assess whether the objective function has changed over time • Allows key parameters to be estimated • Disadvantages: • None!

10. A general framework • Specify a quadratic loss function and AS-AD system such as: subject to the following linear constraints:

11. A general framework • Each period, the central bank attempts to minimize a loss function • Which depends on the deviations from inflation, output gap and interest rate targets • The preferences of the central bank are • The linear constraints are inflation and output gap equations. • Inflation is expected to have an inertia and it is affected from the output gap. • The output gap is affected from the real interest rate

12. Solving via Optimal Linear Regulator • When the loss function is quadratic and the constraints are linear, the problem can be regarded as a stochastic optimal linear regulator problem, for which the solution takes the form: • which means that the control variable, which is the interest rate, is a function of the state variables in the model • The vector contains both the loss function (preference) and the system parameters to be estimated.

13. Estimation • One way to estimate the parameters is to • Cast the model in state space form • Developing a MLE for the problem • Under certain conditions, executing the Kalman filter provide consistent and efficient estimates

14. Main findings • A substantial change in the Fed’s response to inflation and output gap • The response of Fed to inflation has become more aggressive since the late 1970’s. • There is an incentive for the Fed to smooth the interest rates

15. What’s missing? • The preferences that characterize the loss function are assumed to stay constant over time. • In technical terms, previous studies did not allow for a continual drift in the policy objective function. • Thus, these studies could not identify preference shocks of the Federal Reserve.

16. What to do? • We allow for the preference parameters in the loss function to vary over time, while keeping the linear constraints:

17. Estimation method • We use a two-step procedure: • 1st step: Estimate the linear optimization constraints, which are the parameters in the inflation and the output gap equation. • 2nd step: Conditional upon the estimated constraints, estimate the time-varying preferences of the Fed.

18. Main contribution of the paper • Generate a time series that will reflect the preferences of the Fed. • Identify Fed’s preference shocks from the data. • In technical terms: Given the linear constraints and the state variables, estimate the time-varying parameters in a quadratic objective function.

19. Related work • Sargent, Williams and Zha (2006, AER) find that Fed’s optimal policy is changing because of a change in the parameters of the Phillips curve (not because of a change in the parameters of the objective function) • Boivin (2007, JMCB) uses a time-varying set-up to investigate the changes in the parameters of a forward-looking Taylor-type rule. However, he does not consider a change in the preferences of the objective function.

20. OUTLINE: The Model • The Model • Introducing the model • Theoretical support for the loss function • Empirical support for the backward-looking model • Estimating the optimization constraints • Estimating time-varying preferences

21. The Model: Loss Function • We assume that the loss function is: • The preferences vary over time. • We specify a random walk process: • For simplicity, we assume that

22. Theoretical Support: Loss Function • A quadratic loss function, although hypothetical, is convenient set-up for solving and analyzing linear-quadratic stochastic dynamic optimization problems • Supporting references: Svensson (1997) and Woodford (2002) • Since inflation data is constructed as deviation from the mean, we did not specify any inflation target.

23. Theoretical Support: Loss Function • The assumption of random walk: • Cooley and Prescott (1976, Ecta) state that a random walk assumption is the best way to account for the Lucas’ critique. • A TVP specification has the ability to uncover changes of a general and potentially permanent nature for each parameter separately.

24. Linear Constraints • The linear constraints of the model are • To satisfy the long-run Phillips curve, coefficients of the lagged inflation terms sum up to unity. • This backward looking model is adopted from Rudebusch and Svensson and it is used in several studies, including Dennis (2005, JAE)

25. Empirical Support: Backward Looking Model • Forward looking models tend not to fit the data as well as the Rudebusch-Svensson model, which is also reported in Estrella and Fuhrer (2002) • There is no evidence of parameter instability in this version of the backward-looking model, as stated in Ozlale (2003)

26. Estimating the optimization constraints: Data • We use monthly data from 1970:2 to 2004:10, where the output gap is derived by using a linear quadratic trend. • For robustness purposes, we also use quarterly data, where inflation is derived from GDP chain weighted price index, the output gap series is taken from CBO. • In each case, we use federal funds rate as the policy (control) variable.

27. Estimating the optimization constraints: SUR • We estimate the parameters in the backward looking model by using the Seemingly Unrelated Regression. • Estimating each equation by OLS returns similar results, implying weak/no correlation between the residuals.

28. Estimated Parameters

29. Estimating Time Varying Preferences: Method • Step 1: • The solution for the optimal linear regulator is: • Step 2: • Let be the difference (control error) between the observed control variable and the optimal control variable.

30. Some Boring Stuff! • In the Kalman filtering algorithm, the estimate for the state vector is: which can also be written as: • Since the optimal feedback rule for the linear regulator is

31. Still Boring! • The new state vector is • For simplicity, let • Then, the problem reduces down to obtaining the elements of at each step. • Keep in mind that the matrix includes the parameters of the model.

32. How to estimate the loop • The model can be cast in a non-linear state space model. • The linear Kalman filter is inappropriate for the non-linear cases. • Thus, we use the extended Kalman filter and estimate both the optimal control sequence and the time-varying parameters in the model.

33. Outline: Estimation Results • Time varying preference series • Identifying preference shocks • Comparing observed and optimal interest rates • Robustness checks

34. Time varying preferences

35. Time varying preferences • Regardless of the starting values, the preference parameter for output stability goes down to zero. • Such a finding is consistent with Dennis (2005, JAE), which states that output gap enters the policymaking process only because its indirect effect on inflation. • The estimated series follow random walk, which is consistent with our initial assumptions.

36. Preference Shocks

37. Preference shocks • Beginning with the second half of 1980’s we do not observe any significant shocks in the policy preferences. Thus, the Greenspan period is silent in terms of preference changes. • The significantly positive shocks, which indicate an increased emphasis on price stability occur in the Volcker period. • Such a finding supports the view that Volcker period is a one-time discrete change in the policy. • These shocks are found to be normally distributed and autocorrelated.

38. Actual vs. optimal interest rates

39. Actual vs. optimal interest rates • The estimated interest rate is slightly sharper than the observed interest rate, which may be related to the absence of interest rate smoothing in the loss function. • The correlation between the two series is found to be 0.93. • Such a finding implies that the observed control sequence (interest rate) can be generated by putting increasingly more emphasis on price stability.

40. Robustness Checks • In order to see whether the estimated results are robust, we set the optimization constraints according to the findings of two studies, which use the same model • Rudebusch and Svensson (1998, NBER) • Dennis (2005, JAE)

41. Using the estimated coefficients from Rudebusch and Svensson

42. Using the estimated coefficients from Rudebusch and Svensson

43. Using the estimated coefficients from Rudebusch and Svensson

44. Using the estimated coefficients from Dennis

45. Using the estimated coefficients from Dennis

46. Using the estimated coefficients from Dennis

47. Correlation between preference shocks • Corr (RS, DE)=0.98 • Corr (RS, OZ)=0.90 • Corr (OZ, DE)=0.91 • These findings provide robustness for the estimation methodology and the results.

48. Interest rate smoothing • Several studies, including mine!, except Rudebusch (2002, JME) have found that interest rate smoothing is an important criteria for the Fed. • Rudebusch (2002) states that lagged interest rates soak up the persistence implied by serially correlated policy shocks. • Given that, we find a serial correlation in preference shocks, Rudebush (2002) argument seems to be valid.

49. Results • In this paper, we showed that, given the state of the economy, it is possible to estimate the “hidden” time-varying preferences of the Fed. • Such a methodology also allows us to generate the preference shocks of the Fed.

50. Results • The results are consistent with the literature: • The weight of the output gap in the loss function goes down to zero, implying that output gap is important as long as it affects inflation • There is a one-time discrete change in policy in the Volcker period. The Greenspan period is silent. • It is possible to generate almost identical interest rates, even without imposing interest rate smoothing incentive to the loss function.