# Taylor's Rule and the Fed

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Taylor’s Rule and the Fed: 1970 – 1997

Objective: Estimates a simple model of the Federal Reserve’s “reaction function”:

- Relationship between economic developments and the Fed’s response to them.
- How Fed alters monetary policy in response to economic developments.

Fed’s “reaction function” serves 3 functions:

- Basis for forecasting changes in short-term interest rates set by Fed.
- Evaluates Fed policy and the effects of other policy actions or economic shocks.
- When rational expectations are assumed in macro model: knowing the correct reaction function is an important element in estimating the entire model.

No successful in providing a definitive representation of Fed behavior in the past: “One who examines just one of these reaction functions may feel convinced that one has learned how the Fed responds to economic conditions, but that seeming knowledge disappears as one reads a large number of these studies.”

Most important reason: Changes associated with different chairmen. Each new chairman adapt to lessons learned from prior experiences.

Taylor’s Rule:

- Simple rule for monetary policy:
- Nominal federal funds rate equal to the rate of inflation.
- How real federal funds rates reacts to:
- Deviations of inflation from an inflation target and deviations of real output from its long-run potential level.
- It stabilizes both inflation and output reasonably well in a variety of macro models.

Part I Taylor’s Original Rule:

i_t=π_t+r^*+0.5(π_t-π^* )+ 0.5(y_t) Equation (1)

- i = federal funds rate
- r^*= equilibrium real federal funds rate
- π = average inflation rate over the contemporaneous
- π^*= target inflation rate
- y = output gap (100*(real GDP – potential GDP) /potential GDP)
- 0.5 = assumes weights Fed gave to deviations of inflation and output
- Assumes that equilibrium real interest rate and inflation target is 2%.

Overall, by focusing on policy responses to the Fed’s basic goal variables, the Taylor rule implicitly captures policy responses to the many economic factors that affect the evolution of those goal variables.

Part II Estimating the Taylor Rule with Dynamics: i_t^*=π_t+r^*+λ_1 (π_t-π^* )+ λ_2 y_t+λ_3 y_(t-1) Equation (2)

Adjustment of the actual level of the funds rate: 〖Δi〗_t=γ( i_t^*-i_(t-1) )+ρΔi_(t-1) Equation(3)

By substituting equation (2) into (3) 〖Δi〗_t=γα-γi_(t-1)+γ(1+λ_1 ) π_t+rλ_2 y_t+λ_3 y_(t-1)+ρΔi_(t-1) Equation(4)

This equation provides estimates of the weights on inflation and output in the rule and on the speed of adjustment to the rule. Where: α=r^*-λ_1 π^*.

Estimating Potential Real GDP: y = output gap (100*(real GDP – potential GDP) /potential GDP) Potential output is unobserved and must be estimated. The author used a structural approach to estimating the output gap. Output in policy rule may reflect an interest in stabilizing real fluctuations but also may provide policymakers some information on future inflation.

Part III Estimates of reaction function: Our main hypothesis is that taking account of changes in Fed Chairmen helps to account the changes in the Fed’s reaction function.

Chow tests on equation (4) corresponding to the terms of Chairmen Burns, Volcker, and Greenspan. The tests give the null hypothesis of no structural change (p-value of 0.00 and 0.07).

Chow tests: Greenspan Period:

- 71% of the quarterly variation in the change in the funds rate and has a standard error of 27 basis points. This regression has a closer fit with the data than Taylor’s original specification.
- Estimates suggest gradual, rather than instantaneous, adjustment of the funds rate to the rule.
- Estimated weight on the GDP gap of 0.99 is higher than Taylor assumed 0.50.
- A larger weight on the output gap than Taylor assumed produced a lower output variance for a given inflation variance in model simulations.
- Estimates of both inflation target and real equilibrium funds rate all lie in a range from 1.8 to 2.8 percent.
- Not far from Taylor’s assumption of 2 percent.

Volcker Period:

- GDP gap enters: Coefficient on the inflation gap is very close to the 0.5 assumed by Taylor.
- Wilder range of estimates for the implicit inflation target than Greenspan period.
- Average real funds rate 5.35% (Volcker) differs substantially from the average over the entire sample of 2.39%.
- Inflation target range from 6.4% to 0.1%.

Burns period:

- Productivity and potential output both exhibited a surprising slowdown in growth.
- Increase in the natural rate of unemployment that also was unexpected.
- Unemployment rate of 4 or 5 percent was a suitable benchmark rate for policy.
- However, estimates of the natural rate are in the 6% range.
- Such a difference could account for the consistently easy policy during the Burns period.

Part IV Model-Based Evaluation of Alternative Policy Rules: Evaluate the effectiveness of policy rules or reaction functions above in terms of the volatility of inflation and output that might result if the rule were used by policymakers, by using a simple model from Rudebusch and Svensson. It includes an aggregate supply equation or “Phillips Curve” that relates inflation to the output gap and an aggregate demand equation or “IS Curve” that relates output to a short-term interest rate.

Model-Based Volatility Results:

Monetary Policy Standard Deviation Reaction Function π У

Taylor rule: 3.86 2.23 Greenspan period: 3.87 2.18 Volcker period: 4.80 2.73 Burns period: Does not converge

Conclusion:
Read Taylor’s Rule and the Fed: 1970 – 1997 section on conclusion.