T HE Z ERO L OWER B OUND , THE D UAL M ANDATE , AND U NCONVENTIONAL D - - PowerPoint PPT Presentation

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

THE ZERO LOWER BOUND, THE DUAL MANDATE,

AND UNCONVENTIONAL DYNAMICS William T. Gavin

Federal Reserve Bank of St. Louis

Benjamin D. Keen

University of Oklahoma

Alexander W. Richter

Auburn University

Nathaniel A. Throckmorton

College of William & Mary

The views expressed in this presentation are our own and do not necessarily reflect the views of the Federal Reserve Banks of St. Louis or the Federal Reserve System.

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

INTERBANK LENDING RATE (%)

1992 1996 2000 2004 2008 2012 1 2 3 4 5 6 7 US Japan

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

EMPLOYMENT-TO-POPULATION (%)

1992 1996 2000 2004 2008 2012 56 58 60 62 64 66 US Japan

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MOTIVATION

• Five years after the crisis began

◮ the Fed’s target interest rate remains near zero ◮ the economy is below potential

• Motivates the need for a better understanding of

◮ the canonical model used for monetary policy analysis ◮ the effect of the central bank’s dual mandate

• This paper calculates global nonlinear solutions to

standard New Keynesian models with and without capital and a provides a thorough explanation of the dynamics

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

ECONOMIC FRAMEWORK AND QUESTIONS

• Alternative model setups:

◮ Model 1: Labor Only ◮ Model 2: Capital

• Examine both technology and discount factor shocks
• Key questions:
• 1. Do technology shocks have unconventional effects?
• Paradox of Thrift
• Paradox of Toil
• 2. What are the effects of the Fed shifting their focus to the

real economy?

• 3. Is it important to include capital in the model?
• 4. Is it important to solve the fully nonlinear model?

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

KEY FINDINGS

• 1. The output gap specification may reverse the effects of

technology shocks at the ZLB:

◮ Steady-state output gap (y∗

t = ¯

y): unconventional dynamics

◮ Potential output gap (y∗

t = yn t ): conventional dynamics

• 2. When the central bank targets the steady-state output gap,

a technology shock leads to more pronounced unconventional dynamics in Model 2 than in Model 1.

• 3. In Model 1, the constrained linear model provides a decent

approximation of the nonlinear model, but meaningful differences exist between the Model 2 solutions

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

KEY MODEL FEATURES

• Representative Household

◮ Values consumption and leisure with preferences

E0

∞

• t=0
• βt{log(ct) − χn1+η

t

/(1 + η)}

◮ Cashless economy and bonds are in zero net supply ◮ Model 1: no capital accumulation ◮ Model 2: adds capital with quadratic adjustment costs

• Intermediate and final goods firms

◮ Monopolistically competitive intermediate firms produce

differentiated inputs

◮ Rotemberg (1982) quadratic costs to adjusting prices ◮ A competitive final goods firm combines the intermediate

inputs to produce the consumption good

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MONETARY POLICY

• Monetary policy rule

rt = max{1, ¯ r(πt/π∗)φπ(yt/y∗

t )φy}

• Output target (y∗

t )

◮ Steady-state output target: y∗

t = ¯

y

◮ Potential output target: y∗

t = yn t

• Calibration:

◮ Baseline: π∗ = 1.006, ¯

r = 1.011, φπ = 1.5, and φy = 0.1

◮ We also examine alternative values of φy GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

STOCHASTIC PROCESSES AND SOLUTION

• Discount factor (β) follows an AR(1) process

◮ The mean is 0.995 and the AR(1) parameter is 0.8 ◮ The standard deviation of shocks is 0.25% per quarter ◮ The state space is ±1.9% around the mean

• Technology (z) follows an AR(1) process

◮ The mean is 1 and the AR(1) parameter is 0.9 ◮ The standard deviation of shocks is 0.25% per quarter ◮ The state space is ±2.5% around the mean

• Compute nonlinear solutions using policy function iteration

◮ Linear interpolation and Gauss Hermite quadrature ◮ Duration of ZLB events is stochastic ◮ Expectational effects of hitting and leaving ZLB GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 1: DISTRIBUTIONS (y∗

t = ¯

y)

−3 −2 −1 1 2 3 10 20 Technology (ˆ z) −2 −1 1 2 10 20 Discount Factor ( ˆ β) 0.5 1 1.5 2 2.5 3 3.5 5 10 15 Nominal Interest Rate (˜ r) −3 −2 −1 1 2 3 0.1 0.2 0.3 0.4 Technology (ˆ z) −2 −1 1 2 0.1 0.2 0.3 0.4 0.5 Discount Factor ( ˆ β)

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 1: NOMINAL INTEREST RATE (y∗

t = ¯

y)

0.5 0.5 1 1 1 . 5 1 . 5 2 2 2 . 5 2 . 5 3 3 . 5

Technology (ˆ z−1) Discount Factor (ˆ β−1) −2 −1 1 2 −1.5 −0.75 0.75 1.5

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 1: ADJUSTED OUTPUT (y∗

t = ¯

y)

− 8 −6 − 4 −4 −2 − 2 2 4

Technology (ˆ z−1) Discount Factor (ˆ β−1) −2 −1 1 2 −1.5 −0.75 0.75 1.5

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 1: CROSS SECTIONS (y∗

t = ¯

y)

0.5 0.5 1 1 1 . 5 1 . 5 2 2 2 . 5 2 . 5 3 3 . 5

Technology (ˆ z−1) Discount Factor (ˆ β−1) −2 −1 1 2 −1.5 −0.75 0.75 1.5 ˆ z−1 = 0 ˆ β−1 = 0.9

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 1: SOLUTION ACROSS DISC. FACTOR

Adjusted Output (ˆ yadj) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 −4 −2 2 Real Interest Rate ( r/E[π]) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 0.5 1 1.5 Inflation Rate (˜ π) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 −1 1 2 Nominal Interest Rate (˜ r) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 1 2 3

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 1: SOLUTION ACROSS TECHNOLOGY

Adjusted Output (ˆ yadj) Technology (ˆ z−1) −2 −1 1 2 −3 −2 −1 Real Interest Rate ( r/E[π]) Technology (ˆ z−1) −2 −1 1 2 0.5 1 1.5 Inflation Rate (˜ π) Technology (ˆ z−1) −2 −1 1 2 −2 −1 1 Nominal Interest Rate (˜ r) Technology (ˆ z−1) −2 −1 1 2 0.25 0.5 0.75 1 φy = 0 φy = 0.05 φy = 0.1

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

IMPULSE RESPONSE: TECHNOLOGY SHOCK

10 20 −0.25 0.25 0.5 0.75 Adjusted Output (ˆ yadj) 10 20 0.2 0.4 0.6 Real Interest Rate ( r/E[π]) 10 20 −0.5 0.5 Inflation Rate (ˆ π) 10 20 0.25 0.5 0.75 1 Nominal Interest Rate (ˆ r) 10 20 −1 −0.75 −0.5 −0.25 Labor Hours (ˆ n) 10 20 −0.4 0.4 0.8 Real W age Rate ( ˆ w) Steady−State Scenario ZLB Scenario

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 1: OUTPUT GAP

Technology (ˆ z−1) −2 −1 1 2 −3 −2.5 −2 −1.5 −1 Steady-State Output Potential Output

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 1: OUTPUT TARGET COMPARISON

Adjusted Output (ˆ yadj) Technology (ˆ z−1) −2 −1 1 2 −3 −2 −1 Real Interest Rate ( r/E[π]) Technology (ˆ z−1) −2 −1 1 2 0.5 1 1.5 Inflation Rate (˜ π) Technology (ˆ z−1) −2 −1 1 2 −2 −1 1 Nominal Interest Rate (˜ r) Technology (ˆ z−1) −2 −1 1 2 0.25 0.5 0.75 1 No Output Steady-State Output Potential Output

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 1: SIMULATION

Steady-State Output (y∗

t = ¯

y) Potential Output (y∗

t = yn t )

ZLB Binds

• Std. Dev. (% of mean)

ZLB Binds

• Std. Dev. (% of mean)

φy % of quarters Output Inflation % of quarters Output Inflation 0.125 2.73 0.6501 0.3326 1.56 0.6993 0.2800 0.100 2.56 0.6704 0.3308 1.67 0.7107 0.2908 0.075 2.45 0.6925 0.3311 1.80 0.7234 0.3025 0.050 2.38 0.7167 0.3335 1.95 0.7376 0.3152 0.025 2.33 0.7431 0.3379 2.13 0.7537 0.3293 0.000 2.33 0.7719 0.3447 2.33 0.7719 0.3447 *500,000 quarter simulation. φπ = 1.50, ρz = 0.90, σz = 0.0025, ρβ = 0.80, and σβ = 0.0025.

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 2: COMPLETE SOLUTION

. 5 1 1.5 2 2.5 Nominal Interest Rate (˜ r) Capital (ˆ k−1) Discount Factor (ˆ β−1) −5 −2.5 2.5 5 −1.5 −0.75 0.75 1.5 − 8 −6 −4 −2 Adjusted Output (ˆ yadj) Capital (ˆ k−1) Discount Factor (ˆ β−1) −5 −2.5 2.5 5 −1.5 −0.75 0.75 1.5

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 2: COMPLETE SOLUTION

−6 − 4 −2 2 4 Consumption (ˆ c) Capital (ˆ k−1) Discount Factor (ˆ β−1) −5 −2.5 2.5 5 −1.5 −0.75 0.75 1.5 −15 −10 −10 −5 −5 5 1 1 5 Investment (ˆ i) Capital (ˆ k−1) Discount Factor (ˆ β−1) −5 −2.5 2.5 5 −1.5 −0.75 0.75 1.5

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 2: CROSS SECTIONS

−6 − 4 −2 2 4 Consumption (ˆ c) Capital (ˆ k−1) Discount Factor (ˆ β−1) −5 −2.5 2.5 5 −1.5 −0.75 0.75 1.5 −15 −10 −10 −5 −5 5 1 1 5 Investment (ˆ i) Capital (ˆ k−1) Discount Factor (ˆ β−1) −5 −2.5 2.5 5 −1.5 −0.75 0.75 1.5 ˆ k−1 = 0 ˆ k−1 = ˆ kdiag

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 2: SOLUTION ACROSS DISC. FACTOR

Adjusted Output (ˆ yadj) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 −9 −6 −3 Labor Hours (ˆ n) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 −6 −3 Consumption (ˆ c) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 −6 −3 3 Investment (ˆ i) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 −24 −12 12 ˆ k−1 = 0 ˆ k−1 = ˆ kdiag

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 2: SOLUTION ACROSS DISC. FACTOR

Real Interest Rate ( r/E[π]) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 0.5 1 1.5 2 Inflation Rate (˜ π) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 −4 −2 2 Nominal Interest Rate (˜ r) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 1 2 3 Real Rental Rate (rk) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 2.7 2.85 3 3.15 ˆ k−1 = 0 ˆ k−1 = ˆ kdiag

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

IMPULSE RESPONSE: TECHNOLOGY SHOCK

5 10 15 20 −1 −0.5 Adjusted Output (ˆ yadj) 5 10 15 20 0.2 0.4 0.6 Real Interest Rate ( r/E[π]) 5 10 15 20 −1 −0.5 Inflation Rate (˜ π) 5 10 15 20 −2 −1 Labor Hours (ˆ n) Model 1 Model 2

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

SIMULATION COMPARISON (y∗

t = ¯

y)

• Both models only contain discount factor shocks
• Without technology shocks, ¯

y = yn

t in Model 1 Model 1 Model 2 ZLB Binds

• Std. Dev. (% of mean)

ZLB Binds

• Std. Dev. (% of mean)

φy % of quarters Output Inflation % of quarters Output Inflation 0.100 1.20 0.4972 0.2769 1.15 0.4005 0.2979 0.075 1.29 0.5168 0.2878 0.35 0.4127 0.2654 0.050 1.39 0.5382 0.2997 0.16 0.4271 0.2473 0.025 1.51 0.5615 0.3126 0.07 0.4421 0.2304 0.000 1.64 0.5870 0.3268 0.03 0.4581 0.2133 *500,000 quarter simulation. φπ = 1.50, ρβ = 0.80, and σβ = 0.0025.

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 1: NONLINEARITIES (y∗

t = ¯

y)

Output (ˆ y) Technology (ˆ z−1) −2 −1 1 2 −4 −3 −2 −1 Output (ˆ y) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 −4 −2 2 Nonlinear Linear

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

MODEL 2: NONLINEARITIES (y∗

t = ¯

y)

Output (ˆ y) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 −4 −2 2 Real Interest Rate ( r/E[π]) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 0.25 0.5 0.75 1 Inflation Rate (˜ π) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 −2 −1 1 2 Nominal Interest Rate (˜ r) Discount Factor (ˆ β−1) −1.5 −0.75 0.75 1.5 1 2 3 Nonlinear Linear

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS

INTRODUCTION MODELS MODEL 1 RESULTS MODEL 2 RESULTS MODEL COMPARISON CONCLUSION

SUMMARY OF FINDINGS

• Our models show that technology shocks at the ZLB can

have unconventional effects on the economy.

• Whether the central bank targets the steady-state output

gap or the potential output matters.

• Whether capital is included in the model matters.
• Linearization works well for the model without capital but

does not work well in the model with capital.

• The dual mandate probably does not help stabilize output

because potential output is generally unknown in real time.

GAVIN, KEEN, RICHTER AND THROCKMORTON: THE ZLB, THE DUAL MANDATE, AND UNCONVENTIONAL DYNAMICS