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.
INTERBANK LENDING RATE (%) 7 6 US Japan 5 4 3 99 996 4 8
EMPLOYMENT-TO-POPULATION (%) 66 64 US Japan 6 6 58 56 99 996 4 8
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
ECONOMIC FRAMEWORK AND QUESTIONS Alternative model setups: Model : Labor Only Model : Capital Examine both technology and discount factor shocks Key questions:. Do technology shocks have unconventional effects? Paradox of Thrift Paradox of Toil. 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?
KEY FINDINGS. The output gap specification may reverse the effects of technology shocks at the ZLB: Steady-state output gap (y t = ȳ): unconventional dynamics Potential output gap (y t = yt n ): conventional dynamics. When the central bank targets the steady-state output gap, a technology shock leads to more pronounced unconventional dynamics in Model than in Model. 3. In Model, the constrained linear model provides a decent approximation of the nonlinear model, but meaningful differences exist between the Model solutions
KEY MODEL FEATURES Representative Household Values consumption and leisure with preferences E t= β t {log(c t ) χn +η t /(+η)} Cashless economy and bonds are in zero net supply Model : no capital accumulation Model : adds capital with quadratic adjustment costs Intermediate and final goods firms Monopolistically competitive intermediate firms produce differentiated inputs Rotemberg (98) quadratic costs to adjusting prices A competitive final goods firm combines the intermediate inputs to produce the consumption good
MONETARY POLICY Monetary policy rule r t = max{, r(π t /π ) φπ (y t /yt } )φy Output target (yt ) Steady-state output target: y t = ȳ Potential output target: y t = yt n Calibration: Baseline: π =.6, r =., φ π =.5, and φ y =. We also examine alternative values of φy
STOCHASTIC PROCESSES AND SOLUTION Discount factor (β) follows an AR() process The mean is.995 and the AR() parameter is.8 The standard deviation of shocks is.5% per quarter The state space is ±.9% around the mean Technology (z) follows an AR() process The mean is and the AR() parameter is.9 The standard deviation of shocks is.5% per quarter The state space is ±.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
MODEL : DISTRIBUTIONS (y t = ȳ) 5 5 3 3 Technology (ẑ) Discount Factor (ˆβ).4.3...5.4.3.. 3 3 Technology (ẑ).5.5.5 3 3.5 Nominal Interest Rate ( r) Discount Factor (ˆβ)
MODEL : NOMINAL INTEREST RATE (y t = ȳ).5.5 Discount Factor (ˆβ ).75.75.5.5.5.5.5.5 3 3.5 Technology (ẑ )
MODEL : ADJUSTED OUTPUT (y t = ȳ).5 4 6 4 8 Discount Factor (ˆβ ).75.75.5 Technology (ẑ ) 4
MODEL : CROSS SECTIONS (y t = ȳ) ẑ = ˆβ =.9 Discount Factor (ˆβ ).5.75.75.5.5.5.5 3.5 3.5.5.5 Technology (ẑ )
MODEL : SOLUTION ACROSS DISC. FACTOR Adjusted Output (ŷ adj ).5 Real Interest Rate ( r/e[π]).5 4.5.75.75.5 Discount Factor (ˆβ ).5.75.75.5 Discount Factor (ˆβ ) Inflation Rate ( π) 3 Nominal Interest Rate ( r).5.75.75.5 Discount Factor (ˆβ ).5.75.75.5 Discount Factor (ˆβ )
MODEL : SOLUTION ACROSS TECHNOLOGY φ y = φ y =.5 φ y =. 3 Adjusted Output (ŷ adj ) Technology (ẑ ).5.5 Real Interest Rate ( r/e[π]) Technology (ẑ ) Inflation Rate ( π) Technology (ẑ ).75.5.5 Nominal Interest Rate ( r) Technology (ẑ )
IMPULSE RESPONSE: TECHNOLOGY SHOCK.75.5.5 Adjusted Output (ŷ adj ).5.75 Nominal Interest Rate (ˆr) Steady State Scenario Real Interest Rate ( r/e[π]).6.4..5 Labor Hours (ˆn) ZLB Scenario.5.5 Inflation Rate (ˆπ).5.5.5.75.4.8.4 Real Wage Rate (ŵ)
MODEL : OUTPUT GAP Steady-State Output Potential Output.5.5 3 Technology (ẑ )
MODEL : OUTPUT TARGET COMPARISON 3 No Output Steady-State Output Potential Output Adjusted Output (ŷ adj ) Technology (ẑ ).5.5 Real Interest Rate ( r/e[π]) Technology (ẑ ) Inflation Rate ( π) Technology (ẑ ).75.5.5 Nominal Interest Rate ( r) Technology (ẑ )
MODEL : SIMULATION Steady-State Output (y t = ȳ) Potential Output (y t = yn t ) ZLB Binds Std. Dev. (% of mean) ZLB Binds Std. Dev. (% of mean) φ y % of quarters Output Inflation % of quarters Output Inflation.5.73.65.336.56.6993.8..56.674.338.67.77.98.75.45.695.33.8.734.35.5.38.767.3335.95.7376.35.5.33.743.3379.3.7537.393..33.779.3447.33.779.3447 *5, quarter simulation. φ π =.5, ρ z =.9, σ z =.5, ρ β =.8, and σ β =.5.
MODEL : COMPLETE SOLUTION Nominal Interest Rate ( r) Adjusted Output (ŷ adj ).5.5 4 6 8 Discount Factor (ˆβ ).75.75.5.5 Discount Factor (ˆβ ).75.75.5.5.5 5.5.5 5 Capital (ˆk ) 5.5.5 5 Capital (ˆk )
MODEL : COMPLETE SOLUTION Consumption (ĉ) Investment (î) Discount Factor (ˆβ ).5.75.75.5 4 4 6 5.5.5 5 Capital (ˆk ) Discount Factor (ˆβ ).5.75.75.5 5 5 5 5 5 5.5.5 5 Capital (ˆk )
MODEL : CROSS SECTIONS ˆk = ˆk = ˆk diag Consumption (ĉ) Investment (î) Discount Factor (ˆβ ).5.75.75.5 4 4 6 5.5.5 5 Capital (ˆk ) Discount Factor (ˆβ ).5.75.75.5 5 5 5 5 5 5.5.5 5 Capital (ˆk )
MODEL : SOLUTION ACROSS DISC. FACTOR ˆk = ˆk = ˆk diag Adjusted Output (ŷ adj ) Labor Hours (ˆn) 3 6 3 9 3.5.75.75.5 Discount Factor (ˆβ ) Consumption (ĉ) 6.5.75.75.5 Discount Factor (ˆβ ) Investment (î) 3 6.5.75.75.5 Discount Factor (ˆβ ) 4.5.75.75.5 Discount Factor (ˆβ )
MODEL : SOLUTION ACROSS DISC. FACTOR ˆk = ˆk = ˆk diag.5.5 Real Interest Rate ( r/e[π]).5.75.75.5 Discount Factor (ˆβ ) Nominal Interest Rate ( r) 4 Inflation Rate ( π).5.75.75.5 Discount Factor (ˆβ ) Real Rental Rate (r k ) 3 3.5 3.5.75.75.5 Discount Factor (ˆβ ).85.7.5.75.75.5 Discount Factor (ˆβ )
IMPULSE RESPONSE: TECHNOLOGY SHOCK.5 Adjusted Output (ŷ adj ) Model Model.6.4. Real Interest Rate ( r/e[π]) 5 5 Inflation Rate ( π) 5 5 Labor Hours (ˆn).5 5 5 5 5
SIMULATION COMPARISON (y t = ȳ) Both models only contain discount factor shocks Without technology shocks, ȳ = y n t in Model Model Model ZLB Binds Std. Dev. (% of mean) ZLB Binds Std. Dev. (% of mean) φ y % of quarters Output Inflation % of quarters Output Inflation...497.769.5.45.979.75.9.568.878.35.47.654.5.39.538.997.6.47.473.5.5.565.36.7.44.34..64.587.368.3.458.33 *5, quarter simulation. φ π =.5, ρ β =.8, and σ β =.5.
MODEL : NONLINEARITIES (y t = ȳ) Nonlinear Linear Output (ŷ) Output (ŷ) 3 4 Technology (ẑ ) 4.5.75.75.5 Discount Factor (ˆβ )
MODEL : NONLINEARITIES (y t = ȳ) Nonlinear Linear 4 Output (ŷ).5.75.75.5 Discount Factor (ˆβ ).75.5.5 Real Interest Rate ( r/e[π]).5.75.75.5 Discount Factor (ˆβ ) Inflation Rate ( π) 3 Nominal Interest Rate ( r).5.75.75.5 Discount Factor (ˆβ ).5.75.75.5 Discount Factor (ˆβ )
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.