I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION T HE Z ERO L OWER B OUND , THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS 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.
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION I NTERBANK L ENDING R ATE (%) 7 US 6 Japan 5 4 3 2 1 0 1992 1996 2000 2004 2008 2012 G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION E MPLOYMENT - TO -P OPULATION (%) 66 US Japan 64 62 60 58 56 1992 1996 2000 2004 2008 2012 G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION M OTIVATION • 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 G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION E CONOMIC F RAMEWORK AND Q UESTIONS • 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? G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION K EY F INDINGS 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 = y n 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 G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION K EY M ODEL F EATURES • Representative Household ◮ Values consumption and leisure with preferences � ∞ β t { log( c t ) − χn 1+ η � E 0 / (1 + η ) } t t =0 ◮ 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 G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION M ONETARY P OLICY • Monetary policy rule r ( π t /π ∗ ) φ π ( y t /y ∗ t ) φ y } r t = max { 1 , ¯ • Output target ( y ∗ t ) ◮ Steady-state output target: y ∗ t = ¯ y ◮ Potential output target: y ∗ t = y n t • Calibration: ◮ Baseline: π ∗ = 1 . 006 , ¯ r = 1 . 011 , φ π = 1 . 5 , and φ y = 0 . 1 ◮ We also examine alternative values of φ y G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION S TOCHASTIC P ROCESSES AND S OLUTION • 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 G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION M ODEL 1: D ISTRIBUTIONS ( y ∗ y ) t = ¯ 20 0.4 0.3 10 0.2 0 −3 −2 −1 0 1 2 3 0.1 Technology (ˆ z ) 20 0 −3 −2 −1 0 1 2 3 10 Technology (ˆ z ) 0.5 0 −2 −1 0 1 2 0.4 Discount Factor ( ˆ β ) 0.3 15 0.2 10 0.1 5 0 0 0 0.5 1 1.5 2 2.5 3 3.5 −2 −1 0 1 2 Nominal Interest Rate (˜ r ) Discount Factor ( ˆ β ) G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION M ODEL 1: N OMINAL I NTEREST R ATE ( y ∗ y ) t = ¯ 1.5 0.5 β − 1 ) 0.75 1 Discount Factor (ˆ 1 . 5 0.5 0 2 1 1 . 5 −0.75 2 . 5 2 −1.5 3 3 2 . . 5 5 −2 −1 0 1 2 Technology (ˆ z − 1 ) G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION M ODEL 1: A DJUSTED O UTPUT ( y ∗ y ) t = ¯ −4 − −6 8 1.5 − 4 −2 − 2 β − 1 ) 0.75 Discount Factor (ˆ 0 0 0 −0.75 2 −1.5 4 −2 −1 0 1 2 Technology (ˆ z − 1 ) G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION M ODEL 1: C ROSS S ECTIONS ( y ∗ y ) t = ¯ ˆ z − 1 = 0 ˆ β − 1 = 0 . 9 1.5 0.5 β − 1 ) 0.75 1 Discount Factor (ˆ 1 . 5 0.5 0 2 1 1 2 . 5 −0.75 . 5 2 −1.5 3 3 2 . . 5 5 −2 −1 0 1 2 Technology (ˆ z − 1 ) G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION M ODEL 1: S OLUTION A CROSS D ISC . F ACTOR Real Interest Rate ( � y adj ) Adjusted Output (ˆ r/E [ π ]) 2 1.5 0 1 −2 0.5 −4 0 −1.5 −0.75 0 0.75 1.5 −1.5 −0.75 0 0.75 1.5 Discount Factor (ˆ Discount Factor (ˆ β − 1 ) β − 1 ) In fl ation Rate (˜ π ) Nominal Interest Rate (˜ r ) 2 3 1 2 0 1 −1 0 −1.5 −0.75 0 0.75 1.5 −1.5 −0.75 0 0.75 1.5 Discount Factor (ˆ Discount Factor (ˆ β − 1 ) β − 1 ) G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION M ODEL 1: S OLUTION A CROSS T ECHNOLOGY φ y = 0 φ y = 0 . 05 φ y = 0 . 1 Real Interest Rate ( � y adj ) Adjusted Output (ˆ r/E [ π ]) 1.5 −1 1 −2 0.5 −3 0 −2 −1 0 1 2 −2 −1 0 1 2 Technology (ˆ z − 1 ) Technology (ˆ z − 1 ) In fl ation Rate (˜ π ) Nominal Interest Rate (˜ r ) 1 1 0.75 0 0.5 −1 0.25 −2 0 −2 −1 0 1 2 −2 −1 0 1 2 Technology (ˆ z − 1 ) Technology (ˆ z − 1 ) G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION I MPULSE R ESPONSE : T ECHNOLOGY S HOCK Steady−State Scenario ZLB Scenario Real Interest Rate ( � y adj ) Adjusted Output (ˆ r/E [ π ]) In fl ation Rate (ˆ π ) 0.6 0.75 0.5 0.5 0.4 0 0.25 0.2 0 −0.5 0 −0.25 0 10 20 0 10 20 0 10 20 Nominal Interest Rate (ˆ r ) Labor Hours (ˆ n ) Real W age Rate ( ˆ w ) 0.8 0 1 −0.25 0.4 0.75 0.5 −0.5 0 0.25 −0.75 −0.4 0 −1 0 10 20 0 10 20 0 10 20 G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
I NTRODUCTION M ODELS M ODEL 1 R ESULTS M ODEL 2 R ESULTS M ODEL C OMPARISON C ONCLUSION M ODEL 1: O UTPUT G AP Steady-State Output Potential Output −1 −1.5 −2 −2.5 −3 −2 −1 0 1 2 Technology (ˆ z − 1 ) G AVIN , K EEN , R ICHTER AND T HROCKMORTON : T HE ZLB, THE D UAL M ANDATE , AND U NCONVENTIONAL D YNAMICS
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