Objective Findings Comments Discussion on “Stagnation Traps” Jang-Ting Guo Department of Economics University of California, Riverside May 15, 2015 Jang-Ting Guo Discussion on “Stagnation Traps” 1 / 12
Objective Findings Comments Existence and Persistence of Stagnation Trap in a Monetary Endogenous Growth Model with Quality Ladders ⇒ Coexistence of Positive Unemployment, Low Growth, and Liquidity Trap Jang-Ting Guo Discussion on “Stagnation Traps” 2 / 12
Objective Findings Comments Existence and Persistence of Stagnation Trap in a Monetary Endogenous Growth Model with Quality Ladders ⇒ Coexistence of Positive Unemployment, Low Growth, and Liquidity Trap The Key Mechanism (1) Unemployment and Weak Aggregate Demand ⇒ Reduces Firms’ Investment in Innovation ⇒ Low Growth (2) Low Growth ⇒ Reduces Real Interest Rate ⇒ Pushes Nominal Interest Rate to Zero Jang-Ting Guo Discussion on “Stagnation Traps” 2 / 12
Objective Findings Comments Two Steady States in Baseline Model (1) Full Employment y f = 1, High Growth g f , Positive Nominal Interest Rate i f > 0, and Positive/Negative Inflation Rate π f ≷ 1 (2) Unemployment y u < 1, Low Growth g u < g f , Zero Nominal Interest Rate i u = 0, and Negative Inflation Rate π u < 1 Jang-Ting Guo Discussion on “Stagnation Traps” 3 / 12
Objective Findings Comments Two Steady States in Baseline Model (1) Full Employment y f = 1, High Growth g f , Positive Nominal Interest Rate i f > 0, and Positive/Negative Inflation Rate π f ≷ 1 (2) Unemployment y u < 1, Low Growth g u < g f , Zero Nominal Interest Rate i u = 0, and Negative Inflation Rate π u < 1 Two Extensions: Precautionary Savings and Time-Varying Inflation Rate Constant or Countercyclical Subsidy to Firms’ Investment in Innovation ⇒ Removal of Low-Growth Steady State Jang-Ting Guo Discussion on “Stagnation Traps” 3 / 12
Objective Findings Comments Two Steady States: y f = 1 and y u < 1 ⇒ y Denotes the Level of Actual Output ⇒ 1 − y = Output Gap Jang-Ting Guo Discussion on “Stagnation Traps” 4 / 12
Objective Findings Comments Two Steady States: y f = 1 and y u < 1 ⇒ y Denotes the Level of Actual Output ⇒ 1 − y = Output Gap Figure 1 ⇒ Local Stability Property of Each Steady State: Saddle, Sink or Source Possibility of Global Indeterminacy ⇒ Various Forms of Bifurcations Jang-Ting Guo Discussion on “Stagnation Traps” 4 / 12
AD GG (1 , g f ) growth g ( y u , g u ) output gap y
Objective Findings Comments This Paper β t C 1 − σ ∞ − 1 � t max 0 < β < 1 , 1 − σ t =0 �� 1 � � 1 � � C t = exp ln q jt c jt dj and Q t = exp ln q jt dj 0 0 � σ � c t +1 where g t +1 = Q t +1 = β (1 + r t ) g 1 − σ t +1 , c t Q t Jang-Ting Guo Discussion on “Stagnation Traps” 5 / 12
Objective Findings Comments This Paper β t C 1 − σ ∞ − 1 � t max 0 < β < 1 , 1 − σ t =0 �� 1 � � 1 � � C t = exp ln q jt c jt dj and Q t = exp ln q jt dj 0 0 � σ � c t +1 where g t +1 = Q t +1 = β (1 + r t ) g 1 − σ t +1 , c t Q t Need σ > 1 such that (1) Positive Relationship between Present Consumption and Innovation Growth (2) Existence of Unemployment Steady State (3) i f > 0 at Full-Employment Steady State Jang-Ting Guo Discussion on “Stagnation Traps” 5 / 12
Objective Findings Comments Alternative Specification (Footnote 14) β t c 1 − σ ∞ − 1 � t max 0 < β < 1 , 1 − σ t =0 �� 1 � y t = f q jt X jt dj = f ( Q t ) 0 Jang-Ting Guo Discussion on “Stagnation Traps” 6 / 12
Objective Findings Comments Alternative Specification (Footnote 14) β t c 1 − σ ∞ − 1 � t max 0 < β < 1 , 1 − σ t =0 �� 1 � y t = f q jt X jt dj = f ( Q t ) 0 � σ � c t +1 = β (1 + r t ) c t � σ � c t +1 where g t +1 = Q t +1 = β (1 + r t ) g 1 − σ t +1 , c t Q t ⇒ Isomorphic Formulations Only When σ = 1 Jang-Ting Guo Discussion on “Stagnation Traps” 6 / 12
Objective Findings Comments This Paper � σ � c t +1 = β (1 + i t ) g 1 − σ Euler: t +1 ¯ c t π �� c t � σ t +1 ( χγ − 1 y t +1 + 1 − ln g t +2 � g 1 − σ Growth : 1 = β ) c t +1 γ ln γ When σ 1 ⇒ Positive Relationship between y t +1 and g t +1 > Jang-Ting Guo Discussion on “Stagnation Traps” 7 / 12
Objective Findings Comments This Paper � σ � c t +1 = β (1 + i t ) g 1 − σ Euler: t +1 ¯ c t π �� c t � σ t +1 ( χγ − 1 y t +1 + 1 − ln g t +2 � g 1 − σ Growth : 1 = β ) c t +1 γ ln γ When σ 1 ⇒ Positive Relationship between y t +1 and g t +1 > Market Clearing: c t + ln g t +1 χ ln γ = y t � � ı ) y φ Monetary Policy: 1 + i t = max (1 + ¯ t , 1 Jang-Ting Guo Discussion on “Stagnation Traps” 7 / 12
Objective Findings Comments Alternative Specification c 1 − σ − 1 t Period Utility: 1 − σ Jang-Ting Guo Discussion on “Stagnation Traps” 8 / 12
Objective Findings Comments Alternative Specification c 1 − σ − 1 t Period Utility: 1 − σ � 1 ( q jt X jt ) α dj , A > 0 , Final Good: Y t = A 0 < α < 1 0 1 � A α q α � 1 − α jt Demand for X jt : X jt = P jt Jang-Ting Guo Discussion on “Stagnation Traps” 8 / 12
Objective Findings Comments Alternative Specification c 1 − σ − 1 t Period Utility: 1 − σ � 1 ( q jt X jt ) α dj , A > 0 , Final Good: Y t = A 0 < α < 1 0 1 � A α q α � 1 − α jt Demand for X jt : X jt = P jt � 1 L jt dj + L RD Supply for X jt : X jt = L jt , where + U t = L t 0 W t R&D Firms’ Profits: π jt = ( P jt − W t ) X jt , = ¯ π W t − 1 Jang-Ting Guo Discussion on “Stagnation Traps” 8 / 12
Objective Findings Comments Monopoly Pricing: P jt = W t α 1 � A α 2 q α � 1 − α jt Equilibrium Quantity: X jt = W t Jang-Ting Guo Discussion on “Stagnation Traps” 9 / 12
Objective Findings Comments Monopoly Pricing: P jt = W t α 1 � A α 2 q α � 1 − α jt Equilibrium Quantity: X jt = W t − α 1 2 α 1 − α α 1 − α W 1 − α Aggregate Output: Y t = A Q t , t � 1 α 1 − α where Q t = q dj jt 0 Y t α 1 − α Equilibrium Profit: π jt = α (1 − α ) q jt Q t Jang-Ting Guo Discussion on “Stagnation Traps” 9 / 12
Objective Findings Comments Probability of Innovating = χ L RD t = χµ t L Jang-Ting Guo Discussion on “Stagnation Traps” 10 / 12
Objective Findings Comments Probability of Innovating = χ L RD t = χµ t L � − σ � c t +1 Value Function: V t = β [ π jt +1 + (1 − χµ t +1 ) V t +1 ] c t Free Entry: L RD W t = χµ t V t ⇒ LW t = χ V t t Innovation Growth: g t +1 = Q t +1 1 − α ⇒ Y t +1 α − α = χµ t γ = g t +1 ¯ π 1 − α Q t Y t Jang-Ting Guo Discussion on “Stagnation Traps” 10 / 12
Objective Findings Comments Probability of Innovating = χ L RD t = χµ t L � − σ � c t +1 Value Function: V t = β [ π jt +1 + (1 − χµ t +1 ) V t +1 ] c t Free Entry: L RD W t = χµ t V t ⇒ LW t = χ V t t Innovation Growth: g t +1 = Q t +1 1 − α ⇒ Y t +1 α − α = χµ t γ = g t +1 ¯ π 1 − α Q t Y t χ Y t +1 π (1 − g t +2 α � � � � σα g − σ 1 − α Growth: 1 = β ¯ π α (1 − α ) q + ¯ 1 − α ) 1 − α t +1 j ( t +1) LW t Q t +1 α γ 0 ⇒ Positive Relationship between Y t +1 When σ > and g t +1 Q t +1 Jang-Ting Guo Discussion on “Stagnation Traps” 10 / 12
Objective Findings Comments Alternative Specification � σ � c t +1 = β (1 + i t ) Euler: c t ¯ π χ Y t +1 π (1 − g t +2 α � � � � σα g − σ 1 − α Growth: 1 = β ¯ π α (1 − α ) q + ¯ 1 − α ) 1 − α t +1 j ( t +1) LW t Q t +1 α γ 0 ⇒ Positive Relationship between Y t +1 When σ > and g t +1 Q t +1 Jang-Ting Guo Discussion on “Stagnation Traps” 11 / 12
Objective Findings Comments Alternative Specification � σ � c t +1 = β (1 + i t ) Euler: c t ¯ π χ Y t +1 π (1 − g t +2 α � � � � σα g − σ 1 − α Growth: 1 = β ¯ π α (1 − α ) q + ¯ 1 − α ) 1 − α t +1 j ( t +1) LW t Q t +1 α γ 0 ⇒ Positive Relationship between Y t +1 When σ > and g t +1 Q t +1 Market Clearing: c t = Y t ⇒ c t +1 = Y t +1 − α = g t +1 ¯ π 1 − α c t Y t i ) Y t Monetary Policy: 1 + i t = max { (1 + ¯ , 1 } Q t Jang-Ting Guo Discussion on “Stagnation Traps” 11 / 12
AD GG (1 , g f ) growth g ( y u , g u ) output gap y
Objective Findings Comments At Unemployment Steady State (1) Baseline ¯ π < 1 ⇒ Deflation Extension with Precautionary Savings, but Unemployed Households Cannot Borrow or Trade Firms’ Shares Jang-Ting Guo Discussion on “Stagnation Traps” 12 / 12
Objective Findings Comments At Unemployment Steady State (1) Baseline ¯ π < 1 ⇒ Deflation Extension with Precautionary Savings, but Unemployed Households Cannot Borrow or Trade Firms’ Shares (2) Zero Nominal Interest Rate i u = 0 Negative Nominal Interest Rates Observed in Europe: ECB’s Deposit Rate of − 0 . 2%, and Swiss National Bank’s Deposit Rate of − 0 . 75% � � ı ) y φ ⇒ 1 + i t = max (1 + ¯ t , i , where i ¯ < 1 ¯ Jang-Ting Guo Discussion on “Stagnation Traps” 12 / 12
AD GG (1 , g f ) growth g output gap y
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