Discussion on Stagnation Traps Jang-Ting Guo Department of - - PowerPoint PPT Presentation

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 yf = 1, High Growth gf , Positive Nominal Interest Rate if > 0, and Positive/Negative Inflation Rate πf ≷ 1 (2) Unemployment yu < 1, Low Growth gu < gf , Zero Nominal Interest Rate iu = 0, and Negative Inflation Rate πu < 1

Jang-Ting Guo Discussion on “Stagnation Traps” 3 / 12

Objective Findings Comments

Two Steady States in Baseline Model (1) Full Employment yf = 1, High Growth gf , Positive Nominal Interest Rate if > 0, and Positive/Negative Inflation Rate πf ≷ 1 (2) Unemployment yu < 1, Low Growth gu < gf , Zero Nominal Interest Rate iu = 0, and Negative Inflation Rate πu < 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: yf = 1 and yu < 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: yf = 1 and yu < 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

(yu, gu) (1, gf) AD GG growth g

• utput gap y

Objective Findings Comments

This Paper max

∞

• t=0

βt C 1−σ

t

− 1 1 − σ , 0 < β < 1 Ct = exp 1 ln qjtcjtdj

• and

Qt = exp 1 lnqjtdj

• ct+1

ct σ = β (1 + rt) g1−σ

t+1 ,

where gt+1 = Qt+1 Qt

Jang-Ting Guo Discussion on “Stagnation Traps” 5 / 12

Objective Findings Comments

This Paper max

∞

• t=0

βt C 1−σ

t

− 1 1 − σ , 0 < β < 1 Ct = exp 1 ln qjtcjtdj

• and

Qt = exp 1 lnqjtdj

• ct+1

ct σ = β (1 + rt) g1−σ

t+1 ,

where gt+1 = Qt+1 Qt Need σ > 1 such that (1) Positive Relationship between Present Consumption and Innovation Growth (2) Existence of Unemployment Steady State (3) if > 0 at Full-Employment Steady State

Jang-Ting Guo Discussion on “Stagnation Traps” 5 / 12

Objective Findings Comments

Alternative Specification (Footnote 14) max

∞

• t=0

βt c1−σ

t

− 1 1 − σ , 0 < β < 1 yt = f 1 qjtXjtdj

• = f (Qt)

Jang-Ting Guo Discussion on “Stagnation Traps” 6 / 12

Objective Findings Comments

Alternative Specification (Footnote 14) max

∞

• t=0

βt c1−σ

t

− 1 1 − σ , 0 < β < 1 yt = f 1 qjtXjtdj

• = f (Qt)

ct+1 ct σ = β (1 + rt) ct+1 ct σ = β (1 + rt) g1−σ

t+1 ,

where gt+1 = Qt+1 Qt ⇒ Isomorphic Formulations Only When σ = 1

Jang-Ting Guo Discussion on “Stagnation Traps” 6 / 12

Objective Findings Comments

This Paper Euler: ct+1 ct σ = β (1 + it) ¯ π g1−σ

t+1

Growth : 1 = β ct ct+1 σ g1−σ

t+1 (χγ − 1

γ yt+1 + 1 − ln gt+2 ln γ )

• When σ

> 1 ⇒ Positive Relationship between yt+1 and gt+1

Jang-Ting Guo Discussion on “Stagnation Traps” 7 / 12

Objective Findings Comments

This Paper Euler: ct+1 ct σ = β (1 + it) ¯ π g1−σ

t+1

Growth : 1 = β ct ct+1 σ g1−σ

t+1 (χγ − 1

γ yt+1 + 1 − ln gt+2 ln γ )

• When σ

> 1 ⇒ Positive Relationship between yt+1 and gt+1 Market Clearing: ct + ln gt+1 χ ln γ = yt Monetary Policy: 1 + it = max

• (1 + ¯

ı) yφ

t , 1

• Jang-Ting Guo

Discussion on “Stagnation Traps” 7 / 12

Objective Findings Comments

Alternative Specification Period Utility: c1−σ

t

− 1 1 − σ

Jang-Ting Guo Discussion on “Stagnation Traps” 8 / 12

Objective Findings Comments

Alternative Specification Period Utility: c1−σ

t

− 1 1 − σ Final Good: Yt = A 1 (qjtXjt)αdj, A > 0, 0 < α < 1 Demand for Xjt: Xjt = Aαqα

jt

Pjt

• 1

1−α Jang-Ting Guo Discussion on “Stagnation Traps” 8 / 12

Objective Findings Comments

Alternative Specification Period Utility: c1−σ

t

− 1 1 − σ Final Good: Yt = A 1 (qjtXjt)αdj, A > 0, 0 < α < 1 Demand for Xjt: Xjt = Aαqα

jt

Pjt

• 1

1−α

Supply for Xjt: Xjt = Ljt, where 1 Ljtdj + LRD

t

+ Ut = L R&D Firms’ Profits: πjt = (Pjt − Wt)Xjt, Wt Wt−1 = ¯ π

Jang-Ting Guo Discussion on “Stagnation Traps” 8 / 12

Objective Findings Comments

Monopoly Pricing: Pjt = Wt α Equilibrium Quantity: Xjt =

• Aα2qα

jt

Wt

• 1

1−α Jang-Ting Guo Discussion on “Stagnation Traps” 9 / 12

Objective Findings Comments

Monopoly Pricing: Pjt = Wt α Equilibrium Quantity: Xjt =

• Aα2qα

jt

Wt

• 1

1−α

Aggregate Output: Yt = A

1 1−α α 2α 1−α W −α 1−α

t

Qt, where Qt = 1 q

α 1−α

jt

dj Equilibrium Profit: πjt = α(1 − α)q

α 1−α

jt

Yt Qt

Jang-Ting Guo Discussion on “Stagnation Traps” 9 / 12

Objective Findings Comments

Probability of Innovating = χLRD

t

L = χµt

Jang-Ting Guo Discussion on “Stagnation Traps” 10 / 12

Objective Findings Comments

Probability of Innovating = χLRD

t

L = χµt Value Function: Vt = β ct+1 ct −σ [πjt+1 + (1 − χµt+1)Vt+1] Free Entry: LRD

t

Wt = χµtVt ⇒ LWt = χVt Innovation Growth: gt+1 = Qt+1 Qt = χµtγ

α 1−α ⇒ Yt+1

Yt = gt+1¯ π

−α 1−α Jang-Ting Guo Discussion on “Stagnation Traps” 10 / 12

Objective Findings Comments

Probability of Innovating = χLRD

t

L = χµt Value Function: Vt = β ct+1 ct −σ [πjt+1 + (1 − χµt+1)Vt+1] Free Entry: LRD

t

Wt = χµtVt ⇒ LWt = χVt Innovation Growth: gt+1 = Qt+1 Qt = χµtγ

α 1−α ⇒ Yt+1

Yt = gt+1¯ π

−α 1−α

Growth: 1 =

• β¯

π

σα 1−α

• g−σ

t+1

• α(1 − α)q

α 1−α

j(t+1)

χYt+1 LWtQt+1 + ¯ π(1 − gt+2 γ

α 1−α )

• When σ

> 0 ⇒ Positive Relationship between Yt+1 Qt+1 and gt+1

Jang-Ting Guo Discussion on “Stagnation Traps” 10 / 12

Objective Findings Comments

Alternative Specification Euler: ct+1 ct σ = β (1 + it) ¯ π Growth: 1 =

• β¯

π

σα 1−α

• g−σ

t+1

• α(1 − α)q

α 1−α

j(t+1)

χYt+1 LWtQt+1 + ¯ π(1 − gt+2 γ

α 1−α )

• When σ

> 0 ⇒ Positive Relationship between Yt+1 Qt+1 and gt+1

Jang-Ting Guo Discussion on “Stagnation Traps” 11 / 12

Objective Findings Comments

Alternative Specification Euler: ct+1 ct σ = β (1 + it) ¯ π Growth: 1 =

• β¯

π

σα 1−α

• g−σ

t+1

• α(1 − α)q

α 1−α

j(t+1)

χYt+1 LWtQt+1 + ¯ π(1 − gt+2 γ

α 1−α )

• When σ

> 0 ⇒ Positive Relationship between Yt+1 Qt+1 and gt+1 Market Clearing: ct = Yt ⇒ ct+1 ct = Yt+1 Yt = gt+1¯ π

−α 1−α

Monetary Policy: 1 + it = max{(1 + ¯ i)Yt Qt , 1}

Jang-Ting Guo Discussion on “Stagnation Traps” 11 / 12

(yu, gu) (1, gf) AD GG growth g

• utput 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 iu = 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% ⇒ 1 + it = max

• (1 + ¯

ı) yφ

t , i

¯

• , where i

¯ < 1

Jang-Ting Guo Discussion on “Stagnation Traps” 12 / 12

(1, gf) AD GG growth g

• utput gap y