st sts r - - PowerPoint PPT Presentation
st sts r t t tr t rt rt 1 2 1
1❋❡❞❡r❛❧ ❘❡s❡r✈❡ ❇♦❛r❞ ♦❢ ●♦✈❡r♥♦rs 2❯♥✐✈❡rs✐t② ♦❢ ❙♦✉t❤❡r♥ ❈❛❧✐❢♦r♥✐❛
❉■❙❈▲❆■▼❊❘✿ ❚❤❡ ✈✐❡✇s ❡①♣r❡ss❡❞ ❛r❡ s♦❧❡❧② t❤❡ r❡s♣♦♥s✐❜✐❧✐t② ♦❢ t❤❡ ❛✉t❤♦rs ❛♥❞ s❤♦✉❧❞ ♥♦t ❜❡ ✐♥t❡r♣r❡t❡❞ ❛s r❡✢❡❝t✐♥❣ t❤❡ ✈✐❡✇s ♦❢ t❤❡ ❇♦❛r❞ ♦❢ ●♦✈❡r♥♦rs ♦❢ t❤❡ ❋❡❞❡r❛❧ ❘❡s❡r✈❡ ❙②st❡♠ ♦r ♦❢ ❛♥②♦♥❡ ❡❧s❡ ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ❋❡❞❡r❛❧ ❘❡s❡r✈❡ ❙②st❡♠✳
◮ ●♦✈❡r♥♠❡♥t ❞❡❜t ✭▲❙●❇❇✮✱ ✐♥✈❡st♠❡♥t✲❣r❛❞❡ ❝♦r♣♦r❛t❡
◮ ❆✈❡r❛❣❡ ❡✛❡❝ts✿ ▲❛r❣❡ ❡✛❡❝t ♦♥ s♣r❡❛❞s✱ ✐ss✉❛♥❝❡s ◮ ❘❡❧❛t✐✈❡ ❡✛❡❝ts✿ ❇✐❣❣❡r ❡✛❡❝ts ♦♥ ❡❧✐❣✐❜❧❡ ❛ss❡ts
◮ P✉r❝❤❛s❡ ♦❢ ❊❯✲❛r❡❛ ✐♥✈❡st♠❡♥t ❣r❛❞❡ ❝♦r♣✳ ❜♦♥❞s ◮ ❙♣r❡❛❞s ♦❢ ♣✉r❝❤❛s❡❞ ❜♦♥❞s ❢❡❧❧ r❡❧❛t✐✈❡❧② ♠♦r❡
◮ ❍❡t❡r♦❣❡♥❡♦✉s ❡✛❡❝t ♦♥ ❝♦st ♦❢ ❝❛♣✐t❛❧✱ ✐♥✈❡st♠❡♥t ◮ ■♠♣❧✐❝❛t✐♦♥s ❢♦r ❝❛♣✐t❛❧ ✭♠✐s✮❛❧❧♦❝❛t✐♦♥✦ ✶ ✴ ✷✻
◮ ■♠♣❧✐❡s ❛ ♥♦✈❡❧ ▲❙❆P ♣♦❧✐❝② tr❛❞❡✲♦✛ ◮ ✏❉✐str✐❜✉t✐♦♥❛❧ ❡✛❡❝ts✑ ♦❢ ▼P ♦♥ ✜r♠s ◮ ❈♦st ♦❢ ❞✐❣❣✐♥❣ ❞❡❡♣❡r ✐♥t♦ ❝❡♥tr❛❧ ❜❛♥❦ t♦♦❧❦✐t
◮ ❋✐r♠s ❤❡t❡r♦❣❡♥❡♦✉s ✐♥ ♣r♦❞✉❝t✐♦♥ ✫ ✜♥❛♥❝✐♥❣ ◮ ■♥❝♦♠♣❧❡t❡ ✫ s❡❣♠❡♥t❡❞ ♠❛r❦❡ts ◮ ❈♦♠♣❛r❡ ▲❙❈❇❇ ✇✐t❤ ▲❙●❇❇
◮ ❙t❛t✐❝ ♠♦❞❡❧ t♦ ❞❡♠♦♥str❛t❡ ♠❡❝❤❛♥✐s♠ ◮ ❋✉❧❧ ◆❑ ♠♦❞❡❧ ✷ ✴ ✷✻
◮ ▲❙●❇❇ ❛✛❡❝ts s♣r❡❛❞s ❛♣♣r♦①✐♠❛t❡❧② ❡✈❡♥❧② ◮ ▲❙❈❇❇ ❛✛❡❝ts s♣r❡❛❞s ❤❡t❡r♦❣❡♥❡♦✉s❧② ◮ ❚❤✉s✱ ❞✐✛❡r❡♥t ✐♠♣❧✐❝❛t✐♦♥s ❢♦r t❤❡ ✭♠✐s✮❛❧❧♦❝❛t✐♦♥ ♦❢ ❝❛♣✐t❛❧
◮ ❊♠❜❡❞ ✐♥ ◆❑ ♠♦❞❡❧✱ ❛❧❛ ●❡rt❧❡r ❛♥❞ ❑❛r❛❞✐ ✭✷✵✶✸✮ ◮ ❆❧❧ ▲❙❆Ps ❧♦✇❡r ❛✈❡r❛❣❡ s♣r❡❛❞s✱ r❛✐s❡ ✐♥✈❡st♠❡♥t ◮ ▲❙❈❇❇s ✐♥❞✉❝❡ ❤❡t❡r♦❣❡♥❡♦✉s ♠♦✈❡♠❡♥ts ✐♥ s♣r❡❛❞s ❛♥❞
◮ ▼✐s❛❧❧♦❝❛t✐♦♥ ♥♦t ❛♠♣❧✐✜❡❞ ❜② ❩▲❇ ✭t♦ ✜rst✲♦r❞❡r✮ ◮ ▼✐s❛❧❧♦❝✳ ❡✛❡❝t ❃ ♦✉t♣✉t ❣❛✐♥ ❛✇❛② ❢r♦♠ ❩▲❇ ◮ ▼✐s❛❧❧♦❝✳ ❡✛❡❝t ❁ ♦✉t♣✉t ❣❛✐♥ ❛t ❩▲❇ ✸ ✴ ✷✻
◮ ●❡rt❧❡r ✫ ❑❛r❛❞✐ ✭✷✵✶✶✴✷✵✶✸✮❀ ❈✉r❞✐❛ ❛♥❞ ❲♦♦❞❢♦r❞ ✭✷✵✶✺✮❀
◮ ▼✐❞r✐❣❛♥ ✫ ❳✉ ✭✷✵✶✹✮❀ ●✐❧❝❤r✐st✱ ❙✐♠✱ ❩❛❦r❛❥s❡❦ ✭✷✵✶✸✮❀
◮ ❑r✐s❤♥❛♠✉rt❤② ❛♥❞ ❱✐ss✐♥❣✲❏♦r❣❡♥s❡♥ ✭✷✵✶✶✮❀ ❋♦❧❡②✲❋✐s❤❡r✱
✹ ✴ ✷✻
yi
i di
ρ −
Y
◮ Pr♦❞✉❝✐♥❣ K ❝❛♣✐t❛❧ ✉s❡s hkKbk+1
bk+1
bk+1
◮ ♠❛①
K QK − hkKbk+1 bk+1
⋆ Q = hkKbk ✺ ✴ ✷✻
i
◮ ▼✉st ✜♥❛♥❝❡ ❝❛♣✐t❛❧✱ ❣r♦ss ✐♥t❡r❡st r❛t❡ ri ◮ ❆❧s♦ ❛❧❧♦✇ ❢♦r ❛♥ ❡①♦❣❡♥♦✉s ✇❡❞❣❡✱ τ k
i
◮ ♠❛①
ki piyi τ k
i
◮ ki =
i
τ k
i riQ
1−αρ
◮ ❊✈❡r② ✜r♠ i ❜❡❧♦♥❣s ❡①❛❝t❧② t♦ ♦♥❡ ❣r♦✉♣ j ✻ ✴ ✷✻
◮ Sb,i + Sg,i = Qki
Sb,i,Bb
✼ ✴ ✷✻
λ 1+λθ
λ 1+λθ∆jνj
❊q✉✐❧✐❜r✐✉♠ ✽ ✴ ✷✻
◮ ▲♦♦s❡♥s ❝♦❧❧❛t❡r❛❧ ❝♦♥str❛✐♥t ❛♥❞ ♠✉❧t✐♣❧✐❡r
λ 1+λ
◮ Pr♦♣♦rt✐♦♥❛❧❧② ❞❡❝r❡❛s❡s ✜r♠ s♣r❡❛❞s
◮ ▲♦♦s❡♥s ❝♦❧❧❛t❡r❛❧ ❝♦♥str❛✐♥t ❛♥❞ ♠✉❧t✐♣❧✐❡r
λ 1+λ
◮ ❉✐r❡❝t❧② ❧♦✇❡rs s♣r❡❛❞ ❢♦r ✜r♠s i ∈ j ❜✉t ♥♦t i /
✾ ✴ ✷✻
i
i ) αρ
1−αρ
1 ri
1−αρ di
ρ
Aρ
i
τ k
i
1−αρ
1 ri
1−αρ di
i
i ) αρ
1−αρ
ρ
Aρ
i
i )
1−αρ
ri
✶✵ ✴ ✷✻
i
τ k
i
1 1−αρ di
ρ( 1−αρ 1−α )
i
i ) αρ
1−αρ
ρ(1−α)
Aρ
i
i )
1−αρ
τ,i ∝ τ k i
i ∝ rA τ k
i ✶✶ ✴ ✷✻
◮ ❍♦✉s❡❤♦❧❞s ❝❛♥ ❤♦❧❞ ❜♦♥❞s ❢❛❝✐♥❣ ❤♦❧❞✐♥❣ ❝♦sts ❍♦✉s❡❤♦❧❞✬s ♣r♦❜❧❡♠ ⋆ ❍❛❜✐ts ❛♥❞ ❧❛❜♦r s✉♣♣❧② ❡♥t❡r ✉t✐❧✐t② ⋆ ❙♣❧✐t ✐♥t♦ ❜❛♥❦❡rs ❛♥❞ ✇♦r❦❡rs ◮ ■♥t❡r♠❡❞✐❛t❡ ❣♦♦❞s ♣r♦❞✉❝❡rs ✭✷ r❡♣r❡s❡♥t❛t✐✈❡ ✜r♠s✮ ◮ ❈❛♣✐t❛❧ ♣r♦❞✉❝❡rs ⋆ Pr✐❝❡ ♦❢ ❝❛♣✐t❛❧✿ Qt ❈❛♣✐t❛❧ ♣r♦❞✉❝❡r✬s ♣r♦❜❧❡♠ ◮ ▼♦♥♦♣♦❧✐st✐❝❛❧❧② ❝♦♠♣❡t✐t✐✈❡ r❡t❛✐❧❡rs ⋆ ❉❡❧✐✈❡r st✐❝❦② ♣r✐❝❡s ❘❡t❛✐❧ ❣♦♦❞ ✜r♠✬s ♣r♦❜❧❡♠ ◮ ❋✐♥❛♥❝✐❛❧ ✐♥t❡r♠❡❞✐❛r✐❡s ✭❢❛❝❡ ❛❞❞✐t✐♦♥❛❧ r❡❣✉❧❛t♦r②
◮ ❈❡♥tr❛❧ ❜❛♥❦ ❛♥❞ ❣♦✈❡r♥♠❡♥t ✶✷ ✴ ✷✻
j,tL1−α j,t
j,t
ρ ✶✸ ✴ ✷✻
✶✹ ✴ ✷✻
✶✺ ✴ ✷✻
m,t Y ρ j,t
m,t Y ρ j,t
✶✻ ✴ ✷✻
✶✼ ✴ ✷✻
∞
νs,1 b,1,t + θ∆sQtS νs,2 b,2,t + ∆θqtBνb b,t
❙♦❧✉t✐♦♥ ✶✽ ✴ ✷✻
t )) + ǫt
✶✾ ✴ ✷✻
❈❧❡❛r✐♥❣ ❛♥❞ ❊q✉✐❧✐❜r✐✉♠ ✷✵ ✴ ✷✻
Parameters Value From Gertler and Karadi (2013) Households Discount rate, β 0.995 Habit parameter, h 0.815 Relative utility weight of labor, χ 3.482 Steady-state Treasury supply, B/Y 0.450 Proportion of long-term Treasury holdings of the households, ¯ Bh/B 0.750 Portfolio adjustment cost, κ 1.000 Inverse Frisch elasticity of labor supply, ϕ 0.276 Financial Intermediaries and Households Fraction of capital that can be diverted, θ 0.345 Proportional advantage in seizure rate of government debt, ∆ 0.500 Transfer to the entering bankers, X 0.0062 Survival rate of the bankers, σ 0.92 Intermediate Good Firms Capital share, α 0.330 Depreciation rate, δ 0.025 Capital-Producing Firms Inverse elasticity of net investment to the price of capital, ηi 1.728 Retail Firms Elasticity of substitution, ǫ 4.167 Probability of keeping the price constant, γ 0.779 Government Steady-state proportion of government expenditures, G/Y 0.200 Inflation coefficient in the Taylor rule, κπ 1.500 Markup coefficient in the Taylor rule, κX
New Parameters New Parameters Financial Intermediaries and Households Regulatory constraint parameter on government debt, νb 1.000 Regulatory constraint parameter on type 1 securities, νs,1 1.200 Regulatory constraint parameter on type 2 securities, νs,2 1.200 ∆s,2, 1.0531 K1,Int/K1, 0.6 ¯ Kh,1/K1, 0.3 ¯ Kh,2/K2, 0.3 κs,1, 1 κs,2, 1 Intermediate Good Firms CES parameter, ρ 0.9 Type 1 labor share in production 0.5 Type 2 labor share in production 0.5
✷✶ ✴ ✷✻
(a) Central Bank Purchases
10 20 30 40 0.5 1 1.5 2 2.5 % οf GDP Quarters Government Corporate
(b) Y , Baseline
10 20 30 40 −0.01 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 % Change from Steady State Quarters
(c) Y , Perfect Substitutes
10 20 30 40 −0.02 0.02 0.04 0.06 0.08 0.1 0.12 % Change from Steady State Quarters
(d) Y , ZLB
10 20 30 40 0.1 0.2 0.3 0.4 0.5 % Change from Steady State Quarters
Figure 3: Effect of LSAPs on Output with Perfect Substitutes or ZLB
✷✷ ✴ ✷✻
(a) Central Bank Purchases
10 20 30 40 0.5 1 1.5 2 2.5 % οf GDP Quarters Government Corporate
(b) Y
10 20 30 40 −0.01 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 % Change from Steady State Quarters
(c) L
5 10 15 20 25 30 35 40 −0.04 −0.02 0.02 0.04 0.06 0.08 0.1 Quarters
(d) K
10 20 30 40 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 % Change from Steady State Quarters
(e) K1
5 10 15 20 25 30 35 40 −2 −1.5 −1 −0.5 0.5 1 1.5 2 Quarters
(f) K2
5 10 15 20 25 30 35 40 −2 −1.5 −1 −0.5 0.5 1 1.5 2 Quarters
(g) E[RK,2] − E[RK,1]
10 20 30 40 −0.04 −0.02 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Change in Spread Quarters
(h) Sb,1
10 20 30 40 −20 −15 −10 −5 5 10 % Change from Steady State Quarters
(i) Sb,2
5 10 15 20 25 30 35 40 −20 −15 −10 −5 5 10 Quarters
Figure 1: Government and Private Sector Asset Purchase Shocks
✷✸ ✴ ✷✻
10 20 30 40 −0.005 0.005 0.01 0.015 0.02 0.025 0.03 Quarters Change, % of Steady State Output LSAP Output Difference Misallocation Effect Figure 2: Misallocation Effect and Difference in LSAP Effectiveness
t L(1−α) t
1 1−ρ
j
ρ ✷✹ ✴ ✷✻
5 10 15 20 25 30 −0.005 0.005 0.01 0.015 0.02 0.025 Quarters % Change Relative to Baseline No ZLB ZLB
✷✺ ✴ ✷✻
✷✻ ✴ ✷✻
◮ ❇❛❝❦❣r♦✉♥❞ ♦♥ ❊❈❇ ❈♦r♣♦r❛t❡ ❙❡❝t♦r P✉r❝❤❛s❡ Pr♦❣r❛♠ ◮ ❈❤❛♥❣❡s ✐♥ ❨✐❡❧❞s ❛♥❞ ❙♣r❡❛❞s ◮ ❈❤❛♥❣❡s ✐♥ ■ss✉❛♥❝❡s ◮ ❈❤❛♥❣❡s ✐♥ ■♥✈❡st♠❡♥t ✷✻ ✴ ✷✻
◮ ❊❧✐❣✐❜❧❡ ❢♦r ❊✉r♦s②st❡♠ ❝♦❧❧❛t❡r❛❧ ❝r❡❞✐t ♦♣❡r❛t✐♦♥s ◮ ❊✉r♦✲❞❡♥♦♠✐♥❛t❡❞✱ ✻ ♠♦♥t❤ t♦ ✸✵ ②❡❛r ♠❛t✉r✐t② ◮ ■ss✉❡❞ ❜② ♥♦♥✲❜❛♥❦ ❊❯ ❛r❡❛ ✜r♠ ✭❢♦r❡✐❣♥ ♣❛r❡♥t ❛❧❧♦✇❡❞✮ ◮ ❘❛t❡❞ ❇❇❇✲ ♦r ❜❡tt❡r
◮ ❆♥♥♦✉♥❝❡❞ ♦♥ ▼❛r❝❤ ✶✵✱ ✷✵✶✻ ◮ P✉r❝❤❛s❡s ❜❡❣❛♥ ♦♥ ❏✉♥❡ ✽✱ ✷✵✶✻ ◮ ❈♦♥t❡♠♣♦r❛♥❡♦✉s ❇❉ r❡♣♦rts ❛r❣✉❡ t♦ ✐♥✈❡st ❜❛s❡❞ ♦♥
✷✻ ✴ ✷✻
◮ ❆ s✐❣♥✐✜❝❛♥t ❢r❛❝t✐♦♥ ♦❢ ♠❛r❦❡t ✭7 − 10%✮
◮ ❆✈❡r❛❣❡ ❜♦♥❞ ②✐❡❧❞ ❢❡❧❧ ❜② ❃✺✵❜♣s ◮ P✉r❝❤❛s❡❞ ❜♦♥❞s ❝❛♥ ❢❛❧❧ ❜② ♠♦r❡ ◮ ✶✺✪ ❤❛❞ ♥❡❣❛t✐✈❡ ②✐❡❧❞s ✭❛s ♦❢ ✻✴✶✻✮ ✷✻ ✴ ✷✻
❈♦r♣♦r❛t❡s✱ ◆♦t ❇❛♥❦s ❙♦✉r❝❡✿ ❇❛♥❦ ♦❢ ❆♠❡r✐❝❛ ▼❡r✐❧❧✲▲②♥❝❤ ✭✈✐❛ ❋❚✮
✷✻ ✴ ✷✻
❙♦✉r❝❡✿ ❊❈❇✱ ❉❛t❛ ■t❡♠ ❙❊❈✳▼✳■✽✳✶✶✵✵✳❋✸✸✵✵✵✳◆✳■✳❩✵✶✳❆✳❩ ✷✻ ✴ ✷✻
.008 .009 .01 .011 .012 .013
2014q1 2014q3 2015q1 2015q3 2016q1 2016q3
Time
Untreated - bottom 50 Untreated - top 50 Treated
◆♦t❡✿ ❈♦♠♣✉st❛t ●❧♦❜❛❧✱ ❆✉t❤♦r✬s ❈❛❧❝✉❧❛t✐♦♥s✳ ✷✻ ✴ ✷✻
✷✻ ✴ ✷✻
❘❡t✉r♥
i
✷✻ ✴ ✷✻
❘❡t✉r♥
i
i ) αρ
1−αρ
ρ(1−α+bk)
Aρ
i
i )
1−αρ
1−α+bk
αρ
1−α+bk
✷✻ ✴ ✷✻
❘❡t✉r♥
i
i ) αρ
1−αρ
1 ri
1−αρ di
ρ
Aρ
i
τ k
i
1−αρ
1 ri
1−αρ di
i
i ) αρ
1−αρ
ρ
Aρ
i
i )
1−αρ
✷✻ ✴ ✷✻
❘❡t✉r♥
❖✈❡r❝♦♠✐♥❣ s❛✈✐♥❣ ♦✉t ♦❢ ❝♦♥str❛✐♥ts ✷✻ ✴ ✷✻
❘❡t✉r♥
◮ ❲✐t❤ ✐✐❞ ♣r♦❜✳ 1 − σ✱ ❛ ❜❛♥❦❡r ❡①✐ts ♥❡①t ♣❡r✐♦❞✳ ✭❛✈❡r❛❣❡
1 1−σ ✮
◮ ❯♣♦♥ ❡①✐t✐♥❣✱ ❛ ❜❛♥❦❡r tr❛♥s❢❡rs r❡t❛✐♥❡❞ ❡❛r♥✐♥❣s t♦ t❤❡
◮ ❊❛❝❤ ♣❡r✐♦❞✱ (1 − σ)f ✇♦r❦❡rs r❛♥❞♦♠❧② ❜❡❝♦♠❡ ❜❛♥❦❡rs✱
◮ ❊❛❝❤ ♥❡✇ ❜❛♥❦❡r r❡❝❡✐✈❡s ❛ ✧st❛rt ✉♣✧ tr❛♥s❢❡r ❢r♦♠ t❤❡
✷✻ ✴ ✷✻
∞
t+i ]
uC,t
✇✐t❤ ❤♦❧❞✐♥❣ ❝♦sts ✷✻ ✴ ✷✻
❘❡t✉r♥
κj 2
Sh,j)
2
Sh,j
2
Bh)
2
Bh
j=2
j=2
✷✻ ✴ ✷✻
❘❡t✉r♥ ▼♦♥♦♣♦❧✐st✐❝❛❧❧② ❝♦♠♣❡t✐t✐✈❡ r❡t❛✐❧❡rs ❜✉② ✐♥♣✉t ❢r♦♠ ✐♥t❡r♠❡❞✐❛t❡ ❣♦♦❞s ♣r♦❞✉❝❡rs ❛♥❞ r❡✲♣❛❝❦❛❣❡ ❛s ✜♥❛❧ ♦✉t♣✉t✳ ❙❡t ♥♦♠✐♥❛❧ ♣r✐❝❡s ♦♥ ❛ st❛❣❣❡r❡❞ ❜❛s✐s✳ Pm,t ✐s ♠❛r❣✐♥❛❧ ❝♦st ✭P −1
m,t ✐s t❤❡ ♠❛r❦✉♣✮✳
❚❤❡ ✜♥❛❧ ❣♦♦❞✱ Yt✱ ✐s ♣r♦❞✉❝❡❞ ✉s✐♥❣ ❛ ♠❛ss ♦♥❡ ❝♦♥t✐♥✉✉♠ ♦❢ ❞✐✛❡r❡♥t✐❛t❡❞ r❡t❛✐❧ ❣♦♦❞s ✉s✐♥❣ ❈❊❙ ♣r♦❞✉❝t✐♦♥✿ Yt = [ 1 Y
ǫ−1 ǫ ft
d f]
ǫ ǫ−1 .
❚❤❡ r❡t❛✐❧ ❣♦♦❞ ✜r♠ ❢❛❝❡s ❈❛❧✈♦ ♣r✐❝✐♥❣✳ ■t ❝❛♥ ❛❞❥✉st ✐ts ♣r✐❝❡ ✇✐t❤ ♣r♦❜❛❜✐❧✐t② 1 − γ✳ ❚❤❡ ✜r♠s ❝❤♦♦s❡ t❤❡ s❛♠❡ r❡s❡t ♣r✐❝❡ P ∗
t ✳ ❲❡ ❣❡t ❋❖❈✿ ∞
γiΛt,t+i[ P ∗
t
Pt+i − 1 1 − 1/ǫ Pmt+i]Yft+i = 0, ▲❖▼ ❢♦r ♣r✐❝❡s✿ Pt = [(1 − γ)(P ∗
t ) + γ(P 1−ǫ t−1 )] 1 1−ǫ .
✷✻ ✴ ✷✻
❘❡t✉r♥
∞
✷✻ ✴ ✷✻
❘❡t✉r♥ L = Et
νs,1 b,1,t − θ∆sQtS νs,2 b,2,t − ∆θqtBνb b,t
✇❤❡r❡ Nt = Rk,1,tQ1,t−1Sb,1,t−1 + Rk,2,tQ2,t−1Sb,2,t−1 + Rb,tqt−1Bb,t−1 − Rt
▲❡t λt ❜❡ t❤❡ ▲❛❣r❛♥❣❡ ♠✉❧t✐♣❧✐❡r ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ✐♥❝❡♥t✐✈❡ ❝♦♥str❛✐♥t✳ ✷✻ ✴ ✷✻
❚❤❡ ✜rst✲♦r❞❡r ❝♦♥❞✐t✐♦♥s ❤❡r❡ ②✐❡❧❞ Et
∂Vt+1 ∂Nt+1
λt
θνs,1S
νs,1−1 b,1,t
, Et
∂Vt+1 ∂Nt+1
λt
∆sθνs,2S
νs,2−1 b,2,t
, ❛♥❞ Et
∂Vt+1 ∂Nt+1
λt
∆θνbBνb−1
b,t
, ♥♦t✐♥❣ t❤❛t ∂Vt ∂Nt = Et ˜ Λt,t+1
✇❤❡r❡ φt = Et
Λt,t+1Rt+1
νs,1−1 b,1,t
− Et
Λt,t+1
. ✷✻ ✴ ✷✻
❘❡t✉r♥
b,t
b,1,t
b,2,t
b,1,t
✷✻ ✴ ✷✻
❘❡t✉r♥
b,2,t
b,1,t
b,t
b,1,t
✷✻ ✴ ✷✻
❘❡t✉r♥
j=2
✷✻ ✴ ✷✻
❘❡t✉r♥
1,tY 1−ρ m,t
t ,
2,tY 1−ρ m,t
t ,
✷✻ ✴ ✷✻
❘❡t✉r♥
j=2
✷✻ ✴ ✷✻
❘❡t✉r♥ ◆♦t❡✿ ❉❡✉ts❝❤❡ ❇❛♥❦ r❡♣♦rt ❆✉❣✉st ✷♥❞✱ ✷✵✶✻✿ ✧❊❈❇ ❈❙PP✿ ❈✉rr❡♥t ❍♦❧❞✐♥❣s✱ Pr✐♠❛r②✲ ▼❛r❦❡t P✐❝❦s ❛♥❞ P❡r❢♦r♠❛♥❝❡✳✧ ✷✻ ✴ ✷✻
❖✈❡r❛❧❧ 80 90 100 110 120 130
Index
Jun-16 Jul-16 Aug-16 Sep-16 Oct-16 Nov-16 Dec-16 Jan-17
Date
purchased non-purchased
◆♦t❡✿ ▼❛r❦✐t✱ ❆✉t❤♦r✬s ❈❛❧❝✉❧❛t✐♦♥s✳ ✧❆✧ ❇♦♥❞s ♦♥❧②✱ ✺✲②❡❛r ❞✉r❛t✐♦♥✳ ❱❡rt✐❝❛❧ ❧✐♥❡ ❛t ❏✉♥❡ ✽t❤✳ ✷✻ ✴ ✷✻
❘❡t✉r♥
80 90 100 110 120
Index
Jun-16 Jul-16 Aug-16 Sep-16 Oct-16 Nov-16 Dec-16 Jan-17
Date
◆♦t❡✿ ▼❛r❦✐t✱ ❆✉t❤♦r✬s ❈❛❧❝✉❧❛t✐♦♥s✳ ✧❆✧ ❇♦♥❞s ♦♥❧②✱ ✺✲②❡❛r ❞✉r❛t✐♦♥✳ ❱❡rt✐❝❛❧ ❞♦tt❡❞ ❧✐♥❡ ♦♥ ❏✉♥❡ ✽t❤✱ ✷✵✶✻✳ ✷✻ ✴ ✷✻