Lecture 2. (1) Aggregation (2) Permanent Income Hypothesis. Erick Sager. September 14, 2015
|
|
- Morgan Ball
- 5 years ago
- Views:
Transcription
1 Lecture 2 (1) Aggregation (2) Permanent Income Hypothesis Erick Sager September 14, 2015 Econ 605: Adv. Topics in Macroeconomics Johns Hopkins University, Fall 2015
2 Erick Sager Lecture 2 (9/14/15) 1 / 37 Last Time (8/31/15) Considered data Wealth, Consumption, Income Cross-Sectional, Times-Series, Life-Cycle Inequality
3 Erick Sager Lecture 2 (9/14/15) 1 / 37 Last Time (8/31/15) Considered data Wealth, Consumption, Income Cross-Sectional, Times-Series, Life-Cycle Inequality Started thinking about aggregation Gorman Form c i (p, w i ) = a i (p) + b(p)w i = C(p, w) = C(p, W )
4 Erick Sager Lecture 2 (9/14/15) 2 / 37 Today (9/14/15) Finish: Aggregation Negishi Constantinides
5 Erick Sager Lecture 2 (9/14/15) 2 / 37 Today (9/14/15) Finish: Aggregation Negishi Constantinides Start: Permanent Income Hypothesis (PIH) Restrict asset space Derive results for consumption, savings, wealth Empirical evaluation of theory
6 Erick Sager Lecture 2 (9/14/15) 3 / 37 Aggregation Under Complete Markets Overview Pre-trade heterogeneity undone by complete markets Usually admits a representative agent Highly tractable, useful baseline Little/no role for distributional effects
7 Erick Sager Lecture 2 (9/14/15) 4 / 37 Aggregation Under Complete Markets Issue Consider heterogeneous agents with complete markets Suppose Gorman aggregation fails c i (p, w i ) a i (p) + b(p)w i
8 Erick Sager Lecture 2 (9/14/15) 4 / 37 Aggregation Under Complete Markets Issue Consider heterogeneous agents with complete markets Suppose Gorman aggregation fails c i (p, w i ) a i (p) + b(p)w i How do we write the preferences of a representative agent? Can we compute prices and allocation with heterogeneity?
9 Erick Sager Lecture 2 (9/14/15) 4 / 37 Aggregation Under Complete Markets Issue Consider heterogeneous agents with complete markets Suppose Gorman aggregation fails c i (p, w i ) a i (p) + b(p)w i How do we write the preferences of a representative agent? Can we compute prices and allocation with heterogeneity? Negishi Approach FWT: Competitive Equilibrium allocation = Pareto Efficient allocation Allocation can be found as solution to Social Planner Problem Choose Planner weights that recover Competitive Equilibrium allocation
10 Erick Sager Lecture 2 (9/14/15) 5 / 37 Negishi Approach Next Slides: Characterize Competitive Equilibrium allocation Characterize Planner s allocation Show how to choose planner weights
11 Erick Sager Lecture 2 (9/14/15) 6 / 37 Competitive Equilibrium: Consumers N = 2 consumer types u : R + R s.t. u > 0, u < 0, u C 2, Inada Endowed with wealth {a 1 0, a 2 0} Given sequence of prices {p t } t=0 Complete Asset Markets
12 Erick Sager Lecture 2 (9/14/15) 6 / 37 Competitive Equilibrium: Consumers N = 2 consumer types u : R + R s.t. u > 0, u < 0, u C 2, Inada Endowed with wealth {a 1 0, a 2 0} Given sequence of prices {p t } t=0 Complete Asset Markets Agent i s problem: v(p, a i 0) = max {c i t } t=0 { β t u(c i t) t=0 s.t. } p t c i t p 0 a i 0 t=0 λ i multiplier on budget constraint for agent i {1, 2}
13 Erick Sager Lecture 2 (9/14/15) 6 / 37 Competitive Equilibrium: Consumers N = 2 consumer types u : R + R s.t. u > 0, u < 0, u C 2, Inada Endowed with wealth {a 1 0, a 2 0} Given sequence of prices {p t } t=0 Complete Asset Markets Agent i s problem: v(p, a i 0) = max {c i t } t=0 { β t u(c i t) t=0 s.t. } p t c i t p 0 a i 0 t=0 λ i multiplier on budget constraint for agent i {1, 2} First order conditions: β t u (c i t) = λ i p t = u (c 1 t ) u (c 2 t ) = λ1 λ 2
14 Erick Sager Lecture 2 (9/14/15) 7 / 37 Competitive Equilibrium: Firms Representative firm: owns capital, invests Endowed with k 0 Consumers own shares in firm, a a 2 0 = A 0 Production function f : R + R + s.t. f > 0, f < 0, and differentiable
15 Erick Sager Lecture 2 (9/14/15) 7 / 37 Competitive Equilibrium: Firms Representative firm: owns capital, invests Endowed with k 0 Consumers own shares in firm, a a 2 0 = A 0 Production function f : R + R + s.t. f > 0, f < 0, and differentiable Firm s Problem: A 0 = max {k t+1} t=0 First order conditions: { t=0 ( pt p 0 ) } (f(k t ) + (1 δ)k t k t+1 ) 1 = p ( ) t+1 f (k t+1 ) + 1 δ p t Recursive representation: ) A t = (f(k t ) + (1 δ)k t k t+1 + p t+1 A t+1 p t
16 Erick Sager Lecture 2 (9/14/15) 8 / 37 Competitive Equilibrium: Market Clearing p t c i t + τ>t p τ c i τ = p t a i t p t c i t + p t+1 a i t+1 = p t a i t c i t + p t+1 a i t+1 = a i t p t 2 i=1 c i t + p t+1 p t 2 a i t+1 = 2 i=1 i=1 a i t C t + p t+1 A t+1 = A t p t C t + k t+1 = f(k t ) + (1 δ)k t
17 Erick Sager Lecture 2 (9/14/15) 9 / 37 Negishi Planner s Problem Endowed with k 0 (µ 1, µ 2 ) planner weights for each consumer
18 Erick Sager Lecture 2 (9/14/15) 9 / 37 Negishi Planner s Problem Endowed with k 0 (µ 1, µ 2 ) planner weights for each consumer Negishi Planner s Problem: β t λ RC t v NP (µ 1, µ 2, k 0 ) = max {c 1 t,c2 t,kt+1} t=0 s.t. t=0 multiplier on resource constraint β t[ ] µ 1 u(c 1 t ) + µ 2 u(c 2 t ) c 1 t + c 2 t + k t+1 = f(k t ) + (1 δ)k t
19 Negishi Planner s Problem Erick Sager Lecture 2 (9/14/15) 9 / 37 Endowed with k 0 (µ 1, µ 2 ) planner weights for each consumer Negishi Planner s Problem: β t λ RC t v NP (µ 1, µ 2, k 0 ) = max {c 1 t,c2 t,kt+1} t=0 s.t. t=0 multiplier on resource constraint First order conditions for all t: β t[ ] µ 1 u(c 1 t ) + µ 2 u(c 2 t ) c 1 t + c 2 t + k t+1 = f(k t ) + (1 δ)k t Implies for all t: λ RC t µ i u (c i t) = λ RC t ( ) = βλ RC t+1 f (k t+1 ) + 1 δ u (c 1 t ) u (c 2 t ) = µ 2 µ 1
20 Erick Sager Lecture 2 (9/14/15) 10 / 37 Planner Weights Implies for all t: u (c 1 t ) u (c 2 t ) = µ 2 µ 1 (i) planner fully insures: constant relative MUC s (ii) consumption is allocated proportionately to planner weights
21 Erick Sager Lecture 2 (9/14/15) 10 / 37 Planner Weights Implies for all t: u (c 1 t ) u (c 2 t ) = µ 2 µ 1 (i) planner fully insures: constant relative MUC s (ii) consumption is allocated proportionately to planner weights Under Competitive Eq: u (c 1 t ) u (c 2 t ) = λ1 λ 2
22 Erick Sager Lecture 2 (9/14/15) 10 / 37 Planner Weights Implies for all t: u (c 1 t ) u (c 2 t ) = µ 2 µ 1 (i) planner fully insures: constant relative MUC s (ii) consumption is allocated proportionately to planner weights Under Competitive Eq: u (c 1 t ) u (c 2 t ) = λ1 λ 2 Implement CE allocation: Implies via Euler equations: 1 = p t+1 p t µ 2 µ 1 = λ 1 λ 2 ( ) β f (k t+1 ) + 1 δ 1 = λrc ( ) t+1 λ RC β f (k t+1 ) + 1 δ t
23 Erick Sager Lecture 2 (9/14/15) 11 / 37 Constantinides Approach Next Slides: Generalization of Negishi Planner Decompose into allocation across agents representative consumer Example: Maliar and Maliar (2003)
24 Constantinides Approach Erick Sager Lecture 2 (9/14/15) 12 / 37 i = 1, 2,..., N consumers π i population weight s.t. N i=1 π i = 1 Negishi Planner s Problem: N max {c 1 t,c2 t,kt+1} t=0 s.t. t=0 β t i=1 µ i u(c i t) N π i c i t + k t+1 = f(k t ) + (1 δ)k t i=1
25 Constantinides Approach Erick Sager Lecture 2 (9/14/15) 12 / 37 i = 1, 2,..., N consumers π i population weight s.t. N i=1 π i = 1 Negishi Planner s Problem: N max {c 1 t,c2 t,kt+1} t=0 s.t. t=0 β t i=1 µ i u(c i t) N π i c i t + k t+1 = f(k t ) + (1 δ)k t i=1 Constantinides Decomposition: Allocation across agents { N } N U(C t ) = max µ i u(c i t) s.t. π i c i {c i t C t t }N i=1 i=1 i=1
26 Constantinides Approach Erick Sager Lecture 2 (9/14/15) 12 / 37 i = 1, 2,..., N consumers π i population weight s.t. N i=1 π i = 1 Negishi Planner s Problem: N max {c 1 t,c2 t,kt+1} t=0 s.t. t=0 β t i=1 µ i u(c i t) N π i c i t + k t+1 = f(k t ) + (1 δ)k t i=1 Constantinides Decomposition: Allocation across agents { N } N U(C t ) = max µ i u(c i t) s.t. π i c i {c i t C t t }N i=1 i=1 Constantinides Decomposition: Representative consumer { } β t U(C t ) s.t. C t + k t+1 = f(k t ) + (1 δ)k t, k 0 given max {C t,k t+1} t=0 t=0 i=1
27 Erick Sager Lecture 2 (9/14/15) 13 / 37 Taking Stock Method for computing Representative Agent with heterogeneity Only assumption on preferences is strict concavity Gorman Form (homotheticity or quasilinearity) not required Requires complete markets Gorman Form makes no assumption on asset markets Next: example with closed-form solution
28 Erick Sager Lecture 2 (9/14/15) 14 / 37 Maliar and Maliar (2003) Unit continuum of infinitely lived households indexed by i I [0, 1] Let µ i be measure of type i agents s.t. I dµ i = 1
29 Erick Sager Lecture 2 (9/14/15) 14 / 37 Maliar and Maliar (2003) Unit continuum of infinitely lived households indexed by i I [0, 1] Let µ i be measure of type i agents s.t. I dµ i = 1 Endowed with one unit of time, labor (h i t) vs leisure (1 h i t) Idiosyncratic labor productivity shocks: ε i t E s.t. E[ε] = 1 Trade Arrow securities a t+1 (ε) at price p t (ε) Endowed with k 0 and a 0
30 Erick Sager Lecture 2 (9/14/15) 14 / 37 Maliar and Maliar (2003) Unit continuum of infinitely lived households indexed by i I [0, 1] Let µ i be measure of type i agents s.t. I dµ i = 1 Endowed with one unit of time, labor (h i t) vs leisure (1 h i t) Idiosyncratic labor productivity shocks: ε i t E s.t. E[ε] = 1 Trade Arrow securities a t+1 (ε) at price p t (ε) Endowed with k 0 and a 0 Household i s problem max {c t,h t,k t+1,a t+1(ε)} t=0 E 0 t=0 [ (c β t i t ) 1 σ 1 σ + ψ (1 hi t) 1 γ ] 1 γ s.t. c i t + kt+1 i + p t (ε)a i t+1(ε)dε w t ε i th i t + (1 + r t )kt i + a i t(ε i t) E
31 Erick Sager Lecture 2 (9/14/15) 15 / 37 Maliar and Maliar (2003) Representative Firm CRS production technology, Y t = z t F (K t, L t ) z t is an aggregate shock Spot markets for capital and labor (unlike before) Static profits: Π t = z t F (K t, L t ) w t L t (r t + δ)k t
32 Erick Sager Lecture 2 (9/14/15) 16 / 37 Maliar and Maliar (2003) Equilibrium household allocation {c i t, h t, k i t+1, a i t+1(ε)} t=0 for each i, firm allocation {K t, h t, L t } t=0 and prices {w t, h t, r t, p t (ε)} t=0 s.t. (i) satisfy household optimality, (ii) satisfy firm optimality (iii) satisfy market clearing conditions for capital, labor and resources: K t = ktdµ i i I L t = I I ε i th i tdµ i c i tdµ i + K t+1 = z t F (K t, L t ) + (1 δ)k t (iv) Arrow securities are in net zero supply
33 Maliar and Maliar (2003) Erick Sager Lecture 2 (9/14/15) 17 / 37 Planner s Problem U(C t, 1 L t ) = max {c i t,hi t } i I s.t. I α i u(c i t, h i t)dµ i I ci tdµ i C t [λ c t] I εi th i tdµ i L t [λ l t]
34 Maliar and Maliar (2003) Erick Sager Lecture 2 (9/14/15) 17 / 37 Planner s Problem U(C t, 1 L t ) = max {c i t,hi t } i I s.t. I α i u(c i t, h i t)dµ i I ci tdµ i C t [λ c t] I εi th i tdµ i L t [λ l t] First Order Conditions: ( α c i i t = λ c t ) 1 σ and ( ) 1 ψα h i i γ t = 1 λ l tw t ε i t
35 Maliar and Maliar (2003) Erick Sager Lecture 2 (9/14/15) 17 / 37 Planner s Problem U(C t, 1 L t ) = max {c i t,hi t } i I s.t. I α i u(c i t, h i t)dµ i I ci tdµ i C t [λ c t] I εi th i tdµ i L t [λ l t] First Order Conditions: ( α c i i t = λ c t ) 1 σ and ( ) 1 ψα h i i γ t = 1 λ l tw t ε i t Aggregate: C t = L t = I I c i tdµ i = (λ c t) 1 σ I ( α i ) 1 σ dµ i ( ) 1 ψ ε i th i tdµ i γ ( = 1 α i ) 1 γ λ l (ε i t) 1 1 γ dµ i tw t I
36 Maliar and Maliar (2003) First Order Conditions: ( α c i i t = λ c t ) 1 σ and ( ) 1 ψα h i i γ t = 1 λ l tw t ε i t Aggregate: C t = (λ c t) 1 σ I ( α i ) ( ) 1 1 σ ψ dµ i γ ( and L t = 1 α i ) 1 γ λ l (ε i t) 1 1 γ dµ i tw t I Erick Sager Lecture 2 (9/14/15) 18 / 37
37 Maliar and Maliar (2003) First Order Conditions: ( α c i i t = λ c t ) 1 σ and ( ) 1 ψα h i i γ t = 1 λ l tw t ε i t Aggregate: C t = (λ c t) 1 σ I ( α i ) ( ) 1 1 σ ψ dµ i γ ( and L t = 1 α i ) 1 γ λ l (ε i t) 1 1 γ dµ i tw t I Rewrite FOCs: c i t = I ( α i ) 1 σ ( α i ) 1 σ dµ i C t 1 h i t = I ( ) α i 1 ( γ εt) i 1 γ ( α i ) (1 L t ) 1 γ (ε i t) 1 1 γ dµ i Erick Sager Lecture 2 (9/14/15) 18 / 37
38 Erick Sager Lecture 2 (9/14/15) 19 / 37 Maliar and Maliar (2003) I = I [ (c α i i t ) 1 σ 1 σ + ψ (1 ] hi t )1 γ dµ i 1 γ α i I = (Ct)1 σ 1 σ + ψ I ( α i ) 1 σ σ 1 ( α i ) (C t) 1 σ 1 σ dµ i 1 σ + ψ α i (Ct)1 σ 1 σ + (1 L t) 1 γ Ψt 1 γ ( α i ) γ 1 ( ε i ) 1 γ t I (αi ) 1 γ (ε i t )1 1 γ dµ i I 1 γ ( α i ) γ 1 ( 1 γ ε i ) 1 γ t ( α i ) (1 L t) 1 γ 1 γ (ε i t) 1 γ 1 dµ i 1 γ dµi i (1 Lt)1 γ dµ 1 γ ( α i ) 1 ( γ ε i ) 1 1 γ ( t Ψ t ψ ( I ) I (αi ) γ 1 (ε i 1 1 γ dµ i ( = ψ α i ) ) 1 γ γ (ε i t) 1 γ 1 dµ i t )1 γ dµ i I
39 Erick Sager Lecture 2 (9/14/15) 20 / 37 Taking Stock Analytical expression for the representative consumer s preferences Nearly identical to the individual agent s preferences Labor Wedge (Chari, Kehoe and McGrattan (2006)) Ψ t depends on the distribution of idiosyncratic productivity shocks Negishi weights Given U(C, 1 L Ψ), representative agent s allocation: max E 0 {C t,l t,k t+1} t=0 t=0 [ β t (Ct ) 1 σ 1 σ + Ψ (1 L t ) 1 γ t 1 γ ] s.t. C t + K t+1 = z t F (K t, L t ) + (1 δ)k t
40 Permanent Income Hypothesis Erick Sager Lecture 2 (9/14/15) 20 / 37
41 Erick Sager Lecture 2 (9/14/15) 21 / 37 Asset Markets Overview Are complete markets a good representation of the data? Consider two extremes: Complete Markets Autarky Which does the data better support? Consider some intermediate case?
42 Erick Sager Lecture 2 (9/14/15) 21 / 37 Asset Markets Overview Are complete markets a good representation of the data? Consider two extremes: Complete Markets Autarky Which does the data better support? Consider some intermediate case? ( this one)
43 Erick Sager Lecture 2 (9/14/15) 22 / 37 Asset Markets Preliminaries s t : S t : state of the economy at t set of possible states s.t. s t S t s t = {x 0,..., s t } S t : history of states up to t pi(s t ) : y i t(s t ) : probability of a particular history agent i s income following history s t at time t
44 Erick Sager Lecture 2 (9/14/15) 23 / 37 Asset Markets Autarky No possibility for intertemporal substitution of resources No access to asset markets No access to storage technology Then: c i t(s t ) = yt(s i t ) No insurance against income shocks No risk sharing
45 Erick Sager Lecture 2 (9/14/15) 24 / 37 Asset Markets Complete Markets Access to Arrow securities a i t+1(s t+1, s t ) with price q t+1 (s t+1, s t ) Sequential budget constraint (as before): c i t(s t ) + q t (s t+1, s t )a i t+1(s t+1, s t ) yt(s i t ) + a i t(s t ) s t+1 S t+1 Impose a no Ponzi condition: lim q t (s t+1, s t )a i t+1(s t+1, s t ) 0 t s t+1 S t+1 Constant relative MUCs & only aggregate risk: u (c i t(s t )) u (c j t(s t )) = αj α i = c i t(s t ) = (αi ) 1 σ (α j ) 1 σ j I C t (s t )
46 Erick Sager Lecture 2 (9/14/15) 25 / 37 Asset Markets Empirical Evaluation Individual consumption growth vs aggregate consumption growth: log ( c i t/c i t 1) = β log (Ct /C t 1 ) Include income growth (c.f. Mace (1991)) log ( c i t/c i t 1) = β1 log (C t /C t 1 ) + β 2 log ( y i t/y i t 1) + ε i t
47 Erick Sager Lecture 2 (9/14/15) 25 / 37 Asset Markets Empirical Evaluation Individual consumption growth vs aggregate consumption growth: log ( c i t/c i t 1) = β log (Ct /C t 1 ) Include income growth (c.f. Mace (1991)) log ( c i t/c i t 1) = β1 log (C t /C t 1 ) + β 2 log ( y i t/y i t 1) + ε i t β 1 = 1 and β 2 = 0 β 1 = 0 and β 2 = 1
48 Erick Sager Lecture 2 (9/14/15) 25 / 37 Asset Markets Empirical Evaluation Individual consumption growth vs aggregate consumption growth: log ( c i t/c i t 1) = β log (Ct /C t 1 ) Include income growth (c.f. Mace (1991)) log ( c i t/c i t 1) = β1 log (C t /C t 1 ) + β 2 log ( y i t/y i t 1) + ε i t β 1 = 1 and β 2 = 0 β 1 = 0 and β 2 = 1 Data shows something in between
49 Erick Sager Lecture 2 (9/14/15) 26 / 37 Asset Markets Restrictions Want alternative that supports partial risk sharing Incomplete Markets: cannot write contracts contingent on all histories s t
50 Erick Sager Lecture 2 (9/14/15) 26 / 37 Asset Markets Restrictions Want alternative that supports partial risk sharing Incomplete Markets: cannot write contracts contingent on all histories s t Exogenously Incomplete Markets: cannot write contracts on any future contingencies
51 Erick Sager Lecture 2 (9/14/15) 26 / 37 Asset Markets Restrictions Want alternative that supports partial risk sharing Incomplete Markets: cannot write contracts contingent on all histories s t Exogenously Incomplete Markets: cannot write contracts on any future contingencies Then: c i t(s t ) + q t (s t )a i t+1(s t ) y i t(s t ) + a i t(s t ) Going forward: suppress (s t ) notation c i t + q t a i t+1 y i t + a i t
52 Erick Sager Lecture 2 (9/14/15) 27 / 37 Asset Markets Next Steps Write down model of consumer behavior Suppose access to exogenously incomplete markets Make additional assumptions: Permanent Income Hypothesis What are the implications for consumption, savings, income, wealth?
53 Incomplete Markets Erick Sager Lecture 2 (9/14/15) 28 / 37 Canonical Consumption Savings Problem: v i (a i 0, y i 0) = max E 0 {c i t,ai t+1 } t=0 t=0 β t u(c i t) s.t. c i t r t a i t+1 y i t + a i t a i t+1 a i t+1 c i t 0
54 Incomplete Markets Erick Sager Lecture 2 (9/14/15) 28 / 37 Canonical Consumption Savings Problem: Recursive Form: v i (a i 0, y i 0) = max E 0 {c i t,ai t+1 } t=0 t=0 β t u(c i t) s.t. c i t r t a i t+1 y i t + a i t a i t+1 a i t+1 c i t 0 v(a t, y t ) = max c t,a t+1 u(c t ) + βe t [v(a t+1, y t+1 )] s.t. c t r t a t+1 y t + a t a t+1 a t+1 c t 0
55 Erick Sager Lecture 2 (9/14/15) 29 / 37 Permanent Income Hypothesis Restrictions on Canonical Problem Quadratic utility specification: u(c) = α 2 (c t c) 2 c is a bliss point of maximium utility α is a utility parameter One-period returns are certain and pinned down by the discount rate: β(1 + r) = 1 Borrowing constraints are replaced by the No Ponzi Condition for all t 0: [ ( ) j 1 E t lim a j t+j] r
56 Erick Sager Lecture 2 (9/14/15) 30 / 37 PIH Characterization To do at white board: Optimal Consumption
57 Erick Sager Lecture 2 (9/14/15) 30 / 37 PIH Characterization To do at white board: Optimal Consumption Consumption is random walk
58 Erick Sager Lecture 2 (9/14/15) 30 / 37 PIH Characterization To do at white board: Optimal Consumption Consumption is random walk Permanent Income
59 Erick Sager Lecture 2 (9/14/15) 30 / 37 PIH Characterization To do at white board: Optimal Consumption Consumption is random walk Permanent Income Consumption equals permanent income
60 Erick Sager Lecture 2 (9/14/15) 30 / 37 PIH Characterization To do at white board: Optimal Consumption Consumption is random walk Permanent Income Consumption equals permanent income Certainty Equivalence
61 Erick Sager Lecture 2 (9/14/15) 30 / 37 PIH Characterization To do at white board: Optimal Consumption Consumption is random walk Permanent Income Consumption equals permanent income Certainty Equivalence Consumption does not depend on income variance
62 Erick Sager Lecture 2 (9/14/15) 30 / 37 PIH Characterization To do at white board: Optimal Consumption Consumption is random walk Permanent Income Consumption equals permanent income Certainty Equivalence Consumption does not depend on income variance Consumption and Wealth Dynamics
63 Erick Sager Lecture 2 (9/14/15) 30 / 37 PIH Characterization To do at white board: Optimal Consumption Consumption is random walk Permanent Income Consumption equals permanent income Certainty Equivalence Consumption does not depend on income variance Consumption and Wealth Dynamics Response to news Offsets expected income fluctuations
64 Erick Sager Lecture 2 (9/14/15) 31 / 37 Permanent Income Hypothesis Next Steps What are the implications for consumption, savings, income, wealth? Empirically evaluate Excess sensitivity and Excess smoothness Reconciliation of puzzles
65 Erick Sager Lecture 2 (9/14/15) 32 / 37 Empirical Evaluation Excess Sensitivity Is consumption a random walk? c t = γ 0 + γ 1 c t 1 + γ 2 z t 1 z t 1 is any variable known at t 1 (suppose income or stock market returns) PIH implies γ 1 = 1, γ 2 = 0 Hall (1978): γ 1 1, γ 2 > 0 and significant
66 Erick Sager Lecture 2 (9/14/15) 33 / 37 Empirical Evaluation Excess Sensitivity Consumption growth a random walk? c t = +µ 0 + µ 1 z t 1 Suppose z t 1 is income growth y t PIH implies µ 0 = 0 and µ 2 = 0 Flavin (1981): c t = y t 1 (9.7) (3.20) Excess sensitivity of current consumption to lagged income
67 Erick Sager Lecture 2 (9/14/15) 34 / 37 Empirical Evaluation Time Aggregation Suppose consumption data were collected annually t represents a year τ represents six months: τ + (τ + 1) is a year Annual consumption growth: c A t = (c τ + c τ+1 ) (c τ 1 + c τ 2 ) = c τ + c τ+1 c τ 2 = c τ + c τ+1 c τ 2 + ( c τ+1 + c τ + c τ 1 + c τ 2 c τ+1 ) }{{} =0 = c τ c τ + c τ 1 Annual income growth: y A t = y τ y τ + y τ 1
68 Empirical Evaluation Time Aggregation c A t y A t = c τ c τ + c τ 1 = y τ y τ + y τ 1 τ 1 is the second half of t 1 c A t and y A t depend on τ 1 Therefore measure a portion of lagged income/consumption Erick Sager Lecture 2 (9/14/15) 35 / 37
69 Empirical Evaluation Time Aggregation c A t y A t = c τ c τ + c τ 1 = y τ y τ + y τ 1 τ 1 is the second half of t 1 c A t and yt A depend on τ 1 Therefore measure a portion of lagged income/consumption Instrument y t 1 with y t 2 : Excess sensitivity still present! c t = y t 1 (6.83) (2.18) Erick Sager Lecture 2 (9/14/15) 35 / 37
70 Erick Sager Lecture 2 (9/14/15) 36 / 37 Empirical Evaluation Predicatable Income Change What if a fraction λ of consumers are hand-to-mouth? Hand-to-Mouth: consume all income each period c t = λ y t + (1 λ)ε t If past income is a good predictor of future income: Excess sensitivity might be due to large fraction λ Campbell and Mankiw (1989): c t = µ y t Resolution if λ 1/2 of aggregate income consumed by Hand-to-Mouth
71 Erick Sager Lecture 2 (9/14/15) 37 / 37 Permanent Income Hypothesis Next Time Excess smoothness puzzle Two resolutions of the Excess Sensitivity and Excess Smoothness puzzles Inefficient inference / Bias (Campbell and Deaton (1989)) Precautionary savings motives
Lecture 2. (1) Permanent Income Hypothesis (2) Precautionary Savings. Erick Sager. February 6, 2018
Lecture 2 (1) Permanent Income Hypothesis (2) Precautionary Savings Erick Sager February 6, 2018 Econ 606: Adv. Topics in Macroeconomics Johns Hopkins University, Spring 2018 Erick Sager Lecture 2 (2/6/18)
More information1 Two elementary results on aggregation of technologies and preferences
1 Two elementary results on aggregation of technologies and preferences In what follows we ll discuss aggregation. What do we mean with this term? We say that an economy admits aggregation if the behavior
More informationChapter 4. Applications/Variations
Chapter 4 Applications/Variations 149 4.1 Consumption Smoothing 4.1.1 The Intertemporal Budget Economic Growth: Lecture Notes For any given sequence of interest rates {R t } t=0, pick an arbitrary q 0
More informationThe Real Business Cycle Model
The Real Business Cycle Model Macroeconomics II 2 The real business cycle model. Introduction This model explains the comovements in the fluctuations of aggregate economic variables around their trend.
More informationUncertainty Per Krusell & D. Krueger Lecture Notes Chapter 6
1 Uncertainty Per Krusell & D. Krueger Lecture Notes Chapter 6 1 A Two-Period Example Suppose the economy lasts only two periods, t =0, 1. The uncertainty arises in the income (wage) of period 1. Not that
More informationMacroeconomics I. University of Tokyo. Lecture 12. The Neo-Classical Growth Model: Prelude to LS Chapter 11.
Macroeconomics I University of Tokyo Lecture 12 The Neo-Classical Growth Model: Prelude to LS Chapter 11. Julen Esteban-Pretel National Graduate Institute for Policy Studies The Cass-Koopmans Model: Environment
More informationGraduate Macroeconomics 2 Problem set Solutions
Graduate Macroeconomics 2 Problem set 10. - Solutions Question 1 1. AUTARKY Autarky implies that the agents do not have access to credit or insurance markets. This implies that you cannot trade across
More informationPermanent Income Hypothesis Intro to the Ramsey Model
Consumption and Savings Permanent Income Hypothesis Intro to the Ramsey Model Lecture 10 Topics in Macroeconomics November 6, 2007 Lecture 10 1/18 Topics in Macroeconomics Consumption and Savings Outline
More informationLecture 6: Competitive Equilibrium in the Growth Model (II)
Lecture 6: Competitive Equilibrium in the Growth Model (II) ECO 503: Macroeconomic Theory I Benjamin Moll Princeton University Fall 204 /6 Plan of Lecture Sequence of markets CE 2 The growth model and
More informationMacroeconomic Theory and Analysis Suggested Solution for Midterm 1
Macroeconomic Theory and Analysis Suggested Solution for Midterm February 25, 2007 Problem : Pareto Optimality The planner solves the following problem: u(c ) + u(c 2 ) + v(l ) + v(l 2 ) () {c,c 2,l,l
More information1 Bewley Economies with Aggregate Uncertainty
1 Bewley Economies with Aggregate Uncertainty Sofarwehaveassumedawayaggregatefluctuations (i.e., business cycles) in our description of the incomplete-markets economies with uninsurable idiosyncratic risk
More informationA simple macro dynamic model with endogenous saving rate: the representative agent model
A simple macro dynamic model with endogenous saving rate: the representative agent model Virginia Sánchez-Marcos Macroeconomics, MIE-UNICAN Macroeconomics (MIE-UNICAN) A simple macro dynamic model with
More informationPseudo-Wealth and Consumption Fluctuations
Pseudo-Wealth and Consumption Fluctuations Banque de France Martin Guzman (Columbia-UBA) Joseph Stiglitz (Columbia) April 4, 2017 Motivation 1 Analytical puzzle from the perspective of DSGE models: Physical
More informationCompetitive Equilibrium and the Welfare Theorems
Competitive Equilibrium and the Welfare Theorems Craig Burnside Duke University September 2010 Craig Burnside (Duke University) Competitive Equilibrium September 2010 1 / 32 Competitive Equilibrium and
More informationECOM 009 Macroeconomics B. Lecture 2
ECOM 009 Macroeconomics B Lecture 2 Giulio Fella c Giulio Fella, 2014 ECOM 009 Macroeconomics B - Lecture 2 40/197 Aim of consumption theory Consumption theory aims at explaining consumption/saving decisions
More informationMacroeconomic Theory and Analysis V Suggested Solutions for the First Midterm. max
Macroeconomic Theory and Analysis V31.0013 Suggested Solutions for the First Midterm Question 1. Welfare Theorems (a) There are two households that maximize max i,g 1 + g 2 ) {c i,l i} (1) st : c i w(1
More informationHOMEWORK #3 This homework assignment is due at NOON on Friday, November 17 in Marnix Amand s mailbox.
Econ 50a second half) Yale University Fall 2006 Prof. Tony Smith HOMEWORK #3 This homework assignment is due at NOON on Friday, November 7 in Marnix Amand s mailbox.. This problem introduces wealth inequality
More informationproblem. max Both k (0) and h (0) are given at time 0. (a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming
1. Endogenous Growth with Human Capital Consider the following endogenous growth model with both physical capital (k (t)) and human capital (h (t)) in continuous time. The representative household solves
More informationIn the Ramsey model we maximized the utility U = u[c(t)]e nt e t dt. Now
PERMANENT INCOME AND OPTIMAL CONSUMPTION On the previous notes we saw how permanent income hypothesis can solve the Consumption Puzzle. Now we use this hypothesis, together with assumption of rational
More informationAdvanced Macroeconomics
Advanced Macroeconomics The Ramsey Model Marcin Kolasa Warsaw School of Economics Marcin Kolasa (WSE) Ad. Macro - Ramsey model 1 / 30 Introduction Authors: Frank Ramsey (1928), David Cass (1965) and Tjalling
More informationECON607 Fall 2010 University of Hawaii Professor Hui He TA: Xiaodong Sun Assignment 2
ECON607 Fall 200 University of Hawaii Professor Hui He TA: Xiaodong Sun Assignment 2 The due date for this assignment is Tuesday, October 2. ( Total points = 50). (Two-sector growth model) Consider the
More informationProblem 1 (30 points)
Problem (30 points) Prof. Robert King Consider an economy in which there is one period and there are many, identical households. Each household derives utility from consumption (c), leisure (l) and a public
More information1 The Basic RBC Model
IHS 2016, Macroeconomics III Michael Reiter Ch. 1: Notes on RBC Model 1 1 The Basic RBC Model 1.1 Description of Model Variables y z k L c I w r output level of technology (exogenous) capital at end of
More informationAdvanced Macroeconomics
Advanced Macroeconomics The Ramsey Model Micha l Brzoza-Brzezina/Marcin Kolasa Warsaw School of Economics Micha l Brzoza-Brzezina/Marcin Kolasa (WSE) Ad. Macro - Ramsey model 1 / 47 Introduction Authors:
More informationMacroeconomic Theory II Homework 1 - Solution
Macroeconomic Theory II Homework 1 - Solution Professor Gianluca Violante, TA: Diego Daruich New York University Spring 2014 1 Problem 1 Consider a two-sector version of the neoclassical growth model,
More informationECON 581: Growth with Overlapping Generations. Instructor: Dmytro Hryshko
ECON 581: Growth with Overlapping Generations Instructor: Dmytro Hryshko Readings Acemoglu, Chapter 9. Motivation Neoclassical growth model relies on the representative household. OLG models allow for
More informationLecture 2 The Centralized Economy
Lecture 2 The Centralized Economy Economics 5118 Macroeconomic Theory Kam Yu Winter 2013 Outline 1 Introduction 2 The Basic DGE Closed Economy 3 Golden Rule Solution 4 Optimal Solution The Euler Equation
More informationMonetary Economics: Solutions Problem Set 1
Monetary Economics: Solutions Problem Set 1 December 14, 2006 Exercise 1 A Households Households maximise their intertemporal utility function by optimally choosing consumption, savings, and the mix of
More informationECOM 009 Macroeconomics B. Lecture 3
ECOM 009 Macroeconomics B Lecture 3 Giulio Fella c Giulio Fella, 2014 ECOM 009 Macroeconomics B - Lecture 3 84/197 Predictions of the PICH 1. Marginal propensity to consume out of wealth windfalls 0.03.
More informationDynamic Optimization: An Introduction
Dynamic Optimization An Introduction M. C. Sunny Wong University of San Francisco University of Houston, June 20, 2014 Outline 1 Background What is Optimization? EITM: The Importance of Optimization 2
More informationComprehensive Exam. Macro Spring 2014 Retake. August 22, 2014
Comprehensive Exam Macro Spring 2014 Retake August 22, 2014 You have a total of 180 minutes to complete the exam. If a question seems ambiguous, state why, sharpen it up and answer the sharpened-up question.
More informationMacroeconomic Theory II Homework 2 - Solution
Macroeconomic Theory II Homework 2 - Solution Professor Gianluca Violante, TA: Diego Daruich New York University Spring 204 Problem The household has preferences over the stochastic processes of a single
More informationMacroeconomics Qualifying Examination
Macroeconomics Qualifying Examination January 2016 Department of Economics UNC Chapel Hill Instructions: This examination consists of 3 questions. Answer all questions. If you believe a question is ambiguously
More informationLecture 5: Competitive Equilibrium in the Growth Model
Lecture 5: Competitive Equilibrium in the Growth Model ECO 503: Macroeconomic Theory I Benjamin Moll Princeton University Fall 2014 1/17 Competitive Eqm in the Growth Model Recall two issues we are interested
More informationEconomic Growth: Lecture 13, Stochastic Growth
14.452 Economic Growth: Lecture 13, Stochastic Growth Daron Acemoglu MIT December 10, 2013. Daron Acemoglu (MIT) Economic Growth Lecture 13 December 10, 2013. 1 / 52 Stochastic Growth Models Stochastic
More informationTA Sessions in Macroeconomic Theory I. Diogo Baerlocher
TA Sessions in Macroeconomic Theory I Diogo Baerlocher Fall 206 TA SESSION Contents. Constrained Optimization 2. Robinson Crusoe 2. Constrained Optimization The general problem of constrained optimization
More informationAiyagari-Bewley-Hugget-Imrohoroglu Economies
Aiyagari-Bewley-Hugget-Imrohoroglu Economies Quantitative Macroeconomics Raül Santaeulàlia-Llopis MOVE-UAB and Barcelona GSE Fall 2018 Raül Santaeulàlia-Llopis (MOVE-UAB,BGSE) QM: ABHI Models Fall 2018
More informationGrowth Theory: Review
Growth Theory: Review Lecture 1.1, Exogenous Growth Topics in Growth, Part 2 June 11, 2007 Lecture 1.1, Exogenous Growth 1/76 Topics in Growth, Part 2 Growth Accounting: Objective and Technical Framework
More informationNew Notes on the Solow Growth Model
New Notes on the Solow Growth Model Roberto Chang September 2009 1 The Model The firstingredientofadynamicmodelisthedescriptionofthetimehorizon. In the original Solow model, time is continuous and the
More informationDynamic (Stochastic) General Equilibrium and Growth
Dynamic (Stochastic) General Equilibrium and Growth Martin Ellison Nuffi eld College Michaelmas Term 2018 Martin Ellison (Nuffi eld) D(S)GE and Growth Michaelmas Term 2018 1 / 43 Macroeconomics is Dynamic
More informationECON607 Fall 2010 University of Hawaii Professor Hui He TA: Xiaodong Sun Assignment 1 Suggested Solutions
ECON607 Fall 200 University of Hawaii Professor Hui He TA: Xiaodong Sun Assignment Suggested Solutions The due date for this assignment is Thursday, Sep. 23.. Consider an stochastic optimal growth model
More informationRamsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path
Ramsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path Ryoji Ohdoi Dept. of Industrial Engineering and Economics, Tokyo Tech This lecture note is mainly based on Ch. 8 of Acemoglu
More informationNotes on Recursive Utility. Consider the setting of consumption in infinite time under uncertainty as in
Notes on Recursive Utility Consider the setting of consumption in infinite time under uncertainty as in Section 1 (or Chapter 29, LeRoy & Werner, 2nd Ed.) Let u st be the continuation utility at s t. That
More informationNotes on Alvarez and Jermann, "Efficiency, Equilibrium, and Asset Pricing with Risk of Default," Econometrica 2000
Notes on Alvarez Jermann, "Efficiency, Equilibrium, Asset Pricing with Risk of Default," Econometrica 2000 Jonathan Heathcote November 1st 2005 1 Model Consider a pure exchange economy with I agents one
More informationA Modern Equilibrium Model. Jesús Fernández-Villaverde University of Pennsylvania
A Modern Equilibrium Model Jesús Fernández-Villaverde University of Pennsylvania 1 Household Problem Preferences: max E X β t t=0 c 1 σ t 1 σ ψ l1+γ t 1+γ Budget constraint: c t + k t+1 = w t l t + r t
More information(a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming
1. Government Purchases and Endogenous Growth Consider the following endogenous growth model with government purchases (G) in continuous time. Government purchases enhance production, and the production
More informationSuggested Solutions to Homework #3 Econ 511b (Part I), Spring 2004
Suggested Solutions to Homework #3 Econ 5b (Part I), Spring 2004. Consider an exchange economy with two (types of) consumers. Type-A consumers comprise fraction λ of the economy s population and type-b
More informationNeoclassical Business Cycle Model
Neoclassical Business Cycle Model Prof. Eric Sims University of Notre Dame Fall 2015 1 / 36 Production Economy Last time: studied equilibrium in an endowment economy Now: study equilibrium in an economy
More informationLecture 15. Dynamic Stochastic General Equilibrium Model. Randall Romero Aguilar, PhD I Semestre 2017 Last updated: July 3, 2017
Lecture 15 Dynamic Stochastic General Equilibrium Model Randall Romero Aguilar, PhD I Semestre 2017 Last updated: July 3, 2017 Universidad de Costa Rica EC3201 - Teoría Macroeconómica 2 Table of contents
More information1 Jan 28: Overview and Review of Equilibrium
1 Jan 28: Overview and Review of Equilibrium 1.1 Introduction What is an equilibrium (EQM)? Loosely speaking, an equilibrium is a mapping from environments (preference, technology, information, market
More informationLecture 2: Firms, Jobs and Policy
Lecture 2: Firms, Jobs and Policy Economics 522 Esteban Rossi-Hansberg Princeton University Spring 2014 ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring 2014 1 / 34 Restuccia and Rogerson
More informationSmall Open Economy RBC Model Uribe, Chapter 4
Small Open Economy RBC Model Uribe, Chapter 4 1 Basic Model 1.1 Uzawa Utility E 0 t=0 θ t U (c t, h t ) θ 0 = 1 θ t+1 = β (c t, h t ) θ t ; β c < 0; β h > 0. Time-varying discount factor With a constant
More informationu(c t, x t+1 ) = c α t + x α t+1
Review Questions: Overlapping Generations Econ720. Fall 2017. Prof. Lutz Hendricks 1 A Savings Function Consider the standard two-period household problem. The household receives a wage w t when young
More informationRedistributive Taxation in a Partial-Insurance Economy
Redistributive Taxation in a Partial-Insurance Economy Jonathan Heathcote Federal Reserve Bank of Minneapolis and CEPR Kjetil Storesletten Federal Reserve Bank of Minneapolis and CEPR Gianluca Violante
More informationMacroeconomic Topics Homework 1
March 25, 2004 Kjetil Storesletten. Macroeconomic Topics Homework 1 Due: April 23 1 Theory 1.1 Aggregation Consider an economy consisting of a continuum of agents of measure 1 who solve max P t=0 βt c
More informationEconomic Growth: Lectures 5-7, Neoclassical Growth
14.452 Economic Growth: Lectures 5-7, Neoclassical Growth Daron Acemoglu MIT November 7, 9 and 14, 2017. Daron Acemoglu (MIT) Economic Growth Lectures 5-7 November 7, 9 and 14, 2017. 1 / 83 Introduction
More informationEconomic Growth: Lecture 9, Neoclassical Endogenous Growth
14.452 Economic Growth: Lecture 9, Neoclassical Endogenous Growth Daron Acemoglu MIT November 28, 2017. Daron Acemoglu (MIT) Economic Growth Lecture 9 November 28, 2017. 1 / 41 First-Generation Models
More informationChapter 4. Applications. 4.1 Arrow-Debreu Markets and Consumption Smoothing The Intertemporal Budget
Chapter 4 Applications 4.1 Arrow-Debreu Markets and Consumption Smoothing 4.1.1 The Intertemporal Budget For any given sequence {R t } t=0, pick an arbitrary q 0 > 0 and define q t recursively by q t =
More informationGovernment The government faces an exogenous sequence {g t } t=0
Part 6 1. Borrowing Constraints II 1.1. Borrowing Constraints and the Ricardian Equivalence Equivalence between current taxes and current deficits? Basic paper on the Ricardian Equivalence: Barro, JPE,
More informationEconomic Growth: Lecture 8, Overlapping Generations
14.452 Economic Growth: Lecture 8, Overlapping Generations Daron Acemoglu MIT November 20, 2018 Daron Acemoglu (MIT) Economic Growth Lecture 8 November 20, 2018 1 / 46 Growth with Overlapping Generations
More informationEconomics 2010c: Lecture 3 The Classical Consumption Model
Economics 2010c: Lecture 3 The Classical Consumption Model David Laibson 9/9/2014 Outline: 1. Consumption: Basic model and early theories 2. Linearization of the Euler Equation 3. Empirical tests without
More informationTopic 6: Consumption, Income, and Saving
Topic 6: Consumption, Income, and Saving Yulei Luo SEF of HKU October 31, 2013 Luo, Y. (SEF of HKU) Macro Theory October 31, 2013 1 / 68 The Importance of Consumption Consumption is important to both economic
More informationEndogenous Growth Theory
Endogenous Growth Theory Lecture Notes for the winter term 2010/2011 Ingrid Ott Tim Deeken October 21st, 2010 CHAIR IN ECONOMIC POLICY KIT University of the State of Baden-Wuerttemberg and National Laboratory
More informationHigh-dimensional Problems in Finance and Economics. Thomas M. Mertens
High-dimensional Problems in Finance and Economics Thomas M. Mertens NYU Stern Risk Economics Lab April 17, 2012 1 / 78 Motivation Many problems in finance and economics are high dimensional. Dynamic Optimization:
More informationMacroeconomics I. University of Tokyo. Lecture 13
Macroeconomics I University of Tokyo Lecture 13 The Neo-Classical Growth Model II: Distortionary Taxes LS Chapter 11. Julen Esteban-Pretel National Graduate Institute for Policy Studies Environment! Time
More informationLecture notes on modern growth theory
Lecture notes on modern growth theory Part 2 Mario Tirelli Very preliminary material Not to be circulated without the permission of the author October 25, 2017 Contents 1. Introduction 1 2. Optimal economic
More informationThe economy is populated by a unit mass of infinitely lived households with preferences given by. β t u(c Mt, c Ht ) t=0
Review Questions: Two Sector Models Econ720. Fall 207. Prof. Lutz Hendricks A Planning Problem The economy is populated by a unit mass of infinitely lived households with preferences given by β t uc Mt,
More informationLecture 6: Discrete-Time Dynamic Optimization
Lecture 6: Discrete-Time Dynamic Optimization Yulei Luo Economics, HKU November 13, 2017 Luo, Y. (Economics, HKU) ECON0703: ME November 13, 2017 1 / 43 The Nature of Optimal Control In static optimization,
More informationHomework 3 - Partial Answers
Homework 3 - Partial Answers Jonathan Heathcote Due in Class on Tuesday February 28th In class we outlined two versions of the stochastic growth model: a planner s problem, and an Arrow-Debreu competitive
More informationDSGE-Models. Calibration and Introduction to Dynare. Institute of Econometrics and Economic Statistics
DSGE-Models Calibration and Introduction to Dynare Dr. Andrea Beccarini Willi Mutschler, M.Sc. Institute of Econometrics and Economic Statistics willi.mutschler@uni-muenster.de Summer 2012 Willi Mutschler
More informationLecture 2 Real Business Cycle Models
Franck Portier TSE Macro I & II 211-212 Lecture 2 Real Business Cycle Models 1 Lecture 2 Real Business Cycle Models Version 1.2 5/12/211 Changes from version 1. are in red Changes from version 1. are in
More informationNeoclassical Growth Model: I
Neoclassical Growth Model: I Mark Huggett 2 2 Georgetown October, 2017 Growth Model: Introduction Neoclassical Growth Model is the workhorse model in macroeconomics. It comes in two main varieties: infinitely-lived
More informationChapter 7. Endogenous Growth II: R&D and Technological Change
Chapter 7 Endogenous Growth II: R&D and Technological Change 225 Economic Growth: Lecture Notes 7.1 Expanding Product Variety: The Romer Model There are three sectors: one for the final good sector, one
More informationLecture 3: Dynamics of small open economies
Lecture 3: Dynamics of small open economies Open economy macroeconomics, Fall 2006 Ida Wolden Bache September 5, 2006 Dynamics of small open economies Required readings: OR chapter 2. 2.3 Supplementary
More informationEconomic Growth: Lecture 7, Overlapping Generations
14.452 Economic Growth: Lecture 7, Overlapping Generations Daron Acemoglu MIT November 17, 2009. Daron Acemoglu (MIT) Economic Growth Lecture 7 November 17, 2009. 1 / 54 Growth with Overlapping Generations
More informationDynamic stochastic general equilibrium models. December 4, 2007
Dynamic stochastic general equilibrium models December 4, 2007 Dynamic stochastic general equilibrium models Random shocks to generate trajectories that look like the observed national accounts. Rational
More informationPublic Economics The Macroeconomic Perspective Chapter 2: The Ramsey Model. Burkhard Heer University of Augsburg, Germany
Public Economics The Macroeconomic Perspective Chapter 2: The Ramsey Model Burkhard Heer University of Augsburg, Germany October 3, 2018 Contents I 1 Central Planner 2 3 B. Heer c Public Economics: Chapter
More informationThe Ramsey Model. Alessandra Pelloni. October TEI Lecture. Alessandra Pelloni (TEI Lecture) Economic Growth October / 61
The Ramsey Model Alessandra Pelloni TEI Lecture October 2015 Alessandra Pelloni (TEI Lecture) Economic Growth October 2015 1 / 61 Introduction Introduction Introduction Ramsey-Cass-Koopmans model: di ers
More informationSlides II - Dynamic Programming
Slides II - Dynamic Programming Julio Garín University of Georgia Macroeconomic Theory II (Ph.D.) Spring 2017 Macroeconomic Theory II Slides II - Dynamic Programming Spring 2017 1 / 32 Outline 1. Lagrangian
More informationDepartment of Economics The Ohio State University Final Exam Questions and Answers Econ 8712
Prof. Peck Fall 20 Department of Economics The Ohio State University Final Exam Questions and Answers Econ 872. (0 points) The following economy has two consumers, two firms, and three goods. Good is leisure/labor.
More informationLecture 2 The Centralized Economy: Basic features
Lecture 2 The Centralized Economy: Basic features Leopold von Thadden University of Mainz and ECB (on leave) Advanced Macroeconomics, Winter Term 2013 1 / 41 I Motivation This Lecture introduces the basic
More informationIncomplete Markets, Heterogeneity and Macroeconomic Dynamics
Incomplete Markets, Heterogeneity and Macroeconomic Dynamics Bruce Preston and Mauro Roca Presented by Yuki Ikeda February 2009 Preston and Roca (presenter: Yuki Ikeda) 02/03 1 / 20 Introduction Stochastic
More informationEconomics 210B Due: September 16, Problem Set 10. s.t. k t+1 = R(k t c t ) for all t 0, and k 0 given, lim. and
Economics 210B Due: September 16, 2010 Problem 1: Constant returns to saving Consider the following problem. c0,k1,c1,k2,... β t Problem Set 10 1 α c1 α t s.t. k t+1 = R(k t c t ) for all t 0, and k 0
More informationEquilibrium in a Production Economy
Equilibrium in a Production Economy Prof. Eric Sims University of Notre Dame Fall 2012 Sims (ND) Equilibrium in a Production Economy Fall 2012 1 / 23 Production Economy Last time: studied equilibrium in
More informationMacroeconomics: Heterogeneity
Macroeconomics: Heterogeneity Rebecca Sela August 13, 2006 1 Heterogeneity in Complete Markets 1.1 Aggregation Definition An economy admits aggregation if the behavior of aggregate quantities and prices
More informationGrowth Theory: Review
Growth Theory: Review Lecture 1, Endogenous Growth Economic Policy in Development 2, Part 2 March 2009 Lecture 1, Exogenous Growth 1/104 Economic Policy in Development 2, Part 2 Outline Growth Accounting
More informationSession 4: Money. Jean Imbs. November 2010
Session 4: Jean November 2010 I So far, focused on real economy. Real quantities consumed, produced, invested. No money, no nominal in uences. I Now, introduce nominal dimension in the economy. First and
More informationTopic 2. Consumption/Saving and Productivity shocks
14.452. Topic 2. Consumption/Saving and Productivity shocks Olivier Blanchard April 2006 Nr. 1 1. What starting point? Want to start with a model with at least two ingredients: Shocks, so uncertainty.
More informationLecture 3: Growth with Overlapping Generations (Acemoglu 2009, Chapter 9, adapted from Zilibotti)
Lecture 3: Growth with Overlapping Generations (Acemoglu 2009, Chapter 9, adapted from Zilibotti) Kjetil Storesletten September 5, 2014 Kjetil Storesletten () Lecture 3 September 5, 2014 1 / 56 Growth
More information1. Using the model and notations covered in class, the expected returns are:
Econ 510a second half Yale University Fall 2006 Prof. Tony Smith HOMEWORK #5 This homework assignment is due at 5PM on Friday, December 8 in Marnix Amand s mailbox. Solution 1. a In the Mehra-Prescott
More informationFoundations of Neoclassical Growth
Foundations of Neoclassical Growth Ömer Özak SMU Macroeconomics II Ömer Özak (SMU) Economic Growth Macroeconomics II 1 / 78 Preliminaries Introduction Foundations of Neoclassical Growth Solow model: constant
More informationUNIVERSITY OF WISCONSIN DEPARTMENT OF ECONOMICS MACROECONOMICS THEORY Preliminary Exam August 1, :00 am - 2:00 pm
UNIVERSITY OF WISCONSIN DEPARTMENT OF ECONOMICS MACROECONOMICS THEORY Preliminary Exam August 1, 2017 9:00 am - 2:00 pm INSTRUCTIONS Please place a completed label (from the label sheet provided) on the
More information14.06 Lecture Notes Intermediate Macroeconomics. George-Marios Angeletos MIT Department of Economics
14.06 Lecture Notes Intermediate Macroeconomics George-Marios Angeletos MIT Department of Economics Spring 2004 Chapter 3 The Neoclassical Growth Model In the Solow model, agents in the economy (or the
More information2. What is the fraction of aggregate savings due to the precautionary motive? (These two questions are analyzed in the paper by Ayiagari)
University of Minnesota 8107 Macroeconomic Theory, Spring 2012, Mini 1 Fabrizio Perri Stationary equilibria in economies with Idiosyncratic Risk and Incomplete Markets We are now at the point in which
More informationECON FINANCIAL ECONOMICS
ECON 337901 FINANCIAL ECONOMICS Peter Ireland Boston College Spring 2018 These lecture notes by Peter Ireland are licensed under a Creative Commons Attribution-NonCommerical-ShareAlike 4.0 International
More informationHousing with overlapping generations
Housing with overlapping generations Chiara Forlati, Michael Hatcher, Alessandro Mennuni University of Southampton Preliminary and Incomplete May 16, 2015 Abstract We study the distributional and efficiency
More informationECON 5118 Macroeconomic Theory
ECON 5118 Macroeconomic Theory Winter 013 Test 1 February 1, 013 Answer ALL Questions Time Allowed: 1 hour 0 min Attention: Please write your answers on the answer book provided Use the right-side pages
More informationReal Business Cycle Model (RBC)
Real Business Cycle Model (RBC) Seyed Ali Madanizadeh November 2013 RBC Model Lucas 1980: One of the functions of theoretical economics is to provide fully articulated, artificial economic systems that
More informationConsumption / Savings Decisions
Consumption / Savings Decisions 1 The Permanent Income Hpothesis (This is mostl repeated from the first class) Household consumption decisions characterized b 1. Euler equation: u (c t ) = β p t p t+1
More informationMSC Macroeconomics G022, 2009
MSC Macroeconomics G022, 2009 Lecture 4: The Decentralized Economy Morten O. Ravn University College London October 2009 M.O. Ravn (UCL) Lecture 4 October 2009 1 / 68 In this lecture Consumption theory
More information