Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 2 pptx

... (2. 4 .25 ) Population regression 51 0 10 20 30 0 0 .2 0.4 0.6 0.8 1 impulse response 0 1 2 3 10 0 10 1 10 2 spectrum −15 −10 −5 0 5 10 15 2. 2 2. 4 2. 6 2. 8 3 3 .2 covariogram 20 40 60 80 −3 2. 5 2 −1.5 −1 −0.5 0 0.5 sample ... c t +(1−β) U y (I − βA 22 ) −1 C 2 w t+1 (2. 6.18a) b t = U y (I −βA 22 ) −1 z t − 1 1 − β c t (2. 6.18b) y t = U y z t (2. 6.18c) z t+1 = A...

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... the state-contingent consumption to- day and the promised discounted utility tomorrow are functions of the initial promised discounted utility levels. Define v as the expected discounted utility ... extensive cross-history and cross-time consumption smoothing. The constant-fractions-of-consumption characterization comes from these two aspects of the theory: (1) complete mar- kets, and (2) a ho...

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... is simpli ed to one where utility function (14 .2. 1) is maximized subject to resource constraint (14.6 .2) with quantities of intermediate inputs given by equation (14.6. 12) . The first- order condition ... (14 .2. 5a) F 2 (K, X)= ∂Xf(K/X) ∂X = f  ˆ K  − f   ˆ K  ˆ K. (14 .2. 5b) 14 .2. 1. Balanced growth path We seek additional technological assumptions to generate market outcomes...

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... insured away. Higher present-value-of-endowment consumers will have permanently higher consump- tion than lower present-value-of-endowment consumers, so that there is a non- degenerate cross-section ... section 6 See Diaz-Gim´enez,Quadrini, and Rıios-Rull (1997), Krueger and Perri (20 03a, 20 03b), Rodriguez, D´ıiaz-Gim´enez, Quadrini, nd R´ıos-Rull (20 02) and Davies and Shorrocks (20 00)....

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... 1isnotknownatt.Thatis,  t+1 is realized at (t +1), after u t has been chosen at t.Inproblem(3 .2. 1)– (3 .2. 2), uncertainty is injected by assuming that x t follows a random difference equation. Problem (3 .2. 1)–(3 .2. 2) continues ... cycles. 3 .2. Stochastic control problems We now consider a modification of problem (3.1.1) to permit uncertainty. Es- sentially, we add some well-placed shoc...

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... that m = 2. The vectors [v 1 ,v 2 ]obey  v 1 v 2  =  r 1 r 2  +  βP 11 J 1 βP 12 J 1 βP 21 J 2 βP 22 J 2  v 1 v 2  . Then  v 1 v 2  =  I − β  P 11 J 1 P 12 J 1 P 21 J 2 P 22 J 2  −1  r 1 r 2  . ... T ([v 1 ,v 2 ]) that maps a pair of vectors [v 1 ,v 2 ]intoapairof vectors [tv 1 ,tv 2 ]: 2 tv 1 =max{R 1 + βP 11 1v  1 + βP 12 1v  2...

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... implies µ t = −  V 22  −1 V 21 x t . (5.5.10) Butnoticethatbecause(V 21 V 22 ) is the second row block of the inverse of V ,  V 21 V 22   V 11 V 21  =0 which implies V 21 V 11 + V 22 V 21 =0. Therefore −  V 22  −1 V 21 = ... y 0 is evidently y t+1 = V  W t 11 W 12, t 0 W t 22  V −1 y 0 (5.5.8) where W 12, t for t ≥ 1 obeys the recursion W 12, t = W t−1 1...

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... = µ i  n h=ρ(1) µ h . Then γ 2 (j)=Prob{w 2 =˜w j | w 1 ≥ w 1 } = n  i=ρ(1) P 1 (i, j) δ 1 (i) . For i ≥ ρ (2) , define δ 2 (i)=Prob{w 2 =˜w i | w 2 ≥ w 2 ∩ w 1 ≥ w 1 } or δ 2 (i)= γ 2 (i)  n h=ρ (2) γ 2 (h) . Then γ 3 (j)=Prob{w 3 =˜w j | ... w 1 } or δ 2 (i)= γ 2 (i)  n h=ρ (2) γ 2 (h) . Then γ 3 (j)=Prob{w 3 =˜w j | w 2 ≥ w 2 ∩ w 1 ≥ w 1 } = n  i=ρ (2) P...

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... ×k 1 ; b 2 is n × k 2 ; r 1 is n × n; r 2 is n × n; q 1 is k 1 ×k 1 ; q 2 is k 2 ×k 2 ; s 1 is k 2 × k 2 ; s 2 is k 1 × k 1 ; w 1 is n ×k 1 ; w 2 is n ×k 2 ; m 1 is k 2 × k 1 ;andm 2 is k 1 × k 2 . ... P 2t 1 =0: P 2t =(A t − B 1t F 1t ) T P 2t+1 (A t − B 1t F 1t )+  R 2 + F T 1t S 2 F 1t  − (A t − B 1t F 1t ) T P 2t+1 B 2t  B T 2t P 2t+1 B 2t + Q 2  −1 B...

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... issued by the government. We can also think of them as being issued by a private bank. Time-0 trading 26 5 Offer curve Feasibility line c t t+1 c t-1 t y t t cc c c c y t t+1 1 1 2 2 2 3 2 1 0 1 , c t t Figure ... these equilibria is credible, in the sense of subgame perfection, to be studied extensively in chapter 22 . Narayana Kocherlakota (1998) has compared gift-giving and monet...

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