Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 1 potx

... elegantly organized this evidence as follows. Define the stochastic discount factor m t +1, t = β u  (c t +1 ) u  (c t ) (1. 3 .16 ) and write (1. 3 .15 ) as E t m t +1, t R j,t +1 =1. (1. 3 .17 ) Represent the ... taxed. However, if income from capital is taxed at the flat rate marginal rate τ k,t +1 , then the Euler equation (1. 3.8) becomes modi ed U c (t)=βU c (t +1) [F k (t +1) (1 τ...

Ngày tải lên: 04/07/2014, 15:20

... 1  ∞  j=0 β j E t y t+j − β 1 y t . (2.6 .11 ) 68 Time series 0 10 20 30 15 10 −5 0 5 impulse response 0 1 2 3 10 2 .17 72 10 2 .17 76 10 2 .17 8 10 2 .17 84 spectrum 15 10 −5 0 5 10 15 0 50 10 0 15 0 covariogram 20 ... decision rule: c t +1 = c t + (1 β) U y (I − βA 22 ) 1 C 2 w t +1 (2.6 .18 a) b t = U y (I −βA 22 ) 1 z t − 1 1 − β c t (2.6 .18 b) y t = U...

Ngày tải lên: 04/07/2014, 15:20

... Bertsekas (19 76), Bertsekas and Shreve (19 78), Stokey and Lucas (with Prescott) (19 89), Bellman (19 57), and Chow (19 81) . This chapter covers much of the same material as Sargent (19 87b, chapter 1) . – ... gives F = α/ (1 − αβ)andE = (1 β) 1 [ln A (1 −αβ)+ βα 1 αβ ln Aβα]. It follows that ˜ k = βαAk α . (3 .1. 14) Note that the term F = α/ (1 − αβ) can be interpreted as a...

Ngày tải lên: 04/07/2014, 15:20

... ([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 } tv 2 =max{R 2 + βP 21 1v  1 + βP 22 1v  2 }. (4.3 .1) Here ... [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...

Ngày tải lên: 04/07/2014, 15:20

... ,  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 = V 21 V 1 11 . So we can write µ 0 = V 21 V 1 11 x 0 (5.5 .11 ) and µ t = V 21 V 1 11 x t . 12 6 ... T   R ∗ 11 0 00  T where R ∗ 11 is positive definite and T is nonsingular. Notice that x  t Rx t = x ∗ 1t R ∗ 11 x ∗ 1t where x ∗ t = Tx t =  T 1 T...

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... index associated with the cutoff wage. For i ≥ ρ (1) , define δ 1 (i)=Prob{w 1 =˜w i | w 1 ≥ w 1 } = 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 ... =  θ −∞ θdF  θ  |m 0 ,σ 2 1  +  1 1 −β − β 1 −β   ∞ θ θdF  θ  |m 0 ,σ 2 1  . (6.6 .10 ) Adding equation (6.6 .10 ) to (6.6.9) gives θ − m 0 = β 1 −β ...

Ngày tải lên: 04/07/2014, 15:20

... condition P 1t 1 =0: P 1t =(A t − B 2t F 2t ) T P 1t +1 (A t − B 2t F 2t )  R 1 + F T 2t S 1 F 2t  − (A t − B 2t F 2t ) T P 1t +1 B 1t  B T 1t P 1t +1 B 1t + Q 1  1 B T 1t P 1t +1 (A t − B 2t F 2t ) ... solution of player 1 s problem is given by F 1t =  B T 1t P 1t +1 B 1t + Q 1  1 B T 1t P 1t +1 (A t − B 2t F 2t )(7.5.4) t = t 0 ,t 0 +1, ,t 1 − 1 where P 1t is...

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... of E t 1 u{ [1 + Ω t 1 (α)]c t } = E t 1 u[αE t 1 c t + (1 α)c t ]. (8 .11 .6) Differentiate equation (8 .11 .6) with respect to α and evaluate at α =0 toget Ω  t 1 (0) = E t 1 u  (c t )(E t 1 c t − c t 1 ) E t 1 c t u  (c t ) . Multiply ... y(s t )(8 .10 .4a) and a t +1 (s t +1 )=z t ,1 (s t +1 )+[p(s t +1 )+d(s t +1 )] N t + ∞  j=2  s t+j Q j 1 (s t+j |s t +1 )z t,j (s...

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... p 1 provided that y 1 1 − c 1 1 > 0. Determine subsequent price levels from p i +1 = α i p i . Determine the allocation to the initial old from c 0 1 = y 0 1 + M p 1 = y 0 1 +(y 1 1 − c 1 1 ). In the ... function U i (c i )=u(c i i )+u(c i i +1 ),i≥ 1, (9 .1. 1a) U 0 (c 0 )=u(c 0 1 ). (9 .1. 1b) Notice that agent i onlywantsgoodsdatedi and i + 1. The interpretation...

Ngày tải lên: 04/07/2014, 15:20

... level ˆc satisfying ˆc 1 − β = 1 1 − λβ , or ˆc = 1 − β 1 − λβ . Substituting this consumption rate into formula (10 .2.2) and solving forward gives b t = 1 − λ t 1 − βλ . (10 .2.7) The consumer ... b t ≥ 0. 1 10.2 .1. Solution to consumption/savings decision Consider the household’s problem of choosing {c t ,b t +1 } ∞ t=0 to maximize ex- pression (10 .2 .1) subject to (10 .2....

Ngày tải lên: 04/07/2014, 15:20