Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 6 docx

... −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  ∞ θ  θ  − θ  dF  θ  |m 0 ,σ 2 1  . (6. 6.11) The right side of equation (6. 6.11) is positive. The ... = 10,λ= .1] (the dashed line). 5 10 15 20 6. 2 6. 4 6. 6 6. 8 7 7.2 7.4 7 .6 7.8 8 Figure 6. A.2: Mean wages as function of tenure for model with three different parameter...

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... permit uncertainty. Es- sentially, we add some well-placed shocks to the previous non-stochastic prob- lem. So long as the shocks are either independently and identically distributed or Markov, straightforward ... (3.1 .6) Equation (3.1.5) or (3.1 .6) is a functional equation to be solved for the pair of unknown functions V (x),h(x). Methods for solving the Bellman equation are based on math...

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... time 0, (b) the forward-looking behavior of the private sector embedded in the second block of equations (18.2.4). The history dependence of the government’s plan is ex- pressed in the dynamics of ... Q t )=[19.78 .19 − .64 −.15 −.30 ]  z t µ xt  (18.4.12) which can also be represented as u t =0.44u t−1 +     19.7827 0.1885 −0 .64 03 −0.1510      z t +     6. 9509 −0. 067 8 0....

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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 ... notation in chapter 16: A t here conforms to −b t in chapter 16. Chapter 1 Overview 1.1. Warning This chapter provides a non-technical summary of some themes of this book. We debated w...

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... be studied in chapter 16 that impose non-negativity on the consumption path. The first-order condition for maximizing (2 .6. 1) subject to (2 .6. 2) is 15 E t u  (c t+1 )=u  (c t ) . (2 .6. 5) For ... deduce the optimal decision rule, we have to solve the system of differ- ence equations formed by (2 .6. 2) and (2 .6. 6 ) subject to the boundary condition (2 .6. 4). To accomplish this, sol...

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... converges. 4 .6. Sample Bellman equations This section presents some examples. The first two examples involve no opti- mization, just computing discounted expected utility. The appendix to chapter 6 describes ... (c t ) , (4 .6. 1) where β ∈ (0, 1). We can express this equation recursively: V (c t ,λ t )=u (c t )+βE t V (c t+1 ,λ t+1 )(4 .6. 2) We use a guess-and-verify technique to solve...

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... K) j y t−j (5 .6. 6a) or y ∗ t+1 =(1−K) y ∗ t + Ky t , (5 .6. 6b) where y ∗ t+1 is people’s expectation. Friedman used this scheme to describe people’s forecasts of future income. Cagan used it to model ... filter. We now put the Kalman filter to work. 15 5 .6. 1. Muth’s example Phillip Cagan (19 56) and Milton Friedman (19 56) posited that when people wanted to form expectations of future valu...

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... 199 7 .6. Concluding remarks This chapter has introduced two equilibrium concepts and illustrated how dy- namic programming algorithms are embedded in each. For the linear models we have used as ... in exercise 7.1. Exercise 7 .6 Self-control This is a model of a human who has time-inconsistent preferences, of a type proposed by Phelps and Pollak (1 968 ) and used by Laibson (1994). 10 The...

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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 ... that the household in Friedman’s model typically cannot do. See chapter 16. Examples 213 Equation (8 .6. 1) states that time-t elements of consumption allocations to dis- tinct agents are consta...

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... how it can be supported with sequential trad- ing in government-indexed bonds, sequential trading in fiat currency, or time-0 trading in Arrow-Debreu dated securities. 9 .6. 1. The economy Consider ... 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 monetary equi- libria in a...

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