Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 16 pps

... constraint (16. 2.2) becomes c t + b t ≤ βb t+1 + y t (16. 3.1) where in terms of b t+1 , we would express a no-borrowing constraint (a t+1 ≥ y t+1 )as b t+1 ≤ 0. (16. 3.2) The no-borrowing constraint (16. 3.2) ... is allowed in this chapter. A generalization of the single-agent model of this chapter will also be an important component of the incomplete markets models of chapter 17. Fin...

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... linked by a bequest motive. Assume that there is a sequence of one-period-lived agents. For each t ≥ 0 there is a one-period-lived agent who values consumption and the utility of his direct descendant, ... if the borrowing constraint b t ≥ 0isimposed. 3 Examples 1 and 2 illustrate a general result in chapter 16. Given a bor- rowing constraint and a non-stochastic endowment stream, the impa...

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... −w t τ (s τ )n τ (s τ )],asexpressedintermsoftime-t,history-s t con- sumption goods. Thus, the household’s wealth, or the value of all its current and future net claims, expressed in terms of the date-t,history-s t consumption good ... current position. It is all that is needed for a planner to compute an optimal alloca- tion and it is all that is needed for the “invisible hand” to call out p...

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... current-period endowment in exchange for a raised promised utility v t+1 >v t . Promised values never decrease. They stay con- stant for low-y states y s < ¯y(v t ), and increase in high-endowment ... needed to increase the ex ante promised expected utility. As for those lucky households who have received relatively high endowment real- izations, the optimal contract prescribes an uncha...

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... that can be regarded as extending the ap- proach that we used in the villager-money lender model of section 19.3 to an environment with two-sided lack of commitment. We followed Kocherlakota in using ... are identical well-defined optimization prob- lems. The observant reader should not be concerned with the fact that Q k (·) ontheleftsideof(20.4.5) might be evaluated at a promised value outsi...

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... expected discounted costs, using β as the discount factor. We formulate the optimal insurance problem recursively. Let C(V ) be the expected discounted costs of giving the worker expected discounted utility ... characterized by the first-order condition (21.2.4), the so-called ‘first-order’ approach to incentive problems. 3 Hopenhayn and Nicolini let the insurance agency also choose V e , the c...

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... equilibrium. A two-money model 919 c t+1 c t 1-g 1-g 1 1 c = R(1-c ) 0 1 I A B 1-F' H' D I' E Figure 25.8.2: The minimum denomination F and the return on money can be lowered vis-`a-vis their ... east-heading agent at an even-numbered trading post is endowed with one unit of the consumption good, and an odd-numbered trading post has an endowment of zero units (see Figure 25.5.1...

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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...

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... stationary stochastic process, all second moments can be en- coded in a complex-valued matrix called the spectral density matrix. The auto- covariance sequence for the process determines the spectral ... difficult to predict variable; and (b) nevertheless that θ(L) = φ(L) so that the stochastic discount factor has subtle predictable components. Fea- ture (a) is needed to match observed prices...

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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 ... method proceeds by constructing a sequence of value functions and associated policy functions. The sequence is created by iterating on the following equation, starting from V 0 = 0,...

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