Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 20 ppsx

... = w + . 20. 11.2. Pareto frontier As described in section 20. 8, the ex ante division of the gains from an e - cient contract can be viewed as determined by an implicit initial consump- tion level, ... two- and three-state examples in sections 20. 10 and 20. 11 illustrate what determines x j . Attaching Lagrange multipliers µ, βΠ j λ j ,andβΠ j θ j to expressions (20. 3.1b), (20. 3.1c...

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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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... 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 ... humans share a com- mon ancestor called Eve who lived 200 ,000 years ago. All of macroeconomics too seems to have descended from a common source, Irving Fisher’s and Mil- ton Friedman’s consu...

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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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... involve no opti- mization, just computing discounted expected utility. The appendix to chapter 6 describes some related examples based on search theory. 4.6.1. Example 1: calculating expected utility Suppose ... V is a discounted present value that an insurer has promised to an unem- ployed worker, V u is a value for next period that the insurer promises the worker if he remains unemployed,...

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... devoted to characterizing the conditions on A, B, R,and Q under which the optimal closed-loop system matrix (A−BF) is stable. These results are surveyed by Anderson, Hansen, McGrattan, and Sargent ... those prob- lems otherwise is why linear quadratic approximations are used so widely. We describe those approximations in appendix B to this chapter. In chapter 7, we go beyond the single-...

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... each period she remains unemployed, or a fixed wage w that the worker receives if employed. Once employed, the worker is employed forever with no chance of being fired. Every odd period (i.e., t ... revealed by “nature.” (Jovanovic assumed that T = ∞.) We use the recursive projection technique (the Kalman filter) of chapter 5 to handle the firm’s and worker’s sequential learning. The predicti...

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... 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 illustrations, ... technology for “self-control” in this problem. 10 See Gul and Pesendorfer (200 0) for a single-agent recursive representation of preferences exhibiting temptation and self-control. Part I...

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