Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 22 doc

... first-period outcome (˜x, ˜y)issaidtobeself-enforcing if σ| (x,y) = σ if (x, y) =(˜x, ˜y). (22. 10.1) A strategy profile satisfying equation (22. 10.1) is called self-enforcing because after a one-shot ... the gov- ernment maps a promised value and a co-state into a current decision and next period promised value and co-state. Chang and Phelan and Stacchetti’s work has considerably broadened t...

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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 ... can be used for problems that cannot be solved by hand. Here we shall describe the first of two special types of problems for which analytical solutions can be obtained. It involves...

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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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... general- ized eigenvalues split as required. Researchers have used this method to study the determinacy of equilibria under Stackelberg plans with representations like (18.3 .22) and have discovered ... 0 −P −1 22 P 21 P −1 22  z t µ xt  . (18.3.17) Then we have the following complete description of the Stackelberg plan: 7  z t+1 µ x,t+1  =  I 0 P 21 P 22  (A − BF)  I 0 −P −1 2...

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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 consump...

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... program can be downloaded from <ftp://zia.stanford.edu/pub/ ˜ sargent/ webdocs/matlab>. Hint 2: The mean vector is the eigenvector of A associated with a unit eigen- value, scaled so that the mean ... 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 pri...

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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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... 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, ... the parameter values listed 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 (1968) and u...

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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 ... function for a com- plete markets economy with date- and history-contingent commodities, whose markets have been reopened at date τ ,historys τ , given the wealth levels im- plied by the tails ......

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