Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 26 pot

... =Πinequations (26. 7.2) and (26. 7.3) and solve for the reduced-form expressions V c = ψ 1 − β  (1 − β)x + βθxΠ  MΠ+(1− M)x  , (26. 7.4) V m = ψ 1 − β  (1 − β)Π + βθxΠ  MΠ+(1− M)x  , (26. 7.5) where ... expression (26. 4.14). Thus, if {v, n} is taken to be the steady-state outcome of the decentralized econ- omy, it follows that equilibrium condition (26. 4.8) satisfies efficiency condit...

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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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... becomes (ρ + δ)=f  (k), which is a celebrated formula for the so-called ‘augmented golden rule’ capital-labor ratio. It is the asymptotic value of the capital-labor ratio that would be chosen by a ... equilibrium version of the consumption-smoothing motive featured in Milton Friedman’s permanent in- come theory. The variation over time in the equilibrium path of the net-of-taxes gross intere...

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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, ... 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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