Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 12 ppsx

... chooses to shut down. Chapter 12 Recursive competitive equilibria 12. 1. Endogenous aggregate state variable For pure endowment stochastic economies, chapter 8 described two types of com- petitive equilibria, ... Q(X  |X)andr(X)satisfy (12. 8.11). Time-0 trading: Arrow-Debreu securities 369 12. 4.5. Implied wealth dynamics Even though trades are only executed at time 0 in the Arrow...

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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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... 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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... 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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... evidently y t+1 = V  W t 11 W 12, t 0 W t 22  V −1 y 0 (5.5.8) where W 12, t for t ≥ 1 obeys the recursion W 12, t = W t−1 11 W 12, t−1 + W 12 W t−1 22 12 Evan Anderson’s Matlab program schurg.m attains a convenient ... 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,...

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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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