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

... constraint (16. 2.2)becomesct+ bt≤ βbt+1+ yt (16. 3.1)where in terms of bt+1, we would express a no-borrowing constraint (at+1≥yt+1)asbt+1≤ 0. (16. 3.2)The no-borrowing constraint (16. 3.2) ... is allowed inthis chapter. A generalization of the single-agent model of this chapter will alsobe an important component of the incomplete markets models of chapter 17.Finally, the chapter ... impliedby the ﬁrst-order condition for the agent’s optimal intertemporal choice. 16. 8. Concluding remarksThis chapter has maintained the assumption that β(1 + r)=1,whichisaveryimportant ingredient...

Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 10 pps

... linked by a bequest motive. Assume that there isa sequence of one-period-lived agents. For each t ≥ 0 there is a one-period-livedagent who values consumption and the utility of his direct descendant, ... if the borrowing constraintbt≥ 0isimposed.3Examples 1 and 2 illustrate a general result in chapter 16. Given a bor-rowing constraint and a non-stochastic endowment stream, the impact of ... constrained.21We encountered a more general version of equation (10.2.5) in chapter 8when we discussed Arrow securities.2Note bt= 0 does not imply that the consumer is borrowing constrained.He...

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

... −wtτ(sτ)nτ(sτ)],asexpressedintermsoftime-t,history-stcon-sumption goods. Thus, the household’s wealth, or the value of all its currentand future net claims, expressed in terms of the date-t,history-stconsumptiongood ... currentposition. 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 prices andimplement the ﬁrst-best allocation as a ... demonstrated how to obtain a recursive formulationof the equilibrium with sequential trading. This required us to assume thatindividuals’ endowments were governed by a Markov process. Under that as-sumption...

Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 19 ppsx

... current-period endowment in exchange for a raisedpromised utility vt+1>vt. Promised values never decrease. They stay con-stant for low-y statesys< ¯y(vt), and increase in high-endowment ... needed to increase the ex ante promised expected utility. Asfor those lucky households who have received relatively high endowment real-izations, the optimal contract prescribes an unchanged ... (jk=1Πkyk)/(jk=1Πk). Conse-quently, the expected discounted proﬁt stream associated with all future periodsof the limited obligation, expressed in ﬁrst-period values, is∞t=1βtji=1Πitjk=1Πkykjk=1Πk−...

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

... that can be regarded as extending the ap-proach that we used in the villager-money lender model of section 19.3 to anenvironment with two-sided lack of commitment. We followed Kocherlakota inusing ... are identical well-defined optimization prob-lems. The observant reader should not be concerned with the fact that Qk(·)ontheleftsideof(20.4.5) might be evaluated at a promised value outside ... approach in chapter 15 of the first edition of this book. However,when applied to problems with two-sided lack of commitment, this approachencounters a technical difficulty associated with possible...

Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 21 pps

... expected discounted costs, using β as thediscount factor. We formulate the optimal insurance problem recursively. LetC(V ) be the expected discounted costs of giving the worker expected discountedutility ... characterized by the ﬁrst-order condition(21.2.4), the so-called ‘ﬁrst-order’ approach to incentive problems.3Hopenhayn and Nicolini let the insurance agency also choose Ve, the con-tinuation ... impose apermanent per-period history-dependent tax on previously unemployed workers.A recursive lifetime contract 76121.5.1. Compensation dynamics when unemployedIn the unemployed state (s = u),...

Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 25 pps

... equilibrium.A two-money model 919ct+1ct1-g1-g11c = R(1-c )01IAB1-F'H'DI'EFigure 25.8.2: The minimum denomination F and the returnon money can be lowered vis-`a-vis their ... east-heading agent at an even-numbered trading post is endowed withone unit of the consumption good, and an odd-numbered trading post has anendowment of zero units (see Figure 25.5.1). A west-heading ... is endowedwith zero units at an even-numbered trading post and with one unit of the con-sumption good at an odd-numbered trading post. Finally, at the end of eachperiod, each east-heading...

Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 1 potx

... insured away. Higherpresent-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: Athere conforms to −btin chapter 16. Chapter 1Overview1.1. WarningThis chapter provides a non-technical summary of some themes of this book.We debated whether to ... humans share a com-mon ancestor called Eve who lived 200,000 years ago. All of macroeconomicstoo seems to have descended from a common source, Irving Fisher’s and Mil-ton Friedman’s consumption...

Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 2 pptx

... 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 of ... 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...

Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 3 docx

... 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 distributedor Markov, straightforward ... method proceeds by constructing asequence of value functions and associated policy functions. The sequence iscreated by iterating on the following equation, starting from V0= 0, and con-tinuing ... (3.1.17)whereˆk denotes the “two-period-ahead” value of k.Equation(3.1.17) can beexpressed as1=βu(ct+1)u(ct)f(kt+1) ,an Euler equation that is exploited extensively in the theories...

Xem thêm